Perceiving harmonic information (especially weak harmonic information) in time series has important scientific and engineering significance. Fourier spectrum and time-frequency spectrum are commonly used tools for per...Perceiving harmonic information (especially weak harmonic information) in time series has important scientific and engineering significance. Fourier spectrum and time-frequency spectrum are commonly used tools for perceiving harmonic information, but they are often ineffective in perceiving weak harmonic signals because they are based on energy or amplitude analysis. Based on the theory of Normal time-frequency transform (NTFT) and complex correlation coefficient, a new type of spectrum, the Harmonicity Spectrum (HS), is developed to perceive harmonic information in time series. HS is based on the degree of signal harmony rather than energy or amplitude analysis, and can therefore perceive very weak harmonic information in signals sensitively. Simulation examples show that HS can detect harmonic information that cannot be detected by Fourier spectrum or time-frequency spectrum. Acoustic data analysis shows that HS has better resolution than traditional LOFAR spectrum.展开更多
The harmonic wavelet transform（HWT） and its fast realization based on fast Fourier transform（FFT） are introduced. Its ability to maintain the same amplitude-frequency feature is revealed. A new method to construct...The harmonic wavelet transform（HWT） and its fast realization based on fast Fourier transform（FFT） are introduced. Its ability to maintain the same amplitude-frequency feature is revealed. A new method to construct the time-frequency（TF） spectrum of HWT is proposed, which makes the HWT TF spectrum able to correctly reflect the time-frequency-amplitude distribution of the signal. A new way to calculate the HWT coefficients is proposed. By zero padding the data taken out, the non-decimated coefficients of HWT are obtained. Theoretical analysis shows that the modulus of the coefficients obtained by the new calculation way and living at a certain scale are the envelope of the component in the corresponding frequency band. By taking the cross section of the new TF spectrum, the demodulation for the component at a certain frequency band can be realized. A comparison with the Hilbert demodulation combined with band-pass filtering is done, which indicates for multi-components, the method proposed here is more suitable since it realizes ideal band-pass filtering and avoids pass band selecting. In the end, it is applied to bearing and gearbox fault diagnosis, and the results reflect that it can effectively extract the fault features in the signal.展开更多
With respect to flows in a two-dimensional sudden expansion and contraction channel having a pair of cavities, numerical simulation was performed by imposing inlet/outlet boundary conditions giving a velocity distribu...With respect to flows in a two-dimensional sudden expansion and contraction channel having a pair of cavities, numerical simulation was performed by imposing inlet/outlet boundary conditions giving a velocity distribution to the inlet. Periodic flows have been reproduced, which have a discrete spectrum about frequency. A fundamental wave occupies most part of the disturbance components, but higher harmonic waves are also included. The disturbance is excited by Kelvin-Helmholtz instability in a cavity section, where only the fundamental wave is generated. A wavenumber is regulated by a channel length under a periodic boundary condition, but there is no restriction in a main flow direction under the inlet/outlet boundary conditions, and therefore, some wavenumbers can occur. Therefore, an arbitrary frequency component of disturbance is a synthesized wave composed of various wave numbers. There are two kinds of components constituting this synthesized wave: a maximum of a velocity distribution is near a wall and in the center of the channel, which are called as wall mode and central mode in linear stability analysis of the plane Poiseuille flow. The synthesized wave composed of some modes shows a tendency to lower wavenumbers at the center of the channel.展开更多
文摘Perceiving harmonic information (especially weak harmonic information) in time series has important scientific and engineering significance. Fourier spectrum and time-frequency spectrum are commonly used tools for perceiving harmonic information, but they are often ineffective in perceiving weak harmonic signals because they are based on energy or amplitude analysis. Based on the theory of Normal time-frequency transform (NTFT) and complex correlation coefficient, a new type of spectrum, the Harmonicity Spectrum (HS), is developed to perceive harmonic information in time series. HS is based on the degree of signal harmony rather than energy or amplitude analysis, and can therefore perceive very weak harmonic information in signals sensitively. Simulation examples show that HS can detect harmonic information that cannot be detected by Fourier spectrum or time-frequency spectrum. Acoustic data analysis shows that HS has better resolution than traditional LOFAR spectrum.
基金supported by National Natural Science Foundation of China (Grant No. 50575233)National Hi-tech Research and Development Program of China (Grant No. 2008AA042408)
文摘The harmonic wavelet transform（HWT） and its fast realization based on fast Fourier transform（FFT） are introduced. Its ability to maintain the same amplitude-frequency feature is revealed. A new method to construct the time-frequency（TF） spectrum of HWT is proposed, which makes the HWT TF spectrum able to correctly reflect the time-frequency-amplitude distribution of the signal. A new way to calculate the HWT coefficients is proposed. By zero padding the data taken out, the non-decimated coefficients of HWT are obtained. Theoretical analysis shows that the modulus of the coefficients obtained by the new calculation way and living at a certain scale are the envelope of the component in the corresponding frequency band. By taking the cross section of the new TF spectrum, the demodulation for the component at a certain frequency band can be realized. A comparison with the Hilbert demodulation combined with band-pass filtering is done, which indicates for multi-components, the method proposed here is more suitable since it realizes ideal band-pass filtering and avoids pass band selecting. In the end, it is applied to bearing and gearbox fault diagnosis, and the results reflect that it can effectively extract the fault features in the signal.
文摘With respect to flows in a two-dimensional sudden expansion and contraction channel having a pair of cavities, numerical simulation was performed by imposing inlet/outlet boundary conditions giving a velocity distribution to the inlet. Periodic flows have been reproduced, which have a discrete spectrum about frequency. A fundamental wave occupies most part of the disturbance components, but higher harmonic waves are also included. The disturbance is excited by Kelvin-Helmholtz instability in a cavity section, where only the fundamental wave is generated. A wavenumber is regulated by a channel length under a periodic boundary condition, but there is no restriction in a main flow direction under the inlet/outlet boundary conditions, and therefore, some wavenumbers can occur. Therefore, an arbitrary frequency component of disturbance is a synthesized wave composed of various wave numbers. There are two kinds of components constituting this synthesized wave: a maximum of a velocity distribution is near a wall and in the center of the channel, which are called as wall mode and central mode in linear stability analysis of the plane Poiseuille flow. The synthesized wave composed of some modes shows a tendency to lower wavenumbers at the center of the channel.
