Generalized robust H_∞ fault diagnosis filtering based on conditional stochastic distributions of system outputs

The efficiency of fault detection and diagnosis by using output probability density functions (PDFs) for stochastic time-delayed systems has been shown in practical processes. Neural network modelling has been applied to characterize the output PDFs and to the dynamical weighting system. In this paper, the system perturbations and disturbance are considered and the robust fault diagnosis design is studied for the general stochastic system in the presence of time delays. The main objective is to design linear matrix inequality (LMI)-based fault diagnostic filtering (FDF) to estimate the fault and attenuate the disturbances. The modelling errors and system uncertainties resulting from both B-spline expansion and the weighting system are merged into system disturbance. It can be seen that the resulting weighting system comprises non-linearities, uncertainties, disturbances, and time delays, and includes the non-zero initial condition. The generalized H_∞ optimization is presented and applied to the fault diagnosis problem of the weighting system with the non-zero initial condition and truncated norms. Simulations are given to demonstrate the efficiency of the proposed approach.