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Methods for identification of uncorrelated forces acting in the machines

Kaźmierczak H., Kromulski J., Pawłowski T.

Vibrations in Physical Systems

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2008

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Vol. 23

189--194

EN

In the work presented are methods of identification of uncorrelated operational forces based on orthogonal decomposition of crosspower spectrum matrix. In this purpose were used methods based on eigen- and singular value decomposition of PSD matrix. Except methods in frequency domain were used methods in time domain (ICA - Independent Component Analysis) for identification statistically independent and principal component. The methods were used to identify the number of sources of the exciting forces acting during the work of a real mechanical system.

2

Inferring the global and partial system condition by means of multidimensional condition monitoring

Cempel C.

Vibrations in Physical Systems

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2008

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Vol. 23

79--94

EN

Machines have many faults which evolve during its life (operation). If one observe some number of symptoms during the machine operation it is possible to capture needed fault oriented information. One of the methods to extract fault information from such symptom observation matrix (SOM) is to apply the singular value decomposition (SVD), obtaining in this way the generalized fault symptoms. The problem of this paper is to use the total damage symptom, being a sum of all generalized symptoms, and the first generalized symptom to infer better on machine condition. There was some new software created for this purpose, and some cases of machine condition monitoring have been considered as examples. Considering these it seems to the author, that both generalized symptoms should be used for the inference on machine condition. They are complimentary each other in some way, and should be use together to increase the reliability of diagnostic decision.

3

The application of the matrix decomposition into singular values method for detecting changes of the system dynamic characteristics

Kromulski J., Kaźmierczak H., Pawłowski T.

Vibrations in Physical Systems

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2006

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Vol. 22

191--196

4

Properties of a Singular Value Decomposition Based Dynamical Model of Gene Expression Data

Simek K.

International Journal of Applied Mathematics and Computer Science

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2003

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Vol. 13, no 3

337-345

EN

Recently, data on multiple gene expression at sequential time points were analyzed using the Singular Value Decomposition (SVD) as a means to capture dominant trends, called characteristic modes, followed by the fitting of a linear discrete-time dynamical system in which the expression values at a given time point are linear combinations of the values at a previous time point. We attempt to address several aspects of the method. To obtain the model, we formulate a nonlinear optimization problem and present how to solve it numerically using the standard MATLAB procedures. We use freely available data to test the approach. We discuss the possible consequences of data regularization, called sometimes "polishing", on the outcome of the analysis, especially when the model is to be used for prediction purposes. Then, we investigate the sensitivity of the method to missing measurements and its abilities to reconstruct the missing data. Summarizing, we point out that approximation of multiple gene expression data preceded by SVD provides some insight into the dynamics, but may also lead to unexpected difficulties, like overfitting problems.