The hyper Hilbert transform Tnf（x） =∫-1^1 f（x - Γ（t））e^-i｜t｜-β｜t｜^-1-αdt along an appropriate curve Γ（t） on R^n is investigated,where β 〉 α 〉 0.An L^p boundedness theorem of T4 is obtained,which i...The hyper Hilbert transform Tnf（x） =∫-1^1 f（x - Γ（t））e^-i｜t｜-β｜t｜^-1-αdt along an appropriate curve Γ（t） on R^n is investigated,where β 〉 α 〉 0.An L^p boundedness theorem of T4 is obtained,which is an extension of some earlier results of n = 2 and n = 3.展开更多
This work presents an advanced mathematical tool applicable to the recognition and classification of power system transients and disturbances. Disturbances without a periodic pattern or with a non-linear pattern requi...This work presents an advanced mathematical tool applicable to the recognition and classification of power system transients and disturbances. Disturbances without a periodic pattern or with a non-linear pattern require a more suitable tool than the Fourier series （Fast Fourier or Windowed Fourier Transforms）. To overcome these drawbacks, other tools have been broadly used, such as the wavelet transform. However, the wavelet transform also has some drawbacks such as the lack of adaptivity or interpretation of nonlinear phenomena that the Hilbert and Hilbert Huang Transform techniques could mitigate. The Hilbert techniques transform a time domain function into a space representation both in time and frequency. In the paper, the technique is applied to analyse several short-term and steady events, like a short circuit, a capacitor-switching transient, or a line energisation, showing the abilities of the Hilbert-based transforms.展开更多
We consider the oscillatory hyper Hilbert transform Hγ,α,βf（x） = ∫0^∞ f（x - Г（t））eit-βt-（1＋α）dt, where Г（t） = （t, γ（t）） in R^2 is a general curve. When γ is convex, we give a simple condition...We consider the oscillatory hyper Hilbert transform Hγ,α,βf（x） = ∫0^∞ f（x - Г（t））eit-βt-（1＋α）dt, where Г（t） = （t, γ（t）） in R^2 is a general curve. When γ is convex, we give a simple condition on γ such that Hγ,α,βis bounded on L2 when β ≥ 3α, β 〉 0. As a corollary, under this condition, we obtain the LP-boundedness of Hγ,α,β when 2β/（2β - 3α） 〈 p 〈 2β/（3α）. When F is a general nonconvex curve, we give some more complicated conditions on γ such that Hγ,α,βis bounded on L2. As an application, we construct a class of strictly convex curves along which Hγ,α,β is bounded on L2 only if β 〉 2α 〉 0.展开更多
Abstract In this paper, we give counterexamples to show that variation and oscillation operators related to rough truncations of the Hilbert transform are not bounded from H1 to L1, and prove variation, oscillation an...Abstract In this paper, we give counterexamples to show that variation and oscillation operators related to rough truncations of the Hilbert transform are not bounded from H1 to L1, and prove variation, oscillation and A-jump operators related to smooth truncations are bounded from H1 to L1.展开更多
The prediction and compensation control of marine ship motion is crucial for ensuring the safety of offshore wind turbine loading and unloading operations.However,the accuracy of prediction and control is significantl...The prediction and compensation control of marine ship motion is crucial for ensuring the safety of offshore wind turbine loading and unloading operations.However,the accuracy of prediction and control is significantly affected by the hysteresis phenomenon in the wave compensation system.To address this issue,a ship heave motion prediction is proposed in this paper on the basis of the Gauss-DeepAR(AR stands for autoregressive recurrent)model and the Hilbert−Huang time-delay compensation control strategy.Initially,the zero upward traveling wave period of the level 4−6 sea state ship heave motion is analyzed,which serves as the input sliding window for the Gauss-DeepAR prediction model,and probability predictions at different wave direction angles are conducted.Next,considering the hysteresis characteristics of the ship heave motion compensation platform,the Hilbert−Huang transform is employed to analyze and calculate the hysteresis delay of the compensation platform.After the optimal control action value is subsequently calculated,simulations and hardware platform tests are conducted.The simulation results demonstrated that the Gauss-DeepAR model outperforms autoregressive integrated moving average model(ARIMA),support vector machine(SVM),and longshort-term memory(LSTM)in predicting non-independent identically distributed datasets at a 90°wave direction angle in the level 4−6 sea states.Furthermore,the model has good predictive performance and generalizability for non-independent and non-uniformly distributed datasets at a 180°wave direction angle.The hardware platform compensation test results revealed that the Hilbert–Huang method has an outstanding effect on determining the hysteretic delay and selecting the optimal control action value,and the compensation efficiency was higher than 90%in the level 4−6 sea states.展开更多
