# An improved maximum entropy method via fractional moments with Laplace transform for reliability analysis

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## Abstract

The fractional moment-based maximum entropy method (FM-MEM) attracts more and more attention in reliability analysis recently, comparing with the common integer moment-based maximum entropy method. In the present paper, a new approach for reliability analysis is proposed from the improvement of the fractional moment-based maximum entropy method via the Laplace transformation and dimension reduction method (DRM). Different with the traditional FM-MEM with a double-loop multivariate optimization formulation, the proposed method introduces a single-loop univariate optimization algorithm through solving a set of linear equations. Firstly, the single-loop algorithm is proposed for bounded positive random variable and then is extended to arbitrary positive random variable with the help of Laplace transform. Then, a univariate strategy is given to simplify the calculation for the unknown parameters in the single-loop algorithm. Through the improvement, not only the proposed method can predict failure probability accurately but also the computational cost is considerably reduced. Due to the univariate optimization strategy, the proposed method is more robust than common reliability analysis methods, which are sensitive to the initial points, such as the traditional FM-MEM and the first-order reliability method. Several numerical examples are studied to illustrate the efficiency, robustness, and accuracy of the proposed method for the prediction of the failure probability in comparison with other methods.

## Keywords

Fractional moment Laplace transform Maximum entropy method Dimension-reduction method Reliability analysis## Notes

### Funding

The support of the National Basic Research Program of China (Grant Nos. 2014CB046506 and 2014CB046803) and the National Natural Science Foundation of China of 11372061 is greatly appreciated.

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