非线性多自由度系统的数据驱动建模和响应预测

Data‑driven modeling and response prediction of nonlinear multi‑degree‑of‑freedom systems

由于工程系统的复杂性和参数不确定性,利用力学原理建立的动力学控制方程常难以满足精度需求。基于数据驱动的系统建模和响应预测,利用动力学状态方程的数值解模拟实验中测得的不同外激励下的系统响应,并用于训练神经网络,构建包含训练数据间已知关系的损失函数以提高模型精度,得到表达系统状态关系的数据模型。将该神经网络模型纳入常微分方程求解器,可预测系统在不同激励下的响应,并获得幅频响应关系。将建模方法分别应用于含立方型和间隙型非线性的弹簧质量系统,计算结果表明,可根据响应数据建立准确的数据模型,并获得非线性系统主共振时的滞后和跳跃响应。研究还表明,训练数据越多、数据覆盖状态越完整,数据模型精度越好,且预测响应的误差越小。

Due to the complexity of the engineering system and the uncertainty of the parameters,the dynamic control equations es‐tablished by the principles of mechanics are often difficult to meet the requirements of precision.This paper studies data-driven sys‐tem modeling and response prediction.First,the numerical solution of the dynamic state equation is used to simulate the system re‐sponse under different external excitations measured in the experiment,and the neural network model is trained with the response data.The loss function containing the known relationship between the training data is constructed to improve the accuracy of the neural network,and the data model expressing state relationship is obtained.Then,the neural network model is incorporated into the ordinary differential equation solver to predict the response of the system under different excitations and obtain the amplitudefrequency response relationship.The modeling method is applied to the spring mass system with cubic and gap nonlinearity respec‐tively.The calculation results show that an accurate data model can be established based on the response data and the hysteresis and jump responses of the nonlinear system at the main resonance can be obtained.The study also shows that the more the training data has and the more complete the data is,the better the accuracy of the data model and the smaller the error of the predicted re‐sponse will be.