Claudio Coelho et al- Fuzzy Alarm System for Laser Gyroscopes Degradation

8/3/2019 Claudio Coelho et al- Fuzzy Alarm System for Laser Gyroscopes Degradation

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Intelligent Automation and Soft Computing, Vol. 14, No. 3, pp. 351-365, 2008

Copyright 2008, TSI Press

Printed in the USA. All rights reserved

351

FUZZY ALARM SYSTEM FOR LASER

GYROSCOPES DEGRADATION

CLUDIO COELHO,PAULO SERRA,RITA A.RIBEIROUNINOVA CA3

Campus Universidade Nova Lisboa/FCT

2829-516 Caparica, Portugal

[email protected]

R.A.MARQUES PEREIRADipartimento di Informatica e Studi Aziendali

Universit di Trento

Via Inama 5, 38100 Trento, Italy

[email protected]

ANGELA DIETZ,ALESSANDRO DONATIEuropean Space Agency ESA/ ESOC

Robert-Bosch-Str. 5

D-64293 Darmstadt, Germany

[email protected]

ABSTRACTROSETTA is a European Space Agency (ESA) unmanned space probelaunched in 2004 to study the comet 67P/Churyumov-Gerasimenko. This paper discusses

the design of a fuzzy alarm system regarding the intensity degradation of ROSETTAs

laser gyroscopes. The fuzzy alarm system proposed makes use of a novel fuzzy inference

scheme, incorporating the technique of Choquet integration. This research work was donein the scope of an ESA project, as a proof-of-concept for a new fuzzy inference scheme.

Key Words: Fuzzy inference systems, monitoring and alarm systems, aggregationoperators.

1. INTRODUCTION

The ROSETTA equipment includes three Inertial Measurement Packages (IMP), each

containing three laser gyroscopes and three accelerometers [1]. The Laser Intensities (LI) of the

gyroscopes have been showing a significant degradation over time. This degradation is predicted

by the manufacturers and is considered nominal as long as it keeps within a certain range of

values. However, it is important to detect whether the LI values drop more than expected and

when the degradation reaches such levels that the laser might extinguish itself, implying that the

equipment is no longer functional.The aim of this paper is to discuss the design of a fuzzy alarm system to assist human

operators in monitoring the intensity degradation of ROSETTAs laser gyroscopes. This alarm


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352 Intelligent Automation and Soft Computing

system was developed within the scope of a European Space Agency (ESA) financed project [2],

as a proof-of-concept. The main goal of the project was to define a novel inference scheme [3] [4]

by integrating the Choquet integral [5], [6], [7] in a Takagi-Sugeno-Kang type of rule-based fuzzy

inference scheme [8], for handling possible existing synergies between rules. Here, we focus on

the modeling aspects of constructing the fuzzy alarm system to monitor the degradation of the

Rosetta gyroscopes laser intensities.

The motivations for this work are two-folded. First, Fuzzy Logic has been successfullyapplied in many different fault detection problems and diagnosis technical processes [9] [10].

However, most of these applications are related with decision making (automatic control

processes) and not with decision support (human control processes). Further, there is very little

work on the application of fuzzy inference tools in Space monitoring problems to assist human

operators in the task of mission control processes [11] [12]. Hence, here we focus on a Space

monitoring application designed for supporting human operators. Second, we propose to use a

new inference scheme, based in the TSK model [8], which has the advantage of dealing with

existing synergies between the rules. Classical fuzzy inference schemes [8,14,15] assume that all

rules are independent of each other and this can lead to biased results when there exist correlations

between the rules. Further, the new inference scheme provides more robust outputs since

complementarities between rules are given negative correlation weights while redundancies are

given positive correlation weights.

