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中文核心期刊

聚类分析-神经网络-贝叶斯优化联合识别复合材料参数研究

Research on parameter identification of composite materials by combination of self-consistent cluster analysis, neural network and Bayesian optimization

  • 摘要: 目前针对非均质复合材料参数的正逆向识别尚面临正向计算成本高和逆向识别泛用性低的难题。数据驱动的计算均匀化方法可以一方面利用数据科学的先进算法降低控制方程的变量数目,另一方面建立复合材料设计结构与等效参数的联系,从而显著提升计算效率并挖掘参数间的内在关联。本文拟采用数据驱动的聚类分析方法(Self-consistent Clustering Analysis, SCA),依据各网格点的应变集中张量进行聚类划分,并在聚类区域上求解离散的Lippmann-Schwinger方程,在极大程度降低了计算自由度的同时,高效获取等效模量、热膨胀系数、热导率等参数。然而SCA法在处理大量不同结构工况时效率略显不足,因此本文进一步利用人工神经网络方法(Artificial neural network, ANN)作为代理模型加速计算,实现不同工况下等效参数的快速预测。针对于逆向识别非均质材料和结构的反问题,则结合贝叶斯优化(Bayesian optimization)方法,在给定的等效参数下反向识别最优化的材料和几何结构,形成聚类分析-神经网络-贝叶斯优化的联合识别框架。本文以超导EAS股线和颗粒增强复合材料为例,进行联合识别框架与已有实验和数值结果的对比分析,继而从计算精度、求解效率、模型超参数选取、敏感度分析和反向验证等方面进行深入研究,探讨本文建立的聚类分析-神经网络-贝叶斯优化框架的优势和不足,以期为发展精度较高和适用范围较广的复合材料参数识别方法提供思路和参考。

     

    Abstract: At present, the forward and inverse identification of heterogeneous composite materials is still faced with the dilemmas of high forward calculation cost and low universality of inverse identification. On the one hand, the data-driven computational homogenization method utilizes advanced algorithms of data science to reduce the number of variables in the governing equation, and on the other hand, it establishes the connection between the designed structure and the equivalent parameters, thereby significantly improving the computational efficiency and exploring the internal correlation between parameters. In this paper, a data-driven Self-consistent Clustering Analysis (SCA) method is developed to classify clusters according to the strain concentration tensor of each grid point, and the discrete Lippmann-Schwinger equation is solved on the cluster region. The calculation degree of freedom is greatly reduced, and the equivalent Youngs’ modulus, thermal expansion coefficient, thermal conductivity and other parameters are efficiently obtained. However, the efficiency of SCA method is slightly insufficient when dealing with a large number of different structural conditions, so this paper further utilizes Artificial neural network (ANN) as a proxy model to accelerate the calculation and achieve rapid prediction of equivalent parameters under different conditions. For the inverse problem of identify materials and structures, Bayesian optimization is combined to identify the most optimized materials and geometric structures under required equivalent parameters, forming a joint recognition framework of Self-consistent Clustering Analysis-Artificial neural networks-Bayesian optimization. In this paper, superconducting EAS strands and particle reinforced composites are taken as examples, and comparative analyses of the joint identification framework with existing experimental and numerical results are conducted. Then, the aspects of computational accuracy, computational efficiency, model hyperparameter selection, sensitivity analysis and inverse validation of the presented framework are discussed, which help us understand its advantages and shortcomings. Finally, the presented framework could provide ideas and guidelines for the development of higher precision and wider application of composite material parameter identification methods.

     

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