应用随机森林与神经网络算法的足底软组织本构参数反演方法

Inversion Method of Constitutive Parameters from Plantar Soft Tissues Based on Random Forest and Neural Network Algorithms

目的 基于随机森林(random forest, RF)算法和反向传播(back propagation, BP)神经网络算法实现对足底软组织超弹性模型本构参数的预测,以提升本构参数获取方式的效率和准确性。方法 首先建立足底软组织球形压痕实验的有限元模型,并对球形压痕实验过程进行仿真,得到具有非线性关系的位移和压痕力的数据集。将数据集进行划分,得到训练集和测试集,分别对搭建好的RF和BP神经网络(BP neural network, BPNN)模型进行训练,通过实验数据对足底软组织本构参数进行预测。最后,引入均方误差(mean square error, MSE)和决定系数(R2)对模型的预测准确性进行评估,同时对比实验曲线验证模型的有效性。结果 利用RF和BPNN模型结合有限元仿真是确定足底软组织超弹性本构参数的有效、准确的方法。训练后的RF模型MSE达到1.370 2×10^(-3),R^(2)为0.982 9;BPNN模型MSE达到4.858 1×10^(-5),R^(2)为0.999 3。反求得到适用于仿真的足底软组织的超弹性本构参数,预测得到的两组本构参数的计算响应曲线与实验曲线吻合较好。结论 基于人工智能算法模型对足底软组织超弹性本构参数的预测精度很高,相关研究成果也可以应用于足底软组织其他力学特性的研究。同时,研究结果为足底软组织本构参数的获取提供新方法,有助于快速诊断足底软组织病变等临床问题。

Objective To predict the constitutive parameters of a superelastic model of plantar soft tissues based on random forest(RF)and backpropagation(BP)neural network algorithms to improve the efficiency and accuracy of the method for obtaining constitutive parameters.Methods First,a finite element model for a spherical indentation experiment of plantar soft tissues was established,and the spherical indentation experiment process was simulated to obtain a dataset of nonlinear displacement and indentation force,divided into training and testing sets.The established RF and BP neural network(BPNN)models were trained separately.The constitutive parameters of plantar soft tissues were predicted using experimental data.Finally,the mean square error(MSE)and coefficient of determination(R2)were introduced to evaluate the accuracy of the model prediction,and the effectiveness of the model was verified by comparison with the experimental curves.Results Combining the RF and BPNN models with finite element simulation was an effective and accurate method for determining the superelastic constitutive parameters of plantar soft tissues.After training,the MSE of the RF model reached 1.3702×10^(-3),and R^(2) was 0.9829,whereas the MSE of the BPNN model reached 4.8581×10^(-5),and R^(2) was 0.9993.The inverse-determined constitutive parameters of the plantar soft tissues suitable for simulation were obtained.The calculated response curves for the two predicted sets of constitutive parameters were in good agreement with the experimental curves.Conclusions The prediction accuracy for the superelastic constitutive parameters of plantar soft tissues based on an artificial intelligence algorithm model is high,and the relevant research results can be applied to study other mechanical properties of plantar soft tissues.This study provides a new method for obtaining the constitutive parameters of plantar soft tissues and helps to quickly diagnose clinical problems,such as plantar soft tissue lesions.