FAULT DETECTION AND IDENTIFICATION THROUGH VARIANCE OF WAVELET TRANSFORM OF SYSTEM OUTPUTS

Abstract

The problem of fault detection and identification is approached without using a plant model, by means of the variance of the continuous wavelet transform (CWT) of the outputs of the plant or process. If an output may be considered to be a wide sense stationary stochastic process during a time interval, it is shown that the variance of its CWT depends only on the scale a and not on the displacement b. It is also shown that the average with respect to displacement b of the squared CWT, designated b-average (akin to time average), is an unbiased estimator of such variance. Moreover, it turns out that the standard deviation of this b-average decreases as the length of the data record increases, thus suggesting ergodicity. These properties are then used for fault identification by defining variance templates characterizing normal or faultconditions of a process. The problem of fault identification is solved using the ergodic property by finding the distances of the b-average of a single sample (realization, measurement) of the output considered, to normal and fault condition variance templates. The Fisher linear discriminant method is used to optimize the discrimination between fault and normal conditions for single outputs and for combined outputs. For fault detection a window of a relatively small length ending at the present time t is used. The b-averages in this window are found for each t. The change from one condition to another is detected by considering when the difference of the distances of this b-average - as a function of t -to each predetermined fault or normal templates changes sign after using the Fisher transformation and filtering . The method is tested using a spring fault in a two mass-spring-damper system.