Periodic signal extraction of GNSS height time series based on adaptive singular spectrum analysis

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.

THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

This paper is mainly about the spectral properties of a class of Jacobi operators(H_(c,b)u)(n)=c_(n)u(n+1)+c_(n-1)u(n-1)+b_(n)u(n),.where∣c_(n)−1∣=O(n^(−α))and b_(n)=O(n^(−1)).We will show that,forα≥1,the singular continuous spectrum of the operator is empty.

A reweighted damped singular spectrum analysis method for robust seismic 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.

The Multi-Fractal Singularity Value Decomposition and Its Application in Extraction of Gravity Anomaly Associated with Gold Mineralization in Tongshi Gold Field

Because of the complication of geological procedures,the recorded data have the feature of nonlinear.The multi-fractal singularity value decomposition (MSVD) was used to decomposed the gravity data.In this paper,the MSVD was utilized to extract the gravity anomaly associated with the gold mineralization in Tongshi gold field in the southwest of Shandong province.The results showed that the Tongshi complex with negative circular gravity anomaly is an important ore-controlling factor.And the positive ring gravity anomaly distributed

Short-Term Prediction of Photovoltaic Power Generation Based on LMD Permutation Entropy and Singular Spectrum Analysis

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.

Investigation on Singularity, Signature Matrix and Spectrum of Mixed Graphs

The spectral theory of graph is an important branch of graph theory,and the main part of this theory is the connection between the spectral properties and the structural properties,characterization of the structural properties of graphs.We discuss the problems about singularity,signature matrix and spectrum of mixed graphs.Without loss of generality,parallel edges and loops are permitted in mixed graphs.Let G1 and G2 be connected mixed graphs which are obtained from an underlying graph G.When G1 and G2 have the same singularity,the number of induced cycles in Gi(i=1,2)is l(l=1,l>1),the length of the smallest induced cycles is 1,2,at least 3.According to conclusions and mathematics induction,we find that the singularity of corresponding induced cycles in G1 and G2 are the same if and only if there exists a signature matrix D such that L(G2)=DTL(G1)D.D may be the product of some signature matrices.If L(G2)=D^TL(G1)D,G1 and G2 have the same spectrum.

Distinction of self-synchronous scrambled linear blockcodes based on multi-fractal spectrum

This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.

Short-range Climate Prediction Experiment of the Southern Oscillation Index Based on the Singular Spectrum Analysis

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.

Preconditioned prestack plane-wave least squares reverse time migration with singular spectrum constraint

Least squares migration can eliminate the artifacts introduced by the direct imaging of irregular seismic data but is computationally costly and of slow convergence. In order to suppress the migration noise, we propose the preconditioned prestack plane-wave least squares reverse time migration （PLSRTM） method with singular spectrum constraint. Singular spectrum analysis （SSA） is used in the preconditioning of the take-off angle-domain common-image gathers （TADCIGs）. In addition, we adopt randomized singular value decomposition （RSVD） to calculate the singular values. RSVD reduces the computational cost of SSA by replacing the singular value decomposition （SVD） of one large matrix with the SVD of two small matrices. We incorporate a regularization term into the preconditioned PLSRTM method that penalizes misfits between the migration images from the plane waves with adjacent angles to reduce the migration noise because the stacking of the migration results cannot effectively suppress the migration noise when the migration velocity contains errors. The regularization imposes smoothness constraints on the TADCIGs that favor differential semblance optimization constraints. Numerical analysis of synthetic data using the Marmousi model suggests that the proposed method can efficiently suppress the artifacts introduced by plane-wave gathers or irregular seismic data and improve the imaging quality of PLSRTM. Furthermore, it produces better images with less noise and more continuous structures even for inaccurate migration velocities.

Dynamic prediction of landslide displacement using singular spectrum analysis and stack long short-term memory network

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.

The minimal spanning tree method for calculating seismic multi-fractal

There are many methods to calculate seismic fractal at present. However, there are still more or less questions to every method. In this paper, we introduce a new way to calculate seismic fractal-the minimal spanning tree. We make an important improvement for this method. By studying some seismic events of four regions including Wushi, Wusu, Tangshan and Haicheng, we obtain that before the strong earthquake occurrence, the multi-fractal spectrum of the space-time distribution of earthquakes changes from centralized to loose. The result shows that the complexity of fractal structure and the inhomogeneity of the space-time distribution of earthquakes are both increasing. By studying the numerical simulation of point sets, we draw the conclusion that the physical essence of multi-fractal spectrums before and after a strong earthquake occurrence is a changing process from homogeneous to inhomogeneous, from simple to complex.

Denoising Nonlinear Time Series Using Singular Spectrum Analysis and Fuzzy Entropy

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.

