Through analyzing the near-field hydrophone records of the airgun experiment in the Jiemian reservoir,Fujian,we study the time-frequency characteristic of airgun source wavelet and the influence of gun depth and firin...Through analyzing the near-field hydrophone records of the airgun experiment in the Jiemian reservoir,Fujian,we study the time-frequency characteristic of airgun source wavelet and the influence of gun depth and firing pressure,and explain the process of bubble oscillation based on the Johnson( 1994) bubble model. The data analysis shows that:( 1) Airgun wavelet is composed of primary pulse and bubble pulse. The primary pulse,which is of large amplitude,short duration and wide frequency band,is usually used in shallow exploration. The bubble pulse,which is concentrated in the low-frequency range,is usually used in deep exploration with deep vertical penetration and far horizontal propagation.( 2) The variation of primary pulse amplitude with gun depth is very small,bubble pulse amplitude and the dominant frequency increase,and peak-bubble ratio and bubble period decrease. When the gun depth is 10 m,primary pulse amplitude and peakbubble ratio are maximum,which is suitable for shallow exploration; when gun depth is25 m,bubble pulse amplitude is large, and peak-bubble ratio is minimum, which is suitable for deep exploration.( 3) The primary pulse amplitude,bubble pulse amplitude,peak-bubble ratio,and bubble period increase and the dominant frequency decreases with increased firing pressure.展开更多
The local wave method is a very good time-frequency method for nonstationaryvibration signal analysis. But the interfering noise has a big influence on the accuracy oftime-frequency analysis. The wavelet packet de-noi...The local wave method is a very good time-frequency method for nonstationaryvibration signal analysis. But the interfering noise has a big influence on the accuracy oftime-frequency analysis. The wavelet packet de-noising method can eliminate the interference ofnoise and improve the signal-noise-ratio. This paper uses the local wave method to decompose thede-noising signal and perform a time-frequency analysis. We can get better characteristics. Finally,an example of wavelet packet de-noising and a local wave time-frequency spectrum application ofdiesel engine surface vibration signal is put forward.展开更多
The resolution of seismic data is critical to seismic data processing and the subsequent interpretation of fine structures. In conventional resolution improvement methods, the seismic data is assumed stationary and th...The resolution of seismic data is critical to seismic data processing and the subsequent interpretation of fine structures. In conventional resolution improvement methods, the seismic data is assumed stationary and the noise level not changes with space, whereas the actual situation does not satisfy this assumption, so that results after resolution improvement processing is not up to the expected effect. To solve these problems, we propose a seismic resolution improvement method based on the secondary time-frequency spectrum. First, we propose the secondary time-frequency spectrum based on S transform （ST） and discuss the reflection coefficient sequence and time-dependent wavelet in the secondary time frequency spectrum. Second, using the secondary time frequency spectrum, we design a two- dimensional filter to extract the amplitude spectrum of the time-dependent wavelet. Then, we discuss the improvement of the resolution operator in noisy environments and propose a novel approach for determining the broad frequency range of the resolution operator in the time- fi＇equency-space domain. Finally, we apply the proposed method to synthetic and real data and compare the results of the traditional spectrum-modeling deconvolution and Q compensation method. The results suggest that the proposed method does not need to estimate the Q value and the resolution is not limited by the bandwidth of the source. Thus, the resolution of the seismic data is improved sufficiently based on the signal-to-noise ratio （SNR）.展开更多
In this study,we report an analysis of cylinder head vibration signals at a steady engine speed using short-time Fourier transform(STFT).Three popular time-frequency analysis techniques,i.e.,STFT,analytic wavelet tran...In this study,we report an analysis of cylinder head vibration signals at a steady engine speed using short-time Fourier transform(STFT).Three popular time-frequency analysis techniques,i.e.,STFT,analytic wavelet transform(AWT) and S transform(ST),have been examined.AWT and ST are often applied in engine signal analyses.In particular,an AWT expression in terms of the quality factor Q and an analytical relationship between ST and AWT have been derived.The time-frequency resolution of a Gaussian function windowed STFT was studied via numerical simulation.Based on the simulation,the empirical limits for the lowest distinguishable frequency as well as the time and frequency resolutions were determined.These can provide insights for window width selection,spectrogram interpretation and artifact identification.Gaussian function windowed STFTs were applied to some cylinder head vibration signals.The spectrograms of the same signals from ST and AWT were also determined for comparison.The results indicate that the uniform resolution feature of STFT is not necessarily a disadvantage for time-frequency analysis of vibration signals when the engine is in stationary state because it can more accurately localize the frequency components excited by transient excitations without much loss of time resolution.展开更多
In order to investigate the characteristics of sensorimotor cortex during motor execution(ME), voluntary, stimulated and imaginary finger flexions were performed by ten volunteer subjects. Electroencephalogram(EEG) da...In order to investigate the characteristics of sensorimotor cortex during motor execution(ME), voluntary, stimulated and imaginary finger flexions were performed by ten volunteer subjects. Electroencephalogram(EEG) data were recorded according to the modified 10-20 International EEG System. The patterns were compared by the analysis of the motion-evoked EEG signals focusing on the contralateral(C3) and ipsilateral(C4) channels for hemispheric differences. The EEG energy distributions at alpha(8—13 Hz), beta(14—30 Hz) and gamma(30—50 Hz) bands were computed by wavelet transform(WT) and compared by the analysis of variance(ANOVA). The timefrequency(TF) analysis indicated that there existed a contralateral dominance of alpha post-movement event-related synchronization(ERS) pattern during the voluntary task, and that the energy of alpha band increased in the ipsilateral area during the stimulated(median nerve of wrist) task. Besides, the contralateral alpha and beta event-related desynchronization(ERD) patterns were observed in both stimulated and imaginary tasks. Another significant difference was found in the mean power values of gamma band(p<0.01)between the imaginary and other tasks. The results show that significant hemispheric differences such as alpha and beta band EEG energy distributions and TF changing phenomena(ERS/ERD) were found between C3 and C4 areas during all of the three patterns. The largest energy distribution was always at the alpha band for each task.展开更多
We used daily return series for three pairs of datasets from the crude oil markets(WTI and Brent),stock indices(the Dow Jones Industrial Average and S&P 500),and benchmark cryptocurrencies(Bitcoin and Ethereum)to ...We used daily return series for three pairs of datasets from the crude oil markets(WTI and Brent),stock indices(the Dow Jones Industrial Average and S&P 500),and benchmark cryptocurrencies(Bitcoin and Ethereum)to examine the connections between various data during the COVID-19 pandemic.We consider two characteristics:time and frequency.Based on Diebold and Yilmaz’s(Int J Forecast 28:57-66,2012)technique,our findings indicate that comparable data have a substantially stronger correlation(regarding return)than volatility.Per Baruník and Křehlík’(J Financ Econ 16:271-296,2018)approach,interconnectedness among returns(volatilities)reduces(increases)as one moves from the short to the long term.A moving window analysis reveals a sudden increase in correlation,both in volatility and return,during the COVID-19 pandemic.In the context of wavelet coherence analysis,we observe a strong interconnection between data corresponding to the COVID-19 outbreak.The only exceptions are the behavior of Bitcoin and Ethereum.Specifically,Bitcoin combinations with other data exhibit a distinct behavior.The period precisely coincides with the COVID-19 pandemic.Evidently,volatility spillover has a long-lasting impact;policymakers should thus employ the appropriate tools to mitigate the severity of the relevant shocks(e.g.,the COVID-19 pandemic)and simultaneously reduce its side effects.展开更多
A novel method of EEG time-frequency analysis and representation based on a wavelet network is presented. The wavelet network model can represent the EEG data effectively. Based on the wavelet network model, a novel t...A novel method of EEG time-frequency analysis and representation based on a wavelet network is presented. The wavelet network model can represent the EEG data effectively. Based on the wavelet network model, a novel time-frequency energy distribution function is obtained, which has the same time-frequency resolution as Wigner-Ville distribution and is free of cross-term interference. There is a great potential for the use of the novel time-frequency representation of nonstationary biosignal based on a wavelet network in the field of the electrophysiological signal processing and time-frequency analysis.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
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 tim...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
The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wave...The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wavelet, and research the local extreme point and extrema of the wavelet transform on periodic function for the collection of signal＇ s instantaneous amplitude and period.展开更多
