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The proficiencies of Fisher discriminant analysis (FDA), support vector machines (SVM), and proximal support vector machines (PSVM) for fault diagnosis (i.e. classification of multiple fault classes) are investigated. The Tennessee Eastman process (TEP) simulator was used to generate overlapping datasets to evaluate the classification performance. When all variables were used, the datasets were masked with irrelevant information, which resulted in poor classification. With key variables selected by genetic algorithms and the contribution charts, SVM and PSVM outperformed FDA and demonstrated the advantage of using nonlinear technique when data are overlapped. The overall misclassification for the testing data using FDA dropped from 38 to 18%; while those using SVM and PSVM dropped from 44–45 to 6%. The effectiveness of the proposed approach is increased in PSVM by saving significant computation time and memory requirement, while obtaining comparable classification results. For auto-correlated data, the incorporation of time lags into SVM and PSVM improved classification results. The added dimensions decreased the degree to which the data overlap and the overall misclassification for the testing set using SVM and PSVM decreased further to 3%. [Copyright &y& Elsevier]

Many trouble-shooting problems in process industries are related to key variable identification for classifications. The contribution charts, based on principal component analysis (PCA), can be applied for this purpose. Genetic algorithms (GAs) have been proposed recently for many applications including variable selection for multivariate calibration, molecular modeling, regression analysis, model identification, curve fitting, and classification. In this paper, GAs are incorporated with Fisher discriminant analysis (FDA) for key variable identification. GAs are used as an optimization tool to determine variables that maximize the FDA classification success rate for two given data sets. GA/FDA is a proposed solution for the variable selection problem in discriminant analysis. The Tennessee Eastman process (TEP) simulator was used to generate the data sets to evaluate the correctness of the key variable selection using GA/FDA, and the T2 and Q statistic contribution charts. GA/FDA correctly identifies the key variables for the TEP case studies that were tested. For one case study where the correlation changes in two data sets, the contribution charts incorrectly suggest that the operating conditions are similar. On the other hand, GA/FDA not only determines that the operating conditions are different, but also identifies the key variables for the change. For another case study where many key variables are responsible for the changes in the two data sets, the contribution charts only identifies a fraction of the key variables, while GA/FDA correctly identifies all of the key variables. GA/FDA is a promising technique for key variable identification, as is evidenced in successful applications at The Dow Chemical Company. [Copyright &y& Elsevier]

To implement on-line process monitoring techniques such as principal component analysis (PCA) or partial least squares (PLS), it is necessary to extract data associated with the normal operating conditions from the plant historical database for calibrating the models. One way to do this is to use robust outlier detection algorithms such as resampling by half-means (RHM), smallest half volume (SHV), or ellipsoidal multivariate trimming (MVT) in the off-line model building phase. While RHM and SHV are conceptually clear and statistically sound, the computational requirements are heavy. Closest distance to center (CDC) is proposed in this paper as an alternative for outlier detection. The use of Mahalanobis distance in the initial step of MVT for detecting outliers is known to be ineffective. To improve MVT, CDC is incorporated with MVT. The performance was evaluated relative to the goal of finding the best half of a data set. Data sets were derived from the Tennessee Eastman process (TEP) simulator. Comparable results were obtained for RHM, SHV, and CDC. Better performance was obtained when CDC is incorporated with MVT, compared to using CDC and MVT alone. All robust outlier detection algorithms outperformed the standard PCA algorithm. The effect of auto scaling, robust scaling and a new scaling approach called modified scaling were investigated. With the presence of multiple outliers, auto scaling was found to degrade the performance of all the robust techniques. Reasonable results were obtained with the use of robust scaling and modified scaling. [Copyright &y& Elsevier]