期刊
JOURNAL OF ENGINEERING MECHANICS
卷 140, 期 6, 页码 -出版社
ASCE-AMER SOC CIVIL ENGINEERS
DOI: 10.1061/(ASCE)EM.1943-7889.0000722
关键词
Reliability index; Sensitivity/gradient; Iterative algorithm
资金
- Natural Science Foundation of China [11102033, 51138001]
- Fundamental Research Funds for the Central Universities
In reliability analysis, the first-order reliability method (FORM) and various optimization algorithms are widely used to locate the most probable point (MPP) and calculate the reliability index. These algorithms generally require first-order response sensitivities or gradients of the limit-state function. However, in engineering, the reliability analysis is often merged with finite-element (FE) analysis or other structural/mechanical analyses, and the limit-state function is implicit. The sensitivity analysis may be computationally intensive or cumbersome, and several techniques were developed to deal with this problem. In the present paper, a general iterative algorithm that does not need gradients is proposed. This algorithm produces n series of sequence points iteratively in the n-dimension standard normal space. It is proven that the n series of points will converge to the same point, which is just the MPP, and its distance to the origin is the reliability index. The proposed algorithm also introduces new step lengths to control the convergence of the sequence. These step lengths are new because they may be constant during the iteration or varied using the interim evaluations of the reliability index, which means a self-adjust process in essence. Eighteen examples are given to verify the effectiveness of the proposed algorithm. It is indicated that the proposed algorithm is effective and robust.
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