针对如何建立高精度机械结构损伤模型和提高损伤识别的精度和效率两个基本问题，系统地研究基于小波扩展有限元与高维近似模型优化的机械结构损伤识别的方法。提出并研究基于单位分解的多尺度小波扩展有限元方法，拓展多尺度高精度动力学建模理论，基于小波基深入研究扩展有限元富集项构造方法和混合单元处理方法，实现复杂工况下含任意裂纹的机械结构多损伤动力学建模与求解，为结构损伤识别的正问题提供精确辨识模型；提出并研究多损伤结构动力学响应的高维近似模型方法，实现高维、非线性多损伤结构动力响应的高精度拟合。研究多准则序列化自适应采样方法,降低损伤识别反问题中动力学损伤模型的重构和分析计算次数。研究基于损伤结构近似模型优化的损伤参数识别策略，提高复杂结构多损伤识别精度和效率效率,以满足机械结构健康监测的相对实时性要求。最终将正反问题结合实现机床关键结构的损伤识别，丰富高精度、高效率的结构多损伤识别理论并提供使能技术。

Aiming at how to establish the high precision damage model of mechanical structure and improve the accuracy and efficiency of damage identification, systematically study the method of multi-damage identification for mechanical structure based on wavelet expansion finite element method (XFEM) and high dimension approximation model optimization. Firstly, propose and study multi-scale wavelet XFEM based on the local partition of unity approach. Develop high precision multi scale dynamic modeling theory. Further research enriched items and blending elements construction method of XFEM by wavelet basis. And to realize the dynamic modeling and solving for multiple damage mechanical structure containing arbitrary cracks. Ultimately provide accurate identification model for forward problem analysis of structural damage identification. Secondly, propose and study high dimensional approximation model methods for constructing multi-damage structural dynamics responses. In order to reduce reconstruction and analysis times of damage models during inverse problem solving of damage identification, adaptive serialization sampling method based on multi criteria will be studied. Study on the damage identification strategies based on approximate model optimization of damage structures, Increasing the accuracy and efficiency of multi damage identification and meeting relative real-time requirements for structure health monitoring. Finally, the forward and inverse methods will be combined and applied to damage identification of machine tool components. The achievements of research will enrich the multi damage identification theory and provides the enabling technology.