This paper proposes a neural network-based optimized robust nonlinear Kalman filter for concurrent fault estimation of high-speed trains using descriptor systems. Considering the displacement and speed time delays and multi-source disturbances acting on every car, and regarding the concurrent actuator and sensor faults as the auxiliary variables of the train, a time-delay nonlinear descriptor system is established. Fuzzy and fuzzy inference layers are added to the hyper basis function neural network; meanwhile, an accelerated gradient algorithm is used for optimizing the basis function of the network. These strategies derive an improved fuzzy hyper basis function neural network to achieve a higher nonlinear multi-source disturbance approximation accuracy, and robust upper bounds are proposed to enhance the filtering accuracy of descriptor systems. Furthermore, a fusion intelligent optimization algorithm using a circle chaotic mapping method to improve the population initialization is proposed to better estimate the unknown system noise. These measures implement better Kalman filtering of descriptor systems to achieve better concurrent fault estimation, even under unknown noise. Simulation results show that, compared with the improved radial basis function neural network-based optimized robust nonlinear Kalman filter, using the proposed method, the displacement, speed, and fault estimation errors are comprehensively decreased, depending on more accurate multi-source disturbance and noise estimations.
Liang et al. (Mon,) studied this question.