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Article(id=1320122989161595307, tenantId=1146029695717560320, journalId=1263187385517883426, issueId=1320122987781673454, articleNumber=null, orderNo=null, doi=10.14062/j.issn.0454-5648.20260331, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1778774400000, receivedDateStr=2026-05-15, revisedDate=1779984000000, revisedDateStr=2026-05-29, acceptedDate=null, acceptedDateStr=null, onlineDate=1792671447315, onlineDateStr=2026-10-22, pubDate=1785254400000, pubDateStr=2026-07-29, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1792671447315, onlineIssueDateStr=2026-10-22, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1792671447315, creator=13701087609, updateTime=1792671447315, updator=13701087609, issue=Issue{id=1320122987781673454, tenantId=1146029695717560320, journalId=1263187385517883426, year='2026', volume='54', issue='10', pageStart='3315', pageEnd='3812', issueExtLink='null', onlineDate='null', pubDate='1792425600000', pubDateStr='2026-10-20', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1792671446986, creator='13701087609', updateTime=1792720523418, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1320328829357375869, tenantId=1146029695717560320, journalId=1263187385517883426, issueId=1320122987781673454, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1320328829357375870, tenantId=1146029695717560320, journalId=1263187385517883426, issueId=1320122987781673454, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=3373, endPage=3388, ext={EN=ArticleExt(id=1320122990226948524, articleId=1320122989161595307, tenantId=1146029695717560320, journalId=1263187385517883426, language=EN, title=Construction of an Explicit Prediction Formula for Concrete Carbonation Depth Based on Interpretable Machine Learning, columnId=1320122989312586697, journalTitle=Journal of the Chinese Ceramic Society, columnName=Special Issue on Key Inorganic Non-metallic Materials for Intelligent Construction at the 28th Annual Meeting of the China Association for Science and Technology–AI-Driven Innovation in Cement-Based Materials-Research Articles, runingTitle=null, highlight=null, articleAbstract=
Introduction

Accurate prediction of concrete carbonation depth is essential for durability assessment and service-life prediction of reinforced concrete structures, as well as for evaluating the CO2 uptake capacity of cement-based materials. Concrete carbonation is affected by material composition, mix proportions, curing conditions, and the exposure environment, and these factors exhibit complex nonlinear coupling effects. Traditional empirical models are generally based on simplified assumptions and limited variables, making it difficult to fully describe the carbonation process. Machine learning (ML) models can capture nonlinear relationships from large datasets and achieve high prediction accuracy, but they usually lack explicit analytical expressions. To balance prediction accuracy, model simplicity, and interpretability, this study proposes an interpretable ML-based framework for constructing an explicit prediction formula for concrete carbonation depth.

Methods

A natural carbonation database shared by Marani et al. was used in this study. After data cleaning and feature processing, a database containing 35 input features, 2077 carbonation-depth data points, and 709 concrete mixtures was obtained. Decision tree (DT), random forest (RF), XGBoost (XGB), and CatBoost (CB) models were established for carbonation depth prediction. Considering the skewed distribution of carbonation depth, log1p transformation was applied to the target variable. The data were divided by concrete mixture group to avoid data leakage. SHAP analysis was then used to rank feature importance and guide feature selection. Based on the optimal CB model, the relationships between input variables and their SHAP contributions were fitted, and the additive SHAP contribution terms were further transformed into a multiplicative explicit prediction formula.

Results and discussion

The carbonation depth data showed an obvious skewed distribution, and log1p transformation improved model training stability and test-set prediction performance. By comparing different ML algorithms and feature sets, the CB model based on log1p transformation and the FS2 feature set showed the best overall performance. The root mean square error (RMSE) values of the training and test sets were 0.55 mm and 1.14 mm, respectively, and the corresponding coefficient of determination (R2) values were 0.98 and 0.93. These results indicated that the model could accurately predict natural carbonation depth and effectively capture the nonlinear relationship between input variables and carbonation depth. In the final FS2-CB model, SHAP analysis showed that W/CaO, carbonation time, and carbonation environment were the three most important variables affecting the prediction of carbonation depth. Among them, W/CaO showed the highest feature importance, indicating that it was a key combined variable influencing model prediction. Based on the SHAP dependence relationships, variable contribution functions were fitted, thereby enabling transformation from a black-box model to an explicit prediction formula (PF).

