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.
Highlights
In engineering structural design, it is well-known that the experimental data of fatigue testing and structures subject to cyclic loads display large variations, even if under the same loading conditions
A new computational method is proposed in this paper for identifying the probability
A new computational method is proposed in this paper for identifying the probability distribution distribution of fatigue life of materials and structures
Summary
It is well-known that the experimental data of fatigue testing and structures subject to cyclic loads display large variations, even if under the same loading conditions. It is generally assumed that the fatigue lives of metal materials follow a lognormal distribution or a Weibull distribution [1,2,4,10]. The main reason is that only an analytical normal distribution or truncated normal distribution (the nonnegativity of fatigue live is considered in a truncated normal distribution) can be obtained, since the approach only uses the first two statistical moments Their method did not take full advantage of the flexibility and optimal unbiased estimation of the MaxEnt principle when employing it to identify the probability distribution type of fatigue life. A new method to identify the probability distribution of fatigue life based on the MaxEnt principle with the first four statistical moments is proposed. Attention is paid on the goodness-of-fit based on two fit indexes
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