R. Mielimąka

Approximation of average course of measured curvatures of mining area with reference to their forecast values by Bialek’s formulas

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 “Chwalowice” coalmine. The assumed minimising criterion of loss function was referred to the forecast values of vertical ground displacements calculated via Knothe’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.

Smoothing parameter as shape parameter of function approximating the average course of terrain surface subsidence

In this article have been presented the approximation results of average course of mining area subsidence measured at observational line and caused by hard coal exploitation, which was conducted by some hard coal mine in Poland. An approximation has been done with the use of smoothed spline function with value change of smoothing parameter of approximating function. The right value of smoothing parameter has been chosen by the use of least squares method, what means the minimization of differences sum between the measured terrain subsidence and their average values.