Diagnosis of Equipment Failures by Pattern Recognition

The main problems in relation to automatic fault finding and information about the past history of the system (inand diagnosis in equipments or production systems are discussed: cluding maintenance and operational utilization); all these 1) compression of the syndrome and observation spaces for better discrimdata determine the failure pattern vector. ination between failure modes; 2) simultaneous display of the failure patterns and the failure instants, for The actual diagnosis will be made by comparing this maintenance control and review of the reliability design; failure pattern vector with known pattern vectors found to 3) automatic production of a final set of diagnosis assumptions classified characterize the failure modes considered, and called learnaccording to their probabilities. ing patterns. The learning patterns originate from systems 4) sequencing of the inspections in accordance with the failure rates and for which the failure modes were found by maintenance inspection costs. personnel, and we assume that they are all stored in a freREADER AIDS: quently updated reliability and maintenance data bank. Purpose: Widen state of the art Comparing the observed symptoms (described by the failure Special math needed for explanations: Probability pattern vector) with the learning data, and classifying the Special math needed for results: Same ill-working system into one of few classes of possible failure Results useful to: Reliability and systems engineers modes, can therefore be formalized as a pattern recognition problem. Some research about this has been reported since INTRODUCTION 1968 by Becker [1], Cortina [2], Hankley and Merrill [3], Page [4], and Pau [51. The paper is concerned with automated diagnosis of In this paper, we treat some major problems in relation to generic systems which cannot be modeled by a logical netautomatic diagnosis. First, we discuss a compression methwork, and have only a small number of identifiable failure od of the observations about each system, for better dismodes, given only the input and output evolutions. In other crimination between failure modes and to eliminate all words, the analysis is based on representations of causality redundant tests and observations; this is the so-called relations between the failure causes and the corresponding feature extraction problem. In Section 2, we explain how to operating performances. This kind of approach is therefore display simultaneously the failure patterns and the failure specifically useful, for example, for electromechanical equipinstants, for maintenance control or review of the reliability ments, engines, and simple mechanical parts. design of the system. Section 3 deals with the production The purpose of any diagnostic searching procedure is to of a satisfactory list of a few most-relevant diagnostic asrecognize a failure mode, or a set of failures (also called sumptions,eclassifiedaccording to their probabilities. Lastly, syndrome), on the basis of numerical information about the in Section 4, we give some rules for sequencing the inspeccircumstances of the failure, results of non-destructive tests, tions by the element-by-element method, in accordance with the diagnostic assumptions, failure rates, and inspection Manuscript received October 2, 1973. costs. Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on October 9, 2009 at 06:53 from IEEE Xplore. Restrictions apply. PAU: DIAGNOSIS OF EQUIPMENT FAILURES BY PATTERN RECOGNITION 203 1. COMPRESSION OF THE LEARNING DATA of I-J, I-I, or J-J, is an overall statistical measure of the AND MEASUREMENT SELECTION correspondence between these elements, independently of all scale effects. 1.1 Definition of the Learning Data k(I,J) the "varimax" principle used to find orthogonal factors is . .. not applied to the raw data in k(I,J), but to quantities We basically assume that it has been possible to initiate a deducedfo a cte table p(I,J)b good data collection system, monitoring the systems considered over time, and also their main operating parameters ( in service until some observable functional-failure happens. p(i,j) = k(i,j)l k(l,m)) The implementation of such a data bank is a difficult probIeI,meJ lem, extensively discussed in Pau [6]. Let I, J respectively be with estimated marginal probability density functions (at a given date) the set of measurements and the set of (pdf): pattern vectors describing the failures of all systems of the same type. The learning data k(I, J) ={k(i,j) ) 0 iel jeJ} Pi p(i,.) = p(i,j) il Pr{ji} p(i,j)/p(i,.) are either qualitative or quantitative; and can then be JeJ defined as follows: k(i,j) is the value of measurement i concerning the system j; i.e., time since last overhaul TBOj, Pi p=( .,j) = E p(i,j) 1jeJ Pr{i j} p(i,j)/p( .,j) voltage at some point, or any binary parameter indicating i6' that a given subsystem was switched on. Some