Error quantification in mechanics computational models

Abstract

This paper proposes an error quantification methodology for mechanics computational models. The error of a computational model prediction consists of two parts: model form error and numerical error. Numerical error is affected by various sources. This paper focuses on input/output data measurement error, discretization error in FEA, surrogate model error, and uncertainty quantification error. The input/output data measurement error can be characterized based on knowledge about the instruments and the measurement processes. The discretization error in FEA is quantified by the Richardson extrapolation technique. The surrogate model error is quantified using regression analysis results. The overall numerical error is obtained through a nonlinear combination of these error components, some of which can be nested. A sensitivity analysis is performed to asses the contribution of each error component to the variance of the model prediction. Further, uncertainty quantification error arises from sampling techniques used to quantify the above errors, and is also quantified as a second level error in the proposed methodology. Once the overall numerical error is quantified, the model form error is then quantified using observed output data. Numerical examples using structural problems are presented to illustrate the proposed methodology. ©2010 Society for Experimental Mechanics Inc.