硅酸盐学报

面向低碳超高性能混凝土智能设计的可解释贝叶斯网络建模

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李依芮 ¹^,²^,⁴^,⁵ , 曾晓辉 ²^,³ , 曾永平 ³ , 王鑫 ⁶ , 梁昱 ⁷ , 龙广成 ² , 谢友均 ²

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): 3483-3498

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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) : 3483 -3498

面向低碳超高性能混凝土智能设计的可解释贝叶斯网络建模

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李依芮¹^,²^,⁴^,⁵, 曾晓辉²^,³, 曾永平³, 王鑫⁶, 梁昱⁷, 龙广成², 谢友均²

作者信息

^1.伊犁师范大学物理科学与技术学院，新疆　伊犁　835000

^2.中南大学土木工程学院，长沙　410083

^3.海南大学热带海洋工程材料及评价全国重点实验室，海口　570228

^4.新疆凝聚态相变与微结构自治区重点实验室，新疆　伊犁　835000

^5.伊犁绿色硅基材料工程研究中心，新疆　伊犁　835000

^6.建筑材料工业技术情报研究所固废利用与低碳建材研究中心，北京　100024

^7.伊犁师范大学化学化工学院，新疆　伊犁　835000

通讯作者:

曾晓辉（1982-），男，博士，教授。

作者简介:

李依芮（1995-），女，博士，讲师。

Interpretable Bayesian Network Modeling for Intelligent Design of Low-Carbon Ultra-High-Performance Concrete

Yirui LI¹^,²^,⁴^,⁵, Xiaohui ZENG²^,³, Yongping ZENG³, Xin WANG⁶, Yu LIANG⁷, Guangcheng LONG², Youjun XIE²

Affiliations

^1.School of Physical Sciences and Technology, Yili Normal University, Yili 835000, Xinjiang, China

^2.School of Civil Engineering, Central South University, Changsha 410083, China

^3.State Key Laboratory of Tropic Ocean Engineering Materials and Materials Evaluation, Hainan University, Haikou 570228, China

^4.Xinjiang Laboratory of Phase Transitions and Microstructures in Condensed Matters, College of Physical Science and Technology, Yili 835000, Xinjiang, China

^5.Yili Engineering Research Center of Green Silicon-based Materials, Yili 835000, Xinjiang, China

^6.Research Center for Solid Waste Utilization and Low-Carbon Building Materials, Institute of Technical Information for Building Materials Industry of China, Beijing 100024, China

^7.School of Chemistry and Chemical Engineering, Yili Normal University, Yili 835000, Xinjiang, China

Corresponding Author:

ZENG Xiaohui (1982-), male, Ph.D., Professor. E-mail: zxhzlh@126.com

LI Yirui (1995-), female, Ph.D., Lecturer. E-mail: lixiao1117@163.com

出版时间: 2026-09-03 doi: 10.14062/j.issn.0454-5648.20260317

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摘要

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针对低碳超高性能混凝土（UHPC）配合比变量维度高、组分耦合复杂及传统强度预测模型物理可解释性不足的问题，本工作提出一种融合水化-堆积机理先验与数据驱动结构学习的小样本可解释贝叶斯网络（Bayesian network，BN）建模方法。根据系统性文献综述获得491组UHPC原始配合比数据，基于数据完整性和机理变量计算要求，经单位统一、变量转换、异常值核查和有效样本筛选后，获得136组有效建模样本。进一步依据胶凝材料水化反应和颗粒紧密堆积原理，构建包含胶凝材料反应活性指数、水胶比、激发剂掺量、胶砂比、钢纤维掺量、活性钙硅比、活性硫铝比和初始颗粒堆积密实度的水化-堆积特征体系，并建立“材料及工艺参数层-中间机理层-目标性能层”的BN预测模型。结果表明，BN模型在10折交叉验证中获得较高预测精度（R²=0.910 1），同时通过基于机理约束的干预敏感性分析量化了水化效应（47.9%）、堆积效应（35.1%）及水化-堆积协同效应（17.0%）对28 d抗压强度的贡献。5组独立验证结果初步表明，在本工作验证样本范围内，模型预测强度与实测强度具有较好的一致性，实测值均落入模型预测区间内。本工作可为低碳UHPC候选配比筛选、抗压强度预测和智能化设计，提供兼具预测能力与机理解释性的建模工具。

