Abstract

The aim of this research is to identify a distributed load applied to a hyperelastic plate using displacement measurements. This inverse problem is analyzed using a gradient-based method and various machine learning techniques such as the multivariate polynomial regression, support vector regression, k-nearest neighbors, and neural network. The finite element method is used to solve the direct problem of hyperelastic plates and perform necessary sensitivity analyses based on the first-order shear deformation theory (FSDT). Displacements at several sampling points (measurement data) are used for computing the unknown load parameters in the inverse problem. To determine the appropriate locations for sampling points, the method of the minimum condition number of the sensitivity matrix is employed. To compare the performance of the studied methods, the effect of the level of error in measurements and the number of sampling points are investigated. Results obtained in this study show that the gradient-based method and the more efficient algorithms of machine learning, such as support vector regression and neural network models, can accurately identify the distributed non-uniform load applied to the hyperelastic plate. It is also observed that the accuracy of the gradient-based and machine learning methods reduces by increasing the level of measurement error. Providing a proper dataset and training the models in machine learning methods are time consuming. However, after training a machine learning model, the identification process can be carried out quickly. Therefore, machine learning algorithms are effective when more than one load should be identified.

中文翻译：

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使用基于梯度和机器学习方法的超弹性板的分布式载荷识别

摘要

本研究的目的是通过位移测量来确定施加到超弹性板的分布式载荷。使用基于梯度的方法和各种机器学习技术（例如多元多项式回归、支持向量回归、k最近邻和神经网络）来分析该逆问题。采用有限元方法求解超弹性板的直接问题，并基于一阶剪切变形理论（FSDT）进行必要的敏感性分析。多个采样点的位移（测量数据）用于计算反问题中的未知载荷参数。为了确定合适的采样点位置，采用了灵敏度矩阵最小条件数的方法。为了比较所研究方法的性能，研究了测量误差水平和采样点数量的影响。本研究获得的结果表明，基于梯度的方法和更有效的机器学习算法，例如支持向量回归和神经网络模型，可以准确识别施加到超弹性板的分布式非均匀载荷。还观察到，基于梯度和机器学习方法的准确性会随着测量误差水平的增加而降低。提供适当的数据集并用机器学习方法训练模型非常耗时。然而，在训练机器学习模型后，识别过程可以快速进行。因此，当需要识别多个负载时，机器学习算法是有效的。