硅酸盐学报

水工常态混凝土多目标性能概率预测及可信度评价

PDF下载

徐潇航 ¹ , 储大勇 ¹ , 田丹 ² , 杨华美 ² , 胡张莉 ¹ , 刘加平 ¹

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): 3464-3482

收起

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) : 3464 -3482

水工常态混凝土多目标性能概率预测及可信度评价

全屏

徐潇航¹, 储大勇¹, 田丹², 杨华美², 胡张莉¹, 刘加平¹

作者信息

^1.东南大学材料科学与工程学院，南京　211189

^2.中国长江三峡集团有限公司水工程材料与应用技术湖北省重点实验室，武汉　430010

通讯作者:

杨华美（1986-），女，博士，副教授。

作者简介:

徐潇航（1998-），男，博士研究生。

Probabilistic Multi-target Performance Prediction and Credibility Evaluation of Hydraulic Normal Concrete

Xiaohang XU¹, Dayong CHU¹, Dan TIAN², Huamei YANG², Zhangli HU¹, Jiaping LIU¹

Affiliations

^1.School of Materials Science and Engineering, Southeast University, Nanjing 211189, China

^2.Hubei Key Laboratory of Water Engineering Materials and Application Technology China Three Gorges Corporation, Wuhan 430010, China

Corresponding Author:

YANG Huamei (1986-), female, Ph.D., Associate Professor. E-mail: yang_huamei@ctg.com.cn

XU Xiaohang (1998-), male, Doctoral candidate. E-mail: seumaturity@163.com

出版时间: 2026-09-03 doi: 10.14062/j.issn.0454-5648.20260333

文章导航

摘要

收起

水工工程常态混凝土配合比设计需同时满足施工工作性、早龄期强度发展、标准龄期强度达标和体积稳定性等要求，现有预测方法主要以绝对数值预测，难以面向材料非均质性、施工扰动和试验误差引起的各类性能波动。本工作构建了包含457组样本的水工常态混凝土多目标性能数据库，以水泥、粉煤灰、骨料等原材料信息及配合比等45维变量为输入，以坍落度、7 d抗压强度、28 d抗压强度和28 d干燥收缩为输出目标；提出分层多任务异方差概率神经网络模型（HMT-HPNN），该模型通过共享表征、层级任务表征、任务特异分支和异方差概率子网络，实现多目标均值预测与样本相关不确定性估计。结果表明，HMT-HPNN的点预测精度与经典神经网络模型处于同一较优水平，各模型在4个预测目标上的平均NRMSE均小于0.078，具备可靠的基础回归能力；与基于蒙特卡洛Dropout的多层感知机（MLP+MC Dropout）相比，HMT-HPNN表现出更优的不确定性表征能力，各目标平均90%预测区间覆盖率（PICP90）与90%名义置信水平更为接近，总体覆盖率达90.49%；4个目标的负对数似然（NLL）均更低，降低幅度均超过40%；同时，HMT-HPNN在测试集中综合预测误差随综合预测不确定性等级升高而递增，模型输出的不确定性具有误差风险指示能力；针对46组同源工程验证数据，HMT-HPNN对4个目标的R²分别为0.70、0.94、0.90和0.87，平均NLL优于测试集结果，且不确定性等级与预测误差间具有一致性。本工作可为水工常态混凝土性能预判、配合比设计和性能风险感知提供数据驱动支撑。

关键词

概率神经网络 / 多目标预测 / 水工常态混凝土 / 不确定性 / 可信度

Abstract

收起

Introduction

Hydraulic normal concrete is required to satisfy multiple performance demands during mixture proportioning, construction, and long-term service. Its fresh-state workability affects transportation, placement, and vibration; early-age compressive strength governs construction sequence and early load-bearing capacity; standard-age compressive strength is directly related to strength grade assessment; and drying shrinkage reflects dimensional stability of hardened concrete. In engineering practice, these properties are not controlled only by deterministic target values, but are usually associated with allowable fluctuations, quality assurance requirements, and strength guarantee rates. Owing to the multiphase and heterogeneous nature of concrete, the measured properties may still fluctuate even under similar mixture proportions, raw material conditions, and curing conditions. Therefore, deterministic point prediction is insufficient for describing the reliability of performance predictions.

