Suppose that Φ(x)∈L 2(R) with compact support and V= span{Φ(x-k)|k∈Z}. In this note, we prove that if {Φ(x-k)k|k∈Z} is tight frame with bound 1 in V, then {Φ(x-k)|k∈Z} must be an orthonormal basis of V.
This study was performed to investigate the spectral characteristics of micro-seismic signals observed during the rupture of coal. Coal rupture micro-seismic observations were obtained on a test system that included a...This study was performed to investigate the spectral characteristics of micro-seismic signals observed during the rupture of coal. Coal rupture micro-seismic observations were obtained on a test system that included an electro-hydraulic servo pressure tester controlled by a YAW microcomputer, a micro-seismic sensor, a loading system, and a signal collection system. The results show that the micro-seismic signal increases with increasing compressive stress at the beginning of coal rupture. The signal remains stable for a period at this stage. A large number of micro-seismic signals appear immediately before the main rupture event. The frequency of micro-seismic events reaches a maximum immediately after the coal ruptures. Micro-seismic signals were decomposed into several Intrinsic Mode Functions (IMF's) by the empirical mode decomposition (EMD) method using a Hilbert-Huang transform (HHT). The main fre- quency band of the micro-seismic signals was found to range from 10 to 100 Hz in the Hilbert energy spectrum and from marginal spectrum calculations. The advantage of applying an HHT is that this can extract the main features of the signal. This fact was confirmed by an HHT analysis of the coal micro-seis- mic signals that shows the technique is useful in the field of coal rupture.展开更多
Ultrasonic backscatter signals from cancellous bone are sensitive to the microstructure of trabecular bone,and thus enable the feasibility to extract microstructural information of trabecular bone.The mean trabecular ...Ultrasonic backscatter signals from cancellous bone are sensitive to the microstructure of trabecular bone,and thus enable the feasibility to extract microstructural information of trabecular bone.The mean trabecular bone spacing(MTBS)is an important parameter for characterizing bone microstructure.This paper proposes an MTBS estimation method based on the combination of Hilbert transform and fundamental frequency estimation(CHF). The CHF was verified with ultrasonic backscatter signals from simulations and in vitro measurements at a central frequency of 5MHz.The CHF method was compared with the simplified inverse filter tracking(SIFT)method,Simons' Quadratic Transformation(QT)method,Singular Spectrum Analysis(SSA)method,and Spectral Autocorrelation(SAC)method.Monte-Carlo simulations were performed by varying the MTBS,signal-to-noise ratio(SNR),standard deviation of regular spacing(SDRS),amplitude ratio of diffuse scattering to regular scattering(Ad)and frequency dependent attenuation(nBUA).The simulation results showed that the CHF method had a better performance in MTBS estimation under almost all the examination conditions except for SNR.The estimation percentage correct(EPC)was greater than 90% when the MTBS was in the range of 0.4to 1.4mm.In the in vitro measurements,the estimated EPC by the CHF method was91.25±7.81%(mean±standard deviation).A significant correlation was observed for the CHF-estimated MTBS and micro-computed tomography(μ-CT)-measured values(R^2=0.75,p<0.01).These results demonstrate that the CHF method is anti-interference for MTBS estimation and can be used to estimate trabecular bone spacing.展开更多
The local defect in rotating machine always gives rise to repetitive transients in the collected vibration signal. However, the transient signature is prone to be contaminated by strong background noises, thus it is a...The local defect in rotating machine always gives rise to repetitive transients in the collected vibration signal. However, the transient signature is prone to be contaminated by strong background noises, thus it is a challenging task to detect the weak transients for machine fault diagnosis. In this paper, a novel adaptive tunable Q-factor wavelet transform(TQWT) filter based feature extraction method is proposed to detect repetitive transients. The emerging TQWT possesses distinct advantages over the classical constant-Q wavelet transforms, whose Q-factor can be tuned to match the oscillatory behavior of different signals, but the parameter selection for TQWT heavily relies on prior knowledge. Within our adaptive TQWT filter algorithm, the automatic optimization techniques for three TQWT parameters are implemented to achieve an optimal TQWT basis that matches the transient components. Specifically, the decomposition level is selected according to a center frequency ratio based stopping criterion, and the Q-factor and redundancy are optimized based on the minimum energy-weighted normalized wavelet entropy.Then, the adaptive TQWT decomposition can be achieved in a sparse way and result in subband signals at various wavelet scales.Further, the optimum subband signal which carries transient feature information, is identified using a normalized energy to bandwidth ratio index. Finally, the single branch reconstruction signal from the optimum subband is obtained with transient signatures via inverse TQWT, and the frequency of repetitive transients is detected using Hilbert envelope demodulation. It has been verified via numerical simulation that the proposed adaptive TQWT filter based feature extraction method can adaptively select TQWT parameters and the optimum subband for repetitive transient detection without prior knowledge. The proposed method is also applied to faulty bearing vibration signals and its effectiveness is validated.展开更多
文摘Suppose that Φ(x)∈L 2(R) with compact support and V= span{Φ(x-k)|k∈Z}. In this note, we prove that if {Φ(x-k)k|k∈Z} is tight frame with bound 1 in V, then {Φ(x-k)|k∈Z} must be an orthonormal basis of V.
