R. Orchard et al. (Eds.): IEA/AIE 2004, LNAI 3029, pp. 219-228, 2004.© Springer-Verlag Berlin Heidelberg 2004

An Artificial Immune System for Fault Detection

Jose Aguilar

CEMISID, Dpto. de Computación, Facultad de Ingeniería, Av. Tulio Febres. Universidadde los Andes, Mérida 5101, Venezuela

aguilar@ing.ula.ve

Abstract. The oil well instrumentation generates a set of process variables,which must analyzed by the experts in order to determine the well state. Thatimplicates a highly cognition task where the information generated is very im-portant for maintenance tasks, production control, etc. In other way, the naturalenergy of an oil field can not be enough to lift the fluids. In these case is neces-sary to use another procedure to lift the oil, for example gas. That is an inter-esting case to be modeled by an artificial intelligence technique. Particularly, inthis paper we propose an Artificial Immune System for fault detection in gaslift oil well. Our novel approach inspired by the Immune System allows the ap-plication of a pattern recognition model to perform fault detection. A signifi-cant feature of our approach is its ability to dynamically learning the fluid pat-terns of the ‘self’ and predicting new patterns of the ‘non-self’

1 Introduction

When the natural energy of an oil field is not enough to fluid lift, we need a secondaryrecovery procedure on the well (normally, this is called artificial lift) [2, 12]. For thiscase, we can use different techniques such as artificial lift by gas (ALG) [2, 12]. Theidea of the ALG is to inject gas, and in this way to lighten the fluid. The design of thissystem must be made very carefully. One of the aspects to consider is the fault detection[2, 4]. On the other hand, the immune system is a collection of cells and organs able toperform tasks with characteristics such as pattern recognition, learning, noise tolerance,distributed detection, and memory, with the purpose of maintaining the physical integ-rity of an individual [8, 11, 13, 15, 20]. The problem that the immune system solvesmay be described as the distinction between self and non-self entities, being the selfentities the internal cells and molecules produced by the body, while the non-self enti-ties correspond to potentially harmful foreign entities such as viruses, parasites andbacteria. In recent years, some immunity based computational models have been suc-cessfully developed [3, 4, 6, 8, 9, 10, 14, 15, 17, 18, 21], showing an enormous potentialfor practical applications to other fields such as computer security and pattern recogni-tion [6, 7, 14, 16, 19]. In this paper we discuss an immunocomputational framework todefine a fault detection system for a gas lift oil well. Particularly, we propose a faultdetection system based on immune system ideas for gas lift oil well.

220 J. Aguilar

2 Theoretical Aspects

2.1 Artificial Immune Systems

In the recent years, a novel approach has begun to emerge which is the use of con-cepts from immunology to solve problems [8, 11, 13, 15, 20]. The human immunesystem has a very distributed and adaptive, novel pattern recognition mechanism. Thebody recognizes its own cells from those of the invaders [20]. In general, the purposeof the immune system is to protect the body against infection and includes a set ofmechanisms collectively termed humoral immunity. The immune system uses learn-ing, memory, matching, diversity, distributed control and associative retrieval to solverecognition and classification tasks [20]. In particular, it learns to recognize relevantpatterns, remember patterns that have been seen previously, and uses combinatoricsto construct pattern detectors efficiently. The immune system also remembers suc-cessful responses to invasions and can re-use these responses if similar pathogensinvade in the future. Matching refers to the binding between antibodies and antigens.Diversity refers to the fact that, in order to achieve optimal antigen space coverage,antibody diversity must be encouraged. Cloning and hypermutation maintain thediversity of the antibody set. Distributed control means that there is no central con-troller, rather, the immune system is governed by local interactions between cells andantibodies. The antibodies are present through out the body without any central con-trol and thus defend the body by this interaction in a distributed fashion. These re-markable information-processing abilities of the immune system provide severalimportant inspirations to the field of computation [8, 11, 13, 15, 20].

There are many more features of the immune system, including adaptation, idio-typic network and protection against auto-immune attack. The immune system mustmaintain a diverse repertoire of responses because different pathogens must be elimi-nated in different ways. To achieve this, the immune system constantly creates newtypes of responses. These are subject to selection processes that favour more success-ful responses and ensure that the immune system does not respond to self-proteins.Lymphocytes are subject to two types of selection process. Negative selection, whichoperates on lymphocytes maturing in the thymus (called T-cells), ensures that theselymphocytes do not respond to self-proteins. The second selection process, calledclonal selection, operates on lymphocytes that have matured in the bone marrow(called B-cells). Any B-cell that binds to a pathogen is stimulated to copy itself. Thecopying process is subject to a high probability of errors (“hypermutation”). Thecombination of copying with mutation and selection amounts to an evolutionary algo-rithm that gives rise to B-cells that are increasingly specific to the invading pathogen.

2.2 Gas Lift Well

When we search oil (exploration), we need to use scientifique methods to determinethe subsoil characteristic. In this way, we can know if there is a region with anaccumulation of hydrocarbon. When the hydrocarbon has been detected, the

An Artificial Immune System for Fault Detection 221

exploitation of the oil field starts. It consists in bringing the oil to the surface usingthe natural energy of the oil field or other methods (for example gas artificial lift).Normally, at the beginning the natural energy of the oil field allow the oil lift, butwhen the oil field is old we need to use other techniques: gas artificial lift, mechanicalpump, hydraulics pump, and so forth. The gas artificial lift technique is a technologybased on the injection of gas to allow the fluid of the oil to go to the surface. The gascomes from compression plants, through a gas distribution system. The last part iscomposed by gas multiples (MLAG) and pressure high multiple (MAP). In generalthe gas goes to the oil well, and its injection is controlled by control equipment that isin the surface and subsoil. We need to inject the optimal quantity of gas to obtain theminimal pressure to allow the fluid lift. During the perforation, there is a cementationphase to glue a tube called ‘casing’. Inside of it we include another tube called‘tubing’. This last tube is used to transport the oil from the oil field to the surface [2].With the data from the pressure table of the “Casing” and “Tubing” we can determinethe next information [2, 4]: 1. Surface Restriction: a high pressure of the “Tubing”; 2.Freezing: a fault in the gas injection or small quantity of recovery fluid due to thefreezing of the tubes; 3. Sandy or coat well: not continuos lift; 4. Frequent cycles ofvery fast lift: small pressure of the “Casing”; 5. Far cycles with intermittent lift: smallfall of the pressure of the “Casing”; 6. Valve work bad: fall and climb of the pressureof the “Casing”; 7. Valve does not work: the pressure of the “Casing” is smaller thanthe pressure of operation of the valve.

3 Our Fault Detection System

This section introduces our fault detection system based on the AIS. In essence, theimmune system is used here as inspiration to create an unsupervised machine-learning algorithm. We develop a detection mechanism by maintaining immune cellsthat detect an anomaly. Our approach works in two phases: at the beginning is gener-ated the lymphocyte (outline operation phase). Then, our system is included in theenvironment (inline operation phase) to detect the anomalies.

3.1 Outline Operation Phase

This phase is based on the negative selection algorithm to generate the B and T lym-phocytes, where the cells that reactions with the self organism are eliminated. Themacro-algorithm is: i) Recollection of data in normal state. ii) Pre-processing of data.iii) Representation of data. iv) Save the "self cells". v) Generation of detectors.

Recollection of Data in Normal StateWe use the normal and abnormal condition patterns presented in [2, 4] like referencemodel. Each pattern is a set of registers “Tubing-Casing” (see Figure 1). Some of thediagnostic with these patterns are: i) Norma Operation: small variation of the "Tub-

222 J. Aguilar

ing" and "Casing" pressure (Figure 1.a); ii) Low Production: The "Tubing" pressureincreases and the "Casing" pressure is stabled (Figure 1.b); iii) Emulsion: the "Tub-ing" and "Casing" pressures have small opposite tip; iv) Freezing Gas: high varia-tions of the “Tubing” pressure and the "Casing" pressure is stabled.

1200

120

500

1000

Time (h)

Pressure (LPPC)

a) Normal operation

120

500

1000

2424

Casing

Tubing

Pressure (LPPC)

Time (h)

b) Low production

Fig. 1. Registers of the Tubing-Casing Pressures

For this phase, we have used the normal operation pattern (see Figure 1.a) to build thepatterns to be used by the IAS.

