Design of functional observers for fault detection and isolation in nonlinear systems in the presence of noises

This work deals with the problem of designing functional observers for fault diagnosis in nonlinear systems in the presence of noises. It follows up previous work of the authors on design of functional observers (residual generators) for deterministic systems from the point of view of observer error linearization. Here, we consider the effect of noises on residual generation. The effect of sensor noises on the residuals is studied analytically and the associated probability distributions are derived. Following this, a well-known statistical hypothesis testing approach, Generalized Likelihood Ratio, is used to track changes in the mean of the residual to enable robust fault detection. The approach is also extended to process noises (plant-model mismatch) numerically. Throughout the study the methods presented are tested on a non-isothermal CSTR case study. The results show that the fault diagnosis scheme is able to quickly and accurately detect faults in the presence of both sensor and process noises.