Multiple Fault Detection and Isolation Using the Haar Transform, Part 1: Theory

Abstract

Most manufacturing processes involve several process variables which interact with one another to produce a resultant action on the part. A fault is said to occur when any of these process variables deviate beyond their specified limits. An alarm is triggered when this happens. Low cost and less sophisticated detection schemes based on threshold bounds on the original measurements (without feature extraction) often suffer from high false alarm and missed detection rates when the process measurements are not properly conditioned. They are unable to detect frequency or phase shifted fault signals whose amplitudes remain within specifications. They also provide little or no information about the multiplicity (number of faults in the same process cycle) or location (the portion of the cycle where the fault was detected) of the fault condition. A method of overcoming these limitations is proposed in this paper. The Haar transform is used to generate sets of detection signals from the original measurements of process monitoring signals. By partitioning these signals into disjoint segments, mutually exclusive sets of Haar coefficients can be used to locate faults at different phases of the process. The lack of a priori information on fault condition is overcomed by using the Neyman-Pearson criteria for the uniformly most powerful form (UMP) of the likelihood ratio test (LRT).