混合数据信息下不确定性描述的改进最大熵函数法

An improved entorpy-based representation for mixed uncertainty about intervals and points data

可靠性分析的基础在于不确定性的精确描述。工程实际中由于个别变量信息缺乏只能确定其区间范围,提出描述区间和离散点混合不确定性的改进最大熵函数法。该方法建立不同类型数据不确定性的联合熵函数,应用插值技术得到描述区间和离散点混合数据信息下不确定性的非参数概率密度函数,通过优化联合熵函数最大,确定非参数概率密度函数在原始数据空间上下限内均匀离散点处的概率密度值。相比于传统非参数概率确定方法,所提方法将传统分布参数估计寻优过程转化为在原始数据空间内对自定义随机离散点处的概率密度值优化,进而使用插值技术得到描述区间和离散点数据混合不确定性的最少偏见概率密度函数,其混合不确定性描述精度由自定义的随机离散点多少来确定,精度按需可控。此外,在概率理论框架下,尝试将输入混合不确定性信息向输出传递,完成输出响应的可靠性分析。所提方法计算量和精度可通过自定义离散点数量控制,对原始数据不确定性信息挖掘更充分。算例表明所提方法科学性和合理性,为概率理论用于混合不确定性分析奠定基础。

In engineering design problems,intervals refer to any kind of lack of information.This paper presents an improved entorpy-based methodology for a probabilistic representation of a stochastic quantity for which only sparse point data and/or interval data may be available.The combined entropy function is used to measure the uncertainty in data,which is evaluated from the non-parametric probability density function for sparse point data and the cumulative distribution function for interval data,Wherein the entire non-parametric distribution can be discretized at a finite number of points and the probability density values at these points can be inferred using the principle of maximum-entropy,thus avoiding the assumption of any particular distribution.The proposed improved Entorpy-based methodology is then employed in the attempt of interval uncertainty propagation,with the results compared with previous studies.Examples are provided to demonstrate the effectiveness of present method.The study reveals great potentials of the probabilistic method for the treatment of the uncertainty in presence of the sparse point data and/or interval data.