Abstract

This paper reports on an investigation into the relationship between stiffness and applied force of an advanced biological composite structure using four techniques: experimental observation; finite element analysis (FEA); regression learner analysis; and, artificial neural networks (ANNs). The entire hydrated third metacarpal bones (MC3) from 16 thoroughbred horses were loaded in compression in an MTS machine. The stiffness was then determined from the applied force, MC3 displacement, and load exposure time. A variety of mathematical functions were fitted to the sample data points using MATLAB to demonstrate force-dependent stiffness. Two functions were found that exhibited a strong correlation between force and stiffness (R² = 0.75). Additionally, a power function was found that demonstrated a stronger correlation between the stiffness and force (R² = 0.81) if the exposure time was also incorporated. FEA considered the calculated force-dependent stiffness when assigning material properties. FEA results were compared with experimental data (for verification and validation), and a good agreement was found for the displacement (RMSE = 0.032 mm) and strain (RMSE = 61.85 με). Machine learning regression models were also employed to predict the stiffness of this complex structure. Applied force, exposure time, MC3 geometry (length and area of cross sections), and age were defined as the independent variables. The regression learner offered excellent reliability (R² = 0.98) for the prediction of stiffness. Also, feedforward back-propagation artificial neural networks were employed to improve and generalize the stiffness prediction ability to a wider population. ANN regression analysis showed R = 0.992 for training, R = 0.99 for testing, and R = 0.991 for the all datasets. To confirm its accuracy, the ANN was used to predict stiffness of specific samples that were not used in its training. This offered excellent reliability in predicting real-world data that ANNs have not seen before (R = 0.976).

摘要

本文报道了使用四种技术研究先进生物复合结构的刚度和作用力之间的关系：实验观察；有限元分析（FEA）；回归学习器分析；以及人工神经网络（ANN）。来自 16 匹纯种马的全部水合第三掌骨 (MC3) 被压缩加载到 MTS 机器中。然后根据施加的力、MC3 位移和负载暴露时间确定刚度。使用 MATLAB 将各种数学函数拟合到样本数据点，以证明与力相关的刚度。发现两个函数在力和刚度之间表现出很强的相关性 ( R ²= 0.75)。此外，如果还包含暴露时间，则发现了一个幂函数，表明刚度和力之间的相关性更强 ( R ^{2 = 0.81)。}FEA 在分配材料属性时考虑了计算的与力相关的刚度。将 FEA 结果与实验数据（用于验证和验证）进行比较，发现位移（RMSE = 0.032 mm）和应变（RMSE = 61.85 μ ε）具有良好的一致性。机器学习回归模型也被用来预测这种复杂结构的刚度。施加力、暴露时间、MC3 几何形状（横截面的长度和面积）和年龄被定义为自变量。回归学习器提供了出色的可靠性（R ²= 0.98) 用于预测刚度。此外，前馈反向传播人工神经网络被用来提高刚度预测能力并将其推广到更广泛的人群。ANN 回归分析显示 训练R = 0.992，测试R  = 0.99，所有数据集R  = 0.991。为了确认其准确性，人工神经网络用于预测未在其训练中使用的特定样本的刚度。这为预测人工神经网络以前从未见过的真实世界数据提供了出色的可靠性（R  = 0.976）。