A new directional stability transformation method of chaos control for first order reliability analysis

The HL-RF iterative algorithm of the first order reliability method (FORM) is popularly applied to evaluate reliability index in structural reliability analysis and reliability-based design optimization. However, it sometimes suffers from non-convergence problems, such as bifurcation, periodic oscil...

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Vydáno v:	Structural and multidisciplinary optimization Ročník 55; číslo 2; s. 601 - 612
Hlavní autoři:	Meng, Zeng, Li, Gang, Yang, Dixiong, Zhan, Lichao
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2017 Springer Nature B.V
Témata:	Algorithms Bifurcations Computational Mathematics and Numerical Analysis Control stability Convergence Design optimization Directional stability Dynamic stability Engineering Engineering Design Feedback control Iterative algorithms Iterative methods Liapunov exponents Limit states Reliability analysis Reliability engineering Research Paper Robust control Robustness (mathematics) Stability analysis Structural reliability Theoretical and Applied Mechanics Transformations (mathematics) HL-RF iterative algorithm Reliability analysis Convergence control Directional stability Transform method Discrete Chaotic dynamic system
ISSN:	1615-147X, 1615-1488
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Abstract	The HL-RF iterative algorithm of the first order reliability method (FORM) is popularly applied to evaluate reliability index in structural reliability analysis and reliability-based design optimization. However, it sometimes suffers from non-convergence problems, such as bifurcation, periodic oscillation, and chaos for nonlinear limit state functions. This paper derives the formulation of the Lyapunov exponents for the HL-RF iterative algorithm in order to identify these complicated numerical instability phenomena of discrete chaotic dynamic systems. Moreover, the essential cause of low efficiency for the stability transform method (STM) of convergence control of FORM is revealed. Then, a novel method, directional stability transformation method (DSTM), is proposed to reduce the number of function evaluations of original STM as a chaos feedback control approach. The efficiency and convergence of different reliability evaluation methods, including the HL-RF algorithm, STM and DSTM, are analyzed and compared by several numerical examples. It is indicated that the proposed DSTM method is versatile, efficient and robust, and the bifurcation, periodic oscillation, and chaos of FORM is controlled effectively.
AbstractList	The HL-RF iterative algorithm of the first order reliability method (FORM) is popularly applied to evaluate reliability index in structural reliability analysis and reliability-based design optimization. However, it sometimes suffers from non-convergence problems, such as bifurcation, periodic oscillation, and chaos for nonlinear limit state functions. This paper derives the formulation of the Lyapunov exponents for the HL-RF iterative algorithm in order to identify these complicated numerical instability phenomena of discrete chaotic dynamic systems. Moreover, the essential cause of low efficiency for the stability transform method (STM) of convergence control of FORM is revealed. Then, a novel method, directional stability transformation method (DSTM), is proposed to reduce the number of function evaluations of original STM as a chaos feedback control approach. The efficiency and convergence of different reliability evaluation methods, including the HL-RF algorithm, STM and DSTM, are analyzed and compared by several numerical examples. It is indicated that the proposed DSTM method is versatile, efficient and robust, and the bifurcation, periodic oscillation, and chaos of FORM is controlled effectively.
Author	Yang, Dixiong Meng, Zeng Li, Gang Zhan, Lichao
Author_xml	– sequence: 1 givenname: Zeng surname: Meng fullname: Meng, Zeng email: mengz@hfut.edu.cn organization: School of Civil Engineering, Hefei University of Technology – sequence: 2 givenname: Gang surname: Li fullname: Li, Gang organization: Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology – sequence: 3 givenname: Dixiong surname: Yang fullname: Yang, Dixiong organization: Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology – sequence: 4 givenname: Lichao surname: Zhan fullname: Zhan, Lichao organization: Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology
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Keywords	HL-RF iterative algorithm Reliability analysis Convergence control Directional stability Transform method Discrete Chaotic dynamic system
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SubjectTerms	Algorithms Bifurcations Computational Mathematics and Numerical Analysis Control stability Convergence Design optimization Directional stability Dynamic stability Engineering Engineering Design Feedback control Iterative algorithms Iterative methods Liapunov exponents Limit states Reliability analysis Reliability engineering Research Paper Robust control Robustness (mathematics) Stability analysis Structural reliability Theoretical and Applied Mechanics Transformations (mathematics)
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Title	A new directional stability transformation method of chaos control for first order reliability analysis
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