Structural health monitoring assumes that environmental conditions — temperature, humidity, wind — affect measurement means. A bridge's natural frequencies shift when it gets hot. Correct for the temperature effect on the mean, and the residual reveals structural damage.
This assumption is incomplete. Environmental conditions also affect the variances of the measurements and the covariances and correlations between them. A temperature change doesn't just shift all frequencies uniformly — it changes how much each frequency varies and how those variations relate to each other. The statistical relationships between measurement channels are themselves environmentally dependent.
The practical consequence: a damage detection algorithm that corrects only for mean-level environmental effects will produce false alarms when environmental conditions change the variance structure. The signal that looks like damage is actually a covariance shift caused by an unusual temperature pattern.
Two methods are compared for modeling these higher-order effects. Random forests provide interpretable, robust estimates — you can trace which environmental variable drives which covariance change. Kernel-based methods achieve superior accuracy but at the cost of interpretability. The tradeoff is between understanding the correction and optimizing it.
The deeper issue is what constitutes a baseline. If variances and covariances shift with the environment, then the baseline isn't a fixed statistical state — it's a function of conditions. The healthy structure doesn't have a signature. It has a family of signatures, parameterized by the weather. Detecting damage means detecting departure from a moving target.