Machine learning has provided an effective data-driven approach for modeling the nonlinear relationship between mixture composition and concrete properties. Previous studies have demonstrated its applicability in predicting compressive strength, slump, shrinkage, durability-related indicators, and other engineering properties of cement-based materials. Multi-output and multitask learning methods further enable simultaneous prediction of multiple performance indicators by exploiting shared information among related objectives. However, most existing models for concrete performance prediction still focus mainly on deterministic outputs, while uncertainty quantification, prediction interval construction, and credibility evaluation remain insufficiently explored, especially for hydraulic normal concrete. To address this issue, this study developed a hierarchical multi-task heteroscedastic probabilistic neural network (HMT-HPNN) for probabilistic multitarget performance prediction and credibility evaluation of hydraulic normal concrete.

Methods

A multitarget performance database of hydraulic normal concrete was established. The database contained 457 samples, with 45 raw input variables related to cement, fly ash, aggregates, and mixture proportions. Four output targets were selected, including slump, 7 d compressive strength, 28 d compressive strength, and 28 d drying shrinkage. The development database was divided into a training set and a test set at an 8:2 ratio, corresponding to 365 and 92 samples, respectively. In addition, 46 homologous engineering samples were used as an engineering validation set to evaluate the generalization ability of the proposed model in an engineering scenario.

Four neural network models were constructed and compared, including Single-target MLP, Multi-output MLP, MLP + MC Dropout, and HMT-HPNN. The Single-target MLP was used as an independent deterministic modeling baseline, while the Multi-output MLP was adopted as a conventional deterministic multi-output baseline. The MLP + MC Dropout was selected as a classical probabilistic neural-network baseline, in which multiple stochastic forward passes were used to estimate predictive uncertainty. The proposed HMT-HPNN consisted of a shared representation module, a hierarchical task representation module, task-specific branches, and heteroscedastic probabilistic subnetworks. For each target, the model simultaneously output the predictive mean and log-variance, and was trained using a heteroscedastic Gaussian negative log-likelihood (NLL) loss.

To ensure a fair comparison, all models were optimized using the same data partition and preprocessing strategy. The training set was further divided using fixed five-fold stratified cross-validation based on the quantiles of 28 d compressive strength. Randomized grid search was adopted for hyperparameter optimization. Deterministic models were mainly selected according to the five-fold average NRMSE, while probabilistic models were selected by jointly considering prediction accuracy and negative log-likelihood. The final models were retrained on the complete training set and evaluated on the test set. The evaluation metrics included R², MAE, NRMSE, PICP90, NLL, calibration curves, 90% prediction intervals, composite uncertainty, composite error, and credibility classification.

Results and discussion

The target distribution and correlation analysis showed that the four properties had different statistical characteristics and material-control mechanisms. The 7 d and 28 d compressive strengths exhibited a strong positive correlation, reflecting the continuity of strength development. In contrast, slump and 28 d drying shrinkage showed weak linear correlations with strength targets, indicating that workability and dimensional stability should be treated as independent prediction targets rather than being inferred from compressive strength alone. For prediction accuracy, the Single-target MLP achieved the lowest average test NRMSE among the four models. However, the overall accuracy differences among Single-target MLP, Multi-output MLP, MLP + MC Dropout, and HMT-HPNN were relatively small. HMT-HPNN retained reliable regression capability after introducing probabilistic outputs. On the test set, its R² values for 7 d compressive strength, 28 d compressive strength, and 28 d drying shrinkage were approximately 0.875, 0.868, and 0.872, respectively. Slump showed relatively lower prediction accuracy, which was associated with its higher sensitivity to aggregate moisture content, water demand, admixture dispersion, and construction-related disturbances.