The paper is structured as follows. The first section is dedicated to introducing the problem.The second section presents the background concepts and the fuzzy inference scheme used. The

third section discusses the problem analysis and the pre-processing to build the alarm system. The

forth, fifth and sixth sections describe the main components of the alarm system: the definition of

the fuzzy input variables, the definition of the output variable, and the construction of the rule

base. The seventh section illustrative results, obtained with the alarm system proposed. Section

eight presents the conclusions.

2. BACKGROUND

2.1 Fuzzy Inference Systems

Fuzzy Inference Systems (FIS), sometimes also called fuzzy expert systems or fuzzy

knowledge based systems (see for example [13]), express their knowledge through a series of set-

level inferences using a number of conditional and unconditional fuzzy rules. Basically, the fuzzy

variables define the semantics of the problem, while the rules define the way knowledge is

structured, and the inference scheme constitutes the reasoning process towards the result.

A typical FIS [8 [14] [15] includes the following tasks: a) fuzzification of the input variables;

b) definition of the output variables; c) definition of the rule base; d) and selection of the inference

scheme (operators, implication method and aggregation process). In some inference schemes, as

for example the Mamdani model, a defuzzification method is also required to transform the fuzzy

output into a crisp output. Here, because we follow the Takagi-Sugeno-Kang model [8], which

comprises fuzzy inputs but crisp outputs, we will not discuss defuzzification methods.

The fuzzification of the inputs (a) implies their definition as fuzzy linguistic variables [16].

Formally, a linguistic variable is characterized by the five-tuple (X,T,U,G,M) where: X is the

name of the linguistic variable; T is the set of linguistic terms, in which the linguistic variables X

take values; U is the actual physical domain in which the linguistic variable X takes its crisp

values; G is a syntactic rule which creates the terms in the term set; M is a semantic rule that

relates each label in T with a fuzzy set in U. For example, height={short, average, tall} is a

linguistic variable with three terms, where each term is represented by a fuzzy set.


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Fuzzy Alarm System for Laser Gyroscopes Degradation 353

The definition of the outputs (b) depends on the FIS model selected. We can divide it in two

main classes [8]: Mamdani type which uses fuzzy outputs and Takagi-Sugeno-Kang type

(henceforth only called TSK) which uses crisp outputs. The Mamdani consequents are usually

represented by linguistic variables while the TSK consequents are usually crisp functions of the

inputs. In our application we only use constants for the function outputs (TSK model).

The ule base (c) is usually defined by the developer in close collaboration with the domain

expert. The domain expert is essential for the definition of the rule set, because rules representexisting relations between input variables and the desired conclusion for that relation. A fuzzy rule

is usually defined as

YTHENAisXANDANDAisXIF mm...11 (1)

where kX are the variables considered, kA are the fuzzy terms of linguistic variables

representing the variables considered and Y is either a fuzzy term of a fuzzy output (Mamdani

type model) or a crisp function (TSK type model). For example, for a TSK model, the rule IF

Service is goodTHEN Tip=20 expresses that if the service in a restaurant is good(where goodis

a fuzzy set) the tip should be 20% of the meal cost. For a Mamdani model, the rule IF Service is

goodTHEN Tip=high expresses that if service is good the tip should be high (where high is a

fuzzy term of the linguistic output Tip).

Finally we must address the inference scheme (d). This process has two phases: the individual

rule implication, which applies to all rules of the rule-set; and the rule aggregation process, toreach a final result for the FIS. There are many implication operators to derive the conclusion for

each rule [13][15]. However, the most used for FIS implication are, as mentioned before, the

Mamdani implication operator (min) and the TSK implication operator (function of the inputs).

The aggregation process for all the rule implication values depends, again, on the inference

scheme selected. The Mamdani scheme proposes the max operator (other operators could be used

[13][15]) while the TSK model uses a weighted average, where the weights are the (normalized)

firing levels of each of the various rules [8].

In this work we use a different inference scheme, which was devised for the ESA project. The

next sub-section overviews this novel inference scheme.

