{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T12:39:39Z","timestamp":1791981579872,"version":"4.4.0"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,4,19]],"date-time":"2024-04-19T00:00:00Z","timestamp":1713484800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangdong Provincial Key Laboratory of Intelligent Disaster Prevention and Emergency Technologies for Urban Lifeline Engineering","award":["2022B1212010016"],"award-info":[{"award-number":["2022B1212010016"]}]},{"name":"Guangdong Provincial Key Laboratory of Intelligent Disaster Prevention and Emergency Technologies for Urban Lifeline Engineering","award":["12202103"],"award-info":[{"award-number":["12202103"]}]},{"name":"Guangdong Provincial Key Laboratory of Intelligent Disaster Prevention and Emergency Technologies for Urban Lifeline Engineering","award":["2022A1515011324"],"award-info":[{"award-number":["2022A1515011324"]}]},{"name":"Guangdong Provincial Key Laboratory of Intelligent Disaster Prevention and Emergency Technologies for Urban Lifeline Engineering","award":["2017KSYS009"],"award-info":[{"award-number":["2017KSYS009"]}]},{"name":"Guangdong Provincial Key Laboratory of Intelligent Disaster Prevention and Emergency Technologies for Urban Lifeline Engineering","award":["KCYCXPT2017006"],"award-info":[{"award-number":["KCYCXPT2017006"]}]},{"name":"National Natural Science Foundation of China","award":["2022B1212010016"],"award-info":[{"award-number":["2022B1212010016"]}]},{"name":"National Natural Science Foundation of China","award":["12202103"],"award-info":[{"award-number":["12202103"]}]},{"name":"National Natural Science Foundation of China","award":["2022A1515011324"],"award-info":[{"award-number":["2022A1515011324"]}]},{"name":"National Natural Science Foundation of China","award":["2017KSYS009"],"award-info":[{"award-number":["2017KSYS009"]}]},{"name":"National Natural Science Foundation of China","award":["KCYCXPT2017006"],"award-info":[{"award-number":["KCYCXPT2017006"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["2022B1212010016"],"award-info":[{"award-number":["2022B1212010016"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["12202103"],"award-info":[{"award-number":["12202103"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["2022A1515011324"],"award-info":[{"award-number":["2022A1515011324"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["2017KSYS009"],"award-info":[{"award-number":["2017KSYS009"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["KCYCXPT2017006"],"award-info":[{"award-number":["KCYCXPT2017006"]}]},{"name":"KEY Laboratory of Robotics and Intelligent Equipment of Guangdong Regular Institutions of Higher Education","award":["2022B1212010016"],"award-info":[{"award-number":["2022B1212010016"]}]},{"name":"KEY Laboratory of Robotics and Intelligent Equipment of Guangdong Regular Institutions of Higher Education","award":["12202103"],"award-info":[{"award-number":["12202103"]}]},{"name":"KEY Laboratory of Robotics and Intelligent Equipment of Guangdong Regular Institutions of Higher Education","award":["2022A1515011324"],"award-info":[{"award-number":["2022A1515011324"]}]},{"name":"KEY Laboratory of Robotics and Intelligent Equipment of Guangdong Regular Institutions of Higher Education","award":["2017KSYS009"],"award-info":[{"award-number":["2017KSYS009"]}]},{"name":"KEY Laboratory of Robotics and Intelligent Equipment of Guangdong Regular Institutions of Higher Education","award":["KCYCXPT2017006"],"award-info":[{"award-number":["KCYCXPT2017006"]}]},{"name":"DGUT innovation center of robotics and intelligent equipment","award":["2022B1212010016"],"award-info":[{"award-number":["2022B1212010016"]}]},{"name":"DGUT innovation center of robotics and intelligent equipment","award":["12202103"],"award-info":[{"award-number":["12202103"]}]},{"name":"DGUT innovation center of robotics and intelligent equipment","award":["2022A1515011324"],"award-info":[{"award-number":["2022A1515011324"]}]},{"name":"DGUT innovation center of robotics and intelligent equipment","award":["2017KSYS009"],"award-info":[{"award-number":["2017KSYS009"]}]},{"name":"DGUT innovation center of robotics and intelligent equipment","award":["KCYCXPT2017006"],"award-info":[{"award-number":["KCYCXPT2017006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Identifying the structural state without baseline data is an important engineering problem in the field of structural health monitoring, which is crucial for assessing the safety condition of structures. In the context of limited accelerometers available, this paper proposes a correlation-based damage identification method using Variational Autoencoder neural networks. The approach involves initially constructing a Variational Autoencoder network model for bridge damage detection, optimizing parameters such as loss functions and learning rates for the model, and ultimately utilizing response data from limited sensors for model training analysis to determine the structural state. The contribution of this paper lies in the ability to identify structural damage without baseline data using response data from a small number of sensors, reducing sensor costs and enhancing practical applications in engineering. The effectiveness of the proposed method is demonstrated through numerical simulations and experimental structures. The results show that the method can identify the location of damage under different damage conditions, exhibits strong robustness in detecting multiple damages, and further enhances the accuracy of identifying bridge structures.