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Fusing Diagnostic Information Without A PrioriPerformance Knowledge
M. Garbiras
Information Technology Lab
GE Corporate Research & Development
Niskayuna, NY, U.S.A.
K. Goebel
Information Technology Lab
GE Corporate Research & Development
Niskayuna, NY, U.S.A.
Abstract - Diagnostic information fusion is the methodby which one would determine a system’s state for thoseinstances where several different diagnostic tools, andpossibly other sources, are used for state estimation.Because system state predictions from differentdiagnostic tools will disagree at some extent, if notcompletely contradict one another, a robust fusion toolis necessary to produce a reliable assessment of systemstate. This paper addresses the need for a reliablesolution to the problem of diagnostic information fusion,particularly with the absence of a priori knowledge ofdiagnostic tool performance. Tool performancespecifi cations are often times hard to come by, inparticular where data about events are sparse or wherea comprehensive evaluation cannot be performed. Inresponse, a fusion process, using a set of neuralnetworks, was developed to distinguish recognizablepatterns from the output of the individual diagnostictools. This fusion concept was applied to data that weregathered from a high-speed milli ng machine andprocessed by several previously developed diagnostictools.
Keywords: fusion, information fusion, diagnosis,classification, soft computing, neural network,diagnostic information fusion.
1 Introduction and background
An increasing demand for quality and reliability, in bothproduct manufacturing and service providers, raises newissues on the best ways to reach such standards. This isparticularly true, and somewhat difficult to control, inautomated processes. Because these automated processesare often left to run without close human supervision, it isdifficult to determine the health of the machine and itsparts without shutting down and investigating theequipment. One way to achieve high reliability andquality levels for automated processes is through on-linemonitoring and diagnosis of machine health andoperation. New advances in technology have made itpossible to acquire data at a rate and granularity neverbefore possible by human interaction.
With the new capability to receive and analyze data atsuch high rates, high granularity, and high availability,
there is a need for accurate and reliable ways to interpretthe data into a comprehensible result correlating tomachine health. There are many ways to do this,depending on the system we are speaking of, and thelevel of diagnosis we are trying to achieve. And becausethere is an abundance of tools and methods to reliablyand accurately diagnose machine health, it is often thecase that more than one tool is used at a time for a singlemachine, possibly with partially overlapping problemdomains. Hybrid applications that try and yield theadvantages of two or more types of applications, arebecoming more popular as the thought is they add somevalue by having different mechanics acting together toproduce one result. In a sense this is what diagnosticfusion is doing.
Diagnostic information fusion attempts to find areliable way to combine the estimates of differentdiagnostic tools [1]. In some instances, the requirementsfor a diagnostic fusion tool, aside from accurate andreliable results, include its ability to successfully produceresults without a priori knowledge of system limitationsor exceptions. This paper examines the effectiveness ofneural networks (NN) to handle this problem.
1.1 Diagnostic fusion via neural networks
A two-level system was developed, consisting of fourdifferent diagnostic tools in the first level, and a singlefusion tool in the second level. Raw sensor data are fedinto the first level and the resulting outputs are collectedand fed into the second level that produces a bettersolution than the best diagnostic tool for any conditionunder consideration. As shown in Figure 1, the input tothe first level of the system are the measured features.The output consists of four values indicating the degreeof membership for each of the four output classes. Wechose this approach over an approach where the firstlevel subsystem generates a crisp class (from 1 to 4)because this approach gives much more flexibility andinformation to the second level system. In the approachchosen here, the membership approach allows a softerclassification. The second level system then combinesthe results of the first level systems and classifies theinput into a single class. We focus in this paper on the
fusion task and evaluate performance based on the fusedmembership values.
OutputFUSIONNN(s)
Classification
Input
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Figure 1: The system architecture
Since we want to be able to determine the best possibleestimate from all the diagnostic tools, without a prioriknowledge of diagnostic tool performance, a neuralnetwork was chosen to discover patterns related tospecific classifications and to produce an accurate overallassessment.
