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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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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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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DOI: https://doi.org/10.1007/s00366-021-01447-y