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Structural safety evaluation using Bayesian ensemble neural networks SCIE
期刊论文 | 2025 , 328 | ENGINEERING STRUCTURES
Abstract&Keyword Cite Version(2)

Abstract :

Safety evaluation is a pivotal issue for operational civil structures during their service lives. Recently, deep learning-based evaluation strategies have emerged, and such methods often require a substantial amount of training samples to prevent overfitting. However, this precondition is often difficult to satisfy in practice due to insufficient samples. Hence, a Bayesian ensemble neural network (BENN) has been proposed to overcome this drawback. Firstly, the network parameters of a Bayesian neural network (BNN) are established on probability distribution estimation to consider the uncertainties in a structure, which is divided into several substructures for evaluation. A multiple sampling strategy on the network parameter distributions yields different deterministic NNs. Secondly, the Bagging ensemble learning has been adopted to treat a BNN as a base learner, whose prediction will be used for an ensemble prediction of a substructure. A BENN is actually the ensemble of several BNNs (base learners). Specifically, the membership degree of each base learner's predictions is calculated and normalized to derive the corresponding weight. The ensemble prediction is obtained through the weighted summation of the predictions of all base learners. Meanwhile, the entropy that measures the structural uncertainty of each substructure, with corresponding weights calculated via the entropy weight method to construct an overarching structural state indicator. The effectiveness of the BENNs is validated through the numerical simulations and practical experiments conducted on a frame structure. As the structural degradation increased, the state indicator decreased from 16.88 to 14.59 for the numerical frame, as well as from 16.93 to 16.23 for the experimental frame.

Keyword :

Bagging ensemble learning Bagging ensemble learning Bayesian ensemble neural network Bayesian ensemble neural network Entropy weight method Entropy weight method Structural safety evaluation Structural safety evaluation Variational inference Variational inference

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GB/T 7714 Zheng, Jin-Ling , Fang, Sheng-En . Structural safety evaluation using Bayesian ensemble neural networks [J]. | ENGINEERING STRUCTURES , 2025 , 328 .
MLA Zheng, Jin-Ling 等. "Structural safety evaluation using Bayesian ensemble neural networks" . | ENGINEERING STRUCTURES 328 (2025) .
APA Zheng, Jin-Ling , Fang, Sheng-En . Structural safety evaluation using Bayesian ensemble neural networks . | ENGINEERING STRUCTURES , 2025 , 328 .
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Structural safety evaluation using Bayesian ensemble neural networks EI
期刊论文 | 2025 , 328 | Engineering Structures
Structural safety evaluation using Bayesian ensemble neural networks Scopus
期刊论文 | 2025 , 328 | Engineering Structures
A modified blind source separation algorithm for underdetermined structural modal analysis SCIE
期刊论文 | 2025 , 325 | ENGINEERING STRUCTURES
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Abstract :

To improve the mode decomposition capacity for underdetermined and unclear modes, a modified blind source separation (MBSS) method has been proposed, where a multi-synchroextracting transform algorithm with a sliding window is proposed for a higher sparsity time-frequency spectrum. The proposed transform algorithm incorporates an iterative formula of the instantaneous frequency with a sliding window. Then, it is embedded into the existing novel blind source separation (NBSS) method to highly improve the modal decomposition accuracy. The feasibility of the proposed method has been verified against a numerical 3DOF mass-spring-damper system, a numerical three-story frame structure, and an experimental five-story steel frame. The analysis results demonstrate that the proposed MBSS method can well decompose the acceleration signals, providing better precisions than the NBSS method under the circumstance of unclear and underdetermined modes. Moreover, the proposed method has higher decomposition accuracy for close modes.

Keyword :

Mode decomposition Mode decomposition Modified blind source separation Modified blind source separation Multi-synchroextracting transform Multi-synchroextracting transform Sparse matrix Sparse matrix Structural modal analysis Structural modal analysis