2.2 New Choquet-TSK inference schemeSeveral concepts are important to understand the use of the Choquet integral [5], [6], [7] as an

aggregation operator in the context of fuzzy inference systems. The first important definition isthat of a fuzzy measure. Let { }n,...,,21= be a set of interacting criteria and let )( denotethe power set of . A mapping ( ) [ ]1,0: N is called a fuzzy measure [5] [6], if

( ) ( ) 1,0 == N and NST implies ( ) ( )ST , where ST, are two subsets of set .The latter requirement is known as the monotonicity condition.

The difference between fuzzy measures and classical probability measures is the fact that in

the former the additive property, i.e. ( ) ( ) ( )STST += whenever = ST , of probabilitymeasures is relaxed, originating the monotonicity condition as a weaker requirement.

The Choquet integral associated with a fuzzy measure , originally introduced by Gustave

Choquet in the context of capacity theory [17], can be defined as follows,

( ) ( )( ) ( )( )( ) ( )= + n

iiiin xAAxxC 1 11,...,

, where ( ) ( ) ( ) ( ){ }niiA i ...,,1, += and=+ )1(nA

(2)


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The index notation ( ) indicates that the ix elements are ordered so that )n()( x...x 1 .

The Choquet integral with respect to an additive fuzzy measure reduces to a weighted

average, whose weights are given by the ( )i values. In fact, additivity implies

( )( ) ( ) ( ) ( )n...iiA i ++++= 1 and therefore

( ) ( )( ) ( )( )[ ] ( ) ( ) ( )ixiixAAx,...,x ni

n

iiinC ==

==+

1111

(3)

We conclude that the Choquet integral generalizes the weighted averaging operator.

In the new inference scheme we begin by considering a correlation matrix ijcC= with a

null main diagonal and a set of normalized weights 021 nw...,,w,w , 11

==

n

iiw , representing the

normalized values of the rule firing levels. On the basis of these values, we define a 2-additive

[16] Choquet measure [ ]102 ,: N in the following way: given a subset NS of criteria, thevalue )S( is defined as the sum of the singlets and doublets contained in that subset S ,

( ){ } { }

+=

Sj,i

jiji

Si

i /wcw/wS , where the overall normalization factor is the sum of

all singlets and doublets in the set N,{ } { }

+=Nj,i

jijiNi

i wcww . For an analogous

construction of the fuzzy measure in the context of Saatys A.H.P., see [18].

As mentioned before, the new inference scheme used in the alarm system is based on the

TSK-type model (i.e. fuzzy inputs, crisp output), but for the aggregation process we used a novel

method [3] [4]. This method is an extension of the TSK weighted average, by making use of the

Choquet integral approach described above [5,6,7] and using correlation matrices to determine the

combined weights between any 2 rules. With this integration we are able to handle synergies

between rules, where: complementarities between rules are given by negative correlation values;

and redundancies between rules are given by positive correlation values. Figure 1 presents the

architecture.

Another advantage of the Choquet-TSK inference scheme is that similarities between the

membership functions of antecedents relating to the same input variable (e.g. large overlap of

membership functions pertaining to the same linguistic variable) will imply significant

correlations between rule triggering patterns; hence it may bias the results when using the classical

TSK scheme. More details about the new inference scheme can be found in [4].

In Figure 1 above, ijii c,y, are respectively the firing level for rule i, the implication result

for rule i, and the correlation value (see [3][4]) between rule i and rulej. These values are then

used as parameters of the Choquet integral, which determines the crisp output of our FIS.

