# Structural optimization oriented time-dependent reliability methodology under static and dynamic uncertainties

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## Abstract

Uncertainty with characteristics of time-dependency, multi-sources and small-samples extensively exists in the whole process of structural design. Associated with frequent occurrences of material aging, load varying, damage accumulating, traditional reliability-based design optimization (RBDO) approaches by combination of the static assumption and the probability theory will be no longer applicable when dealing with the design problems for lifecycle structural models. In view of this, a new non-probabilistic time-dependent RBDO method under the mixture of time-invariant and time-variant uncertainties is investigated in this paper. Enlightened by the first-passage concept, the hybrid reliability index is firstly defined, and its solution implementation relies on the technologies of regulation and the interval mathematics. In order to guarantee the stability and efficiency of the optimization procedure, the improved ant colony algorithm (ACA) is then introduced. Moreover, by comparisons of the models of the safety factor-based design as well as the instantaneous RBDO design, the physical means of the proposed optimization policy are further discussed. Two numerical examples are eventually presented to demonstrate the validity and reasonability of the developed methodology.

## Keywords

Non-probabilistic time-dependent RBDO method The mixture of time-invariant and time-variant uncertainties The first-passage approach The improved ant colony algorithm (ACA) The safety factor-based design## Notes

### Acknowledgements

The authors would like to thank the National Nature Science Foundation of China (No. 11372025, 11432002, 11602012), the 111 Project (No. B07009), the Defense Industrial Technology Development Program (No. JCKY2016601B001, JCKY2016205C001), and the China Postdoctoral Science Foundation (No. 2016 M591038) for the financial supports. Besides, the authors wish to express their many thanks to the reviewers for their useful and constructive comments.

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