硅酸盐学报

基于融合机器学习方法的机制砂混凝土徐变显式建模

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梅生启 ¹^,² , 武腾 ¹^,³ , 王兴举 ² , 程相旭 ³ , 刘哲 ³ , 李星艳 ³ , 李雪峰 ³

硅酸盐学报 | 研究论文 2025,53(11): 3101-3113

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硅酸盐学报 |研究论文 2025 , 53 (11) : 3101 -3113

基于融合机器学习方法的机制砂混凝土徐变显式建模

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梅生启¹^,², 武腾¹^,³, 王兴举², 程相旭³, 刘哲³, 李星艳³, 李雪峰³

作者信息

^1．省部共建交通工程结构力学行为与系统安全国家重点实验室，石家庄 050043

^2．石家庄铁道大学交通运输学院，石家庄 050043

^3．石家庄铁道大学土木工程学院，石家庄 050043

作者简介:

梅生启（1990—），男，博士，副教授。

Explicit Modeling of Creep in Manufactured Sand Concrete Based on Integrated Machine Learning Approaches

Shengqi MEI¹^,², Teng WU¹^,³, Xingju WANG², Xiangxu CHENG³, Zhe LIU³, Xingyan LI³, Xuefeng LI³

Affiliations

^1.State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang 050043, China

^2.School of Traffic and Transportation, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

^3.School of Civil Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

MEI Shengqi (1990-), male, Ph.D., Associate Professor. E-mail: cshqmei@stdu.edu.cn

出版时间: 2025-11-20 doi: 10.14062/j.issn.0454-5648.20250431

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摘要

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针对既有混凝土徐变模型在多源机制砂混凝土徐变数据的适用性不足问题，提出了一种融合机器学习的机制砂混凝土徐变显式建模方法，用以提升模型精度和增强结构可解释性。首先，收集了81组机制砂混凝土徐变试验数据，评估了现有模型（MC2010、ACI209、B3、B4、GL2000）和机制砂混凝土修正模型的适用性，发现决定系数（R²）最大仅为0.57，存在明显低估或高估机制砂混凝土徐变行为。然后，采用Feature Tokenizer Transformer、PINNs、TabNet与XGBoost机器学习算法进行机制砂混凝土徐变预测，测试集R²最高可达0.98，验证了机器学习模型在机制砂混凝土徐变预测方面的优势。最后，基于特征分析，采用自动特征工程与筛选（AutoFeat）与神经符号回归（NSR）进行显式模型构建。AutoFeat通过XGBoost-SHAP与皮尔逊相关系数进行特征筛选，分别构建了一阶、二阶和三阶模型，R²最高达到0.96；NSR则基于函数符号组合自动挖掘变量间的非线性关系，最终构建的表达式模型在测试集上取得R² = 0.86，具有良好的结构透明性与物理合理性。两种建模计算结果显示，石粉掺量、水胶比、加载龄期、持荷时间与抗压强度是机制砂混凝土徐变的主要影响因素。本工作所提出方法在特征简化的同时保持了模型精度，为机制砂混凝土徐变预测提供了一种兼具准确性与解释性的建模思路。

关键词

机制砂混凝土 / 徐变预测 / 融合机器学习 / 显式建模

Abstract

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Introduction

With the continuous development of infrastructure in China, the demand for concrete has increased significantly. As a critical raw material in concrete production, sand has also seen a sustained rise in consumption. It is estimated that global annual sand usage ranges between 40 and 50 billion tons. Due to the non-renewable and non-recyclable nature of river sand, its excessive extraction has led to the rapid depletion of existing reserves. To enhance resource efficiency, the construction industry has gradually implemented a variety of mitigation strategies, such as incorporating recycled coarse aggregates into concrete and employing manufactured sand as a substitute for river sand. The use of manufactured sand not only alleviates the environmental degradation caused by overexploitation of river sand but also offers a practical solution to the growing scarcity of this natural resource. Manufactured sand is produced by mechanically crushing and screening rock particles. Compared with river sand, it is characterized by a rougher surface texture and a higher content of stone powder, which can significantly influence the long-term mechanical performance of concrete. Creep, defined as the time-dependent deformation of concrete under sustained loading, plays a crucial role in determining the structural stability and durability. However, existing creep models for concrete have proven inadequate in accurately predicting the creep behavior of manufactured sand concrete. In recent years, machine learning techniques have been increasingly applied to the prediction of creep behavior in recycled aggregate concrete, ultra-high-performance concrete, and concrete incorporating mineral admixtures, demonstrating excellent fitting accuracy and generalization capabilities. Compared with traditional predictive models, machine learning approaches are better suited to handling complex issues such as multi-factor coupling and nonlinear relationships. However, their limitations are also notable: these models often function as "black boxes," lacking physical interpretability, and are highly dependent on the quality and quantity of input data, making it difficult to uncover the underlying physical mechanisms of creep. To address these challenges, some researchers have introduced explainable algorithms to improve model transparency and robustness Simultaneously, other studies have explored explicit modeling techniques to directly generate predictive formulas. Nonetheless, the resulting expressions are often overly complex and lengthy, limiting their applicability in practical engineering scenarios.

