應用機器學習於動態三軸試驗資料預測液化循環剪應力比

Abstract

土壤液化一直是大地工程領域中長期關注的重要議題，而動態三軸試驗 (Cyclic Triaxial Test) 作為實驗室中模擬地震載重下，研究土壤行為主要的土壤單元試驗。其中，作為施加荷載能量的關鍵參數的循環剪應力比 (Cyclic Stress Ratio, CSR) ，其設定往往依賴試體的物理性質、試驗條件和試驗者的經驗進行推估。然而，不同參數組合將導致CSR值有所變化，使得在試驗設計階段難以事先準確掌握合適的CSR值，進而影響試驗成功率與數據品質。為解決此問題，本研究蒐集並整理來自23篇文獻，共近千筆的動態三軸試驗資料，建立多種機器學習模型以協助預測不同試體參數所對應之CSR值，希望提供一套可用應於試驗設計階段之預測工具。研究流程分為三階段，第一階段針對資料進行前處理與特徵工程，包含缺失值填補、數值變數標準化與類別變數做編碼等；第二階段使用七種監督式學習方法，包含五種傳統機器學習模型 (Random Forest、CatBoost、XGBoost、Explainable Boosting Machine (EBM)，與Support Vector Machine (SVM)) 以及兩種深度學習模型 (Artificial Neural Network (ANN) 與Bayesian Neural Network (BNN))，並使用決定係數R2和誤差指標 (如MAE、MSE與RMSE) 做為迴歸預測表現之評估依據；第三階段則進一步CSR與循環剪切次數 (N) 之關係建立下限曲線作為二元分類基準，將迴歸問題轉化為液化與非液化樣本之分類任務，並加入特徵解釋性與預測不確定性分析。研究結果顯示，CatBoost、XGBoost與Random Forest整體表現最佳。主要特徵 (如初始孔隙比、循環剪切次數與細粒料含量等) 即可支撐預測能力。MICE為最穩定之補值方式。於深度學習模型中，手動調參表現優於Grid search，可有效避免測試集表現劣化的問題。EBM模型之變數貢獻圖可提供解釋性，BNN模型則能提供預測結果的信賴區間，能量化不確定性。

Soil liquefaction has long been a critical issue in geotechnical engineering. Among the laboratory methods developed to investigate this phenomenon, the cyclic triaxial test is one of the most important experiments for simulating soil behavior under earthquake loading. A key parameter in this test is the Cyclic Stress Ratio (CSR), which reflects the magnitude of loading energy applied to the soil specimen. However, the appropriate CSR value often depends on the specimen’s physical properties, the experimental conditions, and the experience of the test operator. As a result, accurately determining the CSR beforehand is challenging, which may affect the success rate of the test and the quality of the resulting data. To address the problem, this study collected nearly 1000 cyclic triaxial test records from 23 academic papers and theses, and establish multiple machine learning models to predict the target variable –CSR, aiming to provide a useful reference during the test design stage. The study is divided into three main parts. The first part involves data preprocessing and feature engineering, including missing value imputation, numerical variable standardization, and categorical variable encoding. The second part focuses on model development using seven supervised models, including five machine learning models (Random Forest, CatBoost、XGBoost、Explainable Boosting Machine (EBM), and Support Vector Machine (SVM)) and two deep learning models (Artificial Neural Network (ANN) and Bayesian Neural Network (BNN)). Model performance was evaluated using the coefficient of determination (R²) and error metrics. In the third stage, the study further converted the regression task into a binary classification problem by defining a trial-and-error lower bound curve based on the CSR-N relationship to distinguish between liquefied and non-liquefied samples. This stage also incorporated model interpretability and prediction uncertainty analysis. The results show that CatBoost, XGBoost, and Random Forest achieved the best overall performance. Moreover, the models were able to make accurate predictions using only a set of primary features (e.g., initial void ratio e₀, number of loading cycles N, and fine content fc). Among the imputation methods tested, Multiple Imputation by Chained Equations (MICE) produced the most stable outcomes. Manual hyperparameter tuning outperformed Grid search techniques in deep learning models. Finally, EBM provided interpretable visualizations of individual feature contributions, while BNN offered prediction intervals that helped quantify uncertainty and enhance confidence in the results.