基于稀疏重构理论的结构损伤识别方法研究

Numerous vibration-based structural damage detection methods have been developed in aerospace, mechanical and civil engineering societies over the past decades. Finite element model updating is a widely used technique that is capable of locating and quantifying damage. However, applications of vibration-based damage detection to practical civil structures are far from being mature. This project will utilize the sparsity condition of structural damage and develop a new damage detection method based on the latest sparse recovery theory (or sparse reconstruction). The project will focus on following tasks: 1) development of an lp (0 < p ≤ 1) regularized model updating method suitable for civil structural damage detection; 2) optimization of the sensor locations using the combinatory genetic algorithm, such that the sensing matrix in the model updating has the minimal mutual coherence; 3) investigation of the effects of the measurement noise on the damage detection results; and 4) investigation of parameters as the number of damaged elements, severity of damage, and number of sensors on the performance of the proposed technique; suggestions on these parameters will be provided to achieve accurate and reliable sparse damage detection in real applications. Two laboratory structures, namely, a truss and a multi-story frame, will be employed to verify the proposed method.

近二三十年来，基于振动信号的结构损伤识别方法在航空、机械及土木工程等领域得到了较大的发展。有限元模型修正是其中广为应用的一种方法，但它在实际土木工程结构中的应用仍然存在不少问题和难题。针对实际结构的损伤往往出现在少数杆件或部位的特征，本课题将发展一种新的基于稀疏重构理论的结构损伤识别方法。本课题着重研究：1）发展适合土木工程损伤识别的p范数(0 < p ≤ 1)正则化优化算法；2）优化传感器位置使得正则化过程中的敏感度矩阵具有最小的线性相关性；3）研究测量数据噪音对损伤识别结果的影响；4）研究损伤单元数量、损伤程度、传感器数量等参数对损伤识别结果的影响，为实际应用中参数的选取提供建议。课题将用一个空间桁架和平面框架的实验来验证所发展的方法。

本项目基于稀疏重构理论和有限元模型修正方法，发展了l1正则化方法和迭代重加权l1正则化方法并用于识别结构稀疏损伤的位置和程度。主要研究内容：1）提出了基于固有频率和模态振型的l1正则化损伤识别方法；2)提出了迭代重加权l1正则化(等效于l0正则化)损伤识别方法，3)研究正则化方法中正则化参数β的选取方法；4)发展遗传算法研究传感器的优化布置方法；5)研究损伤单元数量、损伤程度、测量数据数量、测量误差等参数对结构损伤识别结果的影响。通过对一个悬臂梁、平面框架和一个空间桁架进行实验室模型试验，并模拟多个损伤工况，验证上述各种算法。与传统基于l1正则化的损伤识别方法相比，新方法可以准确地识别出结构的局部损伤，推进了结构损伤识别方法在实际工程的应用。