随机不确定性下基于时频域特征和能量统计的结构多输出性能全局灵敏度分析

In the environment with random uncertainty, there are redundancy, correlation, diversity, etc. for the multivariate output performance. It is difficult to quantitatively describe, extract and separate these complicated statistical information in multivariate output global sensitivity analysis of structures. This proposal will construct the multivariate output global sensitivity indices from extracting information of output in time and frequency domain and by use of the energy statistics theory. According to the Fourier transformation and wavelet analysis used for extracting information of output from time and frequency domain and the energy distance variance, energy distance correlation coefficient and energy distance component in energy statistics, we will show the comprehensive influence of inputs on the multivariate output performance consistently. Based on the extension of variance analysis for single output to the energy distance component analysis for multivariate output, we will connect the multivariate output global sensitivity analysis with the inherent structure of input-multivariate output to achieve the coincidence for the design of prediction of multivariate output performance. The principal component analysis and kernel principal component analysis are used to solve the problem of dimension disaster for output. The simulation method with only one set of input-output samples and the surrogate model method are utilized to solve the problem of dimension disaster for input. We will obtain the strategy to solve the problem of dimension disaster for both input and output in calculating multivariate output global sensitivity indices. In addition, we will also extend the proposed theory to the problems with time- and space-dependent output and perform the engineering verification. This proposal is valuable for completing the sensitivity analysis theory, identifying the critical inputs affecting the multivariate output correctly, designing and predicting the required multivariate structural performance efficiently.

随机不确定性下，多输出性能存在着信息冗余、相关、多样等特征，对此复杂缠绕的统计信息进行准确定量的刻画、提取和分离是结构多输出性能全局灵敏度分析面临的难题，本项目将从时频域特征提取和能量统计的角度来建立多输出全局灵敏度指标。基于时频域特征提取的傅里叶变换和小波分析，以及能量统计中的能量距离方差、能量距离相关系数和能量距离分量，来协调一致地反映输入对多输出性能的综合影响。推广单输出的方差分析到多输出的能量距离分量分析，将多输出的全局灵敏度与输入-多输出的本质结构关系联系起来，实现多输出性能设计与预测的统一。采用主成分和核主成分分析解决输出维度灾难，采用共用样本的模拟法和代理模型法解决输入维度灾难，研究得到多输出灵敏度计算中两类维度灾难的解决策略。将所建理论推广至时、空输出问题并进行工程验证。本项目对于完善灵敏度理论、正确识别影响多性能的关键输入因素及高效设计并预测结构的多目标性能具有重要意义。

在航空航天等工程领域内，往往存在着许多不确定性因素，这些不确定性因素会对结构输出性能产生显著的影响。为度量随机输入变量对多输出结构性能的影响，并为结构的性能评估及风险控制提供重要依据，本项目研究了随机不确定性下基于时频域特征和能量统计的结构多输出全局灵敏度分析指标及其高效求解算法。在已有单输出全局灵敏度分析方法的基础上，分别从傅里叶变换、协方差分解、主成分分析和能量距离等多个角度建立了多输出情况下的全局灵敏度分析体系，来协调一致地反映输入对多个输出性能的综合影响。为高效求解所建立的多输出全局灵敏度指标，研究了求解全局灵敏度指标的共用样本方法，消除了计算量与输入变量维数之间的相关性。为进一步降低样本法求解全局灵敏度指标的计算量，研究了自适应代理模型结合抽样的求解方法，并通过本项目建立的备选样本池缩减策略和切片逆回归降维策略，极大地提高了多输出全局灵敏度指标的求解效率。最终，将所研究的理论方法应用于飞机机翼结构和发动机涡轮部件的全局灵敏度分析中，检验理论方法的工程适用性，并编制了通用的软件平台。

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