The PF model achieved an RMSE of 2.28 mm on the test set, which was approximately 47.2% lower than that of F4, the best-performing formula model on the same test set. This indicated that the PF model had higher prediction accuracy than traditional formula models on the original dataset. On the external dataset, the PF model achieved an RMSE of 4.48 mm, which was 11.6% lower than that of the ML model (5.07 mm), and also lower than those of formula models F1-F3, which ranged from 5.91 mm to 8.52 mm. These results showed that although the PF model was less accurate than the optimal ML model on the original full dataset, it combined relatively high prediction accuracy, an explicit mathematical expression, and better cross-source generalization ability, indicating its potential for engineering application.

Conclusions

This study proposes an interpretable machine learning-based method for concrete carbonation depth prediction and explicit formula extraction. Through literature database processing, feature selection, machine learning modeling, and SHAP contribution function fitting, a high-accuracy black-box model is transformed into an interpretable formula model. The CB model with log1p transformation and the FS2 feature set achieves the best prediction performance. In the final FS2-CB model, SHAP analysis shows that W/CaO, carbonation time, and carbonation environment are the dominant variables controlling carbonation depth, indicating that concrete carbonation is mainly governed by pore transport conditions, carbonation buffering capacity, exposure time, and environmental effects. The constructed PF model shows higher accuracy than traditional formula models and better cross-source generalization performance than the ML model on the external dataset. Overall, the proposed method improves model simplicity and interpretability while maintaining relatively high prediction accuracy, providing a useful reference for explicit model construction in concrete carbonation depth prediction and other performance prediction tasks of cement-based materials.

, authors=Wenjia LI, Pan FENG, Xin LIU, Hui XIE, Dining LI, authorsList=Wenjia LI, Pan FENG, Xin LIU, Hui XIE, Dining LI, authorCompany=null, correspAuthors=Pan FENG, authorNote=

LI Wenjia (2001-), male, Doctoral candidate. E-mail:

, correspAuthorsNote=
FENG Pan (1988-), female, Ph.D., Professor. E-mail:
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准确预测混凝土碳化深度对于钢筋混凝土结构耐久性评估、服役寿命预测及水泥基材料碳吸收能力分析具有重要意义。传统公式模型难以准确刻画材料组成、养护制度和服役环境之间的非线性耦合作用，而机器学习（ML）模型虽具有较高预测精度，但缺乏明确解析表达形式，限制了其机理分析和工程应用。为实现由高精度黑箱预测模型向可解释公式模型的转化，本工作基于自然碳化文献数据库，采用决策树（DT）、随机森林（RF）、XGBoost（XGB）和CatBoost（CB）建立碳化深度预测模型，并结合沙普利加性解释（Shapley additive explanations，SHAP）方法进行特征筛选和变量贡献函数拟合，构建显式预测模型。结果表明，基于log1p变换、FS2特征组合和CB算法的模型表现最佳，训练集和测试集均方根误差（RMSE）分别为0.55 mm和1.14 mm。SHAP分析表明，在最终FS2-CB模型中，W/CaO、碳化时间和碳化环境是最主要的3个影响变量，说明混凝土碳化深度主要受孔隙传输条件、碳化缓冲能力、暴露时间和环境作用共同控制。其中，W/CaO能够同时反映孔隙传输能力和碳化缓冲能力，是表征混凝土抗碳化能力的重要特征。基于SHAP贡献函数建立的预测公式（PF）模型在外部数据集验证上的RMSE为4.48 mm，低于ML模型和传统公式模型F1~F3，其RMSE分别为5.07 mm和5.91~8.52 mm，表现出更好的跨数据集泛化性能。上述结果表明，本工作提出的“机器学习建模-SHAP解释分析-变量贡献函数拟合-显式公式构建”方法框架能够在保持较高预测精度的同时提高模型简洁性和可解释性，并从数据驱动角度揭示传输条件、碳化缓冲能力和环境作用对混凝土碳化过程的协同影响。

, authors=李文佳, 冯攀, 刘新, 谢辉, 李迪宁, authorsList=李文佳, 冯攀, 刘新, 谢辉, 李迪宁, authorCompany=null, correspAuthors=冯攀, authorNote=

