Fast First Order Reliability Method Based on Adaptive Step Size Parameters

Abstract

Abstract:

Abstract： The key problem for fast first order reliability method (FORM) is to quickly find out the design point of limit state function. After analyzing some HLRFbased design point searching algorithms, a novel FORM was proposed based on the Shi-Shen line search rule. As this FORM is based on adaptive step size parameters, it is referred to as aHLRF. Compared with the traditional HLRF-based method, the aHLRF not only is globally convergent, but also can adaptively estimate some important algorithm parameters using previous iteration information. The robustness and efficiency of the aHLRF were also discussed. Examples illustrate that the aHLRF is very efficiency for estimating the first order reliability probability, especially for problems whose the nonlinearity of limit state function near the design point is very large.

Key words: design point, inexact linear search, Shi-Shen rule, first order reliability method

CLC Number:

ZHOU Shengtong,LI Hongguang. Fast First Order Reliability Method Based on Adaptive Step Size Parameters[J]. Journal of Shanghai Jiaotong University, 2014, 48(11): 1574-1579.

References

［1］Lemaire M. Structural reliability［M］. Hoboken: John Wiley & Sons, 2009.

［2］Hasofer A M, Lind N C. Exact and invariant secondmoment code format［J］. Journal of the Engineering Mechanics Division, ASCE, 1974, 100(1): 111121.

［3］Rackwitz R, Flessler B. Structural reliability under combined random load sequences［J］. Computers & Structures, 1978, 9(5): 489494.

［4］Liu P, Der Kiureghian A. Optimization algorithms for structural reliability［J］. Structural Safety, 1991, 9(3): 161177.

［5］Zhang Y, Der Kiureghian A. Finite element reliability methods for inelastic structures［R］. Berkeley CA: Department of Civil and Environmental Engineering, University of California, 1997.

［6］Santosh T V, Saraf R K, Ghosh A K, et al. Optimum step length selection rule in modified HLRF method for structural reliability［J］. International Journal of Pressure Vessels and Piping, 2006, 83(10): 742748.

［7］Santos S R, Matioli L C, Beck A T. New optimization algorithms for structural reliability analysis［J］. Computer Modeling in Engineering & Sciences(CMES), 2012, 83(1): 2355.

［8］Abdo T, Rackwitz R. A new betapoint algorithm for large timeinvariant and timevariant reliability problems［C］∥Der Kiureghian A, ThoftChristensen P. Reliability and Optimization of Structural Systems ’90. Berlin Heidelberg: Springer, 1991: 112.

［9］Haukaas T, Kiureghian A D. Strategies for finding the design point in nonlinear finite element reliability analysis［J］. Probabilistic Engineering Mechanics， 2006, 21(2): 133147.

［10］秦权，林道锦，梅刚. 结构可靠度随机有限元——理论及工程应用［M］. 北京: 清华大学出版社, 2006.

［11］贡金鑫. 工程结构可靠度计算方法［M］. 大连: 大连理工大学出版社, 2003.

［12］Gong J X, Yi P. A robust iterative algorithm for structural reliability analysis［J］. Struct Multidisc Optim， 2011, 43: 519527.

［13］Shi Z J, Shen J. New inexact line search method for unconstrained optimization［J］. Journal of Optimization Theory and Applications, 2005, 127(2): 425446.

［14］Dennis J E, Schnabel R D. Numerical methods for unconstrained optimization and nonlinear equations［M］. Philadelphia: Society for Industrial and Applied Mathematics, 1996.

[1]	LI Lin-bin. Study for the Derivation Method of Design Current Profiles for Deepwater Structures [J]. Ocean Engineering Equipment and Technology, 2018, 5(增刊): 193-198.
[2]	YANG Jie1,2 (杨杰), HUANG Yi1,2(黄一), ZHANG Qi1,2 (张崎), ZHAO De-you1 (赵德有). Method of a New Iteration Scheme Combined with Kriging Model for Structural Reliability Evaluation [J]. Journal of shanghai Jiaotong University (Science), 2012, 17(4): 415-.