A method is proposed to perform structural health monitoring under varying environmental and operational conditions. The method is based on principal component analysis (PCA) applied to a data set containing vibration characteristics identified during the monitoring of the structure. The advantage of the method is that it does not require the measurement of environmental parameters that are taken into account as embedded variables. As the influence of environmental effects may be effectively eliminated, the residual error of the PCA prediction model remains small if the structure is healthy, and increases significantly when structural damage occurs. Novelty analysis on the residual errors provides a statistical indication of damage. The PCA-based damage detection method is illustrated using experimental data. It will also be shown that when the relationship between the vibration characteristics becomes nonlinear, PCA is advantageously replaced by one of its nonlinear generalizations.