Optimal test and sensor selection for active fault diagnosis using integer programming

Abstract

A model-based method is presented for the simultaneous selection of tests and sensors in fault detection and isolation (FDI) of systems subject to uncertainty. Tests and sensors are selected out of a continuous or discrete set of options based on their contribution to information gain with respect to fault identifiability. The objective of the optimization of the tests designed is to maximize the sensitivity of sensed outputs with respect to faults and minimize the joint confidence between faults and sources of uncertainty. The methodology is intended for active FDI in systems that can be limited to a finite number of input design scenarios, with a set of sensors that may or may not be valuable for the purpose of fault detection. The optimization of discrete sensors and input designs is formulated as a constrained mixed integer non-linear program that maximizes a measure of Fisher information, which calculates output sensitivities with respect to faults and uncertainty, by treating those as parameters in the system model. Kullback–Leibler divergence is used to determine the isolation capacity of a FDI test when there is uncertainty in inputs and parameters. FDI tests are executed using k-nearest neighbor classification, which is used as a verification method for test designs and sensor networks that result in high correct classification rates. The proposed design framework is tested on a virtual benchmark three-tank system, subject to multiple faults and sources of uncertainty.