Three fusion tools were created and evaluated. 1.) asingle 2 layer perceptron NN used to produce a singlefused output; 2.) a set of 2 layer perceptron NNs used tofuse an output value; 3.) a 3 layer perceptron NN thatoutputs the fused value. The set of 2 layer NNs wascreated after drawbacks were discovered fromapproaching the problem with only a single 2 layer NNas the solution. We have chosen to include design notesand results of the single 2 layer NN method as a basis ofcomparison to the eventual solution. This informationalso proves useful in explaining the success of theeventual solution.
We compare the results of all three methods to drawconclusions on their overall effectiveness and makerecommendations for their usefulness.
2 Experimental setup
A milling machine under various operating conditionswas selected as the machine health we wish to diagnose.In particular, tool wear was investigated in a regular cutas well as entry cut and exit cut. Data sampled by threedifferent types of sensors (2 acoustic emission sensors, 2vibration sensors, motor current sensor) were used todetermine the state of the wear of the tool. As the wearmeasure, flank wear VB (the distance from the cuttingedge to the end of the abrasive wear on the flank face ofthe tool) was chosen. The flank wear was observedduring the experiments by taking the insert out andphysically measuring the wear. The basic setupencompasses the spindle and the table of the Matsuuramachining center MC-510V. An acoustic emissionsensor and a vibration sensor are each mounted on to thetable and the spindle of the machining center. Thesignals from all sensors are amplified and filtered, thenfed through two RMS before they enter the computer fordata acquisition. The signal from a spindle motorcurrent sensor is fed into the computer without furtherprocessing. Data are categorized into four classes andare approximated by fuzzy membership functions (nowear, little wear, medium wear, high wear).
Figure 2. Input data
2.1 Input data transformation
Before being used, the following transformations wereapplied to the data:1. The data was smoothed by averaging using a
window of 50 points, and then the sample size wasreduced by sampling the resulting data set at 50point intervals.
2. Each input and the output data was normalized to liebetween 0 and 1
3. Since the output variable was sampled at muchlarger intervals than the input variables, and since itrepresents tool wear, the output data was furthersmoothed by fitting a 3rd order polynomial.
Figure 2. shows the normalized input data. The outputdata was categorized into four classes using fuzzymembership functions as shown in Figure 3.
Figure 3. Membership functions
2.2 Diagnostic tools employed
Nearest Neighbor classifier (NNBR): The first subsystemuses a nearest neighbor scheme for classifying the data.The case base consists of a set of sensor readings and theassociated unclassified wear value. Given an input, thek-nearest data points are determined and the associatedwear values are averaged. This average is then used tocompute the membership degree for each of the fourclasses.
Neural Network (NN1): The second subsystem is aneural network that was trained on binary classes. Thatis, the target values were 0 and 1 vectors determined bythe maximum membership value over the four classes.
Neural Network (NN2): The third subsystem is also aneural network, but this was trained to learn themembership values themselves, as opposed to theclasses.
Fuzzy Inference System (RM): The fourth subsystem isa fuzzy inference system implemented using a relationalmatrix.
2.3 Previous approaches to determine toolwear
On-line tool wear estimation is an issue in manufacturingbecause most of the time it cannot be measured directly.In the case of milli ng operations the diagnostic task isconfounded by extremely high noise as well as signalsseemingly indicating a different than true wear state dueto changes in work piece hardness, non-uniform depth ofcut during the first pass, changing amount and qualit y oflubricant, etc. The highly non-linear nature of thisprocess makes it hard to estimate the current wear state.However, it is desirable to know the current wear state toproperly asses the impact on surface qualiti es thusavoiding the need to throw out work pieces. Furthermore,there is a potential for costly damage to the machine dueto tool conditions (for example chatter) or tool breakage.As a result manufacturers use conservative operatingprocedures to prevent these malfunctions [2]. However,these result in less eff icient and more costly production.A number of diagnostic techniques have been developedin the past attempt to deal with theses problems,including neural networks [3], clustering algorithms [4],Kohonen’s Feature Map [5], fuzzy logic [6], andprobabili stic influence diagrams [7]. To achieve furtherperformance improvement, hybrid systems were proposedto overcome shortcomings of individual systems, such asfuzzy-neural systems [8]. Here, the author tried to copewith the diagnostic task training membership functionsfor each wear state using neural nets and then combiningthem using fuzzy inferencing techniques. The results inmost approaches are optimized to a local level but sufferfrom applicabilit y to a wider range of operatingconditions.
