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Published in: Engineering with Computers 4/2018

24-11-2017 | Original Article

Adaptive stability transformation method of chaos control for first order reliability method

Authors: Zeng Meng, Yuxue Pu, Huanli Zhou

Published in: Engineering with Computers | Issue 4/2018

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Abstract

The efficiency and robustness are two key performance indexes for first-order reliability method (FORM). In this study, two different algorithms, including the adaptive stability transformation method (ASTM) and enhanced adaptive stability transformation method (EASTM), are proposed to improve the efficiency and robustness of FORM. In both ASTM and EASTM, the computation of most probable failure point (MPFP) is converted to find a series of most probable target points (MPTPs), in which the chaos control factor is properly selected by proposing two different algorithms. Four benchmark examples with normal and non-normal random variables and one practical engineering application example are tested to verify the effectiveness of the proposed algorithms. The results illustrate that the proposed algorithms not only are more efficient than other advanced FORM algorithms, but also are very robust.

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Literature
1.
go back to reference Rashki M, Miri M, Azhdary MM (2012) A new efficient simulation method to approximate the probability of failure and most probable point. Struct Saf 39(11):22–29CrossRef Rashki M, Miri M, Azhdary MM (2012) A new efficient simulation method to approximate the probability of failure and most probable point. Struct Saf 39(11):22–29CrossRef
2.
go back to reference Lee IJ, Shin J, Choi KK (2013) Equivalent target probability of failure to convert high-reliability model to low-reliability model for efficiency of sampling-based RBDO. Struct Multidiscip Optim 48(2):235–248MathSciNetCrossRef Lee IJ, Shin J, Choi KK (2013) Equivalent target probability of failure to convert high-reliability model to low-reliability model for efficiency of sampling-based RBDO. Struct Multidiscip Optim 48(2):235–248MathSciNetCrossRef
4.
go back to reference Zhang D, Han X, Jiang C, Liu J, Li Q (2017) Time-dependent reliability analysis through response surface method. J Mech Des 139(4):041404CrossRef Zhang D, Han X, Jiang C, Liu J, Li Q (2017) Time-dependent reliability analysis through response surface method. J Mech Des 139(4):041404CrossRef
5.
go back to reference Lim J, Lee B, Lee I (2016) Post optimization for accurate and efficient reliability-based design optimization using second-order reliability method based on importance sampling and its stochastic sensitivity analysis. Int J Numer Meth Eng 107(2):93–108MathSciNetCrossRefMATH Lim J, Lee B, Lee I (2016) Post optimization for accurate and efficient reliability-based design optimization using second-order reliability method based on importance sampling and its stochastic sensitivity analysis. Int J Numer Meth Eng 107(2):93–108MathSciNetCrossRefMATH
6.
go back to reference Jiang C, Han S, Ji M, Han X (2015) A new method to solve the structural reliability index based on homotopy analysis. Acta Mech 226(4):1067–1083MathSciNetCrossRef Jiang C, Han S, Ji M, Han X (2015) A new method to solve the structural reliability index based on homotopy analysis. Acta Mech 226(4):1067–1083MathSciNetCrossRef
7.
go back to reference Du XP, Chen W (2004) Sequential optimization and reliability assessment method for efficient probabilistic design. J Mech Des 126(2):225–233CrossRef Du XP, Chen W (2004) Sequential optimization and reliability assessment method for efficient probabilistic design. J Mech Des 126(2):225–233CrossRef
8.
