{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T19:24:42Z","timestamp":1776885882483,"version":"3.51.2"},"reference-count":48,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T00:00:00Z","timestamp":1709251200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A methodology for optimal sensor placement is presented in the current work. This methodology incorporates a damage detection framework with simulated damage scenarios and can efficiently provide the optimal combination of sensor locations for vibration-based damage localization purposes. A classic approach in vibration-based methods is to decide the sensor locations based, either directly or indirectly, on the modal information of the structure. While these methodologies perform very well, they are designed to predict the optimal locations of single sensors. The presented methodology relies on the Transmittance Function. This metric requires only output information from the testing procedure and is calculated between two acceleration signals from the structure. As such, the outcome of the presented method is a list of optimal combinations of sensor locations. This is achieved by incorporating a damage detection framework that has been developed and tested in the past. On top of this framework, a new layer is added that evaluates the sensitivity and effectiveness of all possible sensor location combinations with simulated damage scenarios. The effectiveness of each sensor combination is evaluated by calling the damage detection framework and feeding as inputs only a specific combination of acceleration signals each time. The final output is a list of sensor combinations sorted by their sensitivity.<\/jats:p>","DOI":"10.3390\/s24051608","type":"journal-article","created":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T03:31:23Z","timestamp":1709263883000},"page":"1608","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Optimal Sensor Placement for Vibration-Based Damage Localization Using the Transmittance Function"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5544-3157","authenticated-orcid":false,"given":"Ilias","family":"Zacharakis","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Western Macedonia, Bakola & Sialvera, 50100 Kozani, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1044-7485","authenticated-orcid":false,"given":"Dimitrios","family":"Giagopoulos","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Burgos, D.A.T., Vargas, R.C.G., Pedraza, C., Agis, D., and Pozo, F. (2020). Damage Identification in Structural Health Monitoring: A Brief Review from its Implementation to the Use of Data-Driven Applications. Sensors, 20.","DOI":"10.3390\/s20030733"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1016\/j.istruc.2022.08.068","article-title":"A variance-based approach for the detection and localization of cracks in a beam","volume":"44","author":"Kumar","year":"2022","journal-title":"Structures"},{"key":"ref_3","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_4","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1002\/stc.1762","article-title":"Modal identification of damaged frames","volume":"23","author":"Diaferio","year":"2016","journal-title":"Struct. Control Health Monit."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1002\/eqe.3768","article-title":"Detection of infill wall damage due to earthquakes from vibration data","volume":"52","author":"Nicoletti","year":"2023","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"115058","DOI":"10.1016\/j.engstruct.2022.115058","article-title":"A discussion about the Douglas-Reid model updating method and its prospective application to continuous vibration-based SHM of a historical building","volume":"273","author":"Rosati","year":"2022","journal-title":"Eng. Struct."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"114222","DOI":"10.1016\/j.measurement.2024.114222","article-title":"A real-time feature-based clustering approach for vibration-based SHM of large structures","volume":"227","author":"Prasad","year":"2024","journal-title":"Measurement"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2099","DOI":"10.1007\/s00158-018-2024-1","article-title":"Sensor placement optimization applied to laminated composite plates under vibration","volume":"58","author":"Gomes","year":"2018","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1007\/s12065-020-00372-1","article-title":"Sensor placement optimization and damage identification in a fuselage structure using inverse modal problem and firefly algorithm","volume":"13","author":"Gomes","year":"2020","journal-title":"Evol. Intell."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1016\/j.jsv.2018.01.047","article-title":"Structural damage detection-oriented multi-type sensor placement with multi-objective optimization","volume":"422","author":"Lin","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.advengsoft.2018.02.005","article-title":"An efficient approach for optimal sensor placement and damage identification in laminated composite structures","volume":"119","year":"2018","journal-title":"Adv. Eng. Softw."