An Expert System Shell for Fault Diagnosis

Roboticahttp://journals.cambridge.org/ROB

Additional services for Robotica:

Email alerts: Click hereSubscriptions: Click hereCommercial reprints: Click hereTerms of use : Click here

An Expert System Shell for Fault Diagnosis

Jie Yang, Chenzhou Ye and Xiaoli Zhang

Robotica / Volume 19 / Issue 06 / September 2001, pp 669 - 674DOI: 10.1017/S0263574701003460, Published online: 30 October 2001

Link to this article: http://journals.cambridge.org/abstract_S0263574701003460

How to cite this article:Jie Yang, Chenzhou Ye and Xiaoli Zhang (2001). An Expert System Shell for Fault Diagnosis. Robotica, 19, pp 669-674doi:10.1017/S0263574701003460

Request Permissions : Click here

Downloaded from http://journals.cambridge.org/ROB, IP address: 147.226.7.162 on 20 Nov 2014

http://journals.cambridge.org Downloaded: 20 Nov 2014 IP address: 147.226.7.162

An Expert System Shell for Fault Diagnosis*Jie Yang, Chenzhou Ye and Xiaoli ZhangInstitute of Image Processing & Recognition, Shanghai Jiao-Tong University, Shanghai 200030 (P. R. of China)

(Received in Final Form: March 20, 2001)

SUMMARYTraditional expert systems for fault diagnosis have abottleneck in knowledge acquisition, and have limitations inknowledge representation and reasoning. A new expertsystem shell for fault diagnosis is presented in this paper todevelop multiple knowledge models (object model, rules,neural network, case-base and diagnose models) hierarchi-cally based on multiple knowledge. The structure of theexpert system shell and the knowledge representation ofmultiple models are described. Diagnostic algorithms arepresented for automatic modeling and hierarchical reason-ing. It will be shown that the expert system shell is veryeffective in building diagnostic expert systems.

KEYWORDS: Expert system shell; Fault diagnosis; Rough set;Artificial Neural Network; Case-based reasoning.

1. INTRODUCTIONFault Diagnosis is a very important area of research inArtificial Intelligence. Existing diagnostic approaches canbe grouped into four classes: Model-based diagnosis, rule-based diagnosis, neural network-based diagnosis,case-based diagnosis. The knowledge representation andreasoning of model-based and rule-based diagnoses aresymbol-based, while those of neural network-based andcase-based diagnoses are instance-based. Model-baseddiagnosis1,2 uses an operate model that describes theoperating behavior of the device to be examined. Rule-based diagnosis uses rules in abductive reasoning,representing empirical associations that relate symptoms tothe underlying malfunctions. Instance-based diagnosis usesinstances of diagnosis accumulated by experience; it utilizesthe similarity between the current situation and previouslyknown instances to come up with a plausible diagnosis. Forthe diagnostic approach using neural network, responses tothe inputs are determined by the similarity between theinput and the prototypical instances in previous trainingdata, which can be considered as performing featureclustering based on similarity or as performing statisticalinferences. To diagnose a device, case-based diagnosissearches a case-base to find a case that best matches thecurrent situation. The diagnosis and solution of the case willbe adapted for the diagnosis of the device. The approachesof these four classes use different models for knowledgerepresentation, modeling and reasoning. Each of them has

corresponding advantages and can complement eachother.3,4 But existing diagnostic expert systems are seldomused to represent multiple knowledge models and diag-noses, based on multiple knowledge models. Usually, theycannot deal with nonmonotonic reasoning (exceptions inknowledge representation and reasoning).

As the building of an expert system for fault diagnosis isgenerally a complicated and time-consuming task, an expertshell is very useful and efficient. Traditional expert systemsfor fault diagnosis have a bottleneck in knowledge acquisi-tion. For many complicated objects (e.g. chemicalequipment), the operating and diagnostic models of theobjects are difficult to build directly by experts or simula-tion. Traditional expert system shell cannot deal withknowledge acquisition, knowledge representation and com-bined reasoning of multiple models We present a new expertsystem shell which can efficiently represent and automat-ically model multiple diagnostic knowledge. It diagnosesobjects by hierarchical reasoning based on multiple models.The structure of the new expert system shell is described inFig. 1.

