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Wayne State UniversityDigitalCommons@WayneState
Wayne State University Dissertations
1-1-2010
Soft Computing To Sensor Network Reliability,Systems And Their Fpga ImplementationArati M. DixitWayne State University
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Recommended CitationDixit, Arati M., "Soft Computing To Sensor Network Reliability, Systems And Their Fpga Implementation" (2010). Wayne StateUniversity Dissertations. Paper 159.
SOFT COMPUTING TO SENSOR NETWORK
RELIABILITY, SYSTEMS AND THEIR FPGA
IMPLEMENTATION
by
ARATI M. DIXIT
Submitted to the Graduate School
of Wayne State University,
Detroit, Michigan
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
2010
MAJOR: COMPUTER ENGINEERING
Approved by:
_______________________________________
Advisor Date
_______________________________________
_______________________________________
_______________________________________
_______________________________________
© COPYRIGHT BY
ARATI M. DIXIT
2010
All Rights Reserved
ii
ACKNOWLEDGEMENTS
This dissertation would not have been possible without the guidance and the
help of several individuals who in one way or another contributed and extended
their valuable assistance in the preparation and completion of this study.
First & foremost, I am heartily thankful to my advisor, Prof. Harpreet Singh, for
his encouragement, guidance, and support during discussions & evaluations of my
dissertation work. I would also like to express my sincere gratitude towards my
dissertation committee members Dr. Grant R. Gerhart, Prof. Pepe Siy and Prof.
Le Yi Wang for their time & effort, helpful suggestions and constructive
criticism.
In my daily work I have been blessed with a friendly and cheerful group of
fellow students from AICV: Advanced Intelligent Computing and VLSI Lab. I
would like to thank Mr. Kassem Saab for the reliability software development,
implementation and simulation.
I owe my gratitude to my parents, in-laws, relatives and family friends for their
tireless efforts to shape my character and supporting me throughout my studies.
My special gratitude is directed with love, to my husband Mehul for his
companionship, motivation, patience and countless hours of dedicated support,
and to my kids Atharv & Gargi for being patient and a source of energy &
excitement.
Last but not the least; I would like to express my sincere gratitude towards
almighty God for giving me the strength to persevere despite my mind wanting to
give up.
iii
TABLE OF CONTENTS
ACKNOWLEDGEMENT………………………………………………………………...ii
LIST OF TABLES……………………………………………………………….............vii
LIST OF FIGURES……………………………………………………………………....ix
CHAPTER 1 – Introduction……………………………………………………....1
1.1 - Organization…………………………………………………………3
CHAPTER 2 – Literature Review.……………...………………………………...7
2.1 - Reliability of Network Circuits……………………………...............7
2.2 - Basic Concepts and Definitions……………………………..............9
2.3 - Reliability Evaluation Methods…………………………………….11
2.4 – NDT for Armor Plates.…………...………………………………..16
CHAPTER 3 – Multiple Hops Reliability of Sensor Networks…………………19
3.1 - Introduction………………………………………………………...19
3.2 - Minimum Hop Paths Algorithm……………………………………20
3.2.1 - MinHP Illustrative Example……………………………...23
3.3 - Minimum Hop-Cutsets in a Sensor Network………………………25
3.3.1 - Minimum Hop-Cutsets Algorithm-I……………………...25
3.3.2 - Minimum Hop-Cutsets Algorithm-II……………………..29
3.4 - An Efficient WSN Terminal Reliability Scheme……………….….33
3.4.1 - Proposed MinHR Algorithm……………………………..35
3.4.2 - The MinHR Illustrative Examples………………………36
3.5 - An Approximate System Reliability Evaluation Method………….40
3.5.1 - Proposed Min-Max Algorithm…………………………...40
iv
3.5.1 .1- Basic Method Algorithm……………………….42
3.5.1.2 - Min-Max Algorithm……………………………43
3.5.2 - Approximate System Reliability Algorithm Examples…..44
3.6 - Multiple Hops Terminal Reliability (MHTR)……………………...47
3.6.1 - The MHTR Algorithm……………………………………48
3.6.2 - The MHTR Algorithm Example………………………….52
3.6.3 - MHTR Software Implementation and Results…………...56
3.7 – Conclusion…………………………………………………………62
CHAPTER 4 - Reliability of Unmanned Ground Vehicles (UGV)……………..65
4.1 – Introduction………………………………………………………..65
4.2 - UGV Soft Computing Approach…………………………………...66
4.2.1 - UGV Node Reliability Model………….………………....69
4.2.2 - UGV Link Reliability Model……………………………..72
4.2.3 - Fuzzy Branch Reliability: An Illustrative Example……...74
4.3 - UGV Terminal Reliability………………………………………….75
4.4 - UGV Fuzzy System Reliability…………………………………….80
4.4.1 - System Reliability Examples……………………………..84
4.4.2 - Hypercube System Reliability Analysis………………….87
4.5 - UGVR Circuits FPGA Implementation………………....................89
4.6 - Reliability Calculations Using Pipelined Array…………………....93
4.6.1 - FPGA Implementation of Generalized Pipeline Array…...95
4.6.2 – VLSI Implementation of Generalized Pipeline Array…...97
4.6.3 - UGV Reliability using Pipeline Array………….……….101
v
4.7 - Conclusion………………………………………...………………102
CHAPTER 5 - CDISI: Crack Detection and Impact Source Identification System
5.1 - Introduction……………………………………………………….105
5.2 - CD: Crack Detection System……………………………………...105
5.2.1 - CD System Description…………………………………106
5.2.2 - CD Soft Computing Approach………………………….107
5.2.3 - CD FPGA Implementation……………………………...114
5.3 - ISI: Impact Source Identification System…………………………118
5.3.1 - ISI System Description………………………………….119
5.3.2 - ISI Soft Computing Approach…………………………..121
5.3.3 - ISI FPGA Implementation………………………………123
5.4 - Integrated CDISI System………………………………………….127
5.4.1 - CDISI System Description……………………………...128
5.4.2 - CDISI Soft Computing Approach………………………130
5.4.3 - CDISI FPGA Implementation…………………………..136
5.4.4 - CDISI System: An Integrated Approach………………..140
5.5 – Conclusion………………………………………………………..143
CHAPTER 6 – Summary……………………………………………………….145
CHAPTER 7 – Conclusion……………………………………………………..148
CHAPTER 8 – Future Work…………………………………………………...151
Appendix A – Abbreviations Used in the Report……………………...……….152
Appendix B - Data File for captured Impact Waveforms…………...………….155
References………………………………………………………………………156
vi
Abstract…………………………………………………………………………167
Autobiographical Statement………………………………………………….…169
vii
LIST OF TABLES
Table 2.1: Hypercube Topology Examples……………………………………………...11
Table 2.2: Terminal reliability with nodes…...……………………...…….....……….….13
Table 2.3: Actual and approximate TR with/without nodes …….....……………………14
Table 3.1: Results for Example shown in Fig. 3.1……………………………………….24
Table 3.2: Results of MinHC algorithm-I for network in Fig. 3.1…………………….....29
Table 3.3: Results of MinHC algorithm for network in Fig.3.2……………….......…….33
Table 3.4: The MinHR Result for Example 1………………………………………........37
Table 3.5: The MinHR Result for Example 2…………………………………………....37
Table 3.6: The MinHR Result for Example 3…………………………………………....37
Table 3.7: The MinHR Result for Example 4…………………………………………....38
Table 3.8: The MinHR Result for Example 5………………………………………........38
Table 3.9: The MinHR Result for Example 6…………………………………………....38
Table 3.10: MINHR OF EXAMPLE SENSOR NETWORKS………………………………......39
Table 3.11: Examples of Proposed MHTR Method for Some Standard Networks...........53
Table 3.12: Non-series Parallel Network 2-hop and 3-hop Terminal Reliability ….........54
Table 3.13: MHTR results for 13N32L network of Fig. 3.10…………………………....57
Table 3.14: MHTR results for Complete graph Kn for n=5 to 10………………………..59
Table 3.15: MHTR for Well Connected Graph K6……………………………………....62
Table 4.1: Input parameter Labels for FNR and FBR……………………………….......72
Table 4.2: Labels for output parameters for Fuzzy Node and Branch Reliability……….72
Table 4.3: Terminal reliability [34][35]…………………………………………….........76
Table 4.4: Functionality Supported by the reliability software implementation………...79
viii
Table 4.5: BDD Terms and Execution Time for Different Networks…………………...80
Table 4.6: Series and Parallel Network Solved Example……………………………......85
Table 4.7(a): Standard Networks Solved Example…………………………………........85
Table 4.8: System Reliability for different Terrains in Fig 4.7………………………….86
Table 4.9: System Reliability for different Terrains in Fig 4.7……………………….....88
Table 4.10: Hypercube System reliability for different terrains………….......………….88
Table 4.11: Analysis of FPGA Implementation of Hypercube network reliability……...93
Table 4.12: FPGA Implementation of a Generalized pipeline Array: all operation……..97
Table 5.1: Labels for the Input function for Crack Detection Fuzzy System…………..109
Table 5.2: Rule Base for the Crack Detection Fuzzy Inference System………………..111
Table 5.3: Crack Detection FPGA Implementation Output: Plate Status codes………..115
Table 5.4: Analysis of FPGA Implementation of Crack Detection…………………….116
Table 5.5: Range Defined for Inputs……...…………………………………………….121
Table 5.6: Analysis of FPGA Implementation of Source Identification……………….126
Table 5.7: Linguistic labels for the indexlocation parameter………………………......132
Table 5.8: Linguistic labels for parameters…………………………………..................132
Table 5.9: Linguistic label membership function equations for different parameters….134
Table 5.10: Labels for the input function for CDISI fuzzy…………………………….135
Table 5.11: Sample rule base for the CDISI fuzzy inference system…………………..136
Table 5.12: CDISI FPGA implementation output status code bits……………………..137
Table 5.13: CDISI FPGA implementation input status code bits………………………138
Table 5.14: Analysis of FPGA implementation of CDISI……………………………...140
ix
LIST OF FIGURES
Fig. 1.1: Components of Soft Computing…………………………………………………1
Fig. 2.1: Non-series parallel network…………………...…………………..……………12
Fig. 2.2: Directed branch with node and branch reliabilities…………..….……………..14
Fig. 3.1: Sensor Network with 8 nodes and 11 links…………………….………………23
Fig. 3.2: Bridge Sensor Network with 4 nodes and 5 links……………………………...32
Fig. 3.3: WSN Connectivity model (a) non-series parallel, (b) Example 2……………...36
Fig. 3.4: Connectivity model of Example 3 WSN…………………...…………………..37
Fig. 3.5: Connectivity model of Example 4 WSN……………………….………………38
Fig. 3.6: Connectivity model of Example 5 WSN………………...……………………..39
Fig. 3.7: Connectivity model of Example 6 complex WSN……………………..………39
Fig. 3.8A: A series-parallel Network………….…………………………………………45
Fig. 3.9: Plot for m-hop TR for Non-series parallel network (a) m-hop TR Vs LR, (b) TR
Error Vs reliability...............................................................................................55
Fig. 3.10: MHTR software implementation: A 13N32L network with perfect node……56
Fig. 3.11: Benchmark Networks: Complete graph Kn for n=5 to 10…….………………58
Fig. 3.12: Plots of max-hop TR for K5 and K10……………………………………….....60
Fig. 3.13: Plots of execution time, number of BDD terms and unique hops for Kn for n=5
to 10…………………………………………………………………………..60
Fig. 3.14: Plots of max-hop and min-hop TR for Kn: n=5-10 with value of NR=0.8, 0.9
and 1.0………………………………………………………………………...61
Fig. 3.15: Plots of MHTR (1-hop to 5-hops) for K6 with value of NR=1.0……..………62
Fig. 4.1: System of convoys of unmanned vehicle [62]……………...………………….66
Fig. 4.2: Fuzzy system model……………………………………………………………67
Fig. 4.3: FIS: Fuzzy node reliability……………………………………………………..70
x
Fig. 4.4: FNR: (a) Signal Strength membership function, (b) output membership function,
(c) Rule viewer, and (d) Rules editor……………………………………….….71
Fig. 4.5: FIS: Fuzzy Branch reliability……………………..……………………………72
Fig. 4.6: FBR: (a) input weather membership function, (b) output membership function,
(c) Rule Viewer and (d) Rules editor………………………………….……….73
Fig. 4.7: FBR Illustration: (a) Test Data Maximum speed forecast from terrain
classification (b) test UGV [Courtesy of [69])…………………………….......74
Fig. 4.8: FBR: (a) Membership function input for terrain, (b) Neuro Fuzzy output, (c)
terrain rule view, and (d) terrain surface view……………………………........75
Fig. 4.9: Unmanned vehicle network with multiple nodes [34][35]……………….…….80
Fig. 4.10: System reliability for different terrains………………………...……………..87
Fig. 4.11: System reliability for different terrains and different Hypercube Topologies..89
Fig. 4.12: Series-parallel Network (a) RTL Schematic. (b) Technology Schematic….…90
Fig. 4.13: Series-parallel Network a. Synapticad Waveform b. ModelSim snapshot,
c. ModelSim result…………………………………………………………….91
Fig. 4.14: Hypercube network (a). RTL Schematic, (b) Technology Schematic………..92
Fig. 4.15: Hypercube reliability simulation results (a). Synapticad waveform,
(b) ModelSim snapshot………………………………………………………..92
Fig. 4.16: (a) Arithmetic cell, (b) control cell(courtesy of [67])…………………...…….94
Fig. 4.17: Generalized pipeline Array (courtesy of [67])………………………………..95
Fig. 4.18: Pipeline Array FPGA (b) RTL schematic for addition operation,(b) Detailed
RTL schematic for addition operation code…………………………………..96
Fig. 4.19: Simulation result for addition operation…………………………...………….96
Fig. 4.20: Ncsim waveform for multiply operation…………………………..………….98
Fig. 4.21: Detailed Schematic of Pipeline array………………………………...……….98
Fig. 4.22: Layout of Pipeline array in Cadence……………………………...…………..99
Fig. 4.23: Layout with IC Front to Back…………………………………...…………….99
xi
Fig. 4.24: Pipeline Array : (a) The completed test bench, (b) Schematic showing
Padframing………………………………………………………………..…100
Fig. 4.25: Simulation results for 10 * 5………………………………………..……….100
Fig. 4.26: The final route of Generalized Pipeline Array…………………………...….101
Fig. 4.27: The unmanned ground vehicle network…………………………….……….102
Fig. 4.28: The unmanned ground vehicle network FPGA implementation model..……102
Fig. 5.1: Crack Detection Test System Circuit with a ceramic plate(courtesy of [72])...106
Fig. 5.2: Fuzzy system model for Crack Detection…………………………………….109
Fig. 5.3: Multiple input single output Crack Detection Fuzzy Inference System…...….110
Fig. 5.4: Triangular-shaped membership function for consequent NatureOfPlate….....110
Fig. 5.5: Crack Detection Fuzzy Inference System (a) The FIS- Fuzzy Inference System,
(b) The FIS Rule viewer, (c)The FIS surface viewer, (d) The NeuroFuzzy
system[Blue: training data, and Red: testing data]……………………………112
Fig. 5.6: Crack Detection Fuzzy Inference System (a) The FIS- Fuzzy Inference System,
(b) The FIS Rule viewer, (c)The FIS surface viewer, (d) The NeuroFuzzy
system[Blue: training data, and Red: testing data]…………………………...114
Fig. 5.7: Crack Detection (a) Technology Schematic, (b) Simulation HDL Log……..116
Fig. 5.8: Crack Detection System (a). Detailed RTL Schematic, (b). FPGA
Implementation flowchart………………………………………………….....118
Fig. 5.9: An integrated approach towards Crack Detection…………………….………118
Fig. 5.10: Test System Circuit: Two Sensor Arrangement of the ceramic plate with
sample waveform obtained from the sensors. (Courtesy of [89])………...…119
Fig. 5.11: ISI Fuzzy Inference System: (a) five Inputs, (b) Output membership function,
(c, d) Input membership function, (e) Rule Editor, (f) Rule Viewer…...……122
Fig. 5.12: Schematic for FPGA implementation of Impact Source Identification……..124
Fig. 5.13: ISI FPGA Implementation (a) RTL Schematic,(b) FPGA Implementation
process flowchart……………………………………………………………125
xii
Fig. 5.14: (a) Technology Schematic, (b) ModelSim Simulation………………………126
Fig. 5.15: CDISI: crack detection test system circuit …………………………….……128
Fig. 5.16: CDISI: impact source identification test system circuit………………….….129
Fig. 5.17: CDISI fuzzy system model…………………………………………………..131
Fig. 5.18: CDISI Fuzzy Inference System…………………………………………...…133
Fig. 5.19: Input/output parameter Membership Functions (a) AverageRMS, (b) Location,
(c) NatureOfPlate, (d)SourceOfImpact…………………………………...….135
Fig. 5.20: CDISI Fuzzy Inference System (a) The FIS- Fuzzy Inference System, (b) The
FIS rules……………………………………………………………………..136
Fig. 5.21: CDISI system FPGA implementation (a). System design structure (b). RTL
schematic…………………………………………………………………….137
Fig. 5.22: CDISI system (a) Technology schematic, (b) Detailed RTL schematic….....139
Fig. 5.23: CDISI simulation (a) HDL log, (b) waveform simulation……………….….140
Fig. 5.24: An integrated approach towards CDISI……………………………………..140
1
CHAPTER 1
INTRODUCTION
Soft Computing (SC) has emerged as an effective candidate to deal with complex
problems like reliability of unmanned vehicles, crack detection and impact source
identification where there is lack of precision, certainty and complete truth. The concept
of soft computing was introduced by Prof. Lotfi Zadeh in early 1990‘s and definition
adopted form his work is ―Soft computing is tolerant of imprecision, uncertainty, partial
truth, and approximation than the traditional Hard Computing (HC). The role model for
SC is the human brain‖. Soft Computing has now evolved to constitute following
components: Fuzzy Logic (FL), Neural Computing (NC), Evolutionary Computation
(EC), Machine Learning (ML), Probabilistic Reasoning (PR), and Chaos theory as shown
in Fig. 1.1.
Fig. 1.1 Components of Soft Computing
Soft computing is not just limited to these components. Over the period since its
conception these components were identified. Beauty of these components is that they
combine together in different combinations to emerge as a strong technology to tackle
2
complicated problems. It is seen that the Fuzzy Logic is the heart of the soft computing.
Fuzzy Logic approximates the modeling of unknown system or object. Neural Computing
models the systems with help of neural networks. Evolutionary Computation deals with
optimization. Machine Learning component focuses on algorithm design and
development where data can be changed or controlled by machine. Probabilistic
Reasoning takes into consideration and analyzes the result of system influenced by the
probabilistic uncertainty. Chaos theory studies of behavior of dynamic systems
susceptible to initial conditions.
Sensor networks are very popular with very large number of commercial and non-
commercial applications. The security and reliability of these networks is very important.
Some sensor networks and systems are considered in this thesis and modeled with SC
approach and further enhanced by their Field-Programmable Gate Array (FPGA)
implementation. Unmanned ground vehicles have a large number of scientific, military
and commercial applications. A convoy of such vehicles can have collaboration and
coordination. For the movement of such a convoy, it is important to predict the reliability
of the system. A number of approaches are available in the literature, which describes the
techniques for determining the reliability of the system. Graph theoretic approaches are
popular in determining terminal reliability and system reliability. An attempt is made to
exploit Fuzzy and NeuroFuzzy approaches for predicting the node and branch reliability
of the system while Boolean algebra approaches are used to determine terminal reliability
and system reliability. Hence a combination of intelligent approaches like Fuzzy,
NeuroFuzzy and Boolean approaches is used to predict the overall system reliability of a
convoy of vehicles. The node reliabilities may correspond to the collaboration of vehicles
3
while branch reliabilities will determine the terminal reliabilities between different nodes.
An algorithm is proposed for determining the system reliabilities of a convoy of vehicles.
The simulation of the overall system is done. Such simulation should be helpful to the
commander to take an appropriate action depending on the predicted reliability in
different terrain and environmental conditions. The FPGA and Very Large Scale
Integration (VLSI) implementation of some network reliability circuits further enhances
the performance of network reliability circuits.
A great deal of interest has been shown in the literature in the development of new
Non-Destructive Techniques (NDT). In particular, there is increasing interest in
detecting, evaluating and locating cracks as well as the source of the impact causing these
cracks. Soft computing approach turns out to be a significant candidate in detection of
crack, severity of cracks in materials and impact source identification. The fuzzy models
are implemented on the FPGA with a motivation to fit it on a hand-held device.
1.1 Organization
The chapter 2 focuses on the literature review of sensor network reliability. Some basic
concepts and definitions of graph theory, switching theory and reliability can be seen in
this chapter of. Some existing methods for the calculation of the reliability of network
circuits are reviewed in this chapter. Some network circuit examples are solved and
analyzed.
Chapter 3 discusses the Multiple Hops Reliability (MHR) problem of sensor networks.
The packets in sensor network can be advantageously sent through minimum number of
hops rather than all possible hops. It is observed that the Minimum Hops Path (MinHP)
and Minimum Hops cutsets (MinHC) are of significance in a variety of applications like
4
determination of reliability and security of sensor networks for internet and homeland
security. MinHP problem of Sensor Networks determines all possible paths with
minimum number of hops (links) in a sensor network between source and sink nodes.
MinHC problem detect the cutsets with minimum number of links in each term.
Techniques to evaluate MHR, MinHP, MinHC, Approximate terminal and system
reliability algorithms for sensor networks are proposed and explained with illustrative
examples in this chapter.
Chapter 4 proposes a soft computing approach to reliability of a convoy of unmanned
vehicles network with their FPGA implementation. There is an increasing interest in the
use of a convoy of unmanned intelligent vehicles for defense and security. These vehicles
have a number of sensors associated with them. It is very important to have a highly
reliable sensor network so as to determine the dynamic reliability of the intelligent
vehicle system for a safe battlefield environment. The mobility, path planning and
navigation of such convoy of vehicles are in the state of infancy. However, it is
considered important to develop the reliability techniques so that a commander in the
battle of field can predict the reliability of the various stages of the movement of the
convoy. Commander can then take decisions depending on reliabilities determined at
various places and time. In this chapter a combination of intelligent techniques like fuzzy
and Boolean algebra techniques are exploited to determine the reliability of the wireless
sensor network in the battlefield. The branches of reliabilities are determined using
intelligent techniques like fuzzy techniques while terminal reliabilities are determined
using Boolean algebra techniques. Based on this approach, a new algorithm is proposed
in determining the dynamic reliability of convoy of unmanned intelligent vehicles. A
5
coordinated approach of fuzzy and Boolean algebra techniques as proposed presents an
efficient technique for the collaboration and coordination of the convoy of vehicles. A
Fuzzy Reliability model-using MATLAB is discussed which helps in generation of
terminal and branch reliabilities, which could be further used to obtain system reliability
by the proposed method. Some system reliability problems are solved and presented in
this chapter. A hypercube format representation is proposed for the convoy of unmanned
vehicles, and an algorithm is proposed for the same. Hypercube reliability analysis can be
seen in this chapter. FPGA implementation of reliability circuits for series network,
parallel network and some hypercube networks is presented in this chapter. The results
are discussed and analyzed. This chapter also discusses the reliability calculations using
the generalized pipeline array. FPGA and VLSI implementation of generalized pipeline
array is done with an idea that in future this can be extended to floating point operations
so as to improve the performance of the reliability circuit. The unmanned ground vehicle
network can be portrayed as the network consisting of node itself as another network. In
this scenario if the reliability of big network has to be calculated, the reliability of each
individual node has to be calculated. Here the node reliability can be calculated in
parallel using the generalized pipeline array. These values can be further used for the
calculation of the overall system reliability of the network of vehicles.
Chapter 5 discusses an application of soft computing in the area of Non-Destructive
Techniques (NDT) like crack detection, crack extent measurement, crack evaluation and
the identification of the impact source causing the damage in metal plates. In order to
detect the crack and the impact source the Fuzzy logic approach is suggested. The
implementation of the rule base of the FIS for the crack detection and impact source
6
identification is done using Hardware Description Languages (HDL) such as Verilog.
The analysis and simulation of the entire circuit model or schematic is done using
different software for VLSI circuit design, implementation, debugging, verification and
simulation. FPGA implementation and testing is successfully carried out using the
Spartan 3 FPGA.
Chapter 6 summarizes the work done in this report like literature review, multi-hops
sensor network reliability, convoy of unmanned vehicles as an application of network
circuits and non-destructive testing. The solutions are proposed as a soft computing
model, FPGA and VLSI implementation for network reliability circuits and its
applications. Soft Computing model for the NDT applications such as crack detection and
the impact source identification are proposed and supported with their FPGA
implementation.
Chapter 7 concludes the work, and
Chapter 8 focuses on the future work.
Appendix shows Abbreviations and some testing data used in this report.
7
CHAPTER 2
LITERATURE REVIEW
2.1 Reliability of Network Circuits
The expansion in sensor networks [1] and wireless sensor networks [2] has attracted
many researchers in these areas. They play prominent role in large number of military
and commercial areas, so it is important to determine the security and reliability [3] - [9]
of these networks. An attempt is made to review the issues, and algorithms related sensor
networks and reliability [1]-[50]. Researchers have been working on determining the
number of hops [10]-[12] required in a sensor network to carry packets of information
from source to sink nodes. These packets are transferred from the source to sink node
through selective path hops or all possible path hops. Some of the selective cases include
minimum weight path for all hopcounts [10] or all hop shortest path [11][12]. A Multiple
Hops Path (MHP) is a path with multiple numbers of links from the source node to the
sink node. In the literature there has been a great deal of interest in determining all
possible paths [13][14] between the source and sink node in the network.
The terminal reliability (TR) also known as terminal-pair reliability (TPR) is the
reliability from one node to another, typically refers to the reliability from a source node
to the sink node. In other words the TPR is the probability that the two nodes are
connected in a network like a sensor networks. The terminal reliability has been
calculated in the literature by methods using factoring theorem, state enumeration,
Boolean algebra and sum of disjoint products method[15][16][17]. A Multiple Hop
Terminal Reliability (MHTR) is the TR between the source and the sink nodes if the path
expression is composed of multiple between the nodes.
8
An algorithm for the computation of TR between any given pair of nodes is discussed
by various authors in the literature with a path existing between the two nodes. Here the
network is represented as a weighted graph with weight on each link is the link reliability.
A TR algorithm for exact and approximate computation is proposed by transforming a
Boolean sum of products into an equivalent form with all disjoint term [18]. A TR
computation with a unified treatment of the case analysis method for a CCN with
perfectly reliable nodes is presented by reference [19]. An algorithm [20] using faster
method to form disjoint products of Boolean product corresponding to simple paths
between the pair of nodes evaluates the TR. The concept of conditional probability, set
theory, and Boolean algebra are used to formulate an algorithm [21] for calculation of TR
and its software implementation. A minimal cutsets-based g-terminal, 2-terminal, and k-
terminal reliability calculation framework is proposed by reference [22]. An assessment
[23] of path-based and cut-based TR algorithms with respect to computation time is done
and an efficient cut-based algorithm is proposed. A variety of TR algorithms are
presented in [24]-[26]. The Binary Decision Diagram (BDD) [27] based approaches are
used by researchers to evaluate the terminal reliability [28]-[35] of CCN. BDD offers a
number of advantages such as alternatives to truth tables, efficient method of representing
large Boolean expressions and canonical form of the Boolean expressions. A number of
methods have been developed to manipulate and process BDD which become of
importance in large number of areas once the domain specific elements are encoded into
Boolean representation [28].An ordered binary decision diagram OBDD [29][30] based
approach is suggested with a number of applications solutions using OBDD-based
symbolic analysis. BDD play a significant role in generating disjoint non-overlapping
9
expressions and for this reason they can be used to determine reliability. The reference
[31] focuses on detailed method to determine TR of CCN with help of BDD. A k-
terminal network reliability algorithm based on BDD/OBDD is proposed in [32][33]. A
software simulation of TR using BDD can be seen in [34][35]. The case of failure of
nodes is taken into consideration by [36]-[39]. These references assume that the nodes
are not perfect and they do fail. A method for the direct modification of the reliability
expression for networks assuming perfect nodes is suggested [36] so that node failure can
be incorporated.
2.2 Basic Concepts and Definitions
The definitions [51]-[53] of some basic terms used in this thesis are:
Graph consists of a set of nodes and branches, such that each branch from the graph
is associated with an ordered pair of nodes.
Tree is special kind of a graph with a unique simple path from one node to another.
Spanning tree of a connected graph is a sub graph of the graph such that it has all the
nodes. Any graph can have multiple spanning trees. The distance between two
spanning trees of a connected graph is the number of branches present in one tree but
not in the other.
Hypercube is an n-dimensional representation of a square (n = 2) and a cube (n = 3)as
seen in Table 2.1. It is also called as an n-cube. The number of nodes for 0-cube
hypercube is 1. The number of nodes in any n-cube hypercube, such that n>=1 is 2*
nodes (n-1). The number of branches in 0-cube is 0, and 1-cube is 1. The number of
branches in n-cube hypercube such that n>1 is 2* branches (n-1) + nodes (n-1).
10
Cutset is a set of branches of a Graph, which when removed leads to formation of a
disconnected graph.
Vertex Cutset is a set of nodes (vertices) of a Graph, which when removed leads to
formation of a disconnected graph.
Node Reliability is the reliability of a node, when the problem is expressed as a graph
or a communication network.
Branch Reliability is the reliability of a branch, when the problem is expressed as a
graph or a communication network.
Terminal Reliability (TR) refers to the reliability from a source node to the destination
node. Terminal reliability is the reliability between two terminal nodes in a graph,
when reliabilities of the branches connecting the nodes are given. If two branches are
in series, terminal reliability is the product of 2 reliabilities. However, these branches
are in Parallel, terminal reliability can be given by sum of the individual branch
reliabilities minus the product of the reliabilities. This procedure can be extended to a
number of series parallel branches. The approach can also be extended to a number of
non-serials parallel networks.
