This research is focused on modal model technique among indirect input identification methods that estimate multiple system inputs indirectly by measuring vibration responses. An input identification method, which uses modal parameters obtained from the frequency response functions (FRF) measured by exciting other points than operational input points in case those are inaccessible for artificial excitation, is proposed.
The error mechanism by which errors in poles and mode vectors affect input estimation is studied, and it is shown that they have large effects on the estimated values around resonances. In particular, whereas errors in natural frequencies cause errors only on the modal coordinate of the corresponding mode, those in mode vectors do on the other modes as well as that mode itself. Errors in damping have negligible effects than those in poles or mode vectors do. The effect of the residual modes outside of the interested frequency range is almost negligible for the lowly damped system with low modal density.
This study proposes to use discrete modal filter as a countermeasure to the largest error source of inverting modal matrix. It is doubted that the modal filter RMRMV by Shelley may produce more errors by putting modal participation factors (MPF), which are already identified at the same stage of modal parameter fitting as natural frequencies, as unknown values. So, a reduced form of MRMV (RMRMV) is expected to improve input identification by adopting MPF's as known ones. This proposition is verified by numerical experiments, which simulates the cases of measurement errors. And, RMRMV is shown to be the modal filter with the smallest orthogonality error through that simulation.
The input identification procedure by modal model technique is established by proposing the procedure, which selects excitation points for the system identification stage and measurement points for both the system and input identification stages. The procedure, which selects first measurement points and then excitation points, is adopted. Before an experiment for system identification, measurement points are selected by applying EI method to the modal matrix obtained by analytical methods such as FEA, and excitation points are selected by pivoted QR decomposition of the reduced modal matrix for the ready-chosen measurement points. The proposed method is verified by numerical experiment.
Finally, an experiment, which identifies dual loads to a cantilever plate, is carried out to verify the applicability of the proposed method. Through this experiment, modal model technique using RMRMV is shown to be superior to the method using MRMV or direct inverse of modal matrix.
By expanding FRF's measured by exciting at other points than the operational input points in case some of those points are inaccessible for artificial excitation, and by applying discrete modal filter to suppress the errors which may be caused by the fitting errors in modal parameters, operational inputs to the structure are expected to be identified more accurately. However, because the proposed method needs modal model decomposition and the effects of the residual modes can not be considered at all, this one is regarded to have limits on the systems with high modal density or high damping.