Structural and Multidisciplinary Optimization

, Volume 57, Issue 4, pp 1749–1764 | Cite as

A novel evidence theory model dealing with correlated variables and the corresponding structural reliability analysis method

  • Z. Zhang
  • C. Jiang
  • X. X. Ruan
  • F. J. Guan


Evidence theory serves as a powerful tool to deal with epistemic uncertainty which widely exists in the design stages of many complex engineering systems or products. However, the traditional evidence theory model cannot handle parameter correlations that may have profound influences on the reliability analysis results. This paper is supposed to develop a novel evidence theory model with consideration of parameter correlations and its corresponding structural reliability analysis method. First, a multidimensional parallelepiped uncertainty domain which takes into account the influence of parameter correlations is constructed. Second, the corresponding joint basic probability assignments are established for each focal element in the uncertainty domain. Finally, the reliability interval composed of the belief and plausibility measures are computed. Several numerical examples are investigated to demonstrate the effectiveness of the proposed model and the corresponding reliability analysis method.


Epistemic uncertainty Evidence theory Uncertainty modeling Reliability analysis Parameter correlation 



This work is supported by the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 51725502), National Natural Science Foundation of China (Grant No. 51490662), National Key Research and Development Plan (Grant No. 2016YFD0701105), National Natural Science Foundation of China (Grant No. 11402296).


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle EngineeringHunan UniversityChangshaPeople’s Republic of China
  2. 2.Science and Technology on Integrated Logistics Support LaboratoryNational University of Defense TechnologyChangshaPeople’s Republic of China

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