随机不确定性下结构系统性能决策的区域灵敏度研究

项目名称： 随机不确定性下结构系统性能决策的区域灵敏度研究

项目编号： No.51475370

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 机械、仪表工业

项目作者： 吕震宙

作者单位： 西北工业大学

项目金额： 80万元

中文摘要： 为度量随机输入变量的不同取值区域对结构系统输出性能的影响，并达到精确预测和高效设计结构输出性能的目的，本项目拟研究输出性能的统计特征对随机输入的区域灵敏度。针对飞机等结构，建立输入变量对输出性能各种统计特征影响的区域灵敏度指标，研究其物理性质和图解表征，着重研究得到相关输入情况下区域灵敏度的清晰物理解释，揭示区域灵敏度与结构输出性能决策的本质联系；并将输入变量的区域灵敏度指标推广至输入变量的分布参数具有不确定性的情况，直接用于要求目标性能下分布参数的设计。针对区域灵敏度指标计算的高维嵌套积分问题，基于降维算法、拒绝抽样自适应算法及随机森林算法等，建立求解区域灵敏度指标的高效算法，并研究所建理论和算法在复杂结构系统中的工程实现与应用。本项目的研究对于掌握不同区域输入变量-输出性能的不确定性性态、识别输入变量及分布参数不同区域的相对重要性以及高效实现随机环境下结构系统的目标性能具有重要意义。

中文关键词： 区域灵敏度；性能决策；降维；拒绝抽样；随机森林

英文摘要： To quantify regional effect of input on output of structural system and to accurately predict and efficiently design the output performance of the structure, the regional sensitivity of the output performance with respect to the random input is researched in this project. For the complicated structures such as the aircraft, the regional sensitivity index system is established for measuring the contribution of the input to different statistical characteristics of the output. The properties and the visual charactering of the regional sensitivity indices are searched, and the explicit physical explanation for the regional sensitivity indices in case of the correlated input is focused. The intrinsic relation between the regional sensitivity and the decision of the structural output performance is exposed. For the direct design of the distribution parameter satisfying the object performance, the regional sensitivity of the input is extended to that of the uncertain distribution parameter of the random input. The methods based on the dimensionality reduction, adaptive algorithm on rejection sampling and random forest are proposed to solve the integral with nested high dimensionality defined by the regional sensitivity. Then the realization and the application in engineering structure are also studied for the proposed regional sensitivity theory and its solving methods. The research of the project is very important for understanding the input-output relation, identifying the relative importance of the region of the input and realizing the required performance under the random environment efficiently.

英文关键词： regional sensitivity;decision of the performance;dimensionality reduction;rejection sampling;random forest