{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T04:50:37Z","timestamp":1790052637992,"version":"4.0.1"},"reference-count":53,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,4,7]],"date-time":"2022-04-07T00:00:00Z","timestamp":1649289600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Short-time, abrupt events\u2014such as earthquakes and other shock loadings\u2014often lead to damage that is difficult to detect in structures using output-only vibration measurements. The time-variant transmissibility is proposed to tackle this problem. The approach is based on two-dimensional wavelet power spectra. The time-frequency transmissibility and relevant coherence function are used for structural damage detection in structural elements in buildings. Numerical simulations and experimental tests are used in these investigations. The results are compared with the classical transmissibility and time-variant input-output wavelet approach. The paper shows that output-only measurements and wavelet-based transmissibility can be used to monitor abrupt damage-related changes to structural dynamics.<\/jats:p>","DOI":"10.3390\/ma15082722","type":"journal-article","created":{"date-parts":[[2022,4,7]],"date-time":"2022-04-07T21:08:22Z","timestamp":1649365702000},"page":"2722","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Wavelet-Based Transmissibility for Structural Damage Detection"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5703-2642","authenticated-orcid":false,"given":"Kajetan","family":"Dziedziech","sequence":"first","affiliation":[{"name":"Department of Robotics and Mechatronics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wies\u0142aw Jerzy","family":"Staszewski","sequence":"additional","affiliation":[{"name":"Department of Robotics and Mechatronics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3720-6454","authenticated-orcid":false,"given":"Krzysztof","family":"Mendrok","sequence":"additional","affiliation":[{"name":"Department of Robotics and Mechatronics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Biswajit","family":"Basu","sequence":"additional","affiliation":[{"name":"Department of Civil, Structural and Environmental Engineering, School of Engineering, Trinity College Dublin, D02 PN40 Dublin, Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Jablonski, A. (2021). Condition Monitoring Algorithms in Matlab, Springer.","DOI":"10.1007\/978-3-030-62749-2"},{"key":"ref_2","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_3","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1006\/jsvi.2000.3299","article-title":"Damping factor as an indicator of crack severity","volume":"241","author":"Panteliou","year":"2001","journal-title":"J. Sound Vib."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1177\/147592170200100102","article-title":"Damage Detection Using Optical Measurements and Wavelets","volume":"1","author":"Patsias","year":"2002","journal-title":"Struct. Health Monit."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"108188","DOI":"10.1016\/j.measurement.2020.108188","article-title":"Damage detection in connections of steel moment resisting frames using proper orthogonal decomposition and wavelet transform","volume":"166","author":"Teimoori","year":"2020","journal-title":"Measurement"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/j.measurement.2017.02.005","article-title":"Experimental structural damage localization in beam structure using spatial continuous wavelet transform and mode shape curvature methods","volume":"102","author":"Janeliukstis","year":"2017","journal-title":"Measurement"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/0022-460X(91)90595-B","article-title":"Damage detection from changes in curvature mode shapes","volume":"145","author":"Pandey","year":"1991","journal-title":"J. Sound Vib."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1006\/jsvi.1994.1002","article-title":"Damage Detection in Structures Using Changes in Flexibility","volume":"169","author":"Pandey","year":"1994","journal-title":"J. Sound Vib."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1006\/jsvi.2001.4194","article-title":"Identification of crack location in vibrating beams from changes in node positions","volume":"255","author":"Dilena","year":"2002","journal-title":"J. Sound Vib."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/S0045-7825(97)00013-3","article-title":"Structural damage detection using measured FRF data","volume":"147","author":"Wang","year":"1997","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_11","first-page":"14","article-title":"The modal assurance criterion twenty years of use and abuse","volume":"37","author":"Allemang","year":"2003","journal-title":"Sound Vib."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.jsv.2005.07.036","article-title":"Assessment of vibration-based damage identification techniques","volume":"292","author":"Alvandi","year":"2006","journal-title":"J. Sound Vib."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/j.ymssp.2005.04.008","article-title":"Past, present and future of nonlinear system identification in structural dynamics","volume":"20","author":"Kerschen","year":"2006","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1177\/058310249803000201","article-title":"A Summary Review of Vibration-Based Damage Identification Methods","volume":"30","author":"Doebling","year":"1998","journal-title":"Shock Vib. Dig."