|Table of Contents|

[1] HU Qin, GUAN Yunhao, ZHANG Biwei,. Damage detection of an asymmetrical frame based on a deep learning-based surrogate model and an improved CMAES approach [J]. Journal of Southeast University (English Edition), 2026, 42 (3): 306-317. [doi:10.3969/j.issn.1003-7985.2026.03.004]
Copy

Damage detection of an asymmetrical frame based on a deep learning-based surrogate model and an improved CMAES approach()
基于深度学习代理模型和改进CMAES方法的非对称框架损伤识别

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
42
Issue:
2026 3
Page:
306-317
Research Field:
Civil Engineering
Publishing date:
2026-09-06

Info

Title:
Damage detection of an asymmetrical frame based on a deep learning-based surrogate model and an improved CMAES approach
基于深度学习代理模型和改进CMAES方法的非对称框架损伤识别
Author(s):
HU Qin, GUAN Yunhao, ZHANG Biwei
School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
胡琴, 管运豪, 张璧玮
华中科技大学土木与水利工程学院, 武汉 430074
Keywords:
damage detection;  variational Bayesian learning;  surrogate model;  covariance matrix adaptation evolution strategy (CMAES);  deep learning
损伤识别;  变分贝叶斯学习;  代理模型;  协方差矩阵自适应进化策略;  深度学习
PACS:
TU317;O212.8
DOI:
10.3969/j.issn.1003-7985.2026.03.004
Abstract:
This study proposes a time-domain variational Bayesian framework for damage detection that integrates a deep learning-based surrogate model with an improved covariance matrix adaptation evolution strategy (CMAES) algorithm. The surrogate model comprises parallel convolutional neural networks followed by an encoder-decoder long short-term memory module with residual connections, self-attention, and a comprehensive loss function. The proposed approach can achieve accurate dynamic response prediction with a remarkable mean squared error of 0.000 12 and R2 of 0.998 00. Furthermore, an improved CMAES algorithm guided by gradient information derived from the deep-learning surrogate model is developed to accelerate local convergence. The proposed method enables the detection of the location and level of damage while quantifying the associated uncertainties, as validated by experimental case studies on an asymmetrical frame. Furthermore, it significantly enhances computational efficiency, offering a viable technical foundation for structural health monitoring.
将基于深度学习的代理模型与改进协方差矩阵自适应进化策略(CMAES)算法相结合,本文提出一种用于损伤识别的时域变分贝叶斯框架。所构建的代理模型由并行卷积神经网络与编码器-解码器长短期记忆网络组成,并引入残差连接、自注意力机制以及综合损失函数。该模型能够实现对结构动力响应的高精度预测,均方误差为0.000 12,R2达到0.998 00。此外,提出一种由深度学习代理模型梯度信息引导的改进CMAES算法,以加速局部收敛。基于非对称框架结构的实验验证表明,该方法能够同时识别损伤位置与损伤程度,并对结果不确定性进行量化。同时,该方法显著提升了计算效率,为结构健康监测提供了可行的技术基础。

References:

[1]WANG S Q, XU M Q. Modal strain energy-based structural damage identification: A review and comparative study[J]. Structural Engineering International, 2019, 29(2): 234-248.
[2]SHAN J Z, ZHANG X, LOONG C N, et al. Predictive maintenance and its applications in civil engineering structures: A review[J]. Journal of Southeast University (English Edition), 2024, 40(3): 245-256.
[3]HUANG K, YUEN K V, WANG L. Real-time simultaneous input-state-parameter estimation with modulated colored noise excitation[J]. Mechanical Systems and Signal Processing, 2022, 165: 108378.
[4]YUAN Z X, YU K P. Finite element model updating of damped structures using vibration test data under base excitation[J]. Journal of Sound and Vibration, 2015, 340: 303-316.
[5]HUANG Y, BECK J L, LI H. Bayesian system identification based on hierarchical sparse Bayesian learning and Gibbs sampling with application to structural damage assessment[J]. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 382-411.
[6]HU Q, SHEN Y J. CA mortar void identification for slab track utilizing time-domain Markov chain Monte Carlo-based Bayesian approach[J]. Structural Health Monitoring, 2023, 22(6): 3971-3984.
[7]HUANG K, YUEN K V. Introduction[M]//Bayesian Real-Time System Identification. Singapore: Springer Nature Singapore, 2023: 1-24.
[8]MENG X H, BECK J L, HUANG Y, et al. Adaptive meta-learning stochastic gradient Hamiltonian Monte Carlo simulation for Bayesian updating of structural dynamic models[J]. Computer Methods in Applied Mechanics and Engineering, 2025, 437: 117753.
[9]XUE S C, ZHOU W S, BECK J L, et al. Damage localization and robust diagnostics in guided-wave testing using multitask complex hierarchical sparse Bayesian learning[J]. Mechanical Systems and Signal Processing, 2023, 197: 110365.
[10]HU Q, ZHANG B W, CHEN H, et al. Void damage identification of CA mortar layer in slab track system based on neural network surrogate model[J]. Journal of Southeast University (Natural Science Edition), 2026, 56(2): 234-242. (in Chinese)
[11]JACOBS W R, BALDACCHINO T, DODD T, et al. Sparse Bayesian nonlinear system identification using variational inference[J]. IEEE Transactions on Automatic Control, 2018, 63(12): 4172-4187.
[12]CHEN Y, MCFARLAND D M, SPENCER B F, et al. Improved complex modal superposition method with inclusion of overdamped modes [J]. Journal of Southeast University (English Edition), 2023, 39(3): 213-224.
[13]HU Q, GUAN Y H, ZUO Y T, et al. Bayesian void detection of the CA mortar layer in the slab track considering temperature effect[J]. Advances in Structural Engineering, 2025, 28(16): 3161-3179.
[14]ZHOU H L, ZHOU G D, LIU K K, et al. Finite element model updating method for long span bridges based on PSO-GRNN[J]. Journal of Southeast University (Natural Science Edition), 2024, 54(6): 1489-1495. (in Chinese)
[15]RAMANCHA M K, VEGA M A, CONTE J P, et al. Bayesian model updating with finite element vs surrogate models: Application to a miter gate structural system[J]. Engineering Structures, 2022, 272: 114901.
[16]DUAN Y F, DUAN Z T, ZHANG H M, et al. Bridge damage identification based on convolutional autoencoders and extreme gradient boosting trees[J]. Journal of Southeast University (English Edition), 2024, 40(3): 221-229.
[17]SHU Y D, MA T C, LIN Y G. Rolling bearing fault diagnosis based on data-level and feature-level information fusion[J]. Journal of Southeast University (English Edition), 2024, 40(4): 396-402.
[18]ZHANG B, WU S, LIU Y, et al. Bus arrival interval prediction model based on gated recurrent unit network[J]. Journal of Southeast University (English Edition), 2025, 41(2): 226-234.
[19]TAO T Y, DENG P, WANG H, et al. Short-term prediction of thunderstorm wind speeds based on serial difference and double-step modification [J]. Journal of Southeast University (Natural Science Edition), 2024, 55(5): 1399-1405. (in Chinese)
[20]HU Q, LIN Z S, ZHOU N F. Damage identification of a transmission tower via variational Bayesian learning based on enhanced Jaya and DREAM algorithms[J]. Journal of Southeast University (Natural Science Edition), 2026, 56(1): 142-153. (in Chinese)
[21]RAHMAT RABI R, MONTI G. Genetic algorithm-based model updating in a real-time digital twin for steel bridge monitoring[J]. Applied Sciences, 2025, 15(8): 4074.
[22]ALKAYEM N F, CAO M S. Damage identification in three-dimensional structures using single-objective evolutionary algorithms and finite element model updating: Evaluation and comparison[J]. Engineering Optimization, 2018, 50(10): 1695-1714.
