不确定环境下飞机典型结构多维性能的重要性分析方法研究

Most of the existing importance analysis techniques are tailored for models with single output performance, while many structural systems in engineering such as aircraft are often required to satisfy multiple performances. To clearly identify the importance of the inputs for the multivariate output performances of the structural systems, this project devotes to developing importance analysis methods for the structural systems with multivariate outputs. For complex structures like aircraft, the global importance measures and the regional ones are established to reasonably evaluate the effects of the inputs on the statistical performances of the multivariate output. The physical properties of the established importance measures are also investigated. The intrinsic relation between the importance of the input for the multivariate output and that for the single output is explored by virtue of the statistical relation between the single and the multivariate output. To solve the problem that the computational cost of the importance analysis increases exponentially with the number of inputs in case of multivariate output, the efficient and robust solutions of the established importance measures are constructed by employing the state dependent parameter, unscented transformation and space-partition methods. Based on the established importance measures and their efficient solutions, general software for importance analysis of the structural systems with multivariate output is developed for convenience of engineering application. The software is then applied to an aircraft wing to obtain the important inputs and the crucial regions in the distributions of the inputs. The research of the project is very significant for the optimization, dimensionality reduction and achieving an optimum balance among multiple performances of the aircraft with multivariate output.

目前已有的重要性分析绝大多数是针对单一性能的，而在不确定性环境下工作的飞机结构常常需要满足多种性能要求。为了清晰地掌握影响结构系统多维输出性能的输入变量的重要程度，本项目拟研究多维输出结构系统的重要性分析方法。针对飞机等复杂的结构系统，从全局和区域角度建立合理度量输入变量对多维输出统计性能影响的重要性测度指标，研究其物理性质，并利用多输出性能与单输出性能的统计关系，揭示单、多输出性能重要度的关系。研究所建指标求解高效的态相关参数、无迹转换、空间分割等方法，解决复杂结构多维输出情况下重要性测度分析的计算量随变量维数呈指数级增加的问题。将所建理论和方法编制成通用软件，并完成其在飞机机翼等结构中的应用，得到影响机翼结构多维输出性能的重要变量及其内部重要区域。本项目的研究对飞机结构多性能要求下的优化、降维及多性能综合权衡具有重要的意义。

重要性分析能够识别影响结构系统输出性能的主、次输入变量，为结构系统性能的设计和优化提供重要指导信息。目前已有的重要性分析绝大多数是针对单一性能的，而在不确定性环境下工作的飞机结构常常需要满足多种性能要求。为了清晰地掌握影响结构系统多维输出性能的输入变量的重要程度，本项目研究了多维输出结构系统的重要性分析方法。.针对飞机等复杂的结构系统，从全局和区域双重角度建立了合理度量输入变量对多维输出各阶统计矩特征（包括均值、方差、偏度和峰度）以及矩独立特征（包括失效概率、密度函数和信息熵）影响的重要性测度指标体系。研究了各指标的物理性质，并利用多输出性能与单输出性能的统计关系，揭示了单、多输出性能重要度之间的补充与制约的内在联系。基于此，将单一输出性能情况下高效的重要性分析方法引入到多输出性能情况下，得到了所建指标高效求解的代理模型（包括多项式混沌展开以及态相关参数）以及高效抽样方法（包括无极变换和空间分隔），解决了复杂结构多维输出情况下重要性测度分析的计算量随变量维数呈指数级增加的问题。最后，本项目还将所建理论和方法编制成通用软件，并完成其在飞机机翼等结构中的应用，得到影响机翼结构多维输出性能的重要变量及其内部重要区域。研究成果发表在《Reliability Engineering & System Safety》以及《Aerospace Science and Technology》等多个本领域顶级期刊上。本项目的研究成果对飞机结构多性能要求下的优化、降维及多性能综合权衡具有重要的意义。