In summary, the steps of the new inference scheme are (details about the algorithm can be

seen in [3] [4]):

1. Input vectors are randomly generated and the corresponding firing levels for each rule are

computed;


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WeightedAverage

FuzzifierData

Output

Rule Base

FIS

Rule Base

Random Data

CorrelationMatrix

Correlation Module

mm

mm

xcxccyTHEN

AisxANDANDAisxIFR

11

11

10

1

1111

1 ...:

+

mnmnnn

nmm

nn

xcxccyTHEN

AisxANDANDAisxIFR

+11011 ...:

11 ,y

nn y,

ChoquetIntegral

ijc

WeightedAverage

FuzzifierData

Output

Rule Base

FIS

Rule Base

Random Data

CorrelationMatrix

Correlation Module

mm

mm

xcxccyTHEN

AisxANDANDAisxIFR

11

11

10

1

1111

1 ...:

+

mnmnnn

nmm

nn

xcxccyTHEN

AisxANDANDAisxIFR

+11011 ...:

11 ,y

nn y,

ChoquetIntegral

ijc

Figure 1. New Choquet-TSK inference scheme architecture.

2. The sample of firing levels is then used to obtain a correlation matrix associated with the

set of rules;

3. For each input vector the firing level and respective consequent for all rules are calculated.

These values together with the correlation matrix values are used to create the set up

parameters of the Choquet integral;

4. Finally, the parameters are aggregated using the Choquet integral to determine the crisp FISoutput.

3. ROSETTA PROBLEM ANALYSIS AND PRE-PROCESSING

ESA provided a report [1] describing the trend analysis for the health status of the Rosetta

laser gyroscopes. We started by analyzing this report to identify the inputs of the system and we

immediately detected some problems regarding the temperature influence on the laser intensities,

as well as problems in the expected degradation curve provided by the manufacturer.

In order to solve the problems detected, we performed a pre-processing on the initial data,

which included: definition of a new expected degradation curve; cleaning of peaks found on each

LI by the influence of other IMP being turned on or off; standardization of the actual real

input data, to be used by the system, using a simple JAVA application developed specifically for

this purpose.


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3.1 Laser Intensity Degradation CurveThe manufacturer only provided a general qualitative plot showing how the gyroscope IMP

degradation is expected to occur [1]. The expected degradation curve lifespan for each IMP is 7

years.

In addition, since most used IMPs are expected to show more degradation than the least used

ones we defined an expected degradation curve for each gyroscope, following ESA expert advice

on the respective degradation.Since we only had a qualitative degradation curve and knowledge about the most used IMPs,

we had to construct an approximate degradation curve for each IMP. To this effect we performed

a polynomial interpolation of the manufacturer data to be able to have a workable degradation

curve to be used for monitoring purposes. The interpolation was made by minimizing the mean

squared difference between the polynomial and the manufacturer data. The first LI obtained from

this polynomial (for 0=x ) is 1 to facilitate the scaling when this general curve is fitted to the

available data. The actual polynomial expression obtained was:

00001066800501000760 23 .x.x.x.)x(P ++= (4)

where x represents the time in years and the polynomial coefficients were determined by

minimizing the mean squared error between the data and the polynomial. In section 4.1. more

details about the degradation curve and how the LI input variable is fuzzified will be provided.

In addition, it should be noted that the degradation curves can be adapted during the missionto improve the alarm system robustness. Further, these curves will always depend on the

equipment used. However, these issues are out of scope in this work.

3.2 Temperature Influence on Laser IntensityThe laser Intensity (LI) values are temperature dependent [1] and it is estimated that for each

temperature variation of one degree Celsius leads to a change in average LI of approximately

0.01A. Hence, the input variable LI provides a direct measure of the temperature. However,variation over time, as noted in [1], also shows that there is some influence of the temperature

over the LI because when one IMP is turned ON or OFF the overall temperature changes and

the other IMPs LI are affected.

