Analysis of Numerical Methods for Fault Detection and Model Identification in Linear Systems with Delays

Abstract

Recently an approach for multi-model identification and failure detection in the presence of bounded energy noise over finite time intervals has been introduced. This approach involved offline computation of an auxiliary signal and online application of a hyperplane test.

This approach has several advantages; but, as presented, observation over the full time interval was required before a decision could be made. We develop an algorithm which modifies this approach to permit early decision making with the hyperplane test.

In addition, we extend this approach to handle problems that include delays. The original method requires the formulation and solution of an optimal control problem. We approach these problems in three ways. The first is through the Method of Steps, reformulating the system without delays so that we might apply existing theory with modifications. Also, we approximate the delayed systems using splines and central differences, eliminating the delay so that existing theory will apply. Approximations allow for more complicated models than the Method of Steps; however, the Method of Steps is a true solution, rather than an approximate one. Thus, solutions using the Method of Steps serve as a basis of comparison and verification of the approximate methods.