Probabilistic structural damage identification based on hypersphere ring description

doi:10.11772/j.issn.1001-9081.2025050664

Journal of Computer Applications ›› 2026, Vol. 46 ›› Issue (6): 2016-2025.DOI: 10.11772/j.issn.1001-9081.2025050664

• Frontier and comprehensive applications • Previous Articles

Probabilistic structural damage identification based on hypersphere ring description

Maozu GUO¹^,², Qingyu ZHANG¹^,², Lingling ZHAO³(), Yang DENG⁴^,⁵

^1.School of Intelligence Science and Technology，Beijing University of Civil Engineering and Architecture，Beijing 102616，China
^2.Beijing Key Laboratory of Super Intelligent Technology for Urban Architecture （Beijing University of Civil Engineering and Architecture），Beijing 102616，China
^3.Faculty of Computing，Harbin Institute of Technology，Harbin Heilongjiang 150001，China
^4.School of Civil and Transportation Engineering，Beijing University of Civil Engineering and Architecture，Beijing 102627，China
^5.International Joint Laboratory of Safety and Energy Conservation for Ancient Buildings，Ministry of Education，（Beijing University of Civil Engineering and Architecture），Beijing 100044，China

Received:2025-06-23 Revised:2025-11-27 Accepted:2025-12-01 Online:2025-12-15 Published:2026-06-10
Contact: Lingling ZHAO
About author:GUO Maozu， born in 1966， Ph. D.， professor. His research interests include intelligent construction， smart city.
ZHANG Qingyu， born in 1995， Ph. D. candidate. His research interests include machine learning， engineering disaster prevention and reduction.
DENG Yang， born in 1984， Ph. D.， professor. His research interests include engineering disaster prevention and reduction， protection of architectural heritage.
First author contact:ZHAO Lingling， born in 1980， Ph. D.， associate professor. Her research interests include machine learning， intelligent information processing.
Supported by:
National Natural Science Foundation of China(62271036);Beijing Natural Science Foundation(4232021)

基于超球环描述的概率性结构损伤识别

郭茂祖¹^,², 张庆宇¹^,², 赵玲玲³(), 邓扬⁴^,⁵

^1.北京建筑大学智能科学与技术学院，北京 102616
^2.城市建筑超级智能技术北京重点实验室（北京建筑大学），北京 102616
^3.哈尔滨工业大学计算机学部，哈尔滨 150001
^4.北京建筑大学土木与交通工程学院，北京 102627
^5.教育部古建筑安全与节能国际合作联合实验室（北京建筑大学），北京 100044

通讯作者: 赵玲玲
作者简介:郭茂祖（1966—），男，山东夏津人，教授，博士，主要研究方向：智能建造、智慧城市
张庆宇（1995—），男，山东滨州人，博士研究生，主要研究方向：机器学习、工程防灾减灾
邓扬（1984—），男，湖南慈利人，教授，博士，主要研究方向：工程防灾减灾、建筑遗产保护。
第一联系人：赵玲玲（1980—），女，黑龙江克山人，副教授，博士，主要研究方向：机器学习、智能信息处理
基金资助:
国家自然科学基金资助项目(62271036);国家自然科学基金资助项目(52278290);北京市自然科学基金资助项目(4232021)

Abstract

Abstract:

Unsupervised thresholding methods for structural damage identification in civil engineering do not require labelled data， yet suffer from identification inaccuracies near threshold values caused by the uncertainty of data. To address the false positives and false negatives in unsupervised structural damage identification thresholding methods near threshold values， a Deep Support Vector Data Description （Deep-SVDD） based probabilistic structural damage identification method based on a hypersphere ring description， namely VAEKL-RDDP（Variational AutoEncoder with Kullback?Leibler divergence constrained for hypersphere Ring Data Description Probabilistic damage identification）， was proposed. With Variational AutoEncoder （VAE） as the framework， the method constructed a hypersphere ring using KL （Kullback-Leibler） divergence. Firstly， the VAE was pre-trained to reconstruct structural acceleration responses. Then， KL divergence was introduced to train the pre-trained VAE encoder and the hypersphere ring description method jointly， thereby extracting reliable classification boundaries from the posterior distribution of acceleration data features. Finally， a hypersphere ring was constructed on the basis of classification boundaries， structural damage was identified on the basis of the constructed hypersphere ring， and the data in the hypersphere ring were evaluated by using a cumulative probability density method. In experiments of the real Z24 bridge structure involving progressive damage and full-scale vibration table on a wooden pavilion， the results show that VAEKL-RDDP achieves the average improvement of 24.9% in accuracy and 36.7% in recall compared with the baseline AutoEncoder （AE） reconstruction based method； compared to the methods such as Deep-SVDD and Imputed Diffusion （ImDiffusion）， VAEKL-RDDP achieves the average gains of 20.8% and 33.7% in accuracy and recall， respectively， verifying that the proposed method can improve the performance of structural damage detection and reduce the missed detections.

