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Towards a new Fault Diagnosis System for Electric Machinesbased on Dynamic Probabilistic Models

Jos e L. Flores-Quintanilla, Rub en Morales-Men endez

Ricardo A. Ramrez-Mendoza, Luis E. Garza-Casta non, Francisco J. Cant u-Ortiz

Abstract This paper presents a new approach to diagnosefaults in electrical systems based on probabilistic modellingand machine learning techniques. Our framework consist of two phases: an approximated diagnosis on the rst phase anda rened diagnosis on the second phase. On the rst phase thesystem behavior is modelled with a Dynamic Bayesian Networkthat generates a subset of most likely faulty components. In thisphase the structure and parameters of the Dynamic BayesianNetwork are learned off-line from raw data (discrete andcontinuous). On the second phase a Particle Filter algorithm isused to monitor suspicious components and extract the faultycomponents. The feasibility of this approach has been testedin a simulation environment using several interconnectedelectrical machines.

I. INTRODUCTION

When a machine fails in a real process, the maintenancepeople take minutes, hours or even days looking for thefaulty elements depending on the complexity of the system.

Diagnosing in large interconnected process, such aspower electrical systems, is a difcult task due mainlyto the inherent uncertainty in information. The uncertaintyarises due to close interaction between systems components,that in the faulty event hide real fault symptoms. Othersources of uncertainty include: noisy data, non-linearitiesand missing information. An adequate automated decisionsupport system has to deal with the challenge in the faultdiagnosis task. This system enables us to diagnose faultsin an uncertain environment. Extensive research has beendone to develop fault diagnosis methods based in analyticalmethods [1], [2], [3] or articial intelligence techniques [4][5][6], [7]. Recently, attention to probabilistic modellingand machine learning techniques has grown [8], [9], due tothe availability of data and computation power, but mainlybecause of the difculty to model systems with analyticaltechniques. Powerful diagnosis methods are able to dealwith different sources of uncertainty and capable of learningmodels of system behavior from data.

A recent trend is the combination of different techniques,to address challenging environments such as large intercon-

Jose-Leonardo Flores-Quintanilla is at the Mechatronics Program Ofce,ITESM San Luis Campus, M exico, joselfq@itesm.mx

R. Morales-Men endez is at the Center for Innovation in Design andTechnology, ITESM Monterrey Campus, M exico, rmm@itesm.mx

Ricardo A. Ramirez-Mendoza is at the MechatronicsProgram Ofce, ITESM Monterrey Campus, M exico, ri-cardo.ramirez@itesm.mx

Luis E. Garza-Casta non is at the Department of Mechatronics, ITESMMonterrey Campus, M exico, legarza@itesm.mx

Francisco J. Cant u-Ortiz is at the Research and Graduate Studies Ofce,ITESM Monterrey Campus, M exico, fcantu@itesm.mx

nected systems, where discrete and continuous signals arepresent. In such systems, classical mathematical models cannot deal with all sources of uncertainty and are very difcultto obtain as the system grows in complexity.

This paper is mainly focused on the integration of dy-namic Bayesian Networks and Particle Filtering algorithmsto tackle the problem of diagnosis. This approach permitsimprovement in system robustness and allows to accomplisha better performance compared to the separate individualapplication. The study was applied to a simple case of an in-terconnected electrical system in a simulation environment.

The paper is organized as follows. Section II presentsbackground on fault diagnosis methods. Section III de-scribes the interconnected electrical system used as a casestudy. Section IV explains the approach and framework proposed in this paper. Section V shows the simulationresults and nally section VI concludes the paper andincludes future work.

I I . FAULT D IAGNOSIS M ETHODS

The fault diagnosis task can be separated into two steps:fault detection and fault diagnosis. Fault detection is mainlyconcerned with the identication of an abnormal situationin a process.

