Novel decoupled framework for reliability-based design optimization of structures using a robust shifting technique

Abstract

In a reliability-based design optimization (RBDO), computation of the failure probability (P_f) 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.

Keywords

reliability-based design optimization / trusses / sensitivity analysis / shifting technique / cubic B-splines / response surface method

References

[1] Ghasemi H, Park H S, Rabczuk T. Multi-material level set-based topology optimization of flexoelectric composites. Computer Methods in Applied Mechanics and Engineering, 2018, 332: 47–62

[2] Dizangian B, Ghasemi M R. Border-search and jump reduction method for size optimization of spatial truss structures. Frontiers of Structural and Civil Engineering, 2018, 13(1): 123–134

[3] Ghasemi H, Park H S, Rabczuk T. A level-set based IGA formulation for topology optimization of flexoelectric materials. Computer Methods in Applied Mechanics and Engineering, 2017, 313: 239–258

[4] Ghasemi H, Kerfriden P, Bordas S P A, Muthu J, Zi G, Rabczuk T. Probabilistic multiconstraints optimization of cooling channels in ceramic matrix composites. Composites Part B: Engineering, 2015, 81: 107–119

[5] Nanthakumar S S, Lahmer T, Zhuang X, Zi G, Rabczuk T. Detection of material interfaces using a regularized level set method in piezoelectric structures. Inverse Problems in Science and Engineering, 2016, 24(1): 153–176

[6] Ghasemi H, Brighenti R, Zhuang X, Muthu J, Rabczuk T. Optimum fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach. Structural and Multidisciplinary Optimization, 2015, 51(1): 99–112

[7] Khajeh A, Ghasemi M R, Ghohani Arab H. Hybrid particle swarm optimization, grid search method and univariate method to optimally design steel frame structures. International Journal of Optimization Civil Engineering, 2017, 7(2), 171–189

[8] Ghasemi H, Rafiee R, Zhuang X, Muthu J, Rabczuk T. Uncertainties propagation in metamodel-based probabilistic optimization of CNT/polymer composite structure using stochastic multi-scale modeling. Computational Materials Science, 2014, 85: 295–305

[9] Tu J, Choi K K, Park Y H. A new study on reliability-based design optimization. Journal of Mechanical Design, 1999, 121(4): 557–564

[10] Madsen H O, Hansen P F. A Comparison of some algorithms for reliability based structural optimization and sensitivity analysis. In: Rackwitz R, Thoft-Christensen P, eds. Reliability and Optimization of Structural Systems. Berlin: Springer Berlin Heidelberg, 1992, 443–451

[11] Kuschel N, Rackwitz R. Two basic problems in reliability-based structural optimization. Mathematical Methods of Operations Research, 1997, 46(3): 309–333

[12] Kirjner-Neto C, Polak E, Kiureghian A D. An outer approximations approach to reliability-based optimal design of structures. Journal of Optimization Theory and Applications, 1998, 98(1): 1–16

[13] Kharmanda G, Mohamed A, Lemaire M. Efficient reliability-based design optimization using a hybrid space with application to finite element analysis. Structural and Multidisciplinary Optimization, 2002, 24(3): 233–245

[14] Shan S, Wang G G. Reliable design space and complete single-loop reliability-based design optimization. Reliability Engineering & System Safety, 2008, 93(8): 1218–1230

[15] Aoues Y, Chateauneuf A. Benchmark study of numerical methods for reliability-based design optimization. Structural and Multidisciplinary Optimization, 2010, 41(2): 277–294

[16] Du X, Chen W. Sequential optimization and reliability assessment method for efficient probabilistic design. Journal of Mechanical Design, 2004, 126(2): 225–233

[17] Bucher C G, Bourgund U. A fast and efficient response surface approach for structural reliability problems. Structural Safety, 1990, 7(1): 57–66

[18] Faravelli L. Responsealysis. Journal of Engineering Mechanics, 1989, 115(12): 2763–2781

[19] Guan X, Melchers R. Multitangent-plane surface method for reliability calculation. Journal of Engineering Mechanics, 1997, 123(10): 996–1002

