Denoising method based on singular spectrum analysis and its applications in calculation of maximal liapunov exponent

2005 ◽  
Vol 26 (2) ◽  
pp. 179-184 ◽  
Author(s):  
Liu Yuan-feng ◽  
Zhao Mei
Keyword(s):  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Liapunov Exponent ◽  
Denoising Method ◽  
Singular Spectrum

scholarly journals An Improved VMD-Based Denoising Method for Time Domain Load Signal Combining Wavelet with Singular Spectrum Analysis

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Jingjing Fu ◽  
Fuyou Cai ◽  
Yonghao Guo ◽  
Hongda Liu ◽  
Wentie Niu
Keyword(s):  
Time Domain ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Permutation Entropy ◽  
Acquisition Time ◽  
Signal Denoising ◽  
Noisy Signal ◽  
Denoising Method ◽  
Singular Spectrum ◽  
Measured Load

Measured load data play a crucial role in the fatigue durability analysis of mechanical structures. However, in the process of signal acquisition, time domain load signals are easily contaminated by noise. In this paper, a signal denoising method based on variational mode decomposition (VMD), wavelet threshold denoising (WTD), and singular spectrum analysis (SSA) is proposed. Firstly, a simple criterion based on mutual information entropy (MIE) is designed to select the proper mode number for VMD. Detrended fluctuation analysis (DFA) is adopted to obtain the noise level of the noisy signal, which can optimize the selection of MIE threshold. Meanwhile, the noisy signal is adaptively decomposed into band-limited intrinsic mode functions (BLIMFs) by using VMD. In addition, weighted-permutation entropy (WPE) is applied to divide the BLIMFs into signal-dominant BLIMFs and noise-dominant BLIMFs. Then, the signal-dominant BLIMFs are reconstructed with the noise-dominant BLIMFs processed by WTD. Finally, SSA is implemented for the reconstructed signal. Experimental results of synthetic signals demonstrate that the presented method outperforms the conventional digital signal denoising methods and the related methods proposed recently. Effectiveness of the proposed method is verified through experiments of the measured load signals.

scholarly journals Multi-Channel Singular Spectrum Analysis on Geocenter Motion and Its Precise Prediction

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1403
Author(s):  
Xin Jin ◽  
Xin Liu ◽  
Jinyun Guo ◽  
Yi Shen
Keyword(s):  
Solid Earth ◽  
Spectrum Analysis ◽  
Mean Squared Error ◽  
Moving Average ◽  
Singular Spectrum Analysis ◽  
Singular Spectrum ◽  
Autoregressive Moving Average Model ◽  
Seasonal Characteristics ◽  
Geocenter Motion ◽  
Moving Average Model

Geocenter is the center of the mass of the Earth system including the solid Earth, ocean, and atmosphere. The time-varying characteristics of geocenter motion (GCM) reflect the redistribution of the Earth’s mass and the interaction between solid Earth and mass loading. Multi-channel singular spectrum analysis (MSSA) was introduced to analyze the GCM products determined from satellite laser ranging data released by the Center for Space Research through January 1993 to February 2017 for extracting the periods and the long-term trend of GCM. The results show that the GCM has obvious seasonal characteristics of the annual, semiannual, quasi-0.6-year, and quasi-1.5-year in the X, Y, and Z directions, the annual characteristics make great domination, and its amplitudes are 1.7, 2.8, and 4.4 mm, respectively. It also shows long-period terms of 6.09 years as well as the non-linear trends of 0.05, 0.04, and –0.10 mm/yr in the three directions, respectively. To obtain real-time GCM parameters, the MSSA method combining a linear model (LM) and autoregressive moving average model (ARMA) was applied to predict GCM for 2 years into the future. The precision of predictions made using the proposed model was evaluated by the root mean squared error (RMSE). The results show that the proposed method can effectively predict GCM parameters, and the prediction precision in the three directions is 1.53, 1.08, and 3.46 mm, respectively.

Application of singular spectrum analysis in reconstruction of the annual signal from GRACE

2020 ◽  
Vol 14 (3) ◽  
pp. 295-302
Author(s):  
Chuandong Zhu ◽  
Wei Zhan ◽  
Jinzhao Liu ◽  
Ming Chen
Keyword(s):  
Time Series ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Mixture Effect ◽  
Singular Spectrum ◽  
Grace Data ◽  
Terrestrial Water ◽  
Annual Signal ◽  
Long Term Variations

AbstractThe mixture effect of the long-term variations is a main challenge in single channel singular spectrum analysis (SSA) for the reconstruction of the annual signal from GRACE data. In this paper, a nonlinear long-term variations deduction method is used to improve the accuracy of annual signal reconstructed from GRACE data using SSA. Our method can identify and eliminate the nonlinear long-term variations of the equivalent water height time series recovered from GRACE. Therefore the mixture effect of the long-term variations can be avoided in the annual modes of SSA. For the global terrestrial water recovered from GRACE, the peak to peak value of the annual signal is between 1.4 cm and 126.9 cm, with an average of 11.7 cm. After the long-term and the annual term have been deducted, the standard deviation of residual time series is between 0.9 cm and 9.9 cm, with an average of 2.1 cm. Compared with the traditional least squares fitting method, our method can reflect the dynamic change of the annual signal in global terrestrial water, more accurately with an uncertainty of between 0.3 cm and 2.9 cm.

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