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首页> 外文期刊>Mechanical systems and signal processing >Matrix regularization-based method for large-scale inverse problem of force identification
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Matrix regularization-based method for large-scale inverse problem of force identification

机译：基于矩阵正则化的力识别大规模反问题方法

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摘要

Identification of force via structural responses has been widely studied due to the force is always difficult or even impossible to be measured directly. Force identification is a typical ill-posed problem. To overcome this drawback, regularization methods have been widely studied. However, existing regularization methods used for force identification belong to the vector-based method, in which unknown force and structural responses are organized in two vectors, respectively. This characteristic decides that the identified process of a long-duration problem will be time-consuming because the size of system matrix is large. In view of this, a novel matrix regularization-based method is proposed for force identification in this paper. Combing with moving time windows, the structural responses are extracted and organized in a form of matrix. A system matrix is formulated by considering both unknown force and unknown initial conditions. Then a governing equation is established, in which structural excitation sources such as force and initial condition are orderly stored in a form of matrix. To obtain a stable solution, matrix regularization is introduced for improving the matrix-based governing equation. Herein, the sparse penalty term is considered as the sum of absolute values of elements in the matrix of excitation sources. Fast iterative shrinkage-thresholding algorithm (FISTA) is applied for solving the matrix regularization model. The regularization parameter is selected according to Bayesian information criterion (B1C). Finally, numerical simulations and experimental studies are carried out for assessing the feasibility and effectiveness of the proposed method. Illustrated results show that the proposed method is effective and time-saving. It can use a system matrix with a relatively small size to dealing with a large-scale problem of force identification. Some related issues are discussed as well.
机译：由于力总是很难甚至不可能直接测量的，因此通过结构响应来识别力已被广泛研究。力识别是一个典型的不适定问题。为了克服该缺点，已经对正则化方法进行了广泛的研究。但是，现有的用于力识别的正则化方法属于基于向量的方法，其中未知力和结构响应分别组织在两个向量中。该特征决定了由于系统矩阵的大小较大，因此确定长期问题的过程将很耗时。有鉴于此，本文提出了一种基于矩阵正则化的力识别新方法。结合移动的时间窗口，以矩阵形式提取和组织结构响应。通过考虑未知力和未知初始条件来制定系统矩阵。然后建立一个控制方程，其中结构激励源（例如力和初始条件）以矩阵形式有序存储。为了获得稳定的解决方案，引入了矩阵正则化以改进基于矩阵的控制方程。这里，稀疏惩罚项被认为是激发源矩阵中元素的绝对值之和。快速迭代收缩阈值算法（FISTA）用于求解矩阵正则化模型。根据贝叶斯信息准则（B1C）选择正则化参数。最后，进行了数值模拟和实验研究，以评估该方法的可行性和有效性。算例结果表明，该方法有效，省时。它可以使用尺寸相对较小的系统矩阵来处理大规模的力识别问题。还讨论了一些相关问题。

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