Wavelet-Based Data Reduction Techniques for Process Fault Detection

This article presents new data reduction methods based on the discrete wavelet transform to handle potentially large and complicated nonstationary data curves. The methods minimize objective functions to balance the trade-off between data reduction and modeling accuracy. Theoretic investigations provide the optimality of the methods and the large-sample distribution of a closed-form estimate of the thresholding parameter. An upper bound of errors in signal approximation (or estimation) is derived. Based on evaluation studies with popular testing curves and real-life datasets, the proposed methods demonstrate their competitiveness with the existing engineering data compression and statistical data denoising methods for achieving the data reduction goals. Further experimentation with a tree-based classification procedure for identifying process fault classes illustrates the potential of the data reduction tools. Extension of the engineering scalogram to the reduced-size semiconductor fabrication data leads to a visualization tool for monitoring and understanding process problems.