本文選題：概率密度估計(jì)　切入點(diǎn)：可靠性　出處：《南京航空航天大學(xué)學(xué)報(bào)》2017年01期

【摘要】：針對(duì)經(jīng)典最大熵概率密度估計(jì)中拉格朗日乘子計(jì)算目前存在高度非線性、計(jì)算精度不高或有時(shí)難以收斂等問(wèn)題,提出了一種"最大似然+逐次優(yōu)化"的方法�；谧畲笏迫还烙�(jì)法,推導(dǎo)建立了簡(jiǎn)化的拉格朗日優(yōu)化函數(shù);在此基礎(chǔ)上,基于樣本原點(diǎn)矩約束,提出了逐次尋優(yōu)算法。根據(jù)優(yōu)化過(guò)程不穩(wěn)定,重新推導(dǎo)了拉格朗日乘子的線性變換公式,避免矩陣求逆運(yùn)算引起的奇異現(xiàn)象。針對(duì)幾種常見(jiàn)的概率分布類型及可靠性問(wèn)題,采用極大似然最大熵概率密度估計(jì)法與經(jīng)典型最大熵概率密度估計(jì)法分別計(jì)算概率密度及可靠度的對(duì)比表明:極大似然最大熵概率密度估計(jì)法的優(yōu)化函數(shù)非線性程度低,形式簡(jiǎn)單,而且"極大似然最大熵概率密度估計(jì)+逐次優(yōu)化法計(jì)算"精度高,收斂性好。
[Abstract]:Aiming at the problems of Lagrangian multiplier calculation in the classical maximum entropy probability density estimation, such as high nonlinearity, low accuracy or difficulty in convergence, a method of "maximum likelihood successive optimization" is proposed.Based on the maximum likelihood estimation method, a simplified Lagrange optimization function is derived, and a sequential optimization algorithm is proposed based on the origin moment constraint of the sample.According to the instability of the optimization process, the linear transformation formula of Lagrange multiplier is rederived to avoid the singularity caused by matrix inversion.Aiming at several common probability distribution types and reliability problems,The comparison between the maximum likelihood entropy probability density estimation method and the classical maximum entropy probability density estimation method shows that the maximum likelihood maximum entropy probability density estimation method has low nonlinear degree of optimization function.The form is simple and the "maximum likelihood entropy probability density estimation successive optimization method" has high accuracy and good convergence.
【作者單位】： 南京航空航天大學(xué)能源與動(dòng)力學(xué)院;
【基金】：國(guó)家自然科學(xué)基金(51205190)資助項(xiàng)目
【分類號(hào)】：O212.1

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