Comparison of the V&V10.1 and V&V20 Modeling Error Quantification Procedures for the V&V10.1 Example

The determination of the transverse tip deflection of an elastic, hollow, tapered, cantilever, box beam under a uniform loading applied over half the length of the beam presented in the V&V10.1 standard is used to compare the application of the validation procedures presented in the V&V10.1 and V&V20 standards. Both procedures aim to estimate the modeling error of the mathematical/computational model used in the simulations taking into account the variability of the modulus of elasticity of the material used in the beam and the rotational flexibility at the clamped end of the beam. The paper discusses the four steps of the two error quantification procedures: (1) characterization of the problem including all the assumptions and approximations made to obtain the experimental and simulation data; (2) selection of the validation variable; (3) determination of the different quantities required by the validation metrics in the two error quantification procedures; (4) outcome of the two validation procedures and its discussion. The paper also discusses the inclusion of experimental, input, and numerical uncertainties (assumed or demonstrated to be negligible in V&V10.1) in the two validation approaches. This simple exercise shows that different choices are made in the two alternative approaches, which lead to different ways of characterizing the modeling error. The topics of accuracy requirements and validation comparisons (model acceptance/rejection) for engineering applications are not addressed in this paper.