Based on the simple hinge crack model and the local flexibility theorem, thecorresponding dynamic equation of the cracked rotor is modelled, the numerical simulation solutionsof the cracked rotor and the uncracked rot...Based on the simple hinge crack model and the local flexibility theorem, thecorresponding dynamic equation of the cracked rotor is modelled, the numerical simulation solutionsof the cracked rotor and the uncracked rotor are obtained. By the continuous wavelet time-frequencytransform, the wavelet time-frequency properties of the uncracked rotor and the cracked rotor arediscussed. A new detection algorithm that uses the wavelet time-frequency transform to identify thecrack is proposed. The influence of the sampling frequency on the wavelet time-frequency transformis analyzed by the numerical simulation research. The valid sampling frequency is suggested.Experiments demonstrate the validity and availability of the proposed algorithm in identification ofthe cracked rotor for engineering practices.展开更多
This study deduces a general inversion of continuous wavelet transform (CWT) with timescale being real rather than positive. In conventional CWT inversion, wavelet’s dual is assumed to be a reconstruction wavelet or ...This study deduces a general inversion of continuous wavelet transform (CWT) with timescale being real rather than positive. In conventional CWT inversion, wavelet’s dual is assumed to be a reconstruction wavelet or a localized function. This study finds that wavelet’s dual can be a harmonic which is not local. This finding leads to new CWT inversion formulas. It also justifies the concept of normal wavelet transform which is useful in time-frequency analysis and time-frequency filtering. This study also proves a law for CWT inversion: either wavelet or its dual must integrate to zero.展开更多
With the new system radar put into practical use, the characteristics of complex radar signals are changing and developing. The traditional analysis method of one-dimensional transformation domain is no longer applica...With the new system radar put into practical use, the characteristics of complex radar signals are changing and developing. The traditional analysis method of one-dimensional transformation domain is no longer applicable to the modern radar signal processing, and it is necessary to seek new methods in the two-dimensional transformation domain. The time-frequency analysis method is the most widely used method in the two-dimensional transformation domain. In this paper, two typical time-frequency analysis methods of short-time Fourier transform and Wigner-Ville distribution are studied by analyzing the time-frequency transform of typical radar reconnaissance linear frequency modulation signal, aiming at the problem of low accuracy and sen-sitivity to the signal noise of common methods, the improved wavelet transform algorithm was proposed.展开更多
Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properti...Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.展开更多
The mold friction(MDF)is an important parameter reflecting the lubrication between the mold and slab quantitatively.The mold/slab friction was detected using an online monitoring system on a slab continuous caster equ...The mold friction(MDF)is an important parameter reflecting the lubrication between the mold and slab quantitatively.The mold/slab friction was detected using an online monitoring system on a slab continuous caster equipped with hydraulic oscillators.Wavelet entropy theory was introduced to describe the fluctuation characteristics of the MDF signal in order to quantitatively estimate the mold/slab lubrication.Furthermore,MDF signal and its wavelet entropy were analyzed under typical casting conditions,such as normal casting,different models(to control the relationship among the amplitude,the frequency and the casting speed),changing casting speeds and breakout.The results showed that the wavelet entropy could accurately reflect the overall changing trend of the mold friction as well as the local variation features.Besides,the wavelet entropy of the hydraulic cylinder force and the MDF was compared and analyzed,and the relationship between them was further discussed.展开更多
Mirnov signals mixed with interferences are a kind of non-stationary signal. It cannot obtain satisfactory effects to extract MHD signals from mirnov signals by Fourier Transform. This paper suggests that the wavelet ...Mirnov signals mixed with interferences are a kind of non-stationary signal. It cannot obtain satisfactory effects to extract MHD signals from mirnov signals by Fourier Transform. This paper suggests that the wavelet transform can be used to treat mirnov signals. Theoretical analysis and experimental result have indicated that using the time-frequency analysis characteristics of the wavelet transform to filter mirnov signals can remove effectively interferences and extract useful MHD signals.展开更多
