Detection and diagnosis of parameters change in linear systems using time-frequency transformation

A systematic approach to selecting and optimizing kernel functions of a time-frequency transformation for parameter change detection in linear, piecewise-constant-parameter systems is presented. The time-frequency transformation is applied to the system output, and the local moments´ sensitivity with respect to the change is maximized. The local moments´ optimization leads to a partial characterization of the transformation kernel function. Under proper kernel constraints, the local moments are simply related to the characteristic parameters of a linear system (e.g., natural frequencies, time constants, damping coefficients) and thus are suitable for parameter change diagnosis. An illustrative numerical example based on a second-order linear system is given