For uncertainty quantification, HMT-HPNN outperformed MLP+MC Dropout. The PICP90 values of HMT-HPNN for slump, 7 d compressive strength, 28 d compressive strength, and 28 d drying shrinkage were 86.96%, 90.22%, 91.30%, and 93.48%, respectively, which were closer to the nominal confidence level of 90%. In addition, HMT-HPNN achieved lower NLL values for all four targets, indicating a more appropriate balance between prediction error and predicted variance. The calibration curves also showed that HMT-HPNN generally provided better agreement between nominal confidence levels and empirical coverage rates. The 90% prediction intervals generated by HMT-HPNN achieved an overall coverage rate of 90.49% on the test set, demonstrating that the heteroscedastic uncertainty output could be effectively transformed into reliable prediction intervals. To evaluate the risk-indication ability of model uncertainty, composite uncertainty was calculated from the normalized predictive standard deviations of the four targets, while composite error was calculated from the normalized absolute prediction errors. The testing results showed that composite error increased with the composite uncertainty level, confirming that the uncertainty output of HMT-HPNN was informative in identifying sample-level prediction risk.

For the homologous engineering validation set, HMT-HPNN maintained satisfactory generalization performance. The R² values for slump, 7 d compressive strength, 28 d compressive strength, and 28 d drying shrinkage were 0.70, 0.94, 0.90, and 0.87, respectively. The PICP90 values for all four targets reached or exceeded 90%, and an effective correspondence was observed between the level of uncertainty and the prediction error. These results indicate that HMT-HPNN maintained its accuracy, uncertainty quantification capability, and credibility evaluation ability under homologous engineering conditions.

Conclusions

A probabilistic multitarget prediction framework was developed for hydraulic normal concrete. The proposed HMT-HPNN simultaneously predicted slump, 7 d compressive strength, 28 d compressive strength, and 28 d drying shrinkage by integrating shared representation, hierarchical task representation, task-specific branches, and heteroscedastic probabilistic subnetworks. Although the point prediction accuracy of HMT-HPNN was not the highest among all compared models, its testing accuracy was comparable to that of conventional neural network models, confirming its reliable regression capability. Compared with MLP + MC Dropout, HMT-HPNN provided superior uncertainty quantification, with PICP90 values closer to the nominal 90% confidence level and lower NLL values for all four targets. The overall coverage rate of the 90% prediction intervals reached 90.49%, indicating that the model uncertainty could be effectively converted into reliable prediction intervals. The composite uncertainty was consistent with the composite prediction error, which confirmed the ability of HMT-HPNN to identify sample-level prediction risks. Independent homologous engineering validation further demonstrated the generalization capability of HMT-HPNN. The model maintained satisfactory accuracy, reliable prediction interval coverage, and effective credibility classification on 46 engineering validation samples. Therefore, the proposed framework provides a data-driven method for multitarget performance prediction, prediction interval construction, and credibility evaluation of hydraulic normal concrete, and can support mixture proportion design and performance risk assessment.

Key words

probabilistic neural network / multitarget prediction / hydraulic normal concrete / uncertainty / credibility

引用本文

徐潇航, 储大勇, 田丹, 杨华美, 胡张莉, 刘加平. 水工常态混凝土多目标性能概率预测及可信度评价. 硅酸盐学报, 2026 , 54 (10) : 3464 -3482 . DOI: 10.14062/j.issn.0454-5648.20260333

Xiaohang XU, Dayong CHU, Dan TIAN, Huamei YANG, Zhangli HU, Jiaping LIU. Probabilistic Multi-target Performance Prediction and Credibility Evaluation of Hydraulic Normal Concrete[J]. Journal of the Chinese Ceramic Society, 2026 , 54 (10) : 3464 -3482 . DOI: 10.14062/j.issn.0454-5648.20260333

基金

收起

中国长江三峡集团有限公司科研项目(202203397)
湖北省科技创新人才计划项目(2024DJA036)
江苏省研究生科研与实践创新计划项目(KYCX24_0384)

参考文献

收起

文献

收起

参考文献引证文献

排序方式：

[1]

国家能源局. DL/T 5330-2015 水工混凝土配合比设计规程[S]. 北京: 中国电力出版社, 2015.

[2]

中华人民共和国水利部. SL 677-2014 水工混凝土施工规范[S]. 北京: 中国水利水电出版社, 2015.