<\/jats:p>","DOI":"10.3390\/s24082616","type":"journal-article","created":{"date-parts":[[2024,4,19]],"date-time":"2024-04-19T06:28:09Z","timestamp":1713508089000},"page":"2616","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Structural Damage Detection Based on the Correlation of Variational Autoencoder Neural Networks Using Limited Sensors"],"prefix":"10.3390","volume":"24","author":[{"given":"Jun","family":"Lin","sequence":"first","affiliation":[{"name":"School of Environment and Civil Engineering, Dongguan University of Technology, Dongguan 523808, China"},{"name":"Guangdong Provincial Key Laboratory of Intelligent Disaster Prevention and Emergency Technologies for Urban Lifeline Engineering, Dongguan 523808, China"},{"name":"School of Aerospace, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongwei","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Environment and Civil Engineering, Dongguan University of Technology, Dongguan 523808, China"},{"name":"Guangdong Provincial Key Laboratory of Intelligent Disaster Prevention and Emergency Technologies for Urban Lifeline Engineering, Dongguan 523808, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01743515","article-title":"Recent developments in damage detection based on system identification methods","volume":"2","author":"Hajela","year":"1990","journal-title":"Struct. Optim."},{"key":"ref_2","first-page":"1185","article-title":"Structural health monitoring","volume":"6531","author":"Humar","year":"2001","journal-title":"Struct. Eng. Mech. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1006\/jsvi.1999.2340","article-title":"Damage detection using the frequency-response-function curvature method","volume":"226","author":"Sampaio","year":"1999","journal-title":"J. Sound Vib."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1177\/1475921704047500","article-title":"Vibration based condition monitoring: A review","volume":"3","author":"Carden","year":"2004","journal-title":"Struct. Health Monit."},{"key":"ref_5","first-page":"1931","article-title":"Feature extraction and classi cation techniques for health monitoring of structures","volume":"22","author":"Adeli","year":"2015","journal-title":"Sci. Iran."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5584","DOI":"10.1016\/j.jsv.2013.05.003","article-title":"Fundamental mode shape and its derivatives in structural damage localization","volume":"332","author":"Roy","year":"2013","journal-title":"J. Sound Vib."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1243\/03093247V142049","article-title":"The location of defects in structures from measurements of natural frequencies","volume":"14","author":"Cawley","year":"1979","journal-title":"J. Strain Anal. Eng. Des."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.ymssp.2016.06.007","article-title":"The use of a non-probabilistic artificial neural network to consider uncertainties in vibration-based-damage detection","volume":"83","author":"Padil","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1109\/72.159069","article-title":"On fuzzy modeling using fuzzy neural networks with the back-propagation algorithm","volume":"3","author":"Horikawa","year":"1992","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1016\/j.engstruct.2013.02.031","article-title":"The application of a damage detection method using Artificial Neural Network and train-induced vibrations on a simplified railway bridge model","volume":"52","author":"Shu","year":"2013","journal-title":"Eng. Struct."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"440","DOI":"10.4028\/www.scientific.net\/AMM.847.440","article-title":"Application of BP neural network in structural damage diagnosis of bridge behind abutment","volume":"847","author":"Zhang","year":"2016","journal-title":"Appl. Mech. Mater."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1993","DOI":"10.1002\/aic.690351210","article-title":"A neural network methodology for process fault diagnosis","volume":"35","author":"Venkatasubramanian","year":"1989","journal-title":"AIChE J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"e2020","DOI":"10.1002\/stc.2020","article-title":"Fiber optic health monitoring and temperature behavior of bridge in cold region","volume":"24","author":"Xiao","year":"2017","journal-title":"Struct. Control. Health Monit."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.istruc.2023.04.027","article-title":"Damage identification of large-scale space truss structures based on stiffness separation method","volume":"53","author":"Xiao","year":"2023","journal-title":"Structures"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1550147717707929","DOI":"10.1177\/1550147717707929","article-title":"Optimal static strain sensor placement for truss bridges","volume":"13","author":"Xiao","year":"2017","journal-title":"Int. J. Distrib. Sens. Netw."},{"key":"ref_16","first-page":"355","article-title":"Novel plastic hinge modification factors for damaged RC shear walls with bending performance","volume":"202112","author":"Komarizadehasl","year":"2021","journal-title":"Adv. Concr. Constr."