Precise Frequency Domain Algorithm of Half Spectrum and FRF

Abstract

In operational modal analysis, the half spectrum is needed. Its corresponding time wave is the half part of correlating function with positive time delay. In classic modal analysis, the frequency response function (FRF) is needed. Its corresponding time wave is the unit impulse response function (UIRF). In current commercial modal analysis software, the frequency domain algorithm is used to compute half spectrum or FRF first. For algorithm of frequency domain based on FFT, its computation speed is very high, but there are errors caused by the periodic assumption of FFT both for half spectrum and FRF. For algorithm of time domain, the half part of correlating function with positive time delay or the UIRF are computed directly with the best preciseness, but the computation speed is slow and unpractical. The precise frequency domain algorithm put forward here is still based on FFT, with innovation in computing mode. The half spectrum computed out by the new algorithm, can reach the same precise as the time domain algorithm but the computation speed level is similar to traditional frequency domain algorithm. To compute the FRF, let the length of output wave be two times of input data wave, the length of unit impulse wave corresponding to FRF is the same as the input data wave. By this way, the errors caused by periodic assumption of FFT can be totally eliminated both for impact exciting and continuous exciting. For continuous exciting, the initial response is needed to be considered. This consideration can be fulfilled by a few times iteration. The precise of FRF by new algorithm is very close to time domain algorithm. The computation speed of the new algorithm is accelerated more than ten times comparing with the algorithm of time domain. A new coherence function definition, which is suitable for half spectrum, for FRF of the traditional algorithm and new algorithm in frequency domain, as well as for FRF of algorithm in time domain, is introduced. It can be used to evaluate the preciseness of FRF and half spectrum. For impact test, if only the data of one impact is available, the value of traditional coherence function is one in all the spectrum lines, without any physical meaning, but the value of new coherence function will still reflect the ratio of signal to noise in each spectrum lines.