Bifurcation properties of dynamical systems with two parameters are investigated in this paper. The definition of transition set is proposed, and the approach developed is used to investigate the dynamic characteristi...Bifurcation properties of dynamical systems with two parameters are investigated in this paper. The definition of transition set is proposed, and the approach developed is used to investigate the dynamic characteristic of the nonlin- ear forced Duffing system with nonlinear feedback controller. The whole parametric plane is divided into several persistent regions by the transition set, and then the bifurcation dia- grams in different persistent regions are obtained.展开更多
The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and...The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and dynamic processes.Nevertheless,classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres.Furthermore,a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking.In this study,we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry.Notably,power-law models offer distinct advantages over traditional plate cooling models,showcasing robust self-similarity,scale invariance,or scaling properties,and providing a better fit to observed data.The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model.In addition,we applied the similarity method to predict a higher resolution(0.1°×0.1°)global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis.Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures.Finally,combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow,which deviate from traditional plate cooling models.The anomalous regions of subsidence and heat flow show different degrees of anisotropy,providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges.展开更多
By dint of the summer precipitation data from 21 stations in the Dongting Lake region during 1960-2008 and the sea surface temperature(SST) data from NOAA,the spatial and temporal distributions of summer precipitation...By dint of the summer precipitation data from 21 stations in the Dongting Lake region during 1960-2008 and the sea surface temperature(SST) data from NOAA,the spatial and temporal distributions of summer precipitation and their correlations with SST are analyzed.The coupling relationship between the anomalous distribution in summer precipitation and the variation of SST has between studied with the Singular Value Decomposition(SVD) analysis.The increase or decrease of summer precipitation in the Dongting Lake region is closely associated with the SST anomalies in three key regions.The variation of SST in the three key regions has been proved to be a significant previous signal to anomaly of summer rainfall in Dongting region.展开更多
Control Moment Gyroscope（CMG） is an effective candidate for agile satellites and large spacecraft attitude control because of its powerful torque amplification capability. The most serious situation, however, in usi...Control Moment Gyroscope（CMG） is an effective candidate for agile satellites and large spacecraft attitude control because of its powerful torque amplification capability. The most serious situation, however, in using CMG is the inherent geometric singularity problem, where there＇s no torque output along a particular direction. Space expansion method has been proposed in this work for the singularity analysis. Based on inverse mapping transformation, an expanded Jacobian matrix which is a full rank square matrix is obtained. The singular angle sets of the 3-parallel cluster and pyramid cluster are distinguished using space expansion method. An effective hybrid steering strategy, able to deal with the elliptic singularity, is further proposed. Simulation results demonstrate the excellent performance of the proposed steering logic compared to the generalized singular robust logic and pseudo inverse logic in terms of energy consumption and torque error.展开更多
The Southern Oscillation Index (SOI) time series is analyzed by means of the singular spectrum analysis (SSA) method with 60-month window length. Two major oscillatory pairs are found in the series whose periods are q...The Southern Oscillation Index (SOI) time series is analyzed by means of the singular spectrum analysis (SSA) method with 60-month window length. Two major oscillatory pairs are found in the series whose periods are quasi-four and quasi-two years respectively. The auto-regressive model, which is developed on the basis of the Maximum Entropy Spectrum Analysis, is fitted to each of the 9 leading components including the oscillatory pairs. The prediction of SOI with the 36-month lead is obtained from the reconstruction of these extrapolated series. Correlation coefficient between predicted series and 5 months running mean of observed series is up to 0.8. The model can successfully predict the peak and duration of the strong ENSO event from 1997 to 1998. It's also shown that the proper choice of reconstructed components is the key to improve the model prediction.展开更多
Bifurcation properties of a Duffing-van der Pol system with two parameters under multi-frequency excitations are studied. Three cases are discussed： （1） λ 1 is considered as bifurcation parameter, （2） λ 2 is co...Bifurcation properties of a Duffing-van der Pol system with two parameters under multi-frequency excitations are studied. Three cases are discussed： （1） λ 1 is considered as bifurcation parameter, （2） λ 2 is considered as bifurcation parameter, and （3） λ 1 and λ 2 are both considered as bifurcation parameters. According to the definition of transition sets, the whole parametric space is divided into several different persistent regions by the transition sets for different cases. The bifurcation diagrams in different persistent regions are obtained, which provides a theoretical basis for optimal design of the system.展开更多
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