关键词

低碳超高性能混凝土 / 贝叶斯网络 / 抗压强度 / 可解释建模 / 智能设计

Abstract

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Introduction

Ultra-high-performance concrete (UHPC) has been widely used in bridges, tunnels, prefabricated structures, and other demanding engineering applications owing to its high compressive strength, excellent toughness, and superior durability. However, conventional UHPC typically requires a high cement content, high dosages of reactive powders, and steel fiber reinforcement, leading to considerably higher carbon emissions than ordinary concrete. The partial replacement of ordinary Portland cement (OPC) with low-carbon cementitious materials, such as ground granulated blast-furnace slag, fly ash, silica fume, limestone powder, belite cement, and other supplementary cementitious materials, has therefore become an important strategy for developing low-carbon UHPC. The incorporation of low-carbon binders enhances sustainability but also increases the complexity of mixture proportion design. Variations in oxide composition, reaction activity, particle size distribution, and hydration products jointly affect the compressive strength of low-carbon UHPC through hydration reactions, particle packing, fiber reinforcement, and curing conditions. Although machine learning models have shown good prediction performance in concrete strength prediction, most of them remain black-box approaches and provide limited physical interpretability. Post-hoc explanation methods, such as feature importance analysis, SHAP, and LIME, can identify statistical associations, but they may generate physically unrealistic virtual mixture proportions when strict mix proportion constraints and material boundaries are ignored. To address these limitations, this study proposes an interpretable Bayesian network (BN) modelling framework for the intelligent design of low-carbon UHPC. The proposed framework integrates hydration-packing mechanism priors with data-driven structure learning, aiming to describe the conditional dependencies among mixture proportion parameters, intermediate mechanism variables, and 28 d compressive strength. By introducing physically meaningful intermediate variables, the model is expected to provide both reliable strength prediction and mechanistic interpretation for low-carbon UHPC mixture design.

Methods

A total of 491 original UHPC mixture proportion records were collected through a systematic literature review following the PRISMA guidelines. After unit standardization, variable transformation, outlier checking, and valid sample screening, 136 valid samples were retained for model construction. The target variable was the 28 d compressive strength of UHPC, denoted as Z₁. To improve the physical interpretability of the model, the original high-dimensional mixture proportion variables were transformed into a hydration-packing feature system. The material/process variables included the cementitious material reaction activity index X₀, water-to-binder ratio X₁, activator-to-binder ratio X₂, binder-to-sand ratio X₃, and steel fiber volume fraction X₄. The intermediate mechanism variables included the modified CaO/SiO₂ molar ratio Y₁, the modified SO₃/Al₂O₃ molar ratio Y₂, and the initial particle packing density Y₃. These variables were used to represent C-S-H formation potential, sulfate-aluminate reaction balance, and the initial physical compactness of the particle system, respectively. Based on the mechanism of low-carbon UHPC strength formation, a three-layer BN structure was constructed, consisting of a material and process parameter layer, an intermediate mechanism layer, and a target performance layer. Mechanism-informed constraints were introduced to prevent physically unreasonable paths, such as reverse links from compressive strength to mix design variables. Structure learning was performed using a combined strategy involving the hill-climbing, MMHC, and Tabu Search algorithms. bootstrap resampling was adopted to evaluate edge stability, and the BGe score was used as the main scoring criterion, with BIC and AIC used for sensitivity comparison. For parameter learning, maximum likelihood estimation was used for auxiliary variables, while Bayesian ridge regression was adopted for continuous compressive strength prediction. To reduce the risk of data leakage during model evaluation, all preprocessing steps, including variable transformation, standardization parameter estimation, outlier threshold determination, BN structure learning, bootstrap-based stable edge selection, and parameter learning, were embedded within the training folds of a 10-fold cross-validation procedure. The validation folds were used only for final performance evaluation.

