# Frontiers of Structural and Civil Engineering

 Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (4) : 800-820     https://doi.org/10.1007/s11709-019-0517-7
 RESEARCH ARTICLE
Novel decoupled framework for reliability-based design optimization of structures using a robust shifting technique
Mohammad Reza GHASEMI1(), Charles V. CAMP2, Babak DIZANGIAN3
1. Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan 9816745565, Iran
2. Department of Civil Engineering, The University of Memphis, Memphis, TN 38152, USA
3. Department of Civil Engineering, Velayat University, Iranshahr 9911131311, Iran
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 Abstract In a reliability-based design optimization (RBDO), computation of the failure probability (Pf) at all design points through the process may suitably be avoided at the early stages. Thus, to reduce extensive computations of RBDO, one could decouple the optimization and reliability analysis. The present work proposes a new methodology for such a decoupled approach that separates optimization and reliability analysis into two procedures which significantly improve the computational efficiency of the RBDO. This technique is based on the probabilistic sensitivity approach (PSA) on the shifted probability density function. Stochastic variables are separated into two groups of desired and non-desired variables. The three-phase procedure may be summarized as: Phase 1, apply deterministic design optimization based on mean values of random variables; Phase 2, move designs toward a reliable space using PSA and finding a primary reliable optimum point; Phase 3, applying an intelligent self-adaptive procedure based on cubic B-spline interpolation functions until the targeted failure probability is reached. An improved response surface method is used for computation of failure probability. The proposed RBDO approach could significantly reduce the number of analyses required to less than 10% of conventional methods. The computational efficacy of this approach is demonstrated by solving four benchmark truss design problems published in the structural optimization literature. Corresponding Authors: Mohammad Reza GHASEMI Online First Date: 04 March 2019    Issue Date: 10 July 2019
 Cite this article: Mohammad Reza GHASEMI,Charles V. CAMP,Babak DIZANGIAN. Novel decoupled framework for reliability-based design optimization of structures using a robust shifting technique[J]. Front. Struct. Civ. Eng., 2019, 13(4): 800-820. URL: http://journal.hep.com.cn/fsce/EN/10.1007/s11709-019-0517-7 http://journal.hep.com.cn/fsce/EN/Y2019/V13/I4/800
 Fig.1  Normal and lognormal PDF of Young’s modulus with different values of COV Fig.2  Reaching procedure from d* to the first point in the safe space x* using PDF shifting technique Fig.3  Flowchart for the three-phased RBDO approach Fig.4  Flowchart of proposed PSA and ISAP based truss RBDO approach Fig.5  10-bar planar truss, example 1 Tab.1  Statistical properties of 10-bar truss problem Tab.2  RBDO results comparison of 10-bar planar truss example Fig.6  Convergence history for the 10-bar truss problem (Phase 2) Fig.7  A close up view of the first optimum reliable design Fig.8  Final fitted B-spline curves of the 10-bartruss (Phase 2 and 3) Fig.9  Reliable optimum before and after ISAP on the fitted B-spline curves Tab.3  Computational summary of an ISAP, 10-bar planar truss example Fig.10  Convergence history for the 10-bar truss problem (Phase 2 and 3) Fig.11  A close-up convergence history for the 10-bar truss problem Fig.12  13-bar bridge truss Tab.4  Member grouping details of 13-bar truss Tab.5  Statistical properties of random variables, 13-bar truss Tab.6  A comparison of RBDO results for the 13-bar bridge truss Fig.13  Logarithmic convergence history for the 13-bar truss problem (Phase 2) Fig.14  A close up view of the first optimum reliable design Fig.15  Logarithmic fitted B-spline curves of 13-bar truss (Phase 2 and 3) Fig.16  Reliable optimum before and after ISAP on the fitted B-spline curves Fig.17  Convergence history for the 13-bar truss problem (Phase 2 and 3) Fig.18  A close-up Convergence history for the 13-bar truss problem Tab.7  Computational properties of an ISAP, 13-bar truss Fig.19  The 72-bar space truss structure Tab.8  Statistical properties of random variables, 72-bar space truss example Tab.9  RBDO results comparison of 72-bar space truss example Fig.20  Logarithmic convergence history for the 72-bar truss problem (Phase 2) Fig.21  A close up view of the first optimum reliable design Fig.22  Logarithmic fitted B-spline curves of 72-bar truss (Phase 2 and 3) Fig.23  Reliable optimum before and after ISAP on the fitted B-spline curves Fig.24  Convergence history for 72-bar truss problem (Phase 2 and 3) Fig.25  A close-up Convergence history for the 72-bar truss problem Tab.10  Computational summary of an intelligent self-adaptive procedure (Phase 3), 72-bar truss example Fig.26  A 25-Bar space truss Tab.11  Loading condition (kips) for 25-bar space truss Tab.12  RBDO results comparison of 25-bar space truss example Fig.27  Logarithmic convergence history for the 25-bar truss problem (Phase 2) Fig.28  Logarithmic fitted B-spline curves of 25-bar truss (Phase 2 and 3) Fig.29  Reliable optimum before and after ISAP on the fitted B-spline curves Fig.30  Convergence history for 25-bar truss problem (Phase 2 and 3) Fig.31  A close-up convergence history for the 25-bar truss problem Tab.13  Computational properties of an ISAP, 25-bar space truss Tab.14  Summary of computational cost of four RBDO truss problems
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