An accurate landslide displacement prediction is an important part of landslide warning system. Aiming at the dynamic characteristics of landslide evolution and the shortcomings of traditional static prediction models...An accurate landslide displacement prediction is an important part of landslide warning system. Aiming at the dynamic characteristics of landslide evolution and the shortcomings of traditional static prediction models, this paper proposes a dynamic prediction model of landslide displacement based on singular spectrum analysis(SSA) and stack long short-term memory(SLSTM) network. The SSA is used to decompose the landslide accumulated displacement time series data into trend term and periodic term displacement subsequences. A cubic polynomial function is used to predict the trend term displacement subsequence, and the SLSTM neural network is used to predict the periodic term displacement subsequence. At the same time, the Bayesian optimization algorithm is used to determine that the SLSTM network input sequence length is 12 and the number of hidden layer nodes is 18. The SLSTM network is updated by adding predicted values to the training set to achieve dynamic displacement prediction. Finally, the accumulated landslide displacement is obtained by superimposing the predicted value of each displacement subsequence. The proposed model was verified on the Xintan landslide in Hubei Province, China. The results show that when predicting the displacement of the periodic term, the SLSTM network has higher prediction accuracy than the support vector machine(SVM) and auto regressive integrated moving average(ARIMA). The mean relative error(MRE) is reduced by 4.099% and 3.548% respectively, while the root mean square error(RMSE) is reduced by 5.830 mm and 3.854 mm respectively. It is concluded that the SLSTM network model can better simulate the dynamic characteristics of landslides.展开更多
We present a hybrid singular spectrum analysis （SSA） and fuzzy entropy method to filter noisy nonlinear time series. With this approach, SSA decomposes the noisy time series into its constituent components including...We present a hybrid singular spectrum analysis （SSA） and fuzzy entropy method to filter noisy nonlinear time series. With this approach, SSA decomposes the noisy time series into its constituent components including both the deterministic behavior and noise, while fuzzy entropy automatically differentiates the optimal dominant components from the noise based on the complexity of each component. We demonstrate the effectiveness of the hybrid approach in reconstructing the Lorenz and Mackey--Class attractors, as well as improving the multi-step prediction quality of these two series in noisy environments.展开更多
This paper clarifies the essence of the significance test of singular value decomposition analysis （SVD）, and investigates four rules for testing the significance of coupled modes of SVD, including parallel analysis...This paper clarifies the essence of the significance test of singular value decomposition analysis （SVD）, and investigates four rules for testing the significance of coupled modes of SVD, including parallel analysis, nonparametric bootstrap, random-phase test, and a new rule named modified parallel analysis. A numerical experiment is conducted to quantitatively compare the performance of the four rules in judging whether a coupled mode of SVD is significant as parameters such as the sample size, the number of grid points, and the signal-to-noise ratio vary. The results show that the four rules perform better with lower ratio of the number of grid points to sample size. Modified parallel analysis and nonparametric bootstrap perform best to abandon the spurious coupled modes, but the latter is better than the former to retain the significant coupled modes when the sample size is not much larger than the number of grid points. Parallel analysis and random-phase test are robust to abandon the spurious coupled modes only when either （1） the observations at the grid points are spatially uncorrelated, or （2） the coupled signal is very strong for parallel analysis and is not weak for random-phase test. The reasons affecting the accuracy of the test rules are discussed.展开更多
The power output state of photovoltaic power generation is affected by the earth’s rotation and solar radiation intensity.On the one hand,its output sequence has daily periodicity;on the other hand,it has discrete ra...The power output state of photovoltaic power generation is affected by the earth’s rotation and solar radiation intensity.On the one hand,its output sequence has daily periodicity;on the other hand,it has discrete randomness.With the development of new energy economy,the proportion of photovoltaic energy increased accordingly.In order to solve the problem of improving the energy conversion efficiency in the grid-connected optical network and ensure the stability of photovoltaic power generation,this paper proposes the short-termprediction of photovoltaic power generation based on the improvedmulti-scale permutation entropy,localmean decomposition and singular spectrum analysis algorithm.Firstly,taking the power output per unit day as the research object,the multi-scale permutation entropy is used to calculate the eigenvectors under different weather conditions,and the cluster analysis is used to reconstruct the historical power generation under typical weather rainy and snowy,sunny,abrupt,cloudy.Then,local mean decomposition(LMD)is used to decompose the output sequence,so as to extract more detail components of the reconstructed output sequence.Finally,combined with the weather forecast of the Meteorological Bureau for the next day,the singular spectrumanalysis algorithm is used to predict the photovoltaic classification of the recombination decomposition sequence under typical weather.Through the verification and analysis of examples,the hierarchical prediction experiments of reconstructed and non-reconstructed output sequences are compared.The results show that the algorithm proposed in this paper is effective in realizing the short-term prediction of photovoltaic generator,and has the advantages of simple structure and high prediction accuracy.展开更多