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1260\/0266-3511.29.3.121","article-title":"An Improved Genetic Algorithm for Optimal Sensor Placement in Space Structures Damage Detection","volume":"29","author":"Beygzadeh","year":"2014","journal-title":"Int. J. Space Struct."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"109466","DOI":"10.1016\/j.ymssp.2022.109466","article-title":"Multi-objective sensor placement optimization of helicopter rotor blade based on Feature Selection","volume":"180","author":"Pereira","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2775","DOI":"10.1007\/s12206-015-0606-z","article-title":"Sensor placement optimization for structural modal identification of flexible structures using genetic algorithm","volume":"29","author":"Jung","year":"2015","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"114863","DOI":"10.1016\/j.compstruct.2021.114863","article-title":"A methodology for sensor number and placement optimization for vibration-based damage detection of composite structures under model uncertainty","volume":"279","author":"An","year":"2022","journal-title":"Compos. Struct."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1016\/S0045-7949(01)00027-X","article-title":"Genetic algorithm in structural damage detection","volume":"79","author":"Chou","year":"2001","journal-title":"Comput. Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1007\/s00366-018-0613-7","article-title":"A multiobjective sensor placement optimization for SHM systems considering Fisher information matrix and mode shape interpolation","volume":"35","author":"Gomes","year":"2019","journal-title":"Eng. Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2031","DOI":"10.1016\/S0045-7825(03)00237-8","article-title":"Genetic fuzzy system for damage detection in beams and helicopter rotor blades","volume":"192","author":"Pawar","year":"2003","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1016\/j.procs.2015.05.218","article-title":"Variations of Ant Colony Optimization for the Solution of the Structural Damage Identification Problem","volume":"51","author":"Braun","year":"2015","journal-title":"Procedia Comput. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/s13349-018-0318-z","article-title":"Ant lion optimisation algorithm for structural damage detection using vibration data","volume":"9","author":"Mishra","year":"2019","journal-title":"J. Civ. Struct. Health Monit."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.microrel.2010.09.011","article-title":"Structural health monitoring based on continuous ACO method","volume":"51","author":"Yu","year":"2011","journal-title":"Microelectron. Reliab."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zacharakis, I., and Giagopoulos, D. (2022). Vibration-Based Damage Detection Using Finite Element Modeling and the Metaheuristic Particle Swarm Optimization Algorithm. Sensors, 22.","DOI":"10.3390\/s22145079"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"658","DOI":"10.1016\/j.measurement.2018.01.068","article-title":"A new structural damage detection strategy of hybrid PSO with Monte Carlo simulations and experimental verifications","volume":"122","author":"Chen","year":"2018","journal-title":"Measurement"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1177\/1475921718820015","article-title":"Vibration-based damage localization and quantification in a pretensioned concrete girder using stochastic subspace identification and particle swarm model updating","volume":"19","author":"Cancelli","year":"2020","journal-title":"Struct. Health Monit."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1111\/j.1467-8667.2010.00687.x","article-title":"Finite element model updating using evolutionary strategy for damage detection","volume":"26","author":"Jafarkhani","year":"2011","journal-title":"Comput. -Aided Civ. Infrastruct. Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1177\/1369433218797074","article-title":"Optimal wireless sensor network configuration for structural monitoring using automatic-learning firefly algorithm","volume":"22","author":"Zhou","year":"2018","journal-title":"Adv. Struct. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1007\/s00366-018-0620-8","article-title":"A sunflower optimization (SFO) algorithm applied to damage identification on laminated composite plates","volume":"35","author":"Gomes","year":"2019","journal-title":"Eng. Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"106932","DOI":"10.1016\/j.ymssp.2020.106932","article-title":"An inverse damage location problem applied to AS-350 rotor blades using bat optimization algorithm and multiaxial vibration data","volume":"145","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/j.ins.2014.10.014","article-title":"Reliable fault diagnosis for incipient low-speed bearings using fault feature analysis based on a binary bat algorithm","volume":"294","author":"Kang","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1253","DOI":"10.1016\/j.crme.2018.09.003","article-title":"A damage identification technique for beam-like and truss structures based on FRF and Bat Algorithm","volume":"346","author":"Zenzen","year":"2018","journal-title":"Comptes Rendus Mec."