A just published 2015 SAE paper 2015-01-1433 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.
- REFERENCES
From our 2003 SAE paper:
- 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
- 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]"
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Updates: Brach missed 7 Papers in the 2015 sloppy 'literature review'??!! The SAE peer review is pathetic!
Here's a list, more detail on the responses below.
Included in our 2003 SAE paper on 2003 3D optimization/Iteration of SMAC , we found the following papers on Optimization of crash reconstructions:
- "Automated Accident Reconstruction", Jones, Ian. S., SAE paper 750894
- A Computer Model to Operate the SMAC Program Automatically, Moffatt, C.A., Byrd, J. Jr. ,Highway Collision Reconstruction, Winter ASME Meeting 1980
- "CRASH-97 – Refinement of the Trajectory Solution Procedure",McHenry, B.G., McHenry, R.R.,SAE Paper 97-0949
- 'SMAC2003: The Automatic Iteration of SMAC",McHenry, B.G., McHenry, R.R.,SAE Paper 2003-01-0486
The following i found in a quick search in 2015 after reading the Brach paper: - Fengjiao Guan, Aditya Belwadi, Xu Han and King H. Yang , Paper No. IMECE2009-12810, pp. 567-573; 7 pages doi:10.1115/IMECE2009-12810
- SAE paper 2005-01-4063 Optimization Techniques Applied to the Problem of Ground Vehicles Accident Reconsruction
Guilherme Nobrega Martins, Mauro Speranza Neto - SAE paper 2012-01-0604 Sensitivity of Collision SImulation Results to Initial Assumptions
Bradley Heinrichs, Brian Mac Giolla Ri, Ross Hunter