[20] Rajashekhar M R, Ellingwood B R. A new look at the response surface approach for reliability analysis. Structural Safety, 1993, 12(3): 205–220

[21] Wong F. Slope reliability and response surface method. Journal of Geotechnical Engineering, 1985, 111(1): 32–53

[22] Nguyen X S, Sellier A, Duprat F, Pons G. Adaptive response surface method based on a double weighted regression technique. Probabilistic Engineering Mechanics, 2009, 24(2): 135–143

[23] Roussouly N, Petitjean F, Salaun M. A new adaptive response surface method for reliability analysis. Probabilistic Engineering Mechanics, 2013, 32: 103–115

[24] Ren W X, Chen H B. Finite element model updating in structural dynamics by using the response surface method. Engineering Structures, 2010, 32(8): 2455–2465

[25] Zheng Y, Das P. Improved response surface method and its application to stiffened plate reliability analysis. Engineering Structures, 2000, 22(5): 544–551

[26] Kang S C, Koh H M, Choo J F. An efficient response surface method using moving least squares approximation for structural reliability analysis. Probabilistic Engineering Mechanics, 2010, 25(4): 365–371

[27] Wong S, Hobbs R, Onof C. An adaptive response surface method for reliability analysis of structures with multiple loading sequences. Structural Safety, 2005, 27(4): 287–308

[28] Yinga L. Application of stochastic response surface method in the structural reliability. Procedia Engineering, 2012, 28: 661–664

[29] Zhao W, Qiu Z. An efficient response surface method and its application to structural reliability and reliability-based optimization. Finite Elements in Analysis and Design, 2013, 67: 34–42

[30] Wu Y, Wang W. Efficient Probabilistic Design by Converting Reliability Constraints to Equivalent Approximate Deterministic Constraints. Austin: Society for Design and Process Science, 1996

[31] Qu X, Haftka R T. Reliability-based design optimization using probabilistic sufficiency factor. Structural and Multidisciplinary Optimization, 2004, 27(5): 314–325

[32] Dizangian B, Ghasemi M R. A fast decoupled reliability-based design optimization of structures using B-spline interpolation curves. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2016, 38(6): 1817–1829

[33] Dizangian B, Ghasemi M R. An efficient method for reliable optimum design of trusses. Steel and Composite Structures, 2016, 21(5): 1069–1084

[34] Heinzl H, Kaider A. Gaining more flexibility in Cox proportional hazards regression models with cubic spline functions. Computer Methods and Programs in Biomedicine, 1997, 54(3): 201–208

[35] Desquilbet L, Mariotti F. Dose-response analyses using restricted cubic spline functions in public health research. Statistics in Medicine, 2010, 29: 1037–1057

[36] Wolberg G, Alfy I. An energy-minimization framework for monotonic cubic spline interpolation. Journal of Computational and Applied Mathematics, 2002, 143(2): 145–188

[37] de Boor C. A Practical Guide to Splines. New York: Springer, 2001

[38] Dizangian B, Ghasemi M R. Ranked-based sensitivity analysis for size optimization of structures. Journal of Mechanical Design, 2015, 137(12): 121402

[39] Nowak A S, Collins K R. Reliability of Structures, 2nd ed. Abingdon: Taylor & Francis, 2012

[40] Nakib R, Frangopol D M. RBSA and RBSA-OPT: two computer programs for structural system reliability analysis and optimization. Computers & Structures, 1990, 36(1): 13–27

[41] Ghorbani A, Ghasemi M R. An efficient method for reliability based optimization of structures using adaptive Neuro-Fuzzy systems. Journal of Modelling and Simulation of Systems, 2010, 1: 13–21

[42] Shayanfar M, Abbasnia R, Khodam A. Development of a GA-based method for reliability-based optimization of structures with discrete and continuous design variables using OpenSees and Tcl. Finite Elements in Analysis and Design, 2014, 90: 61–73

[43] Ho-Huu V, Nguyen-Thoi T, Le-Anh L, Nguyen-Trang T. An effective reliability-based improved constrained differential evolution for reliability-based design optimization of truss structures. Advances in Engineering Software, 2016, 92: 48–56

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature