Singular spectrum analysis is widely used in geodetic time series analysis.However,when extracting time-varying periodic signals from a large number of Global Navigation Satellite System(GNSS)time series,the selection...Singular spectrum analysis is widely used in geodetic time series analysis.However,when extracting time-varying periodic signals from a large number of Global Navigation Satellite System(GNSS)time series,the selection of appropriate embedding window size and principal components makes this method cumbersome and inefficient.To improve the efficiency and accuracy of singular spectrum analysis,this paper proposes an adaptive singular spectrum analysis method by combining spectrum analysis with a new trace matrix.The running time and correlation analysis indicate that the proposed method can adaptively set the embedding window size to extract the time-varying periodic signals from GNSS time series,and the extraction efficiency of a single time series is six times that of singular spectrum analysis.The method is also accurate and more suitable for time-varying periodic signal analysis of global GNSS sites.展开更多
This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is to approximate a ...This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is to approximate a regular periodic signal, under Dirichlet conditions, via a linear superposition of trigonometric functions, thus Fourier polynomials are constructed. The Dirichlet conditions, are a set of mathematical conditions, providing a foundational framework for the validity of the Fourier series representation. By understanding and applying these conditions, we can accurately represent and process periodic signals, leading to advancements in various areas of signal processing. The resulting Fourier approximation allows complex periodic signals to be expressed as a sum of simpler sinusoidal functions, making it easier to analyze and manipulate such signals.展开更多
Global navigation satellite system(GNSS)technique has irreplaceable advantages in the continuous monitoring of surface deformation.Reducing noise to improve the signal-to-noise ratio(SNR)and extract the concerned sign...Global navigation satellite system(GNSS)technique has irreplaceable advantages in the continuous monitoring of surface deformation.Reducing noise to improve the signal-to-noise ratio(SNR)and extract the concerned signals is of great significance.As an improved algorithm of empirical mode decomposition(EMD),complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN)algorithm has better signal processing ability.Using the CEEMDAN algorithm,the height time series of 29GNSS stations in Chinese mainland were analyzed,and good denoising effects and extraction from periodic signals were achieved.The numerical results showed that the annual signal obtained with the CEEMDAN algorithm was significantly based on Lomb_Scargle spectrum analysis,and large differences in the long-term signals were found between the stations at different locations in Chinese mainland.With respect to data denoising,compared with the EMD and wavelet denoising algorithms,the CEEMDAN algorithm respectively improved the SNR by 29.35% and 36.54%,increased the correlation coefficient by 8.67% and 11.96%,and reduced root mean square error(RMSE)by 44.68% and 43.48%,indicating that the CEEMDAN algorithm had better denoising behavior than the other two algorithms.In addition,the results demonstrated that different denoising methods had little influence on estimating the annual vertical deformation velocity.The extraction of periodic signals showed that more components were retained by using the CEEMDAN algorithm than the EMD algorithm,which indicated that the CEEMDAN algorithm had advantages over frequency aliasing.In conclusion,the CEEMDAN algorithm was recommended for processing the GNSS height time series to analyze the vertical deformation due to its excellent features of denoising and the extraction of periodic signals.展开更多
Seismometers of the InSight probe(Interior Exploration using Seismic Investigation,Geodesy and Heat Transport)currently operating on Mars have recorded not only seismic events but also high-frequency non-seismic perio...Seismometers of the InSight probe(Interior Exploration using Seismic Investigation,Geodesy and Heat Transport)currently operating on Mars have recorded not only seismic events but also high-frequency non-seismic periodic signals that appear to have been induced by variations in the Martian environment and the hardware.Here,we report an observation of a long-period signal with a dominant period of~20 s from Martian solar days(Sol)800 to Sol 1,000.This 20-s signal is detected mostly at quiet nighttime—from22:00 to 04:00 LMST(Local Mean Solar Time)—at the InSight landing site.The measurement of the particle motion suggests that this linearly polarized signal focuses on the horizontal plane with an angle of~30°from the north.By examining the temporal variation of the signal’s amplitude and polarization angle and its times of occurrence in relation to the planet’s atmospheric data,we suggest that this20-s signal may be relevant to wind and temperature variations on Mars.Furthermore,we study the possible influence of this 20-s signal on the noise autocorrelation and find that the stacked autocorrelograms can be quite different when the 20-s signal is present.展开更多