In seismic data processing, random noise seriously affects the seismic data quality and subsequently the interpretation. This study aims to increase the signal-to-noise ratio by suppressing random noise and improve th...In seismic data processing, random noise seriously affects the seismic data quality and subsequently the interpretation. This study aims to increase the signal-to-noise ratio by suppressing random noise and improve the accuracy of seismic data interpretation without losing useful information. Hence, we propose a structure-oriented polynomial fitting filter. At the core of structure-oriented filtering is the characterization of the structural trend and the realization of nonstationary filtering. First, we analyze the relation of the frequency response between two-dimensional（2D） derivatives and the 2D Hilbert transform. Then, we derive the noniterative seismic local dip operator using the 2D Hilbert transform to obtain the structural trend. Second, we select polynomial fitting as the nonstationary filtering method and expand the application range of the nonstationary polynomial fitting. Finally, we apply variableamplitude polynomial fitting along the direction of the dip to improve the adaptive structureoriented filtering. Model and field seismic data show that the proposed method suppresses the seismic noise while protecting structural information.展开更多
The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is applicable to both regular and irregular trains; of waves. The wave data series measured with two wave ga...The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is applicable to both regular and irregular trains; of waves. The wave data series measured with two wave gauges in the experiments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily obtained. The arrival of reflected waves can also be detected for improvement of the accuracy of the reflection coefficient. The reflection performance of the physical model can be estimated exactly without calculation of wave height and phase difference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conducted and compared with Goda's method and satisfactory results are obtained.展开更多
Hilbert transformation and improved ellipse localization method is applied in ultrasonic transducer array tomography to detect defect of metal plate.By combining the improved ellipse localization method and time-rever...Hilbert transformation and improved ellipse localization method is applied in ultrasonic transducer array tomography to detect defect of metal plate.By combining the improved ellipse localization method and time-reversal method,the new ultrasonic tomography algorithm employs smooth Hilbert envelope instead of discrete amplitude to reconstruct defect image.An ultrasonic tomography system with six transducers is built to evaluate the effectiveness of the new ultrasonic tomography algorithm.The S0 mode Lamb wave is excited on special condition,and the mode of received signal is identified by Vigner-Wille distribution.The gray value of image area is defined by envelope of the reflected S0 mode Lamb wave signal from defect boundary.Defect image can be reconstructed by summing gray value of all pixels in the image area.The experimentally reconstructed defect image shows that the new tomography algorithm based on Hilbert transformation is efficient for defect detection in metal plate.展开更多
We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by u...We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.展开更多
In the mechanical fault detection and diagnosis field, it is more and more important to analyze the instantaneous frequency （IF） character of complex vibration signal. The improved IF estimation method is put forwar...In the mechanical fault detection and diagnosis field, it is more and more important to analyze the instantaneous frequency （IF） character of complex vibration signal. The improved IF estimation method is put forward aiming at the shortage of traditional Hilbert transform. It is based on Hilbert transform in wavelet domain. With the help of relationship between the real part and the imaginary part obtained from the complex coefficient of continuous wavelet transform or the analyti- cal signal reconstructed in wavelet packet decomposition, the instantaneous phase function of the subcomponent is extracted. In order to improve the precise of IF estimated out, some means such as Linear regression, adaptive filtering, resampling are applied into the instantaneous phase obtained, then, the central differencing operator is used to get desired IF. Simulation results with synthetic and gearbox fault signals are included to illustrate the proposed method.展开更多
