A Wavelet-Based Procedure for Process Fault Detection

Abstract

The objective of this research is to develop a procedure for detectingfaults in a particular process by analyzing data generated by theprocess on a compressed wavelet scale. In order to compress the data,three different methods are compared for reducing the number ofwavelet coefficients needed to obtain an accurate representation ofthe data. One method is ultimately chosen to compress all data usedin this study. This method, which involves minimizing the relativereconstruction error, effectively balances model parsimony againstreconstruction error. The compressed data from seven in-control runsis used to define a standard, or baseline, by which to compare newdata sets. The compressed baseline process is defined by forming theunion set of the top, or coarsest, coefficient positions selected bythe relative reconstruction error method for each of the seven runs.In order to determine if a new, compressed data set differssignificantly from the baseline, a variant of Hotelling'sT²-statistic for two-sample problems is formulated. This statisticis tested by applying it to four induced-fault data sets, as well asto 21 in-control data sets. The results provide substantial evidenceof the statistic's effectiveness in detecting process faults fromcompressed data. It is also shown that traditional bootstrappingmethods cannot be implemented in this case