This paper presents a wavelet-based approach for estimating the response of the base-isolated structure under seismic ground motions. The seismic ground motion record is expressed as the multi-scale wavelet coefficien...This paper presents a wavelet-based approach for estimating the response of the base-isolated structure under seismic ground motions. The seismic ground motion record is expressed as the multi-scale wavelet coefficients which presents the time frequency characteristics of the seismic excitation. The wavelet domain governing differential equation between the wavelet coefficients of the excitation and response is derived. Numerical study on a one-storey base isolated structure is performed. The result shows that the wavelet based response computation method is of high precision.展开更多
The mould friction is an important parameter reflecting the initial shell and mould lubrication conditions.The research of mould friction is very important to the optimization and developing of continuous casting.The ...The mould friction is an important parameter reflecting the initial shell and mould lubrication conditions.The research of mould friction is very important to the optimization and developing of continuous casting.The measured mould friction under hydraulic oscillation mode was researched with wavelet analysis to reveal its time-frequency characteristics.Firstly,the mould friction signals under different production conditions were monitored and the mould friction was calculated.Then,mother wavelet function was selected from three wavelet functions which were chosen preliminary according to the characteristics of mould friction and wavelet theory.Through wavelet transformation,mould friction signal was projected onto the wavelet domain,and the time-frequency characteristics of mould friction under different production conditions were obtained and discussed.Mould friction under different production conditions such as different oscillation mode,casting speed fluctuation,increasing and decreasing stage of casting speed and breakout occurrence was reported in detail in the wavelet time-frequency maps.The characteristics of mould friction were reflected well through wavelet transformation which proved that wavelet analysis had a good feasibility for mould friction study and can further reveal the nature of mould friction.展开更多
There are few applications of image processing technology for diagnosing andstate monitoring for internal combustion (IC) engines, which is discussed in detail in this paper.The time-frequency distribution images of c...There are few applications of image processing technology for diagnosing andstate monitoring for internal combustion (IC) engines, which is discussed in detail in this paper.The time-frequency distribution images of cylinder head vibration signals are obtained bydecomposing them with a wavelet packet algorithm. It is the first time that we look attime-frequency distribution images from the point of images. Based on this, a new method forapplying image processing technology for diagnosing and state monitoring for internal combustionengines is presented in this paper. A valve fault diagnosis model is set up by image matching, whichis realized on a four-stroke, six-cylinder diesel engine. At the same time, some notes arepresented in this paper. It has been proved that it is of no good effect to diagnose with histogramsof time-frequency images generated by cylinder head vibration signals that have been processed witha wavelet packet algorithm. The reason is given in this paper. Comparisons of diagnosing effect arecarried out between noise-added signals and original signals. It has little effect on diagnosingresults after signals have been added with noise. The results show that this method has a clearphysical meaning and is of good engineering practicability, feasibility, good precision and highspeed.展开更多
基金jointly sponsored the Special Fund for Earthquake Scientific Research of China Earthquake Administration(2015419015)the National Natural Sciences Foundation of China(41474071)
文摘Through analyzing the near-field hydrophone records of the airgun experiment in the Jiemian reservoir,Fujian,we study the time-frequency characteristic of airgun source wavelet and the influence of gun depth and firing pressure,and explain the process of bubble oscillation based on the Johnson( 1994) bubble model. The data analysis shows that:( 1) Airgun wavelet is composed of primary pulse and bubble pulse. The primary pulse,which is of large amplitude,short duration and wide frequency band,is usually used in shallow exploration. The bubble pulse,which is concentrated in the low-frequency range,is usually used in deep exploration with deep vertical penetration and far horizontal propagation.( 2) The variation of primary pulse amplitude with gun depth is very small,bubble pulse amplitude and the dominant frequency increase,and peak-bubble ratio and bubble period decrease. When the gun depth is 10 m,primary pulse amplitude and peakbubble ratio are maximum,which is suitable for shallow exploration; when gun depth is25 m,bubble pulse amplitude is large, and peak-bubble ratio is minimum, which is suitable for deep exploration.( 3) The primary pulse amplitude,bubble pulse amplitude,peak-bubble ratio,and bubble period increase and the dominant frequency decreases with increased firing pressure.
