Discrimination between three different sources of variability in a vibration-based structural health monitoring system is investigated: environmental or operational effects, sensor faults, and structural damage. Separating the environmental or operational effects from the other two is based on the assumption that measurements under different environmental or operational conditions are included in the training data. Distinguishing between sensor fault and structural damage utilizes the fact that the sensor faults are local, while structural damage is global. By localizing the change to a sensor which is then removed from the network, the two different influences can be separated. The sensor network is modelled as a Gaussian process and the generalized likelihood ratio test (GLRT) is then used to detect and localize a change in the system. A numerical and an experimental study are performed to validate the proposed method.