measureCorrespondence analysis may then be summarized as ments i may also be made binary if their intervals of variafollows: tion have been sampled into smaller intervals. a) The metric on I is the distance function d,, while the The past experiments have shown that misleading conmetric on J is the distance function dj clusions may be drawn from once-compressed learning data, either because of too-small learning samples, or because of d (i1 ,i2) =2E [Prj i}}-Pr{j i2}]2/p(.,j) careless reports. Methods to account for these phenomena jEJ have been thoroughly tested in practice and justified theoretically [5]. Other transformations may be made, in order dj1 ,12) = [Pr{ij1l}Pr iJ]21p(i to study the learning data from specific viewpointsI: je a) the learning data k(I, J) are called explicit if one of the The weighing factors, such as 1 /p(i,.) are introduced in sets I, J designates equipments, and the other, observations order to compensate for cases like the following; an obserabout these equipments as previously defined. vation i may always be related to large conditional probab) the learning data k(I,J) are called implicit if both sets bilities Pr{iLj} mainly because p(i,.) is large, and the differI, J are observations; such a tableau is deduced from an ences between Pr {i[j} values will have an excessive imporexplicit tableau by aggregating some observations with tance when comparing a system jI with a system i2. respect to all equipments, or by classifying all equipments b) The element i has Card (J) coordinates (Pr{j i}, j = with respect to some observations. For example, if J has 1, Card (J)); the element j has Card (I) coordinates (Pr become the set of TBO intervals, we may define: k(i,j) is JiL4, i = 1, Card (I)). These coordinates are called profiles the number of learning equipments having had a failure in of i and j resp. The element i has the weight p(i,.), while j the TBO-intervalj, and on which the symptom i was present. has the weight p(.,j). Design review generally uses learning data in the implicit c) Let the constant r be given such that r < Inf{Card (I), form, while automated diagnosis uses the explicit form. Card (J)}. We want to minimize, in the sense of the d, or dj metric, the dependence between I,J defined as the normvalue ||p(I,J) Pi 0 PJ 112. If this quantity had been zero, 1.2 Fetue xtaciobteeasfthen the sets {I} and {J} would have been independent in Correspondence Analysis Correspondence Analysis the probabilistic sense and the observations about each Assume that the tableau k(I,J) of non-negative numbers system would have been independent of the system conis given. The feature extraction procedure used herein is a sidered. But our goal is here to eliminate all redundancy in special form of principal component analysis, characterized the data, and to find as many aggregate observations as by the following additional properties demonstrated in possible (also called features) for which this independence Benzecri [7], Pau [8], Lebart and Fenelon [9]: holds, and r features for which dependence holds so that . . ~~~~~~~~discrimination can be done using only these. It can be no piorhypthess i mae abut he atur ofthedc-shown that the r-dimensional vector basis of basic features ments in the sets I (failures) and J (observations or equipwhc miiie thsdpnec.fe rnfrigCr ments), and all interactions are considered; in other words,()-oCadJ)-imnoalptesinkIJitor we~~~~~~ ~ do no caefrtelbl ntest I n J. dimensional vectors, can be constructed as follows [10)]. all elements in both sets {I; and {J} can be displayed simultaneously in the same reduced feature space, because for {I}, the r base vectorsf1 ,l =(l,r) are the r first printhey play symmetric roles in a tableau; in this reduced patcipal axes of inertia of the solid body made of the discrete tern space, the Euclidean distance between any two elements Card (J) dimensional elements iel having the weights p(i,.); Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on October 9, 2009 at 06:53 from IEEE Xplore. Restrictions apply. 204 IEFE TRANSACTflONS ON REIIABILIl Y, AUGUST 1974 this inertia is computed for the d, distance; let 4(Jf) be the a) If any two observations ' ,i2 in I are conditionally inertia of axisf1,l = (1,r) ordered by X(f1) ) f(f2) ) ... ) associated in the same way to all observations in J, then by )4fr); the f's are normed to the unit length with respect to definition of d1, the corresponding features on a map will d1. Andf1(2,1) is the (I + 1)'st eigenvector (resp. eigenvalue) be identical. Thus, if two failure modes i1 ,i2 are represented of the S =[Sjjl2matrix: almost by the same point in the feature space, then one of the following 2 statements is true: one of these modes is Sil j2 = E P(U,JI)P(l,12)Vp(i,.)