基于遗传算法的数据最大熵概率分布计算  

Calculation of maximum entropy probability distribution of data based on genetic algorithm

作　　者：彭颖 朱南海[2] PENG Ying;ZHU Nanhai(Putian University,Putian 351100 ,China;School of Architectural and Surveying Engineering,Jiangxi University of Science and Technology,Ganzhou 341000,China)

机构地区：[1]莆田学院土木工程学院,福建莆田351100 [2]江西理工大学建筑与测绘工程学院,江西赣州341000

出　　处：《南昌大学学报（工科版）》2020年第1期40-45,共6页Journal of Nanchang University(Engineering & Technology)

基　　金：国家自然科学基金资助项目(51768024)。

摘　　要：为获得工程数据样本所服从的概率分布,针对数据样本的概率分布存在多样性和不确定性等问题,基于最大熵法引入拉格朗日乘子构建样本可能的概率密度函数,而后将拉格朗日乘子的求解转化为最小值优化问题,并利用遗传算法的寻优功能搜索问题的全局最优解。以一标准正态分布N(0,1)的数据点为例,验证了最大熵法与遗传算法在确定数据概率密度函数中的有效性和可行性,且采用五阶约束矩即可获得可靠的计算结果,其最大熵概率密度函数的均值为0.0028和标准差为0.9549均较接近其理论值。同时高层建筑地震响应分布规律的预测结果也表明,最大熵法可获得符合数据样本真实分布的概率密度函数,是数据概率分布分析的有效方法。In order to obtain the true probability distribution of the data sample.A probability density function of the date sample was established by introducing Lagrange multiplier with maximum entropy method to solve the problem of the uncertainty of the probability distribution of the date sample,and the problem was converted to the minimum optimization of the function.Then the global optimal solution of the problem was solved with genetic algorithm.A set of date points that meet the standard normal distribution N(0,1)was taken as an example,the result showed that the maximum entropy method and genetic algorithm was effective and feasible in the determination of the probability density function of the date sample.The five order restriction moment can obtain a reliable calculation results,the mean and the standard deviation of it was 0.0028 and 0.9549,respectively,which were close to their theoretical value.Meanwhile,the prediction of the probability distribution of seismic response of high-rise building also showed the maximum entropy method was an effective method for data probability distribution analysis,which can obtain a result that consistent with the real probability distribution of data samples.

关 键 词：最大熵法 概率密度函数 遗传算法 约束矩 数据样本 

分 类 号：TU317[建筑科学—结构工程]