Key words: unsupervised structural damage identification, time series reconstruction, probabilistic damage evaluation, cumulative probability density, Variational AutoEncoder (VAE)

摘要：

土木工程结构损伤识别中无监督的阈值方法无需标注数据，然而数据的不确定性导致阈值附近存在识别不准的问题。针对无监督结构损伤识别阈值方法在阈值附近存在误报和漏报的问题，基于深度支持向量数据描述（Deep-SVDD）提出基于超球环描述的概率性结构损伤识别方法VAEKL-RDDP（Variational AutoEncoder with Kullback?Leibler divergence constrained for hypersphere Ring Data Description Probabilistic damage identification）。该方法以变分自编码器（VAE）为框架，利用KL（Kullback-Leibler）散度约束构造超球环。首先，预训练VAE，以重建结构加速度响应；其次，引入KL散度，以联合训练预训练的VAE编码器与超球环描述方法，从而在加速度数据特征的后验分布中提取可靠分类边界；最后，依据分类边界构造超球环，依托所构造的超球环对结构进行损伤识别，并采用累积概率密度方法评估超球环内数据。在真实的Z24桥结构的渐进性损伤和足尺木亭振动台实验中，与基于自编码器（AE）重建的基线方法相比，VAEKL-RDDP的准确率和召回率分别平均提高了24.9%和36.7%；而相较于Deep-SVDD和扩散模型的插补预测（ImDiffusion）等方法，VAEKL-RDDP的准确率和召回率分别平均提升了20.8%和33.7%，验证了所提方法提高了损伤检测的性能，降低了漏报可能性。

关键词: 无监督结构损伤识别, 时间序列重构, 概率性损伤评估, 累积概率密度, 变分自编码器

CLC Number:

TP391.9

Maozu GUO, Qingyu ZHANG, Lingling ZHAO, Yang DENG. Probabilistic structural damage identification based on hypersphere ring description[J]. Journal of Computer Applications, 2026, 46(6): 2016-2025.

郭茂祖, 张庆宇, 赵玲玲, 邓扬. 基于超球环描述的概率性结构损伤识别[J]. 《计算机应用》唯一官方网站, 2026, 46(6): 2016-2025.

Figures/Tables 16

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分类序号	工况	序列数
0	无损伤	1 282
1	桥墩沉降20 mm	641
2	桥墩沉降40 mm	641
3	桥墩沉降80 mm	641
4	桥墩沉降95 mm	641
5	基础沉降	641
6	参考测量	641
7	混凝土剥落（12 m²）	641
8	混凝土剥落（24 m²）	641
9	滑坡	641
10	桥墩混凝土铰失效	641
11	后张拉钢筋锚固失效（1 头）	641
12	后张拉钢筋锚固失效（4 头）	641
13	预应力筋断裂（2根）	641
14	预应力筋断裂（4根）	641
15	预应力筋断裂（6根）	641

分类序号	工况	序列数
0	无损伤	1 282
1	桥墩沉降20 mm	641
2	桥墩沉降40 mm	641
3	桥墩沉降80 mm	641
4	桥墩沉降95 mm	641
5	基础沉降	641
6	参考测量	641
7	混凝土剥落（12 m²）	641
8	混凝土剥落（24 m²）	641
9	滑坡	641
10	桥墩混凝土铰失效	641
11	后张拉钢筋锚固失效（1 头）	641
12	后张拉钢筋锚固失效（4 头）	641
13	预应力筋断裂（2根）	641
14	预应力筋断裂（4根）	641
15	预应力筋断裂（6根）	641

方法	Acc	Pre	Rec	F1s	AUC
AE	87.7	100.0	87.4	93.3	96.8
ImDiffusion	95.1	97.4	97.6	97.5	65.5
GPND	87.9	100.0	87.6	93.4	99.9
PNG	97.4	97.4	100.0	98.7	98.7
USVDD	84.4	97.0	86.7	91.6	83.6
VAE-SVDD	94.9	100.0	94.8	97.3	97.4
Deep-SVDD	70.5	100.0	69.7	82.2	84.5
VAEKL-SVDD	98.1	100.0	98.1	99.0	99.0
VAEKL-RDDP	99.6	99.6	100.0	99.8	99.9

方法	Acc	Pre	Rec	F1s	AUC
AE	87.7	100.0	87.4	93.3	96.8
ImDiffusion	95.1	97.4	97.6	97.5	65.5
GPND	87.9	100.0	87.6	93.4	99.9
PNG	97.4	97.4	100.0	98.7	98.7
USVDD	84.4	97.0	86.7	91.6	83.6
VAE-SVDD	94.9	100.0	94.8	97.3	97.4
Deep-SVDD	70.5	100.0	69.7	82.2	84.5
VAEKL-SVDD	98.1	100.0	98.1	99.0	99.0
VAEKL-RDDP	99.6	99.6	100.0	99.8	99.9

方法	Acc	Pre	Rec	F1s	AUC
AE	59.0	100.0	57.9	73.3	79.0
ImDiffusion	77.1	77.1	100.0	87.1	69.0
GPND	58.9	94.5	48.4	64.0	66.0
PNG	75.5	75.5	100.0	86.0	87.7
USVDD	39.0	72.0	31.3	43.7	32.7
VAE-SVDD	68.3	90.7	64.5	75.4	74.3
Deep-SVDD	64.1	91.4	57.8	70.8	78.4
VAEKL-SVDD	74.3	86.7	77.9	82.1	80.3
VAEKL-RDDP	80.4	83.6	92.1	87.7	85.4

Probabilistic structural damage identification based on hypersphere ring description

基于超球环描述的概率性结构损伤识别

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Figures/Tables 16

References 63

Related Articles 8

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Metrics

模型	Acc	Pre	Rec	F1s	AUC
w/o VAE	72.7	81.7	82.3	82.0	78.0
w/o KL	75.5	75.5	100.0	86.0	77.3
w/o Ring	74.3	86.7	77.9	82.1	80.3
VAEKL-RDDP	80.4	83.6	92.1	87.7	85.4

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