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段尊义, 刘亿, 张皓翔, 陈志远, 徐斌, 朱继宏, 阎军. 基于机器学习的变刚度纤维增强复合材料最小化结构柔顺性优化设计. 力学学报, 2024, 56(4): 1-12. DOI: 10.6052/0459-1879-23-521
引用本文: 段尊义, 刘亿, 张皓翔, 陈志远, 徐斌, 朱继宏, 阎军. 基于机器学习的变刚度纤维增强复合材料最小化结构柔顺性优化设计. 力学学报, 2024, 56(4): 1-12. DOI: 10.6052/0459-1879-23-521
Duan Zunyi, Liu Yi, Zhang Haoxiang, Chen Zhiyuan, Xu Bin, Zhu Jihong, Yan Jun. Machine learning-based design optimization of variable stiffness fiber reinforced composites to minimize structural compliance. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(4): 1-12. DOI: 10.6052/0459-1879-23-521
Citation: Duan Zunyi, Liu Yi, Zhang Haoxiang, Chen Zhiyuan, Xu Bin, Zhu Jihong, Yan Jun. Machine learning-based design optimization of variable stiffness fiber reinforced composites to minimize structural compliance. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(4): 1-12. DOI: 10.6052/0459-1879-23-521

基于机器学习的变刚度纤维增强复合材料最小化结构柔顺性优化设计

MACHINE LEARNING-BASED DESIGN OPTIMIZATION OF VARIABLE STIFFNESS FIBER REINFORCED COMPOSITES TO MINIMIZE STRUCTURAL COMPLIANCE

  • 摘要: 纤维增强复合材料层合板的变刚度优化设计, 通过逐点优化纤维铺角的可设计性, 从而匹配结构中应力状态的空间变化, 更高效地发挥纤维增强复合材料层合板在强度与刚度性能上的方向性, 为设计师提供了更广阔的设计空间与设计灵活度. 然而, 基于梯度类算法的传统复合材料变刚度优化设计, 因其设计变量众多, 不可避免地在结构分析与灵敏度分析中面临大规模计算的挑战. 同时, 结构在概念设计阶段存在载荷工况随机性问题, 如何在初始概念设计阶段, 针对随机载荷工况制定高效的设计方案具有重要工程价值. 近年来, 随着人工智能与高性能计算的快速发展, 基于传统优化获得的数据集构建端到端的机器学习模型, 为实现实时的复合材料变刚度优化提供了可能. 文章采用反向传播(back propagation, BP)神经网络算法, 建立了基于机器学习的纤维增强复合材料变刚度优化设计方法. 首先, 基于正态分布纤维优化(normal distribution fiber optimization, NDFO)插值格式, 构建以最小化结构柔顺度为目标的复合材料变刚度优化设计模型, 考虑载荷大小与方向的随机性, 获得神经网络模型训练所需的样本集数据. 其次, 以最小均方误差(means square error, MSE)为目标函数, 采用BP神经网络模型对样本数据集进行训练. 最后, 建立基于皮尔逊相关系数(pearson correlation coefficient)、均方误差(MSE)的模型评价体系, 对生成的神经网络模型进行评价. 数值算例讨论了含圆孔MBB梁与悬臂C型梁变刚度优化设计, 详细阐述了基于机器学习的复合材料变刚度优化方法的实施过程, 系统地对比了所提出的基于机器学习的复合材料变刚度优化与传统基于NDFO插值格式复合材料变刚度优化设计结果在纤维铺角轨迹和目标函数的差异, 验证了本方法的有效性.

     

    Abstract: The variable stiffness design optimization of fiber-reinforced composite laminates optimizes the designability of fiber laying angles point by point to match the spatial variation of stress states in the structure and more efficiently exert the directionality of fiber-reinforced composite laminates in strength and stiffness performance, providing the designers with a broader design space and design flexibility. However, the traditional variable stiffness design optimization of composite material based on gradient algorithms inevitably faces large-scale computational challenges in structural and sensitivity analysis due to its large number of design variables. At the same time, there is a problem with the randomness of load conditions in the conceptual design stage of the structure, and how to formulate an efficient design scheme for random load conditions in the initial conceptual design stage has important engineering value. In recent years, with the rapid development of artificial intelligence and high-performance computing, it has become possible to build end-to-end machine learning models based on the datasets obtained by traditional optimization, which provides the possibility of achieving real-time variable stiffness optimization of composite material. In this paper, the back propagation (BP) neural network algorithm is used to establish a variable stiffness design optimization method for fiber-reinforced composites based on machine learning. Firstly, based on the Normal Distribution Fiber Optimization (NDFO) interpolation scheme, a composite material variable stiffness design optimization model is constructed with minimizing structural compliance as an objective function, and the sample datasets required for neural network model training are obtained by considering the randomness of load magnitude and direction. Secondly, the Means Square Error (MSE) was used as the objective function to train the sample dataset using the BP neural network model. Finally, a model evaluation system based on the Pearson Correlation Coefficient (Pearson) and MSE is established to evaluate the generated neural network model. Numerical examples discuss the variable stiffness design optimization of MBB beam with round holes and C-type cantilever beam, elaborate the implementation process of the variable stiffness design optimization of composite based on machine learning, and systematically compare the differences between the variable stiffness design optimization of composite based on machine learning and the traditional variable stiffness design optimization results of composite based on NDFO in fiber laying trajectory and objective function, and verify the effectiveness of the proposed method.

     

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