This study is concerned with the diagnosis of discrepancies in a steel truss bridge by identifying dynamic properties from the vibration response signals of the bridges.The vibration response signals collected at brid...This study is concerned with the diagnosis of discrepancies in a steel truss bridge by identifying dynamic properties from the vibration response signals of the bridges.The vibration response signals collected at bridges under three different vehicular speeds of 10 km/hr,20 km/hr,and 30 km/hr are analyzed using statistical features such as kurtosis,magnitude of peak-to-peak,root mean square,crest factor as well as impulse factor in time domain,and Stockwell transform in the time-frequency domain.The considered statistical features except for kurtosis show uncertain behavior.The Stockwell transform showed low-resolution outcomes when the presence of noise in the recorded vibration responses.The elimination of noise and extraction of meaningful dynamic properties from the vibration responses is done by applying a new method which comes from the fusion of Hilbert transform with Spectral kurtosis and bandpass filtering.The outcomes obtained from Hilbert transform processed residual signals which are further filtered using bandpass filter show more robustness and accuracy in characterizing bridge modal frequencies from the noisy vibration responses.The proposed method produces a high-resolution frequency response which can unveil the joint discrepancy in the bridge structure.展开更多
Noise is the biggest obstacle that makes the incipient fault diagnosis results of roller bearings uncorrected; a new method for diagnosing incipient fault of roller bearings based on the Wavelet Transform Correlation ...Noise is the biggest obstacle that makes the incipient fault diagnosis results of roller bearings uncorrected; a new method for diagnosing incipient fault of roller bearings based on the Wavelet Transform Correlation Filter and Hilbert Transform was proposed. First, the weak fault information features are picked up from the roller bearings fault vibration signals by use of a de-noising characteristic of the Wavelet Transform Correlation Filter as the preprocessing of the Hilbert Envelope Analysis. Then, in order to get fault features frequency, de-noised wavelet coefficients of high scales which represent high frequency signal were analyzed by Hilbert Envelope Spectrum Analysis. The simulation signals and diagnosing examples analysis results reveal that the proposed method is more effective than the method of direct wavelet coefficients-Hilbert Transform in de-noising and clarifying roller bearing incipient fault.展开更多
Nonlinear response is an important factor affecting the accuracy of three-dimensional image measurement based on the fringe structured light method.A phase compensation algorithm combined with a Hilbert transform is p...Nonlinear response is an important factor affecting the accuracy of three-dimensional image measurement based on the fringe structured light method.A phase compensation algorithm combined with a Hilbert transform is proposed to reduce the phase error caused by the nonlinear response of a digital projector in the three-dimensional measurement system of fringe structured light.According to the analysis of the influence of Gamma distortion on the phase calculation,the algorithm establishes the relationship model between phase error and harmonic coefficient,introduces phase shift to the signal,and keeps the signal amplitude constant while filtering out the DC component.The phase error is converted to the transform domain,and compared with the numeric value in the space domain.The algorithm is combined with a spiral phase function to optimize the Hilbert transform,so as to eliminate external noise,enhance the image quality,and get an accurate phase value.Experimental results show that the proposed method can effectively improve the accuracy and speed of phase measurement.By performing phase error compensation for free-form surface objects,the phase error is reduced by about 26%,and about 27%of the image reconstruction time is saved,which further demonstrates the feasibility and effectiveness of the method.展开更多
In the paper, the author generalized the Hardy and Littlewood's theorem toBa space, i.e. for all Pm satisfying 1 < α = infpm≤ β≤ suppm < ∞, m = 1, 2,..., and the following inequalityholds if and on1y if.
