{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T05:38:24Z","timestamp":1773293904580,"version":"3.50.1"},"reference-count":60,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T00:00:00Z","timestamp":1557878400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Actuators"],"abstract":"<jats:p>A buildings resilience to seismic activity can be increased by providing ways for the structure to dynamically counteract the effect of the Earth\u2019s crust movements. This ability is fundamental in certain regions of the globe, where earthquakes are more frequent, and can be achieved using different strategies. State-of-the-art anti-seismic buildings have, embedded on their structure, mostly passive actuators such as base isolation, Tuned Mass Dampers (TMD) and viscous dampers that can be used to reduce the effect of seismic or even wind induced vibrations. The main disadvantage of this type of building vibration reduction strategies concerns their inability to adapt their properties in accordance to both the excitation signal or structural behaviour. This adaption capability can be promoted by adding to the building active type actuators operating under a closed-loop. However, these systems are substantially larger than passive type solutions and require a considerable amount of energy that may not be available during a severe earthquake due to power grid failure. An intermediate solution between these two extremes is the introduction of semi-active actuators such as magneto\u2013rheological dampers. The inclusion of magneto\u2013rheological actuators is among one of the most promising semi-active techniques. However, the overall performance of this strategy depends on several aspects such as the actuators number and location within the structure and the vibration sensors network. It can be the case where the installation leads to a non-collocated system which presents additional challenges to control. This paper proposes to tackle the problem of controlling the vibration of a non-collocated three-storey building by means of a brain\u2013emotional controller tuned using an evolutionary algorithm. This controller will be used to adjust the stiffness coefficient of a magneto\u2013rheological actuator such that the building\u2019s frame oscillation under earthquake excitation, is mitigated. The obtained results suggest that, using this control strategy, it is possible to reduce the building vibration to secure levels.<\/jats:p>","DOI":"10.3390\/act8020043","type":"journal-article","created":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T11:37:40Z","timestamp":1557920260000},"page":"43","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Semi-Active Vibration Control of a Non-Collocated Civil Structure Using Evolutionary-Based BELBIC"],"prefix":"10.3390","volume":"8","author":[{"given":"Manuel","family":"Braz C\u00e9sar","sequence":"first","affiliation":[{"name":"Instituto Polit\u00e9cnico de Bragan\u00e7a, Escola Superior de Tecnologia e Gest\u00e3o, 5300-253 Bragan\u00e7a, Portugal"},{"name":"Institute of R&amp;D in Structures and Construction (CONSTRUCT), Laboratory for Earthquake and Structural Engineering (LESE), 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7616-1383","authenticated-orcid":false,"given":"Jo\u00e3o Paulo","family":"Coelho","sequence":"additional","affiliation":[{"name":"Instituto Polit\u00e9cnico de Bragan\u00e7a, Escola Superior de Tecnologia e Gest\u00e3o, 5300-253 Bragan\u00e7a, Portugal"},{"name":"CeDRI\u2014Centro de Investiga\u00e7\u00e3o em Digitaliza\u00e7\u00e3o e Rob\u00f3tica Inteligente, 5300-253 Bragan\u00e7a, Portugal"}]},{"given":"Jos\u00e9","family":"Gon\u00e7alves","sequence":"additional","affiliation":[{"name":"Instituto Polit\u00e9cnico de Bragan\u00e7a, Escola Superior de Tecnologia e Gest\u00e3o, 5300-253 Bragan\u00e7a, Portugal"},{"name":"CeDRI\u2014Centro de Investiga\u00e7\u00e3o em Digitaliza\u00e7\u00e3o e Rob\u00f3tica Inteligente, 5300-253 Bragan\u00e7a, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1061\/(ASCE)0733-9399(2000)126:8(795)","article-title":"Semiactive Control Strategies for MR Dampers: Comparative Study","volume":"126","author":"Jansen","year":"2000","journal-title":"J. Eng. Mech."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.jsv.2017.06.007","article-title":"A concept for semi-active vibration control with a serial-stiffness-switch system","volume":"405","author":"Min","year":"2017","journal-title":"J. Sound Vib."},{"key":"ref_3","unstructured":"Lynch, J.P., Loh, K.J., Hou, T.C., Wang, Y., Yi, J., Yun, C.B., Lu, K., and Loh, C.H. (2005, January 16\u201318). Validation case studies of wireless monitoring systems in civil structures. Proceedings of the 2nd International Conference on Structural Health Monitoring of Intelligent Infrastructure, Shenzhen, China."