Fault estimation based on ensemble unscented Kalman filter for a class of nonlinear systems with multiplicative fault

In this paper, a method for fault estimation with a multiplicative model in a nonlinear system by the unscented Kalman filter is introduced. The faults appear in the form of component, sensor, and actuator in the system equations. By using the augmented method, a fault signal will be as state variable of the system, the system dynamic equations are rewritten to represent a fault as a state variable. The existence of nonlinear equations in the presence of system noises results in an identical non-Gaussian noise, which leads to the difficulty in solving the problem of fault estimation with the unscented Kalman filter. Therefore, a filter combining a Gaussian mixture model (GMM) and the augmented ensemble unscented Kalman filter (AEnUKF) is designed to estimate the fault in this class of nonlinear systems. Suitable conditions and assumptions are appointed to guarantee the convergence of the estimation error. Next, the performance of the proposed method is evaluated by simulating a bioreactor system. The results of the simulation for the multiplicative fault estimation demonstrated performance by the AEnUKF-GMM algorithm better than the AUKF in the presence of non-Gaussian noise.

Automated summary

This paper introduces a method for fault estimation in a nonlinear system using the unscented Kalman filter, augmented by a fault signal as a state variable. A filter combining Gaussian mixture model and augmented ensemble unscented Kalman filter is designed for estimating faults in nonlinear systems, with suitable conditions and assumptions for convergence. The proposed method is evaluated in simulating a bioreactor system, demonstrating better performance compared to traditional methods in the presence of non-Gaussian noise.