Neural Network Modeling and Dynamic Behavior Prediction of Nonlinear Dynamic Systems

Abstract

In the complex dynamic problems of practical engineering, the method of establishing dynamic equations and numerical analysis based on theories of mechanics is difficult to meet the needs of high dimension, multi-scale and high precision. In this paper, data-driven models of nonlinear dynamic systems are built through neural network. The numerical solution of state equations is used to simulate the experimental data as well as training data of neural network. The loss function with two coefficients is constructed according to the relationship between the data. Forward Euler method and the trained neural network are combined to predict the response data of different excitation frequencies. Then, whole data-driven modeling and substructure data-driven modeling are presented to model and analyse a five-degree-of-freedom duffing oscillator. By comparison, the prediction accuracy of substructure data-driven modeling is higher. Furthermore, the influence of loss function, hidden layer, training data and noise on the accuracy of the model is studied. The results show that the selection of training data and the number of hidden layers have a great impact on the prediction ability, and verify accuracy, generalization and robustness of the model. In order to improve the prediction accuracy of substructure data-driven modeling, adjustable learning rate is adopted in the optimizer. The effects of adding control parameters to the network input (APNI) and not adding control parameters to the network input (NAPNI) on the dynamic characteristics are considered respectively. The prediction accuracy of the model can be effectively improved by adding control parameters to the network input.