3 Fusion approaches
Three different approaches were used to solve thisproblem. The first approach used a single 2 layerperceptron NN to learn the patterns of all four outputmembership functions. The second approach used was aset of four independent 2 layer perceptron NN, each onerepresenting the output of only one of the membershipfunctions. The final approach used was a 3 layerperceptron NN trained to learn the patterns of all fouroutput membership functions.
The first two approaches were chosen to compare theeffectiveness of a 2 layer NN that is trained to discover
multiple interleaved patterns from a data set of smoothand continuous data versus the effectiveness of multiple 2layer NNs trained on similar data to discover a subset ofthe problem. The hypothesis underlying was that it wasmore effective (and easier to implement) to constructmultiple independent NNs customized to solve a subset ofthe overall problem rather than implement one NN tosolve the entire problem. A side by side comparisonyields evidence for the abilit y, or lack thereof, of a NN tolearn multiple traits from continuous data.
The 3 layer NN approach was chosen to exploit theuniversal generali zation capabiliti es of such a system andcompare its abilit y to model multiple interleaved patternsfrom a data set, versus the effectiveness of simple NNswith only one hidden layer (i.e., 2 layer perceptrons).We expected the 3 layer NN to outperform the 2 layerNNs due to the former’s promise to allow generalnonlinear mappings. However, in comparing results theauthors also note the ease of implementation and trainingof the solutions.
A training set of data was created from the experimentsundertaken choosing one setting for feed and depth of cutwhich were partitioned into four partiall y overlappingstates of tool wear. Data corresponding to “no wear” ,“ littl e wear” , “medium wear” , and “high wear” at variousmembership degrees were used. Although not as smoothor continuous, Figure 3 gives a good representation of theoutput membership values of the training file.
3.1 FNN1
This fusion neural network (FNN1) was a 2-layerperceptron, with 16 inputs, 16 nodes in the hidden layer,and four output nodes. FNN1 was trained using agradient descent backpropagation method, and originall ywas trained using all the data points in the training data,but was unable to model the smooth and continuousnature of the membership functions and the training data.The granularity was too high for this NN to recognizeany distinctions within the data set and to partition thedata into the desired classes. Therefore select featureswere extracted to reduce the size and granularity of thetraining data and to avoid overtraining the network. Theselected features are shown as the shaded regions inFigure 4.
Figure 4. FNN1 Training Data Features
These features, the max range of the membershipfunctions and the overlapping membership functioncrossover points, were chosen because they provide theessential information about the shape of the membershipfunction: it’s height, width, and support. While it wouldbe desirable for a neural network to model the entiresmooth membership function, simply having it model themaximum, minimum, and crossover points reduces thecomplexity of the task. This allows the general shape ofthe membership function to be reali zed, producingacceptable results and limited classification error.
The features corresponding to maximum membershipfunction values contained twice as many data points asthose features corresponding to the membershipcrossover points. This was done because the NN haddiff iculty modeling the steep slope of the membershipfunctions around the crossover points with increasingnumbers of data points. One will also notice that due tothe specific nature of the membership functions used,selecting a larger interval of data representing themaximum range of a membership function gave usinformation about the crossover of non-adjacentmembership functions. The NN was able to model thesecrossover points with the larger number of data pointsfrom the maximum value range because the membershipfunction slopes were much more gradual than at the truecrossover points. Figure 5 shows the architecture ofFNN1, a simple perceptron with 16 inputs, 16 hiddennodes, and 4 output nodes.
Figure 5. FNN1 Architecture
3.2 FNN2
FNN2 consisted of a set of four 2 layer perceptrons, eachone trained to learn the pattern of just one specificoutput membership function. One NN was trained torecognize the “no-wear” function, one for “ littl e wear” ,one for “medium wear” , and one for the “high wear”function. Similar to FNN1 these were also 2-layerperceptrons, with 16 inputs, 16 nodes in the hiddenlayer, and four output nodes, trained using a gradientdescent backpropagation method.
Figure 6. FNN2 Training Data Features
FNN2 was trained with the same data as FNN1,however there was initiall y only minimal improvement.Therefore additional features were extracted from thegeneral training file. Figure 6 ill ustrates the featuresselected. Two major differences between the newfeatures chosen and the originals were the number ofdifferent features selected and the consistent interval sizeof the features. (Each feature was represented by thesame number of data points). Again the maximum ofeach membership function was chosen, but the crossoverpoints were omitted. The reason the crossover pointswere omitted from this feature selection was becausethey did not provide useful information about the shapeof the membership function as once thought.
