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A performance evaluation of three inference engines as

expert systems for failure mode identification in shafts

Moreno C., Espejo E.

Department of Mechanical and Mechatronics Engineering, National University of

Colombia

Abstract

Validation for failure mode identification in shafts for three inference en-gines (rule based reasoning, fuzzy based reasoning and Bayesian based rea-soning) was done with focus on the casuistics and results after their use infailure cases from different industries in wich the systems were tested. Eachsystem was implemented using the same user interface and knowledge base,with different frameworks and techniques as follows: rule based inference rea-soning (prolog, C#), Mamdani-fuzzy based reasoning (C, MATLAB R) andBayesian based reasoning with a variable elimination algorithm (C, MAT-LAB R).The best performance was obtained using the Bayesian inference engine. Theconditional probabilities gives flexibility when evidence is not listed, while thefuzzy and classical IF-THEN systems depend on the rules in the inferenceengine.

The process presented in this paper could be used for validation of any ex-pert system or for comparison with other expert systems (inference engines)when the knowledge base is the same.

Keywords: Failure analysis, expert system, rule based reasoning, fuzzybased reasoning, Bayesian based reasoning.

1. Introduction

Presently it is common to find different applications of experts systemsin several fields of knowledge, especially in medical diagnosis and other in-dustrial applications using rule based reasoning [1, 2], fuzzy inference [3, 4,5, 6, 7, 8] and Bayesian inference [9, 10, 11, 12, 13, 14, 15]. However, there

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is a paucity of literature that shows a comparison of different techniques of

expert systems using the same knowledge base and failure cases, in relationto the human response for failure mode identification in machine elements.In [16] a comparison between the Bayesian and classical systems for medicaldiagnosis is presented.

There are different techniques for comparison between experts systemsresponse such, as index and ratios of agreement [17]. These techniques wereused successfully in previous papers such as [18].

By means of failure cases in shafts, rule based, fuzzy inference, andBayesian inference experts systems were tested and compared with the re-

sponse obtained from an expert human panel. The rule based expert sys-tem was developed using a declarative programming language (prolog+logicserver), the fuzzy inference engine was developed using the fuzzy inferencesystem included in MATLAB Rand the Bayesian inference system was de-veloped using the variable elimination algorithm based on C and MATLABR.

This validation was performed using the same failure cases as follows:sixteen cases for fracture, ten cases for wear, ten cases for corrosion and tencases for plastic deformation. The present paper presents the results of each

inference engine, using quantitative methodologies based on visual inspectionof failed shafts.

At the end of the analysis, the failure mode for each system was shown,as well as its own fault tree analysis diagram (FTA), for corrective actionsaccording to the maintenance procedures.

2. Expert system structure and knowledge base

The structure of each expert system tested is shown in Figure 1. The

knowledge base was obtained from human expert knowledge; thus the non-expert user entered the evidence based on their observations of the failedshaft, and with the evidence the inference engine tried to find the possiblefailure mode, showing the result with the FTA. Using the failure mode resultand the FTA, the non expert user would be able to improve maintenance

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procedures or operations, in order to avoid the same failure mode in the

future.

Figure 1: Basic structure used for each expert system

2.1. Fracture module

The knowledge base for the fracture module includes the following failuremodes: brittle fracture in bending (bfb), torsional brittle fracture (tbf), tor-sional ductile fracture (tdf), bending fatigue fracture (bff), torsional fatiguefracture (tff), torsional fatige fracture in splined shaft (tffss), bending corro-sion fatigue (bcf), torsional corrosion fatigue (tcf), stress corrosion crackingunder bending (sccub) and torsional stress corrosion cracking (tscc).

An example of a table of attributes for fractures is shown in Table 1,where (M) means mandatory and (O) means optional symptom or evidence.The non expert user selects the evidence according to his or her observationsof the failed shaft.

2.2. Wear, corrosion and plastic deformation module

The knowledge base for the wear module includes the following failuremodes: superficial fatigue (sf), abrasive wear (abw), adhesive wear (adw)and fretting (fr). The corrosion module includes pitting corrosion (pc) anduniform corrosion (uc). The plastic deformation module includes the follow-ing failure modes: torsional plastic flow (tpf), bending plastic flow (bpf),

shell buckling under bending (sbub), shell buckling under torsion (sbut), anddamage in keyway or spline (dkws).