In order to remove the undesired temperatures influence from other IMPs on each LI curve,

it was necessary to transform the original LI values. This was achieved by considering the

difference between the actual temperature of an IMP and a reference temperature (TR). Thereference temperatures correspond to the average IMP temperatures for every number of active

IMP, which in our case are for IMP1 (17.977A) and for IMP2 (23.305 A).Since the three IMP were never simultaneously ON or OFF during the time period

considered, the reference temperatures were only calculated when one or two IMP are being used

at the same time. For every LI data, CBA TTT ,, represent the differences between the currenttemperatures of each IMP (A, B and C) and the corresponding reference temperature (for IMP

switched ON at the time). The following equation shows how this influence was removed from

the original LI:

CCBBAAoldnew

TTTLILI +++= (5)

where LInew

and LIold

are transformed values and original values of the LI, respectively;

CBA ,, are constants that represent the intensity of the influence that the temperature has on

each IMP LI. These constants were determined by trial and error with the objective of removing

the peaks from the LI input data (Figure 3). The constants used are shown in Table I.


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Table I Constants for transformation

IMP A IMP B IMP C

A -0.002 0 0.0035

B -0.002 0.005 0

C -0.001 0 0.006

One aspect that should be noted is that IMP A is affected in a different way by the

temperature. While with IMP B and C a rise in temperature increases the value of the LI, IMP A

shows the opposite behavior, this is why the A , B and C values for IMP A are negative.

Figure 2 depicts the stabilized data for the initial time series, where it can be observed that there

are no abrupt changes and the decreasing slope for each IMP is quite smooth.

1

1,1

1,2

1,3

1,4

1,5

1,6

3-Fev-04

5-Mar-04

5-Abr-04

6-Mai-04

6-Jun-04

7-Jul-04

7-Ago-04

7-Set-04

8-Out-04

8-Nov-04

9-Dez-04

9-Jan-05

9-Fev-05

12-Mar-05

12-Abr-05

13-Mai-05

Time

AverageLaserIntens

ity(uA)

IMP A x 1 IMP A x 2 IMP A x 3 IMP B x 1 IMP B x 2

IMP B x 3 IMP C x 1 IMP C x 2 IMP C x 3

Figure 2. Stabilized LI curves.

3.3 Standardization of Real DataAnother important aspect detected in [1] was that the already existing real data for an IMP

(one year of data available) showed a much larger degradation than what was expected, based on

the manufacturer degradation curve. However, since the slope of this degradation was decreasing,

we assumed, as suggested by ESA, that the LI would start performing more like the expected

degradation curve in the near future. Taking that in consideration, we scaled the expected

degradation in order to coincide with the last observed LI data.

Another important aspect in the standardization of the input data is related with ensuring the

consistency of input data. To this purpose we developed a simple JAVA application that performs

the following tasks: a) cleaning of duplicate entries in the files to consider just one entry per day;

b) all files were checked and if gaps were detected the previous value was considered; c) when a

Imp is switched off, instead of considering LI=0 we use the last value occurred, in order to avoid

affecting the other IMP.


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4. FUZZIFICATION OF INPUT VARIABLES

The identified input variables [1] were the LI and the Deviation from the expected

degradation curve. For each input variable we defined the respective linguistic variables, as

follows.

4.1 Laser IntensitiesThe LI of each gyroscope even within the same IMP has a different initial value and a

different behaviour. However, in general, each assumes values high, medium and low.

Figure 3 summarizes the general construction of the LI linguistic variables (left side) and their

correspondence with the stages of life for the expected degradation LI curve.

Figure 3. Stages of life and LI.

A LI is considered high while in Beginning of Life (BOL) and Middle of Life (MOL)

stages. When Rosetta approaches the End of Life (EOL) phase the LI will begin to drop and it is

considered medium. In the extreme of EOL, LI is considered to be low. Values classified as

low were those where the laser might extinguish itself (i.e. below the threshold of 0.7 a value

defined by ESA).Taking the above in consideration, we defined nine linguistic variables for Laser Intensities:

LIA1, LIA2, LIA3, LIB1, LIB2, LIB3, LIC1, LIC2 and LIC3; where A, B and C corresponds to

the three different IMP and 1, 2 and 3 corresponds to each gyroscope on the IMP. Figure 4 a)

shows the three fuzzy terms considered for LIA1 as well as for variable Deviation (explained in

the next sub-section). All the other LI have similar shapes, for the three fuzzy terms, and their

limiting parameters and ranges are described in Table II.

