基于灵敏度的模型更新用于结构损伤识别的总变分正则化
Sensitivity-Based Model Updating for Structural Damage Identification Using Total Variation Regularization
AI总结：
本文提出基于总变分正则化的灵敏度模型更新方法，用于提高结构损伤识别的精度与稳定性，通过对比传统插值正则化方法，验证了该方法在损伤定位和严重程度识别上的优势。
摘要：
基于有限元模型更新（FEMU）的灵敏度方法是用于结构损伤识别的广泛接受技术。FEMU可以表述为数值优化问题，并通过迭代求解来自动更新不确定的模型参数，以最小化测量值与分析结构属性之间的差异。然而，在测量中存在噪声时，更新结果通常容易出错。这在数学上被描述为损伤识别作为逆问题的不稳定性。解决这一问题的一种方法是使用正则化。本文研究了基于不确定模型参数总变分最小化的正则化方法，并将其与一种较为常用的基于插值技术的正则化方法进行比较。对于局部化良好的损伤，结果表明所提出的方法在识别损伤位置和严重程度方面比基于插值的解决方案具有明显优势。为了验证所提方法的实用性，我们使用钢筋混凝土板进行实际测试。首先在未受损的板上进行测量和分析，然后在施加四种不同程度的损伤后再次进行测量和分析。
英文摘要：
Sensitivity-based Finite Element Model Updating (FEMU) is one of the widely accepted techniques used for damage identification in structures. FEMU can be formulated as a numerical optimization problem and solved iteratively making automatic updating of the uncertain model parameters by minimizing the difference between measured and analytical structural properties. However, in the presence of noise in the measurements, the updating results are usually prone to errors. This is mathematically described as instability of the damage identification as an inverse problem. One way to resolve this problem is by using regularization. In this paper we investigate regularization methods based on the minimization of the total variation of the uncertain model parameters and compare this solution with a rather frequently used regularization based on an interpolation technique. For well-localized damages the results show a clear advantage of the proposed solution in terms of the identified location and severity of damage compared with the interpolation based solution. For a practical test of the proposed method we use a reinforced concrete plate. Measurements and analysis were repeated first on an undamaged plate, and then after applying four different degrees of damage.
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