{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T08:40:44Z","timestamp":1769762444481,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,2,19]],"date-time":"2023-02-19T00:00:00Z","timestamp":1676764800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52192663"],"award-info":[{"award-number":["52192663"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51578094"],"award-info":[{"award-number":["51578094"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Under external load excitation, damage such as breathing cracks and bolt loosening will cause structural time domain acceleration to have nonlinear features. To solve the problem of time domain nonlinear damage identification, a damage identification method based on the Kullback\u2013Leibler (KL) distance of time domain model residuals is proposed in this paper. First, an autoregressive (AR) model order was selected using the autocorrelation function (ACF) and Akaike information criterion (AIC). Then, an AR model was obtained based on the structural acceleration response time series, and the AR model residual was extracted. Finally, the KL distance was used as a damage indicator to judge the structural damage source location. The effectiveness of the proposed method was verified by using a multi-story, multi-span stand model experiment and a simulated eight-story shear structure. The results show that the proposed structural nonlinear damage identification method can effectively distinguish the structural damage location of multi-degree-of-freedom shear structures and complex stand structures, and it is robust enough to detect environmental noise and small damage.<\/jats:p>","DOI":"10.3390\/rs15041135","type":"journal-article","created":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T01:36:37Z","timestamp":1676856997000},"page":"1135","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Structural Nonlinear Damage Identification Method Based on the Kullback\u2013Leibler Distance of Time Domain Model Residuals"],"prefix":"10.3390","volume":"15","author":[{"given":"Heng","family":"Zuo","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Chongqing University, Chongqing 400045, China"}]},{"given":"Huiyong","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Chongqing University, Chongqing 400045, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1002\/stc.215","article-title":"A review of nonlinear dynamics applications to structural health monitoring","volume":"15","author":"Worden","year":"2008","journal-title":"Struct. Control. Health Monit."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1177\/1475921702001002005","article-title":"Classifying Linear and Nonlinear Structural Damage Using Frequency Domain ARX Models","volume":"1","author":"Adams","year":"2002","journal-title":"Struct. Health Monit.-Int. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2579","DOI":"10.1080\/17415977.2021.1941922","article-title":"Damage diagnosis of high-rise buildings under variable ambient conditions using subdomain approach","volume":"29","author":"Lakshmi","year":"2021","journal-title":"Inverse Probl. Sci. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1177\/1369433219886962","article-title":"Signal-segments cross-coherence method for nonlinear structural damage detection using free-vibration signals","volume":"23","author":"Li","year":"2020","journal-title":"Adv. Struct. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1007\/s11071-019-04864-3","article-title":"Damage detection in nonlinear systems using an improved describing function approach with limited instrumentation","volume":"96","author":"Prawin","year":"2019","journal-title":"Nonlinear Dyn."},{"key":"ref_6","first-page":"23","article-title":"Nonlinear damage detection using linear ARMA models with classification algorithms","volume":"26","author":"Chen","year":"2020","journal-title":"Smart Struct. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1177\/1475921719836953","article-title":"Vibration-based breathing crack identification using non-linear intermodulation components under noisy environment","volume":"19","author":"Prawin","year":"2019","journal-title":"Struct. Health Monit."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"107209","DOI":"10.1016\/j.measurement.2019.107209","article-title":"Structural damage identification based on short-time temporal coherence using free-vibration response signals","volume":"151","author":"Li","year":"2020","journal-title":"Measurement"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2042009","DOI":"10.1142\/S0219455420420092","article-title":"Damage Detection in Initially Nonlinear Structures Based on Variational Mode Decomposition","volume":"20","author":"Xin","year":"2020","journal-title":"Int. J. Struct. Stab. Dyn."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"105330","DOI":"10.1016\/j.cnsns.2020.105330","article-title":"Nonlinear multiple breathing cracks detection using direct zeros estimation of higher-order frequency response function","volume":"89","author":"Chomette","year":"2020","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.compstruc.2014.10.011","article-title":"Structural damage identification based on power spectral density sensitivity analysis of dynamic responses","volume":"146","author":"Zheng","year":"2015","journal-title":"Comput. Struct."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1896","DOI":"10.1002\/stc.1905","article-title":"An innovative sensitivity-based method for structural model updating using incomplete modal data","volume":"24","author":"Esfandiari","year":"2017","journal-title":"Struct. Control. Health Monit."