PRACA ORYGINALNA
NONLINEAR METHOD OF VEHICLE VELOCITY DETERMINATION BASED ON INVERSE SYSTEM AND TENSOR PRODUCT OF LEGENDRE POLYNOMIALS - INTERMEDIATE CLASS
Lukasz Goslawski 1  
,  
Jacek Gralewski 2, 3  
,  
Mateusz Krukowski 3  
,  
Przemyslaw Kubiak 1  
,  
Maria Manko 4  
,  
Adam Mrowicki 1  
,  
Ewa Sys 1  
 
 
Więcej
Ukryj
1
Department of Vehicles and Fundamentals of Machine Design, Lodz University of Technology, Polska
2
Institute of Social Sciences and Management of Technologies, Lodz University of Technology, Polska
3
Institute of Mathematics, Lodz University of Technology, Polska
4
Institute of Polymer and Dye Technology, Faculty of Chemistry, Lodz University of Technology, Polska
5
Department of Mechanical Engineering, Universidade de Aveiro, Portugal
AUTOR DO KORESPONDENCJI
Przemyslaw Kubiak   

Department of Vehicles and Fundamentals of Machine Design, Lodz University of Technology, 1/15 Stefanowskiego Str.,, 90-924, Lodz, Polska
Data publikacji: 29-03-2019
Data nadesłania: 05-02-2019
Data ostatniej rewizji: 06-03-2019
Data akceptacji: 15-03-2019
 
The Archives of Automotive Engineering – Archiwum Motoryzacji 2019;83(1):133–149
SŁOWA KLUCZOWE
DZIEDZINY
STRESZCZENIE ARTYKUŁU
Presented paper discusses two different nonlinear approaches to precrash velocity determination for vehicles from Intermediate Car Class. Data that was used to perform analyses introduced in this paper was taken from National Highway Traffic Safety Administration (NHTSA) database. Such database is comprised of substantial number of crash cases and main focus was put on frontal impacts. Hitherto used energy methods are based on linear model which proves to be inaccurate and producing significant errors. Presented considerations concern the inverse system and tensor product of Legendre polynomials. The focus of those methods is to establish the value of nonlinear coefficient which is the slope factor of precrash velocity Vt and deformation ratio Cs function. The application of the least square method provides more precise results in both cases than in previously researched solutions, with a slight advantage of the tensor product method. The obtained mean relative error of the velocity determination using the inverse system method is approximately 16,22% for the linear model and 10,58% for the nonlinear model. In the case of the tensor product method the errors for linear and nonlinear models are respectively 6,74% and 6,3%.
 
REFERENCJE (39)
1.
Axler S. Linear Algebra Done Right, Springer, New York, 1997.
 
2.
Campbell BJ. The traffic accident data project scale. InCollision Investigation Methodology Symposium, Warrenton, VA 1969 Aug.
 
3.
Cheney W., Kincaid D. Numerical Analysis. Mathematics of Scientific Computing, Wadsworth Group, 2002.
 
4.
Cromack J.R., Lee SN. Consistency study for vehicle deformation index. SAE Technical Paper; 1974 Feb 1., doi: 10,4271 / 740299.
 
5.
Faraj R., Holnicki-Szulc J., Knap L., Seńko J. Adaptive inertial shock-absorber. Smart Materials and Structures. 2016 Feb 22;25(3):035031., doi: 10.1088 / 0964-1726 / 25/3/035031.
 
6.
Foret-Bruno J.Y., Trosseille X., Le Coz J.Y., Bendjellal F., Steyer C., Phalempin T., Villeforceix D., Dandres P., Got C. Thoracic injury risk in frontal car crashes with occupant restrained with belt load limiter. SAE Technical Paper; 1998 Nov 2., doi: 10.4271 / 983166.
 
7.
Geigl B.C., Hoschopf H., Steffan H., Moser A. Reconstruction of occupant kinematics and kinetics for real world accidents. International journal of crashworthiness. 2003 Jan 1;8(1):17-27., doi: 10,1533/ijcr.2003.0217.
 
8.
Gidlewski M., Żardecki D. Linearization of the lateral dynamics reference model for the motion control of vehicles. Mechanics Research Communications. 2017 Jun 1;82:49-54., doi: 10.1016/j.mechrescom.2016.09.001.
 
9.
Gidlewski M., Jemioł L., Żardecki D. Sensitivity investigations of lane change automated process. 23rd International Conference ENGINEERING MECHANICS 2017, Location: Svratka, Czech Republic, Date: MAY 15-18, 2017. Book Series: Engineering Mechanics 2017, Pages: 361 330-333. 362.
 
