# Safety life analysis under required failure credibility constraint for unsteady thermal structure with fuzzy input parameters

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## Abstract

To measure the safety degree of the unsteady thermal structure under fuzzy uncertainty, the time-dependent failure credibility (TDFC) is presented. TDFC is superior to the existing time-dependent failure possibility because of its self-duality property. Then, the safety life time under given TDFC constraint is defined and analyzed. In order to estimate the safety life time under the TDFC constraint, the optimization based computational method is proposed. In the proposed method, the safety life time is firstly expressed as a bi-level problem where the outer is a univariate rooting problem and the inner is a single-loop or nested-loop optimization problem for different types of cases. Next, the univariate rooting problem is solved by the dichotomy and the optimization problem is solved by the interior point algorithm. Furthermore, to extremely improve the computational efficiency, the Kriging computational method is developed, in which an adaptive Kriging model is firstly constructed to approximate the relationship between the input variables and the model response. Then, the safety life time under any given TDFC constraint can be estimated by employing the current Kriging model and the proposed optimization based computational algorithm without any extra model evaluations. Two numerical examples are used to demonstrate the feasibility and rationality of the defined safety life time and efficiency of two solutions. Results show that the Kriging method greatly reduce the computational burden in solving the unsteady thermal structure problems compared with the optimization based method under given acceptable precision.

## Keywords

Unsteady thermal structure Fuzzy uncertainty Time-dependent failure credibility Safety life time Optimization Kriging model## Notes

### Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. NSFC 51475370, 51775439, 11602197).

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