The Transmissibility Function (TF) has gained considerable interest in structural damage detection because of its relatively high sensitivity to damage and robustness to excitation. This study proposed a distributed damage diagnosis method for beam-like structures based on a long-gauge static strain TF defined as the ratio of the Fourier transform of static strain response under moving loads from a target long-gauge sensor to that from the reference sensor. It has been discovered that each long-gauge static strain TF is independent of moving loads, making it an ideal damage indicator. It exhibits direct proportionality to the ratio of bending stiffness between the two measured zones covered by the target and reference long-gauge strain sensors while being unaffected by the stiffness of any other zones not covered by these two sensors. Moreover, the TF at zero frequency was proved to be equivalent to the ratio of static strain time history areas, relying solely on the stiffness of the covered zones. Leveraged by the physical properties of long-gauge static strain TF, an element-wise parallel deep neural network architecture was developed to decompose damage diagnosis into independent sub-tasks on the element level, utilizing a variational autoencoder (VAE) in the Bayesian inference framework for extracting features from the long-gauge strain TF and a regressor for mapping the features to elemental stiffness reduction. The divide-and-conquer strategy and element-wise parallel learning architecture allow for a significant reduction in the number of labeled training samples generated based on the updated numerical baseline model as it only requires simulated scenarios involving a single damage element. The efficiency and robustness of the proposed method were demonstrated through a numerical simply supported beam and a laboratory experiment on a two-span bridge.

中文翻译：

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利用移动载荷下长规格静态应变传递率的物理特性，进行结构分布式损伤诊断的逐元素并行深度学习


传递函数（TF）因其对损伤相对较高的敏感性和对激励的鲁棒性而在结构损伤检测中引起了极大的兴趣。本研究提出了一种基于长规格静应变TF的梁状结构分布式损伤诊断方法，TF定义为移动载荷下目标长规格传感器与参考传感器的静应变响应的傅里叶变换之比。人们发现，每个长规格静态应变 TF 与移动载荷无关，使其成为理想的损伤指标。它与目标和参考长规格应变传感器覆盖的两个测量区域之间的弯曲刚度比率成正比，同时不受这两个传感器未覆盖的任何其他区域的刚度的影响。此外，零频率下的传递函数被证明相当于静态应变时程区域的比率，仅依赖于覆盖区域的刚度。利用长规格静态应变 TF 的物理特性，开发了一种逐元素并行深度神经网络架构，利用贝叶斯推理框架中的变分自动编码器 (VAE)，将损伤诊断分解为元素级别的独立子任务用于从长规格应变 TF 中提取特征，以及用于将特征映射到单元刚度降低的回归器。分治策略和逐元素并行学习架构可以显着减少基于更新的数值基线模型生成的标记训练样本的数量，因为它只需要涉及单个损伤元素的模拟场景。 通过数值简支梁和两跨桥梁的实验室实验证明了所提出方法的效率和鲁棒性。