【摘要】：針對經(jīng)典最大熵分位值估計中拉格朗日系數(shù)計算目前存在高度非線性、計算結(jié)果精度不高或有時難以收斂等問題,提出了一種對偶型-逐次尋優(yōu)的方法.基于拉格朗日對偶法,推導(dǎo)建立了含有拉格朗日系數(shù)優(yōu)化函數(shù)的對偶表達式;在此基礎(chǔ)上,基于樣本的概率權(quán)重矩約束,提出了逐次尋優(yōu)算法.針對幾種常見的概率分布類型和一種較為復(fù)雜的概率分布類型,采用對偶型最大熵方法和經(jīng)典最大熵方法對其概率累積函數(shù)和分位值進行計算對比分析表明:對偶型最大熵分位值估計不僅具有非線性程度低、形式簡單,而且對偶型-逐次尋優(yōu)的方法具有比較高的計算精度,優(yōu)化迭代的收斂性好等特點.
[Abstract]:In order to solve the problems of high nonlinearity in Lagrangian coefficient calculation in classical maximum entropy estimation, the accuracy of calculation results is not high or sometimes it is difficult to converge. A dual-order optimization method is proposed in this paper. Based on the Lagrangian dual method, the dual expression with Lagrangian coefficient optimization function is derived, and based on the constraint of probability weight moment of samples, a successive optimization algorithm is proposed. For several common types of probability distribution and a more complex type of probability distribution, The dual maximum entropy method and the classical maximum entropy method are used to calculate and compare the probability cumulative function and the quantitive value. The results show that the dual maximum entropy estimation is not only of low nonlinearity, but also simple in form. Moreover, the dual-successive optimization method has the characteristics of high calculation precision and good convergence of optimization iteration.
【作者單位】： 南京航空航天大學(xué)能源與動力學(xué)院;
【分類號】：TB114.3

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