Application of the Monte Carlo Methods for Stability Analysis within the Accident Reconstruction Software PC-CRASH 2003-01-0488
During recent years the accident simulation program PC-CRASH was developed, which allows simulating the vehicles movement before, during and after the impact. As shown in several publications [3, 7], the software allows the calculation of the 3D movement of all involved vehicles. Within SAE 980373 an optimization tool was demonstrated, which allows one to vary pre crash conditions automatically and to determine the solution, which fulfills predefined target functions best. This method has proven to determine a set of initial conditions, which fulfill the predefined target functions, within a reasonable amount of time.
As in most accident reconstruction cases, several parameters, like ground friction or inter-vehicle friction are not well known, as well as many vehicle or driver related parameters. A method was developed, which allows one to vary multiple parameters based on a Monte Carlo method. The error within the fulfillment of the target function can thus easily be used as a quality indicator for the selected initial conditions.
In this way it is possible to determine how stable the solution is and what amount of variation within the input parameters must be expected.
Two algorithms are presented, both based on the Monte Carlo approach. The first one serves as an alternative for the optimizer tool and is included in the current version of PC-Crash. It gives reasonable insight in the variation of certain parameters in reasonable calculation time. The second one was developed by the Netherlands Forensic Institute as a systematic approach to obtain a-posteriori distributions for the pre crash velocities. Both algorithms are illustrated by examples. In both algorithms, the Quality Function or Trajectory Error plays an important role, and will be discussed first.