System Reliability is defined as terminal reliability of all nodes to all other nodes [4].
In literature it is also referred as network, or global or overall reliability.
Reliability Polynomial is a polynomial expressing the reliability of a particular graph
or a topology. Assuming all the branch reliabilities to be p and thus q = 1-p, the
Reliability Polynomial can be calculated. Ex. The reliability expression for 2-D
hypercube is Rs = p1p2 p3 + p1p2q3p4 + p1q2p3 p4 + q1p2 p3p4. Assuming all the
11
branch reliabilities to be p and thus q = 1-p we get the Reliability Polynomial to be
equal to: p.p.p+ p.p.p.(1-p)+ p.p.p .(1-p) + p.p.p .(1-p) = 4p3 - 3p
4
The concepts from references [37]-[66] on soft computing, reliability, fuzzy reliability,
pipelined array implementation, unmanned vehicle reliability and experimental data are
incorporated in this thesis.
TABLE 2.1 Hypercube Topology Examples
N Hypercube Graphical
Representation
Number of
nodes Links
0 0- cube
(0-D)
20 = 1 0
1 1-cube
(1-D)
21 = 2 1
2 2-cube
(2-D)
22 = 4 4
3 3-cube
(3-D)
23 = 8 12
4 4-cube
(4-D)
node = 2-D cube
24 =
16
32
2.3 Reliability Evaluation Methods
Fratta and Montanari [18][19] have proposed calculation of terminal reliability
between the any given pair of nodes, where a path exists from the source node to the
destination node. The network is expressed as a weighted graph where the weight on the
branch represents the branch reliability. Consider Fig. 2.1 with branches X1, X2, X3, X4,
X5 have reliabilities p1, p2, p3, p4, p5 respectively.
12
Fig. 2.1 Non-series parallel network
The given network is expressed as a Boolean function f. This function f represents the
set of disjoint functions, obtained from the Karnaugh map. Boolean Path expression for
Fig. 2.1 is. f= x1x2+ x3x4+ x1x4x5+ x2x3x5. The algorithm [18] can be expressed as:
i. Form f as a Boolean sum of product, which represents all paths from source to
destination, set P=0
ii. If f =0, terminate.
iii. Consider any term A from f, let Ap be the arithmetic expression in terms of
reliabilities p and q. With this P changes to P=P+ Ap.
iv. Update f as f= Ā. f. Continue to step ii.
The steps involved in calculation of TR between nodes A and B in Fig. 2.1 are:
Iteration 1 f= x1x2+ x3x4+ x1x4x5+ x2x3x5 No stop
Iteration 2 A =x1x2, A‘ = p1p2, P=0, P=P+A‘=0+ p1p f=A‘f =( x1x2)‘(x1x2+ x3x4+
x1x4x5+ x2x3x5), f=x1‘x3x4+x1‘x2x3x5+ x2‘x3x4 + x1x2‘x4x5 No Stop
Iteration 3 A = x1‘x3x4, A‘= q1p3p4, P= p1p2 + q1p3p4, f= (x1‘x3x4)‘(x1‘x2x3x5+ x2‘x3x4
+ x1x2‘x4x5) = x1x2‘x3x4+x1x2‘x4x5+x1x2‘x3‘x4x5+x1‘x2x3x4‘x5No Stop
Iteration 4 A = x1x2‘x3x4, A‘=p1q2p3p4, P= p1p2 + q1p3p4+ p1q2p3p5, f = (x1x2‘x3x4)‘
(x1x2‘x4x5+x1x2‘x3‘x4x5+x1‘x2x3x4‘x5) = x1‘x2x3x4‘x5+x1x2‘x3‘x4x5
No Stop
Iteration 5 A = x1x2‘x3‘x4x5, A‘ =q1p2p3q4p5, P= p1p2+q1p3p4+p1q2p3p4+q1p2p3q4p5, f
= (x1‘x2x3x4‘x5)‘(x1x2‘x3‘x4x5) = x1x2‘x3‘x4x5 No Stop
Iteration 6 A = x1x2‘x3‘x4x5, A‘ = p1q2q3p4p5, P= p1p2 + q1p3p4 +p1q2p3p4 +q1p2p3q4p5
+p1q2q3p4p5, f = (x1x2‘x3‘x4x5)‘(x1x2‘x3‘x4x5)=0 Stop
Terminal Reliability P= 0.865 with p1=0.9, p2=0.8, p3=0.7, p4= 0.6, and p5=0.5.
If this algorithm has to be applied to a very big network, it would lead to huge
computations. The approximate algorithm [18] is:
13
i. Form f as a Boolean sum of product, which represents all paths from source to
destination, set P=0, h=0, select ε given error and T as the threshold for the number
of complemented variables.
ii. If f =0, terminate.
iii. f* = f +h, let f‘ = arithmetic equivalent form of f* in terms of the reliabilities. Ex. If
f*=x1x2 then f‘=p1p2. Calculate f‘. If f‘<= ε terminate.
iv. Consider any term A from f, let A' be the arithmetic expression in having reliability
p. With this P changes to P=P+ A‘.
v. Assign g = Ā.f. Express g as sum of product such that g= g‘ + g‘‘. Here g‘ contains
terms from g so that the number of complemented variables is less than T. All the
remaining terms together form g‘‘.
vi. Assign f=g‘ and h = h+ g‘‘. Continue to step ii.
TABLE 2.2: Terminal reliability with nodes
Graph TR Modified Terminal reliability
Series network
p1p2 (p1pA)(p2pB)
Parallel network
p1+ p2 - (p1p2) (p1pA)+(p2pB)-((p1pA) (p2pB))
Series-Parallel network
p1p4+ p1p2q3
+ p1p2p3q4
p1pAp4pD+
p1pAp2pC(1-p3pA)+
p1pAp2pCp3pA(1-p4pD)
Non-Series-Parallel network
p1p2+q1p2p3+
p1q2p3p4+q1p2p3
q4p5 +
p1q2q3p4p5
p1pAp2pC + (1-p1pA)p2pCp3pA +
p1pA(1-pCp2)p3pAp4pD +(1-
p1pA)p2pCp3pA(1-p4pD)p5pDpC +
p1pA(1-pCp2)(1-p3pA)p4pDp5pDpC
14
Fig. 2.2 Directed branch with node and branch reliabilities
Practically in any system the nodes also have some probability of failure and thus it
becomes significant to incorporate the node reliability for the calculation of the system
reliability. It is proposed to consider the node reliability to calculate the terminal
reliability based on a simple concept [36][48]: the failure of node implies the failure of
the incident branches also. Conversely, each branch in the system can be considered as a
series combination of a perfect node and branch with modified branch reliability. For a
unidirectional branch as shown in Fig. 2.2 the modified TR between node A and B is
PB*P1 and that for bidirectional link is PB*P1*PA instead of just P1. Table 2.2 expresses
the modified TR for some standard networks. . This procedure can be extended to any
network reliability expression. The results for above two algorithms for few standard
networks can be seen in Table 2.3. The branch reliability values considered are p1=0.9,
p2=0.8, p3=0.7, p4= 0.6, and p5=0.5. The node reliability values considered are pA=0.8,
pB=0.9, pC=0.7, and pD=0.9.
TABLE 2.3: Actual and approximate TR with/without nodes
Graphs TR TR w/nodes Approx. TR Approx. TR w/nodes
Series network 0.72 0.5184 0.72 0.5184
Parallel network 0.98 0.8992 0.9 0.72
Series-Parallel
network
0.8376 0.6317 0.7242 0.241536
Non-Series-
Parallel network
0.865 0.7085 0.776 0.491008
Reference [54] discusses the spanning tree method for the calculation of the network
reliability. Further it also compares the network as well as the terminal reliability
15
assuming that all the branch reliabilities are equal. The spanning tree algorithm can be
expressed as:
Form the spanning trees for the given communication network graph G.
Form the Cartesian product C of all n-1 vertex cutsets in terms of branches
connecting any of n-1 nodes of G for each spanning tree Ti.
C = C1 C2 C3 Cn-1
Obtain C*, a normalized Cartesian product.
Calculate the probability expression to evaluate the network reliability.
Consider any spanning tree T0 from the set of all spanning trees.
Arrange all Ti‘s in the ascending order of the distance from T0.
System success of network reliability is expressed as:
S = T0 T1 T2 Tn-1
Define Fi for each Ti
F0 = T0, Fi = T0 T1 T2 Ti-1
Each Ti is assigned a Boolean 1, substituted in all predecessor term occurrences.
Form the disjoint expression for the S.
S = T0 [T1 ( F1) T2 ( F2) Tn-1 ( Fn-1)]
Express Rs as a mathematical expression of S using the branch reliabilities.
Substitute the values of branch reliability to get the system reliability.
Reference [54] evaluates the global reliability of hypercubes and the hypernets of
different dimensions, using the spanning tree and clustering technique. The study
concluded that in case of hypercubes, if the link reliability degrades then higher the
dimension hypercubes more the degradation. It was also seen the hypercubes are more
16
reliable then the hypernets of the same dimension. Reliability calculation using the
spanning tree method:
Represent the communication network as a graph G with n nodes.
Form the spanning trees for G. For Each spanning tree with n nodes do the
following.
o Form all n-1 vertex cutsets using the branches it cuts.
o Form the Cartesian product C using all n-1 cutsets.
Normalized Cartesian product C* is the evaluated from C for all spanning trees.
Represent C* as the Sum-of-Products form using the minterms.
Obtain the disjoint expression for C*.
Express C* as a mathematical expression using the branch reliabilities.
Substitute the values of branch reliability to get the system reliability.
2.4 NDT techniques for armor plates
Nondestructive Testing (NDT) given by The American Society of Non Destructive
Testing (ASNT) [70] as ‗the testing of a specimen that determines its serviceability
without damage that could prevent its intended use’. The problem of Crack Detection
(CD) in materials is a renowned problem found in a variety of commercial and military
applications like beams, bridges, turbines, pavements, armor plates, vehicle body plates,
bones, teeth and many more. Similarly another closely related problem is to find the
material which causes the crack: Impact Source Identification (ISI) problem. This thesis
has developed soft computing models for CD [71], ISI and the integrated problem of
Crack Detection and the Impact Source Identification (CDISI). This long standing
interest in development of CDISI is evident from variety of methods proposed in
17
literature. Ultrasonic Guided Waves are used for the Crack Detection [72] and [73]. The
crack detection is done by measuring Lamb wave signals using the dual PZT transducers
[74]. Wireless Inductively-Coupled Transducers are used for the crack detection [75].
The wave velocities of concrete are measured by the portable transient elastic wave
system to track the health of concrete [76]. Automation for different crack detection and
impact source identification methods is lately carried out in the literature using soft
computing and VLSI techniques. Image processing techniques are used for the crack
detection [77] and [78]. One of the most effective tools to deal with complex problems
with lack of certainty, accuracy and absolute truth is the soft computing. A fuzzy
inference system (FIS) [79][80] is developed to predict the location and depth of the
crack of a cracked cantilever beam structure in a close proximity to the real results. A
Hybrid artificial intelligence technique with fuzzy-Neuro controller is used to detect the
crack with its location in cantilever beam [81]. Fuzzy logic and expert system techniques
are efficiently used in evaluation of pavement distress like cracking [82]. A genetic fuzzy
system [83] is used for crack density and crack location detection. The genetic fuzzy
logic system [84] is used as method for automatic rule generation in fuzzy systems for
structural damage detection. The reference [85] has presented a comprehensive structural
fault detection method using fuzzy logic which is better suited to tolerate noise and
uncertainty. A fuzzy rule-based system [86] is developed for the blade of a BO-105
helicopter rotor modeled as a cantilever beam and demonstrated that the fuzzy system
perform accurately even in the existence of noisy data. The sensitivity of the modal
frequencies and other parameters to a crack increases when the crack is near the sensors
and decreases as the crack moves away so a modular neural network architecture [87] is
18
presented as a non-destructive method for health monitoring of structures. The soft
computing techniques can be used to implement the NDT techniques on FPGA using
various tools, and software to achieve an automation of the proposed techniques [88]-
[102].
19
CHAPTER 3
MULTIPLE HOPS RELIABILITY OF SENSOR NETWORKS
3.1 Introduction
Sensor network is a network composed of large number of sensor nodes positioned
randomly even in locations which are not accessible easily [1]. The information is carried
from one node to another with help of packets moving through some selective paths or all
possible simple paths. A Multiple Hops Path (MHP) is a path with multiple numbers of
links from the source node to the sink node. The MHP includes possible one-hop, two-
hops…, maximum-hops paths between the given source and the sink nodes. The terms
used in the area of MHP are:
Multiple Hops Path: It is a simple path which takes ‗m‘ number of links to
communicate between the desired source and the sink nodes. The m-hops path expression
(fmhop) is obtained as the sum of all possible m- hops paths. The m-hops TR is defined as
the TR of data transfer between the given source and sink nodes calculated using the m-
hops path expression.
Minimum hops path (MinHP): It is a simple path which takes minimum number
of links to communicate between the desired source and the sink nodes. The minimum
hops path expression (fminhop) is obtained as the sum of all possible MinHP.
Minimum hops cutsets (MinHC): It is a cutset is a cutset with minimum number
of links in each term such that on elimination of these links there will be no
communication path between the source and sink nodes. It is a subset of a minimal cutset.
The MinHC expression (fminhop) is obtained as the sum of all possible MinHC.
20
Minimum hops TR (MinHTR) is defined as the TR of data transfer between the
given source -sink nodes calculated using the minimum hops or cutsets path expression.
The minimum hops path reliability (MinHPR) is the reliability obtained through
MinHP between the given source and sink nodes of a WSN.
The minimum hops cut-sets reliability (MinHCR) is the reliability obtained through
MinHC between the given source and sink nodes of a WSN.
Maximum hops path (MaxHP): It is a simple path which takes maximum number
of links to communicate between the desired source and the sink nodes. The maximum
hops path expression (fmaxhop) is obtained as the sum of all possible maximum hops paths.
The maximum hops TR is defined as the TR of data transfer between the given source
and sink nodes calculated using the maximum hops path expression.
Consider graph G= (V, E,P,Q) as a sensor network, where
1. V = {v1, v2, …, vn} is set of n sensor nodes
2. E = { e1, e2, …, em } is the set of m communication links between the
various sensor nodes.
3. P = {p1, p2… pm} is the set of reliability of links in E, where pi is the
reliability of link ei. The reliability of each link is defined as the probability of
successful communication through the link.
4. Q = {q1, q2… qm} is the set of unreliability of links in E, where qi is the
ureliability of link ei.. The unreliability of a link is defined as qi = 1-pi.
3.2 Minimum Hop Paths Algorithm in a Sensor Network
The Minimum Hops Path (MinHP) problem determines all possible paths with
minimum number of hops (links) in a sensor network between source and sink nodes.
21
The packets in sensor network can be advantageously sent through minimum number of
hops rather than all possible hops. The MinHP can be of significance in a variety of
applications like determination of reliability and security of sensor networks for internet
and homeland security. In the literature there has been a great deal of interest in
determining all possible paths [13][14] between the source and sink node in the network.
Guerin and Orda [10] suggested a procedure for minimum weight path for all hopcounts
between a given source and sink in networks. Cheng and Ansari [11][12] determined all
hop shortest path by giving weights to each path. To the best of authors‘ knowledge no
author has suggested algorithms for determining MinHP in a sensor network.
Express this graph G as:
S.H = P … (3.1)
where, S = [sij]nxm is the connection matrix of the sensor network. It has a column for each
edge and a row for each node. The hop-vector, H = [hi]mx1 is a column vector such that, hj
is ‗1‘ if link ej is included in the min-hop path and ‗0‘ otherwise. The number of 1‘s in
this matrix defines the number of hops required to carry a packet from the source node to
the sink node. The path-vector, P = [pj]nx1 is path column vector with value of ‗-1‘ for
the source node and ‗+1‘ for the sink node. The matrix S is defined as:
Sij = 0 , if there is no link from sensor node i to j,
= -1, if there is a directed link from node i to j,
= 1, if there is a directed link from node j to i … (3.2)
The path-vector, P = [pi]nx1 is path column vector such that,
pi = -1, if node i is a source sensor node,
= 1, if node i is a sink sensor node,
22
= 0, otherwise … (3.3)
Directed Graph MinHP Method: In order to determine all MinHP in a directed graph
with MinHP length = MinHPL, the procedure is described as below:
1. Construct connection matrix S = [sij]nxm which satisfies conditions expressed in
equation (3.2).
2. Construct path-vector, P = [pi]nx1 which satisfies conditions expressed in eq. (3.3).
3. Set hop-vector H = [hi]mx1 with all elements equal to ‗0‘.
4. Construct ORIGIN= set of edges incident from source, and MERGE= set of edges
incident to sink. At a time only one edge from each of these sets can contribute to form a
path.
5. Set hop_count =1, simple_path_count=0, MinHPL=0, and the set Simple_paths= {}.
6. Compare each column from S with P;
for (j=0,j<m; j++)
{if ( column ‗j‘ matches with path vector P)
{ simple_path_count++;
Add link (ej) to the set of Simple_paths. } }
If simple_path_count> 0, MinHPL = 1, Continue with step 9.
7. Increment hop_count by 1, if hop_count > m, continue with step 9.
8. Determine all possible combinations of hop_count number of columns such that each
combination has only one link (column) from each of ORIGIN and MERGE sets. Add all
possible hop_count column combinations and compare the sum with P;
for (all possible combinations of hop_count columns)
if ( sum of hop_count columns matches with path vector P )
23
{ simple_path_count++;
Add (set of all link columns (ej)) to the set of Simple_paths.}
If (simple_path_count> 0)
{MinHPL= hop_count, Continue with step 9 }
else {continue with step 8.}
9. If (simple_path_count= 0 or hop_count > m)
{ no paths exist between the source and the sink node.}
else {MinHPL= hop_count, Number of paths= simple_path_count, and list of MinHP=
set of Simple_paths.}
The number of vector additions and comparisons to check 1-hop, 2-hop and 3-hop path
length are mC1, mC1 + mC2 and mC1 + mC2 + mC3 resp. Here the mCk = m!/((k!)*(m-k)!).
The best case scenario with MinHPL=1 performs mC1 vector additions and comparisons.
The worst case scenario with MinHPL=m performs vector additions and
comparisons. This procedure can be extended to get all possible simple paths up to path
length ≤ m. This procedure gives flexibility to update the source node and the sink node
by simply changing the Path vector P. The nodes and links are prone to failure in sensor
networks. With this procedure insertion or deletion of a node/link is simply a matter of
insertion or deletion of a row/column.
3.2.1 MinHP Illustrative Example
To find all MinHP for the graph shown in Fig. 3.1 from sensor node 1 to 8.
Fig. 3.1 Sensor Network with 8 nodes and 11 links.
24
The connection matrix S and the Path matrix P of the sensor network: S8x11 * H11x1 =
P8x1 shown in Fig. 3.1 is:
= … (3.4)
ORIGIN = {e1, e5, e7} and MERGE = {e9, e11}
Table 3.1: Results for Example shown in Fig. 3.1
Iterati
on
(hop
count)
Sum of Columns =
P
Minimum Hop
Path (MinHP)
# of vector
additions and
comparisons
1 - - 11C1
2 - - 11C2
3 {(1,2,11),(5,6,9)} {e1e2e11, e5e6e9} 11C3
MinHP obtained after third iteration. The process can be continued
further for hop path lengths > MinHP.
4 {(1,3,10,9),
(7,8,6,9)}
{e1e3e10 e9,
e7e8e6e9} 11C4
5 {(1,2,4,10,9)} {e1e2e4e10e9} 11C5
Table 3.1 show that no single column or any combination of two-column sum matches
with P in iteration 1 and 2. In third iteration two combinations of sum of 3-column pairs
(1, 2, 11) and (5, 6, 9) is equal to P giving the MinHPL=3. Thus the number of
comparisons carried out to evaluate MinHP with MinHPL=3 are: instead of
comparisons. The best case scenario takes 11C1 and worst case takes
vector additions and comparisons.
25
3.3 Minimum Hop-Cutsets in a Sensor Network
The problem of Minimum Hop Cutsets (MinHC) in sensor networks is to determine a
cutset with minimum number of links such that on elimination of these links there will be
no communication path between the source and sink nodes. MinHC is a subset of a
minimal cut set. There has been large number of procedures in literature [22], [42] to
determine minimal cutsets between the source and sink nodes. Traditionally a minimal
cutset is a cutset such that no subset of it forms a cutset [42]. The minimal cutset may
include cutset terms of varying dimensions. The term dimension here refers to the
number of links in a cutset. In some cases it is advantageous to determine cutset of some
specified dimension ‗n‘ and one may not be interested in finding cutsets of dimension
greater than n. The MinHC due to its reduced size and dimension will be advantageous
in determining reliability of sensor networks with very less computations. Depending on
the requirement we can use cutsets of only a specified dimension. The MinHC problem is
of significance in SN when the overall network is to be reduced to have specified cutsets
dimension.
Consider graph G= (V, E,P,Q) as a sensor network. Consider S = [sij]nxm, a connection
matrix of the sensor network.. This matrix is formed in such a manner that column i
represents a link ei and a row i represents node i. The value of Sij = -1, if there is a
directed link from node i to j and the value is Sij = 1, if there is a directed link from node j
to i. Otherwise Sij = 0.
3.3.1 MinHC Algorithm-I
The MinHC in a directed graph with MinHC length = MinHCL is determined using
following steps:
26
1. Construct connection matrix S = [sij]nxm such that sij Є {0(no link between i and j),-
1(link from i to j), 1(link from j to i};
2. Construct path-vector, P = [pi]nx1 such that pi Є {-1(i is source node), 1(i is sink node),
0(otherwise) };
3. Set parameters:
a. MinHC length/dimension: MinHCL=1,
b. The set of MinHC: MinHC= {},
c. The number of terms in MinHC: MinHC_count=0;
4. For all possible combinations of MinHCL links mCMinHCL, remove each combination
of links(columns) from S nxm to form US nx(m-MinHCL)
{ if(is_Path(US nx(m-MinHCL) , H, P)==false)
{ Add edge combination to the set MinHC.
MinHC_count++; } }
5. If (MinHC_count == 0 and MinHCL < m) then (MinHCL++ continue with step 4).
6. If (MinHC_count > 0 )
{ The MinHC length = MinHCL;
The set of Minimum Hop Cutsets = MinHC;
The number terms in MinHC = MinHC_count;}
7. The final MinHC expression is the sum of unique terms present in the set MinHC.
The enumeration and existence of shortest path between the two nodes [10][11] with
minimum number of computations[12] is important. The algorithm for checking whether
a path exists in the given graph with a connection matrix US nx(m-MinHCL) and path vector P
is described below:
27
Algorithm: Boolean is_Path (US nx(m-MinHCL) , P)
{ Compare each column from US nx(m-MinHCL) with P;
if (match found)
{Path does exist; return (True).}
Set hop_count =1;
while (hop_count ≤ m)
{ Add all possible combinations of hop_count columns and compare the sum with P;
if (match found)
{Path does exist; return (True). }
hop_count++; }
No path exists in the network between the source-sink;
return (False); }
The number of iterations performed by the MinHC algorithm is (
)*(is_Path() algorithm). The number of vector additions and comparisons carried out by
is_Path() algorithm for m columns in S matrix is . Thus total amount of
computations done by MinHC algorithm is: . This algorithm can be
extended for the undirected graphs representing the sensor network with the following
modifications:
Redefine S = [sij]nxm with the Boolean value of Sij = 1, if there is a link between
nodes i to j, otherwise Sij = 0.
In the above algorithm for directed networks replace ‗Add‘ by ‗XOR‘ operation.
28
Rest of the steps and the process would remain the same for undirected graphs. This
algorithm can be very easily implemented as a hardware circuit to improve the
performance of the algorithm in the case of very large sensor networks.
Consider MinHC Algorithm-I Example to find MinHC for the graph shown in Fig. 3.1
with 8 nodes and 11 links, from sensor node 1 to 8.
The connection matrix and the Path matrix for the directed graph shown in Fig. 3.1 are
as given in equation (3.4). The connection matrix S= Su and P = Pu for an undirected
network similar to Fig. 3.1 with all links undirected is:
=
Table 3.2 show that no single column elimination cuts the communication between the
source and sink nodes for both the directed and undirected network. It is seen that the
four pairs of 2-column combinations elimination from the connection matrix of the
directed graph results in termination of communication between the source and sink
nodes. These four combinations of 2-column pairs are: (1,6), (1,9), (2,9) and (9,11) with
the MinHCL=2 and MinHC_count = 4. The process can be continued further for hop path
lengths > MinHCL. This generates the MinHC = e1e6 + e1e9 + e2e9 + e9e11 for the directed
graph. Table 3.2 show that two pairs of 2-column combinations elimination from the
connection matrix of the undirected graph results in termination of communication
between the source and sink nodes. These two combinations of 2-column pairs are: (1,6),
29
and (9,11) with the MinHCL=2 and MinHC_count = 2. The process can be continued
further for hop path lengths > MinHCL. This generates the MinHC = e1e6 + e9e11 for the
undirected graph. The number of computations performed with this value of MinHCL
are: instead of . This overall number of computations
are: .
Table 3.2: Results of MinHC algorithm-I for network in Fig. 3.1
Step
Number
(Iteration)
Set of columns if
deleted results in no
path between the
source and sink
nodes.
Minimum Hop
Cutset (MinHC)
Number of vector computations
Directed graph MinHC Algorithm
4(1) - - (11C1)*
4(2) { (1,6), (1,9),
(2,9), (9,11) }
{ e1e6, e1e9, e2e9
, e9e11} (11C2)*
Results: Directed graph MinHC obtained after second iteration of step 4 with MinHCL=2
and MinHC_count = 4. MinHC= e1e6 + e1e9 + e2e9 + e9e11
Undirected graph MinHC Algorithm
4(1) - - (11C1)*
4(2) { (1,6), (9,11) } {e1e6, e9e11} (11C2)*
Results: Undirected graph MinHC obtained after second iteration of step 4 with
MinHCL=2 and MinHC_count = 2. MinHC= e1e6 + e9e11
3.3.2 MinHC Algorithm-II
In order to determine all the MinHC the procedure using the rows of the connection
matrix is uses following steps:
1. Construct connection matrix S = [sij]nxm which satisfies conditions expressed in
equation (3.1). Thus the columns number i maps with the link ei, and the row number i
maps with the node i.
2. Set the initial values to various identifiers:
a. Length of the hop cutsets: hop_count=1,
b. The number of MinHC: number_of_MinHC = 0,
30
c. The set of minimum hop cutsets: MinHC ={};
d. The pivot_row1 = row of source node and pivot_row2 = row of sink node.
3. Set min_Pivot_row = Row with minimum number of nonzero terms from
pivot_row1 and pivot_row2. Set max_Pivot_row = Row with maximum number of
nonzero terms from pivot_row1 and pivot_row2. If the number of nonzero terms are
same then min_Pivot_row = Pivot_row1 and max_Pivot_row = Pivot_row2.
4. Minimum Hop Cutset length: MinHCL = number of nonzero terms
min_Pivot_row;
5. Determine all n-1Chop_count combinations of rows other than the max_Pivot_row.
Add all possible hop_count row combinations and compare the number of nonzero terms
with the MinHCL;
for (all possible combinations of hop_count rows)
{ sum_vector = sum of hop_count number of rows;
if(sum_vector is not a zero vector and number of nonzero Terms (sum_vector) ≤
MinHCL)
{number_of_MinHC++;
Add (set of all links corresponding to non-zero elements from sum_vector as a cutset)
to the set of MinHC.}}
6. Increment hop_count by 1, if hop_count > n-1, continue with step 9. Otherwise
continue with the step 5.
7. sum_vector = sum of all rows except min_Pivot_row.
if(sum_vector is not a zero vector and number of nonzero Terms (sum_vector) ≤
MinHCL)
31
{number_of_MinHC++;
Add (set of all links corresponding to non-zero elements from sum_vector as a cutset)
to the set of MinHC. }
8. check for the number of nonzero terms in max_Pivot_row.
if(number of nonzero Terms (max_Pivot_row) ≤ MinHCL)
{number_of_MinHC++;
Add (set of all links corresponding to non-zero elements from sum_vector as a cutset)
to the set of MinHC. }
9. If number_of_MinHC = 0, no MinHC cuts exist between the source and the sink
node. Otherwise:
The number of MinHC: number_of_MinHC
The set of Minimum Hop Cutsets: MinHC.
The length of MinHC: MinHCL
10. The final MinHC expression is the sum of unique terms present in the set MinHC.
The algorithm for the undirected graph is very similar to the one for directed graph
with few exceptions like:
The Boolean connection matrix S is as defined in equation (2).
The operation ‗Add‘ from directed MinHC algorithm is replaced by ‗XOR‘.
The number of vector operations to check cutsets using any 1-row combinations is: n-
1C1. Similarly for 2-row and 3-row combinations include n-1C2 and n-1C3 vector operations
resp. Thus overall method would take n-1C1 + n-1C 2 + n-1C 3 + … + n-1Cn-2 + n-1Cn-1 + 2 (by
steps 8 and 9) vector operations, which can be expressed as ( . This
32
procedure can be use to generate all possible cutsets in the network between any two
nodes namely the source and sink nodes.
Consider MinHC Algorithm-II Example to find all MinHC for the non-series parallel
network or bridge network shown in Fig. 3.2 from sensor node 1 to 4.
Fig. 3.2 Bridge Sensor Network with 4 nodes and 5 links.
Consider a non-series parallel network (or bridge network), which has got 5 links and 4
nodes. The connection matrix S=SD for the directed SN and S=SU for the undirected SN
shown in Fig. 3.2 is:
The Parameters are set in the following manner:
Length of the hop cutsets: hop_count = 1,
The number of MinHC: number_of_MinHC = 0,
The set of minimum hop cutsets: MinHC={};
The pivot_row1 = row of source node= 1
The pivot_row2 = row of sink node=4
As the number of nonzero terms are equal in both the pivot rows;
min_Pivot_row= pivot_row1=1 and max_Pivot_row= pivot_row2.
