Convexity analysis: A tool for optimization of malfunction isolation

The optimal design of an algorithm for malfunction isolation requires knowledge of the structure of the sources of uncertainty. System and measurement noise are not the only such sources. Also relevant is the uncertainty in the model of the normal behavior of the system, and uncertainty in the precise form which a malfunction will assume. A hypothesis about the structure and systematics of the uncertainties in modelling and in failure is proposed. This hypothesis is developed into a general criterion for the best malfunction isolation capability which can be obtained by any isolation algorithm. Furthermore, the hypothesis engenders a technique for precisely evaluating the performance of multiple hypothesis maximum likelihood algorithms for malfunction isolation. Thus different sets of hypothesized failures can be quantitatively compared so as to optimize the design of the algorithm.