In the expert shell, a instance-base of operating behaviorand a instance-base of fault behavior are built at first.Multiple knowledge models are acquired by a data miningand learning mechanism5 from two bases. According to thefault behavior of an object examined, the blackboard-basedinference mechanism realizes diagnostic reasoning hierar-chically by multiple models in a knowledge-base. After aresult of the diagnosis is inferred, consistency of the resultis maintained by truth maintenance. The explanation of theresult is also given in association with the knowledgemodels used in diagnosis and consistency examination. Theknowledge-base is then revised by learning from the failuresin diagnostic processes.

2. KNOWLEDGE REPRESENTATIONIn object diagnosis, when the instance-base of operatingbehavior and the instance-base of fault behavior are built,four knowledge models (operate model, rule-base, neuralmodel, case-base) are acquired by the data mining andlearning mechanism and represented in the knowledge-basein the order from general to specific.

Knowledge at the top level is composed of an operationmodel describing the most general diagnostic knowledge.For rule-based or case-based diagnosis, abnormal symptomsneed to be determined according to the behavioral discrep-ancy between predicated behavior and observed behavior.The operation model, which is represented by fuzzy rules torealize input-output data approximation, is used to compute

* This research is supported by National Hi-Tech Plan“863-CIMS” and National Science Foundation of China.

Robotica (2001) volume 19, pp. 669–674. Printed in the United Kingdom © 2001 Cambridge University Press

http://journals.cambridge.org


predicated state features and realize truth maintenance infault diagnosis. The form of a fuzzy rule is: if I1 =A1, . . . ,In =An then O1 =B1, . . . . , Om =Bm, where I1, . . . , In,O1, . . . , Om are input variables and state feature variables ofthe object to be diagnosed, A1, . . . , An, B1, . . . Bm are thecategories of fuzziness of the corresponding variables.Triangular membership functions are used to define thecategories of fuzziness of each variable.

Knowledge at the second level consists of diagnosticrules that describe general diagnostic knowledge and areused for rule-based abductive diagnosis. The form of adiagnostic rule: if X1, . . . , Xn then Y represents associationsthat relate symptoms X1, . . . , Xn to the underlying malfunc-tion Y.

Knowledge at the third level is built from neural modelsthat describe relatively specific diagnostic knowledge andare used for neural network-based diagnosis.

A multi-layer perceptron network is selected for theconstruction of neural models. Nodes Z1, . . . , ZM in theinput layer represent the descriptors of symptoms of anobject diagnosed. The nodes O1 . . . OK in the output layerrepresent the result of diagnosis (Fig. 2).

Knowledge at the bottom level is composed of cases thatdescribe the most specific diagnostic knowledge. Cases arerepresented as frames. A feature of a case is a defaultrepresentation of a symptom in the case. Features descrip-tors characterize the value or value domain for features, andare used for case classification. Each case is given a string

of binary signs to indicate the status of its features. The signof a feature is 1 if the feature is abnormal, and 0 if normal.The signs of features are used for case organization and casesearch. Each case representation also gives its diagnosis andthe constraints among features.

(C1 (signs 1,0, · · ·) (featurel F1) (feature2 F2) . . .

· · · (constraint CON1) (diagnosis S1))

The above frame represents case C1: featurel is abnormaland its value is F1; feature2 is normal and its value is F2;the features in C1 should satisfy the constraint CON1; thediagnosis of C1 is S1.

As the knowledge model at a lower level provides morespecific diagnostic knowledge than that at a higher level, theknowledge model at a lower level may represent exceptionsof that at a higher level.