李文佳（2001-），男，博士研究生。

, correspAuthorsNote=
冯攀（1988-），女，博士，教授。
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基于可解释机器学习的混凝土碳化深度显式预测公式构建
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李文佳 , 冯攀 , 刘新 , 谢辉 , 李迪宁
硅酸盐学报 | 第二十八届中国科协年会智能建造关键无机非金属材料–AI驱动水泥基材料创新专题-研究论文 2026,54(10): 3373-3388
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硅酸盐学报 |第二十八届中国科协年会智能建造关键无机非金属材料–AI驱动水泥基材料创新专题-研究论文 2026 , 54 (10) : 3373 -3388
基于可解释机器学习的混凝土碳化深度显式预测公式构建
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李文佳 , 冯攀 , 刘新, 谢辉, 李迪宁
作者信息
  • 东南大学材料科学与工程学院，重大基础设施工程材料全国重点实验室，南京　211189
通讯作者:
冯攀（1988-），女，博士，教授。
作者简介:

李文佳（2001-），男，博士研究生。

Construction of an Explicit Prediction Formula for Concrete Carbonation Depth Based on Interpretable Machine Learning
Wenjia LI , Pan FENG , Xin LIU, Hui XIE, Dining LI
Affiliations
  • School of Materials Science and Engineering, Southeast University, State Key Laboratory of Engineering Materials for Major Infrastructure, Nanjing 211189, China
    • Corresponding Author:
    FENG Pan (1988-), female, Ph.D., Professor. E-mail:

    LI Wenjia (2001-), male, Doctoral candidate. E-mail:

出版时间: 2026-07-29 doi: 10.14062/j.issn.0454-5648.20260331
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摘要
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准确预测混凝土碳化深度对于钢筋混凝土结构耐久性评估、服役寿命预测及水泥基材料碳吸收能力分析具有重要意义。传统公式模型难以准确刻画材料组成、养护制度和服役环境之间的非线性耦合作用，而机器学习（ML）模型虽具有较高预测精度，但缺乏明确解析表达形式，限制了其机理分析和工程应用。为实现由高精度黑箱预测模型向可解释公式模型的转化，本工作基于自然碳化文献数据库，采用决策树（DT）、随机森林（RF）、XGBoost（XGB）和CatBoost（CB）建立碳化深度预测模型，并结合沙普利加性解释（Shapley additive explanations，SHAP）方法进行特征筛选和变量贡献函数拟合，构建显式预测模型。结果表明，基于log1p变换、FS2特征组合和CB算法的模型表现最佳，训练集和测试集均方根误差（RMSE）分别为0.55 mm和1.14 mm。SHAP分析表明，在最终FS2-CB模型中，W/CaO、碳化时间和碳化环境是最主要的3个影响变量，说明混凝土碳化深度主要受孔隙传输条件、碳化缓冲能力、暴露时间和环境作用共同控制。其中，W/CaO能够同时反映孔隙传输能力和碳化缓冲能力，是表征混凝土抗碳化能力的重要特征。基于SHAP贡献函数建立的预测公式（PF）模型在外部数据集验证上的RMSE为4.48 mm，低于ML模型和传统公式模型F1~F3，其RMSE分别为5.07 mm和5.91~8.52 mm，表现出更好的跨数据集泛化性能。上述结果表明，本工作提出的“机器学习建模-SHAP解释分析-变量贡献函数拟合-显式公式构建”方法框架能够在保持较高预测精度的同时提高模型简洁性和可解释性，并从数据驱动角度揭示传输条件、碳化缓冲能力和环境作用对混凝土碳化过程的协同影响。

机器学习  /  碳化深度预测  /  SHAP  /  特征筛选  /  显式公式提炼
Introduction

Accurate prediction of concrete carbonation depth is essential for durability assessment and service-life prediction of reinforced concrete structures, as well as for evaluating the CO2 uptake capacity of cement-based materials. Concrete carbonation is affected by material composition, mix proportions, curing conditions, and the exposure environment, and these factors exhibit complex nonlinear coupling effects. Traditional empirical models are generally based on simplified assumptions and limited variables, making it difficult to fully describe the carbonation process. Machine learning (ML) models can capture nonlinear relationships from large datasets and achieve high prediction accuracy, but they usually lack explicit analytical expressions. To balance prediction accuracy, model simplicity, and interpretability, this study proposes an interpretable ML-based framework for constructing an explicit prediction formula for concrete carbonation depth.