Analytic Hardy and BMO spaces on the quantum torus are introduced. Some basic properties of these spaces are presented. In particular, the associated H 1-BMO duality theorem is proved. Finally, we discuss some possibl...Analytic Hardy and BMO spaces on the quantum torus are introduced. Some basic properties of these spaces are presented. In particular, the associated H 1-BMO duality theorem is proved. Finally, we discuss some possible extensions of the obtained results.展开更多
In agreement with Titchmarsh’s theorem, we prove that dispersion relations are just the Fourier-transform of the identity, g(x′)=±Sgn(x′)g(x′), which defines the property of being a truncated functions at the...In agreement with Titchmarsh’s theorem, we prove that dispersion relations are just the Fourier-transform of the identity, g(x′)=±Sgn(x′)g(x′), which defines the property of being a truncated functions at the origin. On the other hand, we prove that the wave-function of a generalized diffraction in time problem is just the Fourier-transform of a truncated function. Consequently, the existence of dispersion relations for the diffraction in time wave-function follows. We derive these explicit dispersion relations.展开更多
Envelope analysis is an effective method for characterizing impulsive vibrations in wired condition monitoring(CM)systems. This paper depicts the implementation of envelope analysis on a wireless sensor node for obtai...Envelope analysis is an effective method for characterizing impulsive vibrations in wired condition monitoring(CM)systems. This paper depicts the implementation of envelope analysis on a wireless sensor node for obtaining a more convenient and reliable CM system. To maintain CM performances under the constraints of resources available in the cost effective Zigbee based wireless sensor network(WSN), a low cost cortex-M4 F microcontroller is employed as the core processor to implement the envelope analysis algorithm on the sensor node. The on-chip 12 bit analog-to-digital converter(ADC) working at 10 k Hz sampling rate is adopted to acquire vibration signals measured by a wide frequency band piezoelectric accelerometer. The data processing flow inside the processor is optimized to satisfy the large memory usage in implementing fast Fourier transform(FFT) and Hilbert transform(HT). Thus, the envelope spectrum can be computed from a data frame of 2048 points to achieve a frequency resolution acceptable for identifying the characteristic frequencies of different bearing faults. Experimental evaluation results show that the embedded envelope analysis algorithm can successfully diagnose the simulated bearing faults and the data transmission throughput can be reduced by at least 95% per frame compared with that of the raw data, allowing a large number of sensor nodes to be deployed in the network for real time monitoring.展开更多
The primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom （MDOF） linear time invariant （LTI） and linear time vari...The primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom （MDOF） linear time invariant （LTI） and linear time variant （LTV--due to damage） systems based on Time-frequency （TF） techniques--such as short-time Fourier transform （STFT）, empirical mode decomposition （EMD）, and wavelets--is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform （HT） approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their modal components. Once the modal components are obtained, each one is processed using Hilbert transform to obtain the modal frequency and damping ratios. In addition, the ratio of modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only modal identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they arc signal based; hence, can be used for output only modal identification. A three degree of freedom 1：10 scale model test structure is used to validate the proposed output only modal identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration （white noise） response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for modal identification and their potential for real world applications where output only identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based modal identification can be performed.展开更多
In the light of the problem of weak reflection signals shielded by strong reflections from the concrete surface,the detection and the recognition of hidden micro-cracks in the shield tunnel lining were studied using t...In the light of the problem of weak reflection signals shielded by strong reflections from the concrete surface,the detection and the recognition of hidden micro-cracks in the shield tunnel lining were studied using the orthogonal matching pursuit and the Hilbert transform(OMHT method).First,according to the matching pursuit algorithm and the strong reflection-forming mechanism,and based on the sparse representation theory,a sparse dictionary,adapted to the characteristics of the strong reflection signal,was selected,and a matching decomposition of each signal was performed so that the weak target signal submerged in the strong reflection was displayed more strongly.Second,the Hilbert transform was used to extract multiple parameters,such as the instantaneous amplitude,the instantaneous frequency,and the instantaneous phase,from the processed signal,and the ground penetrating radar(GPR)image was comprehensively analyzed and determined from multiple angles.The results show that the OMHT method can accurately weaken the effect of the strong impedance interface and effectively enhance the weak reflected signal energy of hidden micro-crack in the shield tunnel segment.The resolution of the processed GPR image is greatly improved,and the reflected signal of the hidden micro-crack is easily visible,which proves the validity and accuracy of the analysis method.展开更多
Gas–liquid two-phase flow abounds in industrial processes and facilities. Identification of its flow pattern plays an essential role in the field of multiphase flow measurement. A bluff body was introduced in this s...Gas–liquid two-phase flow abounds in industrial processes and facilities. Identification of its flow pattern plays an essential role in the field of multiphase flow measurement. A bluff body was introduced in this study to recognize gas–liquid flow patterns by inducing fluid oscillation that enlarged differences between each flow pattern. Experiments with air–water mixtures were carried out in horizontal pipelines at ambient temperature and atmospheric pressure. Differential pressure signals from the bluff-body wake were obtained in bubble, bubble/plug transitional, plug, slug, and annular flows. Utilizing the adaptive ensemble empirical mode decomposition method and the Hilbert transform, the time–frequency entropy S of the differential pressure signals was obtained. By combining S and other flow parameters, such as the volumetric void fraction β, the dryness x, the ratio of density φ and the modified fluid coefficient ψ, a new flow pattern map was constructed which adopted S（1–x）φ and （1–β）ψ as the vertical and horizontal coordinates, respectively. The overall rate of classification of the map was verified to be 92.9% by the experimental data. It provides an effective and simple solution to the gas–liquid flow pattern identification problems.展开更多
基金Supported by the National Natural Science Foundation of China (1057115610701064)+1 种基金ZJNSF (RC97017)the Zijin Project of Zhejiang University
文摘The hyper Hilbert transform Tnf（x） =∫-1^1 f（x - Γ（t））e^-i｜t｜-β｜t｜^-1-αdt along an appropriate curve Γ（t） on R^n is investigated,where β 〉 α 〉 0.An L^p boundedness theorem of T4 is obtained,which is an extension of some earlier results of n = 2 and n = 3.
