An efficient and robust structural reliability analysis method with mixed variables based on hybrid conjugate gradient direction

Abstract

Traditional reliability analysis is based on probability theory with precise distributions. However, determining the distribution of all variables precisely is impossible due to insufficient information. Therefore, random and interval variables may be encountered, and probabilistic reliability methods are hard to use. The existing interval variables make reliability analysis more difficult. In this article, an efficient and robust hybrid reliability analysis method is proposed for structures with both random and interval variables. Firstly, a single-loop procedure is proposed by performing probabilistic analysis and interval analysis simultaneously in each most probable point search process. Then an improved conjugate sensitivity factor method based on hybrid conjugate gradient direction and adaptive finite step length is developed for probabilistic analysis. Meanwhile, the hybrid conjugate gradient direction together with active set is introduced into the projected gradient method for interval analysis. Finally, a comparison analysis with six numerical examples is provided to validate the performance of the proposed method. The results demonstrate that the proposed method is better than the existing methods in terms of efficiency and robustness for hybrid reliability analysis with random and interval variables.

Solving large scale unconstrained optimization problems with an efficient conjugate gradient class

“…In addition to their original authors, the issue of global convergence of methods (5) has also been investigated by some researchers like Al-Baali [40] and Gilbert and Nocedal [41]. Likewise, for all the CG directions that are presented in previous paragraph, the authors proved global convergence under necessary line searches techniques such as Armijo [14,16,20,29], week Wolfe-Powell [15-18, 21, 23, 24, 26, 27, 30, 35], strong Wolfe-Powell [12,16,19,22,25,28,31], modifications of these three techniques [13,[32][33][34] or some backtracking algorithms [36][37][38][39].…”

“…For example, interested readers can see some modifications of HS method in [12,13], several combinations of FR method in [14][15][16], various developments of PRP method in [17][18][19][20][21], an extended LS method in [22] and variant improvements of DY method in [23][24][25]. Furthermore, some researchers used techniques like quasi-Newton [26][27][28], regularization [29,30], a combination of above methods [31][32][33] or alternative techniques [34,35] and introduced appropriate CG methods to solve optimization problems. Similarly, there exist plenty of CG algorithms that are created to solve systems of nonlinear equations [36][37][38][39].…”

Fatigue reliability of welded joints accounting for uncertainties in weld geometry

“…In this work, the FORM [29][30][31] is used to evaluate the reliability index and the sensitivity factor.…”

A novel approach for multi‐output structural system reliability problem with small failure probability

“…are usually inapplicable especially for the highly nonlinear problems. 1 Fortunately, the surrogate model-based reliability methods have been recently reported to address this issue. Due to the unique advantage in describing the uncertainty, the Kriging model is introduced into the reliability analysis and the active learning Kriging (ALK) based reliability method is further studied to improve the computational efficiency.…”

“…Under this circumstance, the classic reliability methods (FORM, SORM, etc.) are usually inapplicable especially for the highly nonlinear problems 1 . Fortunately, the surrogate model‐based reliability methods have been recently reported to address this issue.…”