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1303","DOI":"10.1002\/eqe.682","article-title":"Experimental verification of a wireless sensing and control system for structural control using MR dampers","volume":"36","author":"Loh","year":"2007","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Swartz, R.A., and Lynch, J.P. (2007, January 9\u201313). Partial Decentralized Wireless Control Through Distributed Computing for Seismically Excited Civil Structures: Theory and Validation. Proceedings of the 2007 American Control Conference (ACC \u201907), New York, NY, USA.","DOI":"10.1109\/ACC.2007.4282884"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"321","DOI":"10.12989\/sss.2007.3.3.321","article-title":"Decentralized civil structural control using real-time wireless sensing and embedded computing","volume":"3","author":"Wang","year":"2007","journal-title":"Smart Struct. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1002\/stc.214","article-title":"Implementation of a closed-loop structural control system using wireless sensor networks","volume":"15","author":"Lynch","year":"2008","journal-title":"Struct. Control Health Monit."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1061\/(ASCE)ST.1943-541X.0000002","article-title":"Strategic Network Utilization in a Wireless Structural Control System for Seismically Excited Structures","volume":"135","author":"Swartz","year":"2009","journal-title":"J. Struct. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1002\/eqe.862","article-title":"Decentralized H\u221e controller design for large-scale civil structures","volume":"38","author":"Wang","year":"2009","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Law, K.H., Wang, Y., Swartz, A., and Lynch, J.P. (September, January 28). Wireless sensing and vibration control of civil structures. Proceedings of the 2010 IEEE International Conference on Wireless Information Technology and Systems, Honolulu, HI, USA.","DOI":"10.1109\/ICWITS.2010.5611849"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kane, M.B., Lynch, J.P., and Law, K. (July, January 29). Market-based control of shear structures utilizing magnetorheological dampers. Proceedings of the 2011 American Control Conference, San Francisco, CA, USA.","DOI":"10.1109\/ACC.2011.5990896"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Swartz, R.A. (July, January 29). Reduced-order modal-domain structural control for seismic vibration control over wireless sensor networks. Proceedings of the 2011 American Control Conference (ACC \u201911), San Francisco, CA, USA.","DOI":"10.1109\/ACC.2011.5990961"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4300","DOI":"10.21595\/jve.2017.18924","article-title":"Multi-agent replicator controller for sustainable vibration control of smart structures","volume":"19","author":"Soto","year":"2017","journal-title":"J. Vibroeng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"e1990","DOI":"10.1002\/stc.1990","article-title":"Low-force magneto\u2013rheological damper design for small-scale structural control","volume":"24","author":"Winter","year":"2017","journal-title":"Struct. Control Health Monit."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Ab\u00e9, M. (1998). Structural Monitoring of Civil Structures using Vibration Measurement\u2014Current Practice and Future. Artificial Intelligence in Structural Engineering, Springer.","DOI":"10.1007\/BFb0030439"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Braz-C\u00e9sar, M.B., Gon\u00e7alves, J., Coelho, J., and de Barros, R.C. (2016, January 14\u201316). Brain Emotional Learning Based Control of a SDOF Structural System with a MR Damper. Proceedings of the CONTROLO 2016, Guimar\u00e3es, Portugal.","DOI":"10.1007\/978-3-319-43671-5_46"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Braz-C\u00e9sar, M., Coelho, J.P., and Gon\u00e7alves, J. (2018). Evolutionary-Based BEL Controller Applied to a Magneto\u2013Rheological Structural System. Actuators, 7.","DOI":"10.3390\/act7020029"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1177\/1045389X08099660","article-title":"Development of LuGre friction model for large-scale magneto\u2013rheological fluid damper","volume":"20","author":"Yang","year":"2009","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.engstruct.2005.06.013","article-title":"Simplified inverse dynamics models for MR fluid dampers","volume":"28","author":"Tsang","year":"2005","journal-title":"Eng. Struct."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1088\/0964-1726\/23\/1\/015019","article-title":"Precise Stiffness and Damping Emulation with MR Dampers and its Application to Semi-active Tuned Mass Dampers of Wolgograd Bridge","volume":"23","author":"Weber","year":"2014","journal-title":"Smart Mater. Struct."},{"key":"ref_21","unstructured":"Wang, E.-R., Ma, X.Q., Rakheja, S., and Su, C.-Y. (2005, January 27\u201329). Force tracking control of vehicle vibration with MR-dampers. Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, Limassol, Cyprus."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1002\/stc.1750","article-title":"Robust force tracking control scheme for MR dampers","volume":"22","author":"Weber","year":"2015","journal-title":"Struct. Control Health Monit."},{"key":"ref_23","unstructured":"Pan, G., Matsuhisa, H., and Honda, Y. (2000, January 22\u201328). Analytical model of a magnetorheological damper and its application to the vibration control. Proceedings of the 26th Annual Conference of the Industrial Electronics Society (IECON 2000), Nagoya, Japan."