目的 基于随机森林算法和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 首先建立了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，得到了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，分别对搭建好的随机森林(RF)模型和BP神经网络(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了预测。最后，引入均方误差(MSE)和决定系数(R2)来对模型的预测准确性进行了评估，同时对比实验曲线验证了模型的有效性。结果 利用RF模型和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模型的MSE达到了1.3702×10-3，R2达到了0.9829；BPNN模型的MSE达到了4.8581×10-5，R2达到了0.9993。反求得到了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模型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的其他力学特性的研究。同时，本研究为足底软组织本构参数的获取提供了新方法，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 the superelastic model of plantar soft tissue based on random forest algorithm and BP neural network algorithm, to improve the efficiency and accuracy of the method for obtaining constitutive parameters.Methods First, a finite element model of the spherical indentation experiment of plantar soft tissue was established, and the spherical indentation experiment process was simulated to obtain a dataset with nonlinear displacement and indentation force relationships.The dataset was divided into a training set and a testing set, and the built random forest (RF) model and BP neural network (BPNN) model were trained separately. The constitutive parameters of plantar soft tissue were predicted through experimental data.Finally, the mean square error (MSE) and the coefficient of determination (R2) were introduced to evaluate the accuracy of the model prediction, and the effectiveness of the model was verified by comparing the experimental curves.Results The combination of RF model and BPNN model with finite element simulation is an effective and accurate method to determine the constitutive parameters of plantar soft tissue superelasticity, after training,the MSE of the RF model reached 1.3702×10-3, and the R2 reached 0.9829;the MSE of the BPNN model reached 4.8581×10-5, and the R2 reached 0.9993.The inverse-determined constitutive parameters of plantar soft tissue suitable for simulation are obtained. The calculated response curves of the two sets of constitutive parameters predicted are in good agreement with the experimental curves.Conclusion The prediction accuracy of the constitutive parameters of plantar soft tissue superelasticity based on artificial intelligence algorithms modelis high, and the relevant research results can also be applied to the study of other mechanical properties of plantar soft tissue. At the same time,this study provides a new method for obtaining constitutive parameters of plantar soft tissue, which helps to quickly diagnose clinical problems such as plantar soft tissue lesions.