Current safety standards are based on maximum stiffness measures over a grid on the frontal surface of a vehicle. The safety of VRU is also influenced by the overall shape of the impacting vehicle. “Initial conditions” [IC] from the dominant crash scenarios are used for CAE simulations in Industrial practice to tweak designs. The IC’s to design for are decided based on cluster analysis from reconstructions of crash data. Currently, CAE methods to predict the outcomes (final resting state of interacting elements) of a crash deterministically, given the initial conditions are available. But there are no established methods to do the inverse process, that is ascertain the conditions at the initiation of the crash given the fina l static state of the interacting elements. Recorded data being the final resting state of the interacting elements, the inverse problem is of significance, and is usually tackled by heuristics and iterations augmenting physical laws. While reconstructions of specific cases require detailed observation and experienced personnel, it is hypothesized that estimating a distribution of the pre-impact measures in crashes is more robust with respect to a distribution of the post impact observation than that of individual crashes.

Individual cases from crash reconstruction, approximated to a Gaussian “normal” probability density function, were assumed for the probability of occurrence of individual cases. Crash physics was captured using a multibody simulation in MADYMO solver. An inverse Monte Carlo [MC] simulation with MADYMO solver as the system under study was modelled in “FME” module in statistical software “R”. A set of post-crash data on head hit location [O1] was generated using forward MC simulation. The variable parameters were four different vehicle profiles, relative position of 50M along vehicle lateral axis [I2] and the relative orientation of with respect to vehicle. The pedestrian represented using one 50th percentile male [50M] pedestrian model was not varied.

Starting with the distribution of “O1” and an “I2” distribution perturbed by up to 20% in mean value as input, an I2 was computed using inverse MC. The “I2” distribution from inverse MC showed less than 10% deviation from the original v3 data set mean with randomized values of untracked variables.

During the inverse MC process, the quality of “fit” to a desired O1 distribution was tracked using the sum of root mean square of differences between normalized density coefficients and a “relaxation parameter” computed as squared logarithmic probability to a normal distribution. The stabilization of the trackin g parameter indicated a robust solution.