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GB/T 7714 Li, Yu-Zu , Fang, Sheng-En . A modified blind source separation algorithm for underdetermined structural modal analysis [J]. | ENGINEERING STRUCTURES , 2025 , 325 .
MLA Li, Yu-Zu 等. "A modified blind source separation algorithm for underdetermined structural modal analysis" . | ENGINEERING STRUCTURES 325 (2025) .
APA Li, Yu-Zu , Fang, Sheng-En . A modified blind source separation algorithm for underdetermined structural modal analysis . | ENGINEERING STRUCTURES , 2025 , 325 .
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A modified blind source separation algorithm for underdetermined structural modal analysis Scopus
期刊论文 | 2025 , 325 | Engineering Structures
A modified blind source separation algorithm for underdetermined structural modal analysis EI
期刊论文 | 2025 , 325 | Engineering Structures
Structural condition evaluation using unsupervised Bayesian optimized BiLSTM networks SCIE
期刊论文 | 2025 | JOURNAL OF CIVIL STRUCTURAL HEALTH MONITORING
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Abstract :

Civil structures are susceptible to performance deterioration during their service lives. Therefore, it is essential to periodically evaluate structural conditions for preventing potential catastrophic failure. Data-driven methods have been widely adopted for this purpose, which often utilize deep learning (DL) algorithms that generally require extensive training data considering various condition scenarios. However, finite element (FE) simulation data are practically affected by uncertainties such as modeling errors and operational environmental variations, limiting the applicability of supervised DL algorithms. Due to this, an unsupervised learning framework has been proposed for structural condition evaluation by establishing a correlation model for the response data measured at different locations of a healthy structure using bidirectional long short-term memory (BiLSTM) networks. During the training process, the optimal hyperparameters of a BiLSTM network is objectively, instead of 'subjectively', determined through Bayesian optimization (BO) without requiring labeled measurement data, improving the network generalization performance. During the testing process, response data from healthy and unknown scenarios are input into the BO-BiLSTM network, and the errors between the reconstructed and actual data are taken as the latent features. Then, the feature similarity between the unknown scenarios and the healthy structure is calculated using the Wasserstein distance as a structural condition indicator. The feasibility of the proposed method has been validated using the IASC-ASCE benchmark frame and an experimental steel frame, demonstrating that the proposed condition indicator is sensitive to structural damage and robust to different noise levels. As structural degradation developed, the condition indicators for the two frames increased from 0.090 and 0.583 to 1.182 and 0.825, respectively. The structural conditions were successfully evaluated without the labeled measurement data, validating the engineering applicability of the proposed method.

Keyword :

Bayesian optimization Bayesian optimization Bidirectional long-short term memory networks Bidirectional long-short term memory networks Structural condition evaluation Structural condition evaluation Unsupervised learning Unsupervised learning Wasserstein distance Wasserstein distance

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GB/T 7714 Zheng, Jin-Ling , Fang, Sheng-En . Structural condition evaluation using unsupervised Bayesian optimized BiLSTM networks [J]. | JOURNAL OF CIVIL STRUCTURAL HEALTH MONITORING , 2025 .
MLA Zheng, Jin-Ling 等. "Structural condition evaluation using unsupervised Bayesian optimized BiLSTM networks" . | JOURNAL OF CIVIL STRUCTURAL HEALTH MONITORING (2025) .
APA Zheng, Jin-Ling , Fang, Sheng-En . Structural condition evaluation using unsupervised Bayesian optimized BiLSTM networks . | JOURNAL OF CIVIL STRUCTURAL HEALTH MONITORING , 2025 .
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Structural condition evaluation using unsupervised Bayesian optimized BiLSTM networks Scopus
期刊论文 | 2025 | Journal of Civil Structural Health Monitoring
A semi-Markov process based digital twin for safety evaluation of cable-stayed bridges with cable corrosion SCIE
期刊论文 | 2025 , 65 | ADVANCED ENGINEERING INFORMATICS
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Abstract :

The cables of a cable-stayed bridge are susceptible to structural degradation due to environmental corrosion and fatigue, which directly affects the safety and operational performance of the bridge. As the process of the degradation in practice is very slow, it is difficult to be monitored during the bridge service life. Hence, this study aims to develop a novel semi-Markov process based digital twin (DT) framework for safety evaluation of cable- stayed bridges considering cable corrosion. The framework encompasses a physical twin layer, a DT layer and the information interaction medium. The physical twin layer mainly comprises the bridge physical entity and its associated monitoring system that provides a variety of perceptual data for DT modeling. In the DT layer, the DT model acts as a virtual counterpart of the physical bridge for mirroring and forecasting the bridge's mechanical behaviors. The information interaction medium plays a crucial role in the bidirectional information communication between the physical and digital twin layers. Two types of information interaction media have been utilized including a cable force influence matrix and a semi-Markov process. The former enables updating the DT model to precisely match the data measured from the physical bridge. Meanwhile, the semi-Markov process depicts the probability of the bridge's condition considering the cable corrosion during the different service periods. The proposed procedure can predict the bridge state and evaluate the safety by comparing the predicted state with the monitored values. The proposed framework has been successfully validated on a real-world cable- stayed bridge. The results showed the proposed DT framework was reliable and effective for evaluating the bridge condition.

