@inproceedings{8dd0ceff1fbc4529b6c15fc4bc27db46,
title = "Approximation of average course of measured curvatures of mining area with reference to their forecast values by Bialek's formulas",
abstract = "The article presents the original results of the study concerning the way of approximation of average course of measured curvatures of mining area. The mean square approximation of average course of mining area subsidence with the use of a flat spline as a approximating function was conducted to determine an approximate course of curvatures observed on a measuring line set over exploitation run by {"}Chwa{\l}owice{"} coalmine. The assumed minimising criterion of loss function was referred to the forecast values of vertical ground displacements calculated via Bialek's formulas. The average courses of inclinations and curvatures of mining area were obtained via the calculation of their values by means of empirical formulas taking into consideration the obtained approximate values of measured subsidence. Subsequently, they were compared with the forecast values by Bialek's formulas and theoretical values obtained on the basis of empirical formulas including subsidence values forecast by Bialek's formulas. Due to that the determination of errors of the forecast and theoretical distributions of curvatures and estimation of usefulness of the conducted analyses was possible.",
author = "Justyna Orwat and Ryszard Mielim{\c a}ka",
note = "Publisher Copyright: {\textcopyright} 2017 Author(s).; International Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016 ; Conference date: 19-09-2016 Through 25-09-2016",
year = "2017",
month = jul,
day = "21",
doi = "10.1063/1.4992302",
language = "English",
series = "AIP Conference Proceedings",
publisher = "American Institute of Physics Inc.",
editor = "Simos, \{Theodore E.\} and Simos, \{Theodore E.\} and Charalambos Tsitouras",
booktitle = "International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016",
address = "United States",
}