Hybrid machine learning with Bayesian optimization methods for prediction of patch load resistance of unstiffened plate girders无加劲板梁局部承载力预测的混合机器学习与 Bayes 优化方法
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Le DN, Pham TH, Papazafeiropoulos G, Kong ZY, Tran VL, Vu QV, 2024. Hybrid machine learning with Bayesian optimization methods for prediction of patch load resistance of unstiffened plate girders. Probabilistic Engineering Mechanics, 76: 103624.DOI: 10.1016/j.probengmech.2024.103624
摘要 | Abstract
本文提出了一种基于混合机器学习 (machine learning, ML) 和 Bayes 优化 (Bayesian optimization, BO) 方法的新模型，用于预测纵向无加劲板梁的局部承载力 (patch load resistance, PLR)。研究收集了共 354 个无加劲板梁在局部荷载下的试验数据，用于训练和测试，以建立所提模型。采用了五种机器学习模型，包括支持向量机 (support vector machines, SVM)、决策树 (decision tree, DT)、梯度提升树 (gradient boosted tree, GBT)、极限梯度提升算法 (extreme gradient boosting algorithm, XGBoost) 和分类提升回归 (CatBoost regression, CAT)，并利用 Bayes 优化方法优化机器学习模型的超参数，以确定哪种模型最适合预测纵向无加劲板梁的局部承载力。研究发现，与其它方法相比，Bayes 优化梯度提升树模型表现出最佳的预测精度。通过将 Bayes 优化梯度提升树模型的预测结果与现有设计标准和公式进行比较，验证了该模型的性能。此外，还采用 Shapley 加性解释 (Shapley additive explanations, SHAP) 方法评估每个输入变量对所提模型的重要性和贡献，并开发了一个图形用户界面 (graphical user interface, GUI) 工具，以便估算无加劲板梁的局部承载力。最后，采用 Bayes 优化梯度提升树模型开发了一种支持工具，用于初步设计阶段寻找纵向无加劲板梁在局部荷载下合适的几何尺寸和材料属性。该优化工具可供用户在线访问，以便实际设计使用。关键词: 局部荷载, 无加劲梁, 机器学习, Bayes 优化This paper aims to propose a new hybrid Machine Learning (ML) with Bayesian Optimization (BO) methods for predicting the patch loading resistance, P_u of longitudinally unstiffened plate girders. A total of 354 tests of the unstiffened plate girder under patch loading are collected and used for the training and testing to establish the proposed models. Five ML models including Support Vector Machines (SVM), Decision Tree (DT), Gradient Boosted Tree (GBT), Extreme Gradient Boosting algorithm (XGBoost), and CatBoost regression (CAT) are employed, and the BO method is used to optimize the hyperparameters of these ML models, in order to show which of them is best-suited for prediction of the PLR of longitudinally unstiffened plate girders. It was found that the BO-GBT presents the best accuracy compared to others. The performance of the BO-GBT model is validated by comparing its predictive results with the current design standards and the existing formulae. Additionally, the Shapley Additive Explanations (SHAP) method is employed to evaluate the importance and contributions of each input variable on the proposed model, and a Graphical User Interface (GUI) tool is developed to conveniently estimate the P_u of the unstiffened plate girders. Finally, the BO-GBT model is used to develop a support tool for finding suitable geometric dimensions and material properties of longitudinally unstiffened girder under patch loading in the preliminary design stage. The optimization tool is accessible online for the users for more convenient use in practical design purposes.Keywords: Patch loading; Unstiffened girders; Machine learning; Bayesian optimization![]()
Fig. 1. Model of an unstiffened plate girder under patch loading and parameters
图 2: 试验数据集变量对的 Pearson 相关系数Fig. 2. Pearson correlation coefficient between variable pairs in the experimental dataset
Fig. 3. Illustration of GBT model
Fig. 4. Illustration of Bayesian optimization algorithm
图 5: 本研究采用的混合 Bayes 优化梯度提升树模型流程图Fig. 5. Flowchart of the hybrid BO-GBT model used in this study
Fig. 6. Performance metrics of different ML models
Fig. 7. Comparison of different ML models
图 8: 各输入参数全局重要性的 Shapley 值Fig. 8. SHAP value of the global importance of each input parameters
Fig. 9. Impact of each features on predicted result of a data point
Fig. 10. Summary plots of BO-GBT
图 11: Bayes 优化梯度提升树与现有公式的对比Fig. 11. Comparison between BO-GBT and the existing equations
Fig. 12. Distribution of the error range of all data
图 13: 本研究开发的局部承载力预测的图形用户界面应用Fig. 13. GUI application developed in the present study for the P_u prediction
图 14: 局部荷载下纵向无加劲板梁的尺寸与材料特性选择流程图Fig. 14. Flowchart of the choosing procedure of the dimension and material properties of the longitudinally unstiffened plate girder under patch loading
Fig. 15. Interface of the optimization tool
作者信息 | Authors
越南河内土木工程大学 (Hanoi University of Civil Engineering) 建筑与工业建造学院
越南河内土木工程大学 (Hanoi University of Civil Engineering) 建筑与工业建造学院
希腊雅典技术大学 (National Technical University of Athens) 结构工程系
英国赫瑞-瓦特大学 (Heriot-Watt University) 可持续建筑环境研究所
越南荣市大学 (Vinh University) 土木工程系
Quang-Viet Vu, 通讯作者 (Corresp.) 越南范朗大学 (Van Lang University) 计算科学与人工智能研究所Email: viet.vuquang@vlu.edu.vn
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