go back to reference Li G, Meng Z, Hu H (2015) An adaptive hybrid approach for reliability-based design optimization. Struct Multidiscip Optim 51(5):1051–1065MathSciNetCrossRef Li G, Meng Z, Hu H (2015) An adaptive hybrid approach for reliability-based design optimization. Struct Multidiscip Optim 51(5):1051–1065MathSciNetCrossRef
9.
go back to reference Rashki M, Miri M, Moghaddam MA (2014) A simulation-based method for reliability based design optimization problems with highly nonlinear constraints. Autom Constr 47(11):24–36CrossRef Rashki M, Miri M, Moghaddam MA (2014) A simulation-based method for reliability based design optimization problems with highly nonlinear constraints. Autom Constr 47(11):24–36CrossRef
10.
go back to reference Meng Z, Zhou HL, Li G, Hu H (2017) A hybrid sequential approximate programming method for second-order reliability-based design optimization approach. Acta Mech 228(5):1965–1978MathSciNetCrossRefMATH Meng Z, Zhou HL, Li G, Hu H (2017) A hybrid sequential approximate programming method for second-order reliability-based design optimization approach. Acta Mech 228(5):1965–1978MathSciNetCrossRefMATH
11.
go back to reference Lee JO, Yang YS, Ruy WS (2002) A comparative study on reliability-index and target-performance-based probabilistic structural design optimization. Comput Struct 80(3–4):257–269CrossRef Lee JO, Yang YS, Ruy WS (2002) A comparative study on reliability-index and target-performance-based probabilistic structural design optimization. Comput Struct 80(3–4):257–269CrossRef
12.
go back to reference Meng Z, Li G, Wang BP, Hao P (2015) A hybrid chaos control approach of the performance measure functions for reliability-based design optimization. Comput Struct 146(1):32–43CrossRef Meng Z, Li G, Wang BP, Hao P (2015) A hybrid chaos control approach of the performance measure functions for reliability-based design optimization. Comput Struct 146(1):32–43CrossRef
13.
go back to reference Hasofer AM, Lind NC (1974) Exact and invariant second moment code format. J Eng Mech Div Asce 100(1):111–121 Hasofer AM, Lind NC (1974) Exact and invariant second moment code format. J Eng Mech Div Asce 100(1):111–121
14.
go back to reference Rackwitz R, Fiessler B (1978) Structural reliability under combined random load sequences. Comput Struct 9(5):489–494CrossRefMATH Rackwitz R, Fiessler B (1978) Structural reliability under combined random load sequences. Comput Struct 9(5):489–494CrossRefMATH
15.
go back to reference Zhang Y, Der Kiureghian A (1995) Two improved algorithms for reliability analysis. Reliability and optimization of structural systems. Springer, Berlin, pp 297–304CrossRef Zhang Y, Der Kiureghian A (1995) Two improved algorithms for reliability analysis. Reliability and optimization of structural systems. Springer, Berlin, pp 297–304CrossRef
16.
go back to reference Periçaro GA, Santos SR, Ribeiro AA, Matioli LC (2015) HLRF–BFGS optimization algorithm for structural reliability. Appl Math Model 39(7):2025–2035MathSciNetCrossRef Periçaro GA, Santos SR, Ribeiro AA, Matioli LC (2015) HLRF–BFGS optimization algorithm for structural reliability. Appl Math Model 39(7):2025–2035MathSciNetCrossRef
17.
go back to reference Lopez RH, Torii AJ, Miguel LFF, Souza Cursi JE (2015) Overcoming the drawbacks of the FORM using a full characterization method. Struct Saf 54(5):57–63CrossRef Lopez RH, Torii AJ, Miguel LFF, Souza Cursi JE (2015) Overcoming the drawbacks of the FORM using a full characterization method. Struct Saf 54(5):57–63CrossRef
18.
go back to reference Santos SR, Matioli LC, Beck AT (2012) New optimization algorithms for structural reliability analysis. Cmes Comp Model Eng 83(1):23–55MathSciNetMATH Santos SR, Matioli LC, Beck AT (2012) New optimization algorithms for structural reliability analysis. Cmes Comp Model Eng 83(1):23–55MathSciNetMATH
19.