Pre-processing of DataWe have defined a new representation of data, because our system uses informationfrom different wells. In this way, we can unify the scale of the input values into theinterval [-1,1]. We define a matrix (D[PxC]), where P is the number of data of eachpattern (each data is a couple “Casing – Tubing” pressure) and C are the variables (inour case C=2, Casing and Tubing pressures). We use 80% of the normal conditionpatterns for generation of the detectors and 20% to test our system (to detect abnor-mal condition operations). The maximum and minimum value of each variable isdetermined using the set points of them. The parameters α and β define the fractionabove or below of the set point that determine the maximum and minimum of eachvariable, respectively. Then, the transformation for each data of D is:

1minmaxmin2 −

−−×=

ik

ik

ik

ijk

ijk DD (1)

where:

ijkD is the value of the row j, column i, of the pattern k modified. with:

( )Pj K,2,1∈ ; ∈i (1,2); ∈k (1..3)

ikmax is the maximum value of the variable or column i of the pattern k:

An Artificial Immune System for Fault Detection 223

[ ik

iik

ik OpOp ×+= αmax 10 ≤≤ iα ; ∈i (1,2) ; ∈k (1..3) ].

ikmin is the minimum value of the variable or column i of the pattern k:

[ ik

iik

ik OpOp ×−= βmin 10 ≤≤ iβ ; ∈i (1,2) ; ∈k (1..3) ].

ikOp is the set point of the variable i of the pattern k.

The value of α and β for each variable are: αCasing = 0.15 βCasing = 0.15 αTubing = 0.5 βTubing = 0.5

Representation of DataWith D, we have built a new vector of representation of data (X) over each variableusing a sliding window with size ( Pl2 <≤ ) and sliding length ( Pshift <≤1 ).

[ ]121111 Pkkkk DDDX K= is a vector with all the elements of column 1 of Dk,

and [ ]222122 Pkkkk DDDX K= is a vector with all the elements of column 2

of Dk.

We build sliding windows for each vector )2,1(iwith,X ik ∈ . Thus, we generate a

matrix for each variable i of each pattern k where the number of rows represents the

numbers of sliding windows generated from vector ikX :

=

ihk

ik

ik

k

X

XX

iMM

2

1

where: ikM is the matrix of the variable i of the pattern k, and its elements are

row vectors which represent the sliding windows generated from ikX .

ijkX is the window j of the variable i of the pattern k. Where j ∈(1,....,h) and h

is the number of sliding windows generated. The size of each vector ijkX is l.

The window is moved according to the sliding length to build a second window.When the sliding window matrix is built for each variable i of each pattern k, weunify the vectors that represent the same position of each variable for each pattern k.Now this matrix is called V with size h x (2 x l ) for each pattern k. For example, thefirst vector of pattern k is:

[ ]22212121111 lkkk

lkkkk DDDDDDV KK=

224 J. Aguilar

Then we determine the angle between contiguous data, and between the last elementand the first element of this vector. That is, for the first vector of the pattern k wedetermine the angle as:

11

211,1 )tan( k

kk

DDA = (2)

and the last angle is determined as:

( )112

112,1 )tan(

−×× =

lk

k

lk

DDA (3)

Where: gkA is the angle matrix of the pattern k, for the vector g,

( ) )n,...,1(kandh,,1g ∈∈ K

[ ]lgk

gk

gk AAA ×= 2,1, LL

Save the "Self Cells"The "self" is the set of sliding windows represents by the angles obtain previously.This, the self set is represented by the k matrices of the angles of size h x ( 2x l ),where the elements are angles inside of the interval [0, 2xΠ radians].