Keyword :

A semi-Markov process A semi-Markov process Cable force influence matrix Cable force influence matrix Cable-stayed bridges Cable-stayed bridges Digital twin Digital twin Safety evaluation Safety evaluation

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GB/T 7714 Guo, Xin-Yu , Fang, Sheng-En , Zhu, Xinqun et al. A semi-Markov process based digital twin for safety evaluation of cable-stayed bridges with cable corrosion [J]. | ADVANCED ENGINEERING INFORMATICS , 2025 , 65 .
MLA Guo, Xin-Yu et al. "A semi-Markov process based digital twin for safety evaluation of cable-stayed bridges with cable corrosion" . | ADVANCED ENGINEERING INFORMATICS 65 (2025) .
APA Guo, Xin-Yu , Fang, Sheng-En , Zhu, Xinqun , Li, Jianchun . A semi-Markov process based digital twin for safety evaluation of cable-stayed bridges with cable corrosion . | ADVANCED ENGINEERING INFORMATICS , 2025 , 65 .
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A semi-Markov process based digital twin for safety evaluation of cable-stayed bridges with cable corrosion Scopus
期刊论文 | 2025 , 65 | Advanced Engineering Informatics
Influence of ultrafine metakaolin and nano-TiO2 on the durability and microstructure of seawater sea- sand concrete SCIE
期刊论文 | 2025 , 473 | CONSTRUCTION AND BUILDING MATERIALS
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Abstract :

The increasing demand for sustainable construction materials has spurred interest in seawater sea-sand concrete (SWSSC) as a substitute for natural resources. However, SWSSC's durability faces challenges from aggressive chloride and sulfate ions existing in seawater, causing structural degradation. Therefore, this study has prepared seven SWSSC formulations with the different ultrafine metakaolin (UMK) and nano-TiO2 (NT) dosages using untreated seawater and sea sand. The SWSSC specimens fabricated using these formulations were evaluated through the wet-dry sulfate cycling, chloride permeability and water permeability tests to assess their durability performance. The advanced microstructural analyses, including the Fourier transform infrared spectroscopy, the scanning electron microscopy and the X-ray diffraction, were also employed to examine the effects of the UMK and NT on the pore refinement, the phase evolution and the functional group changes within the concrete matrix. The test results have revealed that a combined addition of 15 wt% UMK and 0.5 wt% NT significantly reduced the chloride ion permeation and the water permeability, enhancing the initial impermeability of the modified concrete. However, after the 60 cycles of sulfate exposure, the specimens with the 15 wt% UMK addition (with or without NT) lost their strengths, while the unmodified concrete specimens retained the higher residual strengths. The formulation with the addition of 5 wt% UMK and 0.5 wt% NT demonstrated the resistance improvement up to the 60 cycles, although the specimen strength was slightly lower than that of unmodified SWSSC specimen. These findings highlighted the need for optimizing the UMK and NT dosages in order to balance initial impermeability and long-term durability of SWSSC.

Keyword :

Durability Durability Fourier transform infrared spectroscopy Fourier transform infrared spectroscopy Nano-TiO2 Nano-TiO2 Scanning electron microscopy Scanning electron microscopy Seawater sea-sand concrete Seawater sea-sand concrete Ultrafine metakaolin Ultrafine metakaolin X-ray diffraction X-ray diffraction

