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基于机器学习软骨细胞的时间依赖性力学行为研究及本构参数反演

魏新宇 桑建兵 张睿琳 王静远 刘宝友

魏新宇, 桑建兵, 张睿琳, 王静远, 刘宝友. 基于机器学习软骨细胞的时间依赖性力学行为研究及本构参数反演. 力学学报, 2022, 54(11): 1-8 doi: 10.6052/0459-1879-22-344
引用本文: 魏新宇, 桑建兵, 张睿琳, 王静远, 刘宝友. 基于机器学习软骨细胞的时间依赖性力学行为研究及本构参数反演. 力学学报, 2022, 54(11): 1-8 doi: 10.6052/0459-1879-22-344
Wei Xinyu, Sang Jianbing, Zhang Ruilin, Wang Jingyuan, Liu Baoyou. Time-dependent mechanical behavior and constitutive parameter identification of chondrocytes based on machine learning. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(11): 1-8 doi: 10.6052/0459-1879-22-344
Citation: Wei Xinyu, Sang Jianbing, Zhang Ruilin, Wang Jingyuan, Liu Baoyou. Time-dependent mechanical behavior and constitutive parameter identification of chondrocytes based on machine learning. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(11): 1-8 doi: 10.6052/0459-1879-22-344

基于机器学习软骨细胞的时间依赖性力学行为研究及本构参数反演

doi: 10.6052/0459-1879-22-344
基金项目: 河北省自然科学基金项目(A2020202015, A2021202014), 国家自然科学基金项目(12102123)资助项目
详细信息
    作者简介:

    桑建兵, 教授, 主要研究方向: 工程结构分析与智能算法研究. E-mail: sangjianbing@126.com

  • 中图分类号: Q66

TIME-DEPENDENT MECHANICAL BEHAVIOR AND CONSTITUTIVE PARAMETER IDENTIFICATION OF CHONDROCYTES BASED ON MACHINE LEARNING

  • 摘要: 探究软骨细胞机械负载下的力学特性对于理解软骨细胞的正常和病理状态以及骨性关节炎的病因至关重要. 基于软骨细胞有限元计算模型的力学响应与其本构参数之间的高度复杂非线性, 本文提出了分别利用双向深度神经网络(TW-Deepnets)模型和随机森林(RF)模型并结合有限元方法来识别软骨细胞本构参数的两种反演方法. 首先, 建立了软骨细胞的无侧限压缩实验有限元模型, 收集MSnHS本构参数空间点与对应的有限元计算模型的压缩反作用力响应数据集. 其次, 结合贝叶斯超参数优化算法搭建了用于软骨细胞本构参数反求的TW-Deepnets模型和RF模型, 对有限元收集的数据进行训练, 并利用Nguyen等人单个软骨细胞受到50%压缩程度下的实验数据对软骨细胞的MSnHS本构参数进行了反求. 最后, 通过与实验曲线的对比验证了所提出的反演方法的有效性, 并引入决定系数R2对两种模型的预测准确性进行了对比评估, 检验了模型对各本构参数的预测性能, 分析了MSnHS本构模型中各参数影响软骨细胞力学响应的重要性占比. 结果表明, 本研究提出的本构参数反演方法能够有效的获取软骨细胞的本构参数值, 从而准确描述软骨细胞的时间依赖性力学特性, 该方法也可进一步推广到生物细胞在静态或动态负载条件下的的复杂参数反演问题.

     

  • 图  1  软骨细胞压缩有限元模型: (a)三维几何模型(b)八分之一有限元模型

    Figure  1.  Finite element model of chondrocyte compression :(a) three-dimensional geometric model (b) one-eighth finite element model

    图  2  本研究中提出的本构参数识别方法流程图:(a) TW-Deepnets模型; (b) RF模型.

    Figure  2.  The flow chart of the parameter identification method proposed in this study: (a) TW-Deepnets model; (b) RF model.

    图  3  随机森林模型预测结构示意图

    Figure  3.  The structure of the RF model

    图  4  软骨细胞代理模型的误差对比

    Figure  4.  Comparing the MSE of neural network proxy model under different sampling methods

    图  5  TW-Deepnets模型架构

    Figure  5.  TW-Deepnets model architecture

    图  6  TW-Deepnets模型以及RF模型本构参数预测性能检验:(a) TW-Deepnets; (b)RF

    Figure  6.  Test of constitutive parameters prediction (a) TW-Deepnets; (b)RF

    图  7  MSnHS本构参数特征重要性占比

    Figure  7.  Importance ratio of MSnHS constitutive parameters

    图  8  模型预测与实验的时间−力曲线对比

    Figure  8.  Model predictions are compared with experimental time-force curves

    图  9  软骨细胞不同压缩速度下的时间—力曲线

    Figure  9.  Time - force curves of chondrocytes at different compression rates

    图  10  软骨细胞3 s应力松弛前后Mise应力云图

    Figure  10.  Mise stress cloud diagram of chondrocytes before and after 3 s stress relaxation

    表  1  Bayesian优化算法确定的模型超参数

    Table  1.   Hyperparameter values obtained by Bayesian optimization

    The optimized modelHyper-parameter
    Forward problem neural networkLearning rate = 0.00012
    Number of dense layers = 2
    Number of noses for each layers = 20
    Activation function: Relu
    Inverse problem neural networkLearning rate = 0.00018
    Number of dense layers = 3
    Number of noses for each layers = 23
    Activation function: Relu
    Random Forestn_estimators = 250
    max_depth = 69
    min_samples_split = 2
    下载: 导出CSV

    表  2  MSnHS本构模型参数预测结果

    Table  2.   Parameters prediction results

    ParametersTW-DeepnetsRF
    C10 [10−3MPa]1.5065041.461882
    D1243.427301.006
    g10.2899950.300854
    k10.9814070.950895
    τ1 [s]0.1420.242
    R20.9870.912
    下载: 导出CSV
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  • 网络出版日期:  2022-09-21

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