The Structural Analysis Of Multi-input Multi-output Transfer Function Unbiased Estimate

Experimental modal analysis is a technique to build modal model based on the measured data. With the development of the electronic technique and the computer technology, experimental modal analysis has been the main tool to solve complex structure's vibration problems. Frequency Response Function (FRF) is a ring that links the measured data and the modal parameter recognition (MPR). It is the foundation of the modal parameter recognition. The precision of the frequency response function estimation decides the precision of the MPR.Presently, because the existing several unbiased Frequency Response Function estimators are difficult to realize, the most popular and widely-spread used Frequency Response Function estimators are H₁, and H₂, although both of them are biased ones. In allusion to such situation, some typical Frequency Response Function estimators are analyzed. It is pointed that the cross spectrum density technique and the meaning technique is the key technique to get the unbiased and high precision FRF. On the basis of such analysis, a completed cross spectrum density frequency response function estimator- H_n estimator isproduced. Through the combination of the H_n with different excitation methods, single-input single-output and multi-point random and multi-point mono-phased harmonic H_n estimators are deduced. For a multi-degree-of-freedom viscous damping system, simulation analysis is made to realize the single-input single-output and the multi-point mono-phased harmonic H_n estimators and the comparison with the H₁ estimator. For a both end hinged beam, experiment is made which realized the comparison of H_n and H₁ and H₂. Through the simulation analysis and the experiment, it is proved that H_nis an unbiased and high precision estimator. This method makes the best of the cross spectrum density technique and the meaning technique. It realized the unbiased frequency response function estimator need not to measure the third signal. With the same number of measured data, it can mean more times, which improved the precision of the frequency response function estimation.