Fault detection can be based on analytical or heuristicsymptoms. Analytical symptoms are generated by simplelimit value checking or by more elaborated techniques suchas signal analysis (eg. statistical or frequency analysis).Heuristic symptoms are produced by qualitative informationextracted from human operators or process history records.Different approaches of fault detection methods has beendeveloped. Most approaches use mathematical models suchas: Kalman lter, state observers, parity relations, etc. [10].Fault diagnosis consists of the determination of the type,size, and location of a fault, together with the time of

detection.Fault diagnosis methods mainly use classication tech-niques or reasoning methods [2]. Classication techniquesincludes statistical methods, neural networks and fuzzyclustering. Reasoning methods mainly include rst orderlogic, fuzzy logic and Bayesian networks.

A. Bayesian Networks

Bayesian networks are a helpful tool to model multi-fault,multi-symptom dependency relations: every fault and everysymptom is modelled by a random variable with a niterange of possible values. A graph is constructed with a node

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for each variable. The graph constructed has an edge fromone node to another, whenever the rst node models a faultdirectly exhibiting the symptom modelled by the second.In general, Bayesian networks are a representation of prob-ability distributions over complex domains. Formally, weconsider probability spaces dened as the set of possible

assignments to some set of random variables X 1 , . . . , X n ,each of which has a domain Dom [X i ] of possible val-ues. For example the domain of the discrete variable Breaker status is {normal, open, faulty }. The domain of the variable Voltage can be , or it can be discretized intosome appropriate partition. The goal is to represent a jointprobability distribution over these variables.Formally, a Bayesian network is dened by a directedacyclic graph together with a local probabilistic model foreach node. There is a node in the graph for each randomvariable X 1 , . . . , X n . The edges in the graph denote directdependency of a variable X i on its parents Parents (X i ).The graphical structure encodes a set of conditional in-dependence assumptions ( each node X i is conditionallyindependent of its non-descendants given its parents ).The qualitative independence assumptions implied by thenetwork structure, combined with the conditional proba-bility distributions associated with the nodes, are enoughto specify a full joint distribution through the followingeqn (1), known as the chain rule for Bayesian networks :

p(X 1 , . . . , X n ) =n

i =1

p(X i |Parents (X i )) (1)

In discrete networks, an explicit description of the jointdistribution requires a number of parameters that are expo-nential in n (the number of variables). Bayesian networksderive their power from the ability to represent conditionalindependencies among variables, which allows them to takeadvantage of the locality of causal inuences. A variableis independent of its indirect causal inuences given itsdirect causal inuences. However, in order to reduce thecomputational effort, statistically independent symptomshave to be assumed.

B. Particle Filtering

Particle Filtering is a Markov chain Monte Carlo methodthat approximates the belief state using a set of samplescalled particles. The distribution of the particles is updatedtaking into account the latest available evidence as timeincreases. The standard Particle Filtering algorithm consistsof three basic sequential steps:

Monte Carlo step . This step takes into account theevolution of the system as time increases:

zt p(zt |zt 1) (2)x t +1 = A(zt )x t + B (zt ) t + F (zt )u t (3)

yt = C (zt )x t + D (zt )vt (4)

The previous stochastic model of the system is used togenerate the predicted future state ( z ( i )t , x

( i )t , y

( i )t ), see

[11] for details. We sampled a discrete mode, eqn (5),and then the continuous state given the new discretemode, eqn (6).

z( i )t p(zt |z

( i )t 1) (5)

x ( i )t p(x t | z( i )t , x

( i )t 1) (6)

Sequential Importance Sampling step . By conditioningon the new information and using the Bayes rule,each particle is weighted by the likelihood of theobservations in the updated state represented by thatparticle eqn (7).

w( i )t p(yt | z( i )t , x

( i )t ) (7)

Selection step . High-weight particles are replaced byseveral particles while low-weight particles tend todisappear.

Particle Filtering algorithms approximate the true poste-rior belief state given observations y1: t by a set of particles.

p(zt , x t |y1: t ) =1N

N

i =1

w( i )t (z t ,x t ) (z( i )t , x

( i )t ) (8)

where w( i )t is the weight of a particle, z( i )t are the discrete

modes, x ( i )t are the continuous parameters and ( ) () isDirac delta function.

Rao-Blackwellized Particle Filtering ( RBPF ) is a ParticleFiltering variant that uses some of the analytical structureof the model, [12].