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"e2535","DOI":"10.1002\/stc.2535","article-title":"Bridge condition monitoring using fixed moving principal component analysis","volume":"27","author":"Nie","year":"2020","journal-title":"Struct. Control Health Monit."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1016\/0045-7949(92)90132-J","article-title":"Use of neural networks in detection of structural damage","volume":"42","author":"Wu","year":"1992","journal-title":"Comput. Struct."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1561\/2000000039","article-title":"Deep learning: Methods and applications","volume":"7","author":"Deng","year":"2014","journal-title":"Found. Trends\u00ae Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"ref_21","unstructured":"Xu, B., and Wang, N. (2015). Empirical evaluation of rectified activations in convolutional network. arXiv."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"129238","DOI":"10.1016\/j.conbuildmat.2022.129238","article-title":"Review on computer vision-based crack detection and quantification methodologies for civil structures","volume":"356","author":"Deng","year":"2022","journal-title":"Constr. Build. Mater."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1111\/mice.12313","article-title":"Structural damage detection with automatic feature-extraction through deep learning","volume":"32","author":"Lin","year":"2017","journal-title":"Comput.-Aided Civ. Infrastruct. Eng."},{"key":"ref_24","first-page":"507","article-title":"CNN-based damage identification method of tied-arch bridge using spatial-spectral information","volume":"23","author":"Duan","year":"2019","journal-title":"Smart Struct. Syst"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.jsv.2016.10.043","article-title":"Real-time vibration-based structural damage detection using one-dimensional convolutional neural networks","volume":"388","author":"Abdeljaber","year":"2017","journal-title":"J. Sound Vib."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1023\/A:1007617005950","article-title":"Unsupervised learning by probabilistic latent semantic analysis","volume":"42","author":"Hofmann","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Ghojogh, B., and Ghodsi, A. (2021). Generative adversarial networks and adversarial autoencoders: Tutorial and survey. arXiv.","DOI":"10.1007\/978-3-031-10602-6_21"},{"key":"ref_28","unstructured":"Kingma, D.P., and Welling, M. (2013). Auto-encoding variational bayes. arXiv."},{"key":"ref_29","unstructured":"Louizos, C., and Swersky, K. (2015). The variational fair autoencoder. arXiv."},{"key":"ref_30","unstructured":"Dai, H., and Tian, Y. (2018). Syntax-directed variational autoencoder for structured data. arXiv."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000006","article-title":"Learning deep architectures for AI","volume":"2","author":"Bengio","year":"2009","journal-title":"Found. Trends\u00ae Mach. Learn."},{"key":"ref_32","unstructured":"Kendall, A., and Badrinarayanan, V. (2015). Bayesian segnet: Model uncertainty in deep convolutional encoder-decoder architectures for scene understanding. arXiv."},{"key":"ref_33","first-page":"121","article-title":"Stochastic gradient VB and the variational auto-encoder","volume":"19","author":"Kingma","year":"2014","journal-title":"Second Int. Conf. Learn. Represent. ICLR"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1177\/1475921719868930","article-title":"Bridge condition monitoring under moving loads using two sensor measurements","volume":"19","author":"Nie","year":"2020","journal-title":"Struct. Health Monit."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2610","DOI":"10.1109\/TBME.2006.886577","article-title":"Frequency recognition based on canonical correlation analysis for SSVEP-based BCIs","volume":"53","author":"Lin","year":"2006","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1950109","DOI":"10.1142\/S0219455419501098","article-title":"Physical interpretation of principal component analysis for structural dynamics through string vibration","volume":"19","author":"Ma","year":"2019","journal-title":"Int. J. Struct. Stab. Dyn."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1061\/(ASCE)0733-9445(2008)134:5(832)","article-title":"Damage identification of shear connectors with wavelet packet energy: Laboratory test study","volume":"134","author":"Ren","year":"2008","journal-title":"J. Struct. Eng."},{"key":"ref_38","first-page":"230","article-title":"Theorems on Fourier series and power series","volume":"6","author":"Littlewood","year":"1936","journal-title":"J. Lond. Math. Soc."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1109\/89.496217","article-title":"Performance of feedforward and feedback systems for active control","volume":"4","author":"Elliott","year":"1996","journal-title":"IEEE Trans. Speech Audio Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/8\/2616\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:30:58Z","timestamp":1760106658000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/8\/2616"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,19]]},"references-count":39,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["s24082616"],"URL":"https:\/\/doi.org\/10.3390\/s24082616","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,19]]}}}