We report here the observation result of joint observation of long period tremor signals with broadband seismome-ter,tiltmeter and gravimeter at the HUST(Huazhong University of Science and Technology)station.The obser...We report here the observation result of joint observation of long period tremor signals with broadband seismome-ter,tiltmeter and gravimeter at the HUST(Huazhong University of Science and Technology)station.The observed data were compared and analyzed.Since 2005,the several tens of abnormal tremor signals which are weak,com-plex and duration of 2 to 3 days have been synchronously recorded by the different instruments.The tremor signals have the periodic domain in the range of 3 to 5 minutes,20 to 30 minutes and even more than 1 hour.The observa-tion shows such tremors are a physical existence.The analysis indicates that a part of the tremors caused by the typhoon from the western Pacific Ocean.These tremors have a close relationship with wind velocity of typhoon and distance between the typhoon center and the station.Except these,the cause of others is still unclear.展开更多
The phase change between periodic signals is regular. Research on the regular phenomenon between periodic signals is helpful to improve the precision of some measurements and develop some new measurement methods. So i...The phase change between periodic signals is regular. Research on the regular phenomenon between periodic signals is helpful to improve the precision of some measurements and develop some new measurement methods. So it is necessary to analyze the characteristics of the greatest common factor frequency and the least common multiple period universally existing in periodic signals. The regulation of the quantitative phase shift resolution between periodic signals is presented.The cause of difference in phase characteristics between periodic signals is explained well. In this paper we propose different application prospects based on the regular phenomenon between periodic signals, with focusing on the methods for high precision frequency measurement and transient stability measurement. The experimental results are satisfactory.展开更多
This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A ge...This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker-Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity Q, multiplicative noise intensity D, static asymmetry r and delay time T on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry r can restrain stochastic resonance, and the delay time τ can enhance stochastic resonance. Moreover, the longer the delay time τ is, the larger the additive noise intensity Q and the multiplicative noise intensity D are, when the stochastic resonance appears.展开更多
The chaotic oscillator has already been considered as a powerful method to detect weak signals, even weak signals accompanied with noises. However, many examples, analyses and simulations indicate that chaotic oscilla...The chaotic oscillator has already been considered as a powerful method to detect weak signals, even weak signals accompanied with noises. However, many examples, analyses and simulations indicate that chaotic oscillator detection system cannot guarantee the immunity to noises (even white noise). In fact the randomness of noises has a serious or even a destructive effect on the detection results in many cases. To solve this problem, we present a new detecting method based on wavelet threshold processing that can detect the chaotic weak signal accompanied with noise. All theoretical analyses and simulation experiments indicate that the new method reduces the noise interferences to detection significantly, thereby making the corresponding chaotic oscillator that detects the weak signals accompanied with noises more stable and reliable.展开更多
In this letter, with the synthesis of usual cross-correlation detecting method andchaotic detecting method, a new detecting system for the weak periodic pulse signal is constituted,in which the two methods can play re...In this letter, with the synthesis of usual cross-correlation detecting method andchaotic detecting method, a new detecting system for the weak periodic pulse signal is constituted,in which the two methods can play respective preponderance. Theoretical analyses and simulationstudies have shown that the detecting system is very sensitive to the periodic pulse signal understrong noise background and has exceedingly powerful capability of suppressing complex noise.展开更多