If we know the values of the discrete modes zt , it ispossible to calculate the distribution of the continuous statesx t . According to the Rao-Blackwell theorem, this leadsto estimators with less variance than those obtained usingonly pure Monte Carlo sampling. Thus, if we can generateparticles of zt and analytically evaluate the expectationof x t given zt , we will need less particles for a givenaccuracy. We can therefore combine a Particle Filteringthat computes the distribution of the discrete modes witha bank of Kalman lters that computes the distribution of the continuous states.

A further improvement based on look-ahead RBPF isproposed in [13]. While evaluating the importance of

weights for particles at time t , look-ahead RBPF looksahead one step to see the behavior of the measurementsat time t + 1 . It then uses this information to computebetter weights at time t . The basic sequential steps areKalman prediction, Selection, Sequential Importance Sam-pling, and Kalman updating. The look-ahead RBPF algo-rithm is specically exploited in this paper.

III. ELECTRICAL SYSTEM

A production line in a factory can be thought as a setof interconnected electrical machines. These machines aremade up of several components which can be seen as

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series RL circuits. As the ratio of possible failures in thissystem is high because of the number of total components,a monitoring system for faulty component is required.

Figure 1 shows two electrical machines controlled andsupervised by the same control panel.

Fig. 1. Schematic diagram of two electrical machines. Series resistance-inductance circuits are shown.

Each machine is made up of two or three identical RLseries circuits. Besides, each machine as well as its individ-ual circuits has its own breakers that protect the rest of thesystem against over-current. Also, these breakers are usedwhen machines or individual circuits need maintenance.

This electrical system is a typical application where inter-action between continuous and discrete variables are high.Discrete variables are the machines and circuit breakers,and the continuous variables are given by the main currentas well as the circuit parameters.

The main task is to determine when there is a fault, whichof the two machines is in faulty mode and which circuit hasthe problem.

For the simulation it was considered that one seriesRL circuit has been isolated, also it was considered 9possible faulty modes for this circuit. The faulty modes wereimplemented using a change of 5 in the resistance valueof the circuit (starting from 10).

IV. M ETHODOLOGY

The diagnosis system that we are proposing consists of two phases, [14]. Figure 2 shows conceptual ideas.In the rst phase the full system is modelled in probabilis-

tic terms by a Bayesian network. It considers that we have2 interconnected machines. The failure probabilities of eachmachine, based on evidences, are updated periodically. TheBayesian network is used to select the machines with a highprobability of failure. The main difference with [14] con-sists of using rst order logic representation for Bayesiannetworks and a set of heuristics to deal with the bothproblems of combinatorial explosion and selection of themost likely faulty elements. That Independent Choice Logic

Fig. 2. General architecture for the diagnosis system.

framework allows a richer model representation framework,where other features, as explicit time for instance, can bemodelled, [15]. This is a semantic framework which allowsfor independent choices made by various agents, and a logicprogram to give the consequences of the choices. This isan expansion of Probabilistic Horn abduction to include aricher logic, and choices by multiple agents, [16].

In the second phase, gure 2, these machines are con-tinuously monitored to nd the damaged components usinga Particle Filtering algorithm. In the work by [14], sec-ond phase is implemented by using a residual approachwhere normal process behavior is represented by a compactprobabilistic model whose parameters are learned ofineby nding the maximum entropy joint probability massfunction consistent with arbitrary probability constraints.The structure of this model is found by learning the structureof a discrete Bayesian network.

Each block in gure 2 will be described briey:

A. Phase I

The implementation of rst the phase consists of thefollowing steps.

1) Facts, assumptions, knowledge base . In this block atable describes the behavior of all the breakers whichconstitute the whole system as well as the behavior of the main current. We prepares a table with all possiblecombinations of breaker states; as a result, the data isgenerated for the Bayesian network of the full system.

2) Discretization. The discretization of the continuousvariable is made. The key variable in this system isthe main electrical current.

3) Bayesian network. The specialized software Power Constructor 1 developed to learn a Bayesian network from data is included here. It uses data bases in theform of discrete variables. A Bayesian network usesevidence from a set of variables and looks at the restof variables to predict the possible faults that couldbe presented. The Hugin 2 software was used to makeinferences and analysis.

