Abstract
Power spectral density (PSD) is used for evaluating a structure’s vibration process. Moreover, PSD not only shows a discrete form of vibration but also presents various components in a vibration structure. The superposition of multiple vibration patterns on the same spectrum poses difficulty in analyzing the spectral information in the way needed to find the structure’s discrete vibration. This paper proposes a method for separating the synthetic vibration signal into a structure’s discrete vibration and other extraneous vibrations using the maximal overlap discrete wavelet transform (MODWT) method combined with the method of fast Fourier transform (FFT). With the combination of these two algorithms, MODWT and FFT, the signals of the synthesized vibration have been separated into component signals with different frequency ranges. This means that PSD will be formed, which is based on the combination of the single power spectra of the component signals. Thus, the single spectrum of each of these constructed components can be used to evaluate the types of discrete vibrations coexisting in a structure’s vibration process. The survey results in this paper show the sensitivity and suitability of select types of discrete vibrations to be separated out during the assessment of the structural change, so as to achieve the best possible plan for eliminating the unwanted and unexpected noise and vibration components.
Highlights
Advances in Materials Science and Engineering with the other algorithms improves the processing efficiency [34]
Separating the Power Density Spectrum by the maximal overlap discrete wavelet transform (MODWT) Model. e power density spectrum is a conversion of the signal vibration from the time domain to the frequency domain through the FFT transformation for the original signal’s autocorrelation function. us, the spectrum obtained from the variation of the original signal will be a spectrum with a constant frequency. is frequency sequence may contain various discrete frequencies of distinct signal types
Power density spectra corresponding to discrete vibrations separated from the overall original spectrum can effectively reveal the factors causing the main impact on the structure during operating time. e process of signal separation using the technique of multiresolution analysis by the MODWT allows the capture of necessary signals and the elimination of noise signals, those signals having little effect on the structure. e main results obtained from this paper are summarized as follows: (1) e signal of overall vibration measurement is an overall signal combined with various discrete vibrations that exist as considerable noise
Summary
In which x is data corresponding to time τ and y is data corresponding to time T + τ. us, equation (11) allows us to correlate the two moments of the vibration signal. e correlation function will evaluate the signal randomness through the difference between the two datasets. is helps to evaluate the stability of the measured vibration signals. If you want to make the reverse conversion from the frequency domain to the time domain, do the following according to equation f(t). Equation (19) leads to the discrete Fourier transformation: Fn FN[f](n) f tke− i2πkn/N. e FFT solver algorithm in this paper applies only to the case N 2s, s ∈ N. Applying the discrete Fourier from equation (20) to each sequence in equation (21) gives (N/2)− 1. For n ≥ N/2, Sn can be calculated according to the periodic properties of the discrete Fourier transform: Fn Gn− (N/2) + WnHn− (N/2). When n ≥ N/2, the Fourier transform is calculated as follows: Fn Gn− (N/2) − Wn− (N/2)Hn− (N/2). Us, the FFT can process the signals’ autocorrelation function so as to obtain the power density spectrum in the frequency domain quicker than the conventional Fourier transformation can. We can analyze the hidden components in the signal, which would otherwise not be detected if processed in the time domain, by converting signals from the time domain to the frequency domain. e signal variation will lead to a change in the power density spectrum
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