Assuming that the real degradation is comparable to the expected degradation curve, the LI

value should not exceed the maximum value on the expected degradation curve. Taking this in

consideration, the value 1.6 was chosen to be the highest allowed value for all LIs. The lowest

allowed value is 0, because this is the lowest value that the LI may assume. These assumptions set

the range to [0, 1.6], as indicated in Table II.

The variable represents the value of the expected degradation curves local minimum.

Table III contains the values of used for each gyroscope; note that all these values werediscussed with the Space expert.


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LIA1 Deviation

a) b)

Figure 4. Input linguistic variables: LI and Deviation.

Table II. Parameters for fuzzy set definitions of input variable Deviation (Dev) and LI.

GyroscopesA1, A2, A3, B1, B2, B3, C1, C2, C3

big(trapezoidal)

13 17 25 25

small(triangular)

5, 13, 17

acceptable(trapezoidal)

-25, -25, 5, 25

Dev

Range [-25 , 25]

low(trapezoidal)

0, 0, 0.7, (+0.7)/2

medium(triangular)

0.7, (+0.7)/2 ,

high(trapezoidal)

(3+0.7)/4, ,1.6 , 1.6

LI

Range [0 , 1.6]

Table III. Parameters used for calculating fuzzy terms.

Gyroscop A2 A3 B1 B2 B3 C1 C2 C3 A2

Alpha 1.21 1.170 1.241 1.351 1.189 1.065 1.266 1.223 1.154

4.2 DeviationThe linguistic variable Deviation has three terms, for all gyroscopes deviations, as depicted in

Figure 4 b). This variable represents the LI deviation from the expected curve used to measure

the amount of unexpectedness of a given LI.

The fuzzy terms in the linguistic variable Deviation (Figure 4 b) were created taking into

consideration the expert knowledge of ESA on the subject and the parameters used are described

in Table II. Positive deviations from the expected LI curve, i.e. values lower than 5%, (includingnegative values) were considered reasonable and correspond to the term acceptable. Also,

values equal to or higher than 17% are considered big. Finally, medium deviations correspond


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to percentage deviations around 10%. It should be noted that since the values refer to a percentage

there was no need to have different fuzzy sets for each IMP gyroscope.

5. OUTPUT VARIABLES

The alarm levels that were considered for our system are: nominal, notice, danger and

critical (in ascending order in terms of severity). Since we assumed a zero-order Sugeno type

model [8] our outputs are crisp, and in our case we considered simple constants, corresponding tothe respective semantic alarm levels, such as:{0, 0.333, 0.666, 1}. A nominal alarm (consequent

equal to 0) is produced in situations where LI is behaving as expected, i.e. LI high; Notice

alarms (consequent equal to 0.333) are produced when some deviation occurs; when greater

deviations are detected, alongside lower LI values, danger alarms are issued; critical alarms

are produced when the LI reaches low levels, regardless of the level of deviation this is done to

ensure that the operator is warned before the critical 0.7 LI barrier is reached.

6. RULE-BASE

Using the input and output variables described, ten rules were defined for each Laser

Intensity. The rules were defined by the domain expert (ESA) with the help of the developer (the

authors). The complete alarm system, for all three gyroscopes, includes nine sets of rules, one for

each gyroscope and its respective 3 IMPs. Since each of the nine sets has identical rules (only thelabels are different to distinguish the variables) here we present the generic form of the rule-base:

