Publication Date


Document Type


Committee Members

Ramana Grandhi (Advisor), Alan Johnson (Committee Member), Ravi Penmetsa (Committee Member), Joseph Slater (Committee Member), Daniel Voss (Committee Member)

Degree Name

Doctor of Philosophy (PhD)


In general, more than one simulation model can be created to analyze and design engineering systems. Uncertainty is inevitably involved in selecting a single best approximating model from among a set of simulation models. Uncertainty in model selection (called model-form uncertainty in the present research) cannot be ignored, especially when the differences between the predictions by plausible models are significant. Also, each simulation model involves uncertainty in its input parameters and unknown errors in its predictions of system responses. A methodology is developed to quantify model-form uncertainty using the differences between experimental data measured from an engineering system and model predictions of the data which may involve parametric and/or predictive uncertainty under a Bayesian statistical framework. The proposed methodology is numerically demonstrated with two engineering problems.

Given that model-form uncertainty is quantified, two model combination techniques called the adjustment factor approach and model averaging are utilized to incorporate model-form uncertainty in response prediction by combining predictions by a model set. A nonlinear vibration system is used to illustrate the processes for implementing the adjustment factor approach and model averaging.

The proposed methodology is applied to quantify multiple types of uncertainty associated with the finite element simulation of a laser peening process. The adjustment factor approach is utilized to incorporate model-form uncertainty alone into the composite prediction of a residual stress field, while model averaging is utilized to incorporate parametric uncertainty and predictive uncertainty in addition to model-form uncertainty. Using the composite prediction of the residual stress field, a confidence band for the predicted residual stress field is established to indicate the reliability of the composite prediction.

Although the proposed methodology can effectively quantify model-form uncertainty given observed experimental data, it does not supply any practical framework for quantifying model-form uncertainty depending on expert evidence. Another methodology is developed to quantify both model-form and parametric uncertainty using human expertise under evidence theory, which handles imprecise human knowledge more realistically than probability theory. The process for implementing the proposed methodology is numerically demonstrated with the nonlinear vibration system problem. The laser peening process problem is addressed to examine the applicability of the proposed methodology to large-scale physics-based simulations.

Page Count


Department or Program

Ph.D. in Engineering

Year Degree Awarded


Included in

Engineering Commons