Modal model identification with unknown nonstationary base motion

Techniques developed for structural identification are typically devoted to obtaining a model, parametrical or not, on the basis of information on the structural response and on the forcing action, both assumed as known from experimental tests. In many situations, however, it may be necessary, or simply useful, to refer only to the measured response. In this paper we describe the theoretical aspects of a technique we have recently developed to identify the modal model in the frequency domain when the input is unknown. To simplify, we refer to unknown nonstationary base motion, but many of our conclusions can be extended to different situations. We show that, from a theoretical point of view, the identification problem has a unique solution, for this kind of input, when at least three time histories are known, and this circumstance had never been pointed out before. Because the theoretical analysis furnishes only necessary conditions for the existence of a unique solution, an extensive numerical analysis is reported in the second part of the paper, which also shows the sensitivity of the identification procedure.