# In the support system and limited measurement

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Unformatted text preview: rameter estimation method produces a general matrix model that describes the unconstrained (free-free) structural system. All of these newer methods will increase the cost (time, ﬁnancial, technical) of performing structural tests with the attendant incremental increase in the accuracy of the test results. 5.5 Practical Measurement Considerations There are several factors that contribute to the quality of actual measured frequency response function estimates. Some of the most common sources of error are due to measurement mistakes. With a proper measurement approach, most of this type of error, such as overloading the input, extraneous signal pick-up via ground loops or strong electric or magnetic ﬁelds nearby, etc., can be avoided. Violation of test assumptions are often the source of another inaccuracy and can be viewed as a measurement mistake. For example, frequency response and coherence functions have been deﬁned as parameters of a linear system. Nonlinearities will generally shift energy from one frequency to many new frequencies, in a way which may be difﬁcult to recognize. The result will be a distortion in the estimates of the system parameters, which may not be apparent unless the excitation is changed. One way to reduce the effect of nonlinearities is to randomize these contributions by choosing a randomly different input signal for each of the n measurements. Subsequent averaging will reduce these contributions in the same manner that random noise is reduced. Another example involves control of the system input. One of the most obvious requirements is to excite the system with energy at all frequencies for which (5-76) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + measurements are expected. It is important to be sure that the input signal spectrum does not have "holes" where little energy exist. Otherwise, coherence will be very low, and the variance on the frequency response function will be large. Assuming that the system is linear, the excitation is proper, and obvious measurement mistakes are avoided, some amount of error (noise) will be present in the measurement process. Five different approaches can be used to reduce the error involved in frequency response function measurements in current fast Fourier transform (FFT) analyzers. First of all, the use of different frequency response function estimation algorithms (H v compared to H 1 ) will reduce the effect of the leakage error on the estimation of the frequency response function computation. The use of averaging can signiﬁcantly reduce errors of both variance and bias and is probably the most general technique in the reduction of errors in frequency response function measurement. Selective excitation is often used to verify nonlinearities or randomize characteristics. In this way, bias errors due to system sources can be reduced or controlled. The increase of frequency resolution through the zoom fast Fourier transform can improve the frequency respons...
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