### msmac3D HAS Automatic Iteration WHICH IS Nonlinear Optimization!

Posted:

**Fri Apr 24, 2015 1:18 pm****msmac3D HAS Automatic Iteration**

*WHICH IS*Nonlinear Optimization!A SAE paper by Brach on Nonlinear Optimization in Vehicle Crash Reconstruction includes a

**Literature Review**Section which INCORRECTLY states:

- "It appears only two previous papers [1,2] consider the use of optimization methods in the reconstruction of vehicular crashes involving the collision. Both deal with the Optimizer utility that is part of the PC-CRASH reconstruction software[3]"
- REFERENCES

1. Moser, A. and Steffan, H., “Automatic Optimization of Pre-Impact Parameters Using Post Impact Trajectories and Rest Positions,” SAE Technical Paper 980373, 1998, doi:10.4271/980373.

2. Cliff, W. and Moser, A., “Reconstruction of Twenty Staged Collisions with PC-Crash's Optimizer,” SAE Technical Paper 2001-01-0507, 2001, doi:10.4271/2001-01-0507.

3. http://www.pc-crash.com

- REFERENCES

from the paper:

- from the
**ABSTRACT**- This paper describes an automatic iterative procedure which can quickly and efficiently iterate to a "best match" of the physical evidence with SMAC. Quantitative measures of the overall "fit" to the evidence, which guide the procedure, are discussed. Representative results from applications to experimental tests are presented

- from the
**PROBLEM STATEMENT**- "Many different optimization and error minimization routines were investigated [12-16]. A fundamental problem with the use of many of the investigated control algorithms was the inherent requirement that the functions must be continuous and/or linear. The collision and trajectories of vehicles can be highly non-linear events. Minor variations in starting conditions (i.e., speed, impact location) can produce major changes in the resulting rest positions (X, Y, PSI) and discontinuities in the calculated error evaluation terms. For example, during decelerations of the linear and angular velocities, as a vehicle rotates while it travels from separation to rest, the vehicle may “shoot off” tangentially in what has been described as a “dog leg” type of trajectory at any time that the velocity vector aligns with the longitudinal axis. Traditional function minimization techniques which require the evaluation of some form of derivatives (e.g., Cramer's rule, Newton’s method) or include the assumption of a linear function (Powell’s method, Broyden’s method) were found to fail in many instances where step changes were produced in the "function" by minor alterations of the variables. The final form of the function minimization routine is a customized routine roughly based upon an adaptation of the downhill simplex method of Nelder and Mead [17] and Press [15]"
- REFERENCES

12. Hostetter, G.H., Santina, M.S., D’Carpio-Montalvo, P. Analytical Numerical and Computational Methods for Science and Engineering, Prentice Hall,

Englewood Cliffs, NJ 1991, ISBN 0-13-026055-X

13. Forsythe, G.E., Malcolm, M.A., Moler, Computer Methods for Mathematical Computations, C.B.,Prentice-Hall. Inc. Englewood Cliffs, NJ 1977,

ISBN 0-13-165332-6

14. Etter, D.M., Fortran 77 with Numerical Methods for Engineers and Scientists, Benjamin/Cummings Publishing Company, Inc., 1994, ISBN 0-8053-1770-8

15. Press, W.H., Teukolsky, S.A.,Vetterling, W.T., Flannery, B.P., Numerical Recipes in Fortran. The Art of Scientific Computing ,Second Edition,

Cambridge University Press, 1992 ISBN-0 52143064 X

16. http://www.netlib.org/

17. Nelder, J.A., Mead, R. 1965 Computer Journal, vol 7, pp 308-313

- REFERENCES

- "Many different optimization and error minimization routines were investigated [12-16]. A fundamental problem with the use of many of the investigated control algorithms was the inherent requirement that the functions must be continuous and/or linear. The collision and trajectories of vehicles can be highly non-linear events. Minor variations in starting conditions (i.e., speed, impact location) can produce major changes in the resulting rest positions (X, Y, PSI) and discontinuities in the calculated error evaluation terms. For example, during decelerations of the linear and angular velocities, as a vehicle rotates while it travels from separation to rest, the vehicle may “shoot off” tangentially in what has been described as a “dog leg” type of trajectory at any time that the velocity vector aligns with the longitudinal axis. Traditional function minimization techniques which require the evaluation of some form of derivatives (e.g., Cramer's rule, Newton’s method) or include the assumption of a linear function (Powell’s method, Broyden’s method) were found to fail in many instances where step changes were produced in the "function" by minor alterations of the variables. The final form of the function minimization routine is a customized routine roughly based upon an adaptation of the downhill simplex method of Nelder and Mead [17] and Press [15]"

**Nonlinear Optimization!**

*WHICH IS*