动、静不确定性变量同时作用下复杂结构系统时频双角度全局重要性分析方法研究

In the presence of both the dynamic and static uncertain inputs, there are uncertainty, time-dependence, correlation, etc. among both the inputs and output performance of the structural systems, and the uncertainties in the inputs and outputs at different time instants interact. These properties of the complex structural systems put forward a new challenge for the global importance analysis. To clearly quantify the effects of the two kinds of inputs on dynamic output of structural systems and to accurately predict and efficiently design the dynamic output performance, global importance analysis method of the dynamic output performance with respect to the dynamic and static uncertain inputs is researched in this project from the dual perspective of the time and frequency domains. For the complex structures such as the aircraft, the global importance measures are established in both the time and frequency domains based on Karhunen–Loève expansion and Fourier transformation, which can measure the effects on the different statistical characteristics of the dynamic output by the dynamic and static uncertain input variables randomly varying in their values fields. The physical properties of the established global importance measures are investigated and the intrinsic relation between the importance measures in time domain and those in frequency domain is explored. The surrogate modeling methods and single-loop sampling methods with considering both the time and random space variations of the inputs are established, which can solve the problem that the computational cost of the importance analysis increases exponentially with the number of inputs in case of complex dynamic structural systems. The research in this project is significant for understanding input-output relation, identifying the relative importance of the dynamic and static uncertain inputs and efficiently realizing the target dynamic performance of the structural systems with both dynamic and static uncertain inputs.

动、静不确定性变量同时作用下，结构系统的输入和输出性能均存在着不确定、时变、相关等特征，各时刻输入输出不确定性信息相互缠绕，制约给全局重要性分析带来新难题。为清晰度量动、静不确定性变量同时存在下，两类输入变量对结构动态输出性能的影响，达到精确预测和高效设计动态性能的目的，本项目拟从时域和频域双重角度研究动态输出性能统计特征对输入动态和静态不确定性变量的全局重要性分析方法。针对飞机等结构，基于Karhunen–Loève扩展和傅里叶变换，建立时域和频域中度量两类变量在其取值全域内波动时对动态性能各种统计特征影响的全局重要性测度，研究其物理性质，探索时域与频域重要性测度间的内在联系。在考虑时间与随机空间变化下，采用代理模型与单层抽样法解决动态重要性分析计算量巨大问题。本项目对掌握时域与频域中输入-输出不确定性性态、识别动、静不确定性变量相对重要性及高效实现复杂结构系统动态目标性能具有重要意义。

重要性分析是实现航空及土木等领域复杂结构系统高效不确定性设计和优化的主要途径，然而对于工程实际中普遍存在的同时包含动、静不确定性变量的结构系统，由于输入和输出性能均存在着不确定、时变、相关等特征，各时刻输入输出不确定性信息相互缠绕制约等，给重要性分析带来新难题。为清晰度量动、静不确定性变量同时存在下，两类输入变量对结构动态输出性能的影响，达到精确预测和高效设计动态性能的目的，本项目从时域和频域双重角度研究了动态输出性能统计特征对输入动态和静态不确定性变量的全局重要性分析方法。针对飞机等结构，基于Karhunen–Loève扩展，建立了时域中度量两类变量在其取值全域内波动时对动态性能统计矩、概率分布，可靠性影响的全局重要性测度，研究得到了各指标的物理性质及其之间的关系。基于傅里叶变换，建立了频域中度量两类变量在其取值全域内波动时对动态性能幅频特性、相频特性和功率谱密度影响的全局重要性测度，研究得到了各种指标的物理性质及其之间的关系，并探索了时域与频域重要性测度间的内在联系。此外，在同时考虑时间与随机空间变化下，建立了动、静不确定性输入变量全局重要性测度指标求解高效的代理模型与单层抽样方法，解决了动态重要性分析计算量巨大问题。最后，本项目还将所研究的理论编制成软件，与商用有限元软件连接，形成动、静不确定性变量同时作用下复杂结构系统重要性分析软件平台，并应用于真实的机翼等结构，为这些结构动态性能的设计和优化提供了重要的指导信息。事实证明，本项目的研究对掌握时域与频域中输入-输出不确定性性态、识别动、静不确定性变量相对重要性及高效实现复杂结构系统动态目标性能具有重要意义。