文摘This work presents an advanced mathematical tool applicable to the recognition and classification of power system transients and disturbances. Disturbances without a periodic pattern or with a non-linear pattern require a more suitable tool than the Fourier series （Fast Fourier or Windowed Fourier Transforms）. To overcome these drawbacks, other tools have been broadly used, such as the wavelet transform. However, the wavelet transform also has some drawbacks such as the lack of adaptivity or interpretation of nonlinear phenomena that the Hilbert and Hilbert Huang Transform techniques could mitigate. The Hilbert techniques transform a time domain function into a space representation both in time and frequency. In the paper, the technique is applied to analyse several short-term and steady events, like a short circuit, a capacitor-switching transient, or a line energisation, showing the abilities of the Hilbert-based transforms.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11671363, 11471288, 11371136）, the Natural Science Foundation of Zhejiang Province （No. LY14A010015）, and the China Scholarship Council.
文摘We consider the oscillatory hyper Hilbert transform Hγ,α,βf（x） = ∫0^∞ f（x - Г（t））eit-βt-（1＋α）dt, where Г（t） = （t, γ（t）） in R^2 is a general curve. When γ is convex, we give a simple condition on γ such that Hγ,α,βis bounded on L2 when β ≥ 3α, β 〉 0. As a corollary, under this condition, we obtain the LP-boundedness of Hγ,α,β when 2β/（2β - 3α） 〈 p 〈 2β/（3α）. When F is a general nonconvex curve, we give some more complicated conditions on γ such that Hγ,α,βis bounded on L2. As an application, we construct a class of strictly convex curves along which Hγ,α,β is bounded on L2 only if β 〉 2α 〉 0.
基金Supported by NSF of China(Grant Nos.11501169,11371057)
文摘Abstract In this paper, we give counterexamples to show that variation and oscillation operators related to rough truncations of the Hilbert transform are not bounded from H1 to L1, and prove variation, oscillation and A-jump operators related to smooth truncations are bounded from H1 to L1.
基金supported by the National Natural Science Foundation of China(Grant No.52105466).
文摘The prediction and compensation control of marine ship motion is crucial for ensuring the safety of offshore wind turbine loading and unloading operations.However,the accuracy of prediction and control is significantly affected by the hysteresis phenomenon in the wave compensation system.To address this issue,a ship heave motion prediction is proposed in this paper on the basis of the Gauss-DeepAR(AR stands for autoregressive recurrent)model and the Hilbert−Huang time-delay compensation control strategy.Initially,the zero upward traveling wave period of the level 4−6 sea state ship heave motion is analyzed,which serves as the input sliding window for the Gauss-DeepAR prediction model,and probability predictions at different wave direction angles are conducted.Next,considering the hysteresis characteristics of the ship heave motion compensation platform,the Hilbert−Huang transform is employed to analyze and calculate the hysteresis delay of the compensation platform.After the optimal control action value is subsequently calculated,simulations and hardware platform tests are conducted.The simulation results demonstrated that the Gauss-DeepAR model outperforms autoregressive integrated moving average model(ARIMA),support vector machine(SVM),and longshort-term memory(LSTM)in predicting non-independent identically distributed datasets at a 90°wave direction angle in the level 4−6 sea states.Furthermore,the model has good predictive performance and generalizability for non-independent and non-uniformly distributed datasets at a 180°wave direction angle.The hardware platform compensation test results revealed that the Hilbert–Huang method has an outstanding effect on determining the hysteretic delay and selecting the optimal control action value,and the compensation efficiency was higher than 90%in the level 4−6 sea states.