基金support for this work provided by the National Science and Technology Planning Project (No. 2009BAK54B03)the National Natural Science Foundation of China (No. 50834005)
文摘This study was performed to investigate the spectral characteristics of micro-seismic signals observed during the rupture of coal. Coal rupture micro-seismic observations were obtained on a test system that included an electro-hydraulic servo pressure tester controlled by a YAW microcomputer, a micro-seismic sensor, a loading system, and a signal collection system. The results show that the micro-seismic signal increases with increasing compressive stress at the beginning of coal rupture. The signal remains stable for a period at this stage. A large number of micro-seismic signals appear immediately before the main rupture event. The frequency of micro-seismic events reaches a maximum immediately after the coal ruptures. Micro-seismic signals were decomposed into several Intrinsic Mode Functions (IMF's) by the empirical mode decomposition (EMD) method using a Hilbert-Huang transform (HHT). The main fre- quency band of the micro-seismic signals was found to range from 10 to 100 Hz in the Hilbert energy spectrum and from marginal spectrum calculations. The advantage of applying an HHT is that this can extract the main features of the signal. This fact was confirmed by an HHT analysis of the coal micro-seis- mic signals that shows the technique is useful in the field of coal rupture.
基金supported by the NSFC(11327405,11504057&11525416)
文摘Ultrasonic backscatter signals from cancellous bone are sensitive to the microstructure of trabecular bone,and thus enable the feasibility to extract microstructural information of trabecular bone.The mean trabecular bone spacing(MTBS)is an important parameter for characterizing bone microstructure.This paper proposes an MTBS estimation method based on the combination of Hilbert transform and fundamental frequency estimation(CHF). The CHF was verified with ultrasonic backscatter signals from simulations and in vitro measurements at a central frequency of 5MHz.The CHF method was compared with the simplified inverse filter tracking(SIFT)method,Simons' Quadratic Transformation(QT)method,Singular Spectrum Analysis(SSA)method,and Spectral Autocorrelation(SAC)method.Monte-Carlo simulations were performed by varying the MTBS,signal-to-noise ratio(SNR),standard deviation of regular spacing(SDRS),amplitude ratio of diffuse scattering to regular scattering(Ad)and frequency dependent attenuation(nBUA).The simulation results showed that the CHF method had a better performance in MTBS estimation under almost all the examination conditions except for SNR.The estimation percentage correct(EPC)was greater than 90% when the MTBS was in the range of 0.4to 1.4mm.In the in vitro measurements,the estimated EPC by the CHF method was91.25±7.81%(mean±standard deviation).A significant correlation was observed for the CHF-estimated MTBS and micro-computed tomography(μ-CT)-measured values(R^2=0.75,p<0.01).These results demonstrate that the CHF method is anti-interference for MTBS estimation and can be used to estimate trabecular bone spacing.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51335006 & 51605244)
文摘The local defect in rotating machine always gives rise to repetitive transients in the collected vibration signal. However, the transient signature is prone to be contaminated by strong background noises, thus it is a challenging task to detect the weak transients for machine fault diagnosis. In this paper, a novel adaptive tunable Q-factor wavelet transform(TQWT) filter based feature extraction method is proposed to detect repetitive transients. The emerging TQWT possesses distinct advantages over the classical constant-Q wavelet transforms, whose Q-factor can be tuned to match the oscillatory behavior of different signals, but the parameter selection for TQWT heavily relies on prior knowledge. Within our adaptive TQWT filter algorithm, the automatic optimization techniques for three TQWT parameters are implemented to achieve an optimal TQWT basis that matches the transient components. Specifically, the decomposition level is selected according to a center frequency ratio based stopping criterion, and the Q-factor and redundancy are optimized based on the minimum energy-weighted normalized wavelet entropy.Then, the adaptive TQWT decomposition can be achieved in a sparse way and result in subband signals at various wavelet scales.Further, the optimum subband signal which carries transient feature information, is identified using a normalized energy to bandwidth ratio index. Finally, the single branch reconstruction signal from the optimum subband is obtained with transient signatures via inverse TQWT, and the frequency of repetitive transients is detected using Hilbert envelope demodulation. It has been verified via numerical simulation that the proposed adaptive TQWT filter based feature extraction method can adaptively select TQWT parameters and the optimum subband for repetitive transient detection without prior knowledge. The proposed method is also applied to faulty bearing vibration signals and its effectiveness is validated.