[P(.,j)p( .,i2) 1/2 redundant, e.g., the maintenance instructions require stating ii, Card (1) the second failure mode each time the first failure mode is observed; the failure mode i1 can systematically be the for J, we have equivalent definitions and relations for m c th '.ai etr g, 1r.f,l =(,)aehr o main cause of the failure I mode i2 ,or conversely. b) The product p(i,.)G(i,1) is also called contribution of vectors, i.e., linear mappings. the observation i to the feature 1. This notion is strongly d) The coordinates of the learning patterns projected related to the correlation coefficient between i andf, as used into the r-dimensional feature space, are computed as in principal component analysis. This remark may help in follows: finding the interpretation of fl. All observations i of I for {I}, the feature 1= (1,r) of learning pattern iI on the mapped in a small neighborhood of the origion of the axes . . . r* r 11 1 . ~~~(fiJ8m) on the map, are therefore only slightly correlated axisf, originated in the center of inertia of all elements in . o with the features I and m. { is c) If, on such a map, two observation points iI1,2 are more G(i,l) fi [Pr{j i}, j = 1, Card(J) vector] (1) or less close, in the sense of the Euclidean d-distance between them, it means that these observations are more or less for {J}, the feature I of learning pattern jeJ on the axis . is .strongly associated. This association degree is here taken gl, originated in the center of inertia of all elements in J in the sense of the d or dj similarity measures between F(J,l) = g1 [Pr{i[j}, i = 1, Card(I) vector] (2) profiles. Once a close association has been detected, e.g., between a e) It can be shown that 4J1t) = (1 1= (l,r), and that it.. ' ' sufficient to .uteither the 's or the 's because pressure measurement i1l and a maintenance operation i2, then the maintenance department will have to give technical 1 1. . i = column reasons for this, or to demonstrate why it is meaningless. 1= .f Pr{J } c row l (3) Because all elements of I and J can be displayedsimultane ously on the same maps with the same length units on the G(i,1) = E FU,) Pr{i)}~/ d'.(f), I =,1r axes [7, 8] one can also detect associations between obserG(ijl) =1,CaFd(J) Pr{i~j}JV'.(f, 1 vationls J1, J2 in J, or even between an element of I and an element of J. The interpretation procedure is the same as Consequently, it is equivalent to display simultaneously for associations between observations in I. If i is d-close to all elements of I and J in either thef space or the gY space, j, this means that in general the measurement i has a higher (l,r) conditional probability with respect to j than in the mean with respect to the other observations in J (and the same for f) p(i,j) = p(i, . )p(. ,j)(l + £ F(j,l)G(i,i) I.(fXl)) j with respect to i). A careful and systematic analysis ofthe geometric proxim2. DISPLAY OF THE LEARNING DATA, AND ities between elements of I and/or J ought therefore to lead APPLICATIONS TO DESIGN REVIEW AND to a list of suspected causality relations. This proximity MAINTENANCE CONTROL analysis can also be done between clusters of points on maps Iiimplicit of decreasing weights, in order to identify causality relations In thi section, we are only concernedwithbetween syndromes or observation coinplexes. learning data k(I,J) where {I} and {J} are two different sets of observations. The main goal of this interpretation, which can be sustained with the computation of some confidence levels [5], is to draw attention to causality relations among failures, Using correspondence analysis as explained in the premaintenance, modifications, operating conditions, and vious section, we can select r = 2 and thereby find the two times. It has been applied to both electronic and mechanical best features discriminating the observations J and the airborne equipments in order to detect systematic coding observations I. According to Section 1.2.d), all observations errors, criticize maintenance operations and scheduling, can thus be displayed into the (f1 ,f2) plane which contains criticize design parameters, or select sensitive tests during the largest part of the dependence between I and J, namely accelerated field trials [10-12]. Our view is that the learning (X(fl) + 2(f2)), 2(f) ) 2(f2). Such a 2-dimensional repreand interpretation phase must be conducted in parallel with sentation of all learning data k(I,J) will be called a map, the analysis of experts' special reports, in order to compare and any pair of vectors f1 ,fw yields such a map of weight them. (i(f) + 2(fm)). These maps can be used as follows: Another field of active research is the analysis of test data Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on October 9, 2009 at 06:53 from IEEE Xplore. Restrictions apply. PAU: DIAGNOSIS OF EQUIPMENT FAILURES BY PATTERN RECOGNITION 205 for electronic components, in order to relate the failure 25% Axis 2 modes with technological design parameters; the main PPR Axis 1: 44% inertia application of this is in component selection for specific H4 Axis 2: 25% inertia environments [10, 13, 14]. H2 -1 PHU