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| 基于物理信息神经网络的多点摩擦诱发粘-滑振动问题算法 |
| Physics-informed neural networks algorithm for sloving multi-point friction-induced stick-slip vibration problems |
| 投稿时间：2024-07-08 修订日期：2024-10-21 |
| DOI： |
| 中文关键词: 物理信息神经网络 摩擦自激振动 非光滑动力学 粘-滑振动 线性互补问题 |
| 英文关键词:physical-informed neural networks friction-induced vibration nonsmooth dynamics stick-slip vibration linear complementarity problem |
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| 摘要点击次数: 24 |
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| 中文摘要: |
| 针对非光滑动力学中不稳定粘-滑振动问题难以准确求解的挑战，本文提出了一种基于物理信息神经网络PINN (Physics-informed Neural Networks)的求解算法。首先，基于单边约束的线性互补理论对经典滑块-传送带模型进行动力学建模，随后将线性互补关系设计为指导神经网络训练的损失函数，构建了基于PINN的多点摩擦诱发粘-滑振动问题求解算法，进行了摩擦系统中多个滑块粘-滑振动复杂响应的准确模拟。通过与存在事件检测的Switching Model方法和传统无事件检测的Time-Stepping方法的数值计算结果对比，完成了PINN算法准确性的验证。本文提出的PINN算法将传统优化问题计算转化为机器学习算法的网络训练，适用于具有多个接触点的粘-滑振动分析，可实现准确的非光滑状态转换，为多自由度摩擦系统中复杂非线性振动响应的准确模拟提供了一种便捷易用的新方法。 |
| 英文摘要: |
| Addressing the challenge of accurately solving unstable stick-slip vibration problems in non-smooth dynamics, this paper proposes a solution algorithm based on Physics-informed Neural Networks (PINN). Firstly, the classical stick-slip vibration problem is dynamically modeled using the linear complementarity theory under unilateral constraints. Then, the linear complementarity relationship is designed as a loss function to guide the training of the neural network, constructing a PINN algorithm for solving multi-point friction-induced stick-slip vibration problems. The accurate simulation of complex responses of multiple sliders' stick-slip vibrations in frictional systems was conducted. By comparing the numerical results with the Switching Model method that includes event detection and the traditional Time-Stepping method without event detection, the accuracy of the PINN algorithm was verified. The proposed PINN algorithm transforms the traditional optimization problem calculation into network training of the machine learning algorithm, making it suitable for stick-slip vibration analysis with multiple contact points. This method achieves accurate nonsmooth state transitions and provides a convenient and easy-to-use new approach for the accurate simulation of complex nonlinear vibration responses in multi-degree-of-freedom frictional systems. |
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