},{"key":"ref_13","first-page":"698658","article-title":"Damage Detection of Bridges Using Vibration Data by Adjoint Variable Method","volume":"2014","author":"Mirzaee","year":"2014","journal-title":"Shock. Vib."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"e2554","DOI":"10.1002\/stc.2554","article-title":"Damage identification using time series analysis and sparse regularization","volume":"27","author":"Zhu","year":"2020","journal-title":"Struct. Control. Health Monit."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Mei, L., Li, H., Zhou, Y., Li, D., Long, W., and Xing, F. (2020). Output-Only Damage Detection of Shear Building Structures Using an Autoregressive Model-Enhanced Optimal Subpattern Assignment Metric. Sensors, 20.","DOI":"10.3390\/s20072050"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"109914","DOI":"10.1016\/j.engstruct.2019.109914","article-title":"A time series based damage detection method for obtaining separate mass and stiffness damage features of shear-type structures","volume":"208","author":"Do","year":"2020","journal-title":"Eng. Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1950017","DOI":"10.1142\/S0219455419500172","article-title":"Reference-Free Breathing Crack Identification of Beam-Like Structures Using an Enhanced Spatial Fourier Power Spectrum with Exponential Weighting Functions","volume":"19","author":"Prawin","year":"2019","journal-title":"Int. J. Struct. Stab. Dyn."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1177\/1475921720930990","article-title":"Dynamic nonlinearities for identification of the breathing crack type damage in reinforced concrete bridges","volume":"20","author":"Voggu","year":"2021","journal-title":"Struct. Health Monit.-Int. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"108746","DOI":"10.1016\/j.ymssp.2021.108746","article-title":"Fundamental mode shape estimation and element stiffness evaluation of girder bridges by using passing tractor-trailers","volume":"169","author":"Yang","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1109\/TITS.2022.3151529","article-title":"Mode Shape Identification and Damage Detection of Bridge by Movable Sensory System","volume":"24","author":"Yang","year":"2022","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"116754","DOI":"10.1016\/j.jsv.2022.116754","article-title":"A nonlinearity-sensitive approach for detection of \u201cbreathing\u201d cracks relying on energy modulation effect","volume":"524","author":"Cao","year":"2022","journal-title":"J. Sound Vib."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2240014","DOI":"10.1142\/S0219455422400144","article-title":"Damage identification of frame structure based on approximate Metropolis\u2013Hastings algorithm and probability density evolution method","volume":"22","author":"Yang","year":"2022","journal-title":"Int. J. Struct. Stab. Dyn."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1093\/biomet\/60.2.255","article-title":"Maximum Likelihood Identification of Gaussian Autoregressive Moving Average Models","volume":"60","author":"Akaike","year":"1973","journal-title":"Biometrika"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1177\/1475921710395810","article-title":"Structural health monitoring of bolted joints using linear and nonlinear acoustic\/ultrasound methods","volume":"10","author":"Amerini","year":"2011","journal-title":"Struct. Health Monit.-Int. J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1154","DOI":"10.1177\/1475921718788801","article-title":"A method for detecting damage-induced nonlinearity in structures using weighting function augmented curvature approach","volume":"18","author":"Prawin","year":"2019","journal-title":"Struct. Health Monit.-Int. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.ymssp.2020.107185","article-title":"Two-step structural damage detection method for shear frame structures using FRF and Neumann series expansion","volume":"149","author":"Niu","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.ymssp.2014.03.009","article-title":"Nonlinear structural damage detection based on cascade of Hammerstein models","volume":"48","author":"Hajrya","year":"2014","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1750083","DOI":"10.1142\/S0219455417500833","article-title":"Structural Nonlinear Damage Detection Method Using AR\/ARCH Model","volume":"17","author":"Cheng","year":"2017","journal-title":"Int. J. Struct. Stab. Dyn."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.ymssp.2018.12.019","article-title":"A novel vibration based breathing crack localization technique using a single sensor measurement","volume":"122","author":"Prawin","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On information and sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"115734","DOI":"10.1016\/j.jsv.2020.115734","article-title":"Nonlinear pseudo-force in a breathing crack to generate harmonics","volume":"492","author":"Xu","year":"2021","journal-title":"J. Sound Vib."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/4\/1135\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:36:28Z","timestamp":1760121388000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/4\/1135"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,19]]},"references-count":31,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["rs15041135"],"URL":"https:\/\/doi.org\/10.3390\/rs15041135","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,19]]}}}