Time series of EIT chest images and singular value decomposition

1997 ◽  
Author(s):  
W.R.B. Lionheart
Keyword(s):  
Time Series ◽  
Singular Value Decomposition ◽  
Singular Value ◽  
Value Decomposition

Resolution and significant contributions of tidal forcing in flexible harmonic grouping computed using Singular Value Decomposition

2020 ◽  
Author(s):  
Adam Ciesielski ◽  
Thomas Forbriger
Keyword(s):  
Time Series ◽  
Singular Value Decomposition ◽  
Cross Talk ◽  
Singular Value ◽  
Model Parameters ◽  
Tidal Analysis ◽  
Tidal Forcing ◽  
Tidal Harmonics ◽  
Tidal Signal ◽  
Value Decomposition

<p>We present the results of our studies of singular value decomposition (SVD) of the forward operator in tidal analysis. Using the resolution matrix and the ratio between singular values, we distinguish significant contributions that compose the tidal signal and we study cross-talk within and between tidal groups. Using all harmonics from the tidal catalogue we investigate the resolution matrix properties with decreasing amplitude of harmonics. We demonstrate the loss of resolution even for harmonics of large amplitude with decreasing time-series length. Our further investigation shows the cross-talk from atmospherically induced gravity variation into a tidal signal (expected and unexpected, e.g. S1, Fi1, Sig1). We investigate the ability to determine the ratio of gravimetric factors of degree 2 and degree 3 tides from the specific tidal gravity signal recordings.</p><p><span>The main interest of tidal analysis is the accurate and precise determination of tidal parameters, which are amplitude (gravimetric) factor and phase lag, the quantities describing the Earth response to the tidal forcing. Tidal catalogues </span><span>define the tide generating potential in terms </span><span>of harmonics. Widely used software, like ETERNA or Baytap-G, uses a-priori grouping of harmonics which is based on reasonable considerations like the Rayleigh criterion of spectral resolution. Wave grouping is a model parameteri</span><span>s</span><span>ation used to make the analysis problem overdetermined by using assumptions regarding the model parameters (e.g. credo of smoothness, known free-core resonance parameters, known ratio between response to degree 2 and degree 3 forcing). </span><span>If</span><span> those assumptions are incorrect, this can lead to artefacts which might go unnoticed. This presents a limitation for example in the search for causes of temporal variation of tidal parameters, as reported recently. SVD of the unparameterised problem allows us to investigate these limitations.</span></p><p><span>In our analysis, SVD is a factorisation of a linear regression matrix. The regression matrix consists of tidal harmonics in-phase and quadrature signal for rigid Earth tide (tidal forcing to Earth surface). We compute time series for each harmonic present in Tamura tidal catalogue </span><span>by </span><span>using a modified version of "Predict" (ETERNA package). Resulting values can be, but do not need </span><span>to</span><span> be, grouped prior to SVD analysis. Other than with conventional programs, wave groups can not only be defined along the frequency axis. They can as well be used to separate harmonics of degree 2 and degree 3. SVD allows us to study the significance of tidal harmonics, cross-talk between harmonics or groups and matrix null space. Thus, we can discriminate the parameters with small singular value, which do not significantly contribute to the predicted tidal data or are noise-sensitive.</span></p>

A Singular Value Decomposition Approach to Similarity Evaluation Between Servo Loops of CNC Machine Tools

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Zhixiang Xu ◽  
Tim Green
Keyword(s):  
Time Series ◽  
Singular Value Decomposition ◽  
Similarity Measure ◽  
Machine Tools ◽  
Singular Value ◽  
Cnc Machine Tools ◽  
Cnc Machine ◽  
Similarity Ratio ◽  
Value Decomposition ◽  
Circular Interpolation

In most cases, the servo loops of computer numerically controlled (CNC) machine tools consist of position controllers, drivers, power transmissions, and tables. In the process of diagnosis, adjustment, and calibration of CNC machine tools, it is crucial to make servo loops’ performances as similar as possible, and ideally identical. This work is motivated by establishing a measure to evaluate the similarities between all coordinated axes. Based on the singular value decomposition (SVD) of time series, this contribution addresses an innovative approach to set up a similarity measure for evaluating the performances of CNC machines. A circular interpolation is carried out to sample the displacements of two involved axes into two independent time series. Then a special matrix called attractor is constructed from the time series and SVD algorithm is adopted to process attractors. As a result, a series of singular values is produced. From these values, the singular value ratio spectrum is formed and the similarity ratio, which numerically represents the similarity between the coordinated axes, is proposed. According to the similarity ratio, the similarity of the two series is compared. Finally, the approach has been validated by experimental measurements. The similarity measure presented in this paper provides an overall index on evaluating the mismatch between coordinated axes of CNC machine tools.

Acquisition of Embodied Knowledge on Gesture Motion by Singular Value Decomposition

2011 ◽  
Vol 15 (8) ◽  
pp. 1011-1018 ◽  
Author(s):  
Isao Hayashi ◽  
◽  
Yinlai Jiang ◽  
Shuoyu Wang ◽  
Keyword(s):  
Time Series ◽  
Singular Value Decomposition ◽  
Time Series Data ◽  
Singular Spectrum Analysis ◽  
Singular Value ◽  
Series Data ◽  
Embodied Knowledge ◽  
Interval Time Series ◽  
Nonverbal Information ◽  
Value Decomposition

Communication is classified in terms of verbal and nonverbal information. We discuss an acquisition method of knowledge from nonverbal information. In particular, a gesture is an efficient form of nonverbal communication as well as in verbal ways, and we formulate here a method that measures similarity and estimation between gestures. A gesture includes human embodied knowledge, and therefore the visible bodily actions can communicate particular messages. However, we have infinite patterns for gesture, determined by personality. Recently, the singular spectrum analysis method is utilized as an attractive method. In this paper, we propose a new method for acquiring embodied knowledge from time-series data on gestures using singular value decomposition. The motion behavior is categorized into several clusters with similarity and estimation between interval time-series data. We discuss the usefulness of the proposed method using an example of gesture motion.

A Singular Value Decomposition Approach to Servo Systems Diagnosis of CNC Machine Tools

2005 ◽  
Author(s):  
Zhixiang Xu ◽  
Tim Green ◽  
Jian Liu
Keyword(s):  
Time Series ◽  
Singular Value Decomposition ◽  
Machine Tools ◽  
Singular Value ◽  
Cnc Machine Tools ◽  
Cnc Machine ◽  
Servo Systems ◽  
Similarity Ratio ◽  
Value Decomposition ◽  
Circular Interpolation

Based on the Singular Value Decomposition (SVD) of time series, this contribution addresses an innovative approach to provide essential information about the condition of servo systems for servo fault location or servo parameters tuning during diagnosing and calibrating CNC machine tools. When carrying out circular interpolation, the displacements of two involved axes are sampled as two independent time series. We adopt SVD algorithm to process the sampled data. A special matrix called attractor is constructed. By applying the Singular Value Ratio (SVR) spectrum, we have proposed the similarity ratio and then the similarity of two series is compared. The similarity ratio reflects the degree of mismatch between the coordinated axes.

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