System outputs such as eigenfrequencies or strain data, often used in structural health monitoring (SHM), not only react to damage but also depend on environmental conditions. When trying to correct for these confounding effects, it is often (at least implicitly) assumed that only the expected, i.e., mean, output values are affected by environmental conditions. However, the evaluation of real-world SHM data indicates that environmental conditions may influence not only the mean output but also higher-order statistical moments, particularly the variances of and the covariances and correlations between the output quantities, such as eigenfrequencies of different modes or strain sensors at different locations. To address these issues, we discuss two approaches for identifying and quantifying multivariate confounding effects on output covariances and correlations: a random forest and a nonparametric, kernel-based approach. We compare the two competing methods on both artificial and real-world SHM data, finding that the kernel-based approach achieves higher accuracy, but the random forest produces estimates that are more robust and sometimes easier to interpret.

翻译：结构健康监测（SHM）中常用的系统输出，如特征频率或应变数据，不仅对损伤产生响应，还依赖于环境条件。在尝试校正这些混杂效应时，通常（至少隐含地）假定只有输出的期望值（即均值）受环境条件影响。然而，对实际SHM数据的评估表明，环境条件可能不仅影响输出均值，还会影响高阶统计矩，特别是各输出量（如不同模态的特征频率或不同位置的应变传感器）的方差、协方差和相关性。为解决这些问题，我们讨论了两种识别和量化多变量混杂效应对输出协方差与相关性的方法：随机森林方法和非参数核方法。我们在人工数据与实际SHM数据上比较了这两种竞争性方法，发现核方法具有更高的准确度，而随机森林方法产生的估计量更稳健，且有时更易于解释。