Statistical analysis of the damage detection performance under environmental or operational influences

In the design of structural health monitoring (SHM) systems, it is important to know how damage detection performance is affected by environmental or operational variability to decide the number of sensors in the structure. The detection performance is influenced by the data dimensionality and the number of environmental or operational variables. The monitoring data can be divided into two subspaces: the signal space and the noise space. The environmental or operational influences are contained in the signal space. Changes in the data due to damage can appear in either subspace. Damage can be detected in the noise space, whereas in the signal space it may remain undetected. Because no measurements from the damaged structure are usually available in advance, the effect of damage and the corresponding subspace remain unknown. In the statistical study, it is assumed that the orientation of the damage vector is uniformly distributed in the data space and that damage can be detected in the noise space only. The projection of the data onto the noise space determines the detection performance. The result of the statistical analysis is the average detection performance as a function of the data dimensionality and the number of environmental or operational variables. Also, the probability that the detection performance is at least 0.5 of that of the ideal case is plotted. These diagrams can be used in the design of SHM systems.