The periodic short-impulse signals under strong noise background are successfully detected with a special chaotic system invented by the authors. Simulation experiments show that the chaotic system is very sensitive t...The periodic short-impulse signals under strong noise background are successfully detected with a special chaotic system invented by the authors. Simulation experiments show that the chaotic system is very sensitive to periodic short-impulse signals submerged by strong noise background, and it can effectively restrain any zero-mean noise. The system has a stable working-detection limit of -83dB.展开更多
A Loop-Shift Stop & Go Adaptive Filter(LSSGAF) with applications in period detection and signal separation of overlapped periodic signals is presented. The filter places no constraints on the overlapped forms in f...A Loop-Shift Stop & Go Adaptive Filter(LSSGAF) with applications in period detection and signal separation of overlapped periodic signals is presented. The filter places no constraints on the overlapped forms in frequency domain and requires no priori knowledge except for approximate period range of signals to be separated, therefore it provides for an efficient and feasible method to separate periodic signals overlapped both in time and frequency domains. The convergence conditions of the filter and the requirements of all parameter selections are discussed, meanwhile a rough scanning and channel auto-shut algorithm is proposed to reduce the amount of calculation in the searching stage. Experiments show that the filter can separate all kinds of overlapped periodic signals with different initial phases and different relative magnitudes.展开更多
Objective Climate fluctuations over suborbital or millennial timescale display significant instability during the last glacial period,which are often superimposed upon the orbital periodicity.They triggered some abrup...Objective Climate fluctuations over suborbital or millennial timescale display significant instability during the last glacial period,which are often superimposed upon the orbital periodicity.They triggered some abrupt climate events,展开更多
The conventional Duffing oscillator weak signal detection method, which is based on a strong reference signal, has inherent deficiencies. To address these issues, the characteristics of the Duffing oscillator's phase...The conventional Duffing oscillator weak signal detection method, which is based on a strong reference signal, has inherent deficiencies. To address these issues, the characteristics of the Duffing oscillator's phase trajectory in a small- scale periodic state are analyzed by introducing the theory of stopping oscillation system. Based on this approach, a novel Duffing oscillator weak wide-band signal detection method is proposed. In this novel method, the reference signal is discarded, and the to-be-detected signal is directly used as a driving force. By calculating the cosine function of a phase space angle, a single Duffing oscillator can be used for weak wide-band signal detection instead of an array of uncoupled Duffing oscillators. Simulation results indicate that, compared with the conventional Duffing oscillator detection method, this approach performs better in frequency detection intervals, and reduces the signal-to-noise ratio detection threshold, while improving the real-time performance of the system.展开更多
基金supported by the National Natural Science Foundation of China(Grants:42204006,42274053,42030105,and 41504031)the Open Research Fund Program of the Key Laboratory of Geospace Environment and Geodesy,Ministry of Education,China(Grants:20-01-03 and 21-01-04)。
文摘Singular spectrum analysis is widely used in geodetic time series analysis.However,when extracting time-varying periodic signals from a large number of Global Navigation Satellite System(GNSS)time series,the selection of appropriate embedding window size and principal components makes this method cumbersome and inefficient.To improve the efficiency and accuracy of singular spectrum analysis,this paper proposes an adaptive singular spectrum analysis method by combining spectrum analysis with a new trace matrix.The running time and correlation analysis indicate that the proposed method can adaptively set the embedding window size to extract the time-varying periodic signals from GNSS time series,and the extraction efficiency of a single time series is six times that of singular spectrum analysis.The method is also accurate and more suitable for time-varying periodic signal analysis of global GNSS sites.
文摘This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is to approximate a regular periodic signal, under Dirichlet conditions, via a linear superposition of trigonometric functions, thus Fourier polynomials are constructed. The Dirichlet conditions, are a set of mathematical conditions, providing a foundational framework for the validity of the Fourier series representation. By understanding and applying these conditions, we can accurately represent and process periodic signals, leading to advancements in various areas of signal processing. The resulting Fourier approximation allows complex periodic signals to be expressed as a sum of simpler sinusoidal functions, making it easier to analyze and manipulate such signals.