Generation of DetectorsOur system uses the negative selection algorithm. That is, our AIS uses the self cellssets to produce detectors with the capabilities to discriminate the self and non-self.Each detector is an angle string generated randomly, which is defined as valid if itdoes not mate with the self (we avoid false positive). Now, we are going to presentthe negative selection algorithm used in this work, called the Random generation ofdetectors: We generate vectors (detectors) where theirs components are random an-gles inside of the interval [0, 2xΠ radians]. The number of detectors to generate andthe coupling interval of the angle are given by the users. We search detectors thatdon't active them front the self set [3]. That is, we generate vectors (detectors) with

random angles [ ]lBBBB ×= 2,12,11,11 KK , and we compare them with all strings

of the self set ( [ ]lAAAA ×= 2,12,11,11 KK ). Each component of the detector 1Bhas a sweep 1B∆ , and there is a coupling if:

;l2i1withBBAB 1i,1i,1i,1 ×≤≤∆+≤≤ (4)

If a detector couples a string of the self set, then we eliminated this detector, we in-crease the counter of deleted detector and we generate another detector. We finishwith a given sweep when a given number of detectors deleted is achieved. In this

An Artificial Immune System for Fault Detection 225

case, we increase the angle sweep, we reset the counter of deleted detectors and werestart the random generation of new detectors. When we achieve a number given ofpre-defined detectors, then we stop the procedure of generation of detectors.

3.2 Online Operation Phase

In this phase the immune system must identify the self cells. It is composed by thenext tasks:

Recollection of New DataWe test our system using the patterns of the work [2, 4].

Pre-processing of DataWe use the same procedure of the previous phase.

Representation of DataWe represent the data using vectors build according to sliding windows of size l andthe running length shift for each variable, then we use the same procedure like theprevious phase to obtain vectors with component which are angles inside of the inter-val [0, 2xΠ radians].

Define if the Detectors Generated in the Previous Phase Can Identify or Not ThisNew DataThe patterns represent abnormal conditions (antigens). Using each pattern of abnor-mal condition, we test the generated detectors in the previous phase. In this case, weneed to test the coupling between them using a procedure similar than our detectorsgeneration algorithm.

4 Experiments

Because the Tubing and Casing registers have small opposite peak at the same time,we use that to divide a fault pattern in 11 sections. For the case of intermittentinjection, we divide this pattern in 7 sections that represent the fault regions by gasdeficiency (Sections 1, 3, 5 y 7) and regions with quasi-stabilization (sections 2, 4 y6). For freezing gas and low Production we divide the patterns in 4 sections. Wefollow a similar procedure to divide the rest of fault patterns (see [2, 4] for moredetails). The performance measures to evaluate our system are: a) Execution Time(seconds): is the CPU time of our system to generate the detectors. ii) Number ofactivated detectors by fault section. iii) Number of fault sections detected. We use thenext parameters for our algorithms of detectors generation: a) Size of the sliding win-dow (l) = {2, 3, 4}, b) Length of the sliding window (shift) = 1, c) Number of detec-tors to generate (num) = {50000, 60000, 70000}, d) Coupling Interval (asize) = Π / 4.

226 J. Aguilar

The standard case is: l=2, shift=1, num=5000, and asize=Π/4. We have not modifiedshift because when we have modified these parameters we have not obtained impor-tant changes at the level of the result [4]. We have designed the next experiments forthe outline operation phase: a) Different values of l, b) Different values of num. Now,we are going to show the main results, the rest of them can be seen in [4]. We havecompared our algorithm with other work proposed in [4].

4.1 Variation of num

Table 1 shows the CPU time for each algorithm to generate the detectors for the lowproduction fault pattern for different values of number of detectors. For the rest ofcase, the behavior is similar (see [4]). In general, if we increase the number of detec-tors, then the average of detection by fault section increase for both algorithms. Theaverage of detection of our algorithm is bigger than algorithm [4]. We see in table 1that the execution time of the algorithm [4] is smaller than our algorithm, but thenumber of fault sections detected by our algorithm is the biggest (see section 4.2).

Table 1: Execution Time for both Algorithms

Execution Time (seconds)

ParametersNumber of detec-

torsOur Algorithm Algorithm in [4]

50000 20605.77 4256.64l = 2

70000 28226.438 36992.452l = 3 50000 337249.01 120054.52

l = 4 50000 89538.891 52835.915

4.2 Variation of l

The table 2 shows the number of detectors activated for each algorithm in each faultsection for the emulsion fault pattern for the Standard Case. The 11 sections of thepattern have been detected by our detectors. We can see more detectors activated bythe algorithm 1. In [4] we present the rest of tables for the rest of fault patterns. In allcase, our algorithm has a bigger number of detectors activated by section than thealgorithm [4].