An Innovated Integrated Model Using Singular Spectrum Analysis and Support Vector Regression Optimized by Intelligent Algorithm for Rainfall Forecasting

Rainfall forecasting is becoming more and more significant and precipitation anomalies would lead to droughts and floods disasters.However,because of the complexity and non-stationary of rainfall data,it is difficult to forecast.In this paper,a novel hybrid model to forecast rainfall is developed by incorporating singular spectrum analysis (SSA) and dragonfly algorithm (DA) into support vector regression (SVR) method.Firstly,SSA is used for extracting the trend components of the hydrological data.Then,SVR is utilized to deal with the volatility and irregularity of the precipitation series.Finally,the parameter of SVR is optimized by DA.The proposed SSA-DA-SVR method is used to forecast the monthly precipitation for Songbai,Panshui,Lanma and Jiulongchi stations.To validate the efficiency of the method,four compared models,DA-SVR,SSA-GWO-SVR,SSA-PSO-SVR and SSA-CS-SVR are established.The result shows that the proposed method has the best performance among all five models,and its prediction has high precision and accuracy.

An Improved Singularity Computing Algorithm Based on Wavelet Transform Modulus Maxima Method

In order to reduce the hidden danger of noise which can be charactered by singularity spectrum, a new algorithm based on wavelet transform modulus maxima method was proposed. Singularity analysis is one of the most promising new approaches for extracting noise hidden information from noisy time series . Because of singularity strength is hard to calculate accurately, a wavelet transform modulus maxima method was used to get singularity spectrum. The singularity spectrum of white noise and aluminium interconnection electromigration noise was calculated and analyzed. The experimental results show that the new algorithm is more accurate than tradition estimating algorithm. The proposed method is feasible and efficient.

Multichannel singular spectrum analysis of the axial atmospheric angular momentum

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.

Study on Singularity of Chaotic Signal Based on Wavelet Transform

Based on the variations of wavelet transform modulus maxima at multi-scales, the singularity of chaotic signals are studied, and the singularity of these signals are measured by the Lipschitz exponent.In the meantime, a nonlinear method is proposed based on the higher order statistics, on the other aspect, which characterizes the higher order singular spectrum (HOSS) of chaotic signals. All computations are done with Lorenz attractor, Rossler attractor and EEG(electroencephalogram) time series and the comparisions among these results are made. The experimental results show that the Lipschitz exponents and the higher order singular spectra of these signals are significantly different from each other, which indicates these methods are effective for studing the singularity of chaotic signals.

SINGULAR CROSS SPECTRUM APPLIED ON DIAGNOSTIC ANALYSIS OF AIR-SEA INTERACTION

The Singular Cross Spectrum Analysis (SCSA) method was employed to investigate the coupledperiods of air-sea/mid-low circulation interaction using 1951-1993 500-hpa geopotential heights and the seasurface temperature (SST) in the Northern Hemisphere. Results show that air-sea correlation is noticeable on the3-7 year scale which is similar to ENSO circle. In this sense, ENSO is a Strong signal. Quasi-ten/quasi-four yearperiods are prominent in the mid-low interaction, and quasi-if our year oscillation is uniform with the ENSO circle.Studies indicate that the mid-low interaction possess quasi-ten year oscillation beside being affected by ENSO.

DENOISING METHOD BASED ON SINGULAR SPECTRUM ANALYSIS AND ITS APPLICATIONS IN CALCULATION OF MAXIMAL LIAPUNOV EXPONENT

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.

Improved interpolation method based on singular spectrum analysis iteration and its application to missing data recovery

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.

Coupling Singular Spectrum Analysis with Artificial Neural Network to Improve Accuracy of Sediment Load Prediction

Sediment load estimation is generally required for study and development of water resources system. In this regard, artificial neural network (ANN) is the most widely used modeling tool especially in data-constraint regions. This research attempts to combine SSA (singular spectrum analysis) with ANN, hereafter called SSA-ANN model, with expectation to improve the accuracy of sediment load predicted by the existing ANN approach. Two different catchments located in the Lower Mekong Basin (LMB) were selected for the study and the model performance was measured by several statistical indices. In comparing with ANN, the proposed SSA-ANN model shows its better performance repeatedly in both catchments. In validation stage, SSA-ANN is superior for larger Nash-Sutcliffe Efficiency about 24% in Ban Nong Kiang catchment and 7% in Nam Mae Pun Luang catchment. Other statistical measures of SSA-ANN are better than those of ANN as well. This improvement reveals the importance of SSA which filters noise containing in the raw time series and transforms the original input data to be near normal distribution which is favorable to model simulation. This coupled model is also recommended for the prediction of other water resources variables because extra input data are not required. Only additional computation, time series decomposition, is needed. The proposed technique could be potentially used to minimize the costly operation of sediment measurement in the LMB which is relatively rich in hydrometeorological records.