Methods

A natural carbonation database shared by Marani et al. was used in this study. After data cleaning and feature processing, a database containing 35 input features, 2077 carbonation-depth data points, and 709 concrete mixtures was obtained. Decision tree (DT), random forest (RF), XGBoost (XGB), and CatBoost (CB) models were established for carbonation depth prediction. Considering the skewed distribution of carbonation depth, log1p transformation was applied to the target variable. The data were divided by concrete mixture group to avoid data leakage. SHAP analysis was then used to rank feature importance and guide feature selection. Based on the optimal CB model, the relationships between input variables and their SHAP contributions were fitted, and the additive SHAP contribution terms were further transformed into a multiplicative explicit prediction formula.

Results and discussion

The carbonation depth data showed an obvious skewed distribution, and log1p transformation improved model training stability and test-set prediction performance. By comparing different ML algorithms and feature sets, the CB model based on log1p transformation and the FS2 feature set showed the best overall performance. The root mean square error (RMSE) values of the training and test sets were 0.55 mm and 1.14 mm, respectively, and the corresponding coefficient of determination (R2) values were 0.98 and 0.93. These results indicated that the model could accurately predict natural carbonation depth and effectively capture the nonlinear relationship between input variables and carbonation depth. In the final FS2-CB model, SHAP analysis showed that W/CaO, carbonation time, and carbonation environment were the three most important variables affecting the prediction of carbonation depth. Among them, W/CaO showed the highest feature importance, indicating that it was a key combined variable influencing model prediction. Based on the SHAP dependence relationships, variable contribution functions were fitted, thereby enabling transformation from a black-box model to an explicit prediction formula (PF).

The PF model achieved an RMSE of 2.28 mm on the test set, which was approximately 47.2% lower than that of F4, the best-performing formula model on the same test set. This indicated that the PF model had higher prediction accuracy than traditional formula models on the original dataset. On the external dataset, the PF model achieved an RMSE of 4.48 mm, which was 11.6% lower than that of the ML model (5.07 mm), and also lower than those of formula models F1-F3, which ranged from 5.91 mm to 8.52 mm. These results showed that although the PF model was less accurate than the optimal ML model on the original full dataset, it combined relatively high prediction accuracy, an explicit mathematical expression, and better cross-source generalization ability, indicating its potential for engineering application.

Conclusions

This study proposes an interpretable machine learning-based method for concrete carbonation depth prediction and explicit formula extraction. Through literature database processing, feature selection, machine learning modeling, and SHAP contribution function fitting, a high-accuracy black-box model is transformed into an interpretable formula model. The CB model with log1p transformation and the FS2 feature set achieves the best prediction performance. In the final FS2-CB model, SHAP analysis shows that W/CaO, carbonation time, and carbonation environment are the dominant variables controlling carbonation depth, indicating that concrete carbonation is mainly governed by pore transport conditions, carbonation buffering capacity, exposure time, and environmental effects. The constructed PF model shows higher accuracy than traditional formula models and better cross-source generalization performance than the ML model on the external dataset. Overall, the proposed method improves model simplicity and interpretability while maintaining relatively high prediction accuracy, providing a useful reference for explicit model construction in concrete carbonation depth prediction and other performance prediction tasks of cement-based materials.

machine learning  /  carbonation depth prediction  /  SHAP  /  feature selection  /  explicit formula extraction
李文佳, 冯攀, 刘新, 谢辉, 李迪宁. 基于可解释机器学习的混凝土碳化深度显式预测公式构建. 硅酸盐学报, 2026 , 54 (10) : 3373 -3388 . DOI: 10.14062/j.issn.0454-5648.20260331
Wenjia LI, Pan FENG, Xin LIU, Hui XIE, Dining LI. Construction of an Explicit Prediction Formula for Concrete Carbonation Depth Based on Interpretable Machine Learning[J]. Journal of the Chinese Ceramic Society, 2026 , 54 (10) : 3373 -3388 . DOI: 10.14062/j.issn.0454-5648.20260331
基金
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  • 江苏省科技计划专项资金（前沿引领技术基础研究）重大项目(BK20222004)
  • 国家自然科学基金项目(52478238; 52408240)
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doi: 10.14062/j.issn.0454-5648.20260331
  • 接收时间：2026-05-15
  • 首发时间：2026-10-22
  • 出版时间：2026-07-29
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  • 收稿日期：2026-05-15
  • 修回日期：2026-05-29
基金
江苏省科技计划专项资金（前沿引领技术基础研究）重大项目(BK20222004)
国家自然科学基金项目(52478238; 52408240)
作者信息
    东南大学材料科学与工程学院，重大基础设施工程材料全国重点实验室，南京　211189

通讯作者:

冯攀（1988-），女，博士，教授。
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species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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