Results and discussion

The proposed BN model achieved good prediction accuracy for the 28 d compressive strength of low-carbon UHPC. Based on 10-fold cross-validation and Bootstrap evaluation, the model obtained an average RMSE of 0.281 3, an average MAE of 0.203 1, and an average R² of 0.910 1. The predicted mean compressive strength was 162.11 MPa, with a standard deviation of 24.53 MPa and an average confidence interval width of 46.04 MPa. Compared with random forest and support vector regression models, the BN model provided comparable prediction performance while also offering explicit conditional dependency paths and uncertainty representation. Correlation analysis indicated that curing temperature, pozzolanic cementitious materials, quartz sand, and steel fiber content generally were positively correlated with compressive strength, whereas the water-to-binder ratio and cement content were weakly negatively correlated. However, Pearson correlation analysis describes only linear statistical relationships and could not reveal hierarchical conditional dependencies among variables. Therefore, BN modeling was necessary to identify indirect effects and mechanism-related pathways. The final BN structure demonstrated that the modified CaO/SiO₂ molar ratio Y₁ acted as an important upstream node associated with compressive strength. This indicates that the active oxide composition of cementitious materials plays a fundamental role in low-carbon UHPC strength formation. The modified SO₃/Al₂O₃ molar ratio Y₂ served as an important intermediate node, reflecting the role of sulfate-aluminate reaction balance in hydration product formation. The initial particle packing density Y₃ was directly related to the physical compactness of the matrix and contributed substantially to strength development. Mechanism-informed intervention sensitivity analysis further showed that Y₁, Y₂, Y₃, and their interaction contributed 28.7%, 19.2%, 35.1%, and 17.0% to compressive strength, respectively. When Y₁ and Y₂ were combined as the hydration effect, the hydration effect, packing effect, and hydration-packing interaction contributed 47.9%, 35.1%, and 17.0%, respectively. These results suggest that the strength development of low-carbon UHPC is jointly controlled by hydration reactions, particle packing, and their nonlinear coupling. Therefore, intelligent mix design should prioritize the optimization of active oxide ratios, initial particle packing density, and their compatibility with the binder-to-sand ratio, water-to-binder ratio, and steel fiber content. A preliminary independent validation using five unseen low-carbon UHPC mixtures showed that the measured 28 d compressive strengths were consistent with the BN-predicted values and fell within the 95% prediction intervals. The standard deviation of prediction bias was 6.46 MPa, and the average relative deviation was approximately 0.45%. This provides preliminary support for the applicability of the proposed framework for candidate mix screening and strength prediction. Nevertheless, because the number of validation mixtures was limited, further experimental data covering broader cementitious systems, curing regimes, and fiber contents are still needed to improve the generalizability of the model.

Conclusions

In this study, an interpretable Bayesian network modelling framework was developed for the intelligent design of low-carbon UHPC. By integrating hydration-packing mechanism priors with data-driven structure learning, the proposed model described a hierarchical probabilistic relationship among material and process parameters, intermediate mechanism variables, and 28 d compressive strength. The mechanism-constrained BN model achieved high prediction accuracy under small-sample and high-dimensional conditions, with an average R² of 0.91 based on 10-fold cross-validation. Compared with conventional black-box machine learning approaches, the proposed BN framework not only maintained competitive predictive performance but also provided interpretable conditional dependency paths and uncertainty estimation. The modified CaO/SiO₂ molar ratio, modified SO₃/Al₂O₃ molar ratio, and initial particle packing density were identified as key mechanism variables governing compressive strength. The intervention sensitivity analysis showed that hydration effects (47.9%), packing effects (35.1%), and hydration-packing interactions (17.0%) jointly controlled the strength formation of low-carbon UHPC. Independent experimental validation provided preliminary support for the applicability of the proposed framework for candidate mix screening and strength prediction. This method provides a useful probabilistic modeling tool for the interpretable and intelligent design of low-carbon UHPC.

Key words

low-carbon ultra-high-performance concrete / bayesian network / compressive strength / interpretable modeling / intelligent design

引用本文

李依芮, 曾晓辉, 曾永平, 王鑫, 梁昱, 龙广成, 谢友均. 面向低碳超高性能混凝土智能设计的可解释贝叶斯网络建模. 硅酸盐学报, 2026 , 54 (10) : 3483 -3498 . DOI: 10.14062/j.issn.0454-5648.20260317

Yirui LI, Xiaohui ZENG, Yongping ZENG, Xin WANG, Yu LIANG, Guangcheng LONG, Youjun XIE. Interpretable Bayesian Network Modeling for Intelligent Design of Low-Carbon Ultra-High-Performance Concrete[J]. Journal of the Chinese Ceramic Society, 2026 , 54 (10) : 3483 -3498 . DOI: 10.14062/j.issn.0454-5648.20260317

基金

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国家重点研发计划(2023YFB2604304-2)
伊犁师范大学高层次人才引进项目(2025RCYJ24)

参考文献

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2026年第54卷第10期

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文章信息

doi: 10.14062/j.issn.0454-5648.20260317

接收时间：2026-05-13
首发时间：2026-10-22
出版时间：2026-09-03

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文章信息

作者

出版历史

收稿日期：2026-05-13
修回日期：2026-06-15

基金

国家重点研发计划(2023YFB2604304-2)

伊犁师范大学高层次人才引进项目(2025RCYJ24)

作者信息

^1.伊犁师范大学物理科学与技术学院，新疆　伊犁　835000

^2.中南大学土木工程学院，长沙　410083

^3.海南大学热带海洋工程材料及评价全国重点实验室，海口　570228

^4.新疆凝聚态相变与微结构自治区重点实验室，新疆　伊犁　835000

^5.伊犁绿色硅基材料工程研究中心，新疆　伊犁　835000

^6.建筑材料工业技术情报研究所固废利用与低碳建材研究中心，北京　100024

^7.伊犁师范大学化学化工学院，新疆　伊犁　835000

通讯作者:

曾晓辉（1982-），男，博士，教授。

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total 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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