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.swevo.2015.10.010","article-title":"Structural damage detection using artificial bee colony algorithm with hybrid search strategy","volume":"28","author":"Ding","year":"2016","journal-title":"Swarm Evol. Comput."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"e1958","DOI":"10.1002\/stc.1958","article-title":"Optimal placement of triaxial sensors for modal identification using hierarchic wolf algorithm","volume":"24","author":"Yi","year":"2017","journal-title":"Struct. Control Health Monit."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2031","DOI":"10.1109\/JSEN.2018.2789523","article-title":"Robust Optimal Sensor Placement for Uncertain Structures With Interval Parameters","volume":"18","author":"Yang","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1080\/0305215X.2018.1469133","article-title":"Comparison of model order reduction methods for optimal sensor placement for thermo-elastic models","volume":"51","author":"Benner","year":"2019","journal-title":"Eng. Optim."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1016\/S0267-7261(97)00010-9","article-title":"Optimal transducer placement for health monitoring of long span bridge","volume":"16","author":"Heo","year":"1997","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_36","unstructured":"Barthorpe, R.J., and Worden, K. (2009). Encyclopedia of Structural Health Monitoring, John Wiley & Sons."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1002\/eqe.2486","article-title":"Efficient Bayesian sensor placement algorithm for structural identification: A general approach for multi-type sensory systems","volume":"44","author":"Yuen","year":"2015","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1111\/mice.12309","article-title":"Entropy-Based Optimal Sensor Placement for Model Identification of Periodic Structures Endowed with Bolted Joints","volume":"32","author":"Yin","year":"2017","journal-title":"Comput.-Aided Civ. Infrastruct. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1007\/s11431-016-0526-9","article-title":"An interval effective independence method for optimal sensor placement based on non-probabilistic approach","volume":"60","author":"Yang","year":"2016","journal-title":"Sci. Chin. Technol. Sci."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s00521-017-3284-1","article-title":"Structural damage detection using finite element model updating with evolutionary algorithms: A survey","volume":"30","author":"Alkayem","year":"2018","journal-title":"Neural Comput. Appl."},{"key":"ref_41","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the ICNN\u201995\u2014International Conference on Neural Networks 1995, Perth, WA, Australia."},{"key":"ref_42","unstructured":"Eberhart, R., and Kennedy, J. (1995, January 4\u20136). New optimizer using particle swarm theory. Proceedings of the MHS\u201995. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan."},{"key":"ref_43","unstructured":"Shi, Y., and Eberhart, R. (1998, January 4\u20139). A modified particle swarm optimizer. Proceedings of the 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360), Anchorage, AK, USA."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1006\/mssp.1999.1228","article-title":"Structural health monitoring using transmittance functions","volume":"13","author":"Zhang","year":"1999","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1177\/1475921718779190","article-title":"A transmittance-based methodology for damage detection under uncertainty: An application to a set of composite beams with manufacturing variability subject to impact damage and varying operating conditions","volume":"18","author":"Poulimenos","year":"2019","journal-title":"Struct. Health Monit."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.3390\/applmech2040061","article-title":"Response-Only Damage Detection Approach of CFRP Gas Tanks Using Clustering and Vibrational Measurements","volume":"2","author":"Zacharakis","year":"2021","journal-title":"Appl. Mech."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Zacharakis, I., and Giagopoulos, D. (2023). Model-Based Damage Localization Using the Particle Swarm Optimization Algorithm and Dynamic Time Wrapping for Pattern Recreation. Sensors, 23.","DOI":"10.3390\/s23020591"},{"key":"ref_48","unstructured":"MSC Software (2020). MSC Nastran Reference Guide, MSC Software."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/5\/1608\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:07:41Z","timestamp":1760105261000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/5\/1608"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,1]]},"references-count":48,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["s24051608"],"URL":"https:\/\/doi.org\/10.3390\/s24051608","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,1]]}}}