computational intelligence methods for process discovery

Contributed Paper

Computational intelligence methods for process discovery

R. Cass *, J. DePietro

AI WARE Incorporated, 3659 Green Road, Beachwood, OH 44122, USA

Received 1 December 1997; accepted 1 June 1998

Abstract

The challenge in commissioning and maintaining industrial processes is one of managing complexity. When faced with ahighly complex system, an analyst may make simplifying assumptions, ignoring features that are assumed to have minimal

impact, assuming that data will take values in speci®ed regions or that system dynamics will have speci®c forms. When thespeci®cation of the real process is incomplete there may be occasions when the perceived situation does not ®t within theconstrained frame of reference or the responses do not have the expected e�ect. Computational intelligence methods can enable

the analyst or process engineer greater ability to cope with the natural complexity of industrial processes. Unsupervised learningmethods can be used to classify modes of operation. Neural network models can be trained from process data and used on-lineto simulate or replace ine�cient tests. Evolutionary algorithms can be used to e�ect optimal closed-loop supervisory-levelcontrol of processes. Any or all of these technologies can be applied to process monitoring, fault anticipation and aversion, fault

diagnosis and resolution, or process optimization. An example of the use of these methods is presented in the domain ofmetalcasting. # 1998 Published by Elsevier Science Ltd. All rights reserved.

Keywords: Metalcasting; Process discovery; Neural networks; Data analysis; Clustering algorithms

1. Introduction

Managing complexity is a signi®cant challenge incommissioning and maintaining industrial processes.In order to make e�ective decisions e�ciently, an en-gineer requires an understanding of the process, thefeatures, and system dynamics. When faced with ahighly complex system, an engineer may make simpli-fying assumptions, ignoring features that are assumedto have minimal impact, assuming that data will takevalues in speci®ed regions, or that system dynamicswill have speci®c forms. These assumptions serve tocreate a constrained frame of reference, within which amanageable amount of data can be evaluated, judg-ments made, and actions taken in a reasonable periodof time. Rules governing the development of con-clusions and responses to given data patterns are justi-®able within the constrained frame of reference.

However, when the speci®cation of the real processis incomplete, there may be occasions when the per-ceived situation does not ®t within the constrained

frame of reference, or the responses do not have theexpected e�ect. The possibilities of these situations arecommonly taken into account when developing re-sponse rules in order to hedge against excessivelyadverse results. This may cause sub-optimal perform-ance for the process overall.

What is required to maintain processes at optimalperformance are tools that discover the most import-ant relationships in the process, that can predictunmeasured or future process behavior, and which canadapt to changing conditions, both controllable anduncontrollable.

Computational intelligence methods can providethe engineer with greater ability to cope with thenatural complexity of industrial processes by challen-ging assumptions, learning process behavior, andadapting response rules. This paper will report on theprogress of applying computational intelligencemethods to the task of process discovery for a die-casting machine in a production environment.Unsupervised learning methods are used to classifymodes of operation, and neural network models aretrained from process data. Both are in use on-line todiagnose product quality.

Engineering Applications of Arti®cial Intelligence 11 (1998) 675±681

0952-1976/98/$ - see front matter # 1998 Published by Elsevier Science Ltd. All rights reserved.

PII: S0952-1976(98 )00033 -5

PERGAMON

* Corresponding author.

2. Die casting

Die casting is a discrete-part manufacturing processin which liquid metal is injected at high velocity andpressure into a mold. Production rates for such partsare on the order of 1±2 min. Three independent sys-tems control the dependent product. The metal supplyand injection system, the die-casting machine itself,and the die involve many dynamic variables in theiroperation as a casting is made. In addition, the ther-mal and mechanical conditions in each of these threesystems are interrelated over time. The state of the artin decision support for design engineers is the use of®nite-element or ®nite-di�erence mold-®lling and soli-di®cation models. These models show the engineer thepatterns of thermal ¯ows in the mold over the cycletime, enabling him to use his experience to detect po-tential problems in solidi®cation due to improper heattransfer. The results of analysis are used to suggestmodi®cations to the part or die design, including in-ternal die cooling and external spray cooling patterns.Generally, these models will be run only a few times inorder to build con®dence that a design is satisfactoryover a wide range of die-casting machine conditions.The long solution times for the model prevent its usein real time, or by an analytical solver.

