确定飞机最大抖振设计载荷的长期极值估计方法

Long-term extreme value estimation method to determine maximum buffet design loads

确定飞机在抖振工况下的限制载荷是现代飞机动强度设计分析的关键步骤之一。运用次序统计和长期极值估计理论的极值Ⅰ型分布和Ⅲ型分布,在风洞试验数据基础上,分别应用最小二乘法和最大似然估计法进行极值模型的参数估计,并根据预设的重现期指标进行了某型飞机尾部结构抖振设计载荷的极值估计。探讨了极值分布概率模型、估计方法和样本数量对抖振载荷极值估计结果的影响。提出了实现准确有效极值估计的样本数量基本要求的指标,根据该指标可以确定最小振动响应采集时间,以指导测试方案和数据处理方法的制定。实例分析结果表明:极值Ⅲ型分布能够较好地估计抖振试验数据的极值(相对误差在±5%以内),且进行分布模型的参数估计时,最大似然法的精度略高于最小二乘法。对比分析的结果也表明,应用传统的3σ准则进行随机振动结构的限制载荷设计可能偏危险,不适于工程应用。

Determination of the dynamic limit load for a vibrating structure plays an important role in the dynamic strength analysis of aircraft. Based on the order statistics and Gumbel extreme value distribution theory, a method was proposed to estimate maximum load encountered in a long operating time of aircraft by means of the statistics analysis of short duration experimental data. Using the buffet response data of an aircraft empennage structure as an example, the effects of different Gumbel distribution models, parameter estimation methods and number of samples on the estimation accuracy of a long-term extreme value were discussed. The comparison between predicted and test results shows that Gumbel III distribution model is more suitable for prediction of buffet extreme value than Gumbel I distribution model, and the relative estimation error is below± 5 %. The maximum likelihood estimation method also shows a little better than the least square method for the parameter estimation of probability distribution models. The further research shows that the least sample number of test data must reach to the required number for a valid long-term extreme value prediction. Moreover, the investigation shows that the long-term extreme value theory is more reasonable than the traditional 3σ criterion to determine the dynamic limit loads for random vibration problems, and the limit load determined by 3σ criterion is partially dangerous.