Earth＇s variable rotation is mainly produced by the variability of the AAM（atmospheric angular momentum）. In particular, the axial AAM component X_3, which undergoes especially strong variations,induces changes in ...Earth＇s variable rotation is mainly produced by the variability of the AAM（atmospheric angular momentum）. In particular, the axial AAM component X_3, which undergoes especially strong variations,induces changes in the Earth＇s rotation rate. In this study we analysed maps of regional input into the effective axial AAM from 1948 through 2011 from NCEP/NCAR reanalysis. Global zonal circulation patterns related to the LOD（length of day） were described. We applied MSSA（Multichannel Singular Spectrum Analysis） jointly to the mass and motion components of AAM, which allowed us to extract annual, semiannual, 4-mo nth, quasi-biennial, 5-year, and low-frequency oscillations. PCs（Principal components） strongly related to ENSO（El Nino southern oscillation） were released. They can be used to study ENSO-induced changes in pressure and wind fields and their coupling to LOD. The PCs describing the trends have captured slow atmospheric circulation changes possibly related to climate variability.展开更多
This study focuses on addressing kinematic singularity analysis and avoidance issues for a space station remote manipulator system(SSRMS)-type reconfigurable space manipulator.The manipulator is equipped with a non-sp...This study focuses on addressing kinematic singularity analysis and avoidance issues for a space station remote manipulator system(SSRMS)-type reconfigurable space manipulator.The manipulator is equipped with a non-spherical wrist and two lockable passive telescopic links(LPTLs),which enable it to have both active revolute and passive prismatic joints and operate in two distinct modes.To begin with the kinematic singularity analysis,the study derives the differential kinematic equations for the manipulator and identifies the dominant Jacobian matrix that causes singularities.Subsequently,an in-depth analysis of singularities from multiple perspectives is conducted.Firstly,a kinematic singularity map method is proposed to capture the distribution of singularities within the reachable workspace.Then,the influence of the two LPTLs on singularities is thoroughly examined.Finally,a new method based on the matrix rank equivalence principle is introduced to determine singularity conditions,enabling the identification of all the singular configurations for the SSRMS-type reconfigurable manipulator.Notably,this method significantly reduces computational complexity,and the singularity conditions obtained have more concise equations.For the singularity avoidance problem,a novel method is developed,which simultaneously addresses the requirements of real-time performance,high precision,and the avoidance of both kinematic singularities and joint limit constraints.Benefiting from these excellent properties,the proposed method can effectively resolve the singularity issues encountered separately by the SSRMS-type reconfigurable manipulator in its two operational modes.Several typical simulations validate the utility of all the proposed methods.展开更多
A two-degree-of-freedom bifurcation system for an elastic cable with 1：1 internal resonance is investigated in this paper. The transition set of the system is obtained with the singularity theory for three cases. The...A two-degree-of-freedom bifurcation system for an elastic cable with 1：1 internal resonance is investigated in this paper. The transition set of the system is obtained with the singularity theory for three cases. The whole parametric plane is divided into several different persistent regions by the transition set. The bifurcation diagrams in different persistent regions are obtained.展开更多
The total organic carbon (TOC) content series from the lake sediment of Minqin Basin (100°57′–104°57′E, 37°48′–39°17′N) in northwestern China, which has a 10 000-year-long paleo-climatic prox...The total organic carbon (TOC) content series from the lake sediment of Minqin Basin (100°57′–104°57′E, 37°48′–39°17′N) in northwestern China, which has a 10 000-year-long paleo-climatic proxy record, was used to analyze the Holocene climate changes in the local region. The proxy record was established in the Sanjiaocheng (SJC), Triangle Town in Chinese, Section (103°20′25″E, 39°00′38″N), which is located at the northwestern boundary of the present Asian summer monsoon in China, and is sensitive to global environmental and climate changes. Applying singular spectrum analysis (SSA) to the TOC series, principal climatic oscillations and periodical changes were studied. The results reveal 3 major patterns of climate change regulated by reconstructed components (RCs). The first pattern is natural long-term trend of climatic change in the local area (Minqin Basin), indicating a relatively wetter stage in early Holocene (starting at 9.5 kaBP), and a relatively dryer stage with a strong lake desiccation and a declined vegetation cover in mid-Holocene (during 7–6 kaBP). From 4.0 kaBP to the present, there has been a gradually decreasing trend in the third reconstructed component (RC3) showing that the local climate changed again into a dryer stage. The second pattern shows millennial-centennial scale oscillations containing cycles of 1 600 and 800 years that have been present throughout almost the entire Holocene period of the last 10 000 years. The third pattern is a millennial-centennial scale variation with a relatively smaller amplitude and unclear cycles showing a nonlinear interaction within the earth’s climate systems.展开更多
An algorithm based on the data-adaptive filtering characteristics of singular spectrum analysis (SSA) is proposed to denoise chaotic data. Firstly, the empirical orthogonal functions (EOFs) and principal components (P...An algorithm based on the data-adaptive filtering characteristics of singular spectrum analysis (SSA) is proposed to denoise chaotic data. Firstly, the empirical orthogonal functions (EOFs) and principal components (PCs) of the signal were calculated, reconstruct the signal using the EOFs and PCs, and choose the optimal reconstructing order based on sigular spectrum to obtain the denoised signal. The noise of the signal can influence the calculating precision of maximal Liapunov exponents. The proposed denoising algorithm was applied to the maximal Liapunov exponents calculations of two chaotic system, Henon map and Logistic map. Some numerical results show that this denoising algorithm could improve the calculating precision of maximal Liapunov exponent.展开更多