},{"key":"ref_24","unstructured":"Dalvi, B. (2015). Modelling and Testing of MR Dampers. [Master\u2019s Thesis, Coventry University]."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1061\/(ASCE)0733-9399(1997)123:3(230)","article-title":"Phenomenological Model for Magnetorheological Dampers","volume":"123","author":"Spencer","year":"1997","journal-title":"J. Eng. Mech."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1006\/jsvi.2000.3539","article-title":"A hysteresis model for the field-dependent damping force of a magnetorheological damper","volume":"245","author":"Choi","year":"1998","journal-title":"J. Sound Vib."},{"key":"ref_27","unstructured":"Yang, G. (2001). Large-Scale Magnetorheological Fluid Damper for Vibration Mitigation: Modeling, Testing and Control. [Ph.D. Thesis, University of Notre Dame]."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Rossi, A., Orsini, F., Scorza, A., Botta, F., Belfiore, N., and Sciuto, S. (2016). A Review on Parametric Dynamic Models of Magnetorheological Dampers and Their Characterization Methods. Actuators, 7.","DOI":"10.3390\/act7020016"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1088\/0964-1726\/5\/5\/006","article-title":"Modeling and control of magnetorheological dampers for seismic response reduction","volume":"5","author":"Dyke","year":"1996","journal-title":"Smart Mater. Struct."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"e2257","DOI":"10.1002\/stc.2257","article-title":"Curved surface sliders with friction damping, linear viscous damping, bow tie friction damping and semi-actively controlled properties","volume":"25","author":"Weber","year":"2018","journal-title":"Struct. Control Health Monit."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1002\/stc.58","article-title":"LuGre friction model for a magneto\u2013rheological damper","volume":"12","year":"2005","journal-title":"J. Struct. Control. Health Monit."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1080\/10798587.2004.10642862","article-title":"Introducing Belbic: Brain Emotional Learning Based Intelligent Controller","volume":"10","author":"Lucas","year":"2004","journal-title":"Intell. Autom. Soft Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1080\/01969720118947","article-title":"Emotional Learning: A computational model of the amygdala","volume":"32","author":"Balkenius","year":"2001","journal-title":"Cybern. Syst."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Khorashadizadeh, S., and Mahdian, M. (2016, January 27\u201328). Voltage tracking control of DC-DC boost converter using brain emotional learning. Proceedings of the 4th International Conference on Control, Instrumentation, and Automation, Qazvin, Iran.","DOI":"10.1109\/ICCIAutom.2016.7483172"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"158","DOI":"10.5772\/61817","article-title":"A Sliding Mode Control Using Brain Limbic System Control Strategy for a Robotic Manipulator","volume":"12","author":"Yi","year":"2015","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"84","DOI":"10.5772\/51841","article-title":"Implementation of an Intelligent Adaptive Controller for an Electrohydraulic Servo System Based on a Brain Mechanism of Emotional Learning","volume":"9","author":"Sadeghieh","year":"2012","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"478","DOI":"10.5370\/JEET.2013.8.3.478","article-title":"Designing an Emotional Intelligent Controller for IPFC to Improve the Transient Stability Based on Energy Function","volume":"8","author":"Jafari","year":"2013","journal-title":"J. Electr. Eng. Technol."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Javan-Roshtkhari, M., Arami, A., and Lucas, C. (2009, January 10\u201312). Emotional control of inverted pendulum system: A soft switching from imitative to emotional learning. Proceedings of the 4th International Conference on Autonomous Robots and Agents, Wellington, New Zealand.","DOI":"10.1109\/ICARA.2000.4803996"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.jare.2010.08.004","article-title":"PSO-BELBIC scheme for two-coupled distillation column process","volume":"2","author":"Dorrah","year":"2011","journal-title":"J. Adv. Res."},{"key":"ref_40","unstructured":"Fard, F., Shahgholian, G., Rajabi, A., and Habibollahi, M. (2010, January 27\u201329). Brain Emotional Learning Based Intelligent Controller for Permanet Magnet Synchronous Motor. Proceedings of the IPEC2010, Singapore."