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GB/T 7714 Luo, Qing-Hai , Fang, Sheng-En . Influence of ultrafine metakaolin and nano-TiO2 on the durability and microstructure of seawater sea- sand concrete [J]. | CONSTRUCTION AND BUILDING MATERIALS , 2025 , 473 .
MLA Luo, Qing-Hai et al. "Influence of ultrafine metakaolin and nano-TiO2 on the durability and microstructure of seawater sea- sand concrete" . | CONSTRUCTION AND BUILDING MATERIALS 473 (2025) .
APA Luo, Qing-Hai , Fang, Sheng-En . Influence of ultrafine metakaolin and nano-TiO2 on the durability and microstructure of seawater sea- sand concrete . | CONSTRUCTION AND BUILDING MATERIALS , 2025 , 473 .
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Influence of ultrafine metakaolin and nano-TiO₂ on the durability and microstructure of seawater sea - sand concrete Scopus
期刊论文 | 2025 , 473 | Construction and Building Materials
Intelligent inference of structural vulnerability using Bayesian networks; [基于贝叶斯网络的结构易损性智能推理] Scopus
期刊论文 | 2024 , 33 (3) , 130-136 | Journal of Natural Disasters
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Abstract :

In order to realize the intelligent inference of structural vulnerability, Bayesian networks (BNs) have been adopted for reconstructing the analysis system of a truss structure. Firstly, the external load combination, the truss system and its members are defined as the top parent nodes, the middle nodes and the bottom child nodes of the network, respectively. These nodes are connected by some directed edges representing the causality between them. Therefore, the BN topology of the truss structure is defined. Secondly, serious damage is suggested to replace the commonly-used assumption of conceptual removal in vulnerability analysis. Based on the uncertainty distributions of the parameters of members and external loads, the samples are randomly drawn from the probability distributions for learning the conditional probability tables between the different nodes, thereby realizing the BN establishment. Thirdly, the observed state of a specific member is used as the evidence into the established BN for synchronously inferring the state probabilities of the other members, based on which the member importance coefficient is calculated. The sum of all the importance coefficients is further defined as the system vulnerability index. Finally, a member vulnerability index is proposed to predict the most probable failure path of the truss system. The numerical and experimental examples have demonstrated that the proposed method can effectively evaluate the importance of each member within a truss system. The inferred failure path accords well with the experimental observation. The estimated value of the system vulnerability index of the experimental truss is far less than the number of members, and thus, it indicates the low possibility of progressive collapse of the system due to the damaged member. © 2024 Institute of Engineering Mechanics (IEM). All rights reserved.

Keyword :

Bayesian networks Bayesian networks member importance coefficient member importance coefficient member vulnerability index member vulnerability index structural engineering structural engineering system vulnerability index system vulnerability index

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GB/T 7714 Fang, S. , Yu, Q. , Zhang, X. et al. Intelligent inference of structural vulnerability using Bayesian networks; [基于贝叶斯网络的结构易损性智能推理] [J]. | Journal of Natural Disasters , 2024 , 33 (3) : 130-136 .
MLA Fang, S. et al. "Intelligent inference of structural vulnerability using Bayesian networks; [基于贝叶斯网络的结构易损性智能推理]" . | Journal of Natural Disasters 33 . 3 (2024) : 130-136 .
APA Fang, S. , Yu, Q. , Zhang, X. , Lin, Y. . Intelligent inference of structural vulnerability using Bayesian networks; [基于贝叶斯网络的结构易损性智能推理] . | Journal of Natural Disasters , 2024 , 33 (3) , 130-136 .
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Response reconstruction based on measurement matrix optimization in compressed sensing for structural health monitoring SCIE
期刊论文 | 2024 , 28 (6) , 1029-1040 | ADVANCES IN STRUCTURAL ENGINEERING
WoS CC Cited Count: 1
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Abstract :

Structural health monitoring (SHM) data have a large volume, increasing the cost of data storage and transmission and the difficulties of structural parameter identification. The compressed sensing (CS) theory provides a signal acquisition and analysis strategy. Signal reconstruction using limited measurements and CS has attracted significant interest. However, the dynamic responses obtained from civil engineering structures contain noise, resulting in sparse samples and reducing the signal reconstruction accuracy. Therefore, we propose an optimization algorithm for the measurement matrix integrating the Karhunen-Loeve transform (KLT) and approximate QR decomposition (KLT-QR) to improve the accuracy of dynamic response reconstruction of SHM data. The KLT reduces the correlation between the measurement matrix and the sparse basis. The approximate QR decomposition is used to improve the independence between the column vectors of the measurement matrix, optimizing the measurement matrix. The experimental results for a laboratory steel beam indicate that the proposed KLT-QR algorithm outperforms three other algorithms regarding the accuracy of dynamic response reconstruction (acceleration, displacement, and strain), especially at high compression ratios. The acceleration responses from the Ji'an Bridge are utilized to verify the advantages of the proposed algorithm. The results demonstrate that the KLT-QR algorithm has the highest accuracy of reconstructing the vibration signals and yields better Fourier spectra than the conventional Gaussian measurement matrix.