3. Process parameters

Of the three independent systems that comprise theoverall die-casting system, parameters relating to themetal supply and injection system and the die-castingmachine are monitored. Metal composition is sampledperiodically, and maintained within industry-standardlimits. The injection system follows a scheduled patternof velocities and pressures, and the times and actualvelocities are recorded by the production-monitoringsystem. Forces on the die are also monitored andrecorded. The geometry of the die is considered to beconstant. At the current time, thermal data are notmonitored reliably. This is due to the high cost ofinstalling and maintaining thermocouples in an indus-trial production environment. However, some infor-mation on the thermal levels and radiation can beinferred from the production cycle time components.

The primary measures of die-casting quality areexternal and internal defects. External defects includesolder and missing geometry, which are easily detectedby visual inspection. The key cause of internal defectsis porosity, the presence of voids in the ®nished cast-ing. Porosity can be caused by trapped gas in themetal, or when the metal shrinks improperly duringcooling. When describing the severity of the porosity,size and location are taken into account. For example,a porosity deep within a heavy section is less severe

than one close to a surface which will be machined bya customer. Currently, porosities are detected either bysome physical performance test (e.g. whether a regioncan hold a liquid seal) or by X-ray analysis. Few pro-duction facilities employ 100% X-ray inspection, sostatistical quality control techniques (i.e. sampling) areused to track production performance.

The relationships between the measured process par-ameters and product quality are not well known.Statistical process-control methods have been used inthe past to determine control ranges for key processparameters, but it is not known whether these limitsimpact product quality or whether they are the bestlimits.

The goal of this e�ort is to analyze process andquality data from a die-casting machine in production,in order to develop models of product quality whichcan be used as on-line predictors of product quality,and with other decision support tools to suggest howto improve quality.

4. Data analysis

One method of managing the complexity of main-taining an industrial process involves the reduction ofprocess trends using unsupervised learning or ``cluster-ing''. Automated procedures can be used to group his-torical system states into clusters based on thesimilarity of system state vectors. This approach e�ec-tively reduces the history of the process to a moretractable set of prototypical system states. This alonemay simplify the analysis of a process by facilitatingthe task of identifying outliers and so forth. Based onthe prototypical state-space vector in each cluster, andthe values of associated outputs and/or other data, anengineer can determine whether the clusters describemodes of operation and can be used as a basis for ruleformation.

Many clustering algorithms have been developedand presented in the literature, see (Pao, 1989) and(Ripley, 1996) for examples. A novel clustering algor-ithm was used for the analysis. The algorithm startswith no clusters in its set, and a ®xed value for theradius of all clusters that are created. A high-level loopmaintains the integrity of the cluster set. In the ®rstepoch, each pattern in the set is checked for member-ship within each cluster by evaluating whether theEuclidean distance between the pattern and the clustercenter is less than the cluster radius. If the patterndoes not fall within a cluster, a new cluster is createdwith its center at the pattern. If the pattern does fall ina cluster, the pattern is considered a member of thecluster, and the cluster center is updated so that it is atthe new centroid of its member patterns.

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In subsequent epochs, the clustering scheme isculled. Each pattern is checked to see if it is still clo-sest to the center of the cluster to which it was orig-inally assigned. Patterns that violate this condition areconsidered ``unstable'', and are moved from their pre-viously assigned cluster into the nearest one. The clus-ter centers are updated to re¯ect the change inmembership. Clusters that have lost all their membersare deleted. The procedure continues until no unstablepatterns have been found during an epoch, or until aset number of epochs have been run.

When applied recursively, this algorithm can con-struct a hierarchy of clusters. The algorithm is run ®rston the entire set of data, with some speci®ed radius.After the algorithm has completed, each cluster can bechecked against some complexity criteria, e.g. numberof patterns or total variance. A cluster that violatesthe complexity criterion can be broken down into sub-clusters by reapplying the algorithm on the membersof the cluster with a reduced radius. This algorithmhas been used successfully to compress data for analy-sis and detect outliers. A simple illustration of a clusterhierarchy is given in Fig. 1.