[23]LUO H B, GUO Z Y, CHEN W Y, et al. Structural health assessment of historical buildings with nonuniform FE analysis and modified covariance matrix adaptation evaluation strategy (CMAES) updating[J]. Automation in Construction, 2024, 166: 105618.
[24]MAHESWARANATHAN N, METZ L, TUCKER G, et al. Guided evolutionary strategies: Augmenting random search with surrogate gradients[C/OL]// Proceedings of the 36th International Conference on Machine Learning (ICML). Long Beach, CA, USA, 2019. https: //proceedings. mlr. press/v97/maheswaranathan19a/maheswaranathan19a. pdf.
[25]HU Q, YAN Q Z, CHEN H, et al. Damage detection of an asymmetrical frame via sparse Bayesian learning with a PSO algorithm[J]. International Journal of Structural Stability and Dynamics, 2025: 2650098.
[26]HU Q, ZHOU N F, LAM H F, et al. Brace damage identification of a transmission tower via a sparse Bayesian learning method with variational inference and enhanced PSO algorithm[J]. Structures, 2025, 77: 109170.
[27]TIPPING M E. Sparse bayesian learning and the relevance vector machine [J]. Journal of Machine Learning Research, 2001, 1: 211-244.
[28]GHAHREMANI B, BITARAF M, RAHAMI H. A fast-convergent approach for damage assessment using CMA-ES optimization algorithm and modal parameters[J]. Journal of Civil Structural Health Monitoring, 2020, 10(3): 497-511.
[29]HANSEN N, AUGER A. CMA-ES: Evolution strategies and covariance matrix adaptation[C]//Proceedings of the 13th Annual Conference Companion on Genetic and Evolutionary Computation. Dublin, Ireland, 2011: 991-1010.
[30]ZHANG L, FENG D M, WU G. Dynamic vehicle load identification method based on LSTM network[J]. Journal of Southeast University (Natural Science Edition), 2023, 53(2): 187-192. (in Chinese)
[31]MIAO C Q, LÜ Y K, WAN C F. Mechanical property prediction of bridge cable corroded steel wires based on GA-LSTM model[J]. Journal of Southeast University (Natural Science Edition), 2025, 55(1): 140-145. (in Chinese)
[32]SHAH S R B, CHADHA G S, SCHWUNG A, et al. A sequence-to-sequence approach for remaining useful lifetime estimation using attention-augmented bidirectional LSTM[J]. Intelligent Systems with Applications, 2021, 10/11: 200049.
[33]PERACHA F K, KHATTAK M I, SALEM N, et al. Causal speech enhancement using dynamical-weighted loss and attention encoder-decoder recurrent neural network[J]. PLoS One, 2023, 18(5): e0285629.
[34]NAKAGAWA T, SANADA Y, WAIDA H, et al. Denoising cosine similarity: A theory-driven approach for efficient representation learning[J]. Neural Networks, 2024, 169: 226-241.
[35]CHEN C, DONG J. Deep learning approaches for time series prediction in climate resilience applications[J]. Frontiers in Environmental Science, 2025, 13: 1574981.
[36]GUO T, LI A Q, MIAO C Q. Monte Carlo numerical simulation and its application in probability analysis of long span bridges[J]. Journal of Southeast University (English Edition), 2005, 21(4): 469-473.
[37]GUAN Y H, ZHANG B W, LI Z Q, et al. Enhanced flow number prediction of asphalt mixtures using stacking ensemble-based machine learning model and grey relational analysis[J]. Construction and Building Materials, 2025, 463: 140001.
[38]WAN R Z, MEI S P, WANG J, et al. Multivariate temporal convolutional network: A deep neural networks approach for multivariate time series forecasting[J]. Electronics, 2019, 8(8): 876.
[39]LIN T Y, WANG Y X, LIU X Y, et al. A survey of transformers[J]. AI Open, 2022, 3: 111-132.
[40]BECK J L, KATAFYGIOTIS L S. Updating models and their uncertainties. Ⅰ: Bayesian statistical framework[J]. Journal of Engineering Mechanics, 1998, 124(4): 455-461.

Memo

Memo:
Received: 2025-11-23; Revised: 2026-02-10.
Biography: HU Qin (1987-), female, doctor, associate professor, husthuqin@hust.edu.cn.
Foundation items: The National Natural Science Foundation of China (No.52178287), the Fundamental Research Funds for the Central Universities and the Open Project of the Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education (Southeast University) (No.CPCSME2025-09).
Citation: HU Qin, GUAN Yunhao, ZHANG Biwei. Damage detection of an asymmetrical frame based on a deep learning-based surrogate model and an improved CMAES approach[J]. Journal of Southeast University (English Edition), 2026, 42(3): 306-317. DOI: 10. 3969/j. issn. 1003-7985. 2026. 03. 004.
Last Update: 2026-09-20