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/s13349-016-0168-5","article-title":"Vibration-based damage detection techniques used for health monitoring of structures: A review","volume":"6","author":"Das","year":"2016","journal-title":"J. Civ. Struct. Health Monit."},{"key":"ref_16","unstructured":"Sapri, R.C. (2018). A review of damage detection and health monitoring of mechanical systems from changes in the measurement of linear and non-linear vibration. Mechanical Vibrations: Measurement, Effects and Control, Nova Science."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Staszewski, W.J., Boller, C., and Tomlinson, G.R. (2003). Health Monitoring of Aerospace Structures, Wiley & Sons Ltd.","DOI":"10.1002\/0470092866"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2029","DOI":"10.1016\/j.ymssp.2008.11.004","article-title":"Parametric identification of a time-varying structure based on vector vibration response measurements","volume":"23","author":"Spiridonakis","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.measurement.2017.02.027","article-title":"Application of adaptable functional series vector time-dependent autoregressive model for extraction of real modal parameters for identification of time-varying systems","volume":"103","author":"Li","year":"2017","journal-title":"Measurement"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.ymssp.2013.03.011","article-title":"Wavelet-based frequency response function for time-variant systems\u2014An exploratory study","volume":"47","author":"Staszewski","year":"2014","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.ymssp.2014.05.003","article-title":"Wavelet-based modal analysis for time-variant systems","volume":"50\u201351","author":"Dziedziech","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1562","DOI":"10.1177\/1369433217751969","article-title":"Time\u2013frequency analysis and applications in time-varying\/nonlinear structural systems: A state-of-the-art review","volume":"21","author":"Wang","year":"2018","journal-title":"Adv. Struct. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1006\/mssp.1999.1249","article-title":"Reference-based stochastic subspace identification for output-only modal analysis","volume":"13","author":"Peeters","year":"1999","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"108897","DOI":"10.1016\/j.measurement.2020.108897","article-title":"Continuous wavelet transform-based method for enhancing estimation of wind turbine blade natural frequencies and damping for machine learning purposes","volume":"172","author":"Janeliukstis","year":"2020","journal-title":"Measurement"},{"key":"ref_25","unstructured":"Inman, D.J. (2007). Engineering Vibration, Addison-Wesley. [3rd ed.]."},{"key":"ref_26","unstructured":"Liu, W., and Ewins, D.J. (1998, January 2\u20135). Transmissibility properties of MDOF systems. Proceedings of the 16th International Modal Analysis Conference (IMAC), Santa Barbara, CA, USA."},{"key":"ref_27","unstructured":"Ribeiro, A.M.R. (1998, January 3\u201315). On the generalization of transmissibility concept. Proceedings of the NATO\/ASI Conference on Modal Analysis and Testing, Sesimbra, Portugal."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1006\/mssp.1999.1268","article-title":"On the generalization of the transmissibility concept","volume":"14","author":"Ribeiro","year":"2000","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1006\/mssp.2000.1356","article-title":"The transmissibility concept in MDOF systems","volume":"15","author":"Ribeiro","year":"2001","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_30","unstructured":"Beltran-Carbajal, F. (2011). Whys and wherefores of transmissibility. Vibration Analysis and Control, Intech Open."},{"key":"ref_31","unstructured":"Chen, Q., Chan, Y.W., Worden, K., and Tomlinson, G.R. (1994, January 15\u201318). Structural fault detection using neural networks trained on transmissibility functions. Proceedings of the International Conference on Vibration Engineering, Beijing, China."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1115\/1.1500744","article-title":"Transmissibility as a Differential Indicator of Structural Damage","volume":"124","author":"Johnson","year":"2002","journal-title":"J. Vib. Acoust."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1002\/stc.1781","article-title":"A local excitation and measurement approach for decentralized damage detection using transmissibility functions","volume":"23","author":"Zhu","year":"2015","journal-title":"Struct. Control Health Monit."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1006\/jsvi.1996.0747","article-title":"Structural fault detection using a novelty measure","volume":"201","author":"Worden","year":"1997","journal-title":"J. Sound Vib."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1006\/jsvi.1999.2514","article-title":"Damage detection using outlier analysis","volume":"229","author":"Worden","year":"2000","journal-title":"J. Sound Vib."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1006\/jsvi.2002.5168","article-title":"Experimental validation of a structural health monitoring methodology: Part I. Novelty detection on a laboratory structure","volume":"259","author":"Worden","year":"2003","journal-title":"J. Sound Vib."