复杂工程系统多学科不确定性数值计算和优化理论方法及其应用研究

Considering that more advanced numerical calculation and optimization technology is needed in the analysis and design of modern complex engineering systems, as the development and supplement of deterministic multidisciplinary analysis, the technique of numerical calculation and optimization theory based on multidisciplinary uncertainty is gradually becoming a hotspot and difficulty in the world powers. In view of the great demand to the country, the sophisticated aerospace vehicle structures will be regarded as the main objects of the research in this project. Furthermore, by virtue of the mutual integration of interdisciplinary studies, included by the fields of structure, material, aerodynamics, mathematics, software, experimental technique etc, the multidisciplinary numerical calculation and optimization design technologies, which serve the aircraft structures， will be established and developed. Thus, some issues will be investigated, which included by uncertainty/error quantification and computational analytic techniques involved in the procedure of the computational analysis, optimization design or experimental verification subjected to the aircraft structures; the study on advanced algorithms for dealing with the problems of multidisciplinary uncertainty-based optimization as well as verification and validation techniques with reference to the numerical computational and optimization models; construction of the software platform for the realization of uncertainty numerical calculation and optimization in practical aircraft engineering. Through this project, we are committed to transform the theoretical value of the above uncertainty numerical calculation and optimization design into the economic, social and even military values. The research can be treated as the theory basis and technology foundation for the analysis and design of the complex engineering systems on one hand, and further contribute to the development of the model-oriented numerical analysis and optimization design platform.

现代化复杂工程系统的分析和设计需要更加先进的数值计算和优化技术，作为确定性多学科数值计算和优化的发展和补充，多学科不确定性数值计算和优化理论与技术是目前世界强国都在研究的热点和难点问题。本项目将根据航空航天的国家重大需求，以先进的复杂飞行器结构为研究对象，发展和建立面向飞行器结构的多学科不确定性数值计算和优化的理论与方法，交叉融合结构、材料、气动、数学、软件和实验等学科，进行包括飞行器计算分析、优化设计和实验验证中所涉及的各种不确定性和误差的定量化与计算分析技术、多学科不确定性优化技术、以及数值计算和优化的模型验证与确认技术等研究，构建能用于工程实际的飞行器不确定性数值计算和优化的软件平台。努力将多学科不确定性数值计算和优化设计的理论价值转化为经济价值和社会价值，甚至军事价值，为复杂工程系统的分析和设计提供数值计算和优化理论与技术基础，为飞行器型号研制提供先进的数值计算分析与优化设计平台。

多学科不确定性数值计算和优化理论与技术是目前世界强国都在研究的热点和难点问题。本项目根据航空航天的国家重大需求，以先进的复杂飞行器结构为研究对象，开展了多学科数值计算中的不确定性问题模型和算法研究、多学科数值优化问题的不确定性模型和算法研究、不确定性数值计算和优化模型和算法的验证与确认研究、多学科不确定性数值计算和优化设计软件平台的研制及典型飞行器或部件确定性和不确定性数值计算和优化设计验证研究等研究。在多学科不确定性数值计算研究方面，分别发展了非概率不确定性定量化的灰色数学法，随机不确定性结构分析的多项式展开与配点法，结构响应界限预测的级数展开、顶点组合与逐维配点法，以及多学科系统区间响应边界数值计算的迭代法等理论和方法；在多学科不确定性优化技术方面，本项目分别提出了面向不确定性多学科系统的随机鲁棒性/可靠性优化设计方法，考虑多源不确定性的多学科优化设计方法，以及面向多学科/多目标的非概率鲁棒优化设计方法等理论和方法；在不确定性数值计算和优化模型和算法的验证与确认研究方面，分别提出了面向飞行器结构的非概率贝叶斯模型确认方法，以及考虑可靠性指标与安全系数的结构设计方法对比验证；最后结合实际工程的客观情况，开发了基于不确定优化的高超声速飞行器结构功能一体化设计平台，并将所提分析与优化方法应用至飞行器典型结构，完成了不确定性数值计算和优化设计方法的试验验证。经过本项目研究，项目组针对复杂工程中的不确定性多学科系统已形成了一套相对完整的不确定性数值计算与优化设计理论与方法体系，能够为多学科不确定性数值分析与优化问题提供新的理论与技术，为飞行器的研制提供先进技术基础。

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