Structural and Multidisciplinary Optimization

, Volume 58, Issue 3, pp 1187–1203 | Cite as

Structural reliability analysis based on analytical maximum entropy method using polynomial chaos expansion

  • Jianbin Guo
  • Jianyu Zhao
  • Shengkui Zeng


The maximum entropy (ME) method is a promising tool for structural reliability analysis by estimating the unknown probability density function (PDF) of given model response from its moment constraints. However, the classic ME algorithm has to resort to an iterative procedure due to non-linear constraints, and the required high order moment estimations may have large statistical error. In this paper, we (i) propose an analytical ME method based on integration by parts algorithm to transform the non-linear constraints to a system of linear equations and (ii) derive the polynomial chaos expansion (PCE) multiplication for improving higher order moment calculation required in the previous step efficiently. Thus, an analytical formula of response PDF is obtained directly without intensively iterative procedure and associated convergence error, and it is followed by probability failure estimation using numerical integration computation. Two structural engineering cases are implemented to illustrate the accuracy and efficiency of the proposed method.


Structural reliability analysis Maximum entropy method Polynomial chaos expansion Multiplication of orthogonal polynomials 



The authors would like to extend their sincere thanks to anonymous reviewers for their valuable comments.

Funding information

This work was supported by the National Natural Science Foundation of China (NSFC 61304218).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Reliability and Systems EngineeringBeihang UniversityBeijingChina
  2. 2.Science and Technology on Reliability and Environmental Engineering LaboratoryBeihang UniversityBeijingChina

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