OBSERVATIONS Often times, data sets are collected by different groups with different overall objectives as well as different measuring methodologies and systems. The integration of these vastly different databases can pose problems. With the expansion processes discussed in this paper, the subsets of different measurement points over different frequency ranges can be achieved very effectively. For the measurements made in this study, a wide assortment of measuring devices and systems were employed. Obviously, accelerometer measurements are very common in the development of any structural dynamic models; traditional impact and shaker excitation approaches are typically used for the measurement of frequency response functions and the data is reduced using conventional modal parameter estimation approaches. For the very low frequency measurements, several approaches are possible including low frequency accelerometer transducers. However, for the tests identified in this study, optical measurements were employed; digital image correlation and/or dynamic photogrammetry approaches were used. These very low frequency measurements employed dynamic photogrammetry to obtain time response at very limited sets of test locations. FFT processing of the data was performed to obtain frequency response functions. At the very high frequency range, either low mass accelerometers or laser vibrometer measurements could be employed using impact or shaker excitation approaches. Again, these measurements were processed to obtain modal parameters. For the studies performed herein, there was no care exercised to select measurement locations that had any common data points to illustrate the approach suggested in this paper. Obviously, if these measurements can be obtained at a common set of measurement locations then advantages can be obtained. But even if many points are selected in common, there is really no reason to collect the same number of points for all the frequency ranges to be addressed. For instance, in order to properly characterize high frequency modes, many points are required to define the shape sufficiently. However, this large number of points is totally unnecessary in the definition of the rigid body modes. So the expansion process is still necessary in order to meld all the data together for a unified data set to describe the structure. But due to the way the expansion process has been defined, there is no required common set of measurement points. CONCLUSION The development of a hybrid set of mode shapes that come from an assortment of different measurement systems, with drastically different transducer configurations and with a non-coincident set of measurement points, was described. The modal expansion process was used to develop a common data set from each of the individual data sets. A unique set of measurement points was used to expand each of the different measured arrays of points from each of the different tests to obtain one complete, unified set of data that can be used for further processing. Using either Dynamic Expansion or the System Equivalent Reduction Expansion Process (SEREP), test data sets that come from completely different sources (optical, accelerometer, laser, etc), with completely different sets of measured points, can be effectively combined to form one unified set of modal data to describe a structure. This was demonstrated for an example structure and shown to produce useful results. NOMENCLATURE Symbols: ^ `nX full set displacement vector ^ `aX reduced set displacement vector > @ aM reduced mass matrix > @ nM expanded mass matrix > @ aK reduced stiffness matrix > @ nK expanded stiffness matrix > @ aU reduced shape matrix > @g aU generalized inverse of reduced shape matrix > @ nU expanded shape matrix > @T transformation matrix. > @ UT SEREP transformation matrix. > @ n REF reference data at all degrees of freedom (dofs) > @ a RTO real time operating data at measured dofs > @ n ERTO expanded real time operating data at all dofs 171
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