Standard structural health monitoring corrects for temperature by adjusting the mean vibration frequency — warmer days shift it down, colder days shift it up, and after subtraction the residual should reveal damage. This works until it doesn't. In cold weather, the KW51 railway bridge generates false alarms even after mean correction. The damage detection system sees anomalies that aren't structural.
Wittenberg et al. show why: temperature doesn't just shift the mean of the vibration signal. It restructures the variance itself. The eigenfunctions and eigenvalues of the residual covariance change with temperature, meaning the entire shape of normal variability is temperature-dependent. Correcting only the first moment leaves the second moment uncorrected, and the monitoring threshold — set from warm-weather variance — triggers on cold-weather variance that is structurally different but not structurally damaged.
Their fix is covariate-dependent functional principal component analysis, where the eigenfunctions themselves vary smoothly with temperature. This eliminates the false alarms by letting the definition of “normal variation” change with the environmental condition.
The through-claim is about the order of correction. Any monitoring system that corrects for a confounder only at the level of the mean implicitly assumes the confounder doesn't affect variability. That assumption is testable and often wrong. Temperature doesn't just move the signal — it changes what “noisy” looks like. If your anomaly detector compares residual variance to a fixed threshold, it will hallucinate damage whenever the confounder enters a regime where variance has a different structure. The false alarm isn't noise. It's a real pattern — just not the pattern you were looking for.