A framework for structural reliability analysis based on conjugate sensitivity factor and saddlepoint approximation
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DOI 10.1007/s12206-020-0814-z
Journal of Mechanical Science and Technology 34 (9) 2020 Original Article DOI 10.1007/s12206-020-0814-z Keywords: · Reliability analysis · First-order reliability method · Conjugate sensitivity factor · Saddlepoint approximation
A framework for structural reliability analysis based on conjugate sensitivity factor and saddlepoint approximation Peng Huang1,2, Hong-Zhong Huang1,2, Tudi Huang1,2 and Hua-Ming Qian1,2 1
Correspondence to: Hong-Zhong Huang [email protected]
Citation: Huang, P., Huang, H.-Z., Huang, T., Qian, H.-M. (2020). A framework for structural reliability analysis based on conjugate sensitivity factor and saddlepoint approximation. Journal of Mechanical Science and Technology 34 (9) (2020) 3617~3627. http://doi.org/10.1007/s12206-020-0814-z
Received April 1st, 2020 Revised
May 31st, 2020
Accepted June 22nd, 2020 † Recommended by Editor Chongdu Cho
School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of 2 China, Chengdu 611731, China, Center for System Reliability and Safety, University of Electronic Science and Technology of China, Chengdu 611731, China
Abstract
A new structural reliability analysis framework is developed to extend the performance of first-order reliability method, which is low robustness and poor accuracy when dealing with highly nonlinear functions. Initially, an improved conjugate sensitivity factor method is proposed to find the most probable point. The method enhances its robustness of convergence by introducing a conjugate gradient direction based sensitivity factor technique and improves its computational efficiency by putting forward a hybrid conjugate gradient factor and an adaptive step length strategy. Subsequently, the dimension reduction-based saddlepoint approximation method is developed, which uses the dimension reduction approach to construct the limit state function as the additive univariate quadratic functions and applies saddlepoint approximation to obtain the result with higher precision. A comparison analysis from five mathematical and structural examples illustrates that the proposed method is better than most existing methods in terms of robustness, efficiency and accuracy for estimating the failure probability of structures.
1. Introduction Various uncertainties affect the reliability of structures, so that even reasonable structural design cannot guarantee its absolute safety [1-4]. Evaluating the influence of uncertainties on structures is an important task of structural reliability analysis [5-8]. For such analysis, the parameters that determining the structural performance are basic random variables, such as external loads, geometrical dimensions and material properties, which can be expressed as a T vector x = ( x1 , x2 ,", xn ) . If g ( x ) is the corresponding limit state function (LSF), the failure probability can be computed by Pf = ∫ ∫" ∫ f x ( x1 , x2 ,", xn )dx1dx2 " dxn ,
(1)
g ( x ) 1, η k = 1. In terms of the step length, Ref. [20] shows that a fixed step
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