DBPapers
DOI: 10.5593/SGEM2014/B21/S8.094

PRACTICAL QUESTIONS OF THE METHOD OF INTERPRETATION GEOPHYSICAL SIGNAL AS A VECTOR OF HILBERT SPACE

I. Lesso, P. Horovcak, P. Flegner, Z. Gasparova
Wednesday 1 October 2014 by Libadmin2014

References: 14th International Multidisciplinary Scientific GeoConference SGEM 2014, www.sgem.org, SGEM2014 Conference Proceedings, ISBN 978-619-7105-10-0 / ISSN 1314-2704, June 19-25, 2014, Book 2, Vol. 1, 729-736 pp

ABSTRACT
The contribution builds upon the series of papers by the authors in which the subject of utilization of abstract vector spaces for digital signal processing is dealt with. With the applications the authors are oriented on the field of geotechnology. In this contribution is shown the practical aspect in the choice of one out of several possible interpretations of the process signal as a vector of the space with an inner product. The criterion of the choice of the type of signal space and the method of expressing the signal as a vector of this space is the sufficient stability of the location of the stationary signal in this space. This contribution builds upon previous works of the authors in the area of utilization of abstract Hilbert spaces in control of specific processes. In this paper, some possibilities and aspects of visualization of concurrent vibrations in respect to efficient control of drilling are pointed out. In the contribution are processed some data obtained at the experimental drilling stand of the Slovak Academy of Sciences.

Keywords: rotary drilling, vibrations, Hilbert’s space, functional analyses, visualization of vectors

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