(Multichannel)Singular spectrum analysis is considered as one of the most effective methods for seismic incoherent noise suppression.It utilizes the low-rank feature of seismic signal and regards the noise suppression...(Multichannel)Singular spectrum analysis is considered as one of the most effective methods for seismic incoherent noise suppression.It utilizes the low-rank feature of seismic signal and regards the noise suppression as a low-rank reconstruction problem.However,in some cases the seismic geophones receive some erratic disturbances and the amplitudes are dramatically larger than other receivers.The presence of this kind of noise,called erratic noise,makes singular spectrum analysis(SSA)reconstruction unstable and has undesirable effects on the final results.We robustify the low-rank reconstruction of seismic data by a reweighted damped SSA(RD-SSA)method.It incorporates the damped SSA,an improved version of SSA,into a reweighted framework.The damping operator is used to weaken the artificial disturbance introduced by the low-rank projection of both erratic and random noise.The central idea of the RD-SSA method is to iteratively approximate the observed data with the quadratic norm for the first iteration and the Tukeys bisquare norm for the rest iterations.The RD-SSA method can suppress seismic incoherent noise and keep the reconstruction process robust to the erratic disturbance.The feasibility of RD-SSA is validated via both synthetic and field data examples.展开更多
Studying the seasonal deformation in GPS time series is important to interpreting geophysical contributors and identifying unmodeled and mismodeled seasonal signals.Traditional seasonal signal extraction used the leas...Studying the seasonal deformation in GPS time series is important to interpreting geophysical contributors and identifying unmodeled and mismodeled seasonal signals.Traditional seasonal signal extraction used the least squares method,which models seasonal deformation as a constant seasonal amplitude and phase.However,the seasonal variations are not constant from year to year,and the seasonal amplitude and phase are time-variable.In order to obtain the time-variable seasonal signal in the GPS station coordinate time series,singular spectrum analysis(SSA)is conducted in this study.We firstly applied the SSA on simulated seasonal signals with different frequencies 1.00 cycle per year(cpy),1.04 cpy and with time-variable amplitude are superimposed.It was found that SSA can successfully obtain the seasonal variations with different frequencies and with time-variable amplitude superimposed.Then,SSA is carried out on the GPS observations in Yunnan Province.The results show that the time-variable amplitude seasonal signals are ubiquitous in Yunnan Province,and the timevariable amplitude change in 2019 in the region is extracted,which is further explained by the soil moisture mass loading and atmospheric pressure loading.After removing the two loading effects,the SSA obtained modulated seasonal signals which contain the obvious seasonal variations at frequency of 1.046 cpy,it is close with the GPS draconitic year,1.040 cpy.Hence,the time-variable amplitude changes in 2019 and the seasonal GPS draconitic year in the region could be discriminated successfully by SSA in Yunnan Province.展开更多
A novel interval quartering algorithm （IQA） is proposed to overcome insufficiency of the conventional singular spectrum analysis （SSA） iterative interpolation for selecting parameters including the number of the p...A novel interval quartering algorithm （IQA） is proposed to overcome insufficiency of the conventional singular spectrum analysis （SSA） iterative interpolation for selecting parameters including the number of the principal components and the embedding dimension. Based on the improved SSA iterative interpolation, interpolated test and comparative analysis are carried out to the outgoing longwave radiation daily data. The results show that IQA can find globally optimal parameters to the error curve with local oscillation, and has advantage of fast computing speed. The improved interpolation method is effective in the interpolation of missing data.展开更多
The problem of speech enhancement using threshold de-noising in wavelet domain was considered.The appropriate decomposition level is another key factor pertinent to de-noising performance.This paper proposed a new wav...The problem of speech enhancement using threshold de-noising in wavelet domain was considered.The appropriate decomposition level is another key factor pertinent to de-noising performance.This paper proposed a new wavelet-based de-noising scheme that can improve the enhancement performance significantly in the presence of additive white Gaussian noise.The proposed algorithm can adaptively select the optimal decomposition level of wavelet transformation according to the characteristics of noisy speech.The experimental results demonstrate that this proposed algorithm outperforms the classical wavelet-based de-noising method and effectively improves the practicability of this kind of techniques.展开更多
基金supported by the National Natural Science Foundation of China(10632040)
文摘Bifurcation properties of dynamical systems with two parameters are investigated in this paper. The definition of transition set is proposed, and the approach developed is used to investigate the dynamic characteristic of the nonlin- ear forced Duffing system with nonlinear feedback controller. The whole parametric plane is divided into several persistent regions by the transition set, and then the bifurcation dia- grams in different persistent regions are obtained.