3. AUTOMATIC MODELING FOR FAULTDIAGNOSIS

3.1 Learning fuzzy rules as operate model by geneticalgorithmWhen the instance-base of operating behavior is known,each variable is divided into several categories of fuzzinesswhose membership functions are defined as triangularfunctions. To operate a model of an object diagnosed, fuzzyrules6–7 of automatic learning can be considered as theproblem of combination optimization of input-output states;that is, a group of fuzzy rules can be treated as a kind ofcombination. Fuzzy rules of automatic learning are to findthe best one. As an effective technique of optimization, agenetic algorithm (GA) can be used for automatic learningfuzzy rules.8 Key techniques in automatic learning fuzzyrules by GA are chromosome coding of fuzzy rules,operators of inheritance (selection, crossover, mutation),and evaluation of chromosome (fuzzy rules).

Fig. 1. The structure of an expert system shell for fault diagnosis.

Fig. 2. Multi-layer perceptron network.

Fault Diagnosis670



Chromosome coding of fuzzy rules. A group of fuzzyrules can be considered as a kind of combination of fuzzypredicates. As the order of the combinations of fuzzypredicates of input variables can be determined in advance,only fuzzy predicates of output variables (conclusions of thefuzzy rules) under these combinations need be recorded forchromosome coding of fuzzy rules. As the number ofcategories of fuzziness of output variable is usually notmore than 9, numbers between 1 and m (≤9) are used torepresent the categories of fuzziness of output variable (m isnumber of the categories of fuzziness of output variable).

I1 S S S S S S S S S M M M M M M M M M L L L L L L L L LI2 S S S M M M L L L S S S M M M L L L S S S M M M L L LI3 S M L S M L S M L S M L S M L S M L S M L S M L S M L

O1 L L M M S M L L M M M S M L L M S M L M M S S M L M S

For example, chromosome coding of above fuzzy ruleswith three inputs and one output are realized by codingfuzzy predicates of O1: 332212332221233212322112321(1, 2, 3 represent the fuzzy predicates S, M, L respectively).On the contrary, given a chromosome coding of fuzzy rules112233221233221232211122322, it can be transformedinto corresponding fuzzy rules as follows:

I1 S S S S S S S S S M M M M M M M M M L L L L L L L L LI2 S S S M M M L L L S S S M M M L L L S S S M M M L L LI3 S M L S M L S M L S M L S M L S M L S M L S M L S M L

O1 S S M M L L M M S M L L M M S M L M M S S S M M T M M

Operations of chromosome inheritance. (1) Selection:The random selection of chromosome for reproduction isbased on a biased roulette wheel algorithm. (2) Crossover:When two chromosomes are randomly selected for theoperation of crossover, two points are randomly selected inthe length of these two chromosomes. Two new chromo-somes are generated by performing a two-point crossover.(3) Mutation: Given a chromosome for the mutationoperation, one point P is randomly selected in the length ofthe chromosome, the allele of the chromosome at point P isaltered randomly into n� which satisfies the constraint:n�≤m, n�≠n.

Evaluation of a chromosome (fuzzy rules). Given theinstance-base of operating behavior about inputs and theirexpected outputs, the goal of learning fuzzy rules is toreduce the error between expected outputs and outputsderived by an operate model based on fuzzy rules as smallas possible. So evaluating the fitness of a group of fuzzyrules can be realized by computing the cumulative errorsbetween expected outputs and outputs derived by an operatemodel under training examples in the instance-base ofoperating behavior. Given a chromosome operated bycrossover and mutation, it can be transformed into itscorresponding fuzzy rules. According to inputs of trainingexamples, outputs of the operating model can be derived bypredefined algorithms (detailed in section 4): fuzzification,MIN-MAX fuzzy inference according to the fuzzy ruleslearned by GA, defuzzification. The fitness of the group offuzzy rules is evaluated by computing cumulative errors

between real outputs and expected outputs of trainingexamples.

f=�n

i=1�m

j=1

(Oj �Oej )2

where n – the number of training examples; m – the numberof output variables; Oj – the output derived by fuzzy rulesand inputs of training example Ti; Oej – the expected outputof training example Ti.

