Structural Engineering and Mechanics

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A novel evidence theory model and combination rule for reliability estimation of structures

  • Tao, Y.R. (College of Mechanical Engineering, Hebei University of Technology) ;
  • Wang, Q. (Department of Mechanical Engineering, Hunan Institute of Engineering) ;
  • Cao, L. (Department of Mechanical Engineering, Hunan Institute of Engineering) ;
  • Duan, S.Y. (College of Mechanical Engineering, Hebei University of Technology) ;
  • Huang, Z.H.H. (Department of Mechanical Engineering, Hunan Institute of Engineering) ;
  • Cheng, G.Q. (Department of Mechanical Engineering, Hunan Institute of Engineering)
  • Received : 2016.06.12
  • Accepted : 2017.01.26
  • Published : 2017.05.25
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Abstract

Due to the discontinuous nature of uncertainty quantification in conventional evidence theory(ET), the computational cost of reliability analysis based on ET model is very high. A novel ET model based on fuzzy distribution and the corresponding combination rule to synthesize the judgments of experts are put forward in this paper. The intersection and union of membership functions are defined as belief and plausible membership function respectively, and the Murfhy's average combination rule is adopted to combine the basic probability assignment for focal elements. Then the combined membership functions are transformed to the equivalent probability density function by a normalizing factor. Finally, a reliability analysis procedure for structures with the mixture of epistemic and aleatory uncertainties is presented, in which the equivalent normalization method is adopted to solve the upper and lower bound of reliability. The effectiveness of the procedure is demonstrated by a numerical example and an engineering example. The results also show that the reliability interval calculated by the suggested method is almost identical to that solved by conventional method. Moreover, the results indicate that the computational cost of the suggested procedure is much less than that of conventional method. The suggested ET model provides a new way to flexibly represent epistemic uncertainty, and provides an efficiency method to estimate the reliability of structures with the mixture of epistemic and aleatory uncertainties.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

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