# Formula and the characteristic of the excitation

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Unformatted text preview: of random signal input. For systems with small nonlinearities, use of a random input will not differ greatly from the use of a deterministic input. The characterization of the modal parameter estimation is primarily concerned with the type of mathematical model being used to represent the frequency response function. Generally, the model is a linear summation based upon the modal parameters of the system. Unless the mathematical representation of all nonlinearities is known, the parameter estimation process cannot properly weight the frequency response function data to include nonlinear effects. For this reason, random input signals are prevalently used to obtain the best linear estimate of the frequency response function when a parameter estimation process using a linear model is to be utilized. The expected utilization of the data is concerned with the degree of detailed information required by any post-processing task. For experimental modal analysis, this can range from implicit modal vectors needed for trouble-shooting to explicit modal vectors used in an orthogonality check. As more detail is required, input signals, both random and deterministic, will need to match the system characteristics and parameter estimation characteristics more closely. In all possible uses of frequency response function data, the conﬂicting requirements of the need for accuracy, equipment availability, testing time, and testing cost will normally reduce the possible choices of input signal. With respect to the reduction of the variance and bias errors of the frequency response function, random or deterministic signals can be utilized most effectively if the signals are periodic with respect to the sample period or totally observable with respect to the sample period. If either of these criteria are satisﬁed, regardless of signal type, the predominant bias error, leakage, will be minimized. If these criteria are not satisﬁed, the leakage error may become signiﬁcant. In either case, the variance error will be a function of the signal-to-noise ratio and the amount of averaging. Many signals are appropriate for use in experimental modal analysis. Some of the most commonly used random signals, used with single and multiple input shaker testing, are described in the following sections. (5-48) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + Pure Random - The pure random signal is an ergodic, stationary random signal which has a Gaussian probability distribution. In general, the frequency content of the signal contains energy at all frequencies (not just integer multiples of the FFT frequency increment (∆ f = 1/T )). This characteristic is shown in Figure 5-14. This is undesirable since the frequency information between the FFT frequencies is the cause of the leakage error. The pure random signal may be ﬁltered (F min to F max ) to include only information in a frequency band of interest. The measured input spectrum of the pure random signal, as with...
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