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.

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.

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.

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.

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.

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.

A singular spectrum analysis on Holocene climatic oscillation from lake sedimentary record in Minqin Basin, China

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.

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.

Wavelet De-noising of Speech Using Singular Spectrum Analysis for Decomposition Level Selection

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.

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.

Automatic Anomaly Detection of Respiratory Motion Based on Singular Spectrum Analysis

The realization of automatic anomaly detection of respiratory motion could be very useful to prevent accidental damage during radiation therapy. In this paper, we proposed an automatic anomaly detection method using singular value decomposition analysis. Before applying this method, the investigator needs a normal respiratory motion data of a patient. From these data, a trajectory matrix representing normal time-series feature is created. Decomposing the matrix, we obtained the feature of normal time series. Then, we applied the same procedure to real-time data and obtained real-time features. Calculating the similarity of those feature matrixes, an anomaly score was obtained. Patient motion was observed by a depth camera. In our simulation, two types of motion e.g. cough and sudden stop of breathing were successfully detected, while gradual change of respiratory cycle frequency was not detected clearly.

A comparison analysis of multipath extract methods in short-baseline applications of GPS

In order to eliminate the multipath errors existing in static short-baseline applications, a novel de-noising method based on a singular spectrum analysis （named as DSSA） is introduced to extract multipath signals. The multipath error is extracted from the double difference （DD） residuals by DSSA and then applied to the correct multipath error in subsequent measurements based on the correlation among adjacent epochs. Methods based on discrete wavelet transform （DWT） and stationary wavelet transform （SWT） are introduced as comparisons of DSSA based on analysis of a simulated signal. Real baseline residuals are tested to verify different extract methods. Results show that compared with the SWT, the DSSA improves the root mean square （RMS） of the residual by 48.6% and achieves a time reduction of 75.3%.

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.

Singular spectrum analysis for the time-variable seasonal signals from GPS in Yunnan Province

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.

Temperature effect on the structural strains of an ancient Tibetan building based on long-term monitoring data

Many studies have indicated that structural strain will be significantly influenced by temperature variations,and a good understanding of the effect of temperature on structural strain is essential.A structural health monitoring system has been installed in a typical Tibetan timber building to measure the structural strains and ambient temperature since 2012.This paper presents the correlation between temperature and strain data from the monitored structure.A method combining singular spectrum analysis and polynomial regression is proposed for modeling the temperature induced strains in the structure.Singular spectrum analysis is applied to smooth the temperature data,and the correlation between the resulting temperature time series and the measured strains is obtained by polynomial regression.Parameters of the singular spectrum analysis and the regression model are selected to have the least regression error.Results show that the proposed method has both good reproduction and prediction capabilities for temperature induced strains,and that the method is accurate and effective for eliminating the effect of temperature from the measured strain.A standardized Novelty Index based on the residual strain is also used for the condition assessment of the structure.

EXCHANGE RATE FORECASTING WITH OPTIMUM SINGULAR SPECTRUM ANALYSIS

Forecasting exchange rate is undoubtedly an attractive and challenging issue that has been of interest in different domains for many years. The singular spectrum analysis （SSA） technique has been used as a promising technique for time series forecasting including exchange rate series. The SSA technique is based upon two main choices： Window length, L, and the number of singular values, r. These values are very important for the reconstruction stage and forecasting purposes. Here the authors consider an optimum version of the SSA technique for forecasting exchange rates. The forecasting performances of the SSA technique for one-step-ahead forecast of six exchange rate series are used to find the best L and r.

CLIMATOLOGICAL VARIATION OF GLOBAL CROSS-EQUATORIAL FLOWS FOR THE PERIOD 1948-2004

By using monthly NCEP/NCAR meridional gridpoint wind data at the levels of 1000, 850, 700, 600, 500, 400, 300, 200, 150 and 100 hPa from 1948 to 2004, the intensity of global cross-equatorial flows is calculated. The spatial and temporal variation of global cross-equatorial flows at the 850-hPa level are shown and discussed. The results show that the strength of the 850-hPa global cross-equatorial flows represent obvious long-term variation and interdecadal change during the period. Evidence suggests that the cross-equatorial flow of the passages at 45 - 50 °E in June to August, 105 - 115 °E in May to September, 130 - 140 °E in May to September and May to November and 20 - 25 °E in February to April intensified and that the cross-equatorial flow of the passages at 50 - 35 °W in June to August weaken in the past 57 years, with an increase of 0.25m/s/10a for summer Somali Jet and increase of 0.32 m/s/10a for cross- equatorial flow at 130 - 140 °E in May to September The results of Singular Spectrum Analysis （SSA） for the time series indicate that for the cross-equatorial flow at 850 hPa, the interdecadal and long-term trend changes are 35% - 45%, and the interarmual variation is no more than 30%, in variance contribution. The results also reveal that the interarmual variation of intensity of the summer cross-equatorial flows in the Pacific is significantly correlated with Southern Oscillation. With weak Southern Oscillation, strong crossequatorial flows in Pacific will happen, though the summer Somali Jet is only a little positively correlated with North Atlantic Oscillation （NAO）.

An Efficient Reference Free Adaptive Learning Process for Speech Enhancement Applications

In issues like hearing impairment,speech therapy and hearing aids play a major role in reducing the impairment.Removal of noise signals from speech signals is a key task in hearing aids as well as in speech therapy.During the transmission of speech signals,several noise components contaminate the actual speech components.This paper addresses a new adaptive speech enhancement(ASE)method based on a modified version of singular spectrum analysis(MSSA).The MSSA generates a reference signal for ASE and makes the ASE is free from feeding reference component.The MSSA adopts three key steps for generating the reference from the contaminated speech only.These are decomposition,grouping and reconstruction.The generated reference is taken as a reference for variable size adaptive learning algorithms.In this work two categories of adaptive learning algorithms are used.They are step variable adaptive learning(SVAL)algorithm and time variable step size adaptive learning(TVAL).Further,sign regressor function is applied to adaptive learning algorithms to reduce the computational complexity of the proposed adaptive learning algorithms.The performance measures of the proposed schemes are calculated in terms of signal to noise ratio improvement(SNRI),excess mean square error(EMSE)and misadjustment(MSD).For cockpit noise these measures are found to be 29.2850,-27.6060 and 0.0758 dB respectively during the experiments using SVAL algorithm.By considering the reduced number of multiplications the sign regressor version of SVAL based ASE method is found to better then the counter parts.

Theoretical Relationship between SSA and MESA with Both Application

It is theoretically demonstrated that singular spectrum analysis (SSA) is an equivalent form of Maximum Entropy Spectrum Analysis (MESA) which is essential1y a nonlinear estimation of the classical power spectrum. Both methods have respectively some different features in application as a result of the difference of description of manners. The numerical experiments show that SSA possesses some special advantage in climatic diagnosis and prediction, e.g., to steadily and accurately identify periods and investigate on domain of time in combination with frequency,which cannot be replaced by MESA. Thus SSA has extensive application in the near future.