Threshold Computations for Detection of Failures in SISO Systems with Transfer Function Errors

This paper considers the problem of detecting failures in single input single output (SISO) systems using analytic redundancy concepts. Since the models used in such concepts are subject to eror, a method of determining detection thresholds that account for these errors is sought. In many applications, error can be characterized by a bound on the magnitude of the "error transfer function" as a function of frequency. Such a characterization has been used to determine fixed thresholds that account for modeling errors when input signals to the plant are bounded and have known temporal characteristics [1]. Frequently, however, the input signals are not known a-priori and any reasonable bound on their size results in overly conservative (i.e., too large) thresholds. The methodology presented here utilizes a straightforward application of Parseval\´s relation to develop a threshold computation that is performed on-line as a function of the input signal. The threshold is set at a quiescent value to account for sensor noise, and is adjusted (upward) according to the activity of the input signal. An application to detection of actuator failures is presented.