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# Multivariable Monte Carlo Analysis Methods in Traffic Accident Reconstruction Using Python

[+] Author Affiliations
Michael A. Knox

Knox & Associates, LLC, Jacksonville, FL

Paper No. IMECE2011-62242, pp. 639-653; 15 pages
doi:10.1115/IMECE2011-62242
From:
• ASME 2011 International Mechanical Engineering Congress and Exposition
• Volume 9: Transportation Systems; Safety Engineering, Risk Analysis and Reliability Methods; Applied Stochastic Optimization, Uncertainty and Probability
• Denver, Colorado, USA, November 11–17, 2011
• ISBN: 978-0-7918-5495-2

## abstract

The analysis involved in reconstructing a traffic crash often deals with multiple, codependent, stochastic variables such as departure angle measurements, coefficient of friction measurements, vehicle stiffness coefficients, and acceleration rates. The resulting analysis should appropriately lead to a range of possible vehicle speeds rather than a single speed output value. All too often, this speed range is reported as a continuous uniform distribution in which lower- and upper-bound values are just as probable as any value in between. In reality, vehicle speed ranges are more complex than can properly be represented by a range of equally-probable values. By using repeated iterations drawing on pseudo-random number generation algorithms, Monte Carlo methods have long held the key to performing such statistical analyses. Monte Carlo methods allow for the output of values that are, in most cases, normally distributed and can be used to approximate the probability density function associated with the particular output variable. While Monte Carlo analysis in traffic accident reconstruction has been addressed in a number of other papers, the issue of dealing with codependent variables and the propagation of variable values across multiple calculations has been less apparent in the literature. Understanding not only the application of Monte Carlo methods to multi-variable problems but also the codependent nature of the output distributions and the appropriate selection of input values is essential to the successful application of Monte Carlo algorithms. This paper will address the appropriate methods for implementing multi-variable Monte Carlo solutions for traffic accident reconstruction problems and provide a practical platform for developing algorithms using the Python programming language. Appropriate selection of input values and the use of pseudo-random number generators will be addressed, along with methods for handling the propagation of values through the course of multiple, codependent calculations. While this paper focuses on the implementation of algorithms using Python, these methods can just as readily by implemented using MATLAB, C/C++, FORTRAN, or a variety of other capable programming languages.

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