Publications

Sensitivity and uncertainty analysis of a polyurethane foam decomposition model

Hobbs, Michael L.; Robinson, David G.

Sensitivity/uncertainty analyses are not commonly performed on complex, finite-element engineering models because the analyses are time consuming, CPU intensive, nontrivial exercises that can lead to deceptive results. To illustrate these ideas, an analytical sensitivity/uncertainty analysis is used to determine the standard deviation and the primary factors affecting the burn velocity of polyurethane foam exposed to firelike radiative boundary conditions. The complex, finite element model has 25 input parameters that include chemistry, polymer structure, and thermophysical properties. The response variable was selected as the steady-state burn velocity calculated as the derivative of the burn front location versus time. The standard deviation of the burn velocity was determined by taking numerical derivatives of the response variable with respect to each of the 25 input parameters. Since the response variable is also a derivative, the standard deviation is essentially determined from a second derivative that is extremely sensitive to numerical noise. To minimize the numerical noise, 50-micron elements and approximately 1-msec time steps were required to obtain stable uncertainty results. The primary effect variable was shown to be the emissivity of the foam.