基金Research supported by the 863 Program of China(No.2012AA09A20103)the National Natural Science Foundation of China(No.41274119,No.41174080,and No.41004041)
文摘In seismic data processing, random noise seriously affects the seismic data quality and subsequently the interpretation. This study aims to increase the signal-to-noise ratio by suppressing random noise and improve the accuracy of seismic data interpretation without losing useful information. Hence, we propose a structure-oriented polynomial fitting filter. At the core of structure-oriented filtering is the characterization of the structural trend and the realization of nonstationary filtering. First, we analyze the relation of the frequency response between two-dimensional（2D） derivatives and the 2D Hilbert transform. Then, we derive the noniterative seismic local dip operator using the 2D Hilbert transform to obtain the structural trend. Second, we select polynomial fitting as the nonstationary filtering method and expand the application range of the nonstationary polynomial fitting. Finally, we apply variableamplitude polynomial fitting along the direction of the dip to improve the adaptive structureoriented filtering. Model and field seismic data show that the proposed method suppresses the seismic noise while protecting structural information.
基金This project was financially supported by the Trans-Century Training Program Fund for the Talent,Ministry of Education of China.
文摘The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is applicable to both regular and irregular trains; of waves. The wave data series measured with two wave gauges in the experiments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily obtained. The arrival of reflected waves can also be detected for improvement of the accuracy of the reflection coefficient. The reflection performance of the physical model can be estimated exactly without calculation of wave height and phase difference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conducted and compared with Goda's method and satisfactory results are obtained.
基金Supported by the National Natural Science Foundation of China(50975028)"111"Project of China(B08043)
文摘Hilbert transformation and improved ellipse localization method is applied in ultrasonic transducer array tomography to detect defect of metal plate.By combining the improved ellipse localization method and time-reversal method,the new ultrasonic tomography algorithm employs smooth Hilbert envelope instead of discrete amplitude to reconstruct defect image.An ultrasonic tomography system with six transducers is built to evaluate the effectiveness of the new ultrasonic tomography algorithm.The S0 mode Lamb wave is excited on special condition,and the mode of received signal is identified by Vigner-Wille distribution.The gray value of image area is defined by envelope of the reflected S0 mode Lamb wave signal from defect boundary.Defect image can be reconstructed by summing gray value of all pixels in the image area.The experimentally reconstructed defect image shows that the new tomography algorithm based on Hilbert transformation is efficient for defect detection in metal plate.
基金The project supported by the President Foundation of the Chinese Academy of Sciences and National Natural Science Foundation of China under Grant No. 10475056.
文摘We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.
基金This project is supported by National Natural Science Foundation of China (No.50605065)Natural Science Foundation Project of CQ CSTC(No.2007BB2142).
文摘In the mechanical fault detection and diagnosis field, it is more and more important to analyze the instantaneous frequency （IF） character of complex vibration signal. The improved IF estimation method is put forward aiming at the shortage of traditional Hilbert transform. It is based on Hilbert transform in wavelet domain. With the help of relationship between the real part and the imaginary part obtained from the complex coefficient of continuous wavelet transform or the analyti- cal signal reconstructed in wavelet packet decomposition, the instantaneous phase function of the subcomponent is extracted. In order to improve the precise of IF estimated out, some means such as Linear regression, adaptive filtering, resampling are applied into the instantaneous phase obtained, then, the central differencing operator is used to get desired IF. Simulation results with synthetic and gearbox fault signals are included to illustrate the proposed method.
