基于广义多项式混沌展开理论的振动系统不确定性问题研究

The importance of modeling and simulation to mechanical equipment design has been widely acknowledged as it not only can reduce the test cost, shorten the product development period but also can provide essential information for the healthy condition monitoring of the mechanical equipment. However, various uncertainty factors are inevitable during the modeling and simulation, for example the constitutive relation of material, the operation condition and the geometric parameters, all of which are cannot precisely determined. Nowadays, it is widely recognized that it is unwise to ignore the uncertainty factors and, on the contrary, it is necessary to take account of them in modeling and simulation, especially in the case where extreme performance and safety are exactly demanded on the equipment so that the confidence of prediction result of the modeling must be evaluated then. Only by doing so, is it reasonable to use the model as reliable surrogate of the real object for testing purpose during product development. In this study, the Generalized Polynomial Chaos Expansion (gPCE) theory, which has been proposed and fast developed in recent years, will be adopted to investigate the uncertainty problem in vibration system with a demonstration of wind turbine blade. It is expected that, after the project, effective gPCE-based algorithms will be developed to handle the high-dimensional uncertainty problem, uncertainty system identification method will be proposed, and novel healthy condition monitoring method considering the uncertainty factor will be developed for mechanical equipment.

动力学建模与仿真对机械装备开发设计的重要性已不言而喻，它不仅可减少测试成本、加快设计开发周期，而且可为机械装备的健康状态监测提供必要的依据。但在建模和仿真中不可避免地要面对各种不确定性因素，如材料的本构关系、工作环境和几何结构等都存在无法确知的因素。如今，人们意识到忽视这些不确定因素不再是明智的做法，普遍认为必须在建模和计算中对不确定因素加于考虑，在给出模型预测结果的同时对其可信度给予评估，特别是在一些对性能和安全性有严格要求的场合。唯有如此，才可将动力学模型作为实际对象的可靠代理，用于开发过程中的各个测试环节。本项目将采用近年来发展出来的广义多项式混沌展开理论，以风力发电机叶片为研究对象，开展振动系统不确定性问题研究。通过本项目研究，发展出高效的高维不确定性参数问题的分析方法、有效的不确定性系统辨识方法和计及不确定因素的结构健康状态监测方法。

动力学建模与仿真对机械装备开发设计的重要性已不言而喻，它不仅可减少测试成本、加快设计开发周期，而且可为机械装备的健康状态监测提供必要的依据。但在建模和仿真中不可避免地要面对各种不确定性因素，如材料的本构关系、工作环境和几何结构等都存在无法确知的因素。如今，人们意识到忽视这些不确定因素不再是明智的做法，普遍认为必须在建模和计算中对不确定因素加于考虑，在给出模型预测结果的同时对其可信度给予评估，特别是在一些对性能和安全性有严格要求的场合。唯有如此，才可将动力学模型作为实际对象的可靠代理，用于开发过程中的各个测试环节。本项目采用近年来发展出来的广义多项式混沌展开理论，以风力发电机叶片为研究对象，开展振动系统不确定性问题研究。本项目针对广义多项式混沌展开方法长时间计算误差累计的问题，提出了基于时变基函数的随机动力系统不确定性定量分析方法，通过随机响应面的逼近获得更为精确的不确定性分析结果；针对区间不确定性定量分析中的区间扩张问题，提出基于低秩分解的多不确定参数区间计算方法，提高了区间计算的精度；提出了基于张量列的随机有限元分析方法，该方法能有效求解多达几十个不确定参数的随机有限元问题； 基于稀疏网格配点法对带多个不确定参数的动力学系统特征值问题进行求解；提出了一种用于分析随机风激励下的风电齿轮传动系统动态响应区间的分析方法—基于Chebyshev包含函数的功率谱密度区间估计方法；提出了修正的区间谐波平衡法，并将其应用于考虑齿侧间隙非线性的齿轮副系统。