基金supported by the Guangdong Province Introduced Innovative R&D Team of Big Data-Mathematical Earth Sciences and Extreme Geological Events Team(grant number 2021ZT09H399)the National Natural Science Foundation of China(grant number 42430111,42050103).
文摘The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and dynamic processes.Nevertheless,classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres.Furthermore,a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking.In this study,we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry.Notably,power-law models offer distinct advantages over traditional plate cooling models,showcasing robust self-similarity,scale invariance,or scaling properties,and providing a better fit to observed data.The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model.In addition,we applied the similarity method to predict a higher resolution(0.1°×0.1°)global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis.Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures.Finally,combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow,which deviate from traditional plate cooling models.The anomalous regions of subsidence and heat flow show different degrees of anisotropy,providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges.
基金Supported by The Special Foundation of Chinese Meteorological Bureau Climate Changes Program(200920)The Special Foundation of Hunan Major Scientific and Technological Research Program(2008FJ1006)~~
文摘By dint of the summer precipitation data from 21 stations in the Dongting Lake region during 1960-2008 and the sea surface temperature(SST) data from NOAA,the spatial and temporal distributions of summer precipitation and their correlations with SST are analyzed.The coupling relationship between the anomalous distribution in summer precipitation and the variation of SST has between studied with the Singular Value Decomposition(SVD) analysis.The increase or decrease of summer precipitation in the Dongting Lake region is closely associated with the SST anomalies in three key regions.The variation of SST in the three key regions has been proved to be a significant previous signal to anomaly of summer rainfall in Dongting region.
基金support from the National Natural Science Foundation of China (No. 61403197)the National Key Research and Development Plan of China (No. 2016YFB0500901)
文摘Control Moment Gyroscope（CMG） is an effective candidate for agile satellites and large spacecraft attitude control because of its powerful torque amplification capability. The most serious situation, however, in using CMG is the inherent geometric singularity problem, where there＇s no torque output along a particular direction. Space expansion method has been proposed in this work for the singularity analysis. Based on inverse mapping transformation, an expanded Jacobian matrix which is a full rank square matrix is obtained. The singular angle sets of the 3-parallel cluster and pyramid cluster are distinguished using space expansion method. An effective hybrid steering strategy, able to deal with the elliptic singularity, is further proposed. Simulation results demonstrate the excellent performance of the proposed steering logic compared to the generalized singular robust logic and pseudo inverse logic in terms of energy consumption and torque error.
基金This work was supported by the" National Key Project Studies on Short-Range Climate PredictionSystem in China" (96-908-04-02).
文摘The Southern Oscillation Index (SOI) time series is analyzed by means of the singular spectrum analysis (SSA) method with 60-month window length. Two major oscillatory pairs are found in the series whose periods are quasi-four and quasi-two years respectively. The auto-regressive model, which is developed on the basis of the Maximum Entropy Spectrum Analysis, is fitted to each of the 9 leading components including the oscillatory pairs. The prediction of SOI with the 36-month lead is obtained from the reconstruction of these extrapolated series. Correlation coefficient between predicted series and 5 months running mean of observed series is up to 0.8. The model can successfully predict the peak and duration of the strong ENSO event from 1997 to 1998. It's also shown that the proper choice of reconstructed components is the key to improve the model prediction.
基金Project supported by the National Natural Science Foundation of China (No. 10632040)
文摘Bifurcation properties of a Duffing-van der Pol system with two parameters under multi-frequency excitations are studied. Three cases are discussed： （1） λ 1 is considered as bifurcation parameter, （2） λ 2 is considered as bifurcation parameter, and （3） λ 1 and λ 2 are both considered as bifurcation parameters. According to the definition of transition sets, the whole parametric space is divided into several different persistent regions by the transition sets for different cases. The bifurcation diagrams in different persistent regions are obtained, which provides a theoretical basis for optimal design of the system.
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.
