基于多边凸集度量和混合驱动模型的机械结构非概率不确定性反求方法研究

反问题理论与方法将实验测试和数值模拟有机结合，为复杂机械结构的高精度分析与设计提供新思路。本项目针对复杂机械结构反问题所涉及的样本数据缺乏，建模机理不明晰，不确性参量高维、多源、强相关，多层嵌套反求计算量大等关键难点，提出基于多边凸集度量和混合驱动模型的机械结构非概率不确定性反求方法。项目将发展新型基于聚类-多边凸集的非概率不确定性模型，克服传统贝叶斯反求在样本缺乏下遭遇的理论瓶颈；研究基于模型和基于数据混合驱动的多精度融合正向建模方法，使物理力学机制不明晰下的不确定性反求成为可能；研究基于多层降维积分的不确定性传播方法，探明不确定性源-结构映射关系-反求参量间的逐级逆向传递规律；创新性提出基于相似系统分析的高效不确定性反求方法，实质性解决不确定性反求多层嵌套造成的效率瓶颈；开展工业机器人精度反设计的应用与验证研究。项目成果将为机械产品的高置信度和高品质设计提供关键理论支撑和分析工具。

The theory and methods of inverse problems can combine experimental measurement and numerical simulation, which provides the new thought for the high accuracy analysis and design of complex mechanical structures. Aiming at the difficulties in the lack of sample, unclear modeling mechanism, high-dimensional multi-source uncertainties with strong correlation, high computation complexity due to multilayer-nested inversion, this project will focus on the inverse methods based on polygonal-convex-set quantification and hybrid driven model for mechanical structures with non-probabilistic uncertainties. In this project, the new non-probabilistic uncertainty model based on clustering and polygonal convex set will be developed to overcome the theoretical bottleneck of the traditional Bayesian inversion under the lack of sample. The model-based and data-based multi-fidelity fusion method will be studied, which can make the uncertainty inversion possible even if the mechanics mechanism is unclear. The uncertainty propagation method based on multilayer dimension reduction integral will also be researched to find out the gradual transformation rule in uncertainty sources, Structural mapping relationship and inversed parameters. The efficient uncertainty inverse method based on similarity system analysis will be presented, which can overcome the computation bottleneck caused by the multi-layer nested problem in uncertainty inversion. Finally, the studied methods will applied on the accuracy inverse design of industrial robot. The achievements of this project can provide the key theoretical support and analysis tools for the mechanical product design with the high confidence and high quality.