Multiple fault detection and isolation using the haar transform, part 1: Theory

Most manufacturing processes involve several process variables which intera ct with one another to produce a resultant action on the part. A fault is s aid to occur when any of these process variables deviate beyond their speci fied limits. An alarm is triggered when this happens. Low cost and less sop histicated detection schemes based on threshold bounds on the original meas urements (without feature extraction) often suffer from high false alarm an d missed detection rates when the process measurements are plot properly co nditioned. They are unable to detect frequency or phase shifted fault signa ls whose amplitudes remain within specifications. They also provide little or no information about the multiplicity (number of faults in the same proc ess cycle) or location (the portion of the cycle where the fault was detect ed) of the fault condition. A method of overcoming these limitations is pro posed in this paper. The Haar transform is used to generate sets of detecti on 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 t he process. The lack of a priori information on fault condition is overcome d by using the Neyman-Pearson criteria for the uniformly most powerful form ( UMP) of the likelihood ratio test (LRT).