[3]

中华人民共和国水利部. SL/T 352-2020 水工混凝土试验规程[S]. 北京: 中国水利水电出版社, 2021.

[4]

MEHTA P K, MONTEIRO P J M. Concrete: Microstructure, Properties, and Materials[M]. 4th ed. New York: McGraw-Hill, 2014.

[5]

KOSMATKA S H, WILSON M L. Design and Control of Concrete Mixtures[M]. 15th ed. Skokie: Portland Cement Association, 2011.

[6]

NAYAK D K, ABHILASH P P, SINGH R, et al. Fly ash for sustainable construction: A review of fly ash concrete and its beneficial use case studies[J]. Clean Mater, 2022, 6: 100143.

[7]

TERMKHAJORNKIT P, NAWA T, NAKAI M, et al. Effect of fly ash on autogenous shrinkage[J]. Cem Concr Res, 2005, 35(3): 473-482.

[8]

LI Z Z, YOON J, ZHANG R, et al. Machine learning in concrete science: Applications, challenges, and best practices[J]. npj Comput Mater, 2022, 8: 127.

[9]

刘晓, 王思迈, 卢磊, 等. 机器学习预测混凝土材料耐久性的研究进展[J]. 硅酸盐学报, 2023, 51(8): 2062-2073.

LIU Xiao, WANG Simai, LU Lei, et al. J Chin Ceram Soc, 2023, 51(8): 2062-2073.

[10]

龙武剑, 罗盛禹, 程博远, 等. 机器学习算法用于自密实混凝土性能设计的研究进展[J]. 材料导报, 2024, 38(11): 104-113.

LONG Wujian, LUO Shengyu, CHENG Boyuan, et al. Mater Rep, 2024, 38(11): 104-113.

[11]

YOUNG B A, HALL A, PILON L, et al. Can the compressive strength of concrete be estimated from knowledge of the mixture proportions: New insights from statistical analysis and machine learning methods[J]. Cem Concr Res, 2019, 115: 379-388.

[12]

DONG Y H, TANG J H, XU X H, et al. A new method to evaluate features importance in machine-learning based prediction of concrete compressive strength[J]. J Build Eng, 2025, 102: 111874.

[13]

ZHANG M X, LI M C, SHEN Y, et al. Multiple mechanical properties prediction of hydraulic concrete in the form of combined damming by experimental data mining[J]. Constr Build Mater, 2019, 207: 661-671.

[14]

ÖZTAŞ A, PALA M, ÖZBAY E, et al. Predicting the compressive strength and slump of high strength concrete using neural network[J]. Constr Build Mater, 2006, 20(9): 769-775.

[15]

BAL L, BUYLE-BODIN F. Artificial neural network for predicting drying shrinkage of concrete[J]. Constr Build Mater, 2013, 38: 248-254.

[16]

HILLOULIN B, UMUNNAKWE R. Machine learning-aided prediction of shrinkage in modern concrete: Focus on mix proportions and SCMs[J]. J Build Eng, 2024, 98: 111410.

[17]

徐潇航, 胡张莉, 刘加平, 等. 基于机器学习回归模型的三峡大坝混凝土强度预测[J]. 材料导报, 2023, 37(2): 41-49.

XU Xiaohang, HU Zhangli, LIU Jiaping, et al. Mater Rep, 2023, 37(2): 41-49.

[18]

TAFFESE W Z, ESPINOSA-LEAL L. Multitarget regression models for predicting compressive strength and chloride resistance of concrete[J]. J Build Eng, 2023, 72: 106523.

[19]

王琰帅, 万承鹏, 董必钦, 等. 基于混合反向传播神经网络的双输出预测模型构建[J]. 硅酸盐学报, 2026, 54(3): 894-908.

WANG Yanshuai, WAN Chengpeng, DONG Biqin, et al. J Chin Ceram Soc, 2026, 54(3): 894-908.

[20]

BORCHANI H, VARANDO G, BIELZA C, et al. A survey on multi-output regression[J]. WIREs Data Min & Knowl, 2015, 5(5): 216-233.

[21]

CARUANA R. Multitask learning[J]. Mach Learn, 1997, 28(1): 41-75.