Minimum Hop Cutset length: MinHCL = number of nonzero terms
min_Pivot_row=2
33
The results for the directed as well as undirected graphs are tabulated in Table 3.3. It is
observed that for a graph with 4 nodes after 3 iterations of step 5 the desired result is
obtained. Similarly for a graph with n nodes, the MinHC algorithm-II will take n-1
iterations of step 5. The final expression for the MinHC is obtained by sum of unique
MinHC terms, MinHC = e1e2+ e3e4 + e1e2 +e3e4 = e1e2+e3e4.
Table 3.3: Results of MinHC algorithm for network in Fig.3.2
Step#
(iteratio
n)
Row combinations with
non-zero terms ≤ MinHCL
MinHC
term
#vector
computations
5(1) {(1)} {(e1e2)} 3C1
5(2) - - 3C2
5(3) {(1,2,3)} {(e3e4)} 3C3
7(1) {(2,3,4)} {(e1e2)} 1
8(1) {(4)} {(e3e4)} 1
Final MinHC = e1e2+ e3e4 + e1e2 +e3e4 =
e1e2+e3e4
(
3.4 An Efficient WSN Terminal Reliability Scheme
Wireless sensor networks (WSN) are being widely being explored in a variety of
applications [1], [43]-[45]. The number of sensor nodes (SN) is varying from tens to few
thousands. Many associated design and performance issues have been investigated in
detail. Some of the issues ignored are the reliability and security of WSNs while these
have become increasingly important. The problem of computing TR of such WSN has
recently received some attention as possible extension of Computer Communication
Networks (CCNs)[15][16]. With an increased importance of security issues, it has
become critical to determine the reliability of wireless sensor networks (WSN). As the
34
number of sensor nodes is fairly large in a WSN, it is rather impractical to adopt exact
methods of reliability through all paths and cut-sets commonly used in CCN. This thesis
proposes an efficient but approximate scheme that calculate average of TR values
obtained through MinHP and MinHC,. This scheme is shown to provide reasonably
accurate results while the complexity is reduced drastically.
TR in a CCN can be computed by using either all possible paths or cut-sets between
any two terminal pair of nodes [14]-[19]. There are relative advantages and disadvantages
of these two schemes. But, from the complexity point of view, path method works
efficiently with some networks while cut-set method can be more beneficial for some
other networks. Various authors have tried to determine reliability of WSN [3]-[9], [46],
[47], treating them similar to a traditional CCN. But, with large number of sensor nodes,
the size of possible alternate paths between two nodes grows exponentially while the
number of cut-sets could become prohibitively large.
In a WSN, the number of paths along minimum number of hops between the source
and sink nodes are important than all possible paths. Moreover, reliability contributions
by longer paths are negligibly small. The problem of computing shortest paths for any
number of hops[10] and finding all hops shortest paths has been studied in [11][12].
Hence, there has been interest in determining the reliability of a WSN with the help of
only minimum number of hops. Similarly, several authors have shown techniques to
determine reliability with minimal cut-sets in the literature. These techniques make the
overall procedure computationally efficient as they require dealing with a fewer number
of paths/cut-sets, without having much effect on the accuracy. Our proposed approach is
based on this basic idea. We define the Minimum Hops Reliability (MinHR) as the
35
average of MinHPR and MinHCR between the a given source and sink nodes. Thus,
MinHR = (MinHPR + MinHCR)/2.
3.4.1 Proposed MinHR Algorithm
Consider G= (V, E,P,Q) as a representation of the field covered by a WSN as a graph.
The algorithm follows the following steps:
A. Consider the graph G with given source and sink nodes.
B. Determine the MinHPR with the help MinHP algorithm from section 7.1 or any of the
techniques available in the literature to determine minimum hop paths. The proposed
MinHPR algorithm consists of following steps:
a. Determine the MinHP expression (fp) which is a Boolean expression in the sum of
product form. Each term in fp is the MinHP between the source and the sink
nodes.
b. Determine the disjoint expression (fD) of the path expression (fp).
c. Determine an arithmetic expression for reliability R by replacing the each link ei,
by its reliability pi in fD.
d. Evaluate MinHPR by substituting values from P and Q in R with MinHPR =R.
C. Determine MinHCR with the help MinHC algorithm from section 7.2 or any of the
techniques available in the literature to determine minimum hop cutsets. The
proposed MinHCR algorithm consists of following steps:
a. Determine the MinHC expression (fc) which is a Boolean expression as the sum
of products. Each term in fc is the minimum hops cut-set between the source and
the sink nodes, with the least number of links that terminate the communication
between these desired nodes.
36
b. Determine the disjoint expression (fD) of the cut-sets expression (fc).
e. Determine an arithmetic expression for unreliability Ru by replacing the each link
ei by qi and ei' by pi.
c. Substitute the values of P and Q in Ru. Obtain MinHCR= 1- Ru.
D. MinHR between a given source and sink nodes is approximated by the average of
MinHPR and MinHCR. Thus, MinHR = (MinHPR + MinHCR)/2.
3.4.2 The MinHR Illustrative Examples
The proposed scheme is illustrated with the help of some simple examples. The
terminal reliability of a WSN is first evaluated by the general CCN reliability method.
The length of the terms in MinHP and the MinHC is first calculated. The steps of the
proposed algorithms for MinHPR and MinHCR are used to obtain the values of MinHPR
and MinHCR. The MinHR value is acquired as an average of MinHPR and MinHCR.
Consider the following WSN, with the following paths and cut-sets:
Example 1: For the network connectivity model of a WSN of Fig. 3.3(a), assume the
Source node=1 and Sink node=4.Assume {p1, p2, p3, p4, p5} = {0.9, 0.8, 0.7, 0.6, 0.5}.
The results can be seen in Table 3.4.
(a) (b)
Fig. 3.3: WSN Connectivity model (a) non-series parallel, (b) Example 2
Example 2: Assume pi =0.9, for all i from 1 to 3for network shown in Fig. 3.3(b) with
Source node=1 and Sink node=3.The results can be seen in Table 3.5.
37
Table 3.4: The MinHR Result for Example 1.
Method Path Cutsets Existing
Methods
path expression: fp = x1x2+ x3x4 + x1x4x5
+ x2x3x5
Disjoint expression: fD= x1x2+ (x1)'x3x4 +
x1(x2)'x3x4 + x1(x2)'(x3)'x4 x5
+(x1)'x2x3(x4)' x5
R= p1p2+ (1-p1)p3p4 + p1(1-p2)p3p4 +
p1(1-p2)(1-p3)p4 p5 +(1-p1)p2p3(1-p4) p5
Step 2: Rreg= 0.865.
path expression: fc = x1x3+ x2x4 + x1x4x5 +
x2x3x5
Disjoint expression: x1x2+ x2(x3)'x4 + (x1)'
x2x3x4 + (x1)'x2x3(x4)' x5+ x1(x2)'(x3)'x4 x5
Ru= p1p3 + p2(1-p3)p4 + (1-p1) p2p3p4+
p1(1-p2)(1-p3)p4 p5 +(1-p1)p2p3(1-p4) p5
Ru= 0.135
Step 2: Rreg= 1- Ru= 1- 0.135 = 0.865
Proposed
Minimum
hop
methods
MinHP length: 2
MinHP expression: fp = x1x2+ x3x4
Disjoint expression: fD= x1x2+(x1)'x3x4 +
x1(x2)'x3x4
R= p1p2+ (1-p1)p3p4 + p1(1-p2)p3p4
MinHPR = 0.8376.
MinHC length: 2
MinHC expression: fc = x1x3+ x2x4
Disjoint expression: x1x3+ x2(x3)'x4 + (x1)'
x2x3x4
Ru= p1p3 + p2(1-p3)p4 + (1-p1) p2p3p4=
0.03 + 0.056 + 0.0216 = 0.1076
MinHCR= 1- Ru= 1-0.1076= 0.8924
MinHR = (MinHPR + MinHCR)/2 = 0.865. Existing method: Rreg= 0.865.
Table 3.5: The MinHR Result for Example 2.
Proposed MinHP method Proposed MinHC method
MinHP length: 2
MinHP expression: fp = x1x2 + x1x3
Disjoint expression: x1x2+ x1(x2)'x3
R= p1p2+ p1(1-p2)p3
MinHPR = 0.8910
MinHC length: 1
MinHC expression: fc = x1
Disjoint expression: x1
Ru= p1 = 0.1
MinHCR = 1- Ru= 1-0.1= 0.9
MinHR = (MinHPR + MinHCR)/2 = 0.8955. Existing method: Rreg= 0.865.
Example 3: Assume pi =0.9, for all i from 1 to 4 for network shown in Fig. 3.4 with
Source node=1 and Sink node=4.The results can be seen in Table 3.6.
Fig. 3.4: Connectivity model of Example 3 WSN
Table 3.6: The MinHR Result for Example 3.
Proposed MinHP method Proposed MinHC method
MinHP length: 3
MinHP expression: fp = x1x2 x3+ x1x2x4
Disjoint expression: x1x2 x3+ x1 x2(x3)'x4
R= p1p2 p3+ p1p2(1- p3)p4= 2p3
- p4
MinHPR = 0.8019
MinHC length: 1
MinHC expression: fc = x1 + x2
Disjoint expression: x1+ (x1)'x2
Ru= p1+ (1-p1)p2= 2p-p2 = 0.1900
MinHCR = 1- Ru= 0.8100
38
MinHR = (MinHPR + MinHCR)/2 = 0.8059. Existing method: Rreg=0.8019
Example 4: Assume pi =0.9, for all i from 1 to 5 for network shown in Fig. 3.5 with
Source node=1 and Sink node=5.The results can be seen in Table 3.7.
Fig. 3.5: Connectivity model of Example 4 WSN
Table 3.7: The MinHR Result for Example 4
Proposed MinHP method Proposed MinHC method
MinHP length: 4
MinHP expression: fp = x1x2 x3x4+ x1x2
x3x5+ x1x2x3x6
Disjoint expression: x1x2 x3x4+ x1x2
x3(x5)'x6 + x1x2x3x4(x5)'(x6)'
R= p1p2 p3p4+ p1p2 p3(p5)'p6 +
p1p2p3p4(p5)'(p6)' = 3p4 - 3p
5 + p
6
MinHPR = 0.7283
MinHC length: 1
MinHC expression: fc = x1 + x2+ x3
Disjoint expression: x1+ (x1)'x2 +
(x1)'(x2)' x3
Ru= p1+ (1-p1)p2 + (1-p1)(1-p2) p3 = 3p
- 3p2 + p
3= 0.2710
MinHCR = 1- Ru= 1- 0.2710= 0.7290.
MinHR = (MinHPR + MinHCR)/2 =0.7287. Existing method: Rreg=0.7283
Example 5: Assume pi =0.9, for all i from 1 to 8 for network shown in Fig. 3.6 with
Source node=1 and Sink node=8.The results can be seen in Table 3.8.
Table 3.8: The MinHR Result for Example 5.
Proposed MinHC method: Proposed
MinHP method
Proposed MinHC method
MinHP length: 3
MinHP expression: fp = x1x2x11+x5x6x9
Disjoint expression: x5x6x9 +
x1x2x5(x6)' x9x11 + x1x2(x9)' x11 +
x1x2(x5)' x11
R= p5p6p9 + p1p2p5(1- p6)p9p11 +
p1p2(1- p9)p11 + p1p2(1- p5)p11
R= p3 + p
5(1- p) + 2p
3(1- p) = 3p
3+ p
5 -
p6 - 2p
4
Step 4: MinHPR = 0.9338
MinHC length: 2
MinHC expression: fc = x1x6+ x9x11
Disjoint expression: x1x6 + (x1)'
x9x11 + x1(x6)'x9 x11
Ru= p1p6 + (1-p1)p9p11+ p1(1-
p6)p9p11 = p2
+ (1-p1)p2+ p
3(1-p6)=
p2
+ p2– p
3+ p
3 - p
4=2 p
2 - p
4
MinHCR = 1- Ru = 1-0.0199=
0.9801.
MinHR = (MinHPR + MinHCR)/2 = 0.9570. Existing method: Rreg = 0.9745.
39
Fig. 3.6 Connectivity model of Example 5 WSN
Example 6: Assume pi =0.9, for all i from 1 to 32 for network shown in Fig. 3.7 with
Source node=A and Sink node=L. The results can be seen in Table 3.9.
Fig. 3.7 Connectivity model of Example 6 complex WSN
Table 3.9: The MinHR Result for Example 6.
Proposed MinHP method Proposed MinHC method
MinHP length: 4
MinHP expression:
fp = e31e32e25e23
Disjoint expression:
e31e32e25e23
R= p31p32p25p23 =p4
MinHPR = 0.6561
MinHC length: 3
MinHC expression: fp = e1e2e31+ e19e20e23
Disjoint expression: e19e20e23+ e1e2e19(e20)' e23e31 +
e1e2(e23)' e31 + e1e2(e19)' e31
Ru= p19p20p23 + p1p2p19(1- p20) p23p31 + p1p2(1- p23)
p31 + p1p2(1- p19) p31
Ru= p3 + p
5(1- p) + 2p
3(1- p) = 3p
3+ p
5 - p
6 - 2p
4
MinHCR = 1- Ru= 0.9968.
MinHR = (MinHPR + MinHCR)/2 = 0. 8265. Existing method: Rreg = 0.997901.
Table 3.10: MinHR of Example Sensor Networks
Example Rreg MinHPR MinHCR MinHR % Error=│ Rreg– MinHR│
Fig. 3.3 0.865 0.8376 0.8924 0.865 0
Fig. 3.4 0.865 0.8910 0.9 0.8955 3.05
Fig. 3.5 0.8019 0.8019 0.8100 0.8059 0.4988
Fig. 3.6 0.7283 0.7283 0.7290 0.7286 0.0412
Fig. 3.7 0.9745 0.9338 0.9801 0.9570 1.7958
Fig. 3.8 0.9979 0.6561 0.9968 0. 8265 17.61
40
3.5 An Approximate Sensor Network System Reliability Algorithm
An approximate system reliability calculation method for sensor networks based on
the paths and cutsets is proposed in this thesis using min-max method. System Reliability
is defined as terminal reliability of all nodes to all other nodes [48]. In literature it is also
referred as network reliability, or global reliability or overall reliability [49]. The
calculation of system reliability can be carried out with reasonable number of calculations
for simple sensor networks. The number of calculations greatly increases for the large
networks. The system reliability problems are NP-hard [22].A fuzzy reliability concept
for determining terminal reliability [50] was proposed to determine the terminal
reliability by min-max method.
The traditional procedure requires all paths and cutsets between all possible terminal
nodes. The path expression is generated by applying AND operator between all node
pairs paths. The cutset expression is generated by applying OR operator between all
node pairs cutsets. The disjoint expression is then determined for each of them. However
determination of disjoint expression is quite involved. There are several procedures
available in literature which involves techniques for determination of disjoint expression
such as using binary decision diagrams. In the proposed system reliability algorithm we
avoid the determination of disjoint expressions, by considering only the min-max values.
3.5.1 Proposed Min-Max Algorithm
Consider graph G= (V, E, P, Q) as a sensor network .Traditionally paths or cutsets are
used to evaluate the reliability of computer communication networks. The basic method
for the calculation of system reliability is discussed followed by the proposed Min-Max
method using the path and cutsets method. The number of calculations is drastically
41
reduced in Min-Max method for it eliminates the need of calculation of disjoint
expression.
The Common steps involved in both Path method algorithms consist of following three
steps:
1. Form node pair Boolean path expression Nij for paths from node i to j, such that
1<=i< n, and i+1<= j< n, where n is number of nodes in the graph. Thus for an n node
graph we get n*(n-1)/2 path node pairs [3].
for (i=1; i<=n, i++)
{Nij = 1;
for (j = i+1; j<=n, j++)
Nij = (Nij).(edge from node i to node j) }
Example: The node pair Boolean path expression for node pair 1-4 for the bridge network
graph shown in Fig. 3.8 is N14 = e1e4 + e2e5 + e1e3e5 + e2e3e4.
2. Determine the system reliability expression: SrelP,
Let SrelP = 1.
for (i=1; i<=n, i++)
{ for(j = i+1; j<=n, j++)
Srel = (SrelP) AND (Nij)}
3. Simplify the SrelP expression as SrelP = S1 + S2 + …+ St, such that it has t terms,
where each term Si is the product of some links. The simplified SrelP expression is in
the form of Sum of Products.
The Common steps involved in the Cutsets method algorithms involve following three
steps:
42
1. Form node pair Boolean cutsets expression Cij, for cutsets between node i to j, such
that 1<=i< n, and i+1<= j< n, where n is number of nodes in the graph. Thus for an n
node graph we get n*(n-1)/2 cutset node pairs [4].
for (i=1; i<=n, i++)
{Cij = 1;
for (j = i+1; j<=n, j++)
Cij = (Cij).(link from node i to node j) }
Example: The node pair Boolean cutsets expression for node pair 1-4 for the bridge
network graph shown in Fig. 3.8 is C14 = e1e2 + e4e5 + e1e3e5 + e2e3e4.
2. Determine the system reliability expression SrelC:
Let SrelC = 1.
for (i=1; i<=n, i++)
{ for(j = i+1; j<=n, j++)
Srel = (SrelC) OR (Cij)}
3. Simplify the SrelC expression as SrelC = S1 + S2 + …+ St, such that it has t terms,
where each term Si is the product of some links. The simplified SrelC expression is in
the form of Sum of Products.
3.5.1.1 Basic Method Algorithm:
The steps involved in the computation of the system reliability of sensor networks
using Basic Path Method [49] after using the common steps are:
1. Determine disjoint expression (SPDE and SCDE) with help of Karnaugh map or any
other methods from literature.
a. For path method: SPDE is determined from the SrelP expression.
43
b. For cutsets method: SCDE is determined from the for the SrelC expression.
2. Express the SPDE and SCDE expressions in terms of the reliability ‗pi‘ and unreliability
‗qi‘ variables to form an arithmetic expression SPAE for path method and SCAE cutsets
method.
a. For path method: SPAE = [SPDE]ei=pi & ei'=qi, such that for all terms replace ei by pi
and ei' by qi.
b. For cutsets method: SCAE = [SCDE]ei=qi & ei'=pi , such that for all terms replace ei
by qi and ei' by pi.
3. Determine system reliability by basic path method RPM, by substituting the values of
reliability P and the unreliability Q in SPAE.
4. Determine system reliability by basic cutsets method RCM = 1- SCAE, by substituting
the values of reliability P and the unreliability Q in SCAE.
3.5.1.2 Min-Max Method:
The steps involved in the computation of the system reliability of sensor networks
using Min-Max Method after using the common steps are:
1. The simplified SrelP and SrelC expression is in the form of Sum of Products.
a. The sum operation is proposed as a representation of intersection of two sets of
data. The intersection[50] of two fuzzy sets A and B is defined as:
A B = {x, µ(x)} | x A, and µ(x) = max [ µA (x), µB(x)]
Thus ‗a+b+c‘ is equivalent to max (a, b, c).
b. The product operation is proposed as a representation of union of two sets of data.
The union[5]of two fuzzy sets A and B is defined as:
A B = {x, µ(x)} | x X, and µ(x) = min[µA (x), µB(x)]
44
Thus ‗a.b.c‘ is equivalent to min(a, b, c).
2. Obtain the Min-Max expressions fPMM (for path method) and fCMM (for cutsets
method)as: max[min(Individual Terms in S1), min(Individual Terms in S2),…,
min(Individual Terms in St)]
Example: if SrelP = e1e4e5 + e2e4e5 then fPMM = max[min(e1,e4,e5), min(e2,e4,e5)]
3. Express the fPMM and fCMM expression now in terms of the reliability variables (pi, qi)
to form arithmetic expressions fPAE and fCAE respectively for the path and cutsets
method. In this process ei is replaced by pi. Thus fPAE and fCAE are in the form:
max[min(Individual Reliability Terms in S1), min(Individual Reliability Terms in
S2)… min(Individual Reliability Terms in St)].
Example: if fPMM = max[min(e1,e4,e5), min(e2,e4,e5)], then fPAE = max[min(p1,p4,p5),
min(p2,p4,p5)]
4. Determine RPMM and RCMM, the system reliability values for path and cutsets by Min-
Max Method, by substituting the values from P and Q in fPAE and fCAE respectively.
3.5.2 Approximate System Reliability Algorithm Examples
The system reliability of a non-series-parallel network (bridge network) as seen in Fig.
3.8 is evaluated using four methods:
Basic path method(RPM),
Basic cutsets method(RCM),
Min-Max path method(RPMM), and
Min-Max cutsets method (RCMM).
45
Fig. 3.8 A series-parallel Network
For this network the number of sensor nodes is 4 and the number of node pairs is 6.
Assume p= {0.9, 0.9, 0.9, 0.9, 0.9} and Q = {0.1, 0.1, 0.1, 0.1, 0.1}.
Node pair path Boolean expressions are:
N12 = e1 + e2e3 + e2e5e4, N13 = e2 + e1e3 + e1e4e5
N14 = e1e4 + e2e5 + e1e3e5 + e2e3e4
N23 = e3 + e1e2 + e4e5, N24 = e4 + e3e5+ e1e2 e5
N34 = e5 + e3e4 + e1e2e4
SrelP = N12. N13 .N14 .N23. N24 .N34
The simplified SrelP expression can be given as:
SrelP = e1e4e5 + e2e4e5 + e2e3e5+ e1e3e5+ e1e3e4 + e2e3e4 + e1e2e5 + e1e2e4 … (3.5)
Node pair cutsets Boolean expressions are:
C12 = e1e2 + e1e3e4 +e1e3e5,
C13 = e1e2 +e2e3e5 + e2e3e4,
C14 = e1e2 + e4e5 + e1e3e5 + e2e3e4,
C23 = e1e3e4 + e2e3e5+ e2e3e4+ e1e3e5,
C24 = e4e5+ e1e3 e4 + e2e3e4,
C34 = e1e3e5+ e4e5+ e2e3e5+ e1e3e5
SrelP = C12+C13 +C14 +C23+C24 +C34
The simplified SrelC expression can be given as:
46
SrelC = e1e2 + e1e3e4 + e1e3e5+ e2e3e5 + e2e3e4+ e4e5 … (3.6)
Basic Method Solution:
Form the Disjoint expression for the path SrelP expression found in equation (3.5),
SPDE = e1e3e 5 + e1e3e4e 5' +e1e3' e4e 5 + e1' e2e3e5 + e1e2e3'e4'e5+ e1' e2e3e4e5' + e1e2e3'e4e5' + e1'
e2e3'e4e5
The arithmetic form of the disjoint expression above,
SPAE = p1p3p 5 + p1p3p4q 5 +p1q3 p4p 5 + q1 p2p3p5 + p1p2q3q4p5+ q1 p2p3p4q5 + p1p2q3p4q5 + q1
p2q3p4p5 … (3.7)
By substituting all pi‘s as ‗p‘ and qi‘s as ‗(1-p)‘ in SPAE the reliability polynomial obtained
for the series-parallel network is 8p3 – 11p
4 +4p
5. Substitute the values of p and q from P
and Q sets.
RPM = 0.9769… (3.8)
Form the Disjoint expression for the cutsets SrelC expression found in equation (3.6),
SCDE = e1e2 + e1'e4e5 + e1e2' e4e5 + e1'e2e3e4e5'+ e1'e2e3e4'e5+ e1e2'e3e4e5'+ e1e2'e3e4'e5
The arithmetic form of the disjoint expression SCDE above,
SCAE = q1q2 + p1q4q5 + q1p2 q4q5 + p1q2q3q4p5+ p1q2q3p4q5+ q1p2q3q4p5+ q1p2q3p4q5 (3.9)
By substituting all pi‘s as ‗p‘ and qi‘s as ‗(1-p)‘ in SCAE in equation (3.9), the reliability
polynomial obtained for the series-parallel network is 1- 2p2
- 4p3+ 9p
4 - 4p
5. Substitute
the values of p and q from P and Q sets.
RCM = 1- SCAE = 0.9769… (3.10)
Min-Max Method Solution:
The path min-max expression for the equation (3.5) can be expressed as:
47
fPMM = max[min(e1,e4,e5), min(e2,e4,e5), min(e1,e3,e5), min(e2,e3,e5), min(e1,e3,e4),
min(e2,e3,e4), min(e1,e2,e5), min(e1,e2,e4)]
The arithmetic form of fPMM can be expressed as fAE,
fPAE = max[min(p1,p4,p5), min(p2,p4,p5), min(p1,p3,p5), min(p2,p3,p5), min(p1,p3,p4),
min(p2,p3,p4), min(p1,p2,p5), min(p1,p2,p4)] … (3.11)
RPMM = max [0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9, 0.9] = 0.9 … (3.12)
The cutsets min-max expression for the equation (3.6) can be expressed as:
FCMM = max[min(e1,e2),min(e1,e3,e4),min(e1,e3,e5),min(e2,e3,e5), min(e2,e3,e4), min(e4,e5)]
The arithmetic form of fPMM can be expressed as fAE,
fCAE = max[min(p1,p2),min(p1,p3,p4),min(p1,p3,p5),min(p2,p3,p5),min(p2,p3,p4), min(p4,p5)]
… (3.13)
RCMM = max [0.9, 0.9, 0.9, 0.9, 0.9, 0.9] = 0.9 … (3.14)
The equations (3.8), (3.10), (3.12) and (3.14) show that the results obtained with Min-
Max method match with that of the Basic methods.
Assume p= {0.9, 0.8, 0.7, 0.6, 0.5} and Q = {0.1, 0.2, 0.3, 0.4, 0.5}
Using equations (3.7), (3.9), (3.11) and (3.13) we get,
RPM =0.7450, RCM = 0.7450, RPMM = 0.6, RCMM =0.8
3.6 Multiple Hops Terminal Reliability of Sensor Networks
Terminal reliability (TR) of networks has been the subject of several research workers
since last 3 decades. Sensor network is a network composed of large number of sensor
nodes positioned randomly even in locations which are not accessible easily [1].The
information communicated from one node to another with help of packets sent via hops
through some selective paths or all possible simple paths. A Multiple Hops Path (MHP)
48
is a path with multiple numbers of links from the source node to the sink node. The MHP
includes possible one-hop, two-hops…, maximum-hops paths between the given source
and the sink nodes. The minimum number of hops utilizing least number of links plays a
significant role in network security and reliability. This thesis proposes a Multiple Hop
Terminal Reliability (MHTR) algorithm for the sensor networks, with an assumption that
the nodes as well as the links can fail. Some commonly used notations in this section are:
G(V, E
NR,LR)
A graph G with, V: set of nodes
E: set of edges/links
V set of nodes {v1,v2,…, vm }
E set of links\edges {e1, e2,….,en}
m Number of vertices or nodes
n Number of links or edges
pei Reliability of ei
pvi Reliability of vi
qei Unreliability of ei = 1- pei
qvi Unreliability of vi = 1- pvi
NR Set of node reliabilities { pv1, pv2, …, pvm }
LR Set of link reliabilities{ pe1, pe2, …, pen }
f Boolean path expression
Ki A complete graph with i vertices
RPN Reliability with perfect nodes
RNPN Reliability with imperfect nodes
3.6.1 The MHTR Algorithm
The concept of BDD is used to evaluate the TR between the source and the sink nodes
in sensor networks. The major steps involved in this algorithm consist of determining m-
hop links where m varies from 1 to max paths, Boolean expressions, and the disjoint
expressions using the BDD. An assumption is made that the nodes are not perfect. The
network is expressed as a graph G(V,E,NR,LR).The Steps of the proposed MHTR
algorithm are as follows:
49
a) Unique m-hop Path Determination: Determine all possible simple m-hop paths
between the source and sink nodes for G(V,E). The algorithm used to find path is
expressed in the Recursive_FindPath () method.
b) Boolean Path Expression fmhop Determination: Determine the Boolean expression
fmhop corresponding to the simple paths. Here the Boolean variables Є E. The order of
variables in which they will be selected is determined using one of the known
methods as explained in [28][30].
c) Disjoint Expression Generation: Determine the disjoint expressions using the BDD
algorithm expressed in the function Recursive_BDD().
d) Reliability with perfect nodes for m-hop Expression (RPN-mhop) Generation: The TR
expression assuming nodes never fail can be obtained by substituting the values pi for
all e i Є E from LR.
e) Reliability with imperfect nodes Expression (RNPN-mhop) Generation: Update terminal
reliability expressions to incorporate the node reliability [36]. The algorithm for the
node reliability is expressed in function Obtain_TRWithNode().
f) The TR assuming nodes fail can be obtained by incorporating the node reliabilities
values pi for all v i Є V from NR.
Algorithm Recursive_FindPath()
in:
CurrentNode /*Initialized to Source Node*/
VisitedNodes
VisitedEdges
local:
_VisitedEdges
_VistedNodes
foreach Edge in Current_Node.Edges_out
50
/* avoid cyclical paths*/
if (Edge.EndNode in VisitedNodes[]) then
next Edge
/* Update list of visited nodes and Edges */
_VisitedNode = VisitedNodes + Edge.EndNode
_VisitedEdge = VisitedEdges + Edge
/* Save path if End Node */
if (Edge.EndNode = TargetNode) then
SavePath(VisitedEdges[])
next Edge
else (if _VisitedEdgeCount >= MaxHops) then
/* Only MaxHops are allowed*/
next Edge
/* Call recursively */
Recursive_FindPath( Edge.EndNode, _VisitedNodes, _VisitedEdges)
Repeat foreach block if Edge is bidirectional using Edge.StartNode in lieu of
Edge.EndNode
end foreach
BDD was portrayed as a technique of definition, analysis, test, and implementation of a
variety of combinational and sequential digital function devices [27]. BDD is discussed
in details in [28][29] and [30]. The definition of BDD given by [30] is as follows:
A Binary Decision Diagram (BDD) is a rooted, directed acyclic graph with
one or two terminal nodes of out-degree zero labeled 0 or 1, and
a set of variable nodes u of out-degree two. The two outgoing edges are given by two
functions low(u) and high(u). A variable var(u) is associated with each variable node.
