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Neural network modeling and dynamic behavior prediction of nonlinear dynamic systems

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Abstract

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.

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Data availability

The data included in this study are available from the corresponding author upon request.

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Funding

This project was funded by the National Natural Science Foundation of China (Nos. 11902038, 12272058 and 12272057).

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Authors and Affiliations

  1. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, China

    Luying Zhang, Ying Sun & Aiwen Wang

  2. College of Mechanical Engineering, Beijing Information Science and Technology University, Beijing, 100192, China

    Junhua Zhang

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  1. Luying Zhang
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  2. Ying Sun
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  4. Junhua Zhang
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Contributions

All authors contributed to the design and analysis of the model. Material preparation, data collection and analysis were performed by LZ, YS, AW and JZ. The first draft of the manuscript was written by LZ and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Ying Sun.

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Zhang, L., Sun, Y., Wang, A. et al. Neural network modeling and dynamic behavior prediction of nonlinear dynamic systems. Nonlinear Dyn 111, 11335–11356 (2023). https://doi.org/10.1007/s11071-023-08407-9

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