An efficient method for reliability-based design optimization of nonlinear inelastic steel space frames

This paper proposes an effective numerical procedure for reliability-based design optimization (RBDO) of nonlinear inelastic steel frames by integrating a harmony search technique (HS) for optimization and a robust method for failure probability analysis. The practical advanced analysis using the beam-column approach is used for capturing the nonlinear inelastic behaviors of frames, while a detail implement of HS for discrete optimization of steel frames is introduced. The failure probability of structures is evaluated by using the combination of the improved Latin Hypercube (IHS) and a new effective importance sampling (EIS). The efficiency and accuracy of the proposed procedure are demonstrated through three mathematical examples and five steel frames. The results obtained in this paper prove that the proposed procedure is computationally efficient and can be applied in practical design. Furthermore, it is shown that the use of nonlinear inelastic analysis in the optimization of steel frames yields more realistic results.

[1]  R. Rackwitz,et al.  A benchmark study on importance sampling techniques in structural reliability , 1993 .

[2]  Theodore V. Galambos,et al.  Updating Standard Shape Material Properties Database for Design and Reliability , 2003 .

[3]  Shahram Pezeshk,et al.  Design of Nonlinear Framed Structures Using Genetic Optimization , 2000 .

[4]  S. O. Degertekin,et al.  Harmony search algorithm for minimum cost design of steel frames with semi-rigid connections and column bases , 2010 .

[5]  Gerhart I. Schuëller,et al.  Reliability-based optimization considering design variables of discrete size , 2010 .

[6]  Zong Woo Geem,et al.  A New Heuristic Optimization Algorithm: Harmony Search , 2001, Simul..

[7]  T. J. Mitchell,et al.  Exploratory designs for computational experiments , 1995 .

[8]  Kenny Q. Ye,et al.  Algorithmic construction of optimal symmetric Latin hypercube designs , 2000 .

[9]  Murray J. Clarke.  Plastic-Zone Analysis of Frames , 2018 .

[10]  Barron J. Bichon,et al.  Design of Steel Frames Using Ant Colony Optimization , 2005 .

[11]  Seung-Eock Kim,et al.  Practical Advanced Analysis for Unbraced Steel Frame Design , 1996 .

[12]  Kamran Behdinan,et al.  Particle swarm approach for structural design optimization , 2007 .

[13]  S. Rajeev,et al.  Discrete Optimization of Structures Using Genetic Algorithms , 1992 .

[14]  Seung-Eock Kim,et al.  Practical advanced analysis software for nonlinear inelastic analysis of space steel structures , 2009, Adv. Eng. Softw..

[15]  Wai-Kai Chen.  Stability design of steel frames , 1991 .

[16]  Patrick Murren,et al.  Design-driven harmony search (DDHS) in steel frame optimization , 2014 .

[17]  Zong Woo Geem,et al.  Mathematical and Metaheuristic Applications in Design Optimization of Steel Frame Structures: An Extensive Review , 2013 .

[18]  Murray J. Clarke,et al.  Plastic-zone analysis of 3D steel frames using beam elements , 1999 .

[19]  S. O. Degertekin.  Optimum design of steel frames using harmony search algorithm , 2008 .

[20]  Eric M. Lui,et al.  Structural Stability: Theory and Implementation , 1987 .

[21]  J. A. Bland.  Discrete-variable optimal structural design using tabu search , 1995 .

[22]  S. O. Degertekin.  A comparison of simulated annealing and genetic algorithm for optimum design of nonlinear steel space frames , 2007 .

[23]  Boxin Tang,et al.  SELECTING LATIN HYPERCUBES USING CORRELATION CRITERIA , 1998 .

[24]  Mehmet Polat Saka,et al.  Optimum design of unbraced steel frames to LRFD-AISC using particle swarm optimization , 2012, Adv. Eng. Softw..

[25]  Seung-Eock Kim,et al.  LRFD Steel Design Using Advanced Analysis , 1997 .

[26]  Bruce R. Ellingwood,et al.  Probability Based Load Criteria: Load Factors and Load Combinations , 1982 .

[27]  Abhinav Gupta,et al.  A genetic algorithm for design of moment-resisting steel frames , 2011 .

[28]  Mohsen Ali Shayanfar,et al.  Development of a GA-based method for reliability-based optimization of structures with discrete and continuous design variables using OpenSees and Tcl , 2014 .

[29]  Mehmet Polat Saka,et al.  Genetic algorithm based optimum design of nonlinear planar steel frames with various semi- rigid connections , 2003 .

[30]  John F. Abel,et al.  Yield surface applications in nonlinear steel frame analysis , 1982 .

[31]  Richard J. Balling,et al.  Optimal Steel Frame Design by Simulated Annealing , 1991 .

[32]  Kapil Khandelwal,et al.  Comparison of robustness of metaheuristic algorithms for steel frame optimization , 2015 .

[33]  K. Lee,et al.  A new structural optimization method based on the harmony search algorithm , 2004 .

[34]  M. P. Saka,et al.  Adaptive Harmony Search Method for Structural Optimization , 2010 .

[35]  A. Owen.  Controlling correlations in latin hypercube samples , 1994 .

[36]  Yeong-bin Yang,et al.  Solution method for nonlinear problems with multiple critical points , 1990 .

[37]  O. Hasançebi,et al.  Comparison of non-deterministic search techniques in the optimum design of real size steel frames , 2010 .

[38]  Mehmet Polat Saka,et al.  Optimum design of unbraced rigid frames , 1998 .

[39]  Seung-Eock Kim,et al.  An efficient method for optimizing space steel frames with semi-rigid joints using practical advanced analysis and the micro-genetic algorithm , 2017 .

[40]  Manolis Papadrakakis,et al.  Large-scale reliability-based structural optimization , 2004 .

[41]  O. Hasançebi,et al.  Performance evaluation of metaheuristic search techniques in the optimum design of real size pin jointed structures , 2009 .

[42]  Hong-Shuang Li,et al.  Matlab codes of Subset Simulation for reliability analysis and structural optimization , 2016, Structural and Multidisciplinary Optimization.

[43]  Ramana V. Grandhi,et al.  Improved Distributed Hypercube Sampling , 2002 .