基于统计与粗糙集理论的飞机垂尾抖振载荷分布假设选择与评价方法

Selection and evaluation method for distribution assumptions of aircraft buffet load based on statistics and rough set theory

研究飞机垂尾抖振问题的主要任务之一是编制抖振疲劳载荷谱、估算飞机结构的抖振疲劳寿命并校核飞机结构的强度等,一般通过统计方法来建立其抖振疲劳载荷时程的峰(谷)值分布模型,而分布模型的优劣对确定各飞行状态下的极限工况及抖振响应的循环次数与幅值分布等信息影响显著。通过分析五种常用于描述抖振疲劳载荷峰(谷)值的概率分布假设模型:正态分布、对数正态分布、威布尔分布、瑞利分布和极值分布,给出了基于参数估计的概率分布规律,并提出了一种采用各概率分布假设所对应模型的"拟合优劣指标"作为评价和选择的依据。同时,结合各分布模型的特性对飞机抖振载荷时程处理要求的匹配程度,运用粗糙集理论确定了系统评价指标的最小分辨距离与最大分辨率,来消除由于误差引入导致的评价指标数值差异而造成的误判。算例分析表明,该方法可合理且高效地实现对飞机抖振载荷概率分布假设的正确评价与选择。

Aiming at tasks of fatigue spectrum development, buffet fatigue life estimation and strength certification, aircraft buffet problems were investigated by means of establishing a statistical distribution model of peak （or valley） values. But, the selection of probabilistic distribution models had evident effects on determining ultimate load cases, buffet cycles and amplitude distributions under a given flight condition. Five typical models including normal distribution, lognormal distribution, Weibull distribution, Rayleigh distribution and extreme value distribution usually used to describe the probabilistic distribution of peak （or valley ） values of buffet fatigue loading were discussed firstly. Based on the probabilistic distributions given by parameters estimation, a distribution fitting index was proposed to evaluate the probabilistic distribution assumptions. Then, the analysis was performed by considering their matching levels between the distribution characteristics and the requirements of buffet loading data processing. The minimum discernible interval and the maximum resolution were acquired with the theory of rough set to eliminate judgment errors. Numerical example proved that this method can meet the requirement of evaluating probabilistie distribution assumptions well.