文摘The local wave method is a very good time-frequency method for nonstationaryvibration signal analysis. But the interfering noise has a big influence on the accuracy oftime-frequency analysis. The wavelet packet de-noising method can eliminate the interference ofnoise and improve the signal-noise-ratio. This paper uses the local wave method to decompose thede-noising signal and perform a time-frequency analysis. We can get better characteristics. Finally,an example of wavelet packet de-noising and a local wave time-frequency spectrum application ofdiesel engine surface vibration signal is put forward.
基金financially supported by the National 973 Project(No.2014CB239006)the National Natural Science Foundation of China(No.41104069 and 41274124)the Fundamental Research Funds for Central Universities(No.R1401005A)
文摘The resolution of seismic data is critical to seismic data processing and the subsequent interpretation of fine structures. In conventional resolution improvement methods, the seismic data is assumed stationary and the noise level not changes with space, whereas the actual situation does not satisfy this assumption, so that results after resolution improvement processing is not up to the expected effect. To solve these problems, we propose a seismic resolution improvement method based on the secondary time-frequency spectrum. First, we propose the secondary time-frequency spectrum based on S transform （ST） and discuss the reflection coefficient sequence and time-dependent wavelet in the secondary time frequency spectrum. Second, using the secondary time frequency spectrum, we design a two- dimensional filter to extract the amplitude spectrum of the time-dependent wavelet. Then, we discuss the improvement of the resolution operator in noisy environments and propose a novel approach for determining the broad frequency range of the resolution operator in the time- fi＇equency-space domain. Finally, we apply the proposed method to synthetic and real data and compare the results of the traditional spectrum-modeling deconvolution and Q compensation method. The results suggest that the proposed method does not need to estimate the Q value and the resolution is not limited by the bandwidth of the source. Thus, the resolution of the seismic data is improved sufficiently based on the signal-to-noise ratio （SNR）.
基金Project (No. 2011BAE22B05) supported by the National Key Technologies Supporting Program of China during the 12th Five-Year Plan Period
文摘In this study,we report an analysis of cylinder head vibration signals at a steady engine speed using short-time Fourier transform(STFT).Three popular time-frequency analysis techniques,i.e.,STFT,analytic wavelet transform(AWT) and S transform(ST),have been examined.AWT and ST are often applied in engine signal analyses.In particular,an AWT expression in terms of the quality factor Q and an analytical relationship between ST and AWT have been derived.The time-frequency resolution of a Gaussian function windowed STFT was studied via numerical simulation.Based on the simulation,the empirical limits for the lowest distinguishable frequency as well as the time and frequency resolutions were determined.These can provide insights for window width selection,spectrogram interpretation and artifact identification.Gaussian function windowed STFTs were applied to some cylinder head vibration signals.The spectrograms of the same signals from ST and AWT were also determined for comparison.The results indicate that the uniform resolution feature of STFT is not necessarily a disadvantage for time-frequency analysis of vibration signals when the engine is in stationary state because it can more accurately localize the frequency components excited by transient excitations without much loss of time resolution.
基金Supported by the National Natural Science Foundation of China(No.81222021,No.61172008,No.81171423)National Key Technology Research and Development Program of the Ministry of Science and Technology of China(No.2012BAI34B02)Program for New Century Excellent Talents in University of the Ministry of Education of China(No.NCET-10-0618)
文摘In order to investigate the characteristics of sensorimotor cortex during motor execution(ME), voluntary, stimulated and imaginary finger flexions were performed by ten volunteer subjects. Electroencephalogram(EEG) data were recorded according to the modified 10-20 International EEG System. The patterns were compared by the analysis of the motion-evoked EEG signals focusing on the contralateral(C3) and ipsilateral(C4) channels for hemispheric differences. The EEG energy distributions at alpha(8—13 Hz), beta(14—30 Hz) and gamma(30—50 Hz) bands were computed by wavelet transform(WT) and compared by the analysis of variance(ANOVA). The timefrequency(TF) analysis indicated that there existed a contralateral dominance of alpha post-movement event-related synchronization(ERS) pattern during the voluntary task, and that the energy of alpha band increased in the ipsilateral area during the stimulated(median nerve of wrist) task. Besides, the contralateral alpha and beta event-related desynchronization(ERD) patterns were observed in both stimulated and imaginary tasks. Another significant difference was found in the mean power values of gamma band(p<0.01)between the imaginary and other tasks. The results show that significant hemispheric differences such as alpha and beta band EEG energy distributions and TF changing phenomena(ERS/ERD) were found between C3 and C4 areas during all of the three patterns. The largest energy distribution was always at the alpha band for each task.
