Robust design optimization of friction dampers for structural response control

SUMMARY It is known that the use of passive energy dissipation devices, as friction dampers, reduces considerably the dynamic response of a structure subjected to earthquake ground motions. However, the parameters of each damper as well as the best placement of these devices remain difficult to determine. Thus, in this paper, robust design optimization of friction dampers to control the structural response against earthquakes is proposed. In order to take into account uncertainties present in the system, some of its parameters are modeled as random variables, and consequently, the structural response becomes stochastic. To perform the robust optimization of such system, two objective functions are simultaneously considered: the mean and variance of the maximum displacement. This approach allows finding a set of Pareto-optimal solutions. A genetic algorithm, the NSGA-II (Nondominated Sorting Genetic Algorithm), is applied to solve the resulting multi-objective optimization problem. For illustration purposes, a six-story shear building is analyzed. The results showed that the proposed method was able to reduce the mean maximum displacement in approximately 70% and the variance of the maximum displacement in almost 99% with only three dampers. Copyright © 2014 John Wiley & Sons, Ltd.

[1]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[2]  C. C. Lin,et al.  Two‐stage optimum design of tuned mass dampers with consideration of stroke , 2009 .

[3]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[4]  R. J. Rogers,et al.  Equivalent viscous damping models of Coulomb friction in multi-degree-of-freedom vibration systems , 1995 .

[5]  John E. Dennis,et al.  Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems , 1998, SIAM J. Optim..

[6]  Mohtasham Mohebbi,et al.  Designing optimal multiple tuned mass dampers using genetic algorithms (GAs) for mitigating the seismic response of structures , 2013 .

[7]  Marco Antonio Luersen,et al.  Optimization of hybrid laminated composites using a genetic algorithm , 2009 .

[8]  Jorge Daniel Riera,et al.  Controle de vibrações de estruturas utilizando amortecedores por atrito , 2008 .

[9]  H. Tajimi,et al.  Statistical Method of Determining the Maximum Response of Building Structure During an Earthquake , 1960 .

[10]  Naser Mostaghel,et al.  REPRESENTATIONS OF COULOMB FRICTION FOR DYNAMIC ANALYSIS , 1997 .

[11]  Rafael Holdorf Lopez,et al.  Uncertainty quantification for algebraic systems of equations , 2013 .

[12]  Genda Chen,et al.  OPTIMAL PLACEMENT OF MULTIPLE TUNED MASS DAMPERS FOR SEISMIC STRUCTURES , 2001 .

[13]  J. N. Kapur,et al.  Entropy Optimization Principles and Their Applications , 1992 .

[14]  Rafael Holdorf Lopez,et al.  Optimization of a stochastic dynamical system , 2014 .

[15]  J. N. Kapur,et al.  Entropy optimization principles with applications , 1992 .

[16]  Weilian Qu,et al.  Optimum properties of multiple tuned mass dampers for reduction of translational and torsional response of structures subject to ground acceleration , 2006 .

[17]  Ersin Aydin.  Optimal damper placement based on base moment in steel building frames , 2012 .

[18]  John E. Mottershead,et al.  A review of robust optimal design and its application in dynamics , 2005 .

[19]  Olof Friberg,et al.  Optimal placement of dampers in structures using genetic algorithm , 2006 .

[20]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[21]  Rubens Sampaio,et al.  A new algorithm for the robust optimization of rotor-bearing systems , 2014 .

[22]  Yozo Fujino,et al.  Optimal tuned mass damper for seismic applications and practical design formulas , 2008 .

[23]  Letícia Fleck Fadel Miguel,et al.  Estudo teórico e experimental de amortecedores de vibração por atrito , 2002 .

[24]  Jinkoo Kim,et al.  Simple design procedure of a friction damper for reducing seismic responses of a single-story structure , 2010 .

[25]  A. Messac,et al.  The normalized normal constraint method for generating the Pareto frontier , 2003 .

[26]  Ersin Aydin,et al.  Optimal damper distribution for seismic rehabilitation of planar building structures , 2007 .

[27]  Leandro Fleck Fadel Miguel,et al.  Discussion of paper: “Estimating optimum parameters of tuned mass dampers using harmony search” [Eng. Struct. 33 (9) (2011) 2716–2723] , 2013 .

[28]  Mohamed Ichchou,et al.  Reliability based robust design optimization for tuned mass damper in passive vibration control of deterministic/uncertain structures , 2013 .

[29]  Biswajit Basu,et al.  A closed‐form optimal tuning criterion for TMD in damped structures , 2007 .

[30]  Giuseppe Marano,et al.  Constrained reliability-based optimization of linear tuned mass dampers for seismic control , 2007 .

[31]  P. Seshu,et al.  Multi-objective optimization of piezo actuator placement and sizing using genetic algorithm , 2009 .

[32]  Yoyong Arfiadi,et al.  OPTIMUM PLACEMENT AND PROPERTIES OF TUNED MASS DAMPERS USING HYBRID GENETIC ALGORITHMS , 2011 .

[33]  André T. Beck,et al.  Optimization Under Uncertainties , 2013 .

[34]  Zhao-Dong Xu,et al.  Optimal analysis and experimental study on structures with viscoelastic dampers , 2004 .

[35]  T. T. Soong,et al.  Passive Energy Dissipation Systems in Structural Engineering , 1997 .

[36]  Jin-Su Kang,et al.  Robust optimization for engineering design , 2012 .

[37]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[38]  R. H. Lopez,et al.  Robust optimization of a flexible rotor-bearing system using the Campbell diagram , 2011 .

[39]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[40]  S. Narayanan,et al.  Optimal semi-active preview control response of a half car vehicle model with magnetorheological damper , 2009 .

[41]  Giuseppe Marano,et al.  A comparison between different optimization criteria for tuned mass dampers design , 2010 .

[42]  Yen-Po Wang,et al.  Optimal design theories and applications of tuned mass dampers , 2006 .

[43]  Mahendra P. Singh,et al.  Optimal placement of dampers for passive response control , 2002 .

[44]  Nam Hoang,et al.  Optimal placement and tuning of multiple tuned mass dampers for suppressing multi-mode structural response , 2006 .

[45]  Anjan Dutta,et al.  Coupled tuned mass dampers for control of coupled vibrations in asymmetric buildings , 2006 .

[46]  Leandro Fleck Fadel Miguel,et al.  Multimodal size, shape, and topology optimisation of truss structures using the Firefly algorithm , 2013, Adv. Eng. Softw..

[47]  Bernhard Sendhoff,et al.  Robust Optimization - A Comprehensive Survey , 2007 .

[48]  Ehsan Dehghan-Niri,et al.  Generalized framework for robust design of tuned mass damper systems , 2011 .

[49]  Christian Soize,et al.  Design optimization with an uncertain vibroacoustic model , 2008 .

[50]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[51]  Seyed Mehdi Zahrai,et al.  Effectiveness‐robustness objectives in MTMD system design: An evolutionary optimal design methodology , 2010 .

[52]  David W. Coit,et al.  Multi-objective optimization using genetic algorithms: A tutorial , 2006, Reliab. Eng. Syst. Saf..