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Huang, G., Zhen, Z., and Wang, D. (2008, January 20\u201322). Brain Emotional Learning Based Intelligent Controller for Nonlinear System. Proceedings of the Second International Symposium on Intelligent Information Technology Application, Shanghai, China.","DOI":"10.1109\/IITA.2008.530"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Mohammed, M., and Bijoy, K. (2011, January 14\u201316). An Intelligent Automatic Level Controller for Speech Signals: BELBIC. Proceedings of the IEEE International Conference on Signal Processing, Communications and Computing, Xi\u2019an, China.","DOI":"10.1109\/ICSPCC.2011.6061585"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Valikhani, M., and Sourkounis, C. (2014, January 18\u201320). A brain emotional learning-based intelligent controller (BELBIC) for DFIG system. Proceedings of the International Symposium on Power Electronics, Electrical Drives, Automation and Motion, Ischia, Italy.","DOI":"10.1109\/SPEEDAM.2014.6871951"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Mei, Y., Tan, G., and Liu, Z. (2017). An Improved Brain-Inspired Emotional Learning Algorithm for Fast Classification. Algorithms, 10.","DOI":"10.3390\/a10020070"},{"key":"ref_45","unstructured":"Shahmirzadi, D. (2005). Computational Modeling of the Brain Limbic System and Its Application in Control Engineering. [Ph.D. Thesis, Texas A & M University]."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"16009","DOI":"10.1016\/j.ifacol.2017.08.1912","article-title":"A new brain emotional learning Simulink\u00ae toolbox for control systems design","volume":"50","author":"Coelho","year":"2017","journal-title":"IFAC-PapersOnLine"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Jafarzadeh, S., Motlagh, M.R.J., Barkhordari, M., and Mirheidari, R. (2008, January 25\u201327). A new Lyapunov based algorithm for tuning BELBIC controllers for a group of linear systems. Proceedings of the 16th Mediterranean Conference on Control and Automation, Ajaccio, France.","DOI":"10.1109\/MED.2008.4602180"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Garmsiri, N., and Najafi, F. (2010, January 7\u20139). Fuzzy tuning of Brain Emotional Learning Based Intelligent Controllers. Proceedings of the 8th World Congress on Intelligent Control and Automation, Jinan, China.","DOI":"10.1109\/WCICA.2010.5554831"},{"key":"ref_49","unstructured":"Kennedy, J., and Eberhart, R. (1995, January 9\u201313). Particle swarm optimization. Proceedings of the 1995 International Conference on Neural Networks (ICNN\u201995), Paris, France."},{"key":"ref_50","first-page":"1181","article-title":"A Survey of the State of the Art in Particle Swarm Optimization","volume":"49","author":"Eslami","year":"2012","journal-title":"Res. J. Appl. Sci. Eng. Technol."},{"key":"ref_51","first-page":"1","article-title":"A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications","volume":"2015","author":"Zhang","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_52","unstructured":"Eberhart, R.C., Shi, Y., and Kennedy, J. (2001). Swarm Intelligence, Academic Press."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Shi, Y., and Eberhart, R.C. (1998). Parameter selection in particle swarm optimization. Evolutionary Programming VII. EP 1998, Springer.","DOI":"10.1007\/BFb0040810"},{"key":"ref_54","unstructured":"Pedersen, M.E.H. (2010). Good Parameters for Particle Swarm Optimization, Hvass Laboratories. Technical Report HL1001."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.swevo.2011.10.001","article-title":"Constraint-handling in nature-inspired numerical optimization: Past, present and future","volume":"1","author":"Coello","year":"2011","journal-title":"Swarm Evol. Comput."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Valizadeh, S., Jamali, M.R., and Lucas, C. (2008, January 14\u201317). A particle-swarm-based approach for optimum design of BELBIC controller in AVR system. Proceedings of the International Conference on Control, Automation and Systems, Seoul, Korea.","DOI":"10.1109\/ICCAS.2008.4694214"},{"key":"ref_57","unstructured":"Jafari, M., Shahri, A.M., and Elyas, S.H. (November, January 31). Optimal tuning of Brain Emotional Learning Based Intelligent Controller using Clonal Selection Algorithm. Proceedings of the 3th International eConference on Computer and Knowledge Engineering (ICCKE), Mashhad, Iran."},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Valipour, M.H., Maleki, K.N., and Ghidary, S.S. (2015). Optimization of Emotional Learning Approach to Control Systems with Unstable Equilibrium. Software Engineering, Artificial Intelligence, Networking and Parallel\/Distributed Computing, Springer.","DOI":"10.1007\/978-3-319-10389-1_4"},{"key":"ref_59","first-page":"8760351","article-title":"Brain Emotional Learning Based Intelligent Decoupler for Nonlinear Multi-Input Multi-Output Distillation Columns","volume":"2017","year":"2017","journal-title":"Math. Probl. Eng."},{"key":"ref_60","unstructured":"C\u00e9sar, M.T.B. (2015). Vibration Control of Building Structures Using MagnetoRheological Dampers. [Ph.D. Thesis, Faculty of Engineering of the University of Porto]."}],"container-title":["Actuators"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2076-0825\/8\/2\/43\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:52:06Z","timestamp":1760187126000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2076-0825\/8\/2\/43"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,15]]},"references-count":60,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,6]]}},"alternative-id":["act8020043"],"URL":"https:\/\/doi.org\/10.3390\/act8020043","relation":{},"ISSN":["2076-0825"],"issn-type":[{"value":"2076-0825","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,15]]}}}