B. Phase II

Fault diagnosis in this context, is to determine the stateof an electrical system over time given a stream of ob-

1 http://www.cs.ualberta.ca/ jcheng/bnpc.htm2 http://www.hugin.com

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Fig. 5. Electrical system Bayesian net with an evidence of 7 . 35 amperesin the main current.

being turned off. This breaker connects the powersupply to the machine.

Breaker 2 is closed; thus, machine 2 has a probabilityof 93.74% of being turned on.

Breakers 3 and 4 are opened; therefore, machine 1 isturned off.

Breaker 7 is opened. Breakers 6 and 5 are closed. Class F, the nal node, indicates that circuits 2, 3 and

4 have a probability of being faulty. They have themaximum values of probability.

Phase II Once phase I is nished for the full electricalsystem, there are a set of machines with a high probabilityof failure. We must run a closely monitoring system ineach probable faulty machine. In order to show how thealgorithm works, it was selected only one of the circuits of only one machine. The system was tested with more than20 runs for each number of particles. Also, several runs of the experiment were executed taking into account differentlevels of noise. For each level of noise were used 100, 500and 1, 000 particles. The levels of noise used were 0.1%,1%, 5% and 10% for both the process and measurement

noises. Finally, we computed the statistics (mean and stan-dard deviation) of the diagnosis error. Diagnosis error is thepercentage of time steps during which the discrete mode ( zt )was not identied properly. The Maximum A Posteriori wasused to dene the most probable discrete mode over time.

Table I shows a summary of the system performance for

the diagnosis algorithm. Note that the mean error diagnosisis very low when the noise is 0.1% or 1%, while meandiagnosis error grows up when the noise is 5% and 10%.The standard deviation of the error diagnosis is less as thenumber of particle grows up.

TABLE I

LOO K -AHEAD RBPF PERFORMANCE . D IAGNOSIS ERRORS ARE SHOWN

FOR DIFFERENT NUMBER OF PARTICLES AND LEVEL NOISES .

100 Particles 500 Particles 1,000 ParticlesLevelnoise

mean Stddesv

mean Stddesv

mean Stddesv

0.1% 0.04% 0.02% 0.05% 0.00% 0.05% 0.00%1% 0.18% 0.05% 0.12% 0.05% 0.10% 0.00%5% 5.77% 1.08% 5.30% 0.80% 4.76% 0.28%10% 10.63% 3 .82% 9.81% 1.31% 8.75% 0.58%

Figures 6-7 show the diagnosis performance for 100particles with low-level noise. Figure 6 shows the realdiscrete ( zt ) and continuous ( yt ) states over time, whilegure 7 shows the behavior of the look-ahead RBPF (thereal and estimated states are shown). As we can see, thereare few diagnosis errors. The diagnosis errors appear at thetransitions over time.

0 500 1000 1500 20000

2.5

5

7.5

10

z t

0 500 1000 1500 20000

0.05

0.1

0.15

0.2

y t

timesteps

Fig. 6. True faulty states for the system and the measured variable

In presence of noise the algorithm has low performance.We can cope with high-level noise increasing the numberof particle; however, high-level noise kills some look-ahead RBPF features, [11].

VI . C ONCLUSIONS AND FUTURE WORK

We have described a new approach for diagnosing faultsin industrial systems combining dynamic Bayesian learning-inference and particle ltering. Our main contribution is

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0 500 1000 1500 20000

1

2

3

4

5

6

7

8

9

z t

timestep

|laRbPF |8.6 % diagnosis error |0.24839 sec per step|

True state

estimated state

Fig. 7. State estimation with 100 particles and low-level noise

the combination of both dynamic Bayesian networks andparticle ltering in a single framework and its testing indiagnosing faults for an electrical system. The dynamicBayesian network chooses those electric machines withthe highest probability of failure. The particle lteringalgorithm is used to continuously monitor those machinesto detect if a circuit component has changed its parametervalues. The Bayesian network is periodically updated basedon evidence to have a reliable system.

We are working on the applicability of the framework in more complex processes and its use on more complexindustrial applications such as CNC Milling Machines withrecongurable features.