基金supported by the Natural Science Foundation of Shaanxi Province under Grant 2019JQ206in part by the Science and Technology Department of Shaanxi Province under Grant 2020CGXNG-009in part by the Education Department of Shaanxi Province under Grant 17JK0346。
文摘An accurate landslide displacement prediction is an important part of landslide warning system. Aiming at the dynamic characteristics of landslide evolution and the shortcomings of traditional static prediction models, this paper proposes a dynamic prediction model of landslide displacement based on singular spectrum analysis(SSA) and stack long short-term memory(SLSTM) network. The SSA is used to decompose the landslide accumulated displacement time series data into trend term and periodic term displacement subsequences. A cubic polynomial function is used to predict the trend term displacement subsequence, and the SLSTM neural network is used to predict the periodic term displacement subsequence. At the same time, the Bayesian optimization algorithm is used to determine that the SLSTM network input sequence length is 12 and the number of hidden layer nodes is 18. The SLSTM network is updated by adding predicted values to the training set to achieve dynamic displacement prediction. Finally, the accumulated landslide displacement is obtained by superimposing the predicted value of each displacement subsequence. The proposed model was verified on the Xintan landslide in Hubei Province, China. The results show that when predicting the displacement of the periodic term, the SLSTM network has higher prediction accuracy than the support vector machine(SVM) and auto regressive integrated moving average(ARIMA). The mean relative error(MRE) is reduced by 4.099% and 3.548% respectively, while the root mean square error(RMSE) is reduced by 5.830 mm and 3.854 mm respectively. It is concluded that the SLSTM network model can better simulate the dynamic characteristics of landslides.
文摘We present a hybrid singular spectrum analysis （SSA） and fuzzy entropy method to filter noisy nonlinear time series. With this approach, SSA decomposes the noisy time series into its constituent components including both the deterministic behavior and noise, while fuzzy entropy automatically differentiates the optimal dominant components from the noise based on the complexity of each component. We demonstrate the effectiveness of the hybrid approach in reconstructing the Lorenz and Mackey--Class attractors, as well as improving the multi-step prediction quality of these two series in noisy environments.
基金This work was supported by the National Natural Science Foundation of China under Grant No. 40233027.
文摘This paper clarifies the essence of the significance test of singular value decomposition analysis （SVD）, and investigates four rules for testing the significance of coupled modes of SVD, including parallel analysis, nonparametric bootstrap, random-phase test, and a new rule named modified parallel analysis. A numerical experiment is conducted to quantitatively compare the performance of the four rules in judging whether a coupled mode of SVD is significant as parameters such as the sample size, the number of grid points, and the signal-to-noise ratio vary. The results show that the four rules perform better with lower ratio of the number of grid points to sample size. Modified parallel analysis and nonparametric bootstrap perform best to abandon the spurious coupled modes, but the latter is better than the former to retain the significant coupled modes when the sample size is not much larger than the number of grid points. Parallel analysis and random-phase test are robust to abandon the spurious coupled modes only when either （1） the observations at the grid points are spatially uncorrelated, or （2） the coupled signal is very strong for parallel analysis and is not weak for random-phase test. The reasons affecting the accuracy of the test rules are discussed.
文摘The power output state of photovoltaic power generation is affected by the earth’s rotation and solar radiation intensity.On the one hand,its output sequence has daily periodicity;on the other hand,it has discrete randomness.With the development of new energy economy,the proportion of photovoltaic energy increased accordingly.In order to solve the problem of improving the energy conversion efficiency in the grid-connected optical network and ensure the stability of photovoltaic power generation,this paper proposes the short-termprediction of photovoltaic power generation based on the improvedmulti-scale permutation entropy,localmean decomposition and singular spectrum analysis algorithm.Firstly,taking the power output per unit day as the research object,the multi-scale permutation entropy is used to calculate the eigenvectors under different weather conditions,and the cluster analysis is used to reconstruct the historical power generation under typical weather rainy and snowy,sunny,abrupt,cloudy.Then,local mean decomposition(LMD)is used to decompose the output sequence,so as to extract more detail components of the reconstructed output sequence.Finally,combined with the weather forecast of the Meteorological Bureau for the next day,the singular spectrumanalysis algorithm is used to predict the photovoltaic classification of the recombination decomposition sequence under typical weather.Through the verification and analysis of examples,the hierarchical prediction experiments of reconstructed and non-reconstructed output sequences are compared.The results show that the algorithm proposed in this paper is effective in realizing the short-term prediction of photovoltaic generator,and has the advantages of simple structure and high prediction accuracy.
