Fault detection in multi-output stochastic systems: statistical and neural approaches

In this paper, two variations of the chi-squared test are proposed for fault detection in multi-output stochastic systems. We assume that an optimal online estimation technique (such as the Kalman filter) is available for generating a residual sequence. We demonstrate that the unweighted chi-squared test (which implies testing the squared Euclidean norm of the normalized residual vector) is equivalent to the conventional approach of testing the joint probability density function of the residual vector. The weighted chi-squared test is proposed as a refinement of the unweighted test. It is shown that in the absence of a priori information about how to select the weights, a simple neuron can be used as a generator of a weighted chi-squared random variable. In this sense, the idea is to implement a statistical tool by using a neural technique.