Methods

To tackle these challenges, a novel modeling framework that integrates both implicit and explicit techniques is proposed. First, a dataset of manufactured sand concrete creep was constructed. Advanced implicit machine learning models, including the Feature Token Transformer, Physics-Informed Neural Networks (PINNs), TabNet, and XGBoost, were employed to predict the creep behavior of manufactured sand concrete. Feature importance analysis was subsequently conducted based on model outputs to identify the most influential variables. Next, AutoFeat was used to automatically generate and select polynomial features from the identified key variables, thereby constructing a high-order explicit model capable of achieving accurate creep prediction. Furthermore, neural symbolic regression (NSR) was introduced to automatically discover nonlinear relationships among variables through symbolic function composition, yielding concise, physically meaningful analytical expressions.

Results and discussion

Existing concrete creep prediction models, when applied to manufactured sand concrete, exhibit substantial errors due to their inability to effectively capture the material-specific characteristics and time-dependent behavior. This highlights an urgent need for the development of more targeted and robust predictive models.

The constructed implicit machine learning models—TabNet, FT-Transformer, PINNs, and XGBoost—demonstrated excellent predictive performance. These models effectively capture the complex and nonlinear relationships between the creep behavior of manufactured sand concrete and various influencing factors.

Explicit prediction models for concrete creep compliance were developed based on two approaches: AutoFeat and Neural Symbolic Regression (NSR). Both methods successfully generated functional expressions that map input parameters to the target output, thereby enhancing model interpretability. The AutoFeat-based model combined SHAP-based feature importance analysis with Pearson correlation analysis during feature selection, ultimately yielding an interpretable model primarily composed of first-order linear terms, complemented by selected second- and third-order interaction terms. In contrast, the NSR method exhibited a superior capacity for capturing nonlinear dependencies. It automatically identified key variables and constructed complex mathematical formulations characterized by nested structures and nonlinear operator combinations, providing deeper insight into the underlying mechanisms governing creep development.

Conclusions

Under comparable levels of predictive accuracy, both AutoFeat and Neural Symbolic Regression are capable of generating explicit expressions with clear mathematical structures, significantly enhancing model interpretability. Despite differences in feature selection strategies and model architectures between implicit and explicit modeling approaches, both demonstrate strong fitting performance with respect to real-world data, thereby validating the feasibility of modeling concrete creep through multiple methodological pathways. The integrated application of both approaches facilitates an optimized balance between predictive accuracy and interpretability.

Key words

manufactured sand concrete / creep prediction / fusion machine learning / explicit modelling

引用本文

梅生启, 武腾, 王兴举, 程相旭, 刘哲, 李星艳, 李雪峰. 基于融合机器学习方法的机制砂混凝土徐变显式建模. 硅酸盐学报, 2025 , 53 (11) : 3101 -3113 . DOI: 10.14062/j.issn.0454-5648.20250431

Shengqi MEI, Teng WU, Xingju WANG, Xiangxu CHENG, Zhe LIU, Xingyan LI, Xuefeng LI. Explicit Modeling of Creep in Manufactured Sand Concrete Based on Integrated Machine Learning Approaches[J]. Journal of the Chinese Ceramic Society, 2025 , 53 (11) : 3101 -3113 . DOI: 10.14062/j.issn.0454-5648.20250431

基金

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国家自然科学基金项目(52108161)
河北省燕赵黄金台聚才计划骨干人才项目(HJYB202521)
河北省高等学校科学研究项目青年拔尖人才项目(BJK2024127)

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2025年第53卷第11期

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文章信息

doi: 10.14062/j.issn.0454-5648.20250431

接收时间：2025-06-03
首发时间：2026-10-21
出版时间：2025-11-20

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出版历史

收稿日期：2025-06-03
修回日期：2025-06-30

基金

国家自然科学基金项目(52108161)

河北省燕赵黄金台聚才计划骨干人才项目(HJYB202521)

河北省高等学校科学研究项目青年拔尖人才项目(BJK2024127)

作者信息

^1．省部共建交通工程结构力学行为与系统安全国家重点实验室，石家庄 050043

^2．石家庄铁道大学交通运输学院，石家庄 050043

^3．石家庄铁道大学土木工程学院，石家庄 050043

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https://castjournals.cast.org.cn/joweb/gsyxb/CN/10.14062/j.issn.0454-5648.20250431

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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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