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. Compared with RBF, neural network has a more generalized ability with different activation functions. Compared to RBF, neural network (HBF) neural network on the basis of Radial Basis Function (RBF) neural network used to determine the network center. Here, 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 proven by simulation, which is beneficial for real-time online fault detection and diagnosis.