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1006\/jsvi.2002.5167","article-title":"Experimental validation of a structural health monitoring methodology: Part II. Novelty detection on a gnat aircraft","volume":"259","author":"Manson","year":"2003","journal-title":"J. Sound Vib."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1006\/jsvi.2002.5169","article-title":"Experimental validation of a structural health monitoring methodology: Part III. Damage location on an aircraft wing","volume":"259","author":"Manson","year":"2003","journal-title":"J. Sound Vib."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2165","DOI":"10.1016\/S0045-7949(03)00295-5","article-title":"Structural fault diagnosis and isolation using neural networks based on response-only data","volume":"81","author":"Chen","year":"2003","journal-title":"Comput. Struct."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1016\/j.ymssp.2013.01.020","article-title":"Damage localization using transmissibility functions: A critical review","volume":"38","author":"Deraemaeker","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_41","first-page":"1","article-title":"Damage Detection and Quantification Using Transmissibility Coherence Analysis","volume":"2015","author":"Zhou","year":"2015","journal-title":"Shock Vib."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.engstruct.2017.03.030","article-title":"Cosine based extended transmissibility damage indicators for structural damage detection","volume":"141","author":"Zhou","year":"2017","journal-title":"Eng. Struct."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2001","DOI":"10.1177\/1077546316674544","article-title":"Damage detection using transmissibility compressed by principal component analysis enhanced with distance measure","volume":"24","author":"Zhou","year":"2016","journal-title":"J. Vib. Control"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1177\/1475921716680849","article-title":"Structural damage detection using transmissibility together with hierarchical clustering analysis and similarity measure","volume":"16","author":"Zhou","year":"2016","journal-title":"Struct. Health Monit."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2018\/4892428","article-title":"Structural Damage Identification Based on the Transmissibility Function and Support Vector Machine","volume":"2018","author":"Diao","year":"2018","journal-title":"Shock Vib."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1177\/1475921719838079","article-title":"An analytical perspective about structural damage identification based on transmissibility function","volume":"19","author":"Cheng","year":"2020","journal-title":"Struct. Health Monit."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"106880","DOI":"10.1016\/j.measurement.2019.106880","article-title":"Application of transmissibility measurements to operational modal analysis of railway, highway, and pedestrian cable-stayed bridges","volume":"148","author":"Sun","year":"2019","journal-title":"Measurement"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"291","DOI":"10.12989\/sss.2013.12.3_4.291","article-title":"A novel transmissibility concept based on wavelet transform for structural damage detection","volume":"12","author":"Fan","year":"2013","journal-title":"Smart Struct. Syst."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"2307","DOI":"10.1177\/1077546315614685","article-title":"Local variation detection in MDOF system using wavelet based transmissibility and its application in cracked beam","volume":"23","author":"Li","year":"2015","journal-title":"J. Vib. Control"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1016\/j.ijnonlinmec.2011.03.009","article-title":"Transmissibility of non-linear output frequency response functions with application in detection and location of damage in MDOF structural systems","volume":"46","author":"Lang","year":"2011","journal-title":"Int. J. Non-Linear Mech."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"106918","DOI":"10.1016\/j.ymssp.2020.106918","article-title":"Wavelet-based transmissibility for the analysis of time-variant systems","volume":"145","author":"Dziedziech","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2586","DOI":"10.1109\/78.640725","article-title":"Characterization of signals by the ridges of their wavelet transforms","volume":"45","author":"Carmona","year":"1997","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1006\/jsvi.1998.1616","article-title":"Identification of nonlinear systems using multiscale ridges and skeletons of the wavelet transform","volume":"214","author":"Staszewski","year":"1998","journal-title":"J. Sound Vib."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/15\/8\/2722\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:49:58Z","timestamp":1760136598000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/15\/8\/2722"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,7]]},"references-count":53,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["ma15082722"],"URL":"https:\/\/doi.org\/10.3390\/ma15082722","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,7]]}}}