基金supported by the National Natural Science Foundation of China(Grant No.42192535,42174012,42174101,41974023)the Open Fund of Hubei Luojia Laboratory(Grant No.S22H640201)。
文摘Global navigation satellite system(GNSS)technique has irreplaceable advantages in the continuous monitoring of surface deformation.Reducing noise to improve the signal-to-noise ratio(SNR)and extract the concerned signals is of great significance.As an improved algorithm of empirical mode decomposition(EMD),complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN)algorithm has better signal processing ability.Using the CEEMDAN algorithm,the height time series of 29GNSS stations in Chinese mainland were analyzed,and good denoising effects and extraction from periodic signals were achieved.The numerical results showed that the annual signal obtained with the CEEMDAN algorithm was significantly based on Lomb_Scargle spectrum analysis,and large differences in the long-term signals were found between the stations at different locations in Chinese mainland.With respect to data denoising,compared with the EMD and wavelet denoising algorithms,the CEEMDAN algorithm respectively improved the SNR by 29.35% and 36.54%,increased the correlation coefficient by 8.67% and 11.96%,and reduced root mean square error(RMSE)by 44.68% and 43.48%,indicating that the CEEMDAN algorithm had better denoising behavior than the other two algorithms.In addition,the results demonstrated that different denoising methods had little influence on estimating the annual vertical deformation velocity.The extraction of periodic signals showed that more components were retained by using the CEEMDAN algorithm than the EMD algorithm,which indicated that the CEEMDAN algorithm had advantages over frequency aliasing.In conclusion,the CEEMDAN algorithm was recommended for processing the GNSS height time series to analyze the vertical deformation due to its excellent features of denoising and the extraction of periodic signals.
基金supported by B-type Strategic Priority Program of the Chinese Academy of Sciences,Grant XDB41000000National Natural Science Foundation of China 42241117.
文摘Seismometers of the InSight probe(Interior Exploration using Seismic Investigation,Geodesy and Heat Transport)currently operating on Mars have recorded not only seismic events but also high-frequency non-seismic periodic signals that appear to have been induced by variations in the Martian environment and the hardware.Here,we report an observation of a long-period signal with a dominant period of~20 s from Martian solar days(Sol)800 to Sol 1,000.This 20-s signal is detected mostly at quiet nighttime—from22:00 to 04:00 LMST(Local Mean Solar Time)—at the InSight landing site.The measurement of the particle motion suggests that this linearly polarized signal focuses on the horizontal plane with an angle of~30°from the north.By examining the temporal variation of the signal’s amplitude and polarization angle and its times of occurrence in relation to the planet’s atmospheric data,we suggest that this20-s signal may be relevant to wind and temperature variations on Mars.Furthermore,we study the possible influence of this 20-s signal on the noise autocorrelation and find that the stacked autocorrelograms can be quite different when the 20-s signal is present.
