Structural reliability analysis based on analytical maximum entropy method using polynomial chaos expansion
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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.
KeywordsStructural 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.
This work was supported by the National Natural Science Foundation of China (NSFC 61304218).
- Huang W, Mao J et al (2014) The maximum entropy estimation of structural reliability based on Monte Carlo simulation. ASME 2014 33rd International Conference on Ocean, Offshore and Arctic EngineeringGoogle Scholar
- Isukapalli SS (1999) Uncertainty analysis of transport-transformation models. The State University of New Jersey, RutgersGoogle Scholar
- Kelley CT (1999) Iterative methods for optimization. Society for Industrial and Applied MathematicsGoogle Scholar
- Lasota R, Stocki R et al (2015) Polynomial chaos expansion method in estimating probability distribution of rotor-shaft dynamic responses. Bull Pol Acad Sci Tech Sci 63(2):413–422Google Scholar
- Luo W (2006) Wiener chaos expansion and numerical solutions of stochastic partial differential equations. California Institute of TechnologyGoogle Scholar
- Mason JC, Handscomb DC (2002) Chebyshev polynomials. CRC PressGoogle Scholar
- Savin E, Faverjon B (2017) Higher-order moments of generalized polynomial chaos expansions for intrusive and non-intrusive uncertainty quantification. 19th AIAA Non-Deterministic Approaches ConferenceGoogle Scholar