The attributes for wear, corrosion and plastic deformation are shown inTable 2. The non expert user selects the evidence according to his or herobservations of the failed shaft.

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Table 1: Attributes for fracture module that the non expert user identifies for the failed shaft

Attributes bfb tbf tdf bff tff tffss bcf tcf sccub

Cross fracture M - M M - - M - M

Granular appearance M M - - - - - - - Without plastic deformation O O - O O M - - -

Diagonal fracture (45) - M - - M - - M - Fibrous appearance - - M - - - - - -

Plastic deformation in rotation way - - M - - - - - - Two zones (smooth and final fracture) - - - M M M M M M

Radial cracks with 45 at union - - - - - M - - - Beach marks - - - O O O O O O

Radial marks O O - O O O O O O Corrosive environment in operation - - - - - - M M M

Corrosion waste - - - - - - O O O Variable load in operation - - - - - - M M - Constant load in operation - - - - - - - - M

Brittle fracture in bending (bfb), torsional brittle fracture (tbf), torsional ductile fracturebending fatigue fracture (bff ), torsional fatigue fracture (tff), torsional fatige fracture in spline(tffss), bending corrosion fatigue (bcf), torsional corrosion fatigue (tcf), stress corrosion crunder bending (sccub) and torsional stress corrosion cracking (tscc)

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Table 2: Attributes for wear, corrosion and plastic deformation module that the non expert user identifithe failed shaft

Attributes sf abw adw fr uc pc bpf tpf sbub sbut dk

Surface modification M M M M M M - - - - Pitting evidence M - - - - - - - - -

Superficial cracks O - - - - - - - - - Scratch in surface - M - - - - - - - - Metal transfering - - M - - - - - - -

Heat or fusion evidence - - O - - - - - - - Reddish-brown oxide color - - O M - - - - - -

Localized damage - - - M - - - - - - Corrosion waste - - - - M O - - - -

Homogeneous damage - - - - M - - - - - Pitting concentrated damage - - - - - M - - - -

Solid shaft - - - - - - M M - -

Bending deformation - - - - - - M - - - Torsional deformation - - - - - - - M - - Thin wall hollow shaft - - - - - - - - M M

Elliptical collapse - - - - - - - - M - Torsional collapse - - - - - - - - - M

Keyway or spline deformation - - - - - - - - - -

Superficial fatigue (sf), abrasive wear (abw), adhesive wear (adw) and fretting (fr), pitting corro(pc), uniform corrosion (uc), bending plastic flow (bpf), torsional plastic flow (tpf), shell buckunder bending (sbub), shell buckling under torsion (sbut) and damage in keyway or spline (dk

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2.3. Inference process

The rule based inference engine is typically represented as IF-THEN rules(modus ponens); for example IF all the evidence for a failure mode is iden-tified THEN the failure mode is identified.

Fuzzy inference reasoning uses IF-THEN rules, but using fuzzy set theoryit is possible to map the inputs and outputs, using the Mamdani or Sugenosystems. As an example the beach marks could be the following conditions:absence, slight presence or evident.

Fuzzy inference can work with non exact information while informationor evidence in rule based reasoning must be defined exactly and correctly(absent, evident).

Bayesian inference uses Bayesian rules to update the probability whenadditional evidence is identified for a failure mode using conditional proba-bility tables. For example, bending fatigue fracture has a 75% probabilitywhen two zones (smooth and final fracture) are identified as evidence, but ifthere are additional beach marks on the surface this probability increases to85%.

2.4. Development of the principle of operation of experts systems

As an example, in Figure 2, a failed pony rod with a 45

fracture is shown;the fracture surface is shown in Figure 3.

In Figure 4, the first part of the fracture module for the shaft used in allthe inference engines is shown. The non expert user must select the optionsaccording to the failed piece, using the data for the failed pony rod in Figures2 and 3.The first task is to identify which of the following figures or pictures describethe fracture that one is analyzing and the fracture orientation (The non ex-pert user selected fracture with 45).The second task is to identify the pattern of plastic deformation in the frac-ture that one is analyzing (The non expert user selected without deforma-

tion).

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Figure 2: Failed pony rod 1-1/8 .

Figure 3: Fracture surface.

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Figure 4: Task one and two for the fracture module

In Figure 5, third task is to identify the kind of surface in the fracture

zone (the non expert user selected granular appearance); the fourth task isto identify marks at the surface (the non expert user selected radial markswithout beach marks).

