Davis, G. and Mudgal, A., "Bayesian Uncertainty Quantification for Planar Impact Crashes via Markov Chain Monte Carlo Simulation," SAE Technical Paper 2016-01-1481, 2016, doi:10.4271/2016-01-1481.
A continuing topic of interest is how to best use information from Event Data Recorders (EDR) to reconstruct crashes. If one has a model which can predict EDR data from values of the target variables of interest, such as vehicle speeds at impact, then in principle one can invert this model to estimate the target values from EDR measurements. In practice though this can require solving a system of nonlinear equations and a reasonably flexible method for carrying this out involves replacing the inverse problem with nonlinear least-squares (NLS) minimization. NLS has been successfully applied to two-vehicle planar impact crashes in order to estimate impact speeds from different combinations of EDR, crush, and exit angle measurements, but an open question is how to assess the uncertainty associated with these estimates. This paper describes how Markov Chain Monte Carlo (MCMC) simulation can be used to quantify uncertainty in planar impact crashes. The basic ideas are first illustrated with a simple computational example and then the MCMC approach is applied to several examples which have been previously reconstructed using NLS. As would be expected, in each case the MCMC point estimates are similar to those produced by NLS, but defensible confidence intervals for the estimates are also produced.