Sparse Bayesian learning (SBL) is a well-established technique for tackling supervised learning problems, while taking advantage of the prior knowledge that the expected solution is sparse. Based on the premise that initial damage of a structure appears only in a limited number of locations, SBL has been explored for identifying structural damage, showing promising results. Existing SBL methods for structural damage identification use measurements related to modal properties and are thus limited to linear models. In this paper, we present a methodology that allows for application of SBL in nonlinear models, using time history measurements. We develop a two-step optimization algorithm in which the most probable values of the structural model parameters and the hyperparameters are iteratively obtained. An equivalent, single-objective, minimization problem that results in the most probable model parameter values is also derived. We consider the example problem of identifying damage in the form of weld fractures in a 15-story moment-resisting steel-frame building, using a nonlinear finite-element model and simulated acceleration data. Fiber elements and a bilinear material model are used to account for the change in local stiffness when cracks at the welds are subjected to tension, and the model parameters characterize the loss of stiffness as the cracks open under tension. The damage identification results demonstrate the effectiveness and robustness of the proposed methodology in identifying the existence, location, and severity of damage for a variety of different damage scenarios and levels of model and measurement error.

中文翻译：

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使用非线性模型进行损伤识别的稀疏贝叶斯学习：在钢架建筑焊接断裂中的应用

稀疏贝叶斯学习 (SBL) 是一种成熟的技术，用于解决监督学习问题，同时利用预期解决方案稀疏的先验知识。基于结构的初始损坏仅出现在有限数量的位置的前提，SBL已被探索用于识别结构损坏，显示出可喜的结果。用于结构损伤识别的现有 SBL 方法使用与模态特性相关的测量，因此仅限于线性模型。在本文中，我们提出了一种方法，允许在非线性模型中应用 SBL，使用时间历史测量。我们开发了一种两步优化算法，其中迭代获得结构模型参数和超参数的最可能值。等效的单一目标，还导出了导致最可能的模型参数值的最小化问题。我们考虑使用非线性有限元模型和模拟加速度数据来识别 15 层抗弯钢框架建筑中焊接断裂形式的损坏的示例问题。纤维单元和双线性材料模型用于解释当焊缝处的裂纹受到张力时局部刚度的变化，模型参数表征了裂纹在张力下打开时刚度的损失。损伤识别结果证明了所提出的方法在识别各种不同损伤情景以及模型和测量误差水平的损伤的存在、位置和严重程度方面的有效性和稳健性。