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Figure 5: Fracture surface and mark tasks, tasks three and four

In Figure 6, the fifth task is to identify if the piece was in a corrosive

environment (the non expert user selected I dont know). The sixth taskis to identify if there is corrosion waste in the fracture zone (the non expertuser selected No). And finally, the last task is to identify the load beforethe failure (the non expert user selected variable load). The resulting failuremode using the Bayesian inference was torsional brittle fracture (99%). Thefuzzy inference result was torsional brittle fracture.

The rule based inference engine had no response, due to the fact that therule for corrosive environment was not defined in the inference engine as Idont know. For the rule based engine, that question has only two values(corrosive environment, non corrosive environment).

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Figure 6: Corrosion, final tasks, and final failure mode result

Each failure mode had a fault tree analysis diagram, as a tool for iden-tifying the root cause of the failure mode identified. Whit this FTA, themaintenance and operation department can improve their practices and pro-cedures. An example of a fault tree analysis for brittle torsion fracture isshown in Figure 7.

3. Validation

There are different techniques for expert system validation, but ratios andindexes of agreement are frequently used.

One expert system exhibits better performance than another when:

1. The ratios ofsensibility, specificity, and ROCare greater.

2. The index of agreement is higher.

3. The unweighted kappa index () and weighted kappa index w arehigher.

These indexes are presented in the next section.

3.1. Ratios of agreement

The ratios of agreement are based on a 2x2 matrix for each failure mode,as shown in Table 3. Variables a,b,c and d show the relationship between

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Figure 7: Example of fault tree analysis for torsional brittle fracture in shaft

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the total number of concordances between the human experts and the ex-

pert system in the test. Variable D represents the presence of evidence or asymptom, and (D) represents an absence of evidence in a failure case.

Variableaindicates the times in the test when the human expert identi-fied a failure mode and the expert system did too, b is the number of timeswhen the human expert identified an absence of a failure mode and the ex-pert system identified a presence, c is when the human expert identified apresence of a failure mode and the expert system in the test showed an ab-sence and dshows when the human expert identified an absence of a failuremode and the expert system gave the same answer.

Using variables a, b, c and d and their relationships, it is possible to findthe following ratios of agreement: Index of agreement (for ratios), sensibility,specificity, and receiver operating characteristic (ROC).

Table 3: Contingency table for agreement ratio [17]

Human Expert Response

D D

Expert system for testD a b a+b D c d c+d

a+c b+d a+b+c+d

3.1.1. Index of agreement based on ratios

Represented by Iar, it is calculated as shown in Equation 1.

Iar= a+d

a+b+c+d (1)

3.1.2. Sensibility

Represented by S, it is calculated as shown in Equation 2.

S = aa+c

(2)

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3.1.3. Specificity

Represented by Ein this paper, it is calculated as shown in Equation 3.

E = d

b+d (3)

3.1.4. Receiver operating characteristic

Represented byROCin this paper, it is calculated as shown in Equation4.

ROC = Sensibility+Especificity

2 (4)

3.2. Index of agreementIn the agreement strategy indexes, there are three different tools: theindex of agreement, (unweighted kappa index), and w (weighted kappaindex) [17]. Using contingency tables, it is possible to calculate the index ofagreement (Iap) as follows in Equation 5:

Iap=

ki=1,j=1,i=jnij

N =

k

i=1,j=1,i=j

pij (5)

In Equation 5, Nis total number of cases, nij is the total number of casesat cell ij in the contingency table, and pij is the principal diagonal in the

contingency table.

The unweighted kappa () is calculated as shown in Equation 6:

= po pc

1 pc(6)

In Equation 6, po is the proportion of observed agreement and pc is theproportion of agreement due to causality as the sum of the margin propor-tions of the principal diagonal on the contingeny table. pcis calculated as thesum of the relative frequencies of row iand column j, as shown in Equation7.

pc=k

i=1,j=1,i=j

pipj (7)

The weighted Kappa w index is calculated as follows using Equation 8.

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w = 1

k

i=1,j=1v

ijp

oijki=1,j=1vijpcij

(8)

In Equation 8, poij is the agreement proportion observed for cell ij, pcijis the agreement due to causality for cell ij, and vij is the weighted one(punished) in cell ij.