文摘This study is concerned with the diagnosis of discrepancies in a steel truss bridge by identifying dynamic properties from the vibration response signals of the bridges.The vibration response signals collected at bridges under three different vehicular speeds of 10 km/hr,20 km/hr,and 30 km/hr are analyzed using statistical features such as kurtosis,magnitude of peak-to-peak,root mean square,crest factor as well as impulse factor in time domain,and Stockwell transform in the time-frequency domain.The considered statistical features except for kurtosis show uncertain behavior.The Stockwell transform showed low-resolution outcomes when the presence of noise in the recorded vibration responses.The elimination of noise and extraction of meaningful dynamic properties from the vibration responses is done by applying a new method which comes from the fusion of Hilbert transform with Spectral kurtosis and bandpass filtering.The outcomes obtained from Hilbert transform processed residual signals which are further filtered using bandpass filter show more robustness and accuracy in characterizing bridge modal frequencies from the noisy vibration responses.The proposed method produces a high-resolution frequency response which can unveil the joint discrepancy in the bridge structure.
文摘Noise is the biggest obstacle that makes the incipient fault diagnosis results of roller bearings uncorrected; a new method for diagnosing incipient fault of roller bearings based on the Wavelet Transform Correlation Filter and Hilbert Transform was proposed. First, the weak fault information features are picked up from the roller bearings fault vibration signals by use of a de-noising characteristic of the Wavelet Transform Correlation Filter as the preprocessing of the Hilbert Envelope Analysis. Then, in order to get fault features frequency, de-noised wavelet coefficients of high scales which represent high frequency signal were analyzed by Hilbert Envelope Spectrum Analysis. The simulation signals and diagnosing examples analysis results reveal that the proposed method is more effective than the method of direct wavelet coefficients-Hilbert Transform in de-noising and clarifying roller bearing incipient fault.
基金This work is funded by the Scientific and Technological Projects of Henan Province under Grant 152102210115.
文摘Nonlinear response is an important factor affecting the accuracy of three-dimensional image measurement based on the fringe structured light method.A phase compensation algorithm combined with a Hilbert transform is proposed to reduce the phase error caused by the nonlinear response of a digital projector in the three-dimensional measurement system of fringe structured light.According to the analysis of the influence of Gamma distortion on the phase calculation,the algorithm establishes the relationship model between phase error and harmonic coefficient,introduces phase shift to the signal,and keeps the signal amplitude constant while filtering out the DC component.The phase error is converted to the transform domain,and compared with the numeric value in the space domain.The algorithm is combined with a spiral phase function to optimize the Hilbert transform,so as to eliminate external noise,enhance the image quality,and get an accurate phase value.Experimental results show that the proposed method can effectively improve the accuracy and speed of phase measurement.By performing phase error compensation for free-form surface objects,the phase error is reduced by about 26%,and about 27%of the image reconstruction time is saved,which further demonstrates the feasibility and effectiveness of the method.
文摘In the paper, the author generalized the Hardy and Littlewood's theorem toBa space, i.e. for all Pm satisfying 1 < α = infpm≤ β≤ suppm < ∞, m = 1, 2,..., and the following inequalityholds if and on1y if.
文摘Analytic Hardy and BMO spaces on the quantum torus are introduced. Some basic properties of these spaces are presented. In particular, the associated H 1-BMO duality theorem is proved. Finally, we discuss some possible extensions of the obtained results.
文摘In agreement with Titchmarsh’s theorem, we prove that dispersion relations are just the Fourier-transform of the identity, g(x′)=±Sgn(x′)g(x′), which defines the property of being a truncated functions at the origin. On the other hand, we prove that the wave-function of a generalized diffraction in time problem is just the Fourier-transform of a truncated function. Consequently, the existence of dispersion relations for the diffraction in time wave-function follows. We derive these explicit dispersion relations.
