Fleck, G. and Daily, J., "Sensitivity of Monte Carlo Modeling in Crash Reconstruction," SAE Int. J. Passeng. Cars – Mech. Syst. 3(1):100-112, 2010, doi:10.4271/2010-01-0071.
The Monte Carlo method is a well-known technique for propagating uncertainty in complex systems and has been applied to traffic crash reconstruction analysis. The Monte Carlo method is a probabilistic technique that randomly samples input distributions and then combines these samples according to a deterministic model. However, describing every input variable as a distribution requires knowledge of the distribution, which may or may not be available, and the time and expense of determining the distribution parameters may be prohibitive. Therefore, the most influential parameters from the input data, such as mean values, standard deviations, shape parameters, and correlation coefficients, can be determined using an analytical sensitivity calculation based on the score function. In this paper, some probability concepts are reviewed, the score function methodology is explained and a probabilistic sensitivity analysis is completed on a crush energy determination example specific to traffic crash reconstruction. The computed sensitivity values were obtained using analytical derivatives which only required a single Monte Carlo simulation. The analytical derivative values are compared to a finite difference value to demonstrate numerical accuracy. These sensitivity results provide insight into the extent each input parameter will influence the output distribution, thus allowing the analyst to focus efforts on characterizing the most influential input distribution parameters. Moreover, the sensitivity values help determine the effect of correlation in a probabilistic analysis.