Neural network modeling and dynamic behavior prediction of nonlinear dynamic systems

In practical engineering, it is difficult to establish complex nonlinear dynamic equations based on theories of mechanics. Data-driven models are built using neural networks in this paper to meet the needs of high dimension, multi-scale and high precision. We construct a two-coefficient loss function for whole data-driven modeling and substructure data-driven modeling according to the linear multi-step method. The forward Euler method is combined with trained neural networks to predict a five-degree-of-freedom duffing oscillator system. Comparative results show that the prediction accuracy of substructure data-driven modeling is higher than whole data-driven modeling, and the generalization and robustness of the model are verified. Meanwhile, the selection of training data and the number of hidden layers have a great impact on the prediction ability. Adopting an adjustable learning rate, adding control parameters to the network input shows better performance than not adding control parameters to the network input.