Filter-based FDD using PDFs for stochastic systems with time delays

In this paper, a fault detection and diagnosis (FDD) scheme is presented for general stochastic dynamic systems with time delays. Originated from some practical processes, it is supposed that the measured information is the probability density function (PDF) of the system output rather than its actual value, which is different from the classical FDD problem. A B-spline expansion technique is applied so that the output PDF can be formulated in terms of the dynamic weights of the B-spline expansion. This leads to a dynamic model between the input and the weights where nonlinearities, uncertainties and time delays are included. As a result, the concerned FDD problem is transformed into a classic nonlinear FDD problem subject to an uncertain nonlinear system with time delays. Feasible criteria to detect the system fault are obtained and an adaptive fault diagnosis method is further presented to produce an estimate of the size of fault. Simple simulations are given to demonstrate the efficiency of the proposed approach.