A BDD is Ordered (OBDD) if on all paths through the graph the variables respect a
given linear order e1 < e2 < … < en. The BDD are widely used as an efficient data
structure for the representation of Boolean formula and to carry out various operations on
them. The BDD is formed by using the Shannon's expansion theorem [27].
f (e1,e2 ,…,en.) = e1 f (1, e2,…, en.)+ e1‘ f (0, e2,…, en.) (3.15)
51
The equation (3.15) illustrates that different BDD can be formed on basis of the
selection of different variables ei for further expansion. The order does have noticeable
impact on the size of the formed BDD. The factors like size of the network and the
variable ordering are the major ones to decide the performance of the BDD based
algorithm. The techniques like [33] Breadth-first or depth-first search from source vertex
to sink are reasonably sufficient for the application like calculation of TR of a network.
Algorithm Recursive_BDD()
in:
CurrentExp /* BDD Term being constructed*/
ExpList /*Boolean Expression of Simple Paths*/
local:
_ExpList
/*Get _e based on BDD variable ordering */
_e = GetNextBDDVar()
for Pass[1,2]
case 1: _e = 0
/* Evaluate ExpList by removing terms with _e*/
_ExpList = ExpList.RemoveTerms(_e)
case 2: _e = 1
/* Save current expression if _e is the only var in any ExpList terms */
if (ExpList.Terms.AnyIsOnly(_e)) then
SaveCurExp(CurExp)
_ExpList.Clear()
else /*Remove _e from _CurExp Terms*/
_ExpList.Terms.Remove(_e)
end if
/* call recursively if we still have terms*/
if (_ExpList.Count > 0) then
Recursive_BDD( CurrentExp + (Pass1?_e:_e‘), _ExpList)
end if
end for
Algorithm Obtain_TRWithNode ()
in:
52
RelExp /* Terminal Reliability Expression*/
Out:
RelExpWithNode /* Terminal Reliability Expression incorporating node reliability */
/* Copy RelExp to RelExpWithNode */
for each variable term ei in RelExpWithNode /* edge ei between nodes (na and nb)*/
If (edge ei is unidirectional) then
pei = pei * pna;
else
pei = pei * pna * pnb;
end if /*Update the RelExpWithNode with new pei value */
UpdateRelExp(ei)
end for
3.6.2 MHTR ALGORITHM EXAMPLE
The process of calculating the m-hop terminal reliability of a sensor network can be
summarized to consist of following steps to determine:
1. Determine m-hop simple path (source, sink) expression.
2. Form m-hop path Boolean expression.
3. Determine Disjoint path Boolean expression using BDD.
4. Evaluate m-hops TR: (RPN-mhop) by substituting the values of LR and NR
assuming perfect nodes.
5. Evaluate m-hops TR: (RNPN-mhop) expression with an assumption that the nodes
can fail.
The BDD plays a major role in step number 3. The BDD is constructed on the basis of
the path Boolean expression. The Boolean function expression for the TR of some
standard networks is expressed as in Table 3.11.
An example of Non-series Parallel Network is considered in details for different m-hops.
1. One-hop reliability: This is not possible in NSP network configuration as there is no
one-hop paths possible from source to sink.
53
Table 3.11: Examples of Proposed MHTR Method for Some Standard Networks
2. Two-hop reliability:
a. Path expression: f2hop = e1e2 + e3e4
Standard
Network
TR Expression BDD Graph
Series
network
2-hop TR
f2hop = e1e2
RPN-2hop = pe1pe2
RNPN-2hop = (pe1pB)(
pe2pC )
Parallel
network
1-hop TR
f1hop = e1 + e2
RPN-1hop = pe1+ pe2 -
(pe1 pe2)
RNPN-1hop = ( pe1pB)+ (
pe2pB) - (( pe1pB)( pe2pB))
Series-
parallel
network
2-hop TR
f2hop = e1e2 + e3e4
RPN-2hop = pe1 pe4 + pe1
pe2qe3 + pe1pe2pe3qe4
RNPN-2hop = pe1pC pe4pB +
pe1pC pe2pB(1- pe3pD ) +
pe1pC pe2pBpe3pD(1- pe4pB
)
Non-
series-
parallel
network
3-hop TR
f3hop = ele2+ e3e4
+ e1e4 e5 + e2e3 e5
RPN-2hop = pe1pe2 + qe1
pe2 pe3 + pe1qe2 pe3 pe4 +
qe1 pe2 pe3qe4 pe5 +
pe1qe2qe3 pe4 pe5
RNPN-2hop = pe1pC pe2pB
+ (1- pe1pC)pe2pB pe3pD +
pe1pC(1- pB pe2 ) pe3pD
pe4pB +(1- pC)pe2pB
pe3pD(1- pe4pB )pe5pD +
pe1pC (1- pB pe2)(1- pe3pD
) pe4pB pe5pD
Non-
series-
parallel
network
2-hop TR
f2hop = e1e2 + e3e4
RPN-2hop = pe1 pe4 + pe1
pe2qe3 + pe1pe2pe3qe4
RNPN-2hop = pe1pC pe4pB +
pe1pC pe2pB(1- pe3pD ) +
pe1pC pe2pBpe3pD(1- pe4pB
)
54
b. RPN-2hop = pe1 pe4 + pe1 pe2qe3 + pe1pe2pe3qe4
c. RNPN-2hop = pe1pC pe4pB + pe1pC pe2pB(1- pe3pD ) + pe1pC
pe2pBpe3pD(1- pe4pB )
3. Three-hop reliability:
a. f3hop = ele2+ e3e4 + e1e4 e5 + e2e3 e5
b. RPN-3hop = pe1pe2 + qe1 pe2 pe3 + pe1qe2 pe3 pe4 + qe1 pe2 pe3qe4 pe5
+ pe1qe2qe3 pe4 pe5
c. RNPN-3hop = pe1pC pe2pB + (1- pe1pC)pe2pB pe3pD + pe1pC(1- pB
pe2 ) pe3pD pe4pB +(1- pC)pe2pB pe3pD(1- pe4pB )pe5pD + pe1pC (1-
pB pe2)(1- pe3pD ) pe4pB pe5pD
Table 3.12: Non-series Parallel Network 2-hop and 3-hop Terminal reliability
p RPN-2hop RNPN-2hop RPN-3hop RNPN-3hop ErrorNPN ErrorPN
0.1 0.019900 0.016134 0.021520 0.021520 0.005386 0.00162
0.2 0.078400 0.063750 0.088640 0.068150 0.0044 0.01024
0.3 0.171900 0.140486 0.198360 0.152412 0.011926 0.02646
0.4 0.294400 0.242404 0.340480 0.264500 0.022096 0.04608
0.5 0.437500 0.363994 0.500000 0.396571 0.032577 0.0625
0.6 0.590400 0.498169 0.659520 0.538732 0.040563 0.06912
0.7 0.739900 0.636270 0.801640 0.679754 0.043484 0.06174
0.8 0.870400 0.768061 0.911360 0.807775 0.039714 0.04096
0.9 0.963900 0.881733 0.978480 0.911015 0.029282 0.01458
1.0 1.000000 0.963900 1.000000 0.978480 0.01458 0
The reliability polynomial for NSP network configuration assuming that all node and
the link reliabilities=p are:
1. One-hop reliability polynomial: No polynomial can be defined as one-hop reliability
expression doesn‘t exist.
2. Two-hop reliability polynomial:
a. RPN-2hop = p2
+ p2 (1-p) + p
3 (1-p) = p
2 + p
2 - p
3 + p
3 – p
4 = 2 p
2– p
4
55
b. RNPN-2hop = p4
+p4 (1- p
2) + p
6 (1- p
2) = 2 p
4– p
6+ p
6– p
8 = 2 p
4– p
8
3. Three-hop reliability polynomial:
a. RPN-3hop = p2 + p
2 (1-p) + p
3 (1-p) + p
3 (1-p)
2 + p
3 (1-p)
2 = 2 p
2– 5p
4 + 2 p
5
a. RNPN-3hop = p4 +p
4 (1- p
2) + p
6 (1- p
2) + (1-p) p
4 (1- p
2) p
2 + p
2 (1- p
2)2 p
4 =
2 p4– p
8 + (1-p) p
6 (1- p
2) + p
6 (1- p
2)2 =2 p
4+ 2 p
6-2p
7- 3p
8+p
9+p
10
The values of 2-hop and 3-hop TR Terminal reliability for the non-series parallel
network are tabulated in Table 3.12 for different values of p from 0.1 to 1.0 in the
increments of 0.1. The results are plotted in Fig. 3.9 which shows that generally different
reliability values hold relation expressed as: RNPN-2hop < RNPN-3hop < RPN-2hop < RPN-3hop.
Thus the error is defined as the difference between the TR values between 3-hops and 2-
hops as expressed in equations (3.16) and (3.17).
[ErrorPN]p = [RPN-3hop]p - [RPN-2hop]p … (3.16)
[ErrorNPN]p = [RNPN-3hop]p -[RNPN-2hop]p …(3.17)
The following observations are made form Fig. 3.9(b) :
ErrorNPN > ErrorPN for p≥ 0.7 and p ≤ 0.1,
ErrorNPN < ErrorPN for p < 0.7
Fig. 3.9 Plot for m-hop TR for Non-series parallel network (a) m-hop TR Vs LR, (b) TR-Error Vs
reliability.
0
0.2
0.4
0.6
0.8
1
1.2
0.1 0.3 0.5 0.7 0.9
m-h
op
ter
min
al r
elia
bil
ity
Link Reliability (LR)
RPN-2HOP
RNPN-2HOP
RPN-3HOP
RNPN-3HOP
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
1 2 3 4 5 6 7 8 9 10
TR
Err
or(
3-h
op
, 2
-hop
TR
)
Reliability value: (p/10)
Error in 2-hop TR compared with 3-hop TR
ErrorPN
ErrorNPN
56
3.6.3 MHTR: Software Implementation and Results
The software implementation of MHTR (M-Hop terminal reliability) of a sensor
network is done by Kassem Saab[34][35] with help of a computer programming
language. The main components of this software are:
Fig. 3.10 MHTR software implementation: A 13N32L network with perfect nodes.
1. Graph Editor: It supports operations like insert, delete, erase, move, and stretch
node/links. These nodes or links can be dragged and dropped to the preferred location on
the screen. The links can be unidirectional or bidirectional. The node and link reliability
values can be manually entered in the graph. The use of this editor can be avoided by
giving the desired input via a text file. The source and sink nodes can be selected.
1. Path List Window: All possible paths between the source and the sink node displayed
for multiple hops ranging from 1 to maximum possible for the given network.
2. Cut-Set List Window: Displays the Cut-Sets for the given graph.
3. BDD-Binary Decision Diagram List Window: All non-overlapping expressions for a
path between the source and the destination
57
4. Result Window: Display the MHTR value considering NR =1 and also with the given
values of NR.
5. Main Menu: the functionalities supported are: loading a graph from file, save current
graph in a file, run demo, obtain the value of TR with or without considering NR.
6. TABLE 3.13: MHTR results for 13N32L network of Fig. 3.10. 7.
Terminal nodes I-L D-L M-L A-L B-J E-K
Unique paths 917 2041 4013 8267 5251 2685
BDD Terms 7343 30014 166581 439671 267775 59889
Exec. Time (ms) 307 1011 6654 25096 11433 2309
Max-hop
reliability
with
NR = 0.8
P=0.5 0.370021 0.136536 0.047028 0.015180 0.024576 0.066885
P=0.6 0.438024 0.190729 0.078172 0.029818 0.042938 0.101189
P=0.7 0.499087 0.247522 0.117072 0.051553 0.066564 0.139486
P=0.8 0.552808 0.304254 0.162244 0.081449 0.095122 0.179987
P=0.9 0.599500 0.358833 0.211518 0.120267 0.128650 0.221252
Max-hop
reliability
with
NR = 0.9
P=0.5 0.527847 0.285281 0.144553 0.069105 0.109142 0.202323
P=0.6 0.614902 0.381122 0.222493 0.121825 0.171875 0.282529
P=0.7 0.684450 0.468059 0.305071 0.186058 0.237211 0.357093
P=0.8 0.738019 0.542904 0.386994 0.259820 0.301470 0.423298
P=0.9 0.778685 0.605350 0.463922 0.342400 0.364975 0.481180
Max-hop
reliability
with
NR = 1.0
P=0.5 0.814416 0.741139 0.676376 0.567373 0.674161 0.757461
P=0.6 0.912804 0.886100 0.860403 0.791954 0.868363 0.908240
P=0.7 0.966888 0.960538 0.954213 0.924016 0.963139 0.975725
P=0.8 0.991131 0.990347 0.989560 0.980914 0.994054 0.996307
P=0.9 0.998971 0.998949 0.998926 0.997901 0.999716 0.999837
If the number of expressions for path list, cut-set and BDD List windows are more than
1000 then instead of displaying them in the respective windows they are saved in a data
file. Fig. 3.10 shows the MHTR software implementation screenshot of a sample network
with 13 Nodes and 32 Links with source node=A, and sink node=L. The results for the
calculation of MHTR for the Benchmark Networks shown in Fig. 3.10 can be seen in
Table 3.13. MHTR with different values of link reliability (0.5, 0.6, 0.7, 0.8 and 0.9) can
be seen for the value of node reliability = 0.8, 0.9 and 1.0 in Table 3.13. The benchmark
networks considered in Fig. 3.11 are the complete graphs Kn for n=5, 6, 7, 8, 9, and 10.
Table 3.14 shows the values of reliability between any two terminal nodes acting as a
58
source and a sink node for both the scenarios of perfect and imperfect nodes. MHTR with
different values of link reliability (0.5, 0.6, 0.7, 0.8 and 0.9) can be seen for the value of
node reliability = 0.8, 0.9 and 1.0 in Table 3.14 for max-hop TR and also the min-hop
TR. In addition to the values of TR, the number of unique paths between the terminal
nodes, BDD terms and the Execution Time (ms) are also illustrated in these tables. The
reliability expression RPN and RNPN-mhop are generated only once and are further reused
for the calculation of TR value for variety of NR and LR values. This process of reuse of
the expression improves the efficiency and performance of the proposed algorithm, which
otherwise is affected as the failure of nodes also considered.
K5:5N10L K6:6N15L K7:7N21L
K8:8N28L K9:9N36L K10:10N45L
Fig. 3.11 Benchmark Networks: Complete graph Kn for n=5 to 10
The Fig. 3.12 shows the plot of TR for K5 and K10 with variation in LR and NR values.
The K5 plot shows a smooth curve for the NR=1.0 thus showing significant difference in
the value of TR at LR=0.5 and LR = 0.9. The K10 plot shows that the plot for NR=1.0 is
almost a straight line with significant reduction of difference between the value of TR at
59
LR=0.5 and LR = 0.9. This observation leads to a conclusion that the as the degree of
complete graph Kn increases the difference between the value of TR at LR=low and LR =
high reduces. Fig. 3.12 signifies that with the increase in ‗n’ degree of complete graph
Kn, there is prominent increase in the execution time as compared to the number of BDD
terms and the number of unique paths.
TABLE 3.14: MHTR results for Complete graph Kn for n=5 to 10.
Terminal nodes K5 K6 K7 K8 K9 K10
Max-hop paths 16 65 326 1957 13700 109601
Min-hop paths 1 1 1 1 1 1
Max-hop BDD Terms 29 215 2211 29940 540567 12340405
Max-hop Exec. Time
(ms)
115 109 103 828 32095 741424
max-hop
Terminal
reliability
with
NR = 0.8
P=0.5 0.3744248 0.376070 0.376532 0.376669 0.376711 0.376725
P=0.6 0.4412385 0.442183 0.442394 0.442445 0.442457 0.442461
P=0.7 0.5009034 0.501293 0.501359 0.501371 0.501373 0.501373
P=0.8 0.5534984 0.553594 0.553605 0.553606 0.553606 0.553606
P=0.9 0.5996079 0.599615 0.599615 0.599615 0.599615 0.599615
min-hop
Terminal
reliability
with
NR = 0.8
P=0.5 0.32 0.32 0.32 0.32 0.32 0.32
P=0.6 0.384 0.384 0.384 0.384 0.384 0.384
P=0.7 0.448 0.448 0.448 0.448 0.448 0.448
P=0.8 0.512 0.512 0.512 0.512 0.512 0.512
P=0.9 0.576 0.576 0.576 0.576 0.576 0.576
max-hop
Terminal
reliability
with
NR = 0.9
P=0.5 0.5429159 0.553310 0.557055 0.558363 0.558840 0.559021
P=0.6 0.6255636 0.631325 0.632931 0.633386 0.633522 0.633564
P=0.7 0.6903006 0.692556 0.693028 0.693131 0.693154 0.693160
P=0.8 0.7401886 0.740711 0.740786 0.740797 0.740799 0.740799
P=0.9 0.7790166 0.779054 0.779056 0.779057 0.779057 0.779057
min-hop
Terminal
reliability
with
NR = 0.9
P=0.5 0.405 0.405 0.405 0.405 0.405 0.405
P=0.6 0.486 0.486 0.486 0.486 0.486 0.486
P=0.7 0.567 0.567 0.567 0.567 0.567 0.567
P=0.8 0.648 0.648 0.648 0.648 0.648 0.648
P=0.9 0.729 0.729 0.729 0.729 0.729 0.729
max-hop
Terminal
reliability
with
NR = 1.0
P=0.5 0.8535156 0.923583 0.963058 0.982573 0.991690 0.995962
P=0.6 0.9394676 0.976249 0.991060 0.996585 0.998665 0.999471
P=0.7 0.9814253 0.994732 0.998495 0.999557 0.999868 0.999960
P=0.8 0.9965277 0.999341 0.999871 0.999974 0.999994 0.999998
P=0.9 0.9997948 0.999979 0.999997 0.999999 0.999999 0.999999
min-hop
Terminal
reliability
with
NR = 1.0
P=0.5 0.5 0.5 0.5 0.5 0.5 0.5
P=0.6 0.6 0.6 0.6 0.6 0.6 0.6
P=0.7 0.7 0.7 0.7 0.7 0.7 0.7
P=0.8 0.8 0.8 0.8 0.8 0.8 0.8
P=0.9 0.9 0.9 0.9 0.9 0.9 0.9
60
Fig. 3.12 Plots of max-hop TR for K5 and K10
Fig. 3.13 Plots of execution time, number of BDD terms and unique hops for Kn for n=5 to 10
The Fig. 3.14 shows that with the increase in the value of NR from 0.8 to 1.0 there is
significant decrease in the difference between the max-hp TR for different values of LR
from 0.5 to 0.9 in the increments of 0.1. On the other hand the difference is quite constant
for the min-hop TR. All the lines are parallel for LR=05 to LR=0.9. This observation
leads to a conclusion that for the lower values of NR there is not much difference in the
value of max-hop TR and the min-hop TR. Fig. 3.15 shows the MHTR (1-hop TR to 5-
hops TR) for K6 with value of NR=1.0 as tabulated in Table 3.15. The dotted line exhibits
the amount of error or difference in the values of min-hop TR and the max-hop TR
values. It is observed that after 2-hops TR the difference in the values of TR is
significantly low. Thus a 3-hops TR would be a good choice to determine the TR of
communicating data from the source to sink node. This will also improve the
0
0.2
0.4
0.6
0.8
1
1.2m
ax-h
op
Ter
min
al R
elia
bil
ity Complete Graph: K5
NR=0.8
NR=0.9
NR=1.00
0.2
0.4
0.6
0.8
1
1.2
max
-hop
Ter
min
al r
elia
bil
ity
Complete Graph: K10
NR=0.8
NR=0.9
NR=1.0
1
10
100
1000
10000
100000
1000000
K5
K6
K7
K8
K9
K1
0
Exec
uti
on
tim
e(m
S/l
og)
The Complete Graph Kn
Exec. Time
(ms)
1
10
100
1000
10000
100000
1000000
10000000
10000000
K5
K6
K7
K8
K9
K1
0
The Complete Graph Kn
BDD Terms
Unique
paths
61
computational speed of evaluation reliability by reducing the number of terms in the path
expression, disjoint reliability expression for perfect as well as imperfect nodes.
Fig. 3.14 Plots of max-hop and min-hop TR for Kn: n=5-10 with value of NR=0.8, 0.9 and 1.0.
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
K5 K6 K7 K8 K9 K10
max-hop TR for NR = 0.8
LR=0.5
LR=0.6
LR=0.7
LR=0.8
LR=0.9
0.3
0.35
0.4
0.45
0.5
0.55
0.6
K5 K6 K7 K8 K9 K10
min-hop TR for NR = 0.8
LR=0.5
LR=0.6
LR=0.7
LR=0.8
LR=0.9
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
K5 K6 K7 K8 K9 K10
max-hop TR for NR = 0.9
LR=0.5
LR=0.6
LR=0.7
LR=0.8
LR=0.9
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
K5 K6 K7 K8 K9 K10
min-hop TR for NR = 0.9
LR=0.5
LR=0.6
LR=0.7
LR=0.8
LR=0.9
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
K5 K6 K7 K8 K9 K10
max-hop TR for NR = 1.0
LR=0.5
LR=0.6
LR=0.7
LR=0.8
LR=0.9
0.4
0.5
0.6
0.7
0.8
0.9
1
K5 K6 K7 K8 K9 K10
min-hop TR for NR = 1.0
LR=0.5
LR=0.6
LR=0.7
LR=0.8
LR=0.9
62
TABLE 3.15: MHTR for Well Connected Graph K6
MHTR 1-Hop
TR
2-Hops TR 3-Hops TR 4-HopsTR 5-Hops TR
Unique Paths 1 5 17 41 65
BDD Terms 1 16 104 191 215
LR = 0.1 0.1 0.135463591 0.143876385 0.145100633 0.145184316
LR = 0.2 0.2 0.320522752 0.362678863 0.371311747 0.372136381
LR = 0.3 0.3 0.519975273 0.598901069 0.615318992 0.616966388
LR = 0.4 0.4 0.701277184 0.791522379 0.807620894 0.809106911
LR = 0.5 0.5 0.841796875 0.913330078 0.922851563 0.923583984
LR = 0.6 0.6 0.932891136 0.972670282 0.976054079 0.976249768
LR = 0.7 0.7 0.979704397 0.994079416 0.994708904 0.994732722
LR = 0.8 0.8 0.996640768 0.999299747 0.999341019 0.999341824
LR = 0.9 0.9 0.999869679 0.999979672 0.999979922 0.999979923
Fig. 3.15 Plots of MHTR (1-hop to 5-hops) for K6 with value of NR=1.0.
3.7 Conclusion
The sensor network security is an important issue in the current era. The reliability of
the network is one of the measures of security. This thesis presents the following novel
algorithms:
The new and efficient techniques to find out Minimum Hop paths (MinHP)
Minimum Hop Cutsets (MinHC) for a given source-sink nodes communication in a
Sensor Network are suggested. Traditionally if we have to determine all paths and
minimal cutsets between the source and sink nodes, it needs huge number of vector
0
0.2
0.4
0.6
0.8
1
1.2
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Ter
min
al R
elia
bil
ity
Link Reliability
MHTR for K6
1-Hop
2-Hops
3-Hops
4-Hops
5-Hops
63
additions and comparisons. On the other hand with the proposed algorithms the
process gets terminated after couple of iterations of these algorithms resulting in
very few vector additions and comparisons. Some of the features of these
algorithms are:
Flexibility to update the source node and the sink node by simply changing the
Path vector P.
Insertion/deletion of a node/link by insertion/deletion of a row/column.
Simplicity of implementation,
The undirected graph procedure with a Boolean connection matrix can be
implemented on the hardware, as the connection matrix contains only Boolean
data ‗0‘ and ‗1‘. The performance of these algorithms can be improved
drastically for very large sensor networks.
A novel approximate technique for determination of terminal reliability of a wireless
sensor network between the given source and sink nodes is proposed. The Minimum
Hops Reliability (MinHR) can be calculated with very less number of computations
as the number of terms considered for the MinHR is drastically smaller than that
required by the regular methods. The MinHR is calculated as an average of MinHPR
and MinHCR, rather than determining all possible paths and all possible cut-sets.
The MinHPR gives the lower bound of the exact TR while the MinHCR gives the
upper bound on the reliability value. The average of MinHPR and MinHCR gives
the MinHR of a WSN. It is observed that the difference between the exact values of
TR and the approximate values is very small.
64
An approximate technique for determination of system reliability of a sensor
network is proposed in this thesis. The Min-Max system reliability can be calculated
with very less number of computations as in this procedure the need of disjoint
expression is eliminated. Min-Max system reliability calculated using the paths
(RPMM) is lower limit of the approximate system reliability. The Min-Max system
reliability calculated using the cutsets (RCMM) is upper limit of the approximate
system reliability: RPMM ≤ Actual system reliability ≤ RCMM. The value of calculated
approximate value of system reliability can be improved by taking average of these
two reliability {RPMM , RCMM}.
A multiple hops terminal reliability of sensor network algorithm is proposed in this
thesis. The results show that the execution time increases noticeably with the
increase in the degree of the Complete Graph Kn as compared to the number of BDD
terms and the number of unique hops. It is observed that for the lower values of NR
there is not much difference in the value of max-hop TR and the min-hop TR. It is
also observed that after 2-hops TR the difference in the values of higher-hops TR is
significantly low. Thus in most of the cases it is advantageous to evaluate (lower
value)-hops TR rather than going for max-hop TR. This will aid in improving the
performance of the MHTR software implementation with the consideration of very
large sizes and the dynamic nature of the sensor networks. The lower number of
hops will reduce the size of path expression and TR disjoint expressions for the case
of perfect as well as imperfect nodes. This will adequately improve the computation
time by reducing the complexity of the generated expression.
65
CHAPTER 4
RELIABILITY OF UNMANNED GROUND VEHICLES (UGV)
4.1 Introduction
Critical role of unmanned intelligent ground vehicles is evidential from variety of day-
to-day applications. Unmanned ground vehicles (UGV) play a significant role in war and
nations defense-security capability. This is achieved with help of advancement of
technology in sensors, architecture, robotics, standards etc supported by extensive
research. With the advancement of the technology it is important to assure the unmanned
vehicle is safe, sturdy, and efficient in all possible conditions. Thus calculation of
reliability of the convoy of vehicles becomes a vital task. Here the reliability of the whole
system of convoy, reliability of a certain path from one station to another, as well as
reliability of a certain station plays a crucial role for the safety and performance of the
convoy. If the safety and reliability factors of the vehicles are not well considered,
undoubtedly any of the following scenarios may arise like vehicle falling in a ditch,
vehicle rollover, vehicles colliding with each other, vehicle stuck in the mud, etc. This
motivates the calculation of reliability of convoy of unmanned vehicles.
The convoy of unmanned vehicles can be represented as a sensor network where the
nodes are various stations and the paths are the links between these stations. Thus the
modeling the reliability of unmanned vehicles problem essentially becomes the problem
of calculation of the reliability of a network [47]-[65]. The Fig. 4.1(includes tank pictures
from free internet resources.) exhibits several convoys in different places as a network.
This convoy graph is G= {V, E, NR, LR} where V, E, NR and LR are set of nodes, links,
node reliability and link reliability respectively. The network in Fig. 4.1 has 4 stations
66
{A, B, C, D} which are connected by various communication links amongst them. On
need basis these convoy may have to move from one station to another, say from A, B or
C to D. The various factors that are taken into consideration with respect to the convoy of
unmanned vehicles are terrain, obstacle, weather, signal strength, EMC, vehicle mobility
etc.
Fig. 4.1 System of convoys of unmanned vehicle [62]
With the increasing need of unmanned ground vehicle network for combat applications,
the collaboration and coordination of these vehicles have become important design
considerations. Both collaboration and coordination [58] require a large number of
sensors. These sensors form a network. The algorithms to compute the terminal and
system reliability of convoy of UGV is proposed which takes into consideration the
failure of nodes as well as the links.
4.2 UGV Soft Computing Approach
The convoy of unmanned vehicles exhibits a process of intelligent decision based on
the knowledge base and no mathematical relations are easily available. A fuzzy system
[55]-[57] can be modeled as shown in the Fig. 4.2.It consists of following main
components:
A
B
C
D
67
1. Fuzzification: It maps an observed nonfuzzy input space into suitable linguistic
values, which can be viewed as labels of fuzzy sets.
2. Fuzzy Inference Engine: It consists of:
Fig. 4.2 Fuzzy system model
A rule base: Fuzzy rule can be expressed as: If input is A, then output is B,
Where A and B are the input and output linguistic values defined. These rules
are formulated on the basis of past experience, knowledge about the system
that is to be developed.
Fuzzy rule database: Defines the membership functions for each input and
output, which are used by the fuzzy rules, forms.
Reasoning mechanism: Obtains the output by performing the inference
procedure on the given conditions and the formed rules. The result is obtained
by aggregating the result of each rule in the fuzzy rule base.
3. Defuzzification: This component takes inputs as aggregated fuzzy dataset and
maps it to a nonfuzzy output value.
The NeuroFuzzy system (NFS) refers to system which incorporates the way of
applying learning techniques offered by neural networks for parameter identification of
fuzzy models [66]. Thus NFS combines the fuzzy systems human-like reasoning and
neural networks learning technique. An NN (neural network) which essentially is a
68
processor of information can be represented by a set of connected and layered processing
elements (PE‘s). A PE receives an n-dimensional input vector from a PE from previous
layer or other sources. PE processes the data to give a scalar output, y = f (W, X), where
X is current input, and W is the weight of these connections. Learning of NN‘s may be
done by
Unsupervised techniques, needs no information a priori. It constructs internal models,
which capture and extract regularities in their input data.
Supervised techniques, needs information a priori about the input and desired output
data. and
Reinforcement techniques, needs a single scalar evaluation of the produced output.
