Computational Estimation of Heat Computational Estimation of Heat Transfer Curves for Microstructure Transfer Curves for Microstructure Prediction and Decision SupportPrediction and Decision Support

Aparna S. Varde, Mohammed Maniruzzaman, Aparna S. Varde, Mohammed Maniruzzaman, Elke A. Rundensteiner and Richard D. Sisson Jr.Elke A. Rundensteiner and Richard D. Sisson Jr.

Worcester Polytechnic InstituteWorcester Polytechnic Institute

Worcester, MA, USA.Worcester, MA, USA.

Presented at: TMS-04, New Orleans, Louisiana, USA.Presented at: TMS-04, New Orleans, Louisiana, USA.

IntroductionIntroduction The result of a Heat Treating experiment is often represented The result of a Heat Treating experiment is often represented

as a graph called a Heat Transfer Curve, i.e.,as a graph called a Heat Transfer Curve, i.e., Heat Transfer Coefficient as a function of temperature.Heat Transfer Coefficient as a function of temperature.

Performing lab experiment consumes time and resources.Performing lab experiment consumes time and resources.

Desirable to Desirable to computationally estimatecomputationally estimate the Heat Transfer the Heat Transfer Curve, given experimental input conditions.Curve, given experimental input conditions.

Estimation can be used for various applications, e.g.,Estimation can be used for various applications, e.g., Microstructure Prediction.Microstructure Prediction. Decision Support. Decision Support.

GoalsGoals1. Given input conditions in a Heat Treating experiment, estimate the resulting Heat Transfer Curve.

2. Given the desired Heat Transfer Curve in an experiment, estimate the conditions that would obtain it.

ApplicationsApplications

Estimated Heat Transfer Curve can be used to Estimated Heat Transfer Curve can be used to Get boundary conditions useful for simulations with Get boundary conditions useful for simulations with

tools such as DANTE.tools such as DANTE. Obtain the corresponding time-temperature curve Obtain the corresponding time-temperature curve

which when superimposed over a Jominy end quench which when superimposed over a Jominy end quench graph predicts microstructure.graph predicts microstructure.

Estimated input conditions can be used toEstimated input conditions can be used to Select process parameters and products for Heat Select process parameters and products for Heat

Treating in the industry.Treating in the industry.

Hence, this computational estimation enhances decision Hence, this computational estimation enhances decision support in Heat Treating.support in Heat Treating.

State-of-the-artState-of-the-art Mathematical Modeling: [M-95], [S-60], [PG-60]Mathematical Modeling: [M-95], [S-60], [PG-60]

Variables not known in existing models in some cases. Variables not known in existing models in some cases. Precise equations not known in some cases. Precise equations not known in some cases.

Similarity Searching: [HK-01] [WF-00] [M-97]: Similarity Searching: [HK-01] [WF-00] [M-97]: Naïve Search: Non-matching conditions could be significant.Naïve Search: Non-matching conditions could be significant. Weighted Search: Precise weights denoting relative Weighted Search: Precise weights denoting relative

importance not known apriori.importance not known apriori.

Case-based Reasoning: [AP-03], [K-88], [AV-01], [S-88].Case-based Reasoning: [AP-03], [K-88], [AV-01], [S-88]. Regular CBR: Involves human intervention.Regular CBR: Involves human intervention. Exemplar Reasoning: Problem similar to naïve search.Exemplar Reasoning: Problem similar to naïve search. Instance-based Reasoning: Problem similar to weighted Instance-based Reasoning: Problem similar to weighted

search.search.

Proposed Approach: Proposed Approach: AutoDomainMineAutoDomainMine

Performs domain-type-dependent data mining Performs domain-type-dependent data mining to discover knowledge for estimation.to discover knowledge for estimation.

Learning analogous to domain scientists.Learning analogous to domain scientists.

Steps:Steps:1.1. Knowledge Discovery: Grouping graphs, reasoning Knowledge Discovery: Grouping graphs, reasoning

causes of similarity to build representative cases.causes of similarity to build representative cases.2.2. Estimation: Use the reasoning and representative Estimation: Use the reasoning and representative

cases to estimate new cases.cases to estimate new cases.

Learning Analogous to ScientistsLearning Analogous to Scientists

Grouping

Reasoning Cause ofSimilarity

Input Conditions

Source: CHTE

Step 1: Knowledge DiscoveryStep 1: Knowledge Discovery

Step 2: EstimationStep 2: Estimation

ClusteringClustering

Clustering: Technique Clustering: Technique that places a set of that places a set of objects into groups of objects into groups of similar objects [HK-01].similar objects [HK-01].

Used to group Heat Used to group Heat Transfer Curves as a Transfer Curves as a domain scientist would.domain scientist would.

After clustering, labels After clustering, labels become available as become available as Cluster IDs.Cluster IDs.

Clustering

….

ClassificationClassification

Sample Partial Output of Clustering

Snapshot of PartialDecision Tree created

Decision Tree Classifier

Classification is a Classification is a technique to technique to extract models to extract models to predict categorical predict categorical labels [HK-01].labels [HK-01].

After clustering, After clustering, labels available, labels available, so classification so classification can be applied.can be applied.

Decision tree Decision tree classifiers used in classifiers used in AutoDomainMine.AutoDomainMine.

Classification (Contd.)Classification (Contd.)

Decision Trees form Decision Trees form basis for basis for selecting selecting representative cases. representative cases.

Process:Process: From all paths to a From all paths to a

cluster, cluster, select any oneselect any one as representative as representative conditions. conditions.

From all graphs in the From all graphs in the cluster, cluster, select any oneselect any one as a representative as a representative graph.graph.

Decision Trees and Decision Trees and representative cases representative cases used to estimate new used to estimate new cases.cases.

Sample Partial Decision Tree

Sample Representative Case

Estimation Example 1Estimation Example 1

Estimation Example 2Estimation Example 2

SummarySummary

AutoDomainMine proposed as a technique for AutoDomainMine proposed as a technique for computational estimation of Heat Transfer computational estimation of Heat Transfer Curves.Curves.

This aids microstructure prediction and decision This aids microstructure prediction and decision support.support.

Ongoing Work:Ongoing Work: Learning a domain-specific distance metric for Learning a domain-specific distance metric for

clustering to improve accuracy.clustering to improve accuracy. Designing domain-specific representative cases for Designing domain-specific representative cases for

better classification.better classification.