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.

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.

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.

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-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.

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.

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.

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.

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.

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.

联合TVF-EMD和SSA降噪的轴承故障特征提取

针对滚动轴承早期故障信号微弱、故障特征难以提取的问题,文章提出了一种基于时变滤波经验模态分解(time-varying filtering based empirical mode decomposition,TVF-EMD)模态分量自适应融合与奇异谱分析(singular spectrum analysis,SSA)降噪的滚动轴承早期故障特征提取方法。首先,为了降低故障信号的非线性和非平稳性,通过TVF-EMD将轴承信号分解为一系列内蕴模态函数(IMF)。其次,为了克服TVF-EMD分解后IMF分量过多的不足,利用IMF的峭度、复杂度和分形维数构造了复合敏感模态判定因子(composite sensitive mode determination factor,CSMDF),通过CSMDF对IMF分量进行降序排列,并依据复合敏感模态判定因子递增原则对IMF分量依次进行融合,直至找到最优融合分量。最后,通过SSA对最优融合分量降噪,对降噪后分量进行Hilbert包络谱分析,实现轴承故障的特征提取。通过仿真故障信号以及两个实测故障信号对所提方法的性能进行了试验分析,试验结果表明,该方法具有良好的敏感特征筛选融合能力和降噪能力,能更准确地提取出轴承早期故障特征,实现噪声环境下轴承故障类型的准确识别。

基于SSA-LSTM模型的水电站能效综合评价方法

随着我国电力体制改革不断深化,水电已告别传统粗放型发展模式,亟需配套更为成熟、通用的能效评价体系指导水电运行调度工作。因此,提出一种基于深度学习的水电站能效综合评价方法,引入长短期记忆网络(LSTM)构建水电站理论发电量模型,对于给定的原始发电序列,利用奇异谱分析(SSA)提取出其趋势项、周期项及噪声,对前二者分别构建LSTM网络模拟后叠加得到理论发电量计算结果,在此基础上提出相对增发效益指标、能效相对提高率指标,利用熵权法得到水电站综合得分值,进而对南部某省12座电站进行能效评价。结果表明,该方法可以充分反映水电在调度运行中的能效特点,研究结果对优化水电站调度策略、提高水电调度水平具有借鉴意义。

基于SSA−LSTM的转炉炼钢终点锰含量预测

锰是钢铁中重要的合金元素,加入适量锰元素能提高钢铁的性能.在转炉炼钢过程中锰元素的含量直接影响钢铁质量,锰元素加入过少会导致钢铁产品的硬度和强度不足,锰元素加入过量会导致钢铁过脆和生产成本增加.因此,合适的锰元素添加量对提升钢铁质量与减少冶炼成本具有重要意义.转炉炼钢过程中锰元素的添加量主要通过终点锰预测的结果来确定,然而,终点锰含量多少受到多个因素的综合影响,其中包括氧化反应进程和合金中其他元素的添加量,影响因素呈现非线性、高耦合的特征,导致终点锰预测难度大.针对转炉炼钢终点锰预测过程中数据有含噪声、强耦合性等问题,提出了一个转炉炼钢终点锰含量预测研究架构,基于长短期记忆网络(Long Short-term memory,LSTM)预测模型,引入奇异谱分析(Singular spectral analysis,SSA)方法去除终点锰预测过程中非线性、非平稳序列的高频噪声,提出了一种基于SSA−LSTM的终点锰含量预测方法.利用河北敬业钢铁有限公司转炉炼钢生产数据验证所提预测方法的平均绝对误差为1.19%,均方根误差为1.48%.结果表明,该方法能够解决数据存在较多噪声及非线性等问题;与已有的时间序列预测方法相比,经过SSA处理的预测误差均有所减小,证明了该方法的有效性,为实际生产过程中精准加入合金提供了依据.

基于SSA-LMD-GM的大坝变形组合预测模型

为提高大坝变形预测精度,针对大坝原始监测信号中的噪声,以及其非平稳性、非线性等特点,引入奇异谱分析(SSA)和局部均值分解(LMD)方法,提出SSA-LMD-GM模型。采用奇异谱分析(SSA)对原始监测信号进行去噪处理,为充分提取大坝形变信息特征,利用局部均值分解(LMD)对去噪后的监测信号进行分解。针对乘积函数(PF)分量的特征采用合适的模型预测分析,剩下余项则采用GM(1,1)模型。利用实际工程案例进行检验,结果表明,相较于其他模型,SSA-LMD-GM模型预测精度和拟合精度更加优秀,能较好地预测大坝变形趋势,具有一定的应用价值。

SIMULATION OF CRACK DIAGNOSIS OF ROTOR BASED ON MULTI-SCALE SINGUUR-SPECTRUM ANALYSIS

In the diagnosis of rotor crack based on wavelet analysis, it is a painful task to find out an adaptive mother wavelet as many of them can be chosen and the analytic results of different mother wavelets are yet not the same. For this limitation of wavelet analysis, a novel diagnostic approach of rotor crack based on multi-scale singular-spectrum analysis （MS-SSA） is proposed. Firstly, a Jeffcott model of a cracked rotor is developed and the forth-order Runge-Kutta method is used to solve the motion equations of this rotor to obtain its time response （signals）. Secondly, a comparatively simple approach of MS-SSA is presented and the empirical orthogonal functions of different orders in various scales are regarded as analyzing functions. At last, the signals of the cracked rotor and an uncracked rotor are analyzed using the proposed approach of MS-SSA, and the simulative results are compared. The results show that, the data-adaptive analyzing functions can capture many features of signals and the rotor crack can be identified and diagnosed effectively by comparing the analytic results of signals of the cracked rotor with those of the uncracked rotor using the analyzing functions of different orders.

基于CEEMDAN-WP-SSA的GPS/BDS-RTK多路径噪声抑制方法

针对GNSS-RTK技术在复杂环境下的多路径效应误差和随机噪声难以消除的问题,提出一种自适应完备集合经验模态分解(CEEMDAN)、小波包(WP)去噪和奇异谱分析(SSA)结合的联合去噪方法,来消除基线坐标序列的噪声影响,在此基础上构建适用于GPS/BDS组合的恒星日滤波模型。首先采用CEEMDAN方法将原始信号分解成若干个特征模态函数(IMF),使用排列熵区分高频和低频分量,然后分别利用WP和SSA对高频信号和低频信号进行去噪,最后重构去噪后信号并通过恒星日滤波削弱后续坐标序列里的多路径误差。实验结果表明,基于CEEMDAN-WP-SSA构建的恒星日滤波模型能够很好的去除随机噪声以及削弱多路径误差影响,与CEEMDAN和CEEMDAN-WP方法相比,文中方法东(E)、北(N)、高程(U)3个方向的定位精度分别提升约17%、23.6%、13.6%和17%、19.8%、10%。