The following example is used to examine the algorithm.An object with three inputs and one output is constructed,its mathematical model is:

o=0.5� (ei1 + i2� i3� cos(i1� i2)+ i1� i3),

where i1, i2, i3, o�[0,1]. A Fuzzy system is learned for themodeling of the system by our developmental tool, i1, i2, i3

are divided into 5 categories of fuzziness. In order to showthe performance of the fuzzy system in graphic form,i1, i2, i3 are represented by functions with a same variablet�[0,1]: i1 = t,

i2 =� 2� t2�2� t

0≤t<0.50.5≤t≤1

,

i3 =�0.90.1

t�[0, 0.25)� [0.5, 0.75]t�[0.25, 0.5)� [0.75, 1]

.

The following Fig. 3 is the result of the fuzzy systemlearned by genetic algorithm, the curve and the broken linein Fig. 3 separately represent the real output and expectedoutput of the fuzzy system.

3.2 Learning diagnostic rules by rough setThe rough set9,10 has recently emerged as a major mathemat-ical approach for knowledge discovery and data mining, it isused as a tool in the expert shell for extraction of diagnosticrules from the instance-base of fault behavior.11 Somepreliminaries of rough set theory are presented as follows:

An Information system is a pair S={U, A}, where U is anonempty finite set called the universe and A a nonemptyfinite set of attributes. An attribute a can be regarded as afunction from the domain U to some value set Va . With

Fig. 3. The result of the fuzzy rules learnt by GA.

Fault Diagnosis 671



every subset of attributes B�A, an equivalence relation IB onU can be associated as: IB ={(x, y)�U: for every a�B,a(x)=a(y))} then IB =� a�BIa.

If X�U, the sets {x�U: [x]B�X } and{x�U: [x]B ∩X≠�}, where [x]B denotes the equivalenceclass of the object x�U relative to IB , are called the B-lowerand B-upper approximation of X in S and denoted BX, BX,respectively.

The aim of knowledge reduction is to obtain irreducilebut essential parts of the knowledge encoded by a giveninformation system. Diagnostic rules are extracted accord-ing to the Reduct.12

The algorithm for heuristic Reduct Searching:

Input: Instance-base U, Threshold of correctness �, Attribute setC={a1, a2, . . . , an }, Fault Y, Weight set of attributesW={w1, w2, . . . , wn }

Output ReductMethods: Construct C+ ={X +

1 , X +2 , . . . , X+

s } and C� =C *�C+ ={X�1 , X�

2 , . . . , X�t }

Calculate discernible set A={A1, A2, . . . , Aq}Set Reduct=�, R={ai | �ai�A, i=1, . . . , n}While A≠� Do {

For each aI, calculate the number of appearance NI in A.For every ai�R Do

If Aj ={ai} Then the fact of aI is: Qi =–1Else the factor of aI is Qi =wi * Ni

Select the attribute ak where Qk =min{Qi | Qi >0 i=1 . . . n}Reduct=Reduct∪{ai | Qi =–1}A=A�{Aj | ai�Reduct∪{ak}, ai�Aj}If Nk = | A | Then Reduct=Reduct∪{ak}

}

The algorithm for extracting diagnostic rules is:

Input: �, C, Y, WOutput: Diagnostic ruleMethods: The Reduct of C is calculated according to the above algorithm.