R EFERENCES

[1] E C Larson, B E Jr Parker, and B R Clark. Model-based sensorand actuator fault detection and isolation. Proceedings of the 2002 American Control Conference on , 5(2):4215 4219, 8-10 May 2002.

[2] R Isermann. Supervision, fault-detection and fault-diagnosis methods- an Introduction. Control Engineering Practice , 5:639652, 1997.

[3] E Lughofer, E.P. Klement, J.M. Luja, and C Guardiola. Model-basedfault detection in multi-sensor measurement systems. Intelligent Systems, 2004. Proceedings. 2nd International IEEE Conference ,1:184 189, 22-24 June 2004.

[4] R Morales-Men endez, R Ramrez-Mendoza, J Mutch, and F Guedea-Elizalde. Toward a new approach for online fault diagnosis combin-ing particle ltering and parametric identication. Lecture Notes inComputer Science , 2972:555 564, April 2004.

[5] F Valles and R A Ramrez-Mendoza. A statistical hypothesis neuralnetworks approach for fault detection and isolation of an adaptivecontrol system. In Avances en Inteligencia Articial, MICAI/TANIA ,Mrida Mxico, 2002.

[6] M A Awadallah and M M Morcos. Application of AI tools in faultdiagnosis of electrical machines and drives-an overview. EnergyConversion,IEEE Transactions on , 18(2):245 251, June 2003.

[7] Q Sheng, X Z Gao, and Z Xianyi. State-of-the-art in soft computing-based motor fault diagnosis. Proceedings of 2003 IEEE Conferenceon , 2(2):1381 1386, 23-25 June 2003.

[8] A Barigozzi, L Magni, and R Scattolini. A probabilistic approachto fault diagnosis of industrial systems. Control Systems Technology, IEEE Transactions on , 12:950 955, Nov. 2004.

[9] Z Shaoyuan, Z Jianming, and W Shuqing. Fault diagnosis inindustrial processes using principal component analysis and hiddenMarkov model. Proceedings of the 2004 American Control Confer-ence , 6:5680 5685, June 30-July 2, 2004.

[10] J Gertler. Fault detection and diagnosis in engineering systems .Marcel Dekker, Inc., 1998.

[11] N de Freitas, R Dearden, F Hutter, R Morales-Men endez, J Mutch,and D Poole. Diagnosis by a waiter and a Mars explorer. IEEE,Special issue on Sequential State Estimation , 92(3):455468, March2004.

[12] A Doucet, N de Freitas, K Murphy,and S Russell. Rao-Blackwellisedparticle ltering for dynamic Bayesian networks. In C Boutilier andM Godszmidt, editors, Uncertainty in articial intelligence , pages176183. Morgan Kaufmann Publishers, 2000.

[13] R Morales-Men endez, N de Freitas, and D Poole. Real-time monitor-ing of complex industrial processes with particle lters. In Advancesin Neural InformationProcessing Systems 16 , Cambridge, MA, 2002.MIT Press.

[14] L E Garza. Hybrid Systems Fault Diagnosis with a Probabilistic Logic Reasoning Framework . PhD thesis, Center of ArticialIntelligence, ITESM Monterrey campus, Mexico, 2001.

[15] D Poole. The Independent Choice Logic for modelling multipleagents under uncertainty. Articial Intelligence , 94(1-2):7 56, 1997.

[16] D Poole. Logic, knowledge representation and Bayesian DecisionTheory. In First International Conference on Computational Logic ,

London, July 2000.[17] A Doucet. On sequential simulation-based methods for Bayesian

ltering. Technical Report CUED/F-INFENG/TR 310, Dept of Engineering, Cambridge University, 1998.

[18] R Dearden, F Hutter, R Simmons, V Verma, S Thrun, and T Willeke.Real-time fault detection and situational awareness for rovers: Reporton the Mars technology program task. In Proceedings of IEEE Aerospace Conference , Big Sky, MY, March 2004.

[19] R Morales-Men endez, F Cantu, and A Favela. Dynamic modellingof processes using Jump Markov Linear Gaussian Models. In Modelling, Identication and Control , Grindelwald, Switzerland,February 2004.

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