Establish algebraic data-driven constitutive models for elastic solids with a tensorial sparse symbolic regression method and a hybrid feature selection technique
Establish algebraic data-driven constitutive models for elastic solids with a tensorial sparse symbolic regression method and a hybrid feature selection technique
复制标题
利用张量稀疏符号回归方法和混合特征选择技术建立弹性固体的代数数据驱动本构模型
DOI：
10.1016/j.jmps.2021.104742
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发表时间：
2022-02-01
影响因子：
5.3
通讯作者：
Liu, Weijie
中科院分区：
文献类型：
--
作者：
Wang, Mingchuan;Chen, Cai;Liu, Weijie
本文提出了一种张量稀疏符号回归方法，利用细观尺度下的数据直接建立大变形下弹性固体的显式代数张量宏观本构模型。与人工神经网络等“黑箱“数据驱动模型不同，用我们提出的方法建立的模型是张量的“白箱“多项式，这对于从多尺度计算和建模中深入了解变形性质非常重要。该方法首先生成大量的候选基张量项，然后将它们与拟合系数线性组合，其中只有一小部分非零。这样建立的本构模型简洁、精确。提出了一种创新的混合特征选择和回归技术（高维Lasso、基于教-学的优化和递归特征消除的组合）来克服稀疏回归问题中项的高相关性和多重共线性问题。四个基准测试，以验证所提出的方法建立正确的模型直接从基准生成的数据。利用非速率型基准点的数据建立了速率型次弹性模型。最后，以颗粒增强复合材料的本构模型为例，说明了该方法能够从细观计算生成的数据中建立显式的张量宏观模型，表明了其在分层材料多尺度模拟中的广泛应用潜力。
We propose a tensorial sparse symbolic regression method to directly establish explicit algebraic tensorial macroscopic constitutive models for elastic solids under large deformation from data obtained at the mesoscale. Unlike "black-box"data-driven models such as artificial neural networks, the model established with our proposed method is a "white-box"polynomial of tensors, which is important for gaining insights into the deformation nature from multi-scale calculations and modeling. The proposed method first generates a massive number of candidate basis tensor terms and then combines them linearly with fitting coefficients, only a small set of which are non-zero. In this way, the established constitutive models are concise and precise. An innovative hybrid feature selection and regression technique (a combination of high dimensional Lasso, teaching-learning-based optimization and recursive feature elimination) is proposed to overcome the issues of high correlation and multicollinearity of the terms in this sparse regression problem. Four benchmark tests are introduced to verify that the proposed method established correct models directly from data generated by the benchmarks. A rate-type hypoelastic model is also established with the data generated by the not rate-type benchmarks. At last, an example of constitutive modeling for particle-reinforced composites is introduced to illustrate the ability of the proposed method to build explicit tensorial macroscopic models from data generated by mesoscopic calculations, demonstrating its potential for widespread application in multi-scale simulations of hierarchical materials.