An Artificial Immune System for Fault Detection 227

Table 2: Number of detectors generated by our algorithm and the algorithm proposed in [4]activated in each fault section of emulsion

Emulsion Our algorithm algorithm in [4]

IntervalSection size(minutes)

Number of de-tectors activated

Number of detec-tors activated

Section 1 50 12 2

Section 2 90 39 5

Section 3 130 39 3

Section 4 220 70 8

Section 5 90 55 2

Section 6 170 54 8

Section 7 120 39 3

Section 8 230 77 8

Section 9 100 50 2

Section 10 150 52 8

Section 11 90 31 3

Section average 130.909 47.091 4.727

5 Conclusions

This paper presented an artificial immune model specially designed to solve the faultdetection problem for LAG well. Our system has demonstrated to be capable of com-bining exploitation with exploration and showed a good performance. This work hasdemonstrated that taking inspiration from the human immune system, in the form ofthe negative selection algorithm, is suitable for the design of novel error detectionmechanisms. Error detection mechanism is probabilistic and performed in real-time,permitting a trade off between storage requirements and the ability to detect an errorwithin the sequential system. In contrast to others error detection techniques thatconcentrate on single bit errors, and can sometimes fail to detect multiple errors, ourimmune system is adept to detecting this task. Particularly, we have generated detec-tors that determine deviation in the production process. This model can be used insystem of high risk and real system, where we like to detect an abnormal conditionoperation very quickly. This model can be combined with other tools like a fault diag-nostic system to classify the faults. In general, the model must be improved in: Addmore dynamic (learning and memory systems) to avoid to use only the informationcatch outline; Use one algorithm to adapt the parameters of our system (coupling

228 J. Aguilar

interval, size of the sliding window, etc.). Future work would benefit from other as-pect of natural immune system: clonal algorithm, cell memories, etc.

References

1. J. Aguilar, M. Araujo, H. Aponte "Fault Detection System in Gas Lift Well", Proceeding ofthe International Joint Conference on Neural Networks, pp. 1673-1677, 2003.

2. I. Albarran, "Una Aplicación de Redes Neuronales en la caracterización del proceso deLevantamiento Artificial de Petróleo por Gas". Technical Report, Universidad Central deVenezuela. Caracas, 2001.

3. M. Araujo, J. Aguilar, H. Aponte, "Los Sistemas Inmunes Artificiales en problemas deDetección". Technical Report, CEMISID, Universidad de los Andes, 2002.

4. A. Avizienis, “Towards Systematic Design of Fault-Tolerant Systems”, IEEE Computer,Vol. 30:4, pp. 51-58, April 1997.

5. D. Dasgupta (ed), "Artificial Immune Systems and their Applications", Springer-Verlag,1999

6. D. Dasgupta S. Forrest, "An Anomaly Detection Algorithm Inspired by the Immune Sys-tem", in Artificial Immune Systems and Their Applications, Springer-Verlag, pp 262-277,1999.

8. L. de Castro, J. Timmis, "An Introduction to Artificial Immune Systems: A New Computa-tional Intelligence Paradigm", Springer-Verlag, 2002.

9. L. de Castro, F. Von Zuben, “Immune and Neural Network Models: Theoretical and Em-pirical Comparisons”, Int. Journal of Comp. Intelligence and Applications, Vol. 1:3, pp.239-257, 2001.

10. S. Forrest, S. Hofmeyr, “Immunology as Information Processing,” in Design Principles forthe Immune Systems and Other Distributed Autonomous System, pp. 361–388. OxfordUniversity Press, 2001.

11. S. Hofmeyr and S. Forrest, “Architecture for an Artificial Immune System,” EvolutionaryComputation, vol. 7(1), pp. 1289–1296, 1999.

12. A. Tarakanov and D. Dasgupta, "A Formal Model of an Artificial Immune System", Bio-Systems, Vol. 55: 1-3, pp. 151-158, 2000.