Reliability of convoy of unmanned vehicles is taken into consideration which exhibits a
process of intelligent decision based on the knowledge base. Fuzzy decisions are based
on the experience obtained by experts. The factors are identified that have impact of
UGV reliability (UGVR). These are defined by suitable membership function types and
the fuzzy rules are developed. Existing data pertaining to these kinds of systems, expert‘s
previous knowledge about all these conditions is taken into consideration to make the
fuzzy model to determine the reliability of UGV. It is difficult to give an absolute number
to these factors, thus fuzzy logic seems to be the most efficient way of solving this
problem of reliability of convoy of unmanned vehicles. A fuzzy set illustrates vague
concepts. A fuzzy set acknowledges the possibility of partial membership in it. A
membership function (MF) is a curve that defines how each point in the input space is
mapped to a membership value (or degree of membership) between 0 and 1 (e.g., Friday
is a weekend day to the degree 0.8). The only condition a membership function must
69
really satisfy is that it must vary between 0 and 1. The function itself can be an arbitrary
curve whose shape we can define as a function that suits us from the point of view of
simplicity, convenience, speed, and efficiency [55].Fuzzy Logic membership function
and rules are used to define the node, branch, and terminal and system reliability of the
network of unmanned vehicles. The term ‗Fuzzy Reliability‘ is therefore used and can be
defined as ―reliability of a communication network based on the fuzzy logic membership
function and fuzzy rules‖. This reliability essentially is a form of fuzzified reliability,
hence defined as Fuzzy Reliability. This philosophy is further extended to form the
following definitions:
1. Fuzzy Node Reliability (FNR): The reliability of a node/station defined on the
basis of fuzzy logic membership function and rules.
2. Fuzzy Branch Reliability (FBR): The reliability of a branch/link defined on the
basis of fuzzy logic membership function and rules. It is also called as fuzzy link
reliability (FLR).
3. Fuzzy Terminal Reliability (FTR): The TR defined on the basis of fuzzy logic
membership function and rules.
4. Fuzzy System Reliability (FSR): The system reliability defined on the basis of
fuzzy logic membership function and rules.
4.2.1 UGV Node Reliability Model
Each node in a UGV network has its unique reliability to affect the movement decision.
The reliabilities will help commander in making appropriate decision of which convoys
of unmanned vehicle to move forward in terms of their reliabilities. The node reliability
here is defined by three conditions: Signal strength, EMC (Electro Magnetic
70
Compatibility) and vehicle mobility. The facts that aid in setting up the rules for node
reliability are:
Stronger the signal strength, higher is fuzzy node reliability,
Lower the EMC, higher is fuzzy node reliability,
Better the vehicle mobility, higher is fuzzy node reliability.
Fig. 4.3 FIS: Fuzzy node reliability
The EMC is defined as:
Where the TrapezoidalFunction is defined as:
In node reliability, the membership function will show how each point in these 3 input
spaces: signal strength, EMC and vehicle mobility is mapped to a membership value:
reliability between 0 and 1. Since triangular or trapezoidal functions are popular methods
for specifying complex fuzzy sets, so the trapezoidal function is chosen in node
reliability. The labels and the range for the labels for input and output parameters for the
FIS can be seen in Table 4.1 and Table 4.2 respectively.
033,1.3]),0.9667,1. [0.7 (x,lFunction Trapezoida VH
.9667])6333,0.7,0[0.3667,0. (x,lFunction Trapezoida HH
0.6333]).3,0.3667,[0.03333,0 x,lFunction(Trapezoida MM
3])0.03333,0.,-0.03333, [-0.3 x,lFunction(Trapezoida LL
)(xEMC
dxccdxd
cxb
bxaabax
dxax
dcbax
),/()(
,1
),/()(
,,0
]),,,[,(lFunctionTrapezoida
71
(a) (b)
(c) (d)
Fig. 4.4 FNR: (a) Signal Strength membership function, (b) output membership function, (c) Rule viewer,
and (d) Rules editor
Fig. 4.4 shows the FIS for FNR where 4.4(a) and 4.4 (b) show the Signal Strength and
FNR membership functions respectively. The Fig. 4.4 (c,d) reflect the results in terms of
rule viewer and editor respectively for the FNR. This Fuzzy model generates the value of
the node reliability of the UGV network.
1.129]) 1.014 0.9857 [0.8714 x,lFunction(Trapezoida HH
0.9857]) 0.8714 0.8429 [0.7286 x,lFunction(Trapezoida HM
0.8429]) 0.7286 0.7 [0.5857 x,lFunction(Trapezoida HL
0.7]) 0.5857 0.5571 [0.4429 x,lFunction(Trapezoida MH
0.5571]) 0.4429 0.4143 [0.3 x,lFunction(Trapezoida ML
0.4143]) 0.3 0.2714 [0.1571 x,lFunction(Trapezoida LH
0.2714]) 0.1571 0.1286 [0.01429 x,lFunction(Trapezoida LM
0.1286]) 0.01429 0.01429- [-0.1286 x,lFunction(Trapezoida LL
)(xFNR
72
V Table 4.1: Input parameter Labels for FNR and FBR
code Label for factors Trapezoidal membership function
parameters for inputs
1 00 LL [-0.3 ,-0.03333,0.03333,0.3]
2 01 MM [0.03333,0.3,0.3667,0.6333]
3 10 HH [0.3667,0.6333,0.7,0.9667]
4 11 VH [0.7 ,0.9667,1.033,1.3]
Table 4.2: Labels for output parameters for Fuzzy Node and Branch Reliability
# Code Label Label for UGV
node reliability
Range of
reliability
Trapezoidal membership function
parameters
1 000 LL Low-Low (0, 0.2) [-0.1286 -0.01429 0.01429 0.1286]
2 001 LM Low-Medium (0.2, 0.4) [0.01429 0.1286 0.1571 0.2714]
3 010 LH Low-High (0.4, 0.5) [0.1571 0.2714 0.3 0.4143]
4 011 ML Medium-Low (0.5, 0.6) [0.3 0.4143 0.4429 0.5571]
5 100 MH Medium-High (0.6, 0.7) [0.4429 0.5571 0.5857 0.7]
6 101 HL High-Low (0.7, 0.8) [0.5857 0.7 0.7286 0.8429]
7 110 HM High- Medium (0.8, 0.9) [0.7286 0.8429 0.8714 0.9857]
8 111 HH High-High (0.9,1) [0.8714 0.9857 1.014 1.129]
4.2.2 UGV Link Reliability Model
The links/branches {AB, AC, BD, CD} represents the path followed or path of
communication of the convoy of UGV as seen in Fig. 4.1. Branch reliabilities are to be
determined based on Fuzzy rules set up the on basis of following relation between the
factors impacting the branch reliability:
Better the weather, higher is the Fuzzy Branch reliability,
Fewer the Obstacles, higher is the Fuzzy Branch reliability,
Suitable the terrain, higher is the Fuzzy Branch reliability.
Fig. 4.5 FIS: Fuzzy Branch reliability
73
Fig. 4.5 shows the FIS for Fuzzy branch reliability. Fig 4.6(a) and (b) are the input and
output parameter membership functions respectively. Fig 4.6(c) and (d) show the rule
viewer and rule editor for FBR respectively. The order of the rules is unimportant. The
rules are useful because they refer to variables and the adjectives that describe the
conditions. The FBR is defined by following relation:
(a) (b)
(c) (d)
Fig. 4.6 FBR: (a) input weather membership function, (b) output membership function, (c) Rule Viewer
and (d) Rules editor.
1.129]) 1.014 0.9857 [0.8714 x,lFunction(Trapezoida HH
0.9857]) 0.8714 0.8429 [0.7286 x,lFunction(Trapezoida HM
0.8429]) 0.7286 0.7 [0.5857 x,lFunction(Trapezoida HL
0.7]) 0.5857 0.5571 [0.4429 x,lFunction(Trapezoida MH
0.5571]) 0.4429 0.4143 [0.3 x,lFunction(Trapezoida ML
0.4143]) 0.3 0.2714 [0.1571 x,lFunction(Trapezoida LH
0.2714]) 0.1571 0.1286 [0.01429 x,lFunction(Trapezoida LM
0.1286]) 0.01429 0.01429- [-0.1286 x,lFunction(Trapezoida LL
)(xFBR
74
The terminal reliability refers to the reliability from a source node to the destination
node. If each convoy of unmanned vehicles has to move to any one of the remaining
other stations, then the reliability can be defined as the system reliability. System
reliability is defined as terminal reliability of all nodes to all other nodes [48]. The
procedures for calculation of terminal and system reliability can be found in next section.
In this way, we can determine the total reliability of the convoy of unmanned vehicles.
This reliability will help a commander in making appropriate decision in the battlefield.
4.2.3 Fuzzy Branch Reliability: An Illustrative Example
To model the FBR the maximum speed data [69] as in Fig. 4.7(a) is considered which has
been obtained from the experiment performed on different terrains performed by the
UGV test vehicle seen in Fig 4.7(b). An assumption is made that higher the transportation
speed, higher would be the system reliability. The FBR can be expressed as a function of
a triangular function:
(a) (b)
Fig. 4.7 FBR Illustration: (a) Test Data Maximum speed forecast from terrain classification (b) test UGV
[Courtesy of [69])
11.25]) 10 [8.75 x,lFunction(TriangularLot ParkingAsphalt
10]) 8.75 [7.5 x,lFunction(Triangular Roadt Gravel/Dir
8.75]) 7.5 [6.25 x,lFunction(Triangular Outfield Baseball
7.5]) 6.25 [5 x,lFunction(Triangular Infield Baseball
6.25]) 5 [3.75 x,lFunction(Triangular Ground Parade
5]) 3.75 [2.5 x,lFunction(Triangular FieldRough
3.75]) 2.5 [1.25 x,lFunction(Triangular Arena Sand
2.5]) 1.25 [0 x,lFunction(Triangular Field Plowed
1.25]) 0 [-1.25 x,lFunction(Triangular FieldSoyabean
)(xFBR
75
The fuzzy and the NeuroFuzzy model developed for the data obtained for terrain
affecting the branch reliability for the data from Fig. 4.7 can be seen in Fig. 4.8 (a) to (d).
Fig. 4.8 (a) exhibits the membership function for branch reliability terrain input. Fig. 4.8
(b) shows NeuroFuzzy output for the branch reliability of terrain. Fig 4.8 (c) and Fig 4.8
(d) shows terrain rule view and terrain surface view of branch reliability.
(a) (b)
(c) (d)
Fig. 4.8 FBR: (a) Membership function input for terrain, (b) Neuro Fuzzy output, (c) terrain rule view, and
(d) terrain surface view.
4.3 UGV Terminal Reliability
There is an increasing interest in the army of small unmanned robots taking part in
defense operations. It is considered important to predict the reliability of the group of
76
robots taking part in different operations. A group of robots have both coordination and
collaboration. The robot operations are considered as a network graph whose system
reliability can be determined with the help of different techniques. Once a specified
reliability is achieved the commander controlling the operation can take appropriate
action. This paper gives a simulation which can determine the system reliability of the
robotic systems having collaboration and coordination. The procedure developed is based
on binary decision diagrams to obtain a disjoint Boolean expression. The procedure is
applicable for any number of nodes and the branches. For illustration purposes reliability
of simple circuits like series network, parallel network, series-parallel and non-series
parallel network are illustrated. It is hoped that more work in this area will lead to the
development of algorithms which will be ultimately used for a real time environment.
Table 4.3: Terminal reliability [34][35]
Graph Terminal reliability
without node
reliability
Modified Terminal reliability with node
reliability
series network
p1* p2 (p1* pA)*( p2* pB )
parallel network
p1+ p2 - (p1* p2) (p1* pA )+ ( p2* pB ) - ((p1* pA )* ( p2* pB ))
Series parallel network
p1p4+ p1p2q3
+ p1p2 p3q4
p1 pA p4 pD+p1 pA p2 pC (1-p3 pA ) +
p1 pA p2 pC p3 pA(1- p4 pD )
Non-series parallel network
p1p2+q1p2p3+
p1q2p3p4 +q1p2p3q4p5
+ p1q2q3p4p5
p1 pA p2 pC + (1- p1pA )p2 pC p3 pA +
p1 pA (1- pCp2 )p3 pA p4 pD +(1- p1pA )p2 pC p3
pA(1- p4 pD )p5 pD pC + p1 pA (1- pCp2 )(1-p3 pA
) p4 pD p5 pD pC
77
A system of convoy of UGV is represented as a network G = (V, E, NR, LR), where
nodes represent the stations of the convoy and branches represent the possible paths
between the stations. An algorithm is proposed to calculate the terminal reliability of the
convoy of UGV. Some relevant practical constraints are to be taken into consideration
which affects the safety factor of the system at the stations as well as during a move from
one station to another. Some safety factors are affecting the stations can be, signal
strength, and vehicle mobility. Safety factors with respect to the moment from one
station to another can be terrain, weather and many more. For the utmost safety,
reliability of complete system of convoy, reliability of a particular path from one station
to another, as well as reliability of a particular station is to be taken into consideration.
Terminal Reliability refers to the reliability from a source node to the destination node.
Thus in this case it is reliability of the convoy from one station to another. Table 4.3
shows the terminal reliability under two different scenarios. First scenario considers that
nodes never fail, assuming node reliability always equal to 1. Second scenario considers
that nodes also fail and thus they have noticeable impact on the terminal reliability
[36,48]. Table 4.3 shows terminal reliability expressions for different networks like
series, parallel, series-parallel and non-series parallel. Here p1, p2 are the reliabilities of
the branches e1 and e2 respectively. Fuzzy Node Reliability represents the reliability of a
station. Each node has its unique value of the reliability to affect the movement decision.
It affects the system of network of convoys of unmanned vehicle, thus making overall
system more safe and sturdy. The more the number of factors taken into consideration;
the more robust and safe is the convoy. Failure in a node or a branch does affect the
whole system, but it doesn‘t mean that the whole system fails. Fuzzy logic approach is
78
used for the calculation of these reliabilities. Fuzzy Inference System is developed using
software. The Boolean algebra technique is used for the calculation of terminal reliability.
The software calculating the terminal reliability is implemented using a computer
programming language. The reference [60] has implemented software for calculation of
terminal reliability, but it does not support editing facility. It has limitation on number of
nodes and also does not consider node reliability. The implementation in this thesis
supports any number of stations and is very user friendly. To support any number of
nodes parallel programming is done to enhance the speed of the computation.
The proposed algorithm to determine the terminal reliability of UGV is:
1. Determine the fuzzy node reliability which has value between 0 and 1. The various
factors that contribute to the computation of node reliability are EMC, vehicle
mobility, and signal strength. Let nodes A, B, C… have node reliabilities of pA, pB, pC
… respectively.
2. Determine the fuzzy branch reliability which has value between 0 and 1. The various
factors that contribute to the computation of branch reliability are obstacles, terrain,
and weather. Let the branches e1,e2, e3… have reliabilities p1, p2, p3…respectively.
3. The following steps are used for drawing Binary decision Diagrams to obtain the
disjoint expression.
a. Determine simple paths.
b. Determine the Boolean expressions which correspond to the simple paths.
c. Mark all the unique paths between the source and the destination stations.
d. Determine the non-overlapping expressions.
79
e. Determine a disjoint expression corresponding to the Boolean expressions to
obtain terminal reliability expression.
4 Update terminal reliability expression to incorporate the fuzzy node reliabilities as
expressed in Table 4.3.
5 Substitute fuzzy branch reliability and fuzzy node reliability values in the non-
overlapping expression to get terminal reliability. The result is the terminal reliability
between the specified terminal nodes.
A computer programming language is used for the software implementation of the
terminal reliability of communication network. The software developed supports
functionality as shown in Table 4.4.
Table 4.4: Functionality Supported by the reliability software implementation
# Functionality Represents/Facilitates
1 Graph Editor Draw graph with any number of nodes & branches.
Nodes can be dragged and dropped at the desired location
on the screen.
Unidirectional/bidirectional path/branch lines can be drawn.
Insert, delete, erase, move, and stretch node/branches. The
values for the node and branch reliability can be entered
here. Another method of giving input to this software is
graph data can be given in an input file.
2 Path List All possible paths between the source and the destination node
(If number of expressions exceeds 1000, they are stored in a
file.)
3 Cut-Set List All possible Cut-Sets for the given graph (If number of
expressions exceeds 1000, they are stored in a file.)
4 BDD-Binary
Decision Diagram
List
All non-overlapping expressions for a path between the source
and the destination node (If number of expressions exceeds
1000, they are stored in a file.)
5. Result Window Display the terminal reliability values considering node
reliability=1 and also with the given values of node reliabilities.
Fig.4.9 shows the reliability software implementation screenshot for a large network.
80
Fig. 4.9 Unmanned vehicle network with multiple nodes [34][35]
Table 4.5 - BDD Terms and Execution Time for Different Networks
Nodes Connections BDD Terms Time (ms)
4 5 5 86
9 16 16 113
16 24 3362 115
20 33 192044 760
23 34 270969 335
Table 4.5 shows the analysis of the procedure implemented. In addition to the number
of nodes and connections the actual topology of the network is a major factor in
determining the number of BDD terms and the actual time needed for the TR
calculations.
4.4 UGV Fuzzy System Reliability
Fuzzy System Reliability is defined as fuzzy terminal reliability of all nodes to all other
nodes [49]. System Reliability in literature is also referred as network reliability, or
global reliability or overall reliability. The system reliability is the reliability of the
complete system of the network of convoys of UGV. The convoy of unmanned vehicles
is represented as a network in the form of a hypercube topology to support the growing
number of stations. Thus the problem of reliability of UGV becomes a problem of
81
evaluation of reliability of a hypercube. Here the nodes represent the station of the
convoy and branches represent the communication path from one station to another.
Hypercube is an n-dimensional representation of a square (n = 2) and a cube (n = 3). It is
also called as an n-cube. Some examples of hypercube topology can be seen in chapter 2,
Table 2.1. The system reliability of hypercube of various dimensions in terms of fuzzy
branch reliability is explored and evaluated, which in turn calculates the reliability of the
convoy of UGV. This can further be extended to include the fuzzy node reliability too.
Reference [49] addresses the problem of system reliability using the product of possible
node pair reliability. Here if the graph has n nodes, then the number of node pairs is n*(n-
1)/2. This would lead to huge number of computations for large network. Spanning tree
method seems to be more effective for the calculation of system reliability. The proposed
algorithm for this method is as described below:
2 Determine the fuzzy node reliability which has value between 0 and 1. The various
factors that contribute to the computation of node reliability are EMC, vehicle
mobility, and signal strength. Let nodes A, B, C… have node reliabilities of pA, pB, pC
… respectively.
3 Determine the fuzzy branch reliability which has value between 0 and 1. The various
factors that contribute to the computation of branch reliability are obstacles, terrain,
and weather. Let the branches X1, X2, X3… have reliabilities p1, p2, p3…respectively.
4 Determine the expression for terminal reliabilities from all source nodes to all
destination nodes. Form Boolean Path expression function f, which represents the set
of non-overlapping functions, obtained from the Karnaugh map. Express f as a
Boolean sum of product function, which represents all paths from source to
82
destination, set P=0. Decide whether actual or approximate terminal reliability
calculation method is to be used. If approximate method is to be used go to step 4.
i. If f =0, terminate.
ii. Consider any term A from f, let A‘ be the arithmetic expression in terms of
reliabilities p and q. With this P changes to P=P+ A‘.
iii. Update f as f= Ā. f. Continue to step i.
Continue on step 5.
5 Calculate terminal reliability by approximate method.
i. If f =0, terminate.
ii. f* = f +h, let f‘ = arithmetic equivalent form of f* in terms of the
reliabilities. Ex. If f*=x1x2 then f‘=p1p2. Calculate f‘. If f‘<= ε terminate.
iii. Consider any term A from f, let A‘ be the arithmetic expression in terms of
reliabilities p and q. With this P changes to P=P+ A‘.
iv. Assign g = Ā.f. Express g as sum of product such that g= g‘ + g‘‘. Here g‘
contains terms from g so that the number of complemented variables is less
than T. All the remaining terms together forms g‘‘.
v. Assign f=g‘ and h = h+ g‘‘. Continue to step i.
6 Update terminal reliability expressions to incorporate the fuzzy node reliabilities as
explained in Table 2.2(Chapter 2).
7 System reliability can be calculated by basic method (step 7), or spanning tree method
(step 8).
8 Evaluate system reliability values by obtaining reliabilities from all nodes to other
nodes using basic method.
83
i. Form Boolean Path expression Nij for paths from node i to j, such that
1<=i< n, and i+1<= j< n, where n is number of nodes in the graph. Thus for
an n node graph we get n*(n-1)/2 node pairs [49].
ii. Let system reliability be Srel = 1.
for (i=1; i<=n, i++)
{ for(j = i+1; j<=n, j++)
Srel = (Srel).( Nij) }
iii. Obtain a non-overlapping expression for the Srel with help of Karnaugh
map.
iv. Express the Srel expression now in terms of the reliabilities and non-
reliabilities in an arithmetic expression. Let the branches X1, X2, X3… have
reliabilities p1, p2, p3…resp.
v. Calculate Srel by substituting the values of p1, p2, p3…and q1, q 2, q 3….
9 If the node reliabilities are known then we simply change the values of branch
reliabilities as in Table 2.2(Chapter 2).
10 Evaluate system reliability values by obtaining reliabilities from all nodes to other
nodes using the spanning tree algorithm.
i. Form the spanning trees for the given communication network graph G.
ii. Form the Cartesian product C of all n-1 vertex cutsets in terms of branches
connecting the any of n-1 nodes of G for each spanning tree Ti.
i. C = C1 C2 C3 Cn-1
iii. Obtain C*, a normalized Cartesian product.
iv. Calculate the probability expression to evaluate the network reliability.
84
v. Consider any spanning tree T0 from the set of all spanning trees.
vi. Arrange all Ti‘s in the ascending order of the distance from T0.
vii. System success of network reliability is expressed as :
S = T0 T1 T2 Tn-1
viii. Define Fi for each Ti
F0 = T0
Fi = T0 T1 T2 Ti-1
Each Ti is assigned a Boolean 1, substituted in all predecessor term
occurrence.
ix. Form the disjoint expression for the S.
S = T0 [T1 ( F1) T2 ( F2) Tn-1 ( Fn-1)], here ( F1) = ( F1)‘
x. Express Rs as a mathematical expression of S using the branch
reliabilities.
xi. Substitute the values of branch reliability to get the system reliability.
xii. If the node reliabilities are known then we simply change the values of
branch reliabilities as in Table 2.2(Chapter 2).
4.4.1 System Reliability Examples
The examples in Table 4.6 and Table 4.7(a) and (b) show that the results obtained by
the basic algorithm to calculate the system reliability matches with the one obtained using
the spanning tree algorithm for some standard series, parallel, and 2-D hypercube. We
assume branch reliability values p1, p2, p3, p4 and p5 as 0.9, 0.8, 0.7, 0.6, and 0.5
respectively.
85
TABLE 4.6: Series and Parallel Network Solved Example
Basic Method Spanning Tree Method
Number of node=3,
Number of node pairs=3,
Node Boolean expressions:
N12 = X1
N13 = X1 X2
N23 = X2
Srel = X1 X2
Disjoint expression, Srel = X1 X2
Arithmetic Form, Srel = p1 p2 = 0.72
Polynomial: p2
The spanning trees obtained are (X1, X2)
T0 = (X1, X2)
S= X1X2
Disjoint expression:
S = T0 [T1 ( F1) T2 ( F2) Tn-1 ( Fn-1)]
S= X1X2
Rs = p1p2 = 0.72
Reliability Polynomial: p2
Number of node=2,
Number of node pairs=1,
Node Boolean expressions:
N12 = X1 + X2
Srel = X1 + X2
Disjoint expression, Srel = X1 + X1‘X2
Arithmetic Form, Srel = p1+q1 p2 = 0.98
Polynomial: 2p-p2
The spanning trees obtained are (X1) , ( X2)
T0 = (X1)
1-distance trees are: {( X2) }
i Fi (Fi)
1 X1 X1‘
S= X1 X2 X1‘
Disjoint expression:
S = T0 [T1 ( F1) T2 ( F2) Tn-1 ( Fn-1)]
S= X1+ X2 X1‘
Rs = p1+ p2 q1 = 0.98
Reliability Polynomial: 2p-p2
The effect of different types of terrains discussed in section 4.2.3 on system reliability
can be seen in Table 4.8 and the Fig. 4.10 describes the behavior of the system.
Table 4.7(a): Standard Networks Solved Example
Basic Method Spanning Tree Method
Number of node=4,
Number of node pairs=6,
Node Boolean expressions:
N12 = X1 + X2X3X4 , N13 = X2+ X1X3X4
N14 = X1X4 + X2X3, N23 = X1X2 + X3X4
N24 = X4 + X1X2 X3 , N34 = X3 + X1X2X4
Srel = X1X2X4 + X1X3X4 + X1X2X3+ X2X3X4
Disjoint expression: Srel = X1X2 X3 + X1‘X2 X3 X4
+ X1X2‘X3 X4 + X1X2 X3‘X4
Arithmetic Form, Srel = p1p2 p3 + q1p2 p3p4 + p1q2p3
p4 + p1p2q3p4 = 0.7428
Reliability Polynomial: 4p3 - 3p
4
The spanning trees obtained are (X1, X2, X3), (X1,
X2, X4), (X1, X3, X4), (X2, X3, X4).
T0 = (X1, X2, X3)
1 -distance trees are: {(X1, X2, X4), (X1, X3, X4),
(X2, X3, X4)}
S= X1X2X3 X1X2X4 X1X3X4 X2X3X4
i Fi (Fi)
1 X3 X3‘
2 X2 X2‘
3 X1 X1‘
Disjoint expression:
S = T0 [T1 ( F1) T2 ( F2) Tn-1 ( Fn-1)]
S=X1X2X3 + X1X2X4X3‘ + X1X3X4X2‘+ X2X3X4 X1‘
Rs = p1p2 p3 + p1p2q3p4 + p1q2p3 p4 + q1p2
p3p4= 0.7428
Reliability Polynomial: 4p3 - 3p
4
86
Table 4.7(b): Standard Networks Solved Example
Basic Method Spanning Tree Method
Number of node=4,
Number of node pairs=6,
Node Boolean expressions:
N12 = X1 + X2X3 + X2X5X4 , N13 = X2 + X1X3 +
X1X4X5
N14 = X1X4 + X2X5 + X1X3X5 + X2X3X4
N23 = X3 + X1X2 + X4X5, N24 = X4 + X3X5+ X1X2
X5
N34 = X5 + X3X4 + X1X2X4
Srel = X1X4X5 + X2X4X5 + X2X3X5+ X1X3X5+
X1X3X4 + X2X3X4 + X1X2X5 + X1X2X4
Disjoint expression,
Srel = X1X3X5 + X1X3X4X5‘ +X1X3‘X4X5 +
X1‘X2X3X 5 + X1X 2X 3‘X4‘X5+ X1‘X2X3X 4X 5‘+ X1
X2X3‘X4X5‘+ X1‘X2X 3‘X4X5
Arithmetic Form,
Srel = p1p3p 5 + p1p3p 4q5 + p 1 q 3 p 4 p 5 + q 1 p 2 p 3 p 5
+p 1 p 2 p 3 q 4 p 5+q 1 p 2 p 3 p 4 q 5 + p 1 p 2 q 3 p 4 q 5 +
q 1 p 2 q 3 p 4 p 5 = 0.7774
Rel. Polynomial: 8p3 – 11p
4 +4p
5
The spanning trees obtained are (X1, X2, X5), (X1,
X2, X3), (X1, X2, X4), (X1, X4, X5), (X2, X3, X5),
(X1, X3, X4), (X2, X3, X4), (X3, X4, X5)
T0 =(X1, X2, X5),
1-distance trees are: {(X1, X2, X3), (X1, X2, X4), (X1,
X4, X5), (X2, X3, X5)}
2-dist trees: {(X1,X3,X4), (X2,X3, X4), (X3, X4, X5)}
S= X1 X 2 X 5 X 1 X 2 X 3 X 1 X 2 X 4 X 1 X 4 X 5
X 2 X 3 X 5 X 1 X 3 X 4 X 2 X 3 X 4 X 3 X 4 X 5
i Fi (Fi)
1 X5 X5‘
2 X5 + X3 X5 ‘ X3‘
3 X2 X2‘
4 X1 X1‘
5 X2 + X5 X2 ‘ X5‘
6 X1 + X5 X1 ‘ X5‘
7 X1 + X2 X1 ‘ X2‘
S = T0 [T1 ( F1) T2 ( F2) Tn-1 ( Fn-1)]
S=X1X2X5 + X1X2X3X5‘ + X1X2X4X5‘X3‘ +
X1X4X5X2‘ + X2X3X5X1‘ + X1X3X4X2‘X5‘ +
X2X3X4X1‘X5‘ + X3X4X5X1‘X2‘
Rs=p1p2p5 + p1p2p3q5 + p1p2p4q5q3 + p1p4p5q2 +
p2p3p5q1 + p1p3p4q2q5 + p2p3p4q1q5 + p3p4p5q1q2
Rs = 0.7774, Rel. Polynomial: 8p3 - 11p
4 +4p
5
Table 4.8: System Reliability for different Terrains in Fig 4.7
Graph Reliabili
ty
Series Parallel Series-
Parallel
Non-series
Parallel
Soybean Field 0.1 0.01 0.19 0.00316 0.0069
Plowed Field 0.2 0.04 0.16 0.02162 0.041616
Sand Arena 0.3 0.09 0.51 0.08316 0.1366
Rough Field 0.4 0.16 0.64 0.11692 0.21614
Parade Ground 0.5 0.25 0.165 0.3125 0.43165
Baseball infield 0.6 0.36 0.84 0.41652 0.6134
Baseball outfield 0.7 0.49 0.91 0.65116 0.161652
Gravel/Dirt Road 0.8 0.64 0.96 0.8192 0.9011
Asphalt Parking
Lot
0.9 0.81 0.99 0.941616 0.91669
87
Fig.4.10 System reliability for different terrains
4.4.2 Hypercube System Reliability Analysis
1-D hypercube [53] is used to build 2-D hypercube. 2-D hypercube is used to build 3-D
hypercube. 3-D hypercube is used to build 4-D hypercube. Thus recursively higher
dimension hypercube is built using the lower dimension hypercube. From the section
4.4.1 it is seen that 1-D hypercube has Reliability Polynomial R1 = p and 2-D hypercube
has Reliability Polynomial R2 = 4p3 - 3p
4. Similarly 3-D hypercube has reliability
polynomial R3 = (4p3-3p
4)2(1-(1-p)
4). Reference [54] has discussed the following theorem
to express the reliability of 4-D and higher dimension hypercubes in terms R3.
