基于物理知情极限学习机(PIELM)的结构动力响应预测研究

PREDICTION OF STRUCTURAL DYNAMIC RESPONSE BASED ON PHYSICS-INFORMED EXTREME LEARNING MACHINE (PIELM)

  • 摘要: 该文提出了一种基于物理知情极限学习机(Physics-Informed Extreme Learning Machine, PIELM)的结构动力响应预测方法,以解决传统数值方法依赖大量计算资源和数据驱动的机器学习模型需要高质量训练数据的问题。该方法以极限学习机(ELM)架构为基础,通过其高阶导数的共性构造微分算子,将结构动力学问题转变为求解输出权重的问题。通过微分算子的形式将结构动力学的物理信息有效嵌入损失函数之中,方法在进行预测时不依赖训练数据,具有物理可解释性和泛化能力。数值案例表明:本文提出的方法相较于传统数值方法对时间步长的适应性强、预测精度高、误差控制能力强,为结构动力响应预测提供了一种高效、准确的预测方法。

     

    Abstract: This paper proposes a structural dynamic response prediction based on Physics-Informed Extreme Learning Machine (PIELM) to address the limitations of high computational demands in traditional numerical methods and the necessity of high-quality training data for data-driven machine learning models. Based on the Extreme Learning Machine (ELM) framework, the proposed method employs a differential operator derived from commonality of higher-order derivatives, transforming the structural dynamics problem into a task of solving output weights. The physical information is embedded into the loss function in the form of differential operators. The method obviates the reliance on training data for predictions and ensures physical interpretation and generalizability. The numerical studies demonstrate that the proposed method exhibits superior time step adaptability, prediction accuracy and error control capability than traditional numerical methods, providing an efficient and stable prediction method for structural dynamic response prediction.

     

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