Calculate Reduct+ ={X+1 , X+

2 , . . . , X+s } and Reduct� ={X�

1 , X�2 , . . . , X�

t }For X+

i , extract a diagnostic rule DES(X+i ) —→P(Y/X+

i ) Y(Sup(Y | X+i )), DES(X+

i )includes attributes only in Reduct. P(Y | X+

i )= | Y∩X+i | / | X+

i | is theconditional probability of Y on X+

i , which represents the correctness rateof the classification Y on X+

i ; Sup(Y | X+i )= | Y∩X+

i | / | Y | represents thesupport rate of Y on X+

i .For X�

i , extract a diagnostic rule DES(X�i ) —→P(Y/X+

i ) ¬Y(Sup(¬Y | X�i )),

DES(X�i ) includes attributes only in Reduct. P(Y | X�

i )= |¬Y∩X�i | / | X�

i | isthe conditional probability of ¬Y on X�

i , which represents the correctnessrate of the classification ¬Y on X�

i ; Sup(¬Y | X�i )= |¬Y∩X�

i | / |¬Y |represents the support rate of ¬Y on X�

i .

For example, U={inst1~inst13}, C={a1,a2,a3,a4,a5},D={d }, Y={d=1}, �=0.75

Inst1 Inst2 Inst3 Inst4 Inst5 Inst6 Inst7 Inst8 Inst9 Inst10 Inst11 Inst12 Inst13a1 0 1 1 0 0 0 0 1 0 0 0 1 0a2 0 0 0 0 1 0 1 0 0 1 0 0 0a3 1 0 0 1 0 1 0 0 0 1 0 1 0a4 0 1 1 0 0 0 0 1 1 1 1 1 1a5 1 0 0 1 0 1 0 0 0 1 0 0 0d 1 0 1 1 0 1 0 1 0 1 1 1 1

Two diagnostic rules are extracted as follows:

a1=0∧a3=1 —→1 Y(4/9), a1=1∧a3=0 —→0.75 Y(3/9),

After diagnostic rules are acquired from the instance-baseof fault behavior, the instances that can be satisfied by thediagnostic rules are delected from the instance-base.

3.3 Constructing neural modelsNeural models based on multi-layer perceptron network areconstructed according to the instance-base of fault behavior.Nodes Z1 . . . ZM in the input layer represent the descriptors

of symptoms of training instances of fault behavior. Thenodes O1 . . . OK in the output layer represent the diagnosisresults of the training instances. d1 . . . dK represents thedesired outputs of O1 . . . OK ; i.e., d1 . . . dK representdesired diagnosis results of the training instances. Instancesin the instance-base about the diagnosis of faults in anobject are used for the training of multiple perceptronnetwork. According to the Error Back-Propagation Algo-rithm and the differences between the desired and actualneuron’s response, the weights of the output layer and thehidden layer W←W+�oy

t, V←V+�yzt are adjusted until

cumulative cycle error is less than Emax .After neuron models have been constructed by the

instance-base of fault behavior, the instances satisfied by theneural models are deleted from the instance-base.

3.4 Organizing the case-baseAccording to the instance-base of fault behavior, case-basesabout diagnosis of instances in the instance-base can beorganized. Each instance in the base represents a case. Thepredicted state features of the object being diagnosed arecomputed by the operating model and the signs of abnormalfeatures are determined according to the difference betweenobserved features and predicated features of the instance.Cases are organized in the case-base by binary treesaccording to the signs of abnormal features. For a case withfeatures f1 . . . fm , its signs of features are a binary stringwith length of m. Based on the binary string, cases aresorted into binary trees. Each case is located in a leaf of thetree, and the length from a leaf to the root is m. Each leaf isa certain classification. The possible classifications of casesin the binary trees is 2m maximum.

4. DIAGNOSTIC REASONING BASED ONMULTIPLE MODELSAfter the knowledge-base of multiple diagnosis model hasbeen built, the expert system can be used for fault diagnosis.When the observed behavior of an object to be diagnosed isinputted into the expert system, it is described in theblackboard of the inference mechanism. The inferencemechanism uses multiple models in the knowledge-base torealize diagnosis.3,4,13,14 The following are the strategies usedby the inference mechanism for diagnosis.