Theorem [54] Let R3 is the reliability of a 3D hypercube, and then reliability of a d-
dimensional
hypercube can be expressed as
a function of R3, by the
following relation.
d
Rd = R3 A
( 1- qB)
C where A = 2
d-3 , B = 2
n-1 , C = 2
d-n
n=4
System Reliability for different Terrain
0
0.2
0.4
0.6
0.8
1
1.2
Soybean
Fie
ld
Sand
Are
na
Para
de
Gro
und
Baseball
outfie
ld
Asphalt
Park
ing
Terrain
Syste
m R
eliab
ilit
y
Reliability
Series
Parallel
Series-Parallel
Non-series Parallel
88
Thus from the above theorem we can see that a slight increase or decrease in the value
of branch reliability would result in big changes in the value of Rd. If the node reliability
is also to be taken into consideration then the resultant system reliability of n-Dimension
hypercube can be as expressed using Table 4.3. System reliability expressions for some
hypercubes can be found in Table 4.9.
TABLE 4.9: System reliability expressions
Hypercube System reliability expression
1-D R1 = p
2-D R2 = 4p3 - 3p
4
3-D R3 = (4p3-3p
4)2(1-(1-p)
4)
4-D R4 = (4p3-3p
4)2(1-(1-p)
4)[1-(1-p)
8]
5-D R5 = [(4p3-3p
4)2(1-(1-p)
4)]
2[1-(1-p)
8][(1-(1-p)
8]
2[1-(1-p)
16]
The effect of different types of terrains on system reliability for hypercube topologies
from 1-D to 5-D can be seen in Table 4.10. Fig. 4.11 pictorially compares the behavior of
different terrains for different hypercube topologies. It is seen that higher the dimension
of the hypercube, less is the effect of the change in the value of the branch reliability.
This can be seen in the last row of the Table 4.10, which shows the difference in the
reliability for each hypercube between highest branch reliability factor Asphalt parking
lot and the lowest branch reliability factor soybean field terrain.
TABLE 4.10: Hypercube System reliability for different terrains
Graph
P
Hypercube
1-D 2-D 3-D 4-D 5-D
Soybean Field 0.1 0.1 0.0037 0.0013 9.2212e-07 6.9274e-013
Plowed Field 0.2 0.2 0.0272 0.0022 1.3474e-06 1.7645e-012
Sand Arena 0.3 0.3 0.0837 0.0636 0.0038 1.4485e-005
Rough Field 0.4 0.4 0.1792 0.0729 0.0040 1.5816e-005
Parade Ground 0.5 0.5 0.3125 0.2930 0.0855 0.0073
Baseball infield 0.6 0.6 0.4752 0.4630 0.2143 0.0459
Baseball outfield 0.7 0.7 0.6517 0.4714 0.2144 0.0460
89
Gravel/Dirt Road 0.8 0.8 0.8192 0.8179 0.6689 0.4475
Asphalt Parking Lot 0.9 0.9 0.9477 0.8191 0.6689 0.4475
Diff:Asphalt-Soyabean 0.8 0.8 0.944 0.8178 0.668899 0.44749
Fig. 4.11 System reliability for different terrains and different Hypercube Topologies.
4.5 UGVR Circuits FPGA Implementation
FPGA implementation of the fuzzy system reliability is successfully done with help of
Xilinx FPGA Tools [98][101]. Xilinx ISE WebPack is used to design and implement
fuzzy system reliability on Spartan 3 FPGA using Verilog code. The simulation of the
terminal and system reliability of FPGA is done with help of ModelSim [100] and
Synapticad Verilogger Pro [99].
The fuzzy branch reliability values extracted from the MATLAB implementation of
fuzzy branch reliability system are used to calculate the fuzzy terminal reliability for the
series and parallel networks as discussed in Table 4.6. Here a_e, b_e and a_m, b_m are
the exponent and mantissa part of reliability p1and p2. (parallel_e, parallel_m) and
(series_e, series_m) are the results of series and parallel network topology. Fig. 4.12 (a)
shows the RTL schematic and Fig 4.12(b) the technology schematic for series-parallel
network. Fig. 4.13(a) shows Synapticad Waveform, Fig. 4.23(b) shows the ModelSim
snapshot, and Fig. 4.13(c) shows ModelSim result for the series-parallel network
topologies calculating the fuzzy terminal reliability.
90
(a) (b)
Fig. 4.12 Series-parallel Network (a) RTL Schematic. (b) Technology Schematic
Hypercube network RTL Schematic and the technology schematic can be seen in Fig.
4.14(a) and (b) resp. The results of the simulation of FPGA implementation of the fuzzy
system reliability can be seen in Fig. 4.15(a) for the Synapticad result and Fig. 4.15 (b)
for ModelSim result snapshot. Here branch (p_m, p_e) and the result system reliability
(R1_m, R1_e), (R2_m, R2_e), and (R3_m, R3_e) for 1-D, 2-D, 3-D hypercube
respectively are expressed in form of mantissa and exponent. sel selects the dimension of
hypercube. This implementation can further be extended to any generalized network and
also for a hypercube network with dimension n. Table 4.11 analyses the FPGA
Implementation of Hypercube network reliability.
The steps involved in the FPGA implementation of Fuzzy reliability of convoy of
unmanned vehicles are as following [60]:
Develop Fuzzy Inference System using MATLAB‘s Fuzzy Logic Toolbox for Fuzzy
branch reliability.
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(a) (b)
(c) Fig 4.13: Series-parallel Network a. Synapticad Waveform b. ModelSim snapshot, c. ModelSim result
Develop Verilog code for the Fuzzy terminal and system reliability architecture
reading the fuzzy branch reliability.
Create a project in Xilinx 9.1 project Navigator Interface.
Select the device, like Spartan 3 in this case.
Add the existing source (Verilog code file and the test bench file).
Synthesize- XST. Do synthesis of code.
Implement design.
# Reading C:/Program
Files/Modeltech_xe_starter/win32xoem/../tcl/vsim/pref.tcl
# Loading project abc
vsim work.mu_TB_v
# vsim work.mu_TB_v
# Loading work.mu_TB_v
# Loading work.mu
run -all
# a_m = 0, a_e= 0, b_m= 0, b_e= 0, serial_m= 0, serial_e= 0,
parallel_m= 0, parallel_e= 0
# a_m = 9, a_e=65535, b_m= 9, b_e=65535, serial_m= 81,
serial_e=65534, parallel_m= 99, parallel_e=65534
# a_m = 7, a_e=65534, b_m= 6, b_e=65534, serial_m= 42,
serial_e=65532, parallel_m= 218, parallel_e=65532
# a_m = 5, a_e=65535, b_m= 6, b_e=65535, serial_m= 30,
serial_e=65534, parallel_m= 80, parallel_e=65534
# ** Note: $finish : C:/Documents and Settings/student/My
Documents/sp_TB.v(97) # Time: 700 ns Iteration: 0 Instance: /mu_TB_v
# Break at C:/Documents and Settings/student/My Documents/sp_TB.v line 97
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Generate Programming File.
Download the bit file on FPGA and test.
Debug and simulate using ModelSim software.
Debug and simulate using Synapticad‘s Verilogger Pro software.
(a) (b)
Fig 4.14 : Hypercube network (a). RTL Schematic, (b) Technology Schematic
(a) (b)
Fig 4.15: Hypercube reliability simulation results (a). Synapticad waveform, (b) ModelSim snapshot
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Table 4.11: Analysis of FPGA Implementation of Hypercube network reliability
Metric Used Available Utilization
Number of 4 input LUTs 159 12,288 1%
Number of Slices occupied 90 6144 1%
Additional JTAG gate count for IOBs 4,992 - -
Number of bonded IOBs: 104 240 43%
Total equivalent gate count for design 1804 - -
In order to calculate the real time system and terminal reliability in the fields sensors
would give the values of the branch and the node reliabilities. These values can further
lead to calculation of fuzzy reliability. This process is repeated. The main motivation for
FPGA implementation is quick implementation and the flexibility to make any kind of
changes in the implementation. Once desirable performance is achieved VLSI
implementation can be done to have reliability on chip.
4.6 Reliability Calculations Using Pipelined Array
Generalized pipeline Array performs basic arithmetic operations such as multiplication,
division, squaring, and square rooting which could be used in the process of calculation
of reliability. Implementation of generalized pipeline array operations is done with
Hardware Description Language Verilog. The main motivation for the use of FPGA is
that it can be extended and updated to carry out same operations on the floating-point
operands [68]. This floating-point pipelined array can be used for the FPGA
implementation of the reliability of network circuits. A generalized pipeline array [67]
performs arithmetic operations repetitively as it performs all these operations in a
pipelined fashion. The pipeline array uses arithmetic cells, control cells and latch circuits
all pulsed with a clock generator.
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(a) (b)
Fig 4.16.(a) Arithmetic cell, (b) control cell(courtesy of [67]).
The arithmetic cell [67] is defined with following Boolean expressions.
The control cell[67] is defined with following Boolean expressions.
The organization of the arithmetic cells, control cells and the latches is as shown if Fig.
4.17 . The typical input and result pattern can be as seen in this figure. The various bits in
the fig 4.17 are used for different purpose in different operations. The signals serve
different purpose in different operations. For addition operation inputs are in A and B,
with X=0, Fi = 1. The result is available in S. The subtraction is done with operands in A
and B, X=1 and Fi=1 and the result is in S. Square root of 10-bit binary number A
(A1,…, A10) can be obtained by setting all P=0, X=1, C2=B3=B4=1 and rest of C and B
bits are 0. The result is seen F1… F5. Square operation has operand on P1,P2, P3,… and
X=0, A‘s=0, C2=B3=B4=1 and rest of C and B bits are 0. The result is seen A1,…, A10.
The cells marked S are used for squaring and square rooting only The cells marked M are
used to incorporate overflow for multiplication operation only. All X, A, are set to zero,
multiplicand and multiplier are stored in B and P respectively. The result can be seen on
A. The division operation has dividend and divisor in A & B respectively with X=1, B=C
S = [A (B X) C1]Fi + AF1’
CO = (B X)(A+C1)+AC1 D = BC + CFi = C(B + Fi)
E = B + CFi = (B +C)(B +Fi).
Fi = CoX + PiX’
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and all P=0. For multiplication and squaring operations, the control line X is made logical
zero, and for square rooting and division, it is made logical one.
Fig.4.17 Generalized pipeline Array (courtesy of [67]).
4.6.1 FPGA Implementation of Generalized Pipeline Array
FPGA very neatly incorporates the best of the processor based systems and the best of
the Application-Specific Integrated Circuit (ASIC). They exhibit the parallel
performance, so they seem to be the best suited for the application like the generalized
pipelined array. They are advantageous in terms of cost, ease of making changes in the
proposed design and without affecting the current design. The architecture of generalized
pipeline array in Fig. 4.17 is implemented using Verilog code. Xilinx Spartan 3[98][101]
board was used to implement the same. Spartan 3 board is supported with 1536, 4 input
LUTs and 768 slices at 50 MHz clock frequency. The Targeted Device is xc3s50-4pq208.
Xilinx 8.1i ISE was used to implement, synthesize, simulate and device fitting of the
pipeline architecture. Test benches were written to test each of the operations supported.
ModelSim software was used to simulate and debug the Verilog code for the proposed
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design. The results of the implementation of various operations on the Spartan FPGA can
be seen in Table 4.12. It is seen that the speed of the proposed design is reasonably good.
It is also seen from the results that the division operation takes the maximum number of
slices, gate count needed for the design. RTL for addition operation can be seen in the
Fig. 4.18(a) and (b). The proposed architecture was debugged and simulated with the
ModelSim software and the results for addition operation can be seen in the Fig. 4.19.
Similarly all of the operations were debugged, simulated and tested.
Fig. 4.18 Pipeline Array FPGA (b) RTL schematic for addition operation,(b) Detailed RTL schematic for addition
operation code
Fig. 4.19 Simulation result for addition operation
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TABLE 4.12: FPGA Implementation of a Generalized pipeline Array: all operation
Metric Number
of 4
input
LUTs
Number
of Slices
occupied
Additional
JTAG gate
count for
IOBs
Number
of
bonded
IOBs:
Total
equivalent
gate count
for design
Available 1536 768 - 124 -
Addition Used 15 10 1506 22 90
Utilization% 1 1 - 17 -
Square Used 13 7 768 16 87
Utilization% 1 1 - 12 -
Square Root Used 34 17 1056 22 207
Utilization% 2 2 - 17 -
Multiplication Used 33 17 768 16 190
Utilization% 2 2 - 12 -
Division Used 46 23 960 20 276
Utilization% 2 2 - 16 -
4.6.2 VLSI Implementation of a Generalized Pipeline Array
CADENCE [102] is a professional integrated circuit / VLSI design tool which is
widely used in the semiconductor industry. Cadence offers an integrated Electronic
design automation (EDA) solution which encompasses the entire design flow from
behavioral modeling to post-layout simulation. Cadence is one of the EDA tools available
for simulation and IC design. Cadence uses programming languages like Verilog, VHDL
etc for VLSI implementation. We can manually design the IC using IC Front to Back in
Cadence by selecting required tools and components. Cadence facilitates to carry out
check pre layout and post layout simulations that can verify the exact outputs.
The steps followed for the implementation includes-
1. Write the Verilog code for the generalized pipeline array
2. TestBench files are created to carry out simulation and testing of various operations
supported like addition, multiplication, division, square, square root.
3. The Verilog code is compiled using Nclaunch.
4. NCELAB is used to elaborate the design.
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5. Simulation is done with help of NcSim. Fig. 4.20 shows waveform for the multiply
pipeline operations simulation.
Fig. 4.20: Ncsim waveform for multiply operation
Fig. 4.21 Detailed Schematic of Pipeline array
6. Verilog Code Synthesis is done using Ambit BuildGates. Fig. 4.21 shows the detailed
schematic of pipeline array.
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7. Verilog Layout Generation is done using ‗First Encounter‘ silicon virtual prototyping.
8. Verilog Layout using IC Front to Back. Fig. 4.22 show the layout of Pipeline array
and Fig. 4.23 shows the Layout with IC Front to Back
Fig. 4.22 Layout of Pipeline array in Cadence
9. Post Layout Simulation.A post-layout simulation from the extracted view gives an
idea of how the design would work.
Fig. 4.23: Layout with IC Front to Back
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Fig. 4.24: Pipeline Array : (a) The completed test bench, (b) Schematic showing Padframing.
10. Pad frame (Fig 4.24(b)) and auto-routing. This last process involves following :
Create a schematic cell view, Fill in the cell name, Use the symbol in the library,
Padvdd for vdd, Padgnd for gnd, Padinc for input.
11. Check for errors.
Fig. 4.25 Simulation results for 10 * 5
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12. Simulate the pipeline array with SpectreS Spice simulator after creating a symbolic
view of pipeline array and a test bench (Fig 4.24(a)) to test it. Fig 4.25 shows a
simulation of pipeline multiply operation.
13. Using Cadence Chip Assembly Router (CCAR) do the routing. Fig 4.26 shows the
final route of Generalized Pipeline Array. The design is ready to go on chip.
Fig. 4.26 The final route of Generalized Pipeline Array.
4.6.3 UGV Reliability using Pipeline Array
The unmanned ground vehicle network as seen in Fig. 4.27 can be portrayed as the
network consisting of node itself as another network. In this scenario if the reliability of
big network has to be calculated, the reliability of each individual node has to be
calculated. Here the node reliability can be calculated in parallel using the generalized
pipeline array. These values can be further used for the calculation of the overall system
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reliability of the network of vehicles. The FPGA implementation model for this
supplication is presented in Fig. 4.28.
Fig. 4.27 The unmanned ground vehicle network
Fig. 4.28 The unmanned ground vehicle network FPGA implementation model
4.7 Conclusion
Critical role of unmanned intelligent ground vehicles is evident from variety of defense
applications. Fuzzy reliability of a convoy of vehicles is the result of Fuzzy and Boolean
approaches. The node and branch reliability is calculated using the Fuzzy approach. The
terminal reliability is calculated using Boolean algebra. Software implementation of the
fuzzy reliability is done using the binary decision diagrams. The procedure is applicable
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for any number of stations and any links between two terminal stations. The proposed
procedure is computerized and results for several examples are included. To improve the
performance evaluation of the convoy, node failure i.e. failure of convoy station is also
taken into consideration. Depending upon the reliability predicted a commander can take
appropriate decision in the battlefield. Proposed algorithm determines all paths from
source to destination and Boolean expressions are formed. A non-overlapping
simplification is obtained and further transformed into mathematical expression, where
reliability values are substituted. The results of design, implementation and simulation of
the reliability of convoy of unmanned vehicles are given. Hypercube System Reliability
Analysis is done with help of a sample data. The unmanned ground vehicle is used as an
extension of human capability and it operates by itself using number of sensors. The
collaboration means two or more unmanned ground vehicles working together toward a
common goal in a node/station. The unmanned ground vehicles coordination is an
essential process for the vehicles going from one node to another node using a path.
Therefore the collaboration and coordination of unmanned ground vehicles are vital to
the commander in order to complete the mission with success.
FPGA implementation of the fuzzy terminal reliability for the series and parallel
network topologies is done successfully. FPGA implementation of the fuzzy system
reliability for hypercube network topology and fuzzy system reliability is successfully
done. These FPGA implementations are done with help of Xilinx FPGA Tools. Xilinx
ISE WebPack is used to design and implement fuzzy system reliability on Spartan 3
FPGA using Verilog code. The simulation of the terminal and system reliability of FPGA
is done with help of ModelSim XE (Xilinx Edition) and Synapticad Verilogger Pro. The
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results of design, implementation and simulation of the reliability of convoy of unmanned
vehicles is analyzed and presented. This can be further expanded to generalized network
and N-dimension hypercube network topology. The VLSI design of pipeline array is
done to carry out the parallel operations in reliability calculations in the case of network
of networks. Please note that the links in the analysis discussed in this chapter can be
unidirectional and bi-directional depending on the application in mind of the commander
overseeing the UGV operation. Please note that the reliability techniques discussed above
are not based on the statistical data which takes several years for collection. However the
techniques are based on Fuzzy rules which can be implemented instantaneously.
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CHAPTER 5
CDISI: CRACK DETECTION AND IMPACT SOURCE IDENTIFICATION
SYSTEM
5.1 Introduction
The real time Non-Destructive Testing (NDT) for Crack Detection has been of interest
to several investigators. Recently Meitzler et al [72] have proposed an ultrasonic crack
detection system, which uses transducers to detect the crack in metal armor plates. The
existence of cracks is determined by comparing the output voltage waveforms with that
of an undamaged plate manually using metrics. Similarly the Identification of Source
which causes the crack has also been of interest in the literature [88]-[89]. The thesis
suggests a unified approach for both the problems of Crack Detection and Impact Source
Identification (CDISI). CDISI has usually been performed by visual assessment of
waveforms generated by a standard data acquisition system [90]. This thesis suggests an
automation of CDISI for metal armor plates using a SC approach by developing a FIS to
effectively deal with this problem. It is also advantageous to develop a chip which can
contribute towards real time CDISI. The objective of this chapter is to report on efforts to
develop an automated CDISI procedure and to formulate a technique so that the proposed
method can be easily implemented on a chip.
5.2 CD: Crack Detection System
Considerable interest has existed in the literature for a long time in support of real-time
crack detection Non-Destructive Techniques (NDT) in a variety of commercial and non-
commercial applications. Various authors [72]-[75] have suggested different approaches
in finding a solution to this problem. There has been a long standing interest in
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developing non destructive techniques for determining the presence of cracks in
materials. This problem is quite important to issues related to the security and safety of
Soldiers as it affects armored vehicles and Soldier‘s body armor plates on the battlefield.
The NDT for crack detection endeavors to improve the reliability, quality level of product
material and operational readiness of armored vehicles and Soldier‘s body armor at the
battlefield.
5.2.1 CD System Description
The fuzzy logic approach can be efficiently used to model any crack detection system.
The nature of application where it is used would decide what kind of knowledge base is
required to develop the FIS. The fuzzy logic approach will involve an element of
Artificial Intelligence in any crack detection system.
Fig. 5.1 Crack Detection Test System Circuit with a ceramic plate(courtesy of [72])
Meitzler et. al [72] describes a method for the ultrasonic crack detection in ceramic
Vehicle Body Armor Support System (VBASS) plates. In this reference the approach
used is as shown in Fig. 5.1. Meitzler used two piezoelectric lead zirconate titanate (PZT)
transducers. One of these transducers is connected to the variable AC source and the
other is connected to the oscilloscope for transmitted energy and excited vibrational mode
analysis. PZT transducers are used to excite and measure the resonances mode of
rectangular, ceramic armor plates in 50- 300 kHz range of frequencies. The test circuit
[72] as seen in Fig. 5.1 is used to determine the existence of cracks or change in the
107
mechanical structure of the material by comparing the output voltage waveforms with
that of an undamaged plate using metrics.
In the thesis proposed model of automated procedure to detect cracks or plate damage,
these vibration waveforms are used to extract important information in terms of input
driving frequency, output average Root Mean Square (RMS) and standard deviation. The
analysis of these waveforms leads to interesting results which help to distinguish between
the plates of differing status. These observations lead to conclusion about mapping the
status of the plate Є {damaged, undamaged, and slightly damaged} with extracted factors
like input driving frequency, output average RMS voltage and standard voltage deviation.
This generates a sufficiently large database with parameters {status of plate, Frequency,
average RMS, Standard Deviation}. This database becomes instrumental in defining the
relationship between Input Parameters= {Frequency, average RMS, Standard Deviation}
and output parameter= {Status of Plate}. A new term is coined to define the severity of
crack as ‗Degree of Crack‘. The degree of crack essentially portrays the nature of the
plate. The ‗Degree of Crack=0‘ indicates plate is undamaged and ‗Degree of Crack=1‘
indicates that the plate is damaged. As the severity of crack increases, the value of
Degree of Crack increases.
5.2.2 CD Soft Computing Approach
A fuzzy system is a system that is based on the Fuzzy Logic [91][92]. A Fuzzy system
model for CD as seen in Fig. 5.2 consists of following main components:
4. Numerical Data Inputs: The vibration waveforms are used to extract some
significant information that can help to determine the Degree of Crack. The
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numerical values for Input Frequency, Output Average Root Mean Square (RMS)
and Standard Deviation voltage are used as input for the Fuzzy Model.
5. Numerical and Linguistic Data Outputs: The Degree of Crack is the output for the
proposed model such that,
0 ≤ Degree of Crack ≥ 1
The Linguistic output Є {Undamaged, slightly damaged, Damaged, Unknown}.
6. Fuzzification: It maps an observed non-fuzzy input space into suitable linguistic
values, which can be viewed as labels of fuzzy sets.
7. Fuzzy Inference Engine: It consists of:
A rule base: Fuzzy rule can be expressed as: If input is A, then output is B,
where A and B are the input and output linguistic values defined. These rules
are formulated on the basis of past experience, knowledge about the system
that is to be developed. Here A is called as an antecedent and B is called as a
consequent.
Fuzzy rule database: Defines the membership functions for each input and
output, which are used by the fuzzy rules and forms.
Reasoning mechanism: Obtains the output by performing the inference
procedure on the given conditions and the formed rules. The result is obtained
by aggregating the result of each rule in the fuzzy rule base.
8. Defuzzification: This component takes inputs as aggregated fuzzy dataset and
maps it to a nonfuzzy output value ‗Degree of Crack‘.
Fuzzy logic can play a significant role in an application such as crack detection systems
[72, 74, 77, and 93]. Fuzzy logic [94] supports the use of a set of rules which portrays the
109
relationship between the input and the output variables. These user-defined set of rules
governing the crack detection system are updated until the desired result from the system
is not obtained. The Fuzzy model is multiple input single output system. The multiple
inputs include: Input frequency, Output Average Root Mean Square (RMS) voltage and
Standard voltage Deviation. The output is Degree of Crack or Nature of Plate. The
multiple input single output Crack Detection Fuzzy Inference System is shown in Fig. 5.3
Fig. 5.2 Fuzzy system model for Crack Detection
The reference [72] has presented some results for the crack detection for the test circuit
as seen in Fig. 5.1. On the basis of these results an attempt is made to assign the labels to
different ranges of Input frequency, Output Average Root Mean Square voltage and
Standard voltage Deviation. These linguistic labels are eventually assigned some degree
of membership as seen in equation 1. The Table 5.1 shows linguistic labels for the
different factors.
Table 5.1: Labels for the Input function for Crack Detection Fuzzy System
Labels Range Low Medium High
Frequency (KHz) 1-124 1 – 60 61 - 90 91 - 124
Average Root Mean
Square voltage
0-0.002971 ≤ 0.00199 >0.00199 &
<0.002971
≥ 0.002971
Standard Deviation 0-
0.0001889
≤
0.00003229
>0.00003229
&<0.0001889
≥0.0001889
110
The function for factor Frequency with linguistic label is defined in equation (5.1).
These labels Low, Mild and High are assigned a degree of triangular membership
function as seen in equations (5.2) to (5.4) for frequency in equation (5.1). Similarly other
factors like Average Root Mean Square Voltage and Standard Deviation can be defined
as seen in Table 5.1.
Fig. 5.3 Multiple input single output Crack Detection Fuzzy Inference System
124 x91 if High
90 x61 if Medium
60 x1 if Low
)(Frequency x … (5.1)
)4.0,0(
4.0,0
,3.0/)4.0(
,1,0
)( Low x
x
x
x
x
…(5.2) 9.0,0
)9.0,5.0(),4.0/()9.0(
)5.0,1.0(),4.0/()1.0(
1.0,0
)( Medium
x
xx
xx
x
x
…(5.3)
1,0
)1,6.0(),4.0/()6.0(
6.0,0
)(High
x
xx
x
x
… (5.4)
1,1.4]) [0.6,(x, trimfif High
0.9]) 0.5, [1,f(x, trimif Medium
0.4]) 0, [-0.4,f(x, trimif Low
)(ackDegreeOfCr x … (5.5)
where trimf(x, [a, b, c]) is the triangular function [92] with a, b and c are left feet, right
feet and the peak of the triangle.
Fig. 5.4 Triangular-shaped membership function for consequent NatureOfPlate
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The rules are typically in the format of
If Frequency is ‘Low’ and Average RMS is ‘low’ Then NatureOfPlate is ‘ Damaged
Plate‘ or
If Frequency is ‘Low’ or Average RMS is ‘Low’ Then NatureOfPlate is ‘ Damaged
Plate‘
where the If part is called the ‗antecedent‘ and the Then part is called the ‗consequent‘.
The antecedents identified in the crack detection system are input factors. The
antecedents and consequents are connected with help of ‗and‘ or ‗or‘ operators with use
of negation operator if needed. After identifying the antecedents their labels with the
range are identified, which depends on the common sense and the experience.
Table 5.2: Rule Base for the Crack Detection Fuzzy Inference System
Rule
Number
Frequency Average Root
Mean Square RMS
Standard
Deviation
Result: Nature of
Plate
1 High High High Undamaged plate
2 High High Low Slightly Damaged
3 Medium Medium Medium Slightly Damaged
4 Medium Low Low Damaged Plate
5 Low Medium High Slightly Damaged
6 Low Low Low Damaged Plate
Fig. 5.4 shows the triangular membership function for the consequent NatureOfPlate/
DegreeOfCrack. Thus Y-axis shows the DegreeOfCrack value. This function is selected
by trial and error method after trying other membership functions like Gaussian,
Trapezoidal, Gaussian bell and others. It was observed that triangular function works well
with the Crack Detection Fuzzy Inference System.
The relationship between the antecedents and consequents is expressed with help of the
generated rule base. Table 5.2 shows a part of the rule base developed on basis of the
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experimental results found in [72]. If any of the input parameter labels like Low, Medium
or High are ‘true’ for a certain rule then that rule is said to be activated. About dozen
rules are formulated. Some of the example rules are:
1. If (Frequency is High)and(AverageRMS is High)and(StdDeviation is High) then
(NatureOfPlate is Undamaged)
2. If (Frequency is Medium)and(AverageRMS is Medium)and(StdDeviation is Medium)
then (NatureOfPlate is Slightly damaged)
3. If (Frequency is Low)and (AverageRMS is Low) and (StdDeviation is Low) then
(NatureOfPlate is damaged)
4. If (Frequency is Low)and (AverageRMS is Medium) and (StdDeviation is Medium)
then (NatureOfPlate is Slightly damaged)
(a) (b)
(c) (d) Fig. 5.5 Crack Detection Fuzzy Inference System (a) The FIS- Fuzzy Inference System, (b) The FIS Rule
viewer, (c)The FIS surface viewer, (d) The NeuroFuzzy system[Blue: training data, and Red: testing data]
113
Fig. 5.5 shows the software implementation for the Crack Detection Fuzzy Inference
System. Fig. 5.5(a) shows the structure of the TISO (Triple Input Single Output) Fuzzy
Inference System using Mamdani method [92]. This clearly expresses the structure of the
system with three input parameters identified as input factors associated with some
membership functions. This also shows presence of a single output – NatureOfPlate. Fig.
