基于非精确概率模型的复杂装备结构不确定性分析与可靠性优化设计

The structure reliability of complex equipment is very important for national security and national economic development. Due to the problems of high-dimensional, correlative and multi-source uncertainties and nesting optimization are very prominent, uncertainty analysis and reliability-based design optimization for complex equipment based on imprecise probability model will be researched. Firstly, the model of imprecise probability will be constructed by limited sample information and the uncertainty modeling method will be developed based on Copula function; Secondly, an efficient adaptive surrogate model technology is developed and the updating mechanism is proposed to improve the surrogate model precision, which are used to solve the problem of high dimensional structural reliability design of complex equipment; Thirdly, the efficient decoupling strategy will be developed to solve the nesting optimization problem because of the existence of the mixed variables. For improving the solving efficiency, the local-densifying approximation technique will be combined in reliability analysis. Finally, multi-objective reliability-based design optimization method will be researched for complex equipment structure and the corresponding algorithms will be modularized integration for establishing the system of complex equipment structural reliability design. This system is also applied to the design of large bulk material conveying equipment. The completion of this proposal will provide a new approach for the development of complex equipment structural reliability and play an important role in promoting the development of industrial technology of China.

复杂装备结构可靠性对于保障国家安全和国民经济发展至关重要。本项目针对复杂装备结构设计中的高维、相关、多源的不确定性以及嵌套优化求解计算量大等难点，在非精确概率框架下研究复杂装备结构不确定性分析与可靠性优化设计方法。首先，利用有限的样本信息实现非精确概率变量的建模，并发展基于Copula函数的相关结构不确定性建模方法；其次，针对复杂装备结构高维可靠性设计问题，发展高效的自适应代理模型建模方法，并开发有效的模型更新机制来保证代理模型精度；然后，针对含混合变量的结构可靠性分析嵌套求解问题，研究有效的求解策略实现嵌套优化问题的解耦，并与局部加密代理模型技术相结合来提高求解效率；最后，发展复杂装备结构多目标可靠性优化设计方法，并将算法模块化集成，应用到大型散料输送装备设计，开发出具有工程实用性的可靠性设计系统。本项目的实施为复杂装备结构可靠性研发开辟了新思路，对促进我国工业技术发展具有重要推动作用。

复杂装备结构可靠性技术的研究对我国军事实力和工业水平的提升具有重要价值。本项目针对复杂装备结构设计中的高维、相关、多源的不确定性以及嵌套优化求解计算量大等难点，提出了影响复杂装备结构可靠性的非精确概率变量建模方法，并与自适应代理模型技术相结合，研究和开发出了高效的复杂装备结构可靠性分析与优化设计算法。取得的主要研究进展包括：（1）基于非精确概率模型实现了对信息有限的不确定性变量建模，获得了其累积分布函数，并利用Copula函数对不确定性之间的相关性进行处理，为工程设计提供指导；（2）研究了基于反形参数法和样本点局部加密的代理模型管理方法，逐步改进和调整代理模型，从而获得高精度复杂装备结构代理模型；为了处理复杂装备结构多目标优化设计中不确定性变量的相关性，建立了基于椭球模型的复杂装备结构多目标不确定性优化设计数学模型，并与自适应代理模型技术相结合，进一步提高了复杂装备结构优化的效率；（3）针对含混合模型的复杂装备结构可靠性分析问题，利用等概率转换将原混合可靠性分析的双层嵌套优化问题转换为单层优化问题，实现了循环嵌套优化问题的解耦，并基于局部加密代理模型技术来提高可靠性指标求解的效率、精度和适用性；（4）针对含多源不确定性变量的复杂装备结构多目标可靠性优化设计问题，基于不确定性理论实现了不确性优化问题向确定性优化问题的转换；基于最大熵原理，实现了多目标可靠性优化设计问题的解耦；结合自适应代理模型技术和具有全局搜索性能的多目标优化算法，实现了对含随机变量和不确定性变量的可靠性优化设计问题的高效求解；（5）将相关算法集成打包，应用到大型散料输送装备和空降装备的结构设计，开发出了复杂装备结构可靠性设计系统，提高了工程实用性。本项目的完成在一定程度上构筑起了复杂装备结构可靠性理论体系，对促进我国工业技术发展具有重要推动作用。

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