{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T14:07:27Z","timestamp":1765807647090,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T00:00:00Z","timestamp":1547596800000},"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":["51878118"],"award-info":[{"award-number":["51878118"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005047","name":"Natural Science Foundation of Liaoning Province","doi-asserted-by":"publisher","award":["20180551205"],"award-info":[{"award-number":["20180551205"]}],"id":[{"id":"10.13039\/501100005047","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004442","name":"Narodowym Centrum Nauki","doi-asserted-by":"publisher","award":["DEC- 2017\/25\/B\/ST8\/01800"],"award-info":[{"award-number":["DEC- 2017\/25\/B\/ST8\/01800"]}],"id":[{"id":"10.13039\/501100004442","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2018YFC0705604"],"award-info":[{"award-number":["2018YFC0705604"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Adding virtual masses to a structure is an efficient way to generate a large number of natural frequencies for damage identification. The influence of a virtual mass can be expressed by Virtual Distortion Method (VDM) using the response measured by a sensor at the involved point. The proper placement of the virtual masses can improve the accuracy of damage identification, therefore the problem of their optimal placement is studied in this paper. Firstly, the damage sensitivity matrix of the structure with added virtual masses is built. The Volumetric Maximum Criterion of the sensitivity matrix is established to ensure the mutual independence of measurement points for the optimization of mass placement. Secondly, a method of sensitivity analysis and error analysis is proposed to determine the values of the virtual masses, and then an improved version of the Particle Swarm Optimization (PSO) algorithm is proposed for placement optimization of the virtual masses. Finally, the optimized placement is used to identify the damage of structures. The effectiveness of the proposed method is verified by a numerical simulation of a simply supported beam structure and a truss structure.<\/jats:p>","DOI":"10.3390\/s19020340","type":"journal-article","created":{"date-parts":[[2019,1,17]],"date-time":"2019-01-17T11:30:27Z","timestamp":1547724627000},"page":"340","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Optimal Placement of Virtual Masses for Structural Damage Identification"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3554-7036","authenticated-orcid":false,"given":"Jilin","family":"Hou","sequence":"first","affiliation":[{"name":"Department of Civil Engineering &amp; State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1444-6017","authenticated-orcid":false,"given":"Zhenkun","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering &amp; State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China"}]},{"given":"Qingxia","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Dalian Minzu University, Dalian 116650, China"}]},{"given":"Runfang","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering &amp; State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China"},{"name":"College of Urban and Rural Construction, Shanxi Agricultural University, Jinzhong 030801, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9773-0688","authenticated-orcid":false,"given":"\u0141ukasz","family":"Jankowski","sequence":"additional","affiliation":[{"name":"Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw 02-106, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s13349-015-0111-1","article-title":"Recent Advances in Wireless Smart Sensors for Multi-scale Monitoring and Control of Civil Infrastructure","volume":"6","author":"Spencer","year":"2015","journal-title":"J. Civ. Struct. Health Monit."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1002\/stc.1760","article-title":"A degree of dispersion-based damage localization method","volume":"23","author":"An","year":"2016","journal-title":"Struct. Control Health Monit."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Hu, W.H., Tang, D.H., Teng, J., Said, S., and Rohrmann, R.G. (2018). Structural Health Monitoring of a Prestressed Concrete Bridge Based on Statistical Pattern Recognition of Continuous Dynamic Measurements Over 14 Years. Sensors, 18.","DOI":"10.3390\/s18124117"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1002\/stc.426","article-title":"Soft Capacitive Sensor for Structural Health Monitoring of Large-Scale Systems","volume":"19","author":"Laflamme","year":"2012","journal-title":"Struct. Control Health Monit."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"04014186","DOI":"10.1061\/(ASCE)ST.1943-541X.0001151","article-title":"Dynamic Characterization of a Soft Elastomeric Capacitor for Structural Health Monitoring","volume":"141","author":"Laflamme","year":"2014","journal-title":"ASCE J. Struct. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Yang, Y., Zhu, Y.H., Wang, L.L., Jia, B.Y., and Jin, R.Y. (2018). Structural Damage Identification of Bridges from Passing Test Vehicles. Sensors, 18.","DOI":"10.3390\/s18114035"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Fu, Y.G., Hoang, T., Mechiow, K., Kim, J.R., Zhang, D.C., and Spencer, B.F. (2018). Sudden Event Monitoring of Civil Infrastructure Using Demand-Based Wireless Smart Sensors. Sensors, 18.","DOI":"10.3390\/s18124480"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"085024","DOI":"10.1088\/1361-665X\/aa75ef","article-title":"A Large-area Strain Sensing Technology for Monitoring Fatigue Cracks in Steel Bridges","volume":"26","author":"Kong","year":"2017","journal-title":"Smart Mater. Struct."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.12989\/sss.2016.18.6.1189","article-title":"Wavelet analysis based damage localization in steel frames with bolted connections","volume":"18","author":"Pnevmatikos","year":"2016","journal-title":"Smart Struct. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.engstruct.2012.07.031","article-title":"Automated modal identification in operational conditions and its application to bridges","volume":"46","author":"Ubertini","year":"2013","journal-title":"Eng. Struct."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/j.engstruct.2013.12.036","article-title":"Natural frequencies identification of a reinforced concrete beam using carbon nanotube cement-based sensors","volume":"60","author":"Ubertini","year":"2013","journal-title":"Eng. Struct."