YANG Yu, LIANG Yingjie, CHEN Wen. A Cumulative Residual Entropy Method in Selection of Random Load Distributions[J]. Applied Mathematics and Mechanics, 2018, 39(12): 1343-1350. doi: 10.21656/1000-0887.390157
Citation: YANG Yu, LIANG Yingjie, CHEN Wen. A Cumulative Residual Entropy Method in Selection of Random Load Distributions[J]. Applied Mathematics and Mechanics, 2018, 39(12): 1343-1350. doi: 10.21656/1000-0887.390157

A Cumulative Residual Entropy Method in Selection of Random Load Distributions

doi: 10.21656/1000-0887.390157
  • Received Date: 2018-05-31
  • Rev Recd Date: 2018-10-16
  • Publish Date: 2018-12-01
  • A cumulative residual entropy method was proposed to select the most suitable statistical distribution for the random load based on the Lévy stable distribution. In this method, the cumulative distribution and the tail distribution of the water level were fitted with the candidate distributions, and the cumulative residual entropy and the corresponding relative distances between the estimated distribution and the real distribution were respectively calculated, where the smaller the relative distance is, the more accurate the candidate distribution will be. The proposed method was validated by the upstream and downstream water levels of the Yongji 2nd sluice gate. The results show that, the Lévy stable distribution has the highest accuracy compared with the normal and the extreme value type I distributions in describing the heavy tail of the water level. The relative distances between the cumulative entropy and the cumulative residual entropy reveal that the fitting errors of the Lévy stable distribution are the smallest. Thus, based on the Lévy stable distribution, the cumulative residual entropy method is effective in selection of the distribution of the random load, which provides new ideas for the selection of random load distributions, and helps accurately calculate the reliability of engineering structures.
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