Keyword :

compressed sensing compressed sensing Gaussian measurement matrix Gaussian measurement matrix optimization optimization response reconstruction response reconstruction Structural health monitoring Structural health monitoring

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GB/T 7714 Zhang, Xiao Hua , Xiao, Xing Yong , Yang, Ze Peng et al. Response reconstruction based on measurement matrix optimization in compressed sensing for structural health monitoring [J]. | ADVANCES IN STRUCTURAL ENGINEERING , 2024 , 28 (6) : 1029-1040 .
MLA Zhang, Xiao Hua et al. "Response reconstruction based on measurement matrix optimization in compressed sensing for structural health monitoring" . | ADVANCES IN STRUCTURAL ENGINEERING 28 . 6 (2024) : 1029-1040 .
APA Zhang, Xiao Hua , Xiao, Xing Yong , Yang, Ze Peng , Fang, Sheng En . Response reconstruction based on measurement matrix optimization in compressed sensing for structural health monitoring . | ADVANCES IN STRUCTURAL ENGINEERING , 2024 , 28 (6) , 1029-1040 .
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Response reconstruction based on measurement matrix optimization in compressed sensing for structural health monitoring Scopus
期刊论文 | 2025 , 28 (6) , 1029-1040 | Advances in Structural Engineering
Response reconstruction based on measurement matrix optimization in compressed sensing for structural health monitoring Scopus
期刊论文 | 2024 , 28 (6) , 1029-1040 | Advances in Structural Engineering
结合传递比与栈式自编码器的结构损伤识别
期刊论文 | 2024 , 37 (9) , 1460-1467 | 振动工程学报
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Abstract :

如何从土木结构响应数据中挖掘损伤特征并有效分类,是实现损伤模式识别的关键.为此,以框架结构为分析对象,搭建设有自编码器隐藏层和Softmax分类层的栈式自编码器网络,采用无监督联合有监督的混合学习机制;基于有限元分析获取框架不同工况下的传递比函数值,构建训练集、验证集和测试集样本;通过预训练确定自编码器隐藏层的参数值如权重和偏置值,避免网络出现过拟合;采用微调方式进一步调整预训练后的网络参数值,再结合验证集实现对网络超参数的调整;将实测传递比数据输入网络,实现对框架节点损伤的评估.结果表明:所提方法能有效进行损伤特征的提取和分类,准确识别框架节点的单、双损伤工况,相较于传统浅层神经网络具有更高的识别准确度和更好的抗噪性.

Keyword :

传递比函数 传递比函数 损伤识别 损伤识别 栈式自编码器 栈式自编码器 框架结构 框架结构 混合学习机制 混合学习机制

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GB/T 7714 方圣恩 , 刘洋 , 张笑华 . 结合传递比与栈式自编码器的结构损伤识别 [J]. | 振动工程学报 , 2024 , 37 (9) : 1460-1467 .
MLA 方圣恩 et al. "结合传递比与栈式自编码器的结构损伤识别" . | 振动工程学报 37 . 9 (2024) : 1460-1467 .
APA 方圣恩 , 刘洋 , 张笑华 . 结合传递比与栈式自编码器的结构损伤识别 . | 振动工程学报 , 2024 , 37 (9) , 1460-1467 .
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结合深度信念记忆网络的结构损伤识别
期刊论文 | 2024 , 37 (11) , 1917-1924 | 振动工程学报
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Abstract :

从结构响应信号中挖掘敏感损伤特征是基于模式分类的损伤识别方法的关键.为此,将深度信念网络和长短期记忆网络进行混合组网,通过混合学习机制有机结合了两种网络在高阶抽象特征提取和考虑数据序列相关性上的优点.将响应信号传递比值输入深度信念网络,实现初步数据压缩和特征提取,以减少响应中的冗余信息;将特征序列依次输入长短期记忆网络,以考虑响应间的相关性并获取敏感损伤特征;利用Softmax分类层对长短期记忆网络输出的特征进行分类,实现对不同结构损伤模式的识别.三维试验钢框架的损伤识别结果表明:混合学习机制能更好地训练网络参数,整体微调后更有利于后续的损伤特征分类;混合组网方式在包含数值或实测噪声的情况下仍可以有效进行数据压缩、特征提取和分类,准确识别了试验框架的多种损伤工况.

