Bounds approximation of limit‐state surface based on active learning Kriging model with truncated candidate region for random‐interval hybrid reliability analysis

When the reliability analysis of the mechanical products with high nonlinearity and time-consuming response is carried out, there will be the problems of low precision and huge computation using the traditional reliability methods. To solve these issues, the active learning reliability methods have been paid much attention in recent years. It is the key to choose an efficient learning function (such as U, EFF, and ERF). The aim of this study is to further decrease the computation and improve the accuracy of the reliability analysis. Inspired from these learning functions, a new point-selected learning function (called HPF) is proposed to update DOE, and a new point is sequentially added step by step to the DOE. The proposed learning function can consider the features like the sampling density, the probability to be wrongly predicted, and the local and global uncertainty close to the limit state. Based on the stochastic property of the Kriging model, the analytic expression of HPF is deduced by averaging a hybrid indicator throughout the real space. The efficiency of the proposed method is validated by two explicit examples. Finally, the proposed method is applied to the mechanical reliability analysis (involving time-consuming and nonlinear response). By comparing with traditional mechanical reliability methods, the results show that the proposed method can solve the problems of large computation and low precision.

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Structural Reliability Algorithms of Kriging Model Based on Improved Learning Strategy

Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University ◽

10.1051/jnwpu/20203820412 ◽

2020 ◽

Vol 38 (2) ◽

pp. 412-419

Author(s):

Linxiong Hong ◽

Huacong Li ◽

Kai Peng ◽

Hongliang Xiao

Keyword(s):

Active Learning ◽

Reliability Analysis ◽

Structural Reliability ◽

Learning Strategy ◽

Limit State ◽

Surface Region ◽

Kriging Model ◽

State Function ◽

Limit State Function ◽

Highly Nonlinear

Aiming at the problems of implicit and highly nonlinear limit state function in the process of reliability analysis of mechanical products, a reliability analysis method of mechanical structures based on Kriging model and improved EGO active learning strategy is proposed. For the problem that the traditional EGO method cannot effectively select points in the limit state surface region, an improved EGO method is proposed. By dealing with the predicted values of sample point model with absolute values and assume that the distribution state of response values remains the same, the work focus of active learning selection points is moved to the vicinity, where the points are with larger prediction variance or close to the limit state surface. Three examples show that, compared with the classical active learning method, the proposed method has good global and local search ability, and can estimate the exact failure probability value under the condition of less calculation of the limit state function.

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