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.

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.

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>

scholarly journals Using SVD on Clusters to Improve Precision of Interdocument Similarity Measure

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Wen Zhang ◽  
Fan Xiao ◽  
Bin Li ◽  
Siguang Zhang
Keyword(s):  
Singular Value Decomposition ◽  
Linear Algebra ◽  
Similarity Measure ◽  
Latent Semantic Indexing ◽  
Singular Value ◽  
Semantic Indexing ◽  
Discriminative Power ◽  
Good Representative ◽  
Value Decomposition ◽  
Dimension Expansion

Recently, LSI (Latent Semantic Indexing) based on SVD (Singular Value Decomposition) is proposed to overcome the problems of polysemy and homonym in traditional lexical matching. However, it is usually criticized as with low discriminative power for representing documents although it has been validated as with good representative quality. In this paper, SVD on clusters is proposed to improve the discriminative power of LSI. The contribution of this paper is three manifolds. Firstly, we make a survey of existing linear algebra methods for LSI, including both SVD based methods and non-SVD based methods. Secondly, we propose SVD on clusters for LSI and theoretically explain that dimension expansion of document vectors and dimension projection using SVD are the two manipulations involved in SVD on clusters. Moreover, we develop updating processes to fold in new documents and terms in a decomposed matrix by SVD on clusters. Thirdly, two corpora, a Chinese corpus and an English corpus, are used to evaluate the performances of the proposed methods. Experiments demonstrate that, to some extent, SVD on clusters can improve the precision of interdocument similarity measure in comparison with other SVD based LSI methods.

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