Robust fault detection method based on interval neural networks optimized by ellipsoid bundles

Abstract

In this paper, a novel framework for interval prediction neural network model optimized by ellipsoid bundles is designed for data-driven systems with unknown but bounded noise and disturbances. Firstly, a point prediction neural network model is constructed with input and output data, the prediction error is assumed to be unknown but bounded. Then, a feasible set related to the output weights of the neural network model is described by ellipsoid bundles, which allows decreasing conservatism compared to other types of sets such as zonotopes or ellipsoids. To obtain a more precise description shape of the feasible set, an optimal iterative formula is theoretically derived by minimizing the Frobenius norm of ellipsoid bundles. Next, an outer bounding box is established to obtain the maximum and minimum weights that satisfy the feasible set, thereby providing the output prediction interval. This interval characterizes the systems’ disturbance and can be used as the threshold when dealing with fault diagnosis applications. Finally, the effectiveness of the proposed interval neural network model is demonstrated by using faulty data from a wastewater treatment process. Simulation results verify that the proposed method can achieve accurate prediction outputs and fault diagnosis performance.