In this paper, we propose and construct an observer design based on a Self-Recurrent Consequent-Part Fuzzy Wavelet Neural Network (SRCPFWNN) for a class of nonlinear system. We use a Self-Recurrent Wavelet Neural Network (SRWNN) to construct a self-recurrent consequent part for each rule of the Takagi-Sugeno-Kang (TSK) model in the SRCPFWNN and analyze the structure of the fuzzy wavelet neural network model. Based on the Direct Adaptive Control Theory (DACT) and a back propagation-based learning algorithm, all parameters of the consequent parts are updated online in the SRCPFWNN. On this basis, we propose a design method using an adaptive state observer based on an SRCPFWNN for nonlinear systems. Using the Lyapunov function, we then prove the stability of this observer design method. Our simulation results confirm that the observer can accurately and quickly estimate the state values of the system.

In this paper, we propose the Hyper Basis Function (HBF) neural network on the basis of Radial Basis Function (RBF) neural network. Compared with RBF, HBF neural networks have a more generalized ability with different activation functions. A decision tree algorithm is used to determine the network center. Subsequently, we design an adaptive observer based on HBF neural networks and propose a fault detection and diagnosis method based on the observer for the nonlinear modeling ability of the neural network. Finally, we apply this method to nonlinear systems. The sensitivity and stability of the observer for the failure of the nonlinear systems are proved by simulation, which is beneficial for real-time online fault detection and diagnosis.