[22]

RUDER S. An overview of multi-task learning in deep neural networks[EB/OL]. (2017-06-15) [2026-07-29]. https://arxiv.org/abs/1706.05098.

[23]

ZHANG Y, YANG Q. A survey on multi-task learning[J]. IEEE Trans Knowl Data Eng, 2022, 34(12): 5586-5609.

[24]

GAL Y, GHAHRAMANI Z. Dropout as a Bayesian approximation: Representing model uncertainty in deep learning[C]//Proceedings of the 33rd International Conference on Machine Learning. 2016: 1050-1059.

[25]

SRIVASTAVA N, HINTON G E, KRIZHEVSKY A, et al. Dropout: A simple way to prevent neural networks from overfitting[J]. J Mach Learn Res, 2014, 15(1): 1929-1958.

[26]

KENDALL A, GAL Y. What uncertainties do we need in Bayesian deep learning for computer vision?[C]//ADV NEURAL INF PROCESS SYST. 2017, 30: 5574-5584.

[27]

LAKSHMINARAYANAN B, PRITZEL A, BLUNDELL C. Simple and scalable predictive uncertainty estimation using deep ensembles[C]//ADV NEURAL INF PROCESS SYST. 2017, 30: 6402-6413.

[28]

GUO C, PLEISS G, SUN Y, WEINBERGER K Q. On calibration of modern neural networks[C]//PROC 34TH INT CONF MACH LEARN. 2017, 70: 1321-1330.

[29]

TAMULY P, NAVA V. Machine learning based conformal predictors for uncertainty-aware compressive strength estimation of concrete[J]. Constr Build Mater, 2025, 487: 141844.

[30]

HAN B, WU Y Q, LIU L L. Prediction and uncertainty quantification of compressive strength of high-strength concrete using optimized machine learning algorithms[J]. Struct Concr, 2022, 23(6): 3772-3785.

[31]

HASTIE T, TIBSHIRANI R, FRIEDMAN J. The elements of statistical learning: Data mining, inference, and prediction[M]. 2nd ed. New York: Springer, 2009.

[32]

BISHOP C M. Probability Distributions[M]//Pattern Recognition and Machine Learning. New York: Springer, 2006: 68-126.

[33]

GOODFELLOW I, BENGIO Y, COURVILLE A. Deep Learning[M]. Cambridge, Mass.: MIT Press, 2016.

[34]

KOHAVI R. A study of cross-validation and bootstrap for accuracy estimation and model selection[C]//PROC 14TH INT JOINT CONF ARTIF INTELL. 1995: 1137-1145.

[35]

BERGSTRA J, BENGIO Y. Random search for hyper-parameter optimization[J]. J Mach Learn Res, 2012, 13: 281-305.

[36]

MURPHY K P. Probabilistic Machine Learning: An Introduction[M]. Cambridge: MIT Press, 2022.

[37]

GNEITING T, RAFTERY A E. Strictly proper scoring rules, prediction, and estimation[J]. J Am Stat Assoc, 2007, 102(477): 359-378.

2026年第54卷第10期

PDF下载

引用本文

BibTeX

文章信息

doi: 10.14062/j.issn.0454-5648.20260333

接收时间：2026-05-15
首发时间：2026-10-22
出版时间：2026-09-03

补充材料

相关文章

文章信息

作者

出版历史

收稿日期：2026-05-15
修回日期：2026-07-04

基金

中国长江三峡集团有限公司科研项目(202203397)

湖北省科技创新人才计划项目(2024DJA036)

江苏省研究生科研与实践创新计划项目(KYCX24_0384)

作者信息

^1.东南大学材料科学与工程学院，南京　211189

^2.中国长江三峡集团有限公司水工程材料与应用技术湖北省重点实验室，武汉　430010

通讯作者:

杨华美（1986-），女，博士，副教授。

参考文献

分享链接

https://castjournals.cast.org.cn/joweb/gsyxb/CN/10.14062/j.issn.0454-5648.20260333

分享至

全文二维码

扫描看全文

引用本文

BibTeX

本文的引用情况

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

关闭全屏

BibTeX
EndNote
RefWorks
TxT