NOISE REDUCTION METHOD FOR NONLINEAR TIME SERIES BASED ON PRINCIPAL MANIFOLD LEARNING AND ITS APPLICATION TO FAULT DIAGNOSIS

2006 ◽  
Vol 42 (08) ◽  
pp. 154 ◽  
Author(s):  
Jianhong YANG
Keyword(s):  
Time Series ◽  
Fault Diagnosis ◽  
Noise Reduction ◽  
Manifold Learning ◽  
Reduction Method ◽  
Nonlinear Time Series ◽  
Principal Manifold

A SMOOTHING ALGORITHM FOR NONLINEAR TIME SERIES

2004 ◽  
Vol 14 (03) ◽  
pp. 1037-1051 ◽  
Author(s):  
S. A. BILLINGS ◽  
K. L. LEE
Keyword(s):  
Time Series ◽  
Noise Reduction ◽  
Cross Validation ◽  
User Interaction ◽  
Nonlinear Time Series ◽  
Smoothing Algorithm ◽  
Wavelet Thresholding ◽  
Numerical Examples ◽  
Validation Method

A new NARMA based smoothing algorithm is introduced for chaotic and nonchaotic time series. The new algorithm employs a cross-validation method to determine the smoother structure, requires very little user interaction, and can be combined with wavelet thresholding to further enhance the noise reduction. Numerical examples are included to illustrate the application of the new algorithm.

Smooth Projective Nonlinear Noise Reduction

2013 ◽  
Author(s):  
David Chelidze
Keyword(s):  
Time Series ◽  
Noise Reduction ◽  
Broad Spectrum ◽  
Reduction Method ◽  
Orthogonal Decomposition ◽  
Topological Properties ◽  
Noisy Time Series ◽  
Nonlinear Noise ◽  
Proper Orthogonal ◽  
Smooth Orthogonal Decomposition

Many nonlinear or chaotic time series exhibit an innate broad spectrum, which makes noise reduction difficult. Locally projective noise reduction is one of the most effective tools. It is based on proper orthogonal decomposition (POD), and works for both map-like and continuously sampled time series. However, POD only looks at geometrical or topological properties of data and does not take into account the temporal characteristics of time series. Here we present a new smooth projective noise reduction method. It uses bundles of locally reconstructed trajectory strands and their smooth orthogonal decomposition (SOD) to identify smooth local subspaces. Restricting trajectories to these subspaces imposes temporal smoothness on the filtered time series. It is shown that SOD-based noise reduction significantly outperforms the POD-based method for continuously sampled noisy time series.

Multiple-channel Singular Spectrum Analysis-based noise reduction for MT data observed in Boso Peninsula, Japan

2021 ◽  
Author(s):  
Shu Kaneko ◽  
Katsumi Hattori ◽  
Toru Mogi ◽  
Chie Yoshino
Keyword(s):  
Time Series ◽  
Noise Reduction ◽  
Spectrum Analysis ◽  
Reduction Method ◽  
Time Series Data ◽  
Singular Spectrum Analysis ◽  
Series Data ◽  
Boso Peninsula ◽  
Singular Spectrum ◽  
Kanto Earthquake

<p>Off the coast of the Boso Peninsula, there is a triple junction of the Pacific Plate, the Philippine Sea Plate, and the North American Plate and the Boso Peninsula is one of the seismically active areas in Japan. There are also epicenter areas such as the 1703 Genroku Kanto Earthquake (M8.2), the 1923 Taisho Kanto Earthquake (M7.9), and the Boso Slow Slip which occurs every 6 years, which are geologically interesting places. To estimate the subsurface resistivity structure of the whole Boso area, Magnetotelluric (MT) survey with 41 sites (inter-sites distance of 7 km) has been conducted in 2014-2016, using U43 (12 sites, 1 Hz sampling ; Tierra Technica) and MTU-5, 5A, net (41 sites, 15, 150, and 2400 Hz sampling; Phoenix Geophysics). However, the Boso area is greatly affected by leak current from DC-driven trains, factories, and power lines, so the observed data are contaminated by artificial noises. When we tried to apply the conventional noise reduction method (e.g., remote reference (Gamble et al., 1979) and BIRRP (Chave and Thomson, 2004)) in frequency domain, the obtained MT sounding curve was not ideal. In particular, the phase between the periods of 20 and 400 sec was close to 0 degrees. It suggests that the method used is insufficient to reduce the near-field effect for the Boso data. Thus, we developed a new noise reduction method using MSSA (Multi-channel Singular Spectrum Analysis) as a pre-processing method in time domain.</p><p>The procedure is as follows;</p><p>(1) Decompose 6 component data (Hx, Hy, Ex, Ey, Hxr and Hyr: H and E means magnetic and electric field, respectively, x and y indicates NS and EW component, and r denotes the reference field observed at a quiet station) using MSSA into 6×M principal components (PCs).  Here, M shows the window length of MSSA.</p><p>(2) Check contribution and periods of each PC and eliminate the PCs which are corresponding to the longer periods of variation. That is “detrend” of the original data.</p><p>(3) Apply the second MSSA to the detrended time series data to separate signals and noises shorter than 400 sec.</p><p>(4) Calculating correlation coefficients between H and Hr and between E and Hr for each PC and select the PCs with higher correlation to reconstruct time series data to make MT analysis.</p><p>Then, we perform MT analysis by BIRRP to estimate apparent resistivity,</p><p>As a result, the coherences of H-Hr, and E-Hr were improved and the MT sounding curve became smoother than those results by the conventional noise reduction methods. This indicated that the effectiveness of the proposed noise reduction. However, further investigation in different periods and sites will be required.</p>

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