In Structural Engineering, the standard approach for system identification is modal identification, where modal characteristics of the structure are identified from its recorded dynamic response. Modal identification assumes that the damping in the structure is mass and/or stiffness proportional, so that the modal parameters and the mode shapes of the structure are real-valued. A large number of structures can be modelled as chain-like layered systems, such as multi-story buildings. The dynamic response of such systems is basically a one-dimensional wave propagation problem, in which shear and bending waves propagate from one segment to another. The response can also be formulated in terms of the individual frequencies and damping ratios of the layers (i.e., as if each layer were a single-degree-of-freedom system) by using transfer matrix formulation. Using any one of these two formulations, it is possible to show that the top-to-bottom spectral-ratio of the recorded dynamic response at each layer is not influenced by the changes in the characteristics of the layers below. In other words, the spectral ratio of a layer is a function of the structural properties of that layer and the layers above. Thus, noting that the shear force and the moment are zero beyond the top layer, we can start identifying the dynamic characteristics of the system from the top-to-bottom spectral ratios by starting from the top layer, and continuing downward. The identified properties of a layer will not be altered during the identification of the layers below and therefore they will be unique, provided that we start from the top layer. In addition to system identification, the spectral ratio methodology can also be used to calibrate analytical models and to detect damage from vibration records.
doi: 10.12783/SHM2015/172