复杂机械结构不确定力学行为与可靠性分析的新型非概率凸集方法

Complex mechanical structure is the common key component of modern equipment, it is of great significance to study its uncertain mechanical behavior and reliability problem. To deal with the uncertainty with limited information, the non-probabilistic convex model has been developed, but the existing convex methods can not enhance the accuracy and efficiency concurrently in uncertainty propagation analysis, and the corresponding non-probabilistic reliability analysis methods are short of engineering applicability. The present item aims at overcoming the shortages by proposing some new convex method. First, new interval model will be developed to depicts the correlation of uncertain-but-bounded parameters, and some new methods for the construction and quantification of convex model will be investigated when considering multi-source, high-dimensional, correlative model parameters, and the clustering distribution of samples. Second, new uncertain FEM methods based on the new interval model and multi-ellipsoid model will be proposed respectively. Third, establish new method for system reliability problem using ellipsoid model, convert the time-variant reliability problem into time-invariant reliability problem, evaluate the time-variant reliability of structures. Finally, the aforementioned models, algorithms and metrics will be modularized for integration. The proposed new convex set methods in the present item will provide a new approach for the design of complex mechanical structures, and enhance the engineering applicability of convex model.

复杂机械结构通常是装备产品的核心部件，对其不确定力学行为和可靠性分析问题进行研究具有重要意义。本项目针对复杂机械结构传统不确定分析难以兼顾精度与效率、可靠性分析工程普适性不强等难点问题，在凸集模型框架下开展新型非概率凸集方法研究。首先，考虑不确定参数的高维多源相关特性、样本信息的非完备性、样本分布的聚类性，以椭球模型和新的广义区间模型为研究对象，解决凸集模型的构建和不确定性的度量问题；其次，研究基于新的广义区间模型和椭球模型的不确定有限元分析方法，并对具凸集场的结构不确定力学行为进行分析；再次，研究基于椭球模型的体系可靠性近似分析方法，将时变可靠性问题转化为定常的体系可靠性问题，完成对结构时变可靠性的评估；最后，将相关模型、算法、准则等进行集成。本项目提出的新型非概率凸集方法有望为复杂机械结构的设计提供新思路，将有效强化凸集模型的工程实用性。

复杂机械结构的不确定力学行为及可靠性分析，是工程设计领域关注的焦点。我们深入研究了复杂机构结构在有限样本信息条件下的不确定力学行为及可靠性分析方法。具体地，基于非线性规划的基本原理，针对样本信息相关性、非完备性、聚类性，建立了构建椭球模型和区间模型的高效算法；基于新型凸集模型，研究了复杂机械结构中不确定性的传播规律，并应用于其不确定力学行为分析；基于新型凸集模型，建立了复杂机械结构非概率可靠性分析的精确高效算法。本项目的成果成功应用于齿轮系统、滚动轴承、压电层合梁、切削加工分析中，提升了非概率凸集模型的工程普适性。