go back to reference Yang DX, Li G, Cheng GD (2006) Convergence analysis of first order reliability method using chaos theory. Comput Struct 84(8–9):563–571CrossRef Yang DX, Li G, Cheng GD (2006) Convergence analysis of first order reliability method using chaos theory. Comput Struct 84(8–9):563–571CrossRef
20.
go back to reference Meng Z, Li G, Yang DX, Zhan L (2017) A new directional stability transformation method of chaos control for first order reliability analysis. Struct Multidiscip Optim 55(2):601–612MathSciNetCrossRef Meng Z, Li G, Yang DX, Zhan L (2017) A new directional stability transformation method of chaos control for first order reliability analysis. Struct Multidiscip Optim 55(2):601–612MathSciNetCrossRef
21.
go back to reference Keshtegar B (2017) A hybrid conjugate finite-step length method for robust and efficient reliability analysis. Appl Math Model 45(5):226–237MathSciNetCrossRef Keshtegar B (2017) A hybrid conjugate finite-step length method for robust and efficient reliability analysis. Appl Math Model 45(5):226–237MathSciNetCrossRef
22.
go back to reference Keshtegar B (2016) Chaotic conjugate stability transformation method for structural reliability analysis. Comput Methods Appl Mech Eng 310:866–885MathSciNetCrossRef Keshtegar B (2016) Chaotic conjugate stability transformation method for structural reliability analysis. Comput Methods Appl Mech Eng 310:866–885MathSciNetCrossRef
23.
go back to reference Keshtegar B (2017) Limited conjugate gradient method for structural reliability analysis. Eng Comput 33(3):621–629CrossRef Keshtegar B (2017) Limited conjugate gradient method for structural reliability analysis. Eng Comput 33(3):621–629CrossRef
24.
go back to reference Yang DX (2010) Chaos control for numerical instability of first order reliability method. Commun Nonlinear Sci Numer Simula 15(10):3131–3141CrossRefMATH Yang DX (2010) Chaos control for numerical instability of first order reliability method. Commun Nonlinear Sci Numer Simula 15(10):3131–3141CrossRefMATH
25.
go back to reference Tu J, Choi KK, Park YH (1999) A new study on reliability-based design optimization. J Mech Des 121(4):557–564CrossRef Tu J, Choi KK, Park YH (1999) A new study on reliability-based design optimization. J Mech Des 121(4):557–564CrossRef
26.
go back to reference Petkov BH, Vitale V, Mazzola M, Lanconelli C, Lupi A (2015) Chaotic behaviour of the short-term variations in ozone column observed in Arctic. Commun Nonlinear Sci Numer Simulat 26(1–3):238–249CrossRef Petkov BH, Vitale V, Mazzola M, Lanconelli C, Lupi A (2015) Chaotic behaviour of the short-term variations in ozone column observed in Arctic. Commun Nonlinear Sci Numer Simulat 26(1–3):238–249CrossRef
27.
go back to reference Pingel D, Schmelcher P, Diakonos FK (2004) Stability transformation: a tool to solve nonlinear problems. Phys Rep 400(2):67–148MathSciNetCrossRef Pingel D, Schmelcher P, Diakonos FK (2004) Stability transformation: a tool to solve nonlinear problems. Phys Rep 400(2):67–148MathSciNetCrossRef
28.
go back to reference Schmelcher P, Diakonos FK (1998) General approach to the localization of unstable periodic orbits in chaotic dynamical systems. Phys Rev E 57(3):2739–2746CrossRef Schmelcher P, Diakonos FK (1998) General approach to the localization of unstable periodic orbits in chaotic dynamical systems. Phys Rev E 57(3):2739–2746CrossRef
29.
go back to reference Liu PL, Der Kiureghian A (1991) Optimization algorithms for structural reliability. Struct Saf 9(3):161–177 Liu PL, Der Kiureghian A (1991) Optimization algorithms for structural reliability. Struct Saf 9(3):161–177
Metadata
Title
Adaptive stability transformation method of chaos control for first order reliability method
Authors
Zeng Meng
Yuxue Pu
Huanli Zhou
Publication date
24-11-2017
Publisher
Springer London
Published in
Engineering with Computers / Issue 4/2018
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-017-0566-2

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