It should be noted that clusters might not be mean-ingful in their own right. Assigning meaning to a clus-ter requires the work of an analyst to identify, forexample, that a particular cluster center is in an inter-esting part of the independent feature space. Whendependent feature data are present, their values formembers of the clusters can be analyzed to detect dis-tinctive behavior. In this way clusters might be ident-i®ed as meaningful system modes or categories (e.g.``high probability of defects'' or ``nominal'').

For the die-casting process, a distinct time period ofapproximately six months was designated for collec-tion of data, upon which modeling and analysis e�orts

were based. A compressed data set, consisting of ap-proximately 1200 records, was extracted during thisperiod. These records were clustered on their process-parameter values, and statistics on the values of a par-ticular quality parameter (that of a seal leak test) werecomputed for the records in each cluster. The hierarch-ical learning procedure was permitted to sort datarecords into, at most, three levels of clusters, in whicheach cluster could contain, at most, nine subclusters.These constraints were imposed to ensure that theresulting cluster set would be of manageable size tosupport e�cient analysis.

Upon completion of the learning procedure, theresults were examined. Fig. 2 shows the cluster mem-bership indices over time. Note that the clusters havedi�erent frequencies of leak defects. This implies thatthere are separate, identi®able modes or categories ofsystem behavior, distinguishable by the values of theindependent process parameters, with signi®cantlydi�erent associated levels of product quality. Theseclusters can be labeled as ``nominal'' or ``high-defect''modes. In real time, these modes can be identi®ed andreported to the engineer and operator as process diag-notic messages or alarms.

More-detailed analysis revealed that one top-levelcluster contained subclusters with disparate character-istics. Both subclusters were well populated, but itssubcluster 2 contained 9% leakers, while its subcluster5 contained no leakers. Analysis of these two subclus-ters revealed that the discrepancy between themseemed to reside in three components of the systemstate vectors (see Fig. 3). Individual values for theseparameters are shown over the records in these clustersin Figs. 4 and 5, which illustrate these distinctions.Ongoing analysis is being performed in communicationwith die-casting experts to interpret these results.

Fig. 1. Hierarchical clustering.

R. Cass, J. DePietro / Engineering Applications of Arti®cial Intelligence 11 (1998) 675±681 677

5. Modeling

Arti®cial neural networks are powerful compu-tational tools that can be used to construct models forthe estimation and prediction of process responses tovarious system state vectors (Pao, 1989). A neural net-work model is a general-purpose, multivariate, non-lin-ear approximator. Automated learning procedures areused to con®gure or ``train'' a neural network, basedon historical process data, without a priori knowledgeof process dynamics. This training minimizes the meansquare error between the neural network predictionsand the actual data. An analyst can provide a systemstate vector to a trained neural network model, andobtain an estimate of the process response to that vec-tor. This vector can be either an actual vector encoun-tered during process operation, or a contrived vector.The model can easily be re®ned over time to re¯ectmodi®cations in the process.

Two separate modeling e�orts were made in the die-casting application. The ®rst e�ort was an attempt topredict the existence of external defects on localizedregions of a casting surface. The same compresseddata set, consisting of the system state vectors and apresent/absent indicator for each of ®fty-two commondefects, was used to train a neural network. Modelinge�orts were concentrated on three of these defects, dueto their relatively high frequency of occurrence in thedata set. These defects included a broken core, a miss-ing core, and heavy solder buildup.

A neural network model with ®ve nodes on one hid-den layer was used to train the models for these threefeatures. This type of model produces values on thecontinuous range [0,1]. The training algorithm operatesby minimizing the mean square error between theactual and predicted values of the model. This error isnot well suited as an estimate of accuracy for modelsof binary features, as it will incorporate some noise in

Fig. 2. Graph of cluster membership over time, with defects.

Fig. 3. Comparison of cluster centers across parameters with highlighted signi®cant parameters.


the predictions around good predictions, potentiallyhiding large incorrect values. This e�ect is particularlypronounced when the distribution of the binary valuesis non-uniform, a typical feature of defect data acrossmany commercial discrete-part manufacturing pro-cesses.

In order to get a more detailed estimate of modelquality, the output of the model was passed through athreshold function such as:

f(output, T)= 1, if output >= T0, if output<T.

Given binary output from the model to matchagainst the binary data, a standard statistical classi®-cation diagnostic, the confusion matrix, was then used

to diagnose the model quality. For any given value ofthe threshold, the confusion matrix provides the infor-mation given in Table 1.

The results shown in Tables 2 and 3 were obtainedfrom the model for the solder defect. The ®rst tableshows the results for the data used to train the model,while the second shows the results for a data set with-held from training.

It is important to note that the neural network wasable to attain these levels of accuracy despite theabsence of reliable thermal data (temperature isbelieved to be the most in¯uential factor in producingdefective castings) and other readings. This fact engen-ders optimism that future modeling e�orts will be evenmore successful, as more related data becomes avail-able.

Table 1

Confusion matrix

Percentage of real good castings successfully predicted Percentage of real good castings predicted as bad castings

Percentage of real defects incorrectly predicted as good castings Percentage of real defects correctly predicted

Fig. 4. Comparison of parameter values across members of two clusters.

Fig. 5. Comparison of parameter values across members of two clusters.


The second modeling e�ort was an attempt to pre-dict the existence and characteristics of internal defects(porosities) in localized regions of a casting. For thise�ort, some 60 castings were inspected via X-ray, andthe volume, surface area, and depth of the defects asobserved in the resulting X-ray images described eachcasting's porosity characteristics. As such, the systemstate vectors corresponding to these castings were usedto train a neural network to predict the number,volume, surface area, and depth of porosities in eachobserved region.

Because the quality parameters being modeled inthis e�ort take values on continuous ranges, the R-squared statistic was used to measure the quality ofthe models. R-squared measures the amount of thetotal variation in the actual data accounted for in themodel by the formula:

R2 ��1ÿ S�yi ÿ yi�2

S�yi ÿ �yi�2�� 100

where yÃ denotes the predictions of the model and y themean of the actual data.

The results of this modeling e�ort were quite favor-able. The porosity geometry models in one particularregion of the casting were superior to the others. Inthat region, the volume model achieved an R-squaredvalue of 94.4, the surface area model attained an R-squared of 97.3, and the depth model reached an R-squared of 97.7. In addition, the model that predictsthe number of porosities in this region achieved an R-squared of 95.1. Graphs showing the estimates of themodel vs the actual data for the porosity volume forthe data set used to train the model and a test data areset in Figs. 6 and 7.

6. Future work

The clustering and estimation models have beenembedded in the process monitoring system for a die-

Table 2

Confusion matrix for training data set

Percentage of real good castings successfully predicted: 86% Percentage of real good castings predicted as bad castings: 14%

Percentage of real defects incorrectly predicted as good castings: 8% Percentage of real defects correctly predicted: 92%

Fig. 6. Model estimates vs actual data for training data of internal defect model.

Table 3

Confusion matrix for test data set

Percentage of real good castings successfully predicted: 79% Percentage of real good castings predicted as bad castings: 21%

Percentage of real defects incorrectly predicted as good castings: 21% Percentage of real defects correctly predicted: 79%


casting machine at a commercial production facility,and validation of the models against new data isunderway. The prediction of internal defects will beused to augment the shop's current statistical quality-control procedures. Castings for which the models pre-dict high porosity in key features will be set aside forX-ray, in addition to those which are part of the stat-istical quality control sample. The models will also beused as the simulation engine for a closed-loop optim-ization system. This die-casting advisor system willprovide supervisory-level control signals to the oper-

ator, or directly to the process-control system for thedie-casting machine.

References

Pao, Yoh-Han, 1989. Adaptive Pattern Recognition and Neural

Networks. Addison±Wesley, Reading MA.

Ripley, Brian D., 1996. Pattern Recognition and Neural Networks.

Cambridge University Press, Cambridge UK.

Fig. 7. Model estimates vs actual data for test data of internal defect model.


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