3.3. Failure cases

To validate the result for each expert system, forty-six failure cases inshafts were used, as follows:

Sixteen cases for fracture. Ten cases for wear.

Ten cases for corrosion.

Ten cases for plastic deformation.

The cases were analyzed by a panel of four human experts in failure anal-ysis and were then compared with the diagnosis response of each inferencesystem for failure mode identification. Table 4 shown the industry of originfor the cases of failure.

Table 4: Industry source of failure cases

Industry (%)

Oil & gas 47.8Industrial machinery 21.7

Automotive 10.9Aeronautics 10.9

Mining 6.5Food & beverage 2.2

Total 100

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4. Experimental results

The results of the analysis of the fracture cases are shown in Table 5,wear cases in Table 6, corrosion cases in Table 7, and plastic deformation inTable 8. Each table shows the human expert response and the response foreach inference engine tested (rule based, fuzzy inference and Bayesian). Onthe basis of these results, it is possible to find the contingency table for eachfailure mode.

Table 5: Results for fracture cases

Case/Expert Human Experts Rule based Fuzzy inference Bayesian inference

1 bfb No response bfb bfb

2 tbf No response tbf tbf 3 tbf No response tbf tbf 4 bff bfb No response bfb5 bff bff No response bff 6 tbf tbf No response tbf 7 tdf No response tdf tdf 8 bff No response bff bff 9 sccub sccub sccub sccub

10 bff bff No response bff 11 bcf No response bff bcf

12 tdf sccub sccub bfb13 bfb No response No response bfb14 bfb bfb No response bfb15 tbf No response tbf tbf 16 bff bff No response bff

Brittle fracture in bending (bfb), torsional brittle fracture (tbf), torsional ductile frac-ture (tdf), bending fatigue fracture (bff), torsional fatigue fracture (tff), torsional fatiguefracture in splined shaft (tffss), bending corrosion fatigue (bcf), torsional corrosion fa-tigue (tcf), stress corrosion cracking under bending (sccub) and torsional stress corrosioncracking (tscc).

4.1. Results for indicators

Table 9 shows the indicators and ratios for all the modules as a responseof the rule based inference engine:

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Table 6: Results for wear cases


1 sf sf sf sf 2 abw No response abw abw3 adw adw adw adw4 sf sf sf sf 5 adw adw adw adw6 fr fr fr fr7 fr fr fr fr

8 adw adw adw adw9 fr No response fr fr

10 fr No response fr fr

Superficial fatigue (sf), abrasive wear (abw), adhesive wear (adw), fretting (fr).

Table 7: Results for corrosion cases


1 uc uc uc uc2 pc pc pc pc3 uc uc uc uc4 pc pc pc pc5 pc pc pc pc6 pc pc pc pc7 pc pc pc pc8 pc pc pc pc9 pc pc pc pc

10 pc pc pc pc

Pitting corrosion (pc), uniform corrosion (uc).

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Table 8: Results for plastic flow cases


1 tpf tpf tpf tpf 2 tpf No response tpf tpf 3 tpf No response tpf tpf 4 tpf tpf tpf tpf 5 bpf bpf bpf bpf 6 bpf bpf bpf bpf 7 sbub sbub sbub sbub

8 sbut sbut sbut sbut9 dkws dkws dkws dkws

10 tpf No response tpf tpf

Torsional plastic flow (tpf), bending plastic flow (bpf), shell buckling under bending(sbub), shell buckling under torsion (sbut) and damage in keyway or spline (dkws).

Table 9: Indicators and ratios for the rule based inference engine

Iap w Iar S E ROC

Fracture 0.375 0.301 0.154 0.875 0.364 0.976 0.670Wear 0.700 0.620 0.647 0.925 0.750 0.913 0.831

Corrosion 1.000 1.000 1.000 1.000 1.000 1.000 1.000Plastic flow 0.700 0.639 0.558 0.940 0.880 1.000 0.940

Average 0.694 0.640 0.590 0.935 0.748 0.972 0.860 0.255 0.286 0.347 0.051 0.276 0.041 0.145

Iap (Index of agreement), (Unweighted kappa index),w(Weighted

Kappa index), Iar (Index of agreement ratio), S (Sensibility), E(Specificity), ROC (Receiver operating characteristic), (Standarddeviation).

