The use of math models is a major component of engineering design. And almost all designs are based upon simulations. Structural mechanics usually utilize a finite element methodology, thermal-fluid analysis is often based on a finite volume approach, while finite difference numerical approximations can be used for differential equations. The simulations require input parameters that represent constitutive models, material properties, boundary conditions, initial conditions, geometry and often other approximations that influence the model.

Two major questions about simulation are: 1) how sensitive is the model to specific parameters and which parameters affect the desired output from the model, 2) if the inputs are uncertain (e.g., material properties, heat transfer correlations, turbulence models) how does this uncertainty affect the final result.

The course will consist of:

- Discussion of the general nature of uncertainty and validation.
- Statistical properties of uncertainty.
- Analysis of simple problems (bending of a beam, etc.) based on strength of material formulations to describe how the uncertainty affects results (e.g., deflection, stresses).
- Comparable analysis of thermal-fluid systems (conduction, convection and radiation).
- Development of methods to define the sensitivity of the models to the inputs and how this sensitivity is propagated through the model.
- Local and Global sensitivity analysis.
- Application of these ideas to FEM and CFD codes (ANSYS, COMSOL) for more complex systems
- How does one design an experiment to minimize the effects of uncertainty when estimating properties?
- Discussion of the current status of Uncertainty Quantification in the technical world.

Note that the analyses will require data (e.g., forces applied to the beam, heat sources for the thermal problems). While some of the data will be simulated, we will also conduct a few real experiments.These real experiments will be done in the ME labs either as demonstrations or by the students.

Prerequisites: IND E 315 Probability and Statistics for Engineers or an equivalent; Undergraduate courses covering fluids, heat transfer, and strength of materials; ability to use MATLAB.