Instead features about the change in the slopes of themembership functions were chosen as criti cal regions todefine the shape of the membership functions. FromFigure 6 we can see the regions we are speaking ofcorrespond to the slopes with ±45° tangents on each sideof the maximum value of a membership function. Thesesame regions, because of the nature of the membershipfunctions, also gave us information about the change inslope behavior of the adjacent membership functions.
Figure 7. FNN2 Architecture
Note that FNN1 could not be trained with the featuresused for FNN2 because there was too much information
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and the information was too continuous for FNN1 tohandle and accurately represent the four outputmembership functions. FNN2 was able to handle thistraining file because each of the perceptrons withinFNN2 was used to represent only one output membershipfunction. Thus the changing values of all themembership functions and the crossing of thresholdsbetween membership functions did not affect its learning,because each network was interested in only the behaviorof one membership function.
Figure 7 is the architecture of one of the perceptronsFNN2, (recall that FNN2 consisted of 4 suchindependent NNs).
3.3 FNN3
The last implementation was a 3-layer neural network(FNN3), with 2 hidden layers, 8 nodes in the first layer, 4nodes in the second layer, and 4 output nodes. Thisnetwork was trained by a genetic algorithm (GA) usingthe same training data as FNN2. We opted to use GAs fortuning the network weights and thresholds, mainly fortheir ease of use compared to a backpropagationapproach. We will not give a detailed account of GAshere and instead refer to the literature (for example inHolland, [9], Grefenstette [10], and Goldberg [11]).
Chromosomes represented the 192 network weightsand were real valued chromosomes bound on the interval[-1 1]. 500 random chromosomes were used in the initialpopulation. Normalized geometric selection was usedwith crossover rate of 60% and mutation rate of 5%, for5000 generations. 50 trials were run, with the bestperformer from each run tested against the test data set,and the average of these errors is reported. Figure 8shows the architecture of the 3-layer neural network(FNN3) with 16 inputs, 8 units in the first hidden layer, 4units in the second hidden layer, and 4 output nodes.
Figure 8. FNN3 Architecture
FNN1, FNN2, and FNN3 were tested against the sametest data, which was separate from the training data.
4 Baseline case In simple fusion schemes such as majority voting a basicproblem is the danger of ending up with a system that
performed worse than the best individual tool becausethe poor estimates drag down the better one. Onepotential solution is to use an off- line learning system todiscover patterns and useful information in aidingcorrect and accurate fusion of data.
The high success rate of one tool means that if it wereused as part of the majority fusion, the performancedegrades somewhat. This is to be expected, because thevotes of the poor performers will sometimes out vote thecorrect one. The problem is greater with increasingnumber of classification regions, as there will be caseswhen each system will generate a different class, and themajority voting system will t hen pick one randomly.
To avoid that, a priori information about toolperformance can be used to scale the different tools.That is, the diagnostic opinion of some tools becomesmore important than that of others. This can beaccomplished by scaling the tools by a weight, which inturn is based on the tools’ classification rate. This isadmittedly a crude way because it does not take intoaccount the performance for individual classes within atool. However, it serves well as a benchmark tool for ourpurposes. Applying the above described scaled votingscheme to the diagnostic fusion task at hand, we get aslightly improved result of 97.0% classificationaccuracy.
5 Results
Results’ accuracy were measured by comparing the outputof the fusion NNs with the expected value for eachmembership function. An error is calculated as a pointfor which the highest membership value for the fusionNN output does not correspond to the same membershipfunction as the expected value. In other words, an erroris not the difference in magnitude of the outputmembership values, rather the absence of the correctmembership value as having the highest magnitude, i.e.,if for a sample the expected output is for the “mediumwear” membership function to have the largest value, andthe fusion NN outputs “high wear” as having the largestmagnitude, then that is counted as a misclassificationerror. We compare the two different approaches bymeasuring the hit percentage, or number of correctclassifications produced. Table 1 summarizes the resultsof the accuracy rating of the four pre-fusion diagnostictools using this method.
Table 1. Classification RatesSystem Rate (%)
Nearest Neighbor (NNBR) 96.8Neural Network 1 (NN1) 80.6Neural Network 2 (NN2) 86.7Relational Matrix (RM) 81.0
FNN1 was trained to generate four valuescorresponding to the four output membership functions.On the first set of attempts FNN1 was unable to recognizethe “no_wear” membership function and thus scored onlyan accuracy rating of 82.88%. The problem was in the
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feature extraction of the training files because the no weardata were too much undersampled. However, aside fromthe lack of “no_wear” output, the network seemed tomodel the system performance reasonably well . Figure 9shows the output of FFN1 plotted against the expectedvalues (dashed lines). One can see that the output closelyfollows the shape and magnitude of the expected curves.
Figure 9. FNN1 original output
After expanded feature selection (as mentioned insection 2.3.1 and Figure 4) and retraining FNN1 theoutput classification rate improved to 92.89% (stillbeneath the best performing individual tool). The plot ofthe generated output versus the expected values alsoseemed to change for the worse. Figure 10 shows that nolonger do we see a tight tracking with the expected valuesas we did for the first attempt. The fact that this networkwas able to recognize “no_wear” was the reason itsclassification rating went up, but overall the system lostthe abilit y to model the system performance with thesame granularity it once had.
This is the type of performance we would expect to seefrom FNN1 given the close, interleaved, relationships ofall the membership functions, and the continuous, smoothnature of the data. These factors make it diff icult for thisparticular NN (especiall y since it is only a 1-layerperceptron) to distinguish between correct membershipvalues.
Figure 10. FNN1 improved output
The perceptrons within FNN2 were trained to eachlearn the membership function patterns of one outputfunction. Figure 11 shows the result of the trained FNN2module. One can see how by training each membershipfunction separately the network was given a chance tolearn the idiosyncrasies associated with that membershipfunction better than trying to learn all at once. Eachcurve closely follows the predicted value, even betterthan previous networks. As a result the networks withinFNN2 resulted in a classification rate of 97.3%, which isbetter than the best performing diagnostic tool and betterthan the voting using a priori information. Table 2summarizes the accuracy ratings of the different fusionneural network methods.
Figure 11. FNN2 output
The success of FNN2 is attributed to the fact that it wasable to learn more detail s about each membershipfunction than the single FNN1. As the number ofmembership functions (output categories) increases, withmore complex systems, one can infer from the resultsobtained through this study, that multiple NNs trained torecognize each membership function individually willoutperform networks trained to recognize all of thefunctions at one time.
Figure 12. FNN3 output
FNN3 provided the greatest accuracy. On average thetechnique of using a GA to tune a 3-layer NN gave us an
accuracy rating of > 95%, with the single best performerhaving an accuracy of 97.8%. In fact 34% of the trialruns resulted in accuracy > 97%, while only 22% of thetrials gave accuracy less than 96%, with the lowest ratingof 88%. We can see from Figure 12 that the outputmembership functions were closely recognized, andalthough they did not reach the full potential membershipvalue of 1, from the tight following of the desired output,we have high confidence in the actual values of eachoutput value as an accurate result of the diagnostics. Wewould li ke to point out that there is an upper limit forperformance improvement because the tool wear wasapproximated by a polynomial function while in fact wewere looking at finite steps of progressing tool wear.Removal of this condition may further improve theresults.
Table 2. Classification Rates of FusionSystem Rate (%)FNN1 original 82.9FNN1 improved 92.9FNN2 97.3FNN3 (best) 97.8FNN3 (avg) 95.8
6 Summary and final remarks
The use of fusion neural networks provides a means toimprove performance of individual diagnostic tools. Inexperiments with data from a milli ng machine, theperformance of such neural networks is shown. Theadvantage to the off- line learning approach of a neuralnetwork is the abilit y to successfull y fuse the diagnosticinformation without a priori knowledge of individualdiagnostic tool performance. A priori knowledge issometimes hard to come by. Either the classes have notbeen observed suff iciently on the real system or it wouldbe extremely hard to run simulation because of a lack ofa proper model, etc. Therefore, a fusion system that candeal without expli cit a priori tool performancespecifications is very attractive. One has to keep in mindthat there is implicit information about systemperformance embedded in the labeled data. In otherwords, data for each class and information about the realsystem state holds engrained information about how aparticular diagnostic tool behaves.
