In Structural Health Monitoring (SHM), sensor measurements and derived features such as eigenfrequencies often exhibit systematic daily patterns and can therefore be naturally represented as functional data. Furthermore, these patterns are typically influenced by environmental factors, particularly temperature, which can substantially affect the observed system response. While most existing methods for removing environmental effects assume that confounding influences affect only the mean response, it has been shown that environmental and operational factors may also alter the covariance structure of the residual process. To address this limitation in a functional data monitoring framework, we incorporate so-called covariate-dependent functional principal component analysis (CD-FPCA), which allows eigenfunctions and eigenvalues of the residual process to vary smoothly with covariates such as temperature. The proposed methodology is illustrated using an extended version of the KW51 railway bridge eigenfrequency dataset. This case study suggests that accounting for covariate effects beyond the functional mean can improve the robustness of the monitoring procedure, in particular by reducing environmentally induced (false) alarms under challenging low-temperature conditions.

翻译：在结构健康监测中，传感器测量值及衍生特征（如固有频率）常呈现系统性日变化模式，因此可自然地表示为函数型数据。此外，这些模式通常受环境因素（尤其是温度）影响，而温度会显著改变观测的系统响应。现有去除环境效应的方法大多假设混杂因素仅影响均值响应，但研究表明环境与运行因素也可能改变残差过程的协方差结构。为弥补函数型数据监测框架中这一局限，我们引入协变量依赖型函数主成分分析（CD-FPCA）方法，该方法允许残差过程的特征函数与特征值随温度等协变量平滑变化。通过扩展版KW51铁路桥梁固有频率数据集验证所提方法，该案例研究表明：考虑超函数均值的协变量效应可增强监测流程的鲁棒性，尤其在低温挑战环境下能有效减少由环境诱发的误报。