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.

Reduction of Artifacts in Images from MR Truncated Data Using Singularity Spectrum Analysis

In this paper, the theory of signal singularity spectrum analysis(SSA) is proposed. Using SSA theory, a new method is presented to reduce truncation artifacts in magnetic resonance (MR) image due to truncated spectrum data.In the scheme, after detecting signal singularity locations using wavelet analysis inspectrum domain, SSA mathematic model is constructed, where weight coefficientsare determined by known truncated spectrum data. Then, the remainder of thetruncated spectrum can be obtained using SSA. Experiment and simulation resultsshow that the SSA method will produce fewer artifacts in MR image from truncatedspectrum than existing methods.

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.

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.

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.

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.

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.

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.

An Example of Embedded Singular Continuous Spectrum for Discrete Schrödinger Operators

We present an example of a potential such that the corresponding discrete Schrödinger operator has singular continuous spectrum embedded in the absolutely continuous spectrum.

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.

Wavelet-based multifractal analysis of DNA sequences by using chaos-game representation

Chaos game representation （CGR） is proposed as a scale-independent representation for DNA sequences and provides information about the statistical distribution of oligonucleotides in a DNA sequence. CGR images of DNA sequences represent some kinds of fractal patterns, but the common multifractal analysis based on the box counting method cannot deal with CGR images perfectly. Here, the wavelet transform modulus maxima （WTMM） method is applied to the multifractal analysis of CGR images. The results show that the scale-invariance range of CGR edge images can be extended to three orders of magnitude, and complete singularity spectra can be calculated. Spectrum parameters such as the singularity spectrum span are extracted to describe the statistical character of DNA sequences. Compared with the singularity spectrum span, exon sequences with a minimal spectrum span have the most uniform fractal structure. Also, the singularity spectrum parameters are related to oligonueleotide length, sequence component and species, thereby providing a method of studying the length polymorphism of repeat oligonucleotides.

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.

基于奇异谱分析的南方涛动指数短期气候预测试验(英文)

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.

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.

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.

The Variability of the Interannual Oscillations of the Indian Summer Monsoon Rainfall

A new method of analysis namely, Singular Spectrum Analysis (SSA) is applied to the Indian Summer Monsoon (June-September) Rainfall (ISMR) series. The method is efficient in extracting the statistically significant oscillations with periods 2.8 and 2.3 year from the white noise of the ISMR series. The study shows that 2.8 / 2.3 year cycle captures the variability of the ISMR related to Southern Oscillation / Quasi Biennial Oscillation. The temporal structure of these oscillations show that these are in phase in extreme (excess and drought) monsoon conditions as well as in El Nino Southern Oscillation (ENSO) years. Both these oscillations show minimum variability during the period 1920-1940 and there is an increasing trend in the variability of these oscillations in the recent decades. The study enables to obtain pure signal consisting of reconstructed time series using these two Oscillations, from the original white noise series.

Abnormal State Detection of OLTC Based on Improved Fuzzy C-means Clustering

An accurate extraction of vibration signal characteristics of an on-load tap changer(OLTC)during contact switching can effectively help detect its abnormal state.Therefore,an improved fuzzy C-means clustering method for abnormal state detection of the OLTC contact is proposed.First,the wavelet packet and singular spectrum analysis are used to denoise the vibration signal generated by the moving and static contacts of the OLTC.Then,the Hilbert-Huang transform that is optimized by the ensemble empirical mode decomposition(EEMD)is used to decompose the vibration signal and extract the boundary spectrum features.Finally,the gray wolf algorithm-based fuzzy C-means clustering is used to denoise the signal and determine the abnormal states of the OLTC contact.An analysis of the experimental data shows that the proposed secondary denoising method has a better denoising effect compared to the single denoising method.The EEMD can improve the modal aliasing effect,and the improved fuzzy C-means clustering can effectively identify the abnormal state of the OLTC contacts.The analysis results of field measured data further verify the effectiveness of the proposed method and provide a reference for the abnormal state detection of the OLTC.

Multifractal characteristics of cylindrical sludge drying

This paper analyzes dewatered sludge drying using the multifractal theory.The drying rates of cylindrical sludge with equal masses but different crosssectional diameters was studied,from which multifractal parameters such as partition function and quality exponent were obtained.The parameters acquired were used to calculate the multifractal singularity spectrum and indicate the presence of multifractal characteristics.The smaller cross-sectional diameters of the sludge were found to be non-homogeneous,and required quantitative methods to analyze.