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A novel active learning method for profust reliability analysis based on the Kriging model

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Abstract

Profust reliability analysis, in which the failure state of a load-bearing structure is assumed to be fuzzy, is investigated in this paper. A novel active learning method based on the Kriging model is proposed to minimize the number of function evaluations. The new method is termed ALK-Pfst. The sign of performance function at a given random threshold determines the profust failure probability. Therefore, the expected risk function at an arbitrary threshold is derived as the learning function of ALK-Pfst. By making full use of the prediction information of Kriging model, the prediction error of profust failure probability is carefully derived into a closed-form expression. Aided by the prediction error, the accuracy of Kriging model during the learning process can be monitored in real time. As a result, the learning process can be timely terminated with little loss of accuracy. Four examples are provided to demonstrate the advantages of the proposed method.

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Availability of data and material

The simulation data within this submission is available based on the request.

Code availability

Implementation codes are available upon request.

Abbreviations

RA:

Reliability analysis

PDF:

Probability density function

MCS:

Monte Carlo simulation

IS:

Importance sampling

SS:

Subset simulation

ALK:

Active learning methods based on the Kriging

ERF:

Expected risk function

AK-MCS:

Active learning method combining Kriging model and MCS

DS-AK:

Dual-stage adaptive Kriging

ALK-Pfst:

Active learning method based on the Kriging model for the profust RA

DoE:

Design of experiments

CDF:

Cumulative distribution function

WSP:

Wrong sign prediction

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant no. 51705433), the Fundamental Research Funds for the Central Universities (Grant no. 2682017CX028).

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Authors and Affiliations

  1. School of Mechanical Engineering, Southwest Jiaotong University, Chengdu, 610031, People’s Republic of China

    Xufeng Yang, Xin Cheng, Zeqing Liu & Tai Wang

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  1. Xufeng Yang
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  2. Xin Cheng
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  3. Zeqing Liu
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  4. Tai Wang
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Correspondence to Xufeng Yang.

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Yang, X., Cheng, X., Liu, Z. et al. A novel active learning method for profust reliability analysis based on the Kriging model. Engineering with Computers 38 (Suppl 4), 3111–3124 (2022). https://doi.org/10.1007/s00366-021-01447-y

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