阵风响应问题的配点型区间分析方法

Collocation interval analysis method for gust response

最新的先进飞行器设计进展已经认识到定义多种类型的不确定性的重要意义。现有的气动弹性理论面临的一个重要问题是如何处理阵风激励和结构中的不确定性参数。给出了弹性机翼构件受到阵风作用时的控制方程。考虑了阵风模型和机翼结构中存在的不确定性参数,将其用区间向量定量化并一元化处理,基于第一类Chebyshev正交多项式和区间配点方案,结合有限元计算方法,提出了一种阵风响应问题的配点型区间分析方法(CIAM),推导了配点型区间分析方法的数学表达式。该方法避免了计算响应函数对不确定性参数的灵敏度(偏导数),放宽了不确定性参数变化范围为小区间的要求。为解决含有不确定性参数的阵风响应问题提供了一种新的可行途径。通过与Taylor区间分析方法(TIAM)的比较,数值算例表明,该方法能够得到一个包含精确响应值的足够"紧"的阵风响应区间。显示了该方法的优越性,具有工程指导意义。

Latest aircraft design advances have started to recognize the important significance of defining multiple types of uncertainty. An important issue faced in the previous aeroelastic theory is how to deal with uncertain parameters in gust and structure. We describe the governing equation of the structural response of elastic wing in atmosphere due to gust excitation. The uncertain parameters describing the gust model and the wing structure are modeled as interval sets before the unified treatment of the uncertainties. A collocation interval analysis method（ CIAM） for gust response based on the first Chebyshev orthogonal polynomials,interval collocation scheme and finite element method is proposed. The formula of CIAM is derived. The method does not require the sensitivities of the objective function with respect to uncertain variables and the assumption of narrow interval is also not needed. The proposed method can be used to solve gust response problems with uncertainties. Numerical example demonstrates that CIAM gives tighter gust response bound including exact response by comparing its results with Taylor interval analysis method（ TIAM）,which illustrates the efficiency and significant engineering value of the proposed method.