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A novel evidence-based fuzzy reliability analysis method for structures

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Abstract

Epistemic uncertainties always exist in engineering structures due to the lack of knowledge or information, which can be mathematically described by either fuzzy-set theory or evidence theory (ET) In this work, the authors present a novel uncertainty model, namely evidence-based fuzzy model, in which the fuzzy sets and ET are combined to represent the epistemic uncertainty. A novel method for combining multiple membership functions and a corresponding reliability analysis method is also developed. In the combination method, the combined fuzzy-set representations are approximated by the enveloping lines of the multiple membership functions (smoothed by neglecting the valleys in the membership functions curves) and the Murphy’s average combination rule is applied to compute the basic probability assignment for focal elements. Then, the combined membership function is transformed to the equivalent probability density function by means of a normalizing factor. Finally, the Markov Chain Monte Carlo (MCMC) subset simulation method is used to solve reliability by introducing intermediate failure events. A numerical example and two engineering examples are provided to demonstrate the effectiveness of the proposed method.

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Acknowledgments

This work is supported by National Natural Science Foundation of China(51675173), Hunan Provincial Science Fund(2016JJ2039), Aid program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province(Grant no (2014) 207), Project by Hunan Provincial Natural Science Foundation of China (Grant no 14JJ5006)

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Authors and Affiliations

  1. Department of Mechanical Engineering, Hunan Institute of Engineering, Xiangtan City, 411101, China

    Y. R. Tao & L. Cao

  2. Hunan Province Coopperative Innovation Center for Wind power Equipment and Energy Conversion, Xiangtan, 411101, China

    Y. R. Tao & Z. H. H. Huang

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  1. Y. R. Tao
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  2. L. Cao
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  3. Z. H. H. Huang
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Correspondence to Y. R. Tao.

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Tao, Y.R., Cao, L. & Huang, Z.H.H. A novel evidence-based fuzzy reliability analysis method for structures. Struct Multidisc Optim 55, 1237–1249 (2017). https://doi.org/10.1007/s00158-016-1570-7

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  • DOI: https://doi.org/10.1007/s00158-016-1570-7

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