Non-statistical physically reasonable technique for a posteriori estimation of experimental data error

Abstract

In the paper presented is an application of the physically based global method (PBGM) to a posteriori estimation of experimental data error. It is proposed here to build data error measures by spanning a high quality physically reasonable smoothing fit to data and treat it as a reference field for error estimation in a very similar way it is done in the postprocessing type error estimates used widely in FE or meshless methods, where the higher order (superconvergent) solutions are used for building error estimates (post-processing type of error estimators). The new technique is different from classical methods of experimental data error estimation as it provides non-statistical estimates of the data error and as such it may be applied to a wider range of problems, including cases when only a single data set is available (e.g., destructive testing) . And because the new approach builds the estimates while performing its standard physically based global-type approximation, it fully integrates other features of the PBGM approach like data interpolation, extrapolation or differentiation. In the paper the whole PBGM approach is presented, including the concept of the method formulated for the case of analysis of residual stress in railroad rails, discretisation with MFDM, then several PBGM a posteriori error estimates are introduced and results for test problems (benchmark and actual data) are shown.