基于改进堆叠模型的软土压缩性能预测

Prediction of soft soil compression performance based on improved stacking model

摘要

【目的】以构建一种快速预测压缩系数的模型为目的，使用易获取的多种物理性质指标作为输入特征，提出了一种基于主成分分析法(PCA)降维的改进堆叠模型。【方法】以东莞市滨海湾新区获取的360组实际淤泥土数据为基础，进行模型的训练和验证。针对土体数据维度高、特征间可能存在多重共线性的问题，首先采用PCA技术提取特征数据中累计方差贡献率超过95%的前5个主成分。前5个主成分主要反映了含水率、天然孔隙比、液限、塑性指数及密度比等物理性质的综合变化特征。所构建的堆叠模型分为两层学习器：基学习器和元学习器。基学习器层采用随机森林和XGBoost模型；元学习器层采用支持向量回归(SVR)模型。采用交叉验证策略产生的折外预测值作为元学习器层的输入特征。【结果】经验证，所构建的堆叠模型在训练集上的决定系数(R²)达到0.790,均方误差MSE为0.037 MPa^-2;测试集上的R²达到0.781,MSE为0.033 MPa^-2。与传统机器学习模型相比，所提出的改进堆叠模型在预测精度方面表现更好。其中与表现较优的随机森林模型相比，R²指标提升约11.89%,而MSE指标降低幅度约为25%。同时对比了未经PCA降维的模型，该模型测试集上的R²为0.747,MSE为0.048 MPa^-2,均差于采用PCA降维的模型方案。【结论】为提升模型在不同区域数据分布差异条件下的泛用性，引入基于中位数映射的预测结果校准方法，通过对比新区域与源区域压缩系数分布的中位值与方差关系，对预测结果进行线性修正，减弱了分布漂移对模型预测精度的影响。研究结果表明，该模型在软土压缩系数的快速、精准预测中具有较高的可靠性、可推广性与应用价值。

Abstract

[Objective] To establish a model for the rapid prediction of the compression coefficient, multiple easily obtainable physical property indicators are used as input features, and an improved stacking model based on principal component analysis(PCA) for dimensionality reduction is proposed. [Methods] Based on 360 sets of actual silty soil data collected from the Binhaiwan New District in Dongguan City, the model was trained and validated. To address the issues of high dimensionality of soil data and potential multicollinearity among features, PCA was first applied to extract the top five principal components with a cumulative variance contribution rate exceeding 95% from the feature data. These top five principal components mainly reflected the comprehensive variation characteristics of physical properties such as water content, natural void ratio, liquid limit, plasticity index, and specific gravity. The constructed stacking model consisted of two learning layers: base learners and a meta-learner. Random forest and XGBoost models were adopted as base learners, while a support vector regression(SVR) model was employed as the meta-learner. Out-of-fold predictions generated via cross-validation were used as input features for the meta-learner layer. [Results] The validation result indicated that the constructed stacking model achieved a coefficient of determination(R²) of 0.790 and a mean squared error(MSE) of 0.037 MPa^-2 on the training set, and an R² of 0.781 and an MSE of 0.033 MPa^-2 on the test set. Compared to traditional machine learning models, the proposed improved stacking model achieved higher prediction accuracy. Specifically, compared to the relatively better-performing random forest model, the R² increased by approximately 11.89%, while the MSE decreased by about 25%. Furthermore, a comparison was made with the model without PCA dimensionality reduction, which achieved an R² of 0.747 and an MSE of 0.048 MPa^-2 on the test set, both worse than the model using PCA for dimensionality reduction. [Conclusion] To enhance the model's generalization under varying data distributions across regions, a calibration method based on median mapping for prediction result is introduced. By comparing the median and variance relationship of the compression coefficient distributions between new and source regions, linear correction is applied to the prediction result, mitigating the impact of distribution drift on the model's prediction accuracy. The result demonstrate that the proposed model exhibits high reliability, generalizability, and application value in the rapid and accurate prediction of the compression coefficient in soft soil.

关键词

软土压缩系数 / 主成分分析法(PCA) / 堆叠模型 / 支持向量回归(SVR) / 随机森林 / XGBoost / 交叉验证 / 力学性能

Key words

compression coefficient of soft soil / principal component analysis(PCA) / stacking model / support vector regression(SVR) / random forest / XGBoost / cross-validation / mechanical properties

基金资助

国家自然科学基金项目(42002274)

广东省重点建设学科科研能力提升项目(2024ZDJS030)

2025 年广东省住房和城乡建设厅科技创新计划(20250304K0010)