采用l1范数改进的结构损伤定位向量方法

发布时间：2018-11-18 11:50

【摘要】：近年来，基于结构振动的损伤识别得到了快速的发展，其中基于损伤前后柔度矩阵变化的损伤识别方法被认为是具有较大发展前景的方法之一。损伤定位向量（DLVs）法是基于柔度矩阵的一种损伤识别方法，它通过计算一组特定的向量，将这组向量当做荷载施加在无损结构上，则损伤单元处的应力为零或较小值。损伤定位向量为结构损伤前后柔度矩阵差的零空间向量。损伤定位向量方法不依赖于结构类型，，并且适用于多损伤情况，因此相对于其他方法具有较大的优势。当然，这种方法只适用于损伤前后均为线性体系的结构。本文从损伤定位向量的稀疏性出发对损伤定位向量方法进行了研究。首先，我们从损伤定位向量的稀疏性出发分析了损伤定位向量的特质，采用最新发展的p（p2）范数来衡量损伤定位向量的稀疏性。研究发现，对于损伤定位向量而言，稠密的损伤定位向量要优于稀疏的损伤定位向量。基于此，我们提出了新的损伤定位向量选择方法。将新方法与原方法进行了比较，发现新方法对损伤的定位结果优于原方法，同时预测新方法在噪声环境下能够减少损伤误判。本文进一步提出了采用稀疏性恢复算法来求解具有稀疏特征的损伤定位向量的方法，而不再通过奇异值分解（SVD）来获得。基于DLVs所期望具备的性质，采用非稀疏的损伤定位向量对结构进行损伤定位，对一个桁架模型进行了数值模拟和对一个框架模型进行了试验研究，验证了本文提出的改进方法的有效性和对其性能的猜测。损伤定位向量新选择方法由于避免了原方法中将各个损伤定位向量施加在结构上进行静力分析来确定筛选标准的麻烦，因此该方法在应用上更加简便和实用。
[Abstract]:In recent years, the damage identification based on structural vibration has been developed rapidly, among which the damage identification method based on the change of flexibility matrix before and after damage is considered as one of the methods with great development prospects. The damage location vector (DLVs) method is a damage identification method based on the flexibility matrix. By calculating a set of specific vectors and applying the vector as a load on the lossless structure, the stress at the damage element is zero or small. The damage location vector is the null space vector of the flexibility matrix difference before and after damage. The damage location vector method does not depend on the structure type and is suitable for multiple damage cases, so it has a great advantage over other methods. Of course, this method is only suitable for structures with linear systems before and after damage. In this paper, the damage location vector method is studied based on the sparsity of the damage location vector. Firstly, we analyze the characteristics of damage location vector from the sparsity of damage location vector, and use the newly developed p (p2) norm to measure the sparsity of damage location vector. It is found that the dense damage location vector is superior to the sparse damage location vector for the damage location vector. Based on this, we propose a new damage location vector selection method. Comparing the new method with the original method, it is found that the new method is superior to the original method in locating the damage, and the new method can reduce the damage misjudgment in the noise environment. In this paper, we propose a sparse recovery algorithm to solve the damage location vector with sparse characteristics, instead of using singular value decomposition (SVD) to obtain it. Based on the properties expected by DLVs, a truss model is numerically simulated and a frame model is tested by using a non-sparse damage location vector. The effectiveness of the proposed improved method and its performance are verified. Because the new selection method of damage location vector avoids the trouble of applying each damage location vector to the structure to determine the selection criteria, the method is more convenient and practical in application.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TU317

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