文摘We used daily return series for three pairs of datasets from the crude oil markets(WTI and Brent),stock indices(the Dow Jones Industrial Average and S&P 500),and benchmark cryptocurrencies(Bitcoin and Ethereum)to examine the connections between various data during the COVID-19 pandemic.We consider two characteristics:time and frequency.Based on Diebold and Yilmaz’s(Int J Forecast 28:57-66,2012)technique,our findings indicate that comparable data have a substantially stronger correlation(regarding return)than volatility.Per Baruník and Křehlík’(J Financ Econ 16:271-296,2018)approach,interconnectedness among returns(volatilities)reduces(increases)as one moves from the short to the long term.A moving window analysis reveals a sudden increase in correlation,both in volatility and return,during the COVID-19 pandemic.In the context of wavelet coherence analysis,we observe a strong interconnection between data corresponding to the COVID-19 outbreak.The only exceptions are the behavior of Bitcoin and Ethereum.Specifically,Bitcoin combinations with other data exhibit a distinct behavior.The period precisely coincides with the COVID-19 pandemic.Evidently,volatility spillover has a long-lasting impact;policymakers should thus employ the appropriate tools to mitigate the severity of the relevant shocks(e.g.,the COVID-19 pandemic)and simultaneously reduce its side effects.
基金This work is Funded in part by the Science Foundation of Shandong Province (No.Y2000C25 and No.Y2001C02)
文摘A novel method of EEG time-frequency analysis and representation based on a wavelet network is presented. The wavelet network model can represent the EEG data effectively. Based on the wavelet network model, a novel time-frequency energy distribution function is obtained, which has the same time-frequency resolution as Wigner-Ville distribution and is free of cross-term interference. There is a great potential for the use of the novel time-frequency representation of nonstationary biosignal based on a wavelet network in the field of the electrophysiological signal processing and time-frequency analysis.
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.
基金Supported by the National Natural Science Founda-tion of China (49771060)
文摘The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wavelet, and research the local extreme point and extrema of the wavelet transform on periodic function for the collection of signal＇ s instantaneous amplitude and period.
基金This project is supported by National Natural Science Foundation of China (No.10176014) National Fundamental Foundation of Research and Development of China (No.G1998020321).
文摘Based on the simple hinge crack model and the local flexibility theorem, thecorresponding dynamic equation of the cracked rotor is modelled, the numerical simulation solutionsof the cracked rotor and the uncracked rotor are obtained. By the continuous wavelet time-frequencytransform, the wavelet time-frequency properties of the uncracked rotor and the cracked rotor arediscussed. A new detection algorithm that uses the wavelet time-frequency transform to identify thecrack is proposed. The influence of the sampling frequency on the wavelet time-frequency transformis analyzed by the numerical simulation research. The valid sampling frequency is suggested.Experiments demonstrate the validity and availability of the proposed algorithm in identification ofthe cracked rotor for engineering practices.
文摘This study deduces a general inversion of continuous wavelet transform (CWT) with timescale being real rather than positive. In conventional CWT inversion, wavelet’s dual is assumed to be a reconstruction wavelet or a localized function. This study finds that wavelet’s dual can be a harmonic which is not local. This finding leads to new CWT inversion formulas. It also justifies the concept of normal wavelet transform which is useful in time-frequency analysis and time-frequency filtering. This study also proves a law for CWT inversion: either wavelet or its dual must integrate to zero.
文摘With the new system radar put into practical use, the characteristics of complex radar signals are changing and developing. The traditional analysis method of one-dimensional transformation domain is no longer applicable to the modern radar signal processing, and it is necessary to seek new methods in the two-dimensional transformation domain. The time-frequency analysis method is the most widely used method in the two-dimensional transformation domain. In this paper, two typical time-frequency analysis methods of short-time Fourier transform and Wigner-Ville distribution are studied by analyzing the time-frequency transform of typical radar reconnaissance linear frequency modulation signal, aiming at the problem of low accuracy and sen-sitivity to the signal noise of common methods, the improved wavelet transform algorithm was proposed.