(a) For a complicated object diagnosed, according to thefunctions of components in the object, the object is dividedinto some functional groups (that is; some components arecombined to constitute a functional group). For the object,two levels of knowledge models are built: a knowledgemodel for the entire object and a knowledge model for thefunctional groups. In the knowledge model for the entireobject, a functional group is considered as a component.The knowledge model of a functional group describes onlythe diagnostic knowledge of the functional group. Theinference mechanism diagnoses faults in the object hierar-chically. First, the knowledge model of the entire object isused to find the malfunctioning groups whose knowledgemodel is used then to localize fault components.

(b) For diagnosis of an object, the inference mechanismrealization can use diagnostic reasoning in the order from

Fault Diagnosis672



general to specific. The operate model is used at first tocompute a predicated state of the object. Abnormalsymptoms are determined according to the differencebetween observed state features and predicated ones. Thendiagnostic rules are used for the rule-based diagnosis. If theresult derived from rule-based diagnosis doesn’t work,neural models are used for a second level diagnosis. If theneural network-based diagnosis fails, a case-base is used torealize a more specific diagnosis. As the knowledge modelin lower level provides a more specific diagnostic knowl-edge than that at a higher level, the inference mechanismcan deal with nonmonotonic reasoning in diagnosis.2

(c) After the result of diagnosis is inferred with multipleknowledge model, the inference mechanism realizes truthmaintenance by examining the consistency between theoperate model and the result of the diagnosis. The inferencemechanism provides explanations of the diagnosis byshowing the predicated behavior and the knowledge modelused for diagnosis.

(d) If faults in an object cannot be diagnosed withmultiple knowledge models, the inference mechanism canlearn after diagnosis. A new case about the diagnosis of theobject is added to the case-base so that similar faults can bediagnosed in future. When enough cases are assembled,some similar cases can be used to generate new rules andconstruct new neural models.

The following are the approaches of a diagnosis basedon each knowledge model:

(a) Computation of predicated state features based on theoperate model.

When the observed behavior of an object to be diagnosedis inputted the predicated behavior of the object can bederived by the operate model using predefined algorithms:fuzzification, MIN-MAX fuzzy inference according to thefuzzy rules learned by GA, defuzzification. The results offuzzification are memberships [0,1] of fuzzy predicates ofinput variables. Zmn =�Amn

(Im), Amn is the nth category offuzziness of Im. The results of Min-Max fuzzy-inference areAND-operation of premises of fuzzy rules (minimum ofmemberships of input variables), and OR-operation ofconclusions of fuzzy rules (maximum of conclusionsderived by different fuzzy rules). The results of defuzzifica-tion are

Ok =�n

1

Ykl� Ckl��n

1

Ykl ,

Ckl is the middle value of the triangular membershipfunction of Akl , Akl is the l th category of fuzziness of Ok .

(b) Rule-based diagnosisFor an object to be diagnosed, abnormal symptoms aredetermined according to the difference between observedstate features and predicated ones derived by the operatemodel. Then a diagnostic rule is searched in the rule-base,whose premises match the abnormal symptoms of theobject, the conclusion of the rule is derived as the result ofthe diagnosis.

(c) Neural network-based diagnosis

For an object to be diagnosed, according to its abnormalfeatures, a neural model is selected from the knowledgebase. The values of the features which are normalized into[0,1] are inputted into the nodes of the input layer of themultiple-layer preceptron network; the outputs of the outputlayer of the network are calculated as the results of thediagnosis.