基金supported by Russian Foundation for Basic Research grants No. 17-05-00989, No. 16-05-00753,NRU HSE and visiting grants positions at Paris observatory and Wuhan university for the first authorpartially supported by grants by NSF/IGFA Belmont Forum Project (Grant No. ICER-1342644)the Chinese Academy of Sciences/SAFEA International Partnership Program for Creative Research Teams(Grant No. KZZD-EW-TZ-05)
文摘Earth＇s variable rotation is mainly produced by the variability of the AAM（atmospheric angular momentum）. In particular, the axial AAM component X_3, which undergoes especially strong variations,induces changes in the Earth＇s rotation rate. In this study we analysed maps of regional input into the effective axial AAM from 1948 through 2011 from NCEP/NCAR reanalysis. Global zonal circulation patterns related to the LOD（length of day） were described. We applied MSSA（Multichannel Singular Spectrum Analysis） jointly to the mass and motion components of AAM, which allowed us to extract annual, semiannual, 4-mo nth, quasi-biennial, 5-year, and low-frequency oscillations. PCs（Principal components） strongly related to ENSO（El Nino southern oscillation） were released. They can be used to study ENSO-induced changes in pressure and wind fields and their coupling to LOD. The PCs describing the trends have captured slow atmospheric circulation changes possibly related to climate variability.
基金co-supported by the Basic Science Center Project of the National Natural Science Foundation of China(No.T2388101)the Key Program of the National Natural Science Foundation of China(No.92148203).
文摘This study focuses on addressing kinematic singularity analysis and avoidance issues for a space station remote manipulator system(SSRMS)-type reconfigurable space manipulator.The manipulator is equipped with a non-spherical wrist and two lockable passive telescopic links(LPTLs),which enable it to have both active revolute and passive prismatic joints and operate in two distinct modes.To begin with the kinematic singularity analysis,the study derives the differential kinematic equations for the manipulator and identifies the dominant Jacobian matrix that causes singularities.Subsequently,an in-depth analysis of singularities from multiple perspectives is conducted.Firstly,a kinematic singularity map method is proposed to capture the distribution of singularities within the reachable workspace.Then,the influence of the two LPTLs on singularities is thoroughly examined.Finally,a new method based on the matrix rank equivalence principle is introduced to determine singularity conditions,enabling the identification of all the singular configurations for the SSRMS-type reconfigurable manipulator.Notably,this method significantly reduces computational complexity,and the singularity conditions obtained have more concise equations.For the singularity avoidance problem,a novel method is developed,which simultaneously addresses the requirements of real-time performance,high precision,and the avoidance of both kinematic singularities and joint limit constraints.Benefiting from these excellent properties,the proposed method can effectively resolve the singularity issues encountered separately by the SSRMS-type reconfigurable manipulator in its two operational modes.Several typical simulations validate the utility of all the proposed methods.
基金Project supported by the National Natural Science Foundation of China (No. 10632040)
文摘A two-degree-of-freedom bifurcation system for an elastic cable with 1：1 internal resonance is investigated in this paper. The transition set of the system is obtained with the singularity theory for three cases. The whole parametric plane is divided into several different persistent regions by the transition set. The bifurcation diagrams in different persistent regions are obtained.
基金the National Natural Science Foundation of China (NSFC) (No. 40571169)the NSFC’s Innovation Team Project (No. 40421101), and the NSFC’s Key Program Project (No. 90502008)
文摘The total organic carbon (TOC) content series from the lake sediment of Minqin Basin (100°57′–104°57′E, 37°48′–39°17′N) in northwestern China, which has a 10 000-year-long paleo-climatic proxy record, was used to analyze the Holocene climate changes in the local region. The proxy record was established in the Sanjiaocheng (SJC), Triangle Town in Chinese, Section (103°20′25″E, 39°00′38″N), which is located at the northwestern boundary of the present Asian summer monsoon in China, and is sensitive to global environmental and climate changes. Applying singular spectrum analysis (SSA) to the TOC series, principal climatic oscillations and periodical changes were studied. The results reveal 3 major patterns of climate change regulated by reconstructed components (RCs). The first pattern is natural long-term trend of climatic change in the local area (Minqin Basin), indicating a relatively wetter stage in early Holocene (starting at 9.5 kaBP), and a relatively dryer stage with a strong lake desiccation and a declined vegetation cover in mid-Holocene (during 7–6 kaBP). From 4.0 kaBP to the present, there has been a gradually decreasing trend in the third reconstructed component (RC3) showing that the local climate changed again into a dryer stage. The second pattern shows millennial-centennial scale oscillations containing cycles of 1 600 and 800 years that have been present throughout almost the entire Holocene period of the last 10 000 years. The third pattern is a millennial-centennial scale variation with a relatively smaller amplitude and unclear cycles showing a nonlinear interaction within the earth’s climate systems.