R1. IF Deviation is Acceptable AND LI is Low THEN Alarm is Danger

R2. IF Deviation is Acceptable AND LI is Medium THEN Alarm is Notice

R3. IF Deviation is Acceptable AND LI is High THEN Alarm is Nominal

R4. IF Deviation is Medium AND LI is Low THEN Alarm is Danger

R5. IF Deviation is Medium AND LI is Medium THEN Alarm is Notice

R6. IF Deviation is Medium AND LI is High THEN Alarm is Nominal

R7. IF Deviation is High AND LI is Low THEN Alarm is Critical

R8. IF Deviation is High AND LI is Medium THEN Alarm is Danger

R9. IF Deviation is High AND LI is High THEN Alarm is Danger

R10. IF LI is Low THEN Alarm is Critical

The basic principle of the rule base is that the same deviation represents different degrees of

alarm severity, depending on the stage of life where the IMP is (BOL, MOL or EOL Figure 3).

This correspondence is possible because, as stated before, the values for high, medium and

low for the variable LI were chosen so that the Laser Intensity is always high during BOL and

MOL, medium when it enters EOL and low towards the end of EOL.

The seriousness of each situation, presented in the rule base, can be explained by two main

factors: low laser intensities are always dangerous; and a high deviation indicates that the LI

curve is behaving unexpectedly, both contributing to generating alarms.


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Figure 5. Correlation matrix for Rosetta gyroscope A1

7. RESULTS

The correlation matrix was calculated with 10,000 ramdomly generated values for the

variables. The color scheme is shown on the side of Figure 5, where levels of dark gray represent

highly positive or negative correlations (complementarities or redundancies between rules) and

light gray correspond to weak correlations. For example the value -0.31 in line 8 column 2,

corresponds to a redundancy found between rule 8 and rule 2 (see rule set in section 6), whilevalue 0.76 corresponds to complementarity between rule 10 and rule 4.

Extensive validation tests were performed and showed the system was able to accurately

detect low levels of LI, while taking into account the natural degradation of the gyroscopes. In this

section we only present a sample of results obtained for three representative situations: 1) general

decreasing behavior with lots of noise; 2) abrupt changes in LI; 3) real data set. For the first two

situations simulated data was used and for the third one a real data set was provided by ESA.

1. General behavior with noisy data. Figure 6 depicts two graphs: the top one shows arandomly generated input data and the respective degradation curve; the bottom one shows the

alarms triggered for the tested data.


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Figure 6. Example for general behavior with noisy data.

As can be observed, whenever LI is low and deviation is big (around day 2250, for

example) the system triggers a critical alarm. Conversely, when the LI is high and the

deviation is acceptable the alarm level triggered is nominal (around day 250). In between

these extreme cases, all other types of alarm severities can also be seen in Figure 6.

2. Abrupt changes in LI. Figure 7 shows, again, the sample data tested on top and the alarmstriggered below.

As can be observed in Figure 7, the alarms respond immediately to abrupt changes in LI. For

example, between day 400 and 500 we simulated a situation of continuous critical alarm which

drops immediately to nominal when the LI (day 5001) jumps to near the degradation curve.

3. Real data set. The current real data available for the gyroscopes (around 1 year) did notproduce any severe alarm. The reason for this is that the current telemetry is still within the BOL

(beginning of life phase) and there were no faults detected so far. Figure 8 shows the results forthis test.

To conclude, we should also highlight that we also performed tests comparing Choquet-TSK

inference scheme and the classical TSK. These tests showed that, although the differences

between the two methods were small (correlation matrix Figure 5 shows low correlations), the

new inference scheme was more accurate in terms of reacting earlier to any changes in the

telemetry (i.e. more sensitive to differences from nominal values). This improved accuracy

enables the operators to be warned about possible alarms sooner, which may help taking measures

to prevent damaging the probe. A disadvantage of the Choquet-TSK inference is that it is about 3

times slower, in computational terms, than the classical TSK. Clearly there is a trade-off between

more accuracy of the Choquet-TSK at the expense of more computational time to reach a

conclusion.


