114 A. E. Mahmoudi et al. Fig. 15.8 Schematic representation of the operational measurement campaign. The objective of this campaign is to determine the responses at the indicator points u op 4 and validation points u op 3 , caused by the unknown excitation force f unknown 1 . Hereby, the additional shaker is detached [6] Synchronous block averaging averages out most of the signal components f op andu op caused by the operating excitation, since their amplitude distribution varies in each sample of a successive measurement block. Since the shaker excitation has the same waveform in each successive measurement block, the signal components f shaker and ushaker caused by the shaker are preserved (Fig. 15.8). In [14, 15], synchronous block averaging is referred to as cyclic averaging. Any repetitive signal that is periodic with respect to the measurement block duration T can be used for shaker excitation. The OSI method uses a pseudorandom signal, cf. [15]. This is an ergodic, stationary signal whose frequency content consists only of integer multiples of the fundamental frequency f0 =1 =T of the fast Fourier transform (FFT). In addition, the frequency spectrum has a constant amplitude with arbitrary phase shift. Two types of errors appear in the formation of the FFT of a signal: bias errors and random errors. Bias errors are primarily caused by leakage. To avoid leakage, one way is to choose the signal to be transformed so that it is periodic with respect to the measurement blockT. This is called bias error. This is achieved by using the pseudorandom signal. The random error is reduced by minimized by the averaging process of the OSI method. After the averaging process, the FRFs are calculated using ¯Y OSI = ¯ u shaker ¯fshaker . (15.6) To perform the OSI method, the following three conditions must be met. The system must be operated stationary with constant operating parameters throughout the measurement. In addition, to enable synchronous signal averaging, the system must be excited with a shaker signal that is identical in all time blocks. The last condition is that the signal components f op and uop, which are generated by the operational excitation, do not have components that are periodic with respect to the successive measuring blocks. In [6], the entire experimental procedure of the in-situ TPA method for the characterization of an unknown operational excitation by equivalent forces was simulated. The simulation of the sensor signals of the OSI application, the test planning as well as the evaluation of the simulated sensor signals were done with the pyFBS toolbox. The assembly shown in Fig. 15.9 consisting of an active component (blue) and a passive component (gray) serves as a test case. The design of the assembly and subcomponents and the FE modeling of the assembly were done using commercial software. In Fig. 15.10, the influence of the number N of block averaging is investigated. Here, the motor signal is used as the operating excitation. The gain factor is V =3. For the investigation, the FRF between the excitation point f1 and the z direction of the validation sensor u3 is considered. In the top three plots of Fig. 15.10, the FRF from the OSI is shown in green for N =10, 60, and 300 block averages, respectively. The synthesized reference FRF is shown in blue. The fourth plot examines the convergence of the averaged force and acceleration signals against a stable value for an increasing number Nof block averages. For this purpose, the degree of convergence for the force signal is shown in orange, and for the acceleration signal in light blue over N. In the figure, it can be seen that the FRF from the OSI for N =10 in the frequency ranges 0– 50 Hz and 200–700 Hz as well as at 1450 Hz oscillates around a mean curve, which deviates from the synthesized reference FRF. As the number of averages increases, the mean response approaches the synthesized reference FRF. Furthermore, the amplitudes of the oscillations around the mean decrease. This is not immediately apparent due to the logarithmic plot. In the frequency ranges 50–200 Hz and 950–1050 Hz, oscillations around the synthesized reference FRF also occur. These almost
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