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Xu, K., Deng, Q.S., Cai, L.J., Ho, S.C., and Song, G.B. (2018). Damage Detection of a Concrete Column Subject to Blast Loads Using Embedded Piezoceramic Transducers. Sensors, 18.","DOI":"10.3390\/s18051377"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zhang, J., Xu, J.D., Guan, W.Q., and Du, G.F. (2018). Damage Detection of Concrete-Filled Square Steel Tube (CFSST) Column Joints under Cyclic Loading Using Piezoceramic Transducers. Sensors, 18.","DOI":"10.3390\/s18103266"},{"key":"ref_14","first-page":"741","article-title":"Sparsity-constrained extended Kalman filter concept for damage localization and identification in mechanical structures","volume":"21","author":"Ginsberg","year":"2018","journal-title":"Smart Struct. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Jiang, T.Y., Zhang, Y.W., Wang, L., Zhang, L., and Song, G.B. (2018). Monitoring Fatigue Damage of Modular Bridge Expansion Joints Using Piezoceramic Transducers. Sensors, 18.","DOI":"10.3390\/s18113973"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Zhang, H.B., Hou, S., and Ou, J.P. (2018). Validation of Finite Element Model by Smart Aggregate-Based Stress Monitoring. Sensors, 18.","DOI":"10.3390\/s18114062"},{"key":"ref_17","first-page":"157","article-title":"A mass or stiffness addition technique for structural parameter updating","volume":"7","author":"Nalitolela","year":"1992","journal-title":"Int. J. Anal. Exp. Modal Anal."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1006\/mssp.1993.1005","article-title":"Updating model parameters by adding an imagined stiffness to the structure","volume":"7","author":"Nalitolela","year":"1993","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1016\/j.compstruc.2010.07.005","article-title":"Damage identification using modal, static and thermographic analysis with additional control parameters","volume":"88","author":"Dems","year":"2010","journal-title":"Comput. Struct."},{"key":"ref_20","first-page":"295","article-title":"Influencing factors of beam structure damage identification based on additional mass","volume":"18","author":"Lu","year":"2017","journal-title":"J. PLA Univ. Sci. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"04018097","DOI":"10.1061\/(ASCE)EM.1943-7889.0001523","article-title":"Structural Damage Localization and Quantification Based on Additional Virtual Masses and Bayesian Theory","volume":"144","author":"Hou","year":"2018","journal-title":"J. Eng. Mech."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"251","DOI":"10.2514\/3.20635","article-title":"Sensor placement for on-orbit modal identification and correlation of large space structures","volume":"14","author":"Kammer","year":"1991","journal-title":"J. Guid. Control Dyn."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"256","DOI":"10.2514\/2.7509","article-title":"Sensor Placement Methodologies for Dynamic Testing","volume":"36","author":"Papadopoulos","year":"1998","journal-title":"AIAA J."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"380","DOI":"10.2514\/3.2874","article-title":"Reduction of Stiffness and Mass Matrices","volume":"3","author":"GUYAN","year":"1965","journal-title":"AIAA J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1252","DOI":"10.4028\/www.scientific.net\/AMM.670-671.1252","article-title":"An Effective Independence-Improved Modal Strain Energy Method for Optimal Sensor Placement of Bridge Structures","volume":"670\u2013671","author":"Zhan","year":"2014","journal-title":"Appl. Mech. Mater."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1002\/stc.1806","article-title":"Multiaxial sensor placement optimization in structural health monitoring using distributed wolf algorithm","volume":"23","author":"Yi","year":"2016","journal-title":"Struct. Control Health Monit."},{"key":"ref_27","first-page":"148","article-title":"Optimal sensor placement for hydraulic structures based on effective independence-total displacement method","volume":"35","author":"Zhang","year":"2016","journal-title":"J. Vib. Shock"},{"key":"ref_28","unstructured":"Silvers, J.E. (2013). Frequency Response Sensitivity Analysis to Determine Sensor Placement for Vibration-Based Damage Detection in Structural Elements. [Ph.D. Thesis, Purdue University]."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1080\/0305215X.2012.690870","article-title":"Optimization of sensor placement to detect damage in flexible plates","volume":"45","author":"Bruggi","year":"2013","journal-title":"Eng. Optim."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Li, P., Huang, L.W., and Peng, J.C. (2018). Sensor Distribution Optimization for Structural Impact Monitoring Based on NSGA-II and Wavelet Decomposition. Sensors, 18.","DOI":"10.3390\/s18124264"},{"key":"ref_31","unstructured":"Eberhart, R., and Kennedy, J. (1995). A New Optimizer Using Particle Swarm Theory, Micro Machine and Human Science."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1002\/stc.1550","article-title":"Optimal multiaxial sensor placement for modal identification of large structures","volume":"21","author":"He","year":"2014","journal-title":"Struct. Control Health Monit."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Zhang, X., Wang, P., Xing, J.C., and Yang, Q.L. (2014). Optimal Sensor Placement of Long-Span Cable-Stayed Bridges Based on Particle Swarm Optimization Algorithm, Springer. Practical Applications of Intelligent Systems.","DOI":"10.1007\/978-3-642-54927-4_20"},{"key":"ref_34","unstructured":"Kennedy, J., and Eberhart, R.C. (1997, January 12\u201315). A discrete binary version of the particle swarm optimization algorithm. Computational cybernatics and simulation. Proceedings of the 1997 IEEE International Conference on Systems, Man, and Cybernetics\u2014Computational Cybernetics and Simulation (SMC 97), Orlando, FL, USA."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.rser.2018.07.020","article-title":"A review of power management strategies and component sizing methods for hybrid vehicles","volume":"96","author":"Huang","year":"2018","journal-title":"Renew. Sustain. Energy Rev."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/2\/340\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:26:25Z","timestamp":1760185585000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/2\/340"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,16]]},"references-count":35,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["s19020340"],"URL":"https:\/\/doi.org\/10.3390\/s19020340","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,1,16]]}}}