复杂结构系统可靠性全局与局部灵敏度分析的一体化高效方法研究

Reliability based design optimization (RBDO) can guarantee the optimal matching of the performance and the reliability, but its application in the complicated structure is limited by the large amount of computational cost of the RBDO. The efficiently unified algorithm will be studied in this proposal for analyzing the global and local reliability sensitivity. In the proposed algorithm, the global reliability sensitivity is used to simplify the reliability model under the required precision, the local one is used to directly provide the optimization searching direction, then the efficiency of the RBDO can be collaboratively improved by the global and local reliability sensitivity, and the difficulty can be solved for the RBDO application in the complicated structure such as the aircraft structure. Based on the Bayes formula, the global reliability sensitivity and the local one are unified as the classification of the model output, on which the embedded Kriging model and the numerical simulation are both constructed to solve the global reliability sensitivity and the local one. The Kriging model is embedded and adaptively updated in the sample pool of the numerical simulation, and the convergent Kriging model is used to realize the classification of the model output, then the efficiency of the proposed Kriging model can be greatly improved while the precision is satisfied. In the proposed numerical simulation algorithm, the dimensionality reduction of the line sampling and the direction sampling is combined with the wide applicability of the Monte Carlo simulation, and the dimensionality reduction sampling is used to realize the classification of the Monte Carlo sampling, then the proposed numerical simulation algorithm can possess the precision of the Monte Carlo method and the efficiency of the dimensionality reduction simultaneously. The proposed Kriging model and the numerical simulation are applied to the aircraft wing for validating their perspective in the engineering application.

可靠性优化可保证不确定性下性能和可靠性的最佳匹配，但分析复杂结构可靠性及其导数的超大计算量制约了可靠性优化的应用。本项目拟研究可靠性全局和局部灵敏度的一体化高效方法，利用全局灵敏度在保证精度同时简化模型，并利用局部灵敏度直接提供优化搜索方向，从而协同提高复杂结构可靠性优化的效率，解决应用难题。所研究的一体化方法依据贝叶斯公式将两类灵敏度统一为输出分类问题，再分别从嵌入式代理模型和数字模拟两方面来建立求解方法。所建嵌入式Kriging模型法在数字模拟样本池内自适应更新代理模型，并利用收敛后的代理模型实现输出分类，从而在保证模拟法精度的同时大幅提高计算效率。所建数字模拟法将结合线抽样和方向抽样的降维特性及蒙特卡洛法的普适性，以降维抽样实现蒙特卡洛样本的分类，使得所提方法在达到蒙特卡洛法精度同时保持降维抽样效率。将两种方法应用于某机翼结构，验证方法的精度、效率及在复杂结构可靠性优化中的应用前景。

可靠性全局和局部灵敏度分别从简化可靠性分析模型和直接提供可靠性优化搜索方向的不同角度来提高可靠性优化设计的效率。因此，研究两类可靠性灵敏度的一体化高效方法对可靠性优化设计具有重要的意义。本项目研究了两类可靠性灵敏度的共性特征，并提出了多种高效一体化分析方法。依据可靠性灵敏度的基本定义和贝叶斯公式，从输出分类的角度揭示可靠性全局和局部灵敏度的共性特征，从而将可靠性全局和局部灵敏度分析统一转化成了输出分类问题，为建立同时求解可靠性局部和全局灵敏度分析的一体化分析方法奠定了基础。进一步地，建立了同时高效求解两类可靠性灵敏度指标的的嵌入式代理模型法和降维抽样法。嵌入式代理模型法中主要研究了自适应Kriging耦合重要抽样数字模拟的AK-in-IS方法和元重要抽样与自适应Kriging相结合的Meta-IS-AK方法，并发展了针对两类可靠性灵敏度分析的嵌入式代理模型的试验设计、学习函数和迭代停止准则，协调计算精度和计算效率的矛盾。降维抽样法中研究了线抽样和方向抽样，建立了降维抽样样本与蒙特卡洛样本之间的关系，并通过自适应Kriging进一步提高了计算效率。最终，将所研究的理论方法应用于机翼前缘加强肋、机翼翼盒以及导弹舵面等工程复杂结构的可靠性及其灵敏度分析，得到了有工程意义的指导意见。

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