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Figure 7. Example for abrupt changes in LI

Figure 8. Example for real LI data (around 310 days).


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8. CONCLUSIONS

In this paper we addressed the construction of a fuzzy inference system for monitoring the

degradation of the Rosettas gyroscopes laser intensities. This system is a fault detection tool able

to provide warnings and alarms, to assist and support the mission control team in their monitoring

tasks.

Then, we discussed the results obtained by the system, which uses a new inference scheme

that takes into account synergies between rules. The tests clearly show that the system performsquite well and is able to trigger all types of alarm levels, depending on possible failures in the

laser intensity of the gyroscopes.

ACKNOWLEDGMENTS

This research was developed under the project New Operators for Monitoring and Diagnosis

Intelligent Systems, contract No: 18989/05/NL/MV, financed by the European Space Agency

(ESA/ESOC).

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ABOUT THE AUTHORS

C. Coelho is a consultant at Solenix GmbH. He earned his degree inInformatics Engineering at the Universidade Nova de Lisboa having

developed his thesis in Data Mining techniques applied to Mission

Operations during his internship at the European Space Agency (ESA).

Eng. C. Coelhos experience has focused mainly on working directly or

indirectly for ESA, namely for the project NOMDIS, later as a Ground

Segment engineer and currently as a contractor. In parallel with his current

work, C. Coelho is currently attending a Masters course in Computer

Sciences specializing on Data Mining and Artificial Intelligence.

P. Serra is currently pursuing an Msc. degree in Mathematics at UtrechtUniversity (Holand) and earned a B.S. in Applied Mathematics at the New

University of Lisbon (PT). He was employed at UNINOVA (PT) were he

developed a novel inference scheme for monitoring systems, that was

applied in the space sector.

R. A. Ribeiro obtained her B.A. (5 years degree) in Management &Business Administration from ISEG (PT) in 1981. She received her M.Sc.

in Information Systems technology from George Washington University

(USA) in 1988 and her PhD in Artificial Intelligence from the University of

Bristol (UK) in 1993. She is the head of research group ComputationalIntelligence at UNINOVA (www.uninova.pt/ca3) and she is an Associate

Professor at Universidade Nova Lisboa. Since 2004 she also works at

HOLOS (PT) as Director of R&D where she leads international projects in

collaboration with UNINOVA. She has been involved in several national

and international research projects and she published more than 90

scientific articles mainly in the topics of fuzzy multicriteria decision

making, fuzzy knowledge-based systems and applied decision support

systems.

R. A. Marques Pereira is Full Professor at the Economics Faculty of theUniversity of Trento, Italy. He obtained the Ph.D. in Mathematical Physics

at Imperial College, University of London. Prof. R. A. Marques Pereiras

current research interests include primarily Decision Theory and

Aggregation Theory, with implications in Fuzzy Set Theory and

Cooperative Game Theory. He has around 15 years of academic experience

and has authored over 70 research publications.


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A. Dietz is a spacecraft operations engineer at the European SpaceOperations Centre (ESOC) in Darmstadt, Germany. She studied physics at

the University of Jena, Germany and specialised in the area of

semiconductors. A. Dietz was employed for two years as part of the Young

Graduate Programme (YGT) of ESA, before being hired as permanent staff

in summer 2007. During her trainee period, she worked in the Flight

Control Team for the interplanetary mission Rosetta. Now she is employedfor the upcoming ESA mission to Mercury, BepiColombo.

A. Donati earned his master degree in electronic engineering from the LaSapienza University of Rome, Italy. He has 18 years of working

experience at the European Space Agency (ESA). He is currently manager

of the Advanced Mission Concepts and Technologies Office at the

European Space Operations Centre of ESA in Darmstadt, Germany, where

he leads the development and validation of prototype applications

implementing innovative operation concepts for the future ESA missions.

Documents

Claudio Coelho et al- Fuzzy Alarm System for Laser Gyroscopes Degradation