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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Vydané v:Structural and multidisciplinary optimization Ročník 55; číslo 2; s. 601 - 612
Hlavní autori: Meng, Zeng, Li, Gang, Yang, Dixiong, Zhan, Lichao
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2017
Springer Nature B.V
Predmet:
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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Popis
Shrnutí: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.
Bibliografia:ObjectType-Article-1
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ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-016-1525-z