Abstract
This paper verifies the feasibility of the relative entropy method in selecting the most suitable statistical distribution for the experimental data, which do not follow an exponential distribution. The efficiency of the relative entropy method is tested through the fractional order moment and the logarithmic moment in terms of the experimental data of carbon fiber/epoxy composites with different stress amplitudes. For better usage of the relative entropy method, the efficient range of its application is also studied. The application results show that the relative entropy method is not very fit for choosing the proper distribution for non-exponential random data when the heavy tail trait of the experimental data is emphasized. It is not consistent with the Kolmogorov–Smirnov test but is consistent with the residual sum of squares in the least squares method whenever it is calculated by the fractional moment or the logarithmic moment. Under different stress amplitudes, the relative entropy method has different performances.
Highlights
We will check the efficiency of the relative entropy method which is realized through the fractional order moment and the logarithmic moment by using the real experiment data of the fatigue life of the carbon fiber/epoxy composites instead of the produced random numbers using the Monte Carlo method
The relative entropy is valid according to the statistical theory [17,28,29], but it is a difficult problem for computing with a high cost to obtain the estimations of the probability density function and the Shannon entropy of the M-L distribution
According to the former research, the relative entropy is better for the random variable with a spike probability density function (PDF) just as the M-L distribution is
Summary
Study on the fatigue of materials has become more and more significant since Wilhelm. We would like to investigate the feasibility of the M-L distribution in fitting the fatigue data based on the relative entropy method [17]. The M-L distribution has been applied as a novelty statistical tool to describe non-exponential statistical phenomena in diverse fields [18,19], such as bridge fatigue life assessment [12] and modeling of an anomalous diffusion with hereditary effects for the importance of the M-L function in the fractional calculus [20,21]. We will check the efficiency of the relative entropy method which is realized through the fractional order moment and the logarithmic moment by using the real experiment data of the fatigue life of the carbon fiber/epoxy composites instead of the produced random numbers using the Monte Carlo method.
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