硅酸盐学报

多元矿物材料对水泥性能影响的数学模型及多目标优化方法

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郑伟鹏 ¹^,² , 黄建国 ³ , 宋奔 ¹^,² , 屠金昌 ³ , 盛月强 ³ , 杨明秋 ³ , 杨露 ¹ , 王发洲 ¹^,² , 胡传林 ¹

硅酸盐学报 | 研究论文 2024,52(9): 3036-3046

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硅酸盐学报 |研究论文 2024 , 52 (9) : 3036 -3046

多元矿物材料对水泥性能影响的数学模型及多目标优化方法

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郑伟鹏¹^,², 黄建国³, 宋奔¹^,², 屠金昌³, 盛月强³, 杨明秋³, 杨露¹, 王发洲¹^,², 胡传林¹

作者信息

^1．武汉理工大学硅酸盐建筑材料国家重点实验室，武汉 430070

^2．武汉理工大学材料科学与工程学院，武汉 430070

^3．浙江新都水泥有限公司，浙江嘉兴 314511

通讯作者:

杨露（1985—），男，博士，研究员。

作者简介:

郑伟鹏（1999—），男，硕士研究生。

Mathematical Model and Multi-Objective Optimization of the Influence of Multiple Mineral Materials on Cement Properties

Weipeng ZHENG¹^,², Jianguo HUANG³, Ben SONG¹^,², Jinchang TU³, Yueqiang SHENG³, Mingqiu YANG³, Lu YANG¹, Fazhou WANG¹^,², Chuanlin HU¹

Affiliations

^1.State Key Laboratory of Silicate Materials for Architectures, Wuhan University of Technology, Wuhan 430070, China

^2.School of Materials Science and Engineering, Wuhan University of Technology, Wuhan 430070, China

^3.Zhejiang Xindu Cement Co., Ltd., Jiaxing 314511, Zhejiang, China

Corresponding Author:

YANG Lu (1985-), male, Ph.D., Professor. E-mail: yanglu@whut.edu.cn

ZHENG Weipeng (1999-), male, Master candidate. E-mail: 1848357180@qq.com

出版时间: 2024-09-20 doi: 10.14062/j.issn.0454-5648.20230811

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摘要

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随着“碳中和”、“碳达峰”战略的持续推进，降低水泥生产的碳排放刻不容缓。采用响应面法研究了水泥与多元矿物材料的复合效应。首先，采用四因素三水平Box-Behnken设计来讨论粉煤灰、石灰石粉、凝灰岩粉和矿粉这4个自变量对水泥力学性能和水化性能的影响并构建了数学模型。方差分析结果表明，多元矿物材料对水泥的力学性能具有显著影响。然后，在响应面模型的基础上进行可靠性分析和基于非支配排序遗传算法（NSGA-Ⅱ）的多目标优化。最后，得到可靠性不低于6Sigma（99.9997%）的最佳优化结果，即当粉煤灰掺量为2.72%（质量分数），石灰石粉掺量为7.14%（质量分数），凝灰岩粉掺量为9.95%（质量分数），矿粉掺量为19.93%（质量分数）时，多元矿物材料体系的性能将在综合考虑力学性能、水化性能和节能减排的前提下达到最优。证实了组合设计（响应面设计和基于NSGA-Ⅱ的多目标优化）在多元矿物材料体系的鲁棒性和可行性，获得了更加可靠和精度更高的多目标优化方法，对水泥基材料的实际生产具有极高的实际意义和参考价值。

关键词

多元矿物材料 / 多目标优化 / 响应面 / 非支配排序遗传算法

Abstract

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Introduction

With the continuous promotion of the "carbon neutrality" and "carbon peak" strategies, reducing carbon emissions from cement production is urgent. Replacing cement with a combination of one or multiple mineral materials can not only improve the physical properties of cement products, but also reduce the use of cement clinker, thereby reducing carbon emissions in cement production and saving resources. However, due to the complex properties and multiple interrelated properties of cement matrix composites, the optimization design of these materials in cement matrix composites faces challenges. Therefore, it is necessary to find more efficient and accurate methods for optimizing the design of cement matrix composites.

Methods

Response surface experiments were conducted by using Shangfeng cement clinker that meets the Chinese national standard GB 21372-2008, standard sand that meets the European standard EN 196-1∶2005, multiple mineral materials (grade II fly ash, S95 mineral powder, limestone powder, and tuff powder), and external gypsum (natural gypsum, desulfurization gypsum). The response surface experiment was conducted using Design Expert 13.0 software for Box Behnken response surface design. The response surface design consists of four factors and three levels. Four factors were selected: fly ash content (A), limestone powder content(B), tuff powder content(C), and slag content(D). The response values were cement 3 d compressive strength, 28 d compressive strength, and the cumulative hydration heat release of cement within 3 d, and 29 experimental points were designed.