It has also become apparent how important properfeature selection is. Ideally one would li ke to choose theoptimal features before venturing off to design theclassification and fusion tasks. Tools have beendeveloped to automate the feature selection process [12].However, this is often times an iterative process becauseparticular tools can deal with particular features andadditional or other features need to be chosen when adifferent tool is considered. This area still has some openquestions that are outside the scope of this paper.
Although we have shown the application for diagnosticinformation fusion, the task is essentiall y the same forany classification task. Similarly, the tool wear exampleshall not be understood as limiti ng this process to a
manufacturing environment. Rather, applications fromthe finance world, business, etc. are equally pertinent.
6.1 Future work
The networks used in this discussion were trained using asimple backpropogation technique, as well as byevolving GAs to discover optimal weight settings.Another use of GAs would be to evolve a population toconstruct the actual NN architectures as well .
Other future activities include attempting to solve thisproblem by using genetic algorithms for fuzzy rulediscovery. One could attempt to evolve a set of fuzzyrules describing the data coming from the differentdiagnostic tools and mapping it to an appropriateclassification. This approach will address the searchcapabiliti es of the GA, as well as its emergent propertiesto discover sets of schemata to represent broad-basedrules. The problem of input universe coverage andsuccessive overlap and fusion of these rules will also bean issue to consider.
Since it became apparent that proper feature selectionposed a bottleneck early in the project, a proper featureselection process needs to be employed to choose themost relevant features upfront.
References
[1] K. Goebel, V. Badami, and A. Perera, DiagnosticInformation Fusion for Manufacturing Processes,Proceedings of the 2nd International Conference onInformation Fusion, Fusion’99, Sunnyvale, CA, 1999. [2] S.S. Rangwala, and D. Dornfeld, Learning andOptimization of Machining Operations Using ComputingAbilities of Neural Networks, IEEE Transactions ofSystems, Man & Cybernetics, Vol. 19, No. 2,March/April 1989.[3] S.S. Rangwala, Machine Process Characterizationand Intelligent Tool Condition Monitoring UsingAcoustic Emission Signal Emission Signal Analysis, PhDthesis, UC Berkeley, 1988.[4] L.I. Burke, Automated Identifcation of Tool WearStudies in Machine Processes: An Application of SelfOrganizing Neural Networks, PhD thesis, UC Berkeley,1989.[5] C.S. Leem, Input Feature Scaling Algorithm forCompetitive Learning Based Cognitive Modeling withTwo Applications, PhD thesis, UC Berkeley, 1992.[6] J. Fei and I. S. Jawahir, A Fuzzy ClassificationTechnique for Predictive Assessment of ChipBreakability in Intelligent Machining Systems, Proc.IEEE Joint Conference on Fuzzy Logic and NeuralNetworks, San Fransisco, 1993.[7] A.M. Agogino and K. Rumamurthi Real TimeInfluence Diagrams for Monitoring and ControllingMechanical Systems, Influence Diagrams, Belief Netsand Decision Analysis, Ed: Oliver, R. M., and J.O. SmithJ.R Wiley & Sons, Ltd., 1990.[8] K. Goebel and P.K. Wright Monitoring andDiagnosing Manufacturing Processes Using a Hybrid
Architecture with Neural Networks and Fuzzy Logic,EUFIT, Proceedings, Vol. 2, Aachen, Germany, 1993.[9] J.H. Holland, Adaptation in Natural and ArtificialSystems, MIT Press, Cambridge, MA, 1975.[10] J.J. Grefenstette, GENESIS: A system for UsingSearch Procedures, Proceedings of the 1984 Conf. onIntelligent Systems and Machines, pp. 161-165, 1984.[11] D.E. Goldberg, Genetic Algorithms in Search,Optimization, and Machine Learning, Addison Wesley,Reading, MA, 1989.[12] K. Goebel and W. Yan, Feature Selection for ToolWear Diagnosis Using Soft Computing Techniques,submitted for presentation and publication in theProceedings of the 2000 ASME International MechanicalEngineering Congress and Exposition, Orlando, FL,2000.
