对偶型最大熵概率密度函数模型及其优化解法

针对经典型最大熵概率密度函数模型及其计算目前存在的非线性程度高，优化不收敛，求解效率低等问题，提出了一种对偶型最大熵概率密度函数模型+逐次优化的方法.根据优化过程不稳定，重新推导了拉格朗日系数的线性变换公式.针对几种常见及一种复杂的概率密度函数，采用经典型与对偶型最大熵概率密度函数模型分别计算概率密度及可靠度的对比表明:与经典型最大熵概率密度函数模型相比，对偶型最大熵概率密度函数模型优化函数形式简单，非线性程度低.逐次优化法求解拉格朗日系数不仅克服了初始值敏感性问题，而且计算效率高.对偶型最大熵概率密度函数模型+逐次优化法与其他方法相比，计算精度最高，且能很好的应用于复杂概率分布及可靠性问题. 

Dual maximum entropy probability density function model and optimization

Based on high nonlinearity, hard convergence, low computational efficiency in the computational process by the classic maximum entropy probability density function model, a method called dual maximum entropy probability density function model+sequential updating method was proposed. Because of the unsteady optimization routine, a transformation formula of Lagrangian coefficient was rededuced. The probability density function and reliability of several common distributions and one complex distribution was calculated by classic and dual maximum entropy probability density function models. This shows that compared with classic maximum entropy probability density function model, the optimization function of dual maximum entropy probability density function model has advantages of low nonlinearity and simple form, the sequential updating method not only overcomes the sensitivity problem of initial value but exhibits high computational efficiency; dual maximum entropy probability density function model+sequential updating method has the highest computational accuracy, and can be well applied to the reliability problems of complex distribution.