5.5(b) shows Fuzzy Inference System Rule Viewer, which shows fuzzy inference rule
diagram. It shows the effect of each individual membership function of input factors
affecting on the result. This gives a facility to change the values of the input parameters
by moving the bar present on first three columns for the input factors which in turn
updates the result found in fourth column. This window shows a result NatureOfPlate
=0.5 (Slightly damaged), for inputs Average RMS = 0.5(medium), Standard deviation
=0.5(medium), Frequency =0.5(medium).It is also seen that Rule number 14 was
activated to generate the result. The Fig. 5.5(c) shows the surface viewer which displays
the interdependence between the two inputs (Standard deviation, Average RMS) and the
output result (Nature of Plate) in 3-dimensions. The Fig. 5.5(d) shows the NeuroFuzzy
system for CD system.The Proposed algorithm for Development of Crack Detection
Fuzzy Inference System consists of following steps:
1. Identify the input and the output parameters for the Fuzzy Inference System.
2. Set the range for the input and output parameters. Their range is tabulated in
Table 5.2 range.
3. Fuzzify the input parameters maps and observed non-fuzzy input space into
suitable linguistic values.
114
4. Define membership function for each parameter. The membership function can be
triangular, Gaussian, trapezoidal etc.
5. Develop Fuzzy rule base.
6. The result is obtained by aggregating the result of each rule in the fuzzy rule base
for the considered input.
7. Defuzzify the output and map it to nonfuzzy linguistic output value ‗Degree of
Crack‘.
5.2.3 CD FPGA Implementation
The Field-programmable gate array (FPGA) plays a significant role in rapid
prototyping of a chip [95]. It can be programmed and reprogrammed using reasonably
priced hardware and software on the field. Here the hardware is the FPGA board and
software is circuit design, implementation, debugging, verification and simulation
software that sometimes are provided with the hardware. FPGA also is a cheaper option
over the respective chip, taking into consideration the manufacturing cost and complexity
of the chip. The FPGA is a general-purpose, multi-level Programmable Logic Device
(PLD).
(a) (b)
Fig. 5.6 FPGA implementation of Crack Detection: (a). System design structure (b). RTL schematic
115
The reference [72] discusses design of a standalone device which can detect cracks and
identify the source of impact. This motivates an attempt to develop a chip which can
detect crack on basis of logic used in the CD FIS discussed in Section 5.3.2. A rapid
prototyping of the chip design is handled by FPGA implementation of the crack design
Fuzzy Inference System. To program or design FPGA a HDL is used.
Table 5.3: Crack Detection FPGA Implementation Output: Plate Status codes
Nature of Plate Status Output 2-bit Code Numerical value
Unknown 00 0
undamaged 01 1
slightly damaged 10 2
damaged 11 3
Some of the advantages of the FPGA [94]-[97] implementation are rapid prototyping of
the system, flexibility to change the rule-base or antecedents or consequent, and without
much cost can be downloaded back on the FPGA. Different VLSI circuit design,
implementation, verification and simulation software [98]-[100] are used to design and
implement fuzzy crack detection on the FPGA using HDL code. The Table 5.3 shows the
consequent which is 2-bit bus representing the Nature of Plate codes and its
interpretation. Table 5.3 shows the value of this output bus and the meaning behind the
result. For example, if the result generated is ‗10‘, then it would mean that the plate is
slightly damaged. The system design is expressed as a block diagram in Fig. 5.6(a). The
antecedents are Frequency, Average RMS, Standard Deviation each 2-bit buses with ‘00‘,
‗01‘, ‗10‘ representing labels Low, Medium and High respectively. Fig. 5.6(b) shows the
Register Transfer Level (RTL) schematic of the system developed. RTL schematic
basically tells how the HDL code is interpreted by the synthesis tool and mapped with the
target technology. RTL schematic view represents design in terms of macro blocks which
116
further shows the detailed circuit with combinatorial logic mapped onto elementary logic
function gates. Fig. 5.7(a) shows technology schematic. Technology schematic
represents the design in terms of logic elements optimized to the target device. Fig. 5.7(b)
shows the result of software simulation HDL Log of the system developed. Fig 5.8(a)
shows the Detailed RTL schematic for the design. The FPGA Implementation process is
described in a flowchart shown in Fig. 5.8(b). Table 5.4 shows the analysis of device
usage for the CD system implementation. Here LUT stands for Lookup table. Slice is an
elementary programmable logic block which includes: two 4-input LUTs, two
multiplexers, arithmetic logic unit, and two 1-bit registers. It is seen that the results
obtained using FIS developed using Fuzzy Logic software matches reasonably good with
the results obtained on the FPGA board.
(a) (b)
Fig. 5.7 Crack Detection (a) Technology Schematic, (b) Simulation HDL Log
Table 5.4: Analysis of FPGA Implementation of Crack Detection
Metric Used Available Utilization
Number of 4 input LUTs 4 3,840 1%
Number of Slices occupied 2 1,920 1%
Additional JTAG gate count for IOBs 384 - -
Number of bonded IOBs: 8 173 4%
Total equivalent gate count for design 27 - -
117
(a) (b)
Fig. 5.8 Crack Detection System (a). Detailed RTL Schematic, (b). FPGA Implementation flowchart
START Crack Detection FPGA Process
Write Crack Detection HDL code using design,
implementation & simulation software
Select device as FPGA
Generate PROM file to be downloaded on FPGA
End Crack Detection FPGA Process
Assign package pins for Crack Detection design
on FPGA
Synthesize Crack Detection design to generate
RTL schematic
Implement Crack Detection design to
place, map and route it.
Configure the FPGA
Program FPGA; verify the design using input
output signal pins/buttons on board
Error?
Yes
No
Error
Yes
No
118
An integrated approach towards CD includes combination of soft computing and the
FPGA implementation as shown in Fig. 5.9. The test circuit [72] captures vibrations
through the plate and generates waveforms which can be displayed on an oscilloscope.
The test circuit results in the form of waveforms are further decoded to obtain the data
which acts as input for the crack detection Fuzzy Inference System. This FIS generates
the result ‗Nature of Plate‘ Є {Unknown, Undamaged, Slightly damaged, Damaged}.
The rule base from CD FIS is implemented using FPGA. The test circuit results in the
form of waveforms are further decoded to obtain the data in term of bits which acts as
input for the crack detection FPGA Implementation. The FPGA implementation results in
a conclusion about the status of the ‗Nature of Plate‘ Є {Unknown, Undamaged, Slightly
damaged, Damaged}.
Fig. 5.9 An integrated approach towards Crack Detection.
5.3 ISI: Impact Source Identification System
Fuzzy logic has emerged as an effective tool in section 5.2 for crack detection in
materials. A related problem, Impact Source Identification (ISI), has not received much
consideration. This thesis makes an effort to focus attention on the identification of
material of source of impact. The large number of variables involved makes the task of
impact source determination very unwieldy. Some of the variables include, the material
being impacted, the impacting material, size of the impacting object, striking force etc.
119
An approach for ISI is proposed in this thesis and through the experimental techniques it
is observed that fuzzy logic can be used successfully. The proposed methodology has
been implemented as a Mamdani Fuzzy Inference System (FIS) using the Fuzzy Logic
Toolbox [92] in MATLAB. Further FPGA implementation of the proposed ISI-FIS is
done with an intention to develop a chip for the ISI system to fit in a hand held device.
A ceramic plate is divided to 16 sections, to obtain and analyze results precisely. When
the ceramic plate is hit on any section by different impact sources, it will generate
waveforms with different behavior. An approach of analyzing the output waveform for
ISI is proposed. FIS is used to identify Impact Source. When the surface of the plate is
hit, it will generate a waveform. Using a Data Acquisition System (DAS), an Excel data
sheet is obtained from the waveforms. The data sheet incorporates important information
that is extracted from the waveforms like RMS values, Mean, Median, Mode, Peak Value
and Fast Fourier Transform (FFT) value. These outputs act as the inputs to the Fuzzy
Inference Model. The procedure to get the output by considering data values directly
from the text file having inputs such as RMS values, Mean, Median, Mode, Peak Value
and Fast Fourier Transforms is discussed.
5.3.1 ISI System Description
Fig. 5.10 Test System Circuit: Two Sensor Arrangement of the ceramic plate with sample waveform
obtained from the sensors. (Courtesy of [89])
120
The experimental setup for the detection of the impact source consists of a ceramic
plate [89] as shown in Fig. 5.1. This plate has 16 sections where the source can be hit.
This S00 to S33 are the location indexes for different sections. The sensors A and B are
located on two sides of the plate which reads the waveforms when the plate is hit by the
source. Sensors sense the acoustic emissions from submicron cracking caused by the
hitting pressure. Data is extracted from these waveforms for the diagnosis of the source
of impact. The parameters extracted from the waveforms obtained from both sensors are:
RMS value, Peak value, and Median, Mode and FFT value. After analytic study of
parameters it was noticed that some of them are obsolete. The parameters that uniquely
affected the decision making are the Location Index, Arms, Amax, Brms and Bmax. Here
Location Index stands for the location index. Arms and Amax are the RMS value and the
peak value for sensor A. Brms and Bmax are the RMS value and the peak value for
sensor B.The scope of this experiment is described by the following constraints:
The impact was simulated through an electric impact hammer.
The device hit the impacted surface with a force, adjusted to be within a relatively
small range, from a fixed distance.
The only variable was the material used for impacting head. The impacting
materials used were Steel® and a durable plastic Delrin
®.
The different impacting materials will generate different impact acoustic waves, but the
impact waves will not differ significantly if the impacting source is the same. The
variables like RMS, mean, median, mode, peak value and FFT value of the generated
impact waves may be used as parameters to differentiate the impact waves. The ISI
method consists of the following steps:
121
1. Consider two sensor arrangements for impact source identification
2. Hit the surface with defined source. (Steel and Delrin® sources are used.)
3. DAS acquires waveforms generated by the impact. (Two waveforms from sensor A
and sensor B, respectively.)
4. Save these waveforms from sensor A and sensor B in two data files.
5. Obtain RMS value, Mean, Median, Mode, Peak value and FFT value from output
files generated by DAS. (Apply MATLAB or LABVIEW commands.)
6. Define fuzzy model using Mamdani type FIS by considering absolute values of the
parameters.
The waveforms in Fig. 5.10 shows different sample waveforms obtained after creating
impact with Steel and Delrin® on a section of the plate, from one of the two sensors. Data
extracted from these waveforms can be seen in the Appendix B.
Table 5.5: Range Defined for Inputs
Labels LL LH ML MM MH HL HH
Arms 0.1 –
1.1
1.1 -
1.4
1.4 –
1.7
1.7 –
1.9
1.9 – 2.3 2.3 – 3.5 3.5 - 4
Amax 0 - 6.5 -- 6.5 – 8 -- 8 – 10 -- 10 - 18
Brms 0 – 1.5 1.5 –
2.4
2.4 –
2.9
-- 2.9 – 3.3 -- 3.3 - 5
Bmax 0 – 10 -- 10 – 13 -- 13 –
15.4
-- 15.4 -
18
5.3.2 ISI Soft Computing Approach
In a real time environment for ISI following parameters are used: RMS value, Peak
value, Median, Mode and FFT value. There are two sensors present on either side of the
plate i.e., A and B as described. The values obtained from the DAS are in the form of
waveforms obtained from sensor A and Sensor B for same parameter. So there are eleven
inputs used in the FIS, corresponding to the above defined five input parameters for each
122
of the two sensors. All the parameters are used to develop a fuzzy model in order to
implement it in a real time environment.
(a) (b)
(c ) (d)
(e) (f)
Fig. 5.11 ISI Fuzzy Inference System: (a) five Inputs, (b) Output membership function, (c, d) Input
membership function, (e) Rule Editor, (f) Rule Viewer
The FIS consists of 11 input parameters (1 location index, 5 inputs from sensor A, and
5 inputs from Sensor B) and one output, which the source of impact. On analyzing this
approach, some of the inputs were found to be superfluous; therefore, only five inputs
rather than ten were used. The parameters that were ultimately used are the Location
Index, Arms, Amax, Brms and Bmax for they are proved to be the most effective in
determining the source of impact. The ranges that were taken into consideration for the
123
FIS formation are described in Table 5.5. Range sets for these Input parameters are
determined after analyzing data obtained and the membership functions were decided
accordingly. As outputs in Fuzzy Logic are always measured between 0 and 1, it was
observed that a value of around 0.25 corresponds to Delrin® and 0.75 to Steel. Fig. 5.11
shows the various snapshots for ISI-FIS developed using Fuzzy Logic Toolbox in
MATLAB for five Inputs. Fig. 5.11(a),(b),(c) and (d) shows the input and the output
membership functions. Fig. 5.11(e) and (f) are the snapshots for the rule editor and the
viewer respectively for the ISI-FIS.
5.3.3 ISI FPGA Implementation
The method used for the impact source identification [71] consists of following steps:
Consider two sensor arrangements for impact source identification.
Hit the surface with defined source. (Steel and Delrin® sources are used.)
DAS (Data Acquisition System) acquires waveforms generated by the impact.
(Two waveforms from sensor A and sensor B, respectively.)
Save these waveforms from sensor A and sensor B in two data files.
Obtain RMS value, Mean, Median, Mode, Peak value and FFT value from output
files generated by DAS. (Implement it as a computer program.)
Generate rule-base for the parameters that contribute the most in the process of
the source identification.
Define fuzzy model using Mamdani type FIS by considering absolute values of
the parameters.
Verify the results with that obtained experimentally.
124
FPGA implementation of the ISI system is done using Verilog HDL using the
Xilinx ISE WebPack [98], ModelSim XE [100] and Spartan 3 FPGA.
The Fig. 5.12. and Fig. 5.13(a) illustrates the schematic for the FPGA implementation
of ISI system. The implementation is done using Verilog HDL. The system has the
following inputs: 4-bit location index, 3-bit Amax, 3-bit Arms, 3-bit Bmax and 3-bit
Brms. The output is n-bit source identifier. The output for the implementation done is 1-
bit where ‗0‘ indicates the source is steel and ‗1‘ indicates it is Delrin.
Fig. 5.12 Schematic for FPGA implementation of Impact Source Identification
The steps for VLSI algorithm development [88] are represented in a flowchart in Fig.
5.13(b). These steps are described below.
1. Develop Verilog/VHDL code for source identification in ceramic plates Simulation.
2. Select device as Spartan 3 FPGA.
3. Assign package pins for source identification design on FPGA.
4. Generate a PROM file to be downloaded on the FPGA.
5. Configure the FPGA using iMPACT.
6. Program FPGA; verify the design using input output signal pins/buttons on board.
7. Write a TestBench file to simulate and verify the FPGA implementation.
125
8. Run the test bench file with help of ModelSim software from Mentor Graphics.
(a) (b)
Fig. 5.13 ISI FPGA Implementation (a) RTL Schematic,(b) FPGA Implementation process flowchart
START Source Identification FPGA
Verilog/VHDL code for source identification in
ceramic plates Simulation in Xilinx 10.1i
Select device as Spartan 3 FPGA
Generate PROM file to be downloaded on FPGA
End Source Identification Chip Process
Assign package pins for source identification
design on FPGA
Synthesize source identification design to
generate RTL schematic
Implement Source identification design
to place, map and route it.
Configure the FPGA using iMPACT
Program FPGA; verify the design using input
output signal pins/buttons on board
Error?
Yes
No
Error
Yes
No
126
(a) (b)
Fig. 5.14 (a) Technology Schematic, (b) ModelSim Simulation
Table 5.6: Analysis of FPGA Implementation of Source Identification
Metric Used Available Utilization
Number of 4 input LUTs 14 3,840 1%
Number of Slices occupied 8 1,920 1%
Additional JTAG gate count for
IOBs
768 - -
Number of bonded IOBs: 16 173 9%
Total equivalent gate count for
design
87 - -
The main motivation for the FPGA implementation is to get flexibility to change the
rule-base, and without much cost can be downloaded back on the FPGA. The FPGA
implementation is done using Xilinx FPGA Tools [98]. Xilinx ISE WebPack is used to
design and implement fuzzy source identification on Spartan 3 FPGA using Verilog code.
The simulation of the system on FPGA is done with help of ModelSim XE (Xilinx
Edition). The analysis of the implementation can be seen in Table 5.6. Fig. 5.13(a) shows
the RTL schematic of the system developed. Fig. 5.14(a) shows technology schematic
and Fig 5.14(b) shows the result transcript of the ModelSim simulation of the system
developed. It is seen that the results obtained using ISI-FIS matches with the results
127
obtained on the FPGA and also with the actual results obtained from the experimental
setup.
5.4 An Integrated CDISI System
NDT of an object determines its usefulness without ruining it to avoid its intended use.
A Crack Detection and Impact Source Identification(CDISI problem) is quite important
to issues related to the security and safety of soldiers as it affect armored vehicles body
plates and soldier‘s body armor on the battlefield. The NDT for CDISI accomplishes to
perk up the reliability by assuring the quality level of armor material and operational
readiness of armored vehicles and Soldier‘s body armor plate prior to or during its day to
day use. A CDISI system for armor plates is presented as in this thesis a new Soft
Computing method based on the Fuzzy Logic component. The FPGA implementation of
CDISI fuzzy inference system is done with an intention to embed it on a chip designed
for a CDISI handheld device. The proposed approach uses the theory of Soft Computing
to develop a model supported by VLSI design to determine:
1. Nature of Plate: It is diagnosed to be in one of the four possible states like unknown,
undamaged, slightly damaged and damaged. The system generates Degree of crack
value in the range of [0, 1] where 0 represents an unknown state and 1 represents a
damaged plate. As the Degree of crack value increases, the amount of crack in the
plate also increases.
2. Source of Impact: The CDISI system currently recognizes two different sources of
impact. This can be expanded for incorporation of larger range of sources.
128
5.4.1 CDISI SYSTEM DESCRIPTION
Crack detection and Impact source identification has been widely studied problem in
the literature using NDT approaches. The work of Meitzler et al [72] is reviewed here for
the ready reference. An ultrasonic crack detection system [72] for ceramic Vehicle Body
Armor Support System (VBASS) plates as shown in Fig. 5.15 uses two piezoelectric lead
zirconate titanate (PZT) transducers attached with ceramic plate to be tested for the crack.
Generally transducers are used to transmit energy from one type to another. Here they are
used to stimulate and measure the resonances mode of rectangular ceramic armor plates
in 50- 300 kHz range of frequencies. PZT Transducer/Sensor A is connected to the
variable AC source and the PZT Transducer/Sensor B is connected to the oscilloscope for
transmitted energy and excited vibrational mode analysis. The alteration in the
mechanical structure or the presence of cracks is determined by comparing the output
voltage waveforms with that of an undamaged plate manually using metrics.
Fig. 5.15 CDISI: crack detection test system circuit
The impact source identification system consists of a ceramic plate [88], [89] as shown
in Fig. 5.2. The two sensors, Sensor A and Sensor B are positioned on two sides of the
ceramic plate which sense the acoustic emissions from submicron cracking caused by the
hitting pressure. These sensors read the waveforms when the plate is hit by the source.
The Data Acquisition System (DAS) extracts data from these waveforms. The location
hit on the plate affects the decision of impact source identification, so it has 16 parts
where the source can be hit. These parts are labeled P00 to P33 as seen in Fig. 5.16. The
129
accuracy of the identification of the source of impact depends on the part number being
hit by a source.
An automated procedure for the CDISI is proposed, which reads the waveforms from
the sensors A and B in the test circuits seen in Fig 5.15 and Fig. 5.16 with the help of a
DEWESoft Data Acquisition [90] System. The various parameters extracted from the
CDISI System waveforms are: Frequency, average RMS, Standard Deviation, RMS
value, Peak value, and Median, Mode and FFT value. After systematic study of
parameters it was noticed that some of these parameters are instrumental in the process of
decision making of the conclusion = {Nature of plate, Source of Impact} and some are
redundant. The unique parameters extracted from sensors A and B for the CDISI
assessment are: Input Frequency, average RMS, Standard Deviation, Location Index,
Arms, Amax, Brms and Bmax. The Arms and Brms are the RMS value for sensor A and
B. Amax and Bmax are the peak value for the sensor A and B. The details of the input
and output parameters of the CDISI are:
Input Parameter = {Input Frequency, average RMS, Std. Deviation, Location Index,
Arms, Amax, Brms , Bmax} (a)
Output Parameters= {Nature of Plate, Source of Impact} (b)
Nature of plate = {unknown, undamaged, damaged, slightly damaged} (c)
Source of Impact = {SourceType1, SourceType2, SourceUnknown} (d)
Fig. 5.16 CDISI: impact source identification test system circuit
130
The CDISI test circuits as shown in Fig.5.15 and Fig. 5.16 generate a sufficiently large
database for {Input Parameters, Output Parameters} which is instrumental in defining
fuzzy relation between these input and output parameters. In practice the time and
frequency domain analyses of the sensor waveforms is used for CDISI which many times
turns out to be very expensive. To the best of authors knowledge Fuzzy Logic is the best
candidate to express the relation between these input and the output parameters, due to
the lack of strong mathematical model to represent this system. CDISI Fuzzy System
outperforms the conventional comparison method involving human error due to manual
comparison of the waveforms with that of an ideal plate and the known source of impact.
The CDISI Fuzzy Inference System is a fast, reasonably priced fault diagnosis solution in
the complex system which involves human thinking. The CDISI fuzzy model is discussed
in Section 5.4.2.
5.4.2 CDISI SYSTEM: Soft Computing Approach
A fuzzy system is developed on the basis of the Fuzzy Logic which is based on the
fuzzy set theory [80]. Fuzzy logic supports approximate reasoning by taking a broader
view of Boolean values of ‗1‘ and ‗0‘ with fine merger of symbolic and numeric
computation. All the input and output parameters in a fuzzy system are essentially fuzzy
subset [91] with each element having some degree of membership in the subset.
The CDISI Fuzzy system model portrayed in Fig. 5.17 consists of following elements:
1. Numerical Data Inputs: The numerical values for all Input parameters are extracted
from the output waveforms generated with the help of Data Acquisition System.
These numerical values for different parameters are used as inputs to CDISI Fuzzy
131
Model. The numerical data inputs for CDISI system are: Input Frequency, average
RMS, Standard Deviation, Location Index, Arms, Amax, Brms, and Bmax.
2. Numerical and Linguistic Data Outputs: The CDISI output waveform parameters lead
to determine the Nature of plate and the Source of Impact. The nature of plate Є [0, 1]
is also represented as Degree of Crack; with smaller the value of degree less is the
amount of crack. The Linguistic labels applied to the output parameters are:
NatureOfPlate Є {Unknown, Undamaged, slightly damaged, Damaged} Є [0, 1]
SourceOfImpact Є {SourceType1, SourceType2, SourceUnknown} Є [0, 1]
Fig. 5.17 CDISI fuzzy system model
3. Fuzzification: It maps observed non-fuzzy input parameters into suitable linguistic
values, which are defined as the labels of fuzzy parameter sets. The linguistic labels
for input parameter Location Index can be seen in Table 5.7. The Near label segments
are shaded grey, Far label segments are white and Faraway label segments are
shaded in gradient in Fig. 5.16. The linguistic labels for input parameters Input
Frequency, average RMS, Std. Deviation, Arms, Amax, Brms, and Bmax can be
132
illustrated in Table 5.8. The transformation of data into linguistic labels and vice-
versa is done with help of equations (5.6) - (5.8) and Table 5.9.
110 if VH
100 x90 if HH
90 x80 if HL
80 x70 if MH
70 x 60 if ML
60 x30 if LH
30 x1 0 if LL
)(Frequency x (5.6)
In equation (5.6) label is allocated to the different values of the input frequency.
These labels are further associated with membership functions from Table 5.9
equations for the different values of the linguistic labels used in the Fuzzy model.
Table 5.7: Linguistic labels for the indexlocation parameter
Table 5.8: Linguistic labels for parameters
Labels LL LH ML MM MH HL HH VH
Range of
value
Low-
Low
Low-
High
Medium-
Low
Medium-
Medium
Medium-
High
High-
Low
High-
High
Very-
High
4. Fuzzy Inference Engine: The major components of this block are:
A rule base: Fuzzy rule can be expressed as:
‗If input1 is A or input2 is B and input3 is C, then output is D‘, where A, B and C
are the input and D is output linguistic label values defined. With some
experimentation, trial-error, past experience, familiarity with the system that is to
be developed the rules are formulated.
Fuzzy rule database: Sets up the relation and defines the membership functions
for each input and output parameter being used by the CDISI fuzzy rules.
Parameter\Labels Near Far Faraway
IndexLocation
Segments
Segments adjacent
to sensor
Segments adjacent sidewise to
the Near section
Rest of the
Segments
133
Reasoning mechanism: This block generates the result by implementing the
inference procedure on the given conditions and the formed rules. Different
reasoning mechanisms can be used in a Fuzzy System to obtain the desired result.
The CDISI results are obtained by aggregating the result of each rule in the fuzzy
rule base.
5. Defuzzification: This component takes inputs as aggregated fuzzy dataset the result of
fuzzy inference engine, and maps it to a nonfuzzy output value for the ‗Degree of
Crack‘/‗Nature of Plate‘ and ‗Source of Impact‘ outputs. This is the reverse process
of the Fuzzification.
1,1.4]) [0.6,x, trimf(if SrcUnknown
0.9]) 0.5, [1,x, trimf(if SrcType2
0.4]) 0, [-0.4,x, trimf(if SrcType1
)(pactSourceOfIm x
(5.7)
,1.333]) [0.6667,1, trimf(xif Damaged
6667,1])[0.3333,0., trimf(xif gedSlightDama
]) 6670.3333,0.6 [0,, trimf(xif Undamaged
0.3333]) 0, [-0.3333,, trimf(xif UnKnown
)(ateNatureOfPl x
(5.8)
where trimf(x, [a, b, c]) is the triangular function [89] with a, b and c as left feet, right
feet and the peak of triangle.
Fig. 5.18 CDISI Fuzzy Inference System
134
Table 5.9: Linguistic label membership function equations for different parameters
Membership Function Equations Membership Function Equations
)1429.0,0(
1429.0,0
,1429.0/)1429.0(
,0,0
)( LL x
x
x
x
x
2857.0,0
)2857.0,1429.0(),1428.0/()3.0(
)1429.0,0(),1429.0.0/(
1429.0,0
)( LH
x
xx
xx
x
x
4286.0,0
)4286.0,2857.0(),1429.0/()2857.0(
)2857.0,1429.0(),1428.0/()1429.0(
1429.0,0
)( ML
x
xx
xx
x
x
5714.0,0
)5714.0,4286.0(),1428.0/()4286.0(
)4286.0,2857.0(),1429.0/()2857.0(
2857.0,0
)( MM
x
xx
xx
x
x
7143.0,0
)7143.0,5714.0(),1429.0/()5714.0(
)5714.0,4286.0(),1428.0/()4286.0(
4286.0,0
)( MH
x
xx
xx
x
x
8571.0,0
)8571.0,7143.0(),1428.0/()7143.0(
)7143.0,5714.0(),1429.0/()5714.0(
5714.0,0
)( HL
x
xx
xx
x
x
1,0
)1,8571.0(),1429.0/()857.0(
)8571.0,7143.0(),1428.0/()7143.0(
7143.0,0
)( HL
x
xx
xx
x
x
1,0
)1,8571.0(),1429.0/()8571.0(
8571.0,0
)( VH
x
xx
x
x
Taking into consideration the automation of CDISI system for armor plates and the
uncertainties pertaining to these kinds of systems, the fuzzy logic approach [93], [94]
seems to be one of the promising candidates. Fuzzy approach was suggested for this
problem in reference [93].
The CDISI Fuzzy Inference System is multiple inputs multiple output system as shown in
Fig. 5.18, with eight input and two output parameters. The Linguistic labels for the
IndexLocation parameter are tabulated in Table 5.7 and rest of the input parameters in
Table 5.8. The linguistic labels for the output parameters are expressed in equations (5.7)
and (5.8).Table 5.10 shows the labels and range of values for different input parameters.
The membership functions are assigned to each of these parameters. All of the CDISI
135
parameter membership functions are selected triangular-functions after some trial and
error upon trying other membership functions like Gaussian, Trapezoidal, Gaussian bell
and few more. It was observed that triangular function works well with the CDISI Fuzzy
Inference System. Fig. 5.19 shows the triangular membership function for the various
input and output parameters like: AverageRMS, Location NatureOfPlate and
SourceOfImpact.
Table 5.10: Labels for the input function for CDISI fuzzy
(a) (b) (c) (d)
Fig. 5.19 Input/output parameter Membership Functions (a) AverageRMS, (b) Location, (c) NatureOfPlate,
(d) SourceOfImpact
Table 5.11 shows a sample of the rule base, expressing the relationship between the
input and output parameters. If any of the input parameter labels like are ‘true’ for a
certain rule then that rule is said to be activated. About five dozen rules are incorporated
in the CDISI System.
Range
\Label
LL LH ML MM MH HL HH VH
Arms 0.1 –
1.1
1.1 -
1.4
1.4 – 1.7 1.7 – 1.9 1.9 – 2.3 2.3 – 3.5 3.5 -4 >4
Amax 0 - 6.5 6.5 6.5 – 8 8 8 – 10 10 10- 17 >17
Brms 0 – 1.5 1.5 –
2.4
2.4 – 2.9 2.9 2.9 – 3.3 3.3 3.3- 4.0 >4
Bmax 0 – 10 10 10 – 13 13 13 – 15.4 15.4 15.4 - 17 >17
Freq.
(KHz)
1 – 30 30 – 60 60 - 70 70 - 80 80 - 90 90 - 100 100 - 110 >110
Avg.
RMS
volt.
0-0.001 0.001-
0.00199
0.00199-
0.00225
0.00225-
0.00250
0.00250-
0.002971
0.002971-
0.003111
0.003111-
0.004
>0.00
4
Std.
Deviat
ion
≤
0.00003
0.00003
-
0.00003
229
0.00003229-
0.00006229
0.00006229
-0.0001
0.0001-
0.0001889
0.0001889
-0.000199
0.000199-
0.00021
>0.00
021
136
Table 5.11: Sample rule base for the CDISI fuzzy inference system
Fuzzy Logic Toolbox from MATLAB is used to build the CDISI fuzzy Inference
System using Mamdani method [92]. The CDISI Fuzzy Inference System implementation
snapshots can be seen in Fig. 5.20. Fig. 5.20(a) shows the structure of the multiple inputs
multiple outputs (MIMO) CDISI Fuzzy Inference System. This portrays the input and the
output parameters as discussed in section II and III. CDISI Fuzzy System Rule Editor
Window snapshot can be seen in Fig. 5.20(b), which provides an environment to add,
delete and update rules in the rule database.