文摘Envelope analysis is an effective method for characterizing impulsive vibrations in wired condition monitoring(CM)systems. This paper depicts the implementation of envelope analysis on a wireless sensor node for obtaining a more convenient and reliable CM system. To maintain CM performances under the constraints of resources available in the cost effective Zigbee based wireless sensor network(WSN), a low cost cortex-M4 F microcontroller is employed as the core processor to implement the envelope analysis algorithm on the sensor node. The on-chip 12 bit analog-to-digital converter(ADC) working at 10 k Hz sampling rate is adopted to acquire vibration signals measured by a wide frequency band piezoelectric accelerometer. The data processing flow inside the processor is optimized to satisfy the large memory usage in implementing fast Fourier transform(FFT) and Hilbert transform(HT). Thus, the envelope spectrum can be computed from a data frame of 2048 points to achieve a frequency resolution acceptable for identifying the characteristic frequencies of different bearing faults. Experimental evaluation results show that the embedded envelope analysis algorithm can successfully diagnose the simulated bearing faults and the data transmission throughput can be reduced by at least 95% per frame compared with that of the raw data, allowing a large number of sensor nodes to be deployed in the network for real time monitoring.
基金National Science Foundation Grant NSF CMS CAREER Under Grant No.9996290NSF CMMI Under Grant No.0830391
文摘The primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom （MDOF） linear time invariant （LTI） and linear time variant （LTV--due to damage） systems based on Time-frequency （TF） techniques--such as short-time Fourier transform （STFT）, empirical mode decomposition （EMD）, and wavelets--is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform （HT） approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their modal components. Once the modal components are obtained, each one is processed using Hilbert transform to obtain the modal frequency and damping ratios. In addition, the ratio of modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only modal identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they arc signal based; hence, can be used for output only modal identification. A three degree of freedom 1：10 scale model test structure is used to validate the proposed output only modal identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration （white noise） response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for modal identification and their potential for real world applications where output only identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based modal identification can be performed.
基金Projects(51678071,51608183)supported by the National Natural Science Foundation of ChinaProjects(CX2018B530,CX2018B531)supported by the Postgraduate Research and Innovation-funded Project of Hunan Province,ChinaProjects(16BCX13,16BCX09)supported by Changsha University of Science and Technology,China
文摘In the light of the problem of weak reflection signals shielded by strong reflections from the concrete surface,the detection and the recognition of hidden micro-cracks in the shield tunnel lining were studied using the orthogonal matching pursuit and the Hilbert transform(OMHT method).First,according to the matching pursuit algorithm and the strong reflection-forming mechanism,and based on the sparse representation theory,a sparse dictionary,adapted to the characteristics of the strong reflection signal,was selected,and a matching decomposition of each signal was performed so that the weak target signal submerged in the strong reflection was displayed more strongly.Second,the Hilbert transform was used to extract multiple parameters,such as the instantaneous amplitude,the instantaneous frequency,and the instantaneous phase,from the processed signal,and the ground penetrating radar(GPR)image was comprehensively analyzed and determined from multiple angles.The results show that the OMHT method can accurately weaken the effect of the strong impedance interface and effectively enhance the weak reflected signal energy of hidden micro-crack in the shield tunnel segment.The resolution of the processed GPR image is greatly improved,and the reflected signal of the hidden micro-crack is easily visible,which proves the validity and accuracy of the analysis method.
基金Project(51576213)supported by the National Natural Science Foundation of ChinaProject(2015RS4015)supported by the Hunan Scientific Program,ChinaProject(2016zzts323)supported by the Innovation Project of Central South University,China
文摘Gas–liquid two-phase flow abounds in industrial processes and facilities. Identification of its flow pattern plays an essential role in the field of multiphase flow measurement. A bluff body was introduced in this study to recognize gas–liquid flow patterns by inducing fluid oscillation that enlarged differences between each flow pattern. Experiments with air–water mixtures were carried out in horizontal pipelines at ambient temperature and atmospheric pressure. Differential pressure signals from the bluff-body wake were obtained in bubble, bubble/plug transitional, plug, slug, and annular flows. Utilizing the adaptive ensemble empirical mode decomposition method and the Hilbert transform, the time–frequency entropy S of the differential pressure signals was obtained. By combining S and other flow parameters, such as the volumetric void fraction β, the dryness x, the ratio of density φ and the modified fluid coefficient ψ, a new flow pattern map was constructed which adopted S（1–x）φ and （1–β）ψ as the vertical and horizontal coordinates, respectively. The overall rate of classification of the map was verified to be 92.9% by the experimental data. It provides an effective and simple solution to the gas–liquid flow pattern identification problems.
