A Bayesian approach for quantification of model uncertainty

In most engineering problems, more than one model can be created to represent an engineering systemʹs behavior. Uncertainty is inevitably involved in selecting the best model from among the models that are possible. Uncertainty in model selection cannot be ignored, especially when the differences between the predictions of competing models are significant. In this research, a methodology is proposed to quantify model uncertainty using measured differences between experimental data and model outcomes under a Bayesian statistical framework. The adjustment factor approach is used to propagate model uncertainty into prediction of a system response. A nonlinear vibration system is used to demonstrate the processes for implementing the adjustment factor approach. Finally, the methodology is applied on the engineering benefits of a laser peening process, and a confidence band for residual stresses is established to indicate the reliability of model prediction.