硅酸盐学报

基于背散射电子图像与反卷积密度网络的水泥熟料化学成分概率密度回溯估测

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吴旭 ¹ , 李苏杭 ² , 宁帅 ¹ , 王琳 ²^,³ , 李长姣 ² , 叶家元 ⁴ , 杨波 ²^,³

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): 3518-3529

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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) : 3518 -3529

基于背散射电子图像与反卷积密度网络的水泥熟料化学成分概率密度回溯估测

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吴旭¹, 李苏杭², 宁帅¹, 王琳²^,³, 李长姣², 叶家元⁴, 杨波²^,³

作者信息

^1.济南大学，山东省绿色与智能建筑材料重点实验室，济南　250022

^2.济南大学，山东省泛在智能计算重点实验室，济南　250022

^3.泉城省实验室，济南　250014

^4.中国建筑材料科学研究总院有限公司，北京　100024

通讯作者:

王琳（1983-），男，博士，教授。

作者简介:

吴旭（1995-），男，博士研究生

李苏杭（2000-），男，硕士研究生。

Retrospective Estimation of Probability Density of Cement Clinker Chemical Composition Based on BSE Images and Deconvolutional Density Network

Xu WU¹, Suhang LI², Shuai NING¹, Lin WANG²^,³, Changjiao LI², Jiayuan YE⁴, Bo YANG²^,³

Affiliations

^1.Shandong Provincial Key Laboratory of Green and Intelligent Building Materials, University of Jinan, Jinan 250022, China

^2.Shandong Key Laboratory of Ubiquitous Intelligent Computing, University of Jinan, Jinan 250022, China

^3.Quan Cheng Laboratory, Jinan 250014, China

^4.China Building Materials Academy Co., Ltd, Beijing 100024, China

Corresponding Author:

WANG Lin (1983-), male, Ph.D., Professor. E-mail: ise_wanglin@ujn.edu.cn

WU Xu (1995-), male, Doctoral candidate. E-mail: wuxvforever@foxmail.com

LI Suhang (2000-), male, Master candidate. 1541168367@qq.com

出版时间: 2026-09-02 doi: 10.14062/j.issn.0454-5648.20260349

文章导航

摘要

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水泥基材料作为道路、桥梁及房屋建筑等现代土木工程中用量最大、应用最广的建筑材料，其产品质量是决定工程结构安全性与服役寿命的关键因素。然而，在工程质量事故责任追溯中，熟料氧化物含量至关重要，其检测高度依赖未水化的原始留样，缺失后无法补测。利用水泥基材料微观结构图像反推其宏观力学性能、水灰比乃至初始组成特征已有相关研究。但是，基于微观图像的传统回归模型呈现“黑箱”特性，缺乏可量化的精度依据。本工作基于条件概率密度估计方法，提出一种基于反卷积密度网络（DDN）的模型，利用已硬化水泥浆体的背散射电子（BSE）图像，结合残差网络（ResNet）的特征提取与水灰比、龄期等养护条件编码，实现了对水泥熟料中主要氧化物（如CaO、SiO₂等）百分含量的概率密度估计。实验结果表明，该方法在精度为90%时，对测试集中5种氧化物的百分含量估测准确率可以达到90%以上，不仅能够输出各氧化物含量的最可能值，还能给出概率密度估计及对应精度。为工程质量事故追责提供了一条客观、定量且具备精度评定的熟料质量回溯检测新途径，有望推动水泥基材料质量仲裁技术范式的革新。

关键词

水泥基材料 / 背散射电子图像 / 反卷积密度网络 / 化学成分回溯检测 / 概率密度估计

Abstract

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Introduction

The chemical composition of cement clinker, particularly the percentage of key oxides, is crucial for evaluating cement quality and is vital for engineering-accident liability tracing. However, traditional methods for chemical composition analysis rely heavily on unhydrated original cement samples, which are often missing, improperly stored, or ambiguously labeled in engineering management, resulting in an insufficient basis for subsequent identification. Once cement hydrates, active minerals undergo irreversible reactions, making it challenging to invert the original clinker composition directly from the hardened paste. In contrast, backscattered electron (BSE) images of the hardened cement paste contain sufficient physical information to distinguish the original chemical compositions of different cement clinkers, thus providing a potential pathway for post-event tracing. Although deep learning methods have been explored for microstructural image mapping to infer macroscopic properties, conventional regression models are typically "black-box" point predictors that cannot quantify prediction uncertainty. The conditional probability density estimation method can not only provide the most probable predicted value, but also output the complete estimated probability-density curve along with its confidence assessment, thereby enabling quantitative characterization of prediction uncertainty. Accordingly, this study proposes a conditional probability density estimation method based on a Deconvolutional Density Network (DDN). Utilizing BSE images of hardened paste together with encoded water-to-cement (W/C) ratios and curing ages as conditional inputs, this model directly predicts the full conditional probability density of the main clinker oxide contents, providing a new objective and quantitative pathway for quality liability tracing.

