Constructing a damage-sensitive factor (DSF) is one of the key steps in structural damage detection. In this paper, innovation series extracted from the auto-regressive conditional heteroscedasticity (ARCH) model are proposed to construct a DSF, which is defined as the standard deviation of innovation (SDI). A three-story shear building structure is used to demonstrate and verify the performance of the proposed method, and the results are compared with the standard deviation of the residuals (SDR) based on an auto-regressive (AR) model. In the proposed method, the AR model is established using the acceleration responses obtained from the reference and test states. The residual series are then extracted for fitting the SDR. Subsequently, the ARCH model is constructed based on the residual series from the AR model, and a new DSF of SDI is defined. This study focuses on analyzing the accuracy of fitting AR model and ARCH model to vibration response data via the normal probability distribution, and identifying the characteristics of the residual and innovation series. The mean squared error (MSE) is used as the loss function to calculate the loss on residual and innovation series from the AR model and ARCH model, respectively. The results demonstrate that the SDR can be used for nonlinear damage detection. However, the proposed SDI can provide more accurate nonlinear damage identification and is robust to varying environmental condition and small damages. Thus, the innovation series developed based on ARCH model are promising for expressing and constructing nonlinear DSFs.

中文翻译：

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基于创新系列的结构非线性损伤敏感因素研究

构造损伤敏感因子（DSF）是结构损伤检测的关键步骤之一。在本文中，提出了从自回归条件异方差（ARCH）模型中提取的创新序列来构造一个DSF，它被定义为创新的标准差（SDI）。使用三层剪力建筑结构来演示和验证所提出方法的性能，并将结果与​​基于自回归 (AR) 模型的残差标准差 (SDR) 进行比较。在所提出的方法中，AR 模型是使用从参考和测试状态获得的加速度响应建立的。然后提取残差序列以拟合 SDR。随后，基于AR模型的残差序列构建ARCH模型，并定义了新的SDI DSF。本研究重点分析AR模型和ARCH模型通过正态概率分布拟合振动响应数据的准确性，识别残差序列和创新序列的特征。均方误差 (MSE) 用作损失函数，分别计算来自 AR 模型和 ARCH 模型的残差和创新序列的损失。结果表明，SDR可用于非线性损伤检测。然而，所提出的 SDI 可以提供更准确的非线性损伤识别，并且对变化的环境条件和小损伤具有鲁棒性。因此，基于 ARCH 模型开发的创新序列有望用于表达和构建非线性 DSF。