Firstly, use Monte Carlo sampling method to analyze the reliability of each response quantity. Select process factors as noise, randomly select 8 000 samples points to analyze the contribution of each random input variable to the response, and confirm its distribution characteristics including mean value, standard deviation, and Sigma level. Next, Further construct optimization objectives that meet the minimum 3 d compressive strength value (Y₁), maximum 28 d compressive strength value (Y₂), and minimum the cumulative hydration heat release value of cement within 3 d (Y₃), as well as the maximum content of multiple mineral materials (Y₄). The deterministic constraint range for Y₁ is 17.0-27.0 MPa, and the deterministic constraint range for Y₂ is 42.5-52.5 MPa. Y₃ is set to be no higher than the mean value of reliability analysis and not lower than 170.0 J/g; Y₄ is set to not less than 30% of the total material quantity. And the reliability of each performance response and design variable should be not less than 6-Sigma. A multi-objective optimization design for multi mineral materials, based on the mathematical model obtained from response surface experiments and the multi-objective optimization design of multivariate mineral materials, the non-dominated sorting genetic algorithm (NSGA-II) is used for multi-objective optimization. When optimizing, set the initial population size of NSGA-II to 200, genetic algebra to 20, cross distribution index to 10, and mutation operator to 20.

Results and discussion

Based on the response surface experimental matrix, the experimental results were obtained. After removing the insignificant items (p-value>0.05) from the response surface experimental results, the mathematical model was obtained as follows:

Y₁=12.148+0.748A+0.690B-0.392C+2.089D-0.078A×D-0.066B²-0.065D²

Y₂=49.595-1.179A+0.893B+0.654C+0.381D+0.042A×C+0.073B×C-0.048C×D+0.048A²-0.155B²-0.094C²

Y₃=368.801-12.309A+0.369B-12.273C-7.958D-0.192A×B+0.258A×C+0.757A×D+0.569C×D

A 6-Sigma reliability analysis was conducted on the response surface mathematical model, and the sigma level values for Y₁ and Y₂ were 1.144 and 1.497, respectively, with reliability values of 74.76% and 86.55%, both lower than 90%. However, the sigma level value for Y₃ was 3.953, with reliability values of 93.83%. After multi-objective optimization of the mathematical model, the obtained Pareto solutions were sorted to get the optimal process parameters: A of 2.72%, B of 7.14%, C of 9.95%, and D of 19.93%. The optimized Y₁ of cement is 23.43 MPa, and the Y₂ is 46.82 MPa, the Y₃ is 214.36 J/g, and the total content of cement multi mineral materials is 39.74%. Five repeated experiments were conducted to verify the optimal process parameters, and the experimental values were close to the optimized values. The maximum relative error is 3.71%, which is within an acceptable error range (>90% confidence level).

Conclusions

According to the mathematical model obtained from the response surface, it is found that there is a good correlation between the multi mineral material system and the mechanical properties of cement. There is an excellent linear correlation between the multi mineral material system and the hydration heat of cement. Based on mathematical models, a multi-objective optimization method based on NSGA-II can be used to solve the optimal formula. In addition, by using the 6sigma robust multi-objective optimization method, the reliable multi-objective optimization results can be obtained. When the content of fly ash is 2.72%, the content of limestone powder is 7.14%, the content of tuff powder is 9.95%, and the content of slag is 19.93%, the three-dimensional compressive strength value of cement is 23.43 MPa, the 28 d compressive strength value is 46.82 MPa, and the Y₃ is 214.36 J/g. This study validated the robustness and feasibility of composite design methods (including response surface design and multi-objective optimization based on NSGA-II) in multi-component mineral systems.

Key words

multi-mineral materials / multi-objective optimization / response surface / non-dominated sorting genetic algorithm

引用本文

郑伟鹏, 黄建国, 宋奔, 屠金昌, 盛月强, 杨明秋, 杨露, 王发洲, 胡传林. 多元矿物材料对水泥性能影响的数学模型及多目标优化方法. 硅酸盐学报, 2024 , 52 (9) : 3036 -3046 . DOI: 10.14062/j.issn.0454-5648.20230811

Weipeng ZHENG, Jianguo HUANG, Ben SONG, Jinchang TU, Yueqiang SHENG, Mingqiu YANG, Lu YANG, Fazhou WANG, Chuanlin HU. Mathematical Model and Multi-Objective Optimization of the Influence of Multiple Mineral Materials on Cement Properties[J]. Journal of the Chinese Ceramic Society, 2024 , 52 (9) : 3036 -3046 . DOI: 10.14062/j.issn.0454-5648.20230811

基金

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国家自然科学基金项目(52172025)

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2024年第52卷第9期

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文章信息

doi: 10.14062/j.issn.0454-5648.20230811

接收时间：2023-10-21
首发时间：2026-10-22
出版时间：2024-09-20

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收稿日期：2023-10-21
修回日期：2023-11-10

基金

国家自然科学基金项目(52172025)

作者信息

^1．武汉理工大学硅酸盐建筑材料国家重点实验室，武汉 430070

^2．武汉理工大学材料科学与工程学院，武汉 430070

^3．浙江新都水泥有限公司，浙江嘉兴 314511

通讯作者:

杨露（1985—），男，博士，研究员。

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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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