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中南大学学报(自然科学版)

Journal of Central South University

第51卷    第6期    总第310期    2020年6月

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文章编号:1672-7207(2020)06-1692-11
基于正态信息扩散原理的极值型工程参数概率分布推断方法
宫凤强1, 2,王天成1,黄天朗1

(1. 中南大学 资源与安全工程学院,湖南 长沙,410083;
2. 东南大学 土木工程学院,江苏 南京,211189
)

摘 要: 在工程可靠度分析中存在大量的极值型工程参数,为了获得这类参数的最优概率分布,提出基于正态信息扩散原理的极值型工程参数概率分布推断方法。在考虑偏度的“3 ”统计原理的截尾区间下,以年最大标准风压和内摩擦角样本为例,分别利用正态信息扩散分布和极值型分布拟合2组样本,并运用K-S方法进行假设检验。为了考察样本个数对2种分布在拟合精度方面的影响,利用Monte-Carlo方法生成母函数为极值型分布的8组模拟样本,样本个数分别为15,20,30,50,100,200,500和1 000,并采用K-S检验法对不同样本个数下推断得到的概率分布进行检验。结合正态信息扩散分布的拟合优势,将其应用于核管道工程最大腐蚀深度预测。研究结果表明:不论是实际工程样本还是模拟样本,正态信息扩散分布和极值型分布均通过K-S检验,其中正态信息扩散分布的检验值均低于极值型分布的检验值;随着样本个数增加,正态信息扩散分布表现出更好的收敛优势。正态信息扩散分布的累积概率在10-4误差量级上表现出等于1的效果,而极值型分布的累积概率在同样的误差量级上达不到1。算例结果表明:利用正态信息扩散分布作为核管道腐蚀深度的预测模型,能够更加精确地预测其最大腐蚀深度。

 

关键字: 岩土工程;可靠度;极值型参数;最优概率分布;正态信息扩散

An inference method for probability distribution of extreme value engineering parameters based on normal information diffusion principle
GONG Fengqiang1, 2, WANG Tiancheng1, HUANG Tianlang1

1. School of Resources and Safety Engineering, Central South University, Changsha 410083, China;
2. School of Civil Engineering, Southeast University, Nanjing 211189, China

Abstract:There are a lot of extremum-types of engineering parameters in the reliability analysis. In order to obtain the optimal probability distribution of such parameters, an inferential method for the probability distributions of extremum-type of engineering parameters based on the normal information diffusion(NID) principle was proposed. Considering the truncated interval combining “3 ” statistical principle and the effect of skewness, the annual maximum standard wind pressure and friction angle were used as the engineering examples. The NID distribution and extremum-type distribution were used to deduce the corresponding probability distribution,and the K-S method was used to test the goodness of fit of the corresponding distributions. In order to investigate the influence of sample numbers on the fitting accuracy for two distributions,the Monte-Carlo method was used to generate eight groups of simulated samples,and the sample numbers were 15, 20, 30, 50, 100, 200, 500 and 1 000,respectively. And the corresponding K-S test method was also used to test the inferred probability distributions at different sample numbers. Combining the fitting advantages of the NID distribution, it was applied to the prediction of the maximum corrosion depth for nuclear pipelines engineering. The results show that whether for engineering samples or simulated samples, both the NID distribution and extremum-type distribution pass the test. The K-S test values of the NID distribution are always lower than those of extremum-type distribution and show great advantages in convergence with the increase of sample numbers. The cumulative probabilities of the NID distribution are equal to 1 at the fitting error magnitude of 10-4, while these extremum-type distributions are less than 1 at the same of fitting error magnitude. The NID distribution is used as a predictive model for the corrosion depth of nuclear pipelines,which can predict the maximum corrosion depth more accurately.

 

Key words: geotechnical engineering; reliability; extremum-type parameters; optimal probability distribution; normal information diffusion(NID)

中南大学学报(自然科学版)
  ISSN 1672-7207
CN 43-1426/N
ZDXZAC
中南大学学报(英文版)
  ISSN 2095-2899
CN 43-1516/TB
JCSTFT
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