DBPapers
DOI: 10.5593/SGEM2014/B12/S2.003

ABSTRACT SPACES AS ALTERNATIVE METHOD OF DATA PROCESSING ACQUIRED FROM UNDERGROUND ENGINEERING

K. Feriancikova, E. Lazarova, I. Lesso, V. Krupa, L. Ivanicova
Wednesday 1 October 2014 by Libadmin2014

References: 14th International Multidisciplinary Scientific GeoConference SGEM 2014, www.sgem.org, SGEM2014 Conference Proceedings, ISBN 978-619-7105-08-7 / ISSN 1314-2704, June 19-25, 2014, Book 1, Vol. 2, 17-24 pp

ABSTRACT
Hilbert spaces represent an individual chapter of modern mathematics, specifically within the functional analysis. In such space the process signal is considered as a function, i.e. a vector of abstract signal space. This fact allows to classify the process states based on geometric relations, without need for extracting the attributes. The method was applied in such process conditions, where it was impossible to use conventional mathematical methods in data processing due to process non-linearity, non-stationarity and stochastic behaviour, as well as due to inhomogeneities in the environment. Mechanized excavation of underground structures served as an example of such hard-to-identify process. The paper presents the application of abstract spaces for processing of data acquired from the tunnel excavation monitoring.

Keywords:functional analysis, geometric relations, abstract spaces