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Table 10 shows the indicators and ratios for all the modules as a response

of the fuzzy inference engine.Table 10: Indicators and ratios for the fuzzy inference engine

Iap w Iar S E ROC

Fracture 0.500 0.426 0.340 0.885 0.464 0.974 0.719Wear 1.000 1.000 1.000 1.000 1.000 1.000 1.000


Average 0.875 0.857 0.835 0.971 0.866 0.993 0.930 0.250 0.287 0.330 0.057 0.268 0.013 0.141

Iap (Index of agreement), (Unweighted kappa index),w(WeightedKappa index), Iar (Index of agreement ratio), S (Sensibility), E(Specificity), ROC (Receiver operating characteristic), (Standarddeviation).

Table 11 shows the indicators and ratios for all the modules as a responseof the Bayesian inference engine.

Table 11: Indicators and ratios for the Bayesian inference engine

Iap w Iar S E ROC

Fracture 0.875 0.841 0.837 0.958 0.883 0.974 0.929Wear 1.000 1.000 1.000 1.000 1.000 1.000 1.000


Average 0.969 0.960 0.959 0.990 0.971 0.994 0.982 0.063 0.080 0.082 0.021 0.058 0.013 0.036

Iap (Index of agreement), (Unweighted kappa index),w(WeightedKappa index), Iar (Index of agreement ratio), S (Sensibility), E(Specificity), ROC (Receiver operating characteristic), (Standarddeviation).

Figure 8 shows a comparison of the indicators based on indexes of agree-ment as Iap, and w for the three inference engines.

According to Figure 8, the index of agreement (Iap) showed that Bayesianinference exhibited better performance (96.9 %), in comparison to fuzzy in-

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Figure 8: Index agreement comparision

ference (87.5%) and the rule based inference engine (69.4%). Using the un-weighted index and the weighted w index, the rule based inference engineexhibited the worst performance, with 64% for and 59% for w. The fuzzyinference engine obtained 85.7% forand 83.5% forw. Finally, the Bayesianinference engine gave a result of 96% for and 95.9% for w.

Figure 9 shows a comparison of the indicators based on ratios of agreementasS,E, andROCobtained for the rule based, fuzzy inference, and Bayesianinference engines.

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Figure 9: Ratios of agreement comparison

The best sensibility (S) and specificity (E) performance was obtained withthe Bayesian inference engine, with S=97.1% and E=99.4%. The highestvalue for the ROC (the relationship between the sensibility and specificity),was for the Bayesian inference engine (98.2%), followed by the fuzzy inferenceengine (93%) and the rule based engine(86%).

5. Discussion

The fracture module had the most complex system of relationships be-tween evidence and failure modes. There are several failure modes withsimilar evidence in their symptoms (e.g. beach marks, radial marks and twozones of fracture). The experimental results showed that more relationshipsincrease the completeness in the expert system. It will be challenging toidentify all the differences between the different failure modes.

Bayesian inference had the best indicators compared with fuzzy inference

and rule based reasoning. Bayesian inference is more flexible due to thefact that uses conditional probabilities to evaluate a failure mode between0 100%, while fuzzy inference and rule based systems use if-then rules.

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If an evidence (rule) is not listed in a failure mode, Bayesian inference

decreases the probability, but it is still possible at the end of the analysis toidentify the correct failure mode with a small similarity. In this case the if-then systems (rule based and fuzzy) can not identify the failure mode unlessa new rule is added to the knowledge base. This condition gives an advantageto Bayesian inference in complex failure cases such as fracture identification.

That fuzzy inference can accept non exact information that depends onobservations of the non expert user (beach mark identification as an example)compares with the rule based system where it is necessary to define all therules in order to solve the failure mode.

6. Conclusion

1. More relationships between the same evidence and multiple failuremodes increase the complexity of the diagnosis. Bayesian inference had thebest performance index compared with fuzzy and rule based systems.

2. Failure analysis is a non-deterministic procedure due to the differentinterpretations and possibilities that a failure analyst could find in a case.Even though rule based reasoning (ROC 86%) has been applied with successin previous papers, the use of other inference techniques such as fuzzy (ROC93%) or Bayesian inference (ROC 98.2%) could improve the failure modeidentification process in organizations, for the complex diagnosis process.

3. The process of validation for an expert system presented in this papercould be used as an example for quantitative validation of any expert system,when the result is compared with human expert response.

4. According to results presented in this paper in the future, it will bebetter to implement an expert system for failure mode identification basedon Bayesian inference.

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