Integrating Monte Carlo Simulation, Momentum-Based Impact Modeling, and Restitution Data to Analyze Crash Severity

Abstract

Crash severity is quantified by the change in velocity experienced by a vehicle during an impact along with the time duration over which that change in velocity occurs. Since the values of the input parameters for calculating the change in velocity are not known exactly, there is uncertainty associated with the calculated change in velocity. Accurate evaluation of the crash severity will, therefore, include analysis of the effect that uncertainties in the values of the input parameters have on the calculated change in velocity. Monte Carlo simulation, a statistical technique, enables the reconstructionist to evaluate the effect of uncertainty on the analysis of crash severity. Use of the Monte Carlo simulation technique is beneficial since a reconstructionist can enter a range of values for each input parameter. A probability distribution can be assigned to the range of values, which indicates the likelihood that any value in that range corresponds to the actual value of the parameter. The simulation generates thousands of possible combinations of the input parameters selected from the specified ranges, monitors the results of the combinations and analyzes them statistically. Application of the Monte Carlo technique is intended to improve the legitimacy of crash severity analysis by helping the reconstructionist consider a wide range of possible solutions within the bounds of the imperfect data and report statistically meaningful ranges for the change in velocity. This paper demonstrates the application of the Monte Carlo technique to impact severity analysis using a derived two-dimensional, rigid body, momentum-based impact model. Thorough guidance is given to aid the reconstructionist in integrating the momentum model with the Monte Carlo simulation technique and this method is illustrated with a case study. Since the impact model employs restitution constraints in the normal and tangential directions, the effect of uncertainty in formulating appropriate ranges for the values of the restitution coefficients is discussed. NOTATION m mass I moment of inertia V velocity