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Entropy 2016, 18(4), 111; doi:10.3390/e18040111

Identifying the Probability Distribution of Fatigue Life Using the Maximum Entropy Principle

1
Key Laboratory of Fundamental Science for National Defense-Advanced Design Technology of Flight Vehicles, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2
Beijing Aeronautical Science and Technology Research Institute, Beijing 102211, China
*
Author to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Received: 17 December 2015 / Revised: 7 March 2016 / Accepted: 23 March 2016 / Published: 30 March 2016
(This article belongs to the Section Information Theory)
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Abstract

It is well-known that the fatigue lives of materials and structures have a considerable amount of scatter and they are commonly suggested to be considered in engineering design. In order to reduce the introduction of subjective uncertainties and obtain rational probability distributions, a computational method based on the maximum entropy principle is proposed for identifying the probability distribution of fatigue life in this paper. The first four statistical moments of fatigue life are involved to formulate constraints in the maximum entropy principle optimization problem. An accurate algorithm is also presented to find the Lagrange multipliers in the maximum entropy distribution, which can avoid the numerical singularity when solving a system of equations. Two fit indexes are used to measure the goodness-of-fit of the proposed method. The rationality and effectiveness of the proposed method are demonstrated by two groups of fatigue data sets available in the literature. Comparisons among the proposed method, the lognormal distribution and the three-parameter Weibull distribution are also carried out for the investigated groups of fatigue data sets. View Full-Text
Keywords: maximum entropy principle; fatigue life; statistical moments; maximum entropy distribution; Lagrange multiplier maximum entropy principle; fatigue life; statistical moments; maximum entropy distribution; Lagrange multiplier
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Li, H.; Wen, D.; Lu, Z.; Wang, Y.; Deng, F. Identifying the Probability Distribution of Fatigue Life Using the Maximum Entropy Principle. Entropy 2016, 18, 111.

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