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<p>This study conducted 537 force-controlled compression tests on shoe soles to measure strain energy. Various features were studied, including midsole and outsole structures, sole geometry, sole hardness, and loading conditions including applied compression force, angle, and loading speed. Strain energies during compression tests were recorded, followed by correlation analysis, analysis of variance (ANOVA), and Tukey tests. Subsequently, different machine learning (ML) algorithms—i.e., simple linear regression (SLR), support vector regression (SVR), random forest (RF), and multi-layer perceptron (MLP)—were applied for curve fitting. The correlation matrix revealed that strain energy exhibits a strong dependence on the applied force (correlation = 0.89), which stands out significantly compared to other features. This is followed by geometry and shoe hardness, both of which show a correlation of approximately 0.25. To validate these findings, ANOVA tests were conducted, and all <i>p </i>values were significant (<i>p</i> &lt; 0.05). Additionally, it was found that auxetic midsole structures achieve similar strain energy values as simple midsoles (mean = 2.978&#xa0;J), while maintaining a lighter overall weight. In contrast, weight-reducing holes were not as effective (mean = 2.080&#xa0;J). It was also shown that initial contact position (i.e., changed with the compression angle) can affect the strain energy; that is, initial contact with the heel generates less strain energy (mean = 2.643&#xa0;J) compared to the first touch with the toes (mean = 2.839&#xa0;J). After tuning ML hyperparameters through grid search, RF outperformed other models (MSE = 0.0089), followed by SVR with polynomial kernel (MSE = 0.0105), SVR with RBF kernel (MSE = 0.0146), and MLP (MSE = 0.0251). The developed models offer a practical tool for shoe manufacturers to optimize sole designs and prevent injury during high-stress activities.</p>

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Machine learning-based prediction of compressive energy absorption in shoe soles with different features

  • 期刊论文

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  • 发表日期：

    2025年10月23日

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  • Mohammad Mahdi Mohammadi,
  • Amir Nourani

摘要

This study conducted 537 force-controlled compression tests on shoe soles to measure strain energy. Various features were studied, including midsole and outsole structures, sole geometry, sole hardness, and loading conditions including applied compression force, angle, and loading speed. Strain energies during compression tests were recorded, followed by correlation analysis, analysis of variance (ANOVA), and Tukey tests. Subsequently, different machine learning (ML) algorithms—i.e., simple linear regression (SLR), support vector regression (SVR), random forest (RF), and multi-layer perceptron (MLP)—were applied for curve fitting. The correlation matrix revealed that strain energy exhibits a strong dependence on the applied force (correlation = 0.89), which stands out significantly compared to other features. This is followed by geometry and shoe hardness, both of which show a correlation of approximately 0.25. To validate these findings, ANOVA tests were conducted, and all p values were significant (p < 0.05). Additionally, it was found that auxetic midsole structures achieve similar strain energy values as simple midsoles (mean = 2.978 J), while maintaining a lighter overall weight. In contrast, weight-reducing holes were not as effective (mean = 2.080 J). It was also shown that initial contact position (i.e., changed with the compression angle) can affect the strain energy; that is, initial contact with the heel generates less strain energy (mean = 2.643 J) compared to the first touch with the toes (mean = 2.839 J). After tuning ML hyperparameters through grid search, RF outperformed other models (MSE = 0.0089), followed by SVR with polynomial kernel (MSE = 0.0105), SVR with RBF kernel (MSE = 0.0146), and MLP (MSE = 0.0251). The developed models offer a practical tool for shoe manufacturers to optimize sole designs and prevent injury during high-stress activities.