Ordinary and neural Chi-squared tests for fault detection in multi-output stochastic systems

In this paper, two variations of the Chi-squared test are proposed for fault detection in multioutput stochastic systems. It is assumed that an optimal online estimation technique (such as the Kalman filter) is available in order to generate a residual sequence. We demonstrate that the ordinary (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. However, the Chi-squared test is the simpler of the two, and requires less computation. The neural (weighted) Chi-squared test is proposed as a refinement of the ordinary (unweighted) test. It is shown that the weighted Chi-squared test can be easily implemented by a neural learning technique, in the absence of a priori information about how to select the weights. An example of how to implement the Chi-squared test is also presented, using real power system data recorded by digital monitors