文摘Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.
基金The project was supported by the National Natural Science Foundation of China(No.51204063)the Anhui Provincial Natural Science Foundation(No.1308085QE72).
文摘The mold friction(MDF)is an important parameter reflecting the lubrication between the mold and slab quantitatively.The mold/slab friction was detected using an online monitoring system on a slab continuous caster equipped with hydraulic oscillators.Wavelet entropy theory was introduced to describe the fluctuation characteristics of the MDF signal in order to quantitatively estimate the mold/slab lubrication.Furthermore,MDF signal and its wavelet entropy were analyzed under typical casting conditions,such as normal casting,different models(to control the relationship among the amplitude,the frequency and the casting speed),changing casting speeds and breakout.The results showed that the wavelet entropy could accurately reflect the overall changing trend of the mold friction as well as the local variation features.Besides,the wavelet entropy of the hydraulic cylinder force and the MDF was compared and analyzed,and the relationship between them was further discussed.
基金This work was supported by the National Nature Science Foundation of China No.19889504.
文摘Mirnov signals mixed with interferences are a kind of non-stationary signal. It cannot obtain satisfactory effects to extract MHD signals from mirnov signals by Fourier Transform. This paper suggests that the wavelet transform can be used to treat mirnov signals. Theoretical analysis and experimental result have indicated that using the time-frequency analysis characteristics of the wavelet transform to filter mirnov signals can remove effectively interferences and extract useful MHD signals.
文摘This paper presents a wavelet-based approach for estimating the response of the base-isolated structure under seismic ground motions. The seismic ground motion record is expressed as the multi-scale wavelet coefficients which presents the time frequency characteristics of the seismic excitation. The wavelet domain governing differential equation between the wavelet coefficients of the excitation and response is derived. Numerical study on a one-storey base isolated structure is performed. The result shows that the wavelet based response computation method is of high precision.
基金Sponsored by National Natural Science Foudation of China(51204063)Natural Science Foundation of Anhui Province of China(1308085QE72)
文摘The mould friction is an important parameter reflecting the initial shell and mould lubrication conditions.The research of mould friction is very important to the optimization and developing of continuous casting.The measured mould friction under hydraulic oscillation mode was researched with wavelet analysis to reveal its time-frequency characteristics.Firstly,the mould friction signals under different production conditions were monitored and the mould friction was calculated.Then,mother wavelet function was selected from three wavelet functions which were chosen preliminary according to the characteristics of mould friction and wavelet theory.Through wavelet transformation,mould friction signal was projected onto the wavelet domain,and the time-frequency characteristics of mould friction under different production conditions were obtained and discussed.Mould friction under different production conditions such as different oscillation mode,casting speed fluctuation,increasing and decreasing stage of casting speed and breakout occurrence was reported in detail in the wavelet time-frequency maps.The characteristics of mould friction were reflected well through wavelet transformation which proved that wavelet analysis had a good feasibility for mould friction study and can further reveal the nature of mould friction.
文摘There are few applications of image processing technology for diagnosing andstate monitoring for internal combustion (IC) engines, which is discussed in detail in this paper.The time-frequency distribution images of cylinder head vibration signals are obtained bydecomposing them with a wavelet packet algorithm. It is the first time that we look attime-frequency distribution images from the point of images. Based on this, a new method forapplying image processing technology for diagnosing and state monitoring for internal combustionengines is presented in this paper. A valve fault diagnosis model is set up by image matching, whichis realized on a four-stroke, six-cylinder diesel engine. At the same time, some notes arepresented in this paper. It has been proved that it is of no good effect to diagnose with histogramsof time-frequency images generated by cylinder head vibration signals that have been processed witha wavelet packet algorithm. The reason is given in this paper. Comparisons of diagnosing effect arecarried out between noise-added signals and original signals. It has little effect on diagnosingresults after signals have been added with noise. The results show that this method has a clearphysical meaning and is of good engineering practicability, feasibility, good precision and highspeed.