文摘An algorithm based on the data-adaptive filtering characteristics of singular spectrum analysis (SSA) is proposed to denoise chaotic data. Firstly, the empirical orthogonal functions (EOFs) and principal components (PCs) of the signal were calculated, reconstruct the signal using the EOFs and PCs, and choose the optimal reconstructing order based on sigular spectrum to obtain the denoised signal. The noise of the signal can influence the calculating precision of maximal Liapunov exponents. The proposed denoising algorithm was applied to the maximal Liapunov exponents calculations of two chaotic system, Henon map and Logistic map. Some numerical results show that this denoising algorithm could improve the calculating precision of maximal Liapunov exponent.
基金supported by the National Natural Science Foundation of China under grant no.42374133the Beijing Nova Program under grant no.2022056+1 种基金the Fundamental Research Funds for the Central Universities under grant no.2462020YXZZ006the Young Elite Scientists Sponsorship Program by CAST(YESS)under grant no.2018QNRC001。
文摘(Multichannel)Singular spectrum analysis is considered as one of the most effective methods for seismic incoherent noise suppression.It utilizes the low-rank feature of seismic signal and regards the noise suppression as a low-rank reconstruction problem.However,in some cases the seismic geophones receive some erratic disturbances and the amplitudes are dramatically larger than other receivers.The presence of this kind of noise,called erratic noise,makes singular spectrum analysis(SSA)reconstruction unstable and has undesirable effects on the final results.We robustify the low-rank reconstruction of seismic data by a reweighted damped SSA(RD-SSA)method.It incorporates the damped SSA,an improved version of SSA,into a reweighted framework.The damping operator is used to weaken the artificial disturbance introduced by the low-rank projection of both erratic and random noise.The central idea of the RD-SSA method is to iteratively approximate the observed data with the quadratic norm for the first iteration and the Tukeys bisquare norm for the rest iterations.The RD-SSA method can suppress seismic incoherent noise and keep the reconstruction process robust to the erratic disturbance.The feasibility of RD-SSA is validated via both synthetic and field data examples.
基金funded by National Natural Science Foundation of China(Grant No.11803065)Natural Science Foundation of Shanghai(Grant No.22ZR1472800)。
文摘Studying the seasonal deformation in GPS time series is important to interpreting geophysical contributors and identifying unmodeled and mismodeled seasonal signals.Traditional seasonal signal extraction used the least squares method,which models seasonal deformation as a constant seasonal amplitude and phase.However,the seasonal variations are not constant from year to year,and the seasonal amplitude and phase are time-variable.In order to obtain the time-variable seasonal signal in the GPS station coordinate time series,singular spectrum analysis(SSA)is conducted in this study.We firstly applied the SSA on simulated seasonal signals with different frequencies 1.00 cycle per year(cpy),1.04 cpy and with time-variable amplitude are superimposed.It was found that SSA can successfully obtain the seasonal variations with different frequencies and with time-variable amplitude superimposed.Then,SSA is carried out on the GPS observations in Yunnan Province.The results show that the time-variable amplitude seasonal signals are ubiquitous in Yunnan Province,and the timevariable amplitude change in 2019 in the region is extracted,which is further explained by the soil moisture mass loading and atmospheric pressure loading.After removing the two loading effects,the SSA obtained modulated seasonal signals which contain the obvious seasonal variations at frequency of 1.046 cpy,it is close with the GPS draconitic year,1.040 cpy.Hence,the time-variable amplitude changes in 2019 and the seasonal GPS draconitic year in the region could be discriminated successfully by SSA in Yunnan Province.
基金the State Key Program for Basic Research of China(No.2007CB816003)the Open Item of the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics of China
文摘A novel interval quartering algorithm （IQA） is proposed to overcome insufficiency of the conventional singular spectrum analysis （SSA） iterative interpolation for selecting parameters including the number of the principal components and the embedding dimension. Based on the improved SSA iterative interpolation, interpolated test and comparative analysis are carried out to the outgoing longwave radiation daily data. The results show that IQA can find globally optimal parameters to the error curve with local oscillation, and has advantage of fast computing speed. The improved interpolation method is effective in the interpolation of missing data.
文摘The problem of speech enhancement using threshold de-noising in wavelet domain was considered.The appropriate decomposition level is another key factor pertinent to de-noising performance.This paper proposed a new wavelet-based de-noising scheme that can improve the enhancement performance significantly in the presence of additive white Gaussian noise.The proposed algorithm can adaptively select the optimal decomposition level of wavelet transformation according to the characteristics of noisy speech.The experimental results demonstrate that this proposed algorithm outperforms the classical wavelet-based de-noising method and effectively improves the practicability of this kind of techniques.
