Bounded error modeling using interval neural networks with parameter optimization

Aiming at the issue of interval modeling of uncertain systems, this article proposes a data-based interval neural network (INN) optimization modeling method that combines interval analysis with a neural network and particle swarm optimization (PSO) algorithm, adopts an INN model with interval weights and interval thresholds, and constructs an interval multiobjective PSO (IMOPSO) algorithm to evolve the network, thereby modeling an uncertain system under an unknown-but-bounded error (UBBE) condition. Considering the cases of known and unknown error bounds in UBBE, two optimization objectives, i.e., interval coverage and interval width, are constructed to optimize the parameters of INN, aiming to improve the accuracy and reliability of prediction. The proposed method effectively solves many constraints such as the model structure demanded and error bounds known in UBBE modeling, and provides a new method of data-based interval system modeling. The method was applied to model linear and nonlinear systems, and simulation results showed that the established INN models have good prediction effects and dynamic characteristics, which demonstrate the effectiveness of the method.