(d) Case-based diagnosisFor an object to be diagnosed, the abnormal signs of its statefeatures are determined according to the difference betweenobserved features and predicated ones derived by theoperate model. The binary string of the signs of features isused as the index for case retrieve in the case-base. Thoughthere may be 2m classifications in the case-base at most, acase classification can be searched in the binary trees by mtimes of bit matching. If there is only one case in the caseclassification, then the diagnosis of the case is adopted asthe result of the diagnosis of the object. If there is more thanone case in the case classification, the distances between theobject and each case in the case classification are calculatedin form of

Di =1n ��n

j=1

( fij � foj )2 i=1, · · · , N

where fij – the jth feature of the ith case in the caseclassification, foj – the jth feature of the object, n – thenumber of features of a case, N – the number of cases in thecase classification. The nearest case is selected; its diagnosisis adopted as the result of the diagnosis of the object.

5. CONCLUSIONSFault diagnosis is an important area of research in AI, and akey technique in Computer-Integrated Manufacturing Sys-tems. The bottleneck in building an expert system for faultdiagnosis is knowledge acquisition and multiple knowledgemodeling. Traditional expert system shells cannot deal withautomatic modeling of fault diagnosis and diagnosis basedon multiple knowledge models. In this paper, a new expertsystem shell for fault diagnosis is discussed. The new expertsystem shell can learn multiple knowledge models (objectmodel, rules, neural network, case-base) using geneticalgorithms, rough sets, multi-layer perceptron networks andcase-learning. It can diagnose hierarchically (from generalto specific) based on multiple knowledge models. Theexpert system shell has been used in a steel-makingcompany in Shanghai. It has been verified to be moreeffective than traditional expert system shells for faultdiagnosis.

References1. J. de Kleer and B.C. Williams, “Diagnosis with behavioral

models”, IJCAI-89, (1989) pp. 1324–1330.2. Jie Yang, Prioritized Justification-based Nonmonotonic Logic

and its Applications (Shaker Verlag, Aachen, Germany,1994).

3. M.P. Feret and J.I. Glasgow, “Combining Case-Based andModel-Based Reasoning for the diagnosis of Complex

Fault Diagnosis 673



Devices”, Journal of Applied Intelligence 7, No. 1, 57–78(1997).

4. A.R. Golding and P.S. Rosenbloom, “Improving accuracy bycombining rule-based and case-based reasoning”, ArtificialIntelligence 87, No. 1-2, 215–254 (1996).

5. N. Shan et al., “GRG : Knowledge Discovery Using Informa-tion Generalization, Information Reduction, and RuleGeneration”, 7th International Conference on Tools withArtificial Intelligence, Washington, D.C., USA (1995),pp. 372–379.

6. C.T. Lin et al., “Fuzzy adaptive learning control network withon-line neural learning”, Fuzzy Sets and Systems 71, No. 1,25–45 (1995).

7. M. Mohammadian et al., “A Case Study of KnowledgeAcquisition: from Connectionist Learning to an OptimizedFuzzy Knowledge Base”, IEEE 2nd International Workshopon Emerging Technologies and Factory Automation (1993)pp. 106–111.

8. M.H. Lim et al., “A GA paradigm for learning fuzzy rules”,Fuzzy Sets and Systems 82, 177–186 (1996).

9. Z. Pawlak, “Rough Set”, International Journal of Computerand Information Science 11, No. 5, 341–356 (1982).

10. Z. Pawlak, Rough Set, Theoretical Aspects of ReasoningAbout Data (Dordrecht, The Netherlands: Kluwer, 1991).

11. A. Mrozek, “Rough Sets and Dependency Analysis amongAttributes in Computer Implementations of Expert’s inferencemodels”, International Journal of Man-Machine Studies 30,457–473 (1989).

12. J.H. Chen, “Algorithm of Knowledge Discovery and ItsApplications”, Ph.D. Dissertation (Shanghai Jiao-tong Uni-versity, China, 1998).

13. Ron Sun, “Commonsense reasoning with rules, and con-nectionist models: A paradigmatic comparison”, Fuzzy Setand Systems, 82, 187–200 (1996).

14. L.R. Wedsker, Hybrid Neural Network and Expert Systems(Kluwer Academic Publishers, 1994).

Fault Diagnosis674


Documents

An Expert System Shell for Fault Diagnosis