Methods of statistical uncertainty analysis applied to evaluation algorithms of a video-extensometer system

Abstract

This paper addresses methods for statistical uncertainty analysis to determine the measurement accuracy associated with a video-extensometer system. Two different approaches for statistical uncertainty analysis - a purely statistical and an analytical approximation - are presented. The statistical method is based on evaluation of images acquired at conditions of repeatability; whereas the analytical approach consists of application of the law of first order error propagation to the particular processing steps of the evaluation procedure. The derivation of the law of first order error propagation is briefly revised in order to emphasize possible sources of error caused by its application. Moreover, the computation of the Jacobian matrix required for first order approximations of error propagation is illustrated for explicit and implicit vector-valued functions as well as for linear least squares problems as this represents a task typically arising in metric vision applications. Finally, the two approaches are applied to the specific processing steps for the evaluation of the images acquired with the video-extensometer system. Comparison of the results obtained with the different methods show negligible deviations, proving the application of the law of first order error propagation to be a suitable means to analytically estimate statistical uncertainty.