Determination of the Sensitivity of Heat Transfer Systems Using Global Sensitivity and Gaussian Processes

A critical aspect of the design of systems or experiments is a sensitivity analysis to determine the effects of the different variables. This is usually done by representing the response by a Taylor series and evaluating the first-order derivatives at a nominal operating point. When there is uncertainty about the operating point, the common approach is the construction of a response surface and Monte Carlo sampling based on the probability distribution of these uncertain variables. Because of the expense of Monte Carlo sampling, it is important to restrict the analysis to those variables to which the response is most sensitive. Identification of the most sensitive parameters can be conveniently done using Global sensitivity, which both defines the most critical variables and also quantifies the effects of interacting variables. This also can be a computationally expensive process and, for complex models, is generally prohibitively expensive. A solution is the use of Gaussian processes that allows one to create a response surface using easy-to-evaluate functions. This paper describes the use of these ideas for a heat transfer problem.