文摘We report here the observation result of joint observation of long period tremor signals with broadband seismome-ter,tiltmeter and gravimeter at the HUST(Huazhong University of Science and Technology)station.The observed data were compared and analyzed.Since 2005,the several tens of abnormal tremor signals which are weak,com-plex and duration of 2 to 3 days have been synchronously recorded by the different instruments.The tremor signals have the periodic domain in the range of 3 to 5 minutes,20 to 30 minutes and even more than 1 hour.The observa-tion shows such tremors are a physical existence.The analysis indicates that a part of the tremors caused by the typhoon from the western Pacific Ocean.These tremors have a close relationship with wind velocity of typhoon and distance between the typhoon center and the station.Except these,the cause of others is still unclear.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10978017 and 61201288)
文摘The phase change between periodic signals is regular. Research on the regular phenomenon between periodic signals is helpful to improve the precision of some measurements and develop some new measurement methods. So it is necessary to analyze the characteristics of the greatest common factor frequency and the least common multiple period universally existing in periodic signals. The regulation of the quantitative phase shift resolution between periodic signals is presented.The cause of difference in phase characteristics between periodic signals is explained well. In this paper we propose different application prospects based on the regular phenomenon between periodic signals, with focusing on the methods for high precision frequency measurement and transient stability measurement. The experimental results are satisfactory.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10872165 and 10902085)
文摘This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker-Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity Q, multiplicative noise intensity D, static asymmetry r and delay time T on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry r can restrain stochastic resonance, and the delay time τ can enhance stochastic resonance. Moreover, the longer the delay time τ is, the larger the additive noise intensity Q and the multiplicative noise intensity D are, when the stochastic resonance appears.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10731050)the Program for Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China (Grant No. IRTO0742)
文摘The chaotic oscillator has already been considered as a powerful method to detect weak signals, even weak signals accompanied with noises. However, many examples, analyses and simulations indicate that chaotic oscillator detection system cannot guarantee the immunity to noises (even white noise). In fact the randomness of noises has a serious or even a destructive effect on the detection results in many cases. To solve this problem, we present a new detecting method based on wavelet threshold processing that can detect the chaotic weak signal accompanied with noise. All theoretical analyses and simulation experiments indicate that the new method reduces the noise interferences to detection significantly, thereby making the corresponding chaotic oscillator that detects the weak signals accompanied with noises more stable and reliable.
文摘In this letter, with the synthesis of usual cross-correlation detecting method andchaotic detecting method, a new detecting system for the weak periodic pulse signal is constituted,in which the two methods can play respective preponderance. Theoretical analyses and simulationstudies have shown that the detecting system is very sensitive to the periodic pulse signal understrong noise background and has exceedingly powerful capability of suppressing complex noise.
文摘The periodic short-impulse signals under strong noise background are successfully detected with a special chaotic system invented by the authors. Simulation experiments show that the chaotic system is very sensitive to periodic short-impulse signals submerged by strong noise background, and it can effectively restrain any zero-mean noise. The system has a stable working-detection limit of -83dB.
基金Supported by the National Natural Science Foundation of China
文摘A Loop-Shift Stop & Go Adaptive Filter(LSSGAF) with applications in period detection and signal separation of overlapped periodic signals is presented. The filter places no constraints on the overlapped forms in frequency domain and requires no priori knowledge except for approximate period range of signals to be separated, therefore it provides for an efficient and feasible method to separate periodic signals overlapped both in time and frequency domains. The convergence conditions of the filter and the requirements of all parameter selections are discussed, meanwhile a rough scanning and channel auto-shut algorithm is proposed to reduce the amount of calculation in the searching stage. Experiments show that the filter can separate all kinds of overlapped periodic signals with different initial phases and different relative magnitudes.
基金co-supported by the National Natural Science Foundation of China(Grants Nos:41572162.41290253)International Partnership Program of the Chinese Academy of Sciences(No:132B61KYS20160002)
文摘Objective Climate fluctuations over suborbital or millennial timescale display significant instability during the last glacial period,which are often superimposed upon the orbital periodicity.They triggered some abrupt climate events,
基金Project supported by the National Natural Science Foundation of China(Grant No.61673066)
文摘The conventional Duffing oscillator weak signal detection method, which is based on a strong reference signal, has inherent deficiencies. To address these issues, the characteristics of the Duffing oscillator's phase trajectory in a small- scale periodic state are analyzed by introducing the theory of stopping oscillation system. Based on this approach, a novel Duffing oscillator weak wide-band signal detection method is proposed. In this novel method, the reference signal is discarded, and the to-be-detected signal is directly used as a driving force. By calculating the cosine function of a phase space angle, a single Duffing oscillator can be used for weak wide-band signal detection instead of an array of uncoupled Duffing oscillators. Simulation results indicate that, compared with the conventional Duffing oscillator detection method, this approach performs better in frequency detection intervals, and reduces the signal-to-noise ratio detection threshold, while improving the real-time performance of the system.