Keyword :

损伤识别 损伤识别 框架结构 框架结构 深度信念网络 深度信念网络 混合学习机制 混合学习机制 长短期记忆网络 长短期记忆网络

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GB/T 7714 方圣恩 , 刘洋 . 结合深度信念记忆网络的结构损伤识别 [J]. | 振动工程学报 , 2024 , 37 (11) : 1917-1924 .
MLA 方圣恩 et al. "结合深度信念记忆网络的结构损伤识别" . | 振动工程学报 37 . 11 (2024) : 1917-1924 .
APA 方圣恩 , 刘洋 . 结合深度信念记忆网络的结构损伤识别 . | 振动工程学报 , 2024 , 37 (11) , 1917-1924 .
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Temperature coupling effects and cable force prediction of cable-stayed bridge with steel arch tower; [钢 拱 塔 斜 拉 桥 的 温 度 耦 合 效 应 和 索 力 预 测] Scopus CSCD PKU
期刊论文 | 2024 , 46 (2) , 146-153 | Journal of Civil and Environmental Engineering
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The mechanical system of a cable-stayed bridge with a steel arch tower is different from that of a traditional cable-stayed bridge. In order to investigate the effects of ambient temperature variations on the main components of a cable-stayed bridge with a tower in an abnormal shape, an actual cable-stayed bridge with a steel arch tower has been used as the engineering prototype. The online temperature data of the onsite environment and the bridge components were first collected and used to analyze the time-varying effects of the environmental temperature on the cable forces, the tower obliquity and the stress of the main girder. Subsequently, the analysis was focused on the cable forces. The temperature variation simulation was applied to the finite element model of the bridge, and the temperature coupling effects caused by the temperature difference between different bridge components on the cable forces were analyzed. Lastly, the temperatures of the environment, the tower and the main girder were used as the inputs, while the cable forces were defined as the outputs of a long short-term memory neural network. The network was trained using the actual measurement samples of the temperatures and the cable forces. Data compression and feature extraction were realized during the training process. Then, the prediction model for the cable forces was established, and new temperature monitoring data were input into the network model for predicting the cable forces. The analysis results show that the temperature variations of the main girder and the steel arch tower follow a periodic rule and lag behind the ambient temperature. The strain variation tendency of the main girder accords well with the ambient temperature, but the latter has a time lag. The influence of the ambient temperature variation on the obliquity of the arch tower is very small without any periodic rule. A linear negative correlation is found between the cable forces and the ambient temperature. The temperature coupling effect caused by the temperature difference between different bridge components should be considered in the analysis. The long and short-term memory neural network is suitable for the data with timing characteristics. The cable force prediction model based on the neural network has high prediction accuracy, and it can be used for the real-time prediction of this bridge. © 2024 Chongqing University. All rights reserved.

Keyword :

bridge engineering bridge engineering cable force prediction cable force prediction cable-stayed bridge with a steel arch tower cable-stayed bridge with a steel arch tower long short-term memory neural network long short-term memory neural network temperature coupling effects temperature coupling effects

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GB/T 7714 Fang, S. , Qin, J. , Zhang, W. et al. Temperature coupling effects and cable force prediction of cable-stayed bridge with steel arch tower; [钢 拱 塔 斜 拉 桥 的 温 度 耦 合 效 应 和 索 力 预 测] [J]. | Journal of Civil and Environmental Engineering , 2024 , 46 (2) : 146-153 .
MLA Fang, S. et al. "Temperature coupling effects and cable force prediction of cable-stayed bridge with steel arch tower; [钢 拱 塔 斜 拉 桥 的 温 度 耦 合 效 应 和 索 力 预 测]" . | Journal of Civil and Environmental Engineering 46 . 2 (2024) : 146-153 .
APA Fang, S. , Qin, J. , Zhang, W. , Jiang, X. . Temperature coupling effects and cable force prediction of cable-stayed bridge with steel arch tower; [钢 拱 塔 斜 拉 桥 的 温 度 耦 合 效 应 和 索 力 预 测] . | Journal of Civil and Environmental Engineering , 2024 , 46 (2) , 146-153 .
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