Methods

Cement clinker samples from 47 different plants were used to prepare cement paste specimens with W/C ratios ranging from 0.25 to 0.70 and curing ages from 1 d to 28 d. The hydration was terminated by immersion in anhydrous ethanol, and the samples were polished for subsequent scanning. BSE images were acquired via a JSM-7610F field-emission SEM at 200× magnification and an accelerating voltage of 15 kV. For each sample, two scans were performed, and nine non-overlapping regions were captured per scan, resulting in a dataset of 844 independent BSE images. The proposed model consists of a feature extraction layer based on a residual network (ResNet) with self-supervised learning and cross-layer skip connections, a conditional encoder, and deconvolutional layers. The ResNet extracts multiscale morphological features from local textures to global patterns. The conditional encoder embeds the W/C ratio and curing-age conditions into the image features. The DDN is then employed to output the conditional probability density distributions for the percentages of eight oxides (CaO, SiO₂, Al₂O₃, Fe₂O₃, SO₃, Na₂O, MgO, and K₂O). The deconvolutional layers map the fused features to a smooth probability distribution over 256 discretized intervals. To evaluate the model, accuracy (ACC) under different confidence levels (α), mean absolute error (MAE), and mean squared error (MSE) were adopted as evaluation metrics.

Results and discussion

The estimation results of the proposed model indicate that, at a confidence level of α = 90%, the model achieves an accuracy of over 90% in estimating the percentage contents of five oxides (SiO₂, Al₂O₃, Fe₂O₃, SO₃, and Na₂O) on the test set. When the confidence level is relaxed to α = 75%, the estimation accuracy for all eight oxides exceeds 90%. This could be attributed to the DDN's capability of modeling complete probability density distributions instead of simple point estimates, effectively resolving the nonunique-solution problem stemming from the intrinsic information ambiguity of BSE imaging. In terms of MAE and MSE metrics, the model exhibits relatively higher absolute errors for components with higher contents, such as CaO. This is generally attributed to the nature of absolute error metrics, which are positively correlated with the oxide content. Conversely, low-content oxides like Na₂O show smaller estimation errors, possibly because their larger fluctuation ranges among different samples allow the model to capture clearer mapping relationships. In addition, ablation experiments further reveal that removing the W/C ratio and age inputs leads to a decrease in estimation accuracy across all confidence levels, demonstrating the effectiveness of the conditional encoder in integrating critical hydration parameters. Compared with the deterministic ResNet regression model, the proposed DDN model exhibits significantly better stability of estimation performance under higher precision requirements. This result demonstrates that the DDN model effectively mitigates the inherent uncertainty in the mapping from BSE images to chemical compositions, a limitation typical of deterministic regression models that lack reliability quantification.

Conclusions

The main conclusions of this study are summarized as follows. The proposed probability density estimation method successfully maps BSE images of hardened cement paste to the oxide contents of clinker. Experimental results demonstrate that the model achieves an accuracy of over 90% for five oxides at a confidence level of 90%. The adoption of the Deconvolutional Density Network enables the model not only to output the most probable value of each oxide content but also to provide a complete probability density curve with corresponding confidence assessment, thereby overcoming the limitation of traditional regression models that lack quantifiable reliability for quality tracing applications. Moreover, the ResNet-based feature extraction with cross-layer skip connections effectively captures multiscale features from BSE images, while the integration of W/C ratio and curing age via the conditional encoder significantly enhances the model predictive capability. This study demonstrates that the probabilistic retrospective estimation based on BSE images and DDN offers a robust and objective means to quantitatively infer the original clinker composition from hardened paste. As such, it holds promise as a transformative technique for cement-quality arbitration in engineering-accident liability investigations.

Key words

cement-based materials / backscattered electron images / deconvolutional density network / chemical composition retrospective detection / probability density estimation

引用本文

吴旭, 李苏杭, 宁帅, 王琳, 李长姣, 叶家元, 杨波. 基于背散射电子图像与反卷积密度网络的水泥熟料化学成分概率密度回溯估测. 硅酸盐学报, 2026 , 54 (10) : 3518 -3529 . DOI: 10.14062/j.issn.0454-5648.20260349

Xu WU, Suhang LI, Shuai NING, Lin WANG, Changjiao LI, Jiayuan YE, Bo YANG. Retrospective Estimation of Probability Density of Cement Clinker Chemical Composition Based on BSE Images and Deconvolutional Density Network[J]. Journal of the Chinese Ceramic Society, 2026 , 54 (10) : 3518 -3529 . DOI: 10.14062/j.issn.0454-5648.20260349

基金

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国家自然科学基金面上项目(62676171; 62072213)
全国建材行业重大科技攻关“揭榜挂帅”项目(2023JBGS11-03)
山东省自然科学基金重大基础研究项目(ZR2022ZD01)
山东省自然科学基金杰出青年基金项目(ZR2022JQ30)
山东省自然科学基金(ZR2023LZH006)

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.0454-5648.20260349

接收时间：2026-05-21
首发时间：2026-10-22
出版时间：2026-09-02

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出版历史

收稿日期：2026-05-21
修回日期：2026-06-18

基金

国家自然科学基金面上项目(62676171; 62072213)

全国建材行业重大科技攻关“揭榜挂帅”项目(2023JBGS11-03)

山东省自然科学基金重大基础研究项目(ZR2022ZD01)

山东省自然科学基金杰出青年基金项目(ZR2022JQ30)

山东省自然科学基金(ZR2023LZH006)

作者信息

^1.济南大学，山东省绿色与智能建筑材料重点实验室，济南　250022

^2.济南大学，山东省泛在智能计算重点实验室，济南　250022

^3.泉城省实验室，济南　250014

^4.中国建筑材料科学研究总院有限公司，北京　100024

通讯作者:

王琳（1983-），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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