A direct time-domain algorithm for damage detection is introduced. It is based on hardware redundancy in which the number of sensors is greater than the number of excited modes plus the number of environmental varia-bles. Therefore, for a structure with complex modes, the minimum number of sensors is foreseen to be higher that of the same structure with real modes. A two-step detection algorithm is proposed. First, the accuracy of each sen-sor is increased using Bayesian virtual sensing applied to each measurement independently. The more accurate Bayesian virtual sensors replace the phys-ical sensors in the subsequent step. Second, the reading of each sensor is es-timated using those of the remaining sensors by applying a model built from the training data under different environmental conditions. The residual is the difference between the actual sensor reading and the corresponding esti-mate and its increase beyond the threshold is an indication of damage. The algorithm was studied in a numerical experiment of a frame structure having a discrete damper element, which resulted in complex mode shapes. A com-parison was made with the same structure having real modes. It was shown that the required number of sensors indeed increased if complex modes were present. The performance of damage detection was studied with five damage levels using either actual measurements or virtual sensors. It was shown that virtual sensors outperformed the raw measurements and the performance of damage detection was higher with real modes.