(a) (b)
Fig. 5.20 CDISI Fuzzy Inference System (a) The FIS- Fuzzy Inference System, (b) The FIS rules
5.4.3 CDISI FPGA Implementation
CDISI System automation is done by rapid prototyping of a chip with the help of
FPGA implementation [95] –[97]. The reference [72] has discussed about the standalone
Rule
No.
Freq Avg.
RMS
Std.
Dev.
Loc. Arms Amax Brms Bmax Nature of
Plate
Impact
Source
1 MM MM MM Far HL HH LH ML Unknown Source-
Type2
5 MM MM MM Far-
away
HL HH MH ML Unknown Source-
Type1
18 MM MM MM Near VH HH ML MH Unknown Source-
Type1
35 HH LL HH Far MM MM MM MM Damaged Source-
Unknown
42 HH HH MM Far MM MM MM MM Undamag
ed
Source-
Unknown
54 MM HH LL Far MM MM MM MM Slightly
Damaged
Source-
Unknown
137
device designed to detect cracks in armor plates. An effort is made to develop a chip
which can detect crack and identify the source of impact on basis of logic used in the
CDISI Fuzzy Inference System discussed in Section IV. FPGA implementation of the
CDISI system is done using Hardware Description Language Verilog with the Xilinx ISE
WebPack [98], SynaptiCAD [99], and ModelSim XE [100] using Spartan 3 FPGA [101].
CDISI FPGA implementation which is a general-purpose, multi-level Programmable
Logic Device supported with advantages like:
1. Flexibility to change rules on the hardware,
2. Program and reprogram using reasonably priced hardware and software on the field,
3. Cheaper option over the respective chip, with respect to the manufacturing cost and
complexity of the chip.
(b) (b)
Fig. 5.21 CDISI system FPGA implementation (a). System design structure (b). RTL schematic
Table 5.12: CDISI FPGA implementation output status code bits
CDISI
output
Nature of Plate Status(2-bit) Source of Impact(1-bit)
Unknown undamaged slightly
damaged
damaged ImpactSource-
One
ImpactSource-
Two
Output-Bus
Code
00 01 10 11 0 1
Numerical
Value
0 1 2 3 0 1
138
Table 5.13: CDISI FPGA implementation input status code bits
Input
Labels
3-bit input Parameters 2-bit input Parameters
LL LH ML MM MH HL HH VH Nea
r
Far Far-
away
Range of
value
Low
-
Low
Low
-
High
Medium
-Low
Medium
-
Medium
Medium
- High
High
-Low
High
-
High
Very
-
High
low mediu
m
high
Input-Bus
Code
000 001 010 011 100 101 110 111 00 01 11
Numerica
l Value
0 1 2 3 4 5 6 7 0 1 3
Fig. 5.21(a) and Fig. 5.21(b) show the structure of CDISI FPGA system and the RTL
schematic respectively. The system has the following 3-bit inputs: Input Frequency,
average RMS, Standard Deviation, Amax, Arms, Bmax and Brms. The input Location
Index is the only 2-bit input parameter. The output is restricted for the experimental
purpose to 1-bit ImpactSource and 2-bit Pltstatus for source of impact and the nature of
plate respectively. The number of bits can be extended further to expand the input and the
output domain.
The status code bits care tabulated in Table 5.6, which show the value of output bus
and the meaning associated with each numerical value result. For example, Pltstatus=11
indicates that the plate is damaged, and ImpactSource=1 indicates that the source of
impact is ImpactSource-Two. The Table 5.13 shows the CDISI FPGA Implementation
input Status Code bits for various 3-bit and 2-bit input parameters. This table has
tabulated the possible input values that can be assigned to different input buses.
CDISI System Technology Schematic can be seen in Fig. 5.22(a), which represents the
design in terms of logic elements optimized to the target device. Fig. 5.22(b) shows the
Detailed CDISI System Register Transfer Level (RTL) schematic of the system
developed. RTL schematic view symbolizes design in terms of macro blocks. Each macro
block has combinatorial logic mapping onto elementary logic function gates.
139
Fig. 5.23(a) shows the result HDL Log of the software simulation using SynaptiCAD
software of the system developed. Fig. 5.23(b) shows the waveform simulation for the
CDISI system. Table14 shows the analysis of CDISI System implementation device
usage. It can be seen that LUT (Lookup table) utilization is 1%. Slice, an elementary
programmable logic block which includes: two 4-input LUTs, two multiplexers,
arithmetic logic unit, and two 1-bit registers has the utilization of 1%. Thus the Table
5.14 shows the minimal device usage for the CDISI System.
(a) (b)
Fig. 5.22 CDISI system (a) Technology schematic, (b) Detailed RTL schematic
(a) (b)
Fig. 5.23 CDISI simulation (a) HDL log, (b) waveform simulation
140
Table 5.14: Analysis of FPGA implementation of CDISI
5.4.4 CDISI System: An Integrated Approach
CDISI System supports an automated and integrated approach towards crack detection
and the impact source identification in ceramic plates. This integrated approach consists
of CDISI Fuzzy Inference System and the CDISI FPGA implementation as shown in Fig.
5.24. The test circuit discussed in section II generates waveforms which can be displayed
on an oscilloscope. The test circuit results are used to extract the data which acts as input
for the CDISI System. The CDISI Fuzzy Inference System generates the result {Pltstatus,
ImpactSource}. CDISI FPGA Implementation utilizes and implements the rule base from
Fuzzy Inference System.
Fig. 5.24 An integrated approach towards CDISI
The Proposed algorithm for an Integrated Approach towards CDISI consists of
following subsystems:
Metric Used Availa
ble
Utiliza
tion
Number of 4 input LUTs 10 3,840 1%
Number of Slices occupied 6 1,920 1%
Additional JTAG gate count for IOBs 912 - -
Number of bonded IOBs: 19 173 10%
Total equivalent gate count for design 66 - -
141
1. CDISI System Test Circuit Parameter Extraction: Extract the parameters from the
results generated by the circuits discussed in section II with the help of DEWESoft
Data acquisition system.
2. CDISI Fuzzy Inference System: Develop CDISI Fuzzy Inference System which
essentially is a multiple-input, multiple-output Fuzzy System, based on the behavior
extracted from the data.
3. CDISI FPGA Implementation: Identify the inputs and outputs for the CDISI chip.
Develop Verilog code for CDISI in ceramic plates on Spartan 3 FPGA. Write a Test-
bench file to simulate and verify the FPGA implementation.
4. Display Output: Nature of Plate (Pltstatus) and Source of Impact (ImpactSource) are
the two outputs displayed by both the Fuzzy and the FPGA implementations.
The detailed proposed algorithm for overall development of CDISI System which
consists of the Fuzzy Inference and FPGA implementation consists of following steps:
1. Acquire sensor A & B waveforms using DEWESoft 7 DAS (Data Acquisition
System) and save them in two data files.
2. Extract the input parameters from the waveform data obtained by the test circuit
discussed in section II.
3. Identify the input and output parameters for CDISI Fuzzy Inference System as seen in
equation (a) and (b).
4. Set the range for the input and output parameters. CDISI parameter range is tabulated
in Table 5.4.
5. Define CDISI fuzzy model using Mamdani type Fuzzy Inference System, considering
absolute values of parameters.
142
6. Fuzzify the input parameters. Map an observed non-fuzzy input space into suitable
linguistic values.
7. Define membership function for each input and output parameter with
experimentation.
8. Develop Fuzzy rule base on the basis of data collected.
9. The result is obtained by aggregating the result of each rule in the fuzzy rule base for
the considered input.
10. Defuzzify the output and map it to nonfuzzy linguistic output values ‗NatureofPlate‘
and ‗SourceOfImpact‘.
11. Identify number of bits required to represent the CDISI system input and output
parameters on a chip, same as identified for the Fuzzy System. Determine the
dimension of the system structure as seen in Fig. 5.17.
12. Develop Verilog Hardware Description Language code for CDISI System for ceramic
plates.
13. Select device as FPGA and assign package pins for CDISI design on FPGA.
14. Generate a netlist PROM file to be downloaded on the Spartan 3 FPGA.
15. Configure the FPGA and program FPGA; verify the design using input output signal
pins/buttons on FPGA.
16. Write a Verilog Test-bench file for software simulation and Verification of the FPGA
implementation.
17. Run the test bench file with help of any SynaptiCAD VeriloggerPro and ModelSim.
143
5.5 Conclusion
The soft computing modeling approach is explored and presented as a candidate for the
detection of cracks in armor plates and the impact source identification. This SC
approach overcomes the human error present in manual method of comparing the
waveforms with that of an undamaged plate and the known sources of impact. In this
chapter fuzzy and NeuroFuzzy approaches are suggested to determine the presence of
cracks in body armor. A new metric of severity of crack has been suggested for the first
time to determine the extent of severity of crack. The value of severity of crack is based
on the membership function whose value lies between 0 and 1. Fuzzy algorithm is based
on Mamdani‘s approach while NeuroFuzzy approach is based on Sugeno approach. The
approach will be useful for reliably assessing the health of armor in the field.The CD and
ISI systems generate acceptable results and needs very little effort as compared to a
conventional mathematical method. The ISI experiment was performed on limited data
and only two sources of impact though had a high correlation to training data. Future
work will involve more data and identification of more number of impact sources to
validate the proposed technique. The FIS identifies whether the source of impact is Steel
or Delrin®. A unified approach for crack detection and the impact source identification is
proposed. Because of the importance of the problem it is important to develop the chip
which can have the algorithm for CD, ISI and CDISI problem implemented. The fuzzy
rule base can be developed in the form of a Verilog code so as to lead to approach of the
FPGA implementation of the suggested technique. The suggested techniques are
implemented using Xilinx‘s Spartan 3 FPGA and ISE WebPACK 9.1i software. The
software simulation and debugging is done by means of SynaptiCAD's Verilog Simulator
144
– VeriLoggerPRO and ModelSim. The proposed FPGA implementation reads the values
of input parameters and displays the nature of plate and also the source of impact. The
entire algorithm has been successfully implemented for CD, ISI and CDISI problem and
can possibly act as a hand held device for the detection of crack and to identify the source
of impact. The current CDISI System can be expanded by inclusion of more parameters
and extended range for the parameters. The suggested procedure can lead to several
other NDT problems of interest in the industry.
145
CHAPTER 6
SUMMARY
Soft computing technique is used to propose solution to various problems convoy of
unmanned vehicle network reliability, sensor networks reliability, crack detection and
impact source identification. These techniques have come forward as good methods to
tackle complicated network and system applications. The report can be summarized
chapter wise as following.
The chapter 2 focuses on the literature review of sensor networks, network reliability
and the NDT techniques. Basic concepts, definitions, some effective reliability
calculation methods and examples are incorporated here for network circuits.
Chapter 3 discussed the Multiple Hops Reliability (MHR) problem of sensor networks.
The packets in sensor network can be beneficially sent through minimum number of hops
rather than all possible hops. It is observed that the Minimum Hops Path (MinHP) and
Minimum Hops cutsets (MinHC) are of importance in determination of reliability and
security of sensor networks. MinHP problem of Sensor Networks determines all possible
paths with minimum number of hops (links) in a sensor network between source and sink
nodes. MinHC problem detect the cutsets with minimum number of links in each term.
Techniques to evaluate MHR, MinHP, MinHC, Approximate terminal and system
reliability algorithms for sensor networks are proposed and explained with illustrative
examples in this chapter.
Chapter 4 proposes a soft computing approach to reliability of a convoy of unmanned
vehicles network. It is considered important to develop the reliability techniques so that a
commander in the battle of field can predict the reliability of the various stages of the
146
movement of the convoy. Commander can then take decisions depending on reliabilities
determined at various places and time. Fuzzy and Boolean algebra techniques are
combined to determine the reliability. The branches and node reliabilities are determined
using soft computing like Fuzzy Logic and terminal reliability is determined using
Boolean algebra techniques. A combined approach of fuzzy and Boolean algebra
techniques as proposed presents an efficient technique for the collaboration and
coordination of the convoy of vehicles. A Fuzzy Reliability model-using MATLAB®
Fuzzy Logic Toolbox is discussed. Some system reliability problems are solved and
presented in this chapter. A hypercube format representation is proposed for the convoy
of unmanned vehicles, and an algorithm is proposed for the same. Hypercube reliability
analysis with proposed algorithm and some examples are included. This Chapter presents
FPGA implementation of reliability circuits for series network, parallel network and
some hypercube networks are resented, discussed and analyzed. This Chapter 5 discusses
the reliability calculations using generalized pipeline array. FPGA and VLSI
implementation of generalized pipeline array is done. The unmanned ground vehicle
network can be portrayed as the network consisting of node itself as another network. In
this scenario if the reliability of overall network has to be calculated, the reliability of
each individual node has to be calculated. Here the node reliability can be calculated in
parallel using the generalized pipeline array. These values can be further used for the
calculation of the overall system reliability of the network of vehicles.
Chapter 5 discusses an application of soft computing in the area of Non-Destructive
Techniques (NDT) like crack detection, crack extent measurement, crack evaluation and
the identification of the impact source causing the damage in metal plates. Soft
147
computing approach for the crack detection and impact source identification is
implemented supported with use of HDL such as Verilog. The analysis and simulation of
the entire circuit model or schematic is done using different software for VLSI circuit
design, implementation, debugging, verification and simulation is presented.
148
CHAPTER 7
CONCLUSION
A soft computing approach using the Fuzzy Logic has emerged as a good candidate to
deal with the problem of:
Sensor network reliability, because of packet communication.
Determination of reliability of convoys of unmanned vehicle network,
Crack detection in metal plates, and
Impact source identification.
Hops are better candidates for efficient implementation. The sensor network reliability
is one of the measures of security. This thesis presents the following algorithms:
Minimum Hop paths (MinHP),
Minimum Hop Cutsets (MinHC),
A novel approximate technique for determination of terminal reliability of a wireless
sensor network between the given source and sink nodes,
An approximate technique for determination of system reliability,
A multiple hops terminal reliability of sensor network algorithm.
Some of the features of these algorithms are:
o Flexibility to update the source node and the sink node by simply changing
the Path vector P.
o Insertion/deletion of a node/link by insertion/deletion of a row/column.
o Simplicity of implementation.
149
Convoy of unmanned vehicle network is represented as a graph with stations as nodes
and branches as the path between the nodes. As the node, branch, terminal and system
reliability is calculated using the fuzzy logic supported by fuzzy rules, they can be
referred to fuzzy reliability. Several conditions as inputs are considered. For Fuzzy
Branch reliability, terrain, obstacle, weather are considered as main parameters, which
will affect the branch reliability. For Fuzzy Node reliability, signal strength, EMC and
mobility are considered as main parameter to affect the node reliability. A procedure for
determining node reliability, branch reliability and terminal reliability has been proposed.
Boolean algebra is used for determining a terminal reliability. This algorithm uses fuzzy
and NeuroFuzzy Logic. The hypercube topology is used to represent the convoy of
unmanned vehicles expressed as a communication network. Thus successful evaluation
of reliability of hypercube essentially evaluates the reliability of the convoy of unmanned
vehicles. The spanning tree method outperforms the traditional method of evaluation of
the reliability of hypercube. FPGA implementation of the fuzzy terminal reliability for
the series and parallel network topologies is done successfully. FPGA implementation of
the fuzzy system reliability for hypercube network topology and fuzzy system reliability
is successfully done with help of Xilinx FPGA Tools. Xilinx ISE WebPack is used to
design and implement fuzzy system reliability on Spartan 3 FPGA using Verilog code.
The simulation of the terminal and system reliability of FPGA is done with help of
ModelSim XE (Xilinx Edition) and SynaptiCAD VeriloggerPro. The results of design,
implementation and simulation of the reliability of convoy of unmanned vehicles is
analyzed and presented.
150
The generalized pipelined array architecture is successfully synthesized, simulated and
implemented on the Xilinx Spartan 3 FPGA. The hardware performance is discussed, and
observations are tabulated. This model is used to calculate the reliability of convoy of
vehicles where each node is a network in itself.
The Fuzzy and NeuroFuzzy approach is recommended for crack detection in the armor
plates. The inputs and outputs for the system are identified and used from the results
appeared in reference [72]. A software implementation is done for the development of the
Fuzzy Inference System for crack detection. These results are used to develop a rule base,
which is used in the formation of FIS. An attempt is made to incorporate the software for
crack detection on a chip, which is prototyped on FPGA board. The implementation
procedure for the crack detection is described and done successfully using Verilog code
on Spartan 3 FPGA board.
The Fuzzy Logic approach was investigated and shown to be a candidate for impact
source identification. A MATLAB® FIS is implemented for the identification of
material of impact source. The FIS identifies whether the source of impact is Steel or
Delrin®. A method for development of a chip for source identification is given. The
inputs and outputs are identified. FPGA implementation for this is done successfully
using Verilog code.
Some novel applications soft computing for the sensor networks, systems are studied and
solutions are proposed. These solutions are supported with the software implementation
of the algorithm with respective FPGA implementations.
151
CHAPTER 8
FUTURE WORK
System reliability evaluation using minimum hops paths and cutsets.
Practical implementation of reliability circuits and NDT
Expanding the problem to other areas of interest like reliability of automobiles and
automobile network.
VLSI chip implementation of the proposed algorithms.
Extending the concepts to other areas of interest such as survivability, complexity and
quality.
Parallel implementation of the proposed procedures so that these procedures can be
implemented on cluster and cloud computing.
Dynamic implementation of reliability of sensor networks.
Determination of percentage error between the exact and approximate methods for very
large networks.
152
APPENDIX A
Abbreviations Used in the Report
Abbreviations Term
BDD Binary decision diagram
CC Chaotic computing
CCN Computer communication network
CDISI Crack detection and impact source identification
CLB Configurable logic block
CT Chaos theory
DCM Digital clock manager
EC Evolutionary computation
EDA Electronic design automation
FBR Fuzzy branch reliability
FIS Fuzzy inference system
FL Fuzzy logic
FLA Fuzzy logic algorithm
FLC Fuzzy logic controller
FLR Fuzzy Link Reliability
FNR Fuzzy node reliability
FPGA Field-programmable gate array
FS Fuzzy systems
FSR Fuzzy system reliability
FTR Fuzzy terminal reliability
153
GA Genetic algorithms
HC Hard computing
HDL Hardware description language
IOB Input/output block
ISI Impact source identification
LUT Look-up table
MaxHP Maximum hops path
MHP Multiple hops path
MHTR Multiple hop terminal reliability
MinHC Minimum hops cutsets
MinHP Minimum hops path
MinHR Minimum hops reliability
MinHTR Minimum hops terminal reliability
MIQ Machine intelligence quotient
ML Machine learning
NC Neural computing
NDT Non-destructive techniques
NFS Neuro fuzzy system
NN Neural network
NSPN Non-series parallel network
OBDD Ordered binary decision diagram
PIP Programmable interconnect point
PLD Programmable logic device
154
PR Probabilistic reasoning
PZT Piezoelectric lead zirconate titanate
SC Soft computing
SN Sensor network
SPN Series parallel network
TPR Terminal pair reliability
TR Terminal reliability
UGVR Unmanned ground vehicle reliability
VLSI Very large scale integration
WSN Wireless sensor network
155
APPENDIX B
Data File for captured Impact Waveforms.
INDEX A-RMS A-MEAN A-MEDIAN A-MODE A-MAX A-FFT B-RMS B-MEAN B-MEDIAN B-MODE B-MAX B-FFT OUTPUT
(0,0) 2.853457 -0.14467 -0.20569 0.089661 17.63706 0.550063 2.232264 0.070128 0.0966 -0.23224 11.12996 -0.5005 Steel
(0,0) 2.12684 -0.04041 0.402387 -1.36973 10.24457 0.506629 1.197423 0.035839 -0.15435 -0.11974 5.262808 -0.50915 Delrin®
(0,1) 2.625784 -0.10151 0.098347 0.506629 14.74435 0.506629 2.556979 -0.02271 -0.06782 -0.76011 12.49723 -0.5005 Steel
(0,1) 1.90866 -0.03329 0.358952 0.367639 8.611444 0.506629 2.448746 0.016999 0.243712 0.001411 9.304045 0.50332 Delrin®
(0,2) 2.786107 -0.09544 0.202589 0.402387 16.05606 0.506629 2.995505 -0.05068 0.113908 -17.6866 10.78381 0.537935 Steel
(0,2) 1.854013 -0.03527 0.367639 0.367639 8.029426 0.515315 2.875283 0.035245 0.451399 -0.68223 8.101193 0.50332 Delrin®
(0,3) 2.703809 -0.04608 -0.0059 0.689052 15.73465 -0.52711 3.831043 0.381775 0.131215 -17.6866 17.74997 0.520628 Steel
(0,3) 2.110172 -0.01396 -0.44024 -1.1873 12.96355 -0.50104 3.070854 0.11412 0.312941 -17.6866 9.529039 0.511974 Delrin®
(1,0) 2.005689 -0.09951 0.072287 -0.55317 8.342152 -0.50104 2.187488 -0.01156 -0.11109 -0.73415 9.892491 0.537935 Steel
(1,0) 2.874385 -0.02179 0.133095 0.020166 9.888408 0.506629 1.603892 0.012873 -0.26685 -0.82934 8.300226 -0.5005 Delrin®
(1,1) 1.676259 -0.04012 -0.04064 0.3937 8.724373 -0.50104 1.573216 -0.0493 -0.02455 0.511974 6.34451 -0.5005 Steel
(1,1) 2.009339 -0.06173 0.028853 0.202589 6.830643 -0.50973 1.532659 -0.05534 -0.11109 -0.48319 8.568488 -0.50915 Delrin®
(1,2) 1.364033 -0.22585 -0.05802 -0.15357 4.832671 0.654305 2.122266 -0.10742 -0.06782 0.840811 9.174241 -0.5005 Steel
(1,2) 1.409268 0.04077 -0.10145 -0.62266 5.866405 -0.50973 2.107622 0.023921 0.105254 0.235058 8.040618 -0.5005 Delrin®
(1,3) 1.84302 -0.02824 -0.07539 -0.07539 10.27063 0.506629 2.782996 -0.12632 -0.11109 -0.46588 10.46363 -0.5005 Steel
(1,3) 1.506111 0.009663 -0.10145 -0.10145 7.681953 -0.50973 3.466485 0.095551 0.312941 0.581203 9.399235 0.50332 Delrin®
(2,0) 3.196053 -0.11055 -0.04064 -0.30993 17.02899 -0.50104 3.197639 0.013569 0.018718 -0.76876 17.08364 0.511974 Steel
(2,0) 4.061507 0.308466 0.219963 -17.7097 15.52616 0.506629 2.745315 -0.04166 -0.36204 1.559061 13.04241 -0.5005 Delrin®
(2,1) 2.037907 0.004193 0.167842 -0.9267 8.038113 -0.51842 1.761954 -0.08027 -0.11974 -0.12839 9.191549 0.650432 Steel
(2,1) 2.866071 0.050799 0.107034 -0.67478 11.7387 -0.50104 1.23982 -0.00197 -0.0332 -0.18032 5.574338 -0.5005 Delrin®
(2,2) 1.214743 0.009582 0.03754 0.054913 5.258326 0.515315 2.696384 -0.07744 -0.13705 0.442745 14.13276 -0.5005 Steel
(2,2) 1.034875 0.03807 -0.02327 -0.08408 4.198533 -0.50973 1.96891 -0.00735 0.027372 -0.57838 7.045452 -0.50915 Delrin®
(2,3) 1.993676 -0.05754 -0.04933 -0.64003 10.10558 0.506629 3.392241 -0.01939 -0.13705 -17.6866 17.74997 -0.5005 Steel
(2,3) 1.569075 -0.00172 0.011479 -0.90933 6.995693 0.515315 4.025684 0.23467 0.200444 -17.6866 15.24908 0.50332 Delrin®
(3,0) 2.042179 0.020811 0.298145 0.58481 6.517917 0.515315 1.195682 -0.09605 -0.09378 -0.10243 5.74741 -0.51781 Steel
(3,0) 2.442594 0.067239 0.193903 -0.18832 11.0177 0.506629 1.271079 -0.0109 -0.0159 -0.21493 3.739772 0.50332 Delrin®
(3,1) 2.328408 0.026579 0.107034 -0.01458 8.316091 0.532689 2.34575 -0.12826 -0.04186 -0.89857 9.130973 -0.51781 Steel
(3,1) 2.777088 0.028069 0.454508 0.619557 9.905782 0.506629 2.584544 0.009786 0.209097 -1.2101 9.918452 0.511974 Delrin®
(3,2) 1.685406 -0.00442 0.159155 0.341579 6.109636 0.515315 2.451635 -0.14123 -0.11974 -1.16683 10.37709 0.555242 Steel
(3,2) 2.226247 -0.03299 -0.01458 0.03754 7.212864 0.506629 3.210857 -0.07702 -0.1457 -17.6866 9.269431 0.50332 Delrin®
(3,3) 1.549162 -0.02246 0.0636 0.402387 7.74276 -0.53579 2.293778 -0.12116 -0.1457 -0.17166 11.104 0.581203 Steel
(3,3) 2.083231 -0.10249 -0.0059 -0.43155 5.82297 0.515315 2.387345 0.088187 0.200444 -1.25336 6.950263 0.50332 Delrin®
156
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ABSTRACT
SOFT COMPUTING TO SENSOR NETWORK
RELIABILITY, SYSTEMS AND THEIR FPGA
IMPLEMENTATION
by
ARATI M. DIXIT
December 2010
Advisor: Dr. Harpreet Singh
Major: Computer Engineering
Degree: Doctor of Philosophy
Soft Computing(SC) has emerged as an effective candidate to deal with complex
problems like unmanned Ground Vehicles Reliability(UGVR), Crack Detection and
Impact Source Identification (CDISI) where there is lack of precision, certainty and
complete truth. This dissertation describes some novel applications of SC in area of
sensor networks (SN) and systems with their FPGA implementation. With an increased
importance of security issues, it has become critical to determine reliability of SN. As
number of sensor nodes is fairly large in SN, it‘s rather impractical to adopt traditional
reliability evaluation methods. The minimum number of communication hops utilizing
least number of links rather than all possible hops plays a significant role in network
security and reliability. The Minimum Hops Path(MinHP) takes minimum number of
links to communicate between the source and the sink node. The Minimum Hops
Cutsets(MinHC) is the cutset with minimum number of links in each of the cutset terms.
An efficient but approximate Minimum Hop Terminal Reliability scheme that utilizes
168
MinHP and MinHC is proposed. The proposed approximate Min-Max system reliability
algorithm for SN outperforms traditional algorithms. These algorithms are shown to
provide reasonably accurate results with significant reduction in number of computations.
The SN has wide range of military and commercial applications, with UGVR analysis,
CDISI as some of the SN and system applications considered in this thesis. The convoy
of unmanned vehicles is portrayed as a network, with stations as nodes and links as
communication paths between them. The UGVR is evaluated using graph theoretic
approaches like spanning tree and BDD, supported by Fuzzy and Neuro-Fuzzy
techniques for predicting node and link reliability. The UGVR is simulated with some
existing data. Further this network is expanded with each node being network in itself.
The FPGA implementation of some standard networks reliability is done. The Fuzzy and
NeuroFuzzy CDISI system proposed is implemented on FPGA with objective to fit it in a
handheld device. The validation of proposed models was done using Xilinx‘s Spartan-3
FPGA, ModelSim-XE and SynaptiCAD-VeriLoggerPRO. It is hoped that proposed
techniques will go a long way in finding applications in SN areas.
169
AUTOBIOGRAPHICAL STATEMENT
Arati M. Dixit
Education:
2007: The Certificate in Scientific Computing Program,
Scientific Computing Program, Wayne State University, USA
1999: Master of Technology in Computer Science and Engineering.
Indian Institute of Technology, Powai, Mumbai, INDIA
1994: Bachelors of Engineering in Computer Science and Engineering.
S.R.E.S. College of Engineering, Kopargaon, University of Pune, INDIA.
Awards and Achievements:
2010 Summer Dissertation Fellowship
Graduate Student Professional Travel Award: The SPIE Defense, Security, and
Sensing Conference, April 2010
Travel Award: The 2009 International Conference on Artificial Intelligence
(ICAI'09), July 2009
Andrzej Olbrot Travel Award for Excellence in Graduate Student Research, 2009
Thomas C. Rumble Fellowship, ECE, Wayne State University: 2008- 2009
Graduate Teaching Assistant, ECE, Wayne State University: Fall 07 – Winter 08
Instructional Assistant, ECE Wayne State University: Summer 2007
IGERT NSF National Science Fellow: January 2005 - May 2007
Graduate Teaching Assistant, ECE Wayne State University: Fall 2004
Graduate Teaching Assistant, Computer Science & Engg. Department, Indian
Institute of Technology, Powai, Mumbai, July 1997- January 1999
Number of Referred International Conference, Journal, Electronic letter
Publications:
o Submitted:24 Accepted: 17 Waiting for decision: 6
Academic Experience:
Graduate Teaching Assistant, ECE Wayne State University: 2007–2008
Instructional Assistant, ECE Wayne State University: Summer2007
Graduate Teaching Assistant, ECE Wayne State University: Fall 2004
Adjunct Faculty, Dept of Computer & Information Science, University of
Michigan, Dearborn.
o Period: Jan 2001 to Jun 2002
Adjunct Faculty, Dept. of Computer & Information Systems, Univ. of Detroit
Mercy, Detroit o Period: Jan 2001 to April 2001
GTA, Computer Science & Engg. Dept, IIT, Bombay: July 97- Jan 99.
Lecturer, Dept of Computer Science and Engg., S.E.S. COE, Univ. of Poona, India
o Period: July 94 to July 97
Instructor, Pratik Computer Systems, Kopargaon, India
o Period: Jan 93 to Jul 97