10.
Gidlewski M., Prochowski L. Analysis of motion of the body of a motor car hit on its side by another passenger car. Scientific Conference on Automotive Vehicles and Combustion 36 Engines (KONMOT) Location: Krakow, POLAND, Date: SEP 22-23, 2016. Book Series: IOP 369 Conference Series: Materials Science and Engineering. Vol. 148/2016 Paper Number 012039., doi: 10.1088/1757-899X/148/1/012039.
 
11.
Gidlewski M., Żardecki D. Simulation-Based Sensitivity Studies of a Vehicle Motion Model. 20th International Scientific Conference TRANSPORT MEANS 2016, Location: Juodkrante, Lithuania, Date: OCT 05- 07, 2016. Book Series: Transport Means –Proceedings of the International Conference, Pages: 236-240., Issn:1822-296X.
 
12.
Grolleau V., Galpin B., Penin A., Rio G. Modelling the effect of forming history in impact simulations: evaluation of the effect of thickness change and strain hardening based on experiments. International journal of crashworthiness. 2008 Jul 15;13(4):363-73., doi: 10.1080/13588260801976120.
 
13.
Han I., Kang H., Park J.C., Ha Y. Three-dimensional crush measurement methodologies using two- dimensional data. Transactions of the Korean Society of Automotive Engineers. 2015;23(3):254-62.
 
14.
Han I. Analysis of vehicle collision accidents based on qualitative mechanics. Forensic science international. 2018 Oct 1;291:53-61., doi: 10.1016 / j.forsciint.2018.08.004.
 
15.
Han I. Vehicle collision analysis from estimated crush volume for accident reconstruction. International Journal of Crashworthiness. 2018 Feb 1:1-6., doi: 10.1080/13588265.2018.1440499.
 
16.
Hight P.V., Fugger T.F., Marcosky J. Automobile damage scales and the effect on injury analysis. SAE Technical Paper; 1992 Feb 1., doi: 10.4271/920602.
 
17.
Iraeus J., Lindquist M. Pulse shape analysis and data reduction of real-life frontal crashes with modern passenger cars. International Journal of Crashworthiness. 2015 Nov 2;20(6):535-46., doi: 10.1080/13588265.2015.1057005.
 
18.
Kubiak P., Mierzejewska P., Krukowski M. Nonlinear methods of vehicle velocity determination based on inverse systems and tensor products of Legendre polynomials in compact car class. Forensic Science International. 2019 Feb., Vol. 295, pp. 19-29., doi: 10.1016/j.forsciint.2018.11.023.
 
19.
Krukowski M., Kubiak P., Mrowicki A., Siczek K., Gralewski J. Non-linear method of determining vehicle pre-crash speed based on tensor B-spline products with probabilistic weights — Intermediate Car Class. Forensic Science International. 2018 Dec., Vol. 293, pp. 7-16., doi: 10.1016/j.forsciint.2018.10.011.
 
20.
Kubiak P. Nonlinear approximation method of vehicle velocity Vt and statistical population of experimental cases. Forensic Science International. 2017 Dec 31; Vol. 281, pp. 147-51., doi: 10.1016/j.forsciint.2017.10.032.
 
21.
Kubiak P. Work of non-elastic deformation against the deformation ratio of the Subcompact Car Class using the variable correlation method. Forensic science international. 2018 Jun 1; Vol. 287, pp.47-53., doi: 10.1016 / j.forsciint.2018.03.033.
 
22.
Lindquist M., Hall A., Björnstig U. Real world car crash investigations - A new approach. International Journal of Crashworthiness. 2003 Jan 1;8(4):375-84., doi: 10,1533/ijcr.2003.0245.
 
23.
Mackay G.M., Hill J., Parkin S., Munns J.A. Restrained occupants on the nonstruck side in lateral collisions. Accident Analysis & Prevention. 1993 Apr 1;25(2):147-52., doi: 10,1016/0001-4575(93)90054-Z.
 
24.
Mannering F.L., Bhat C.R. Analytic methods in accident research: Methodological frontier and future directions. Analytic methods in accident research. 2014 Jan 1;1:1-22., doi: 10.1016 / j.amar.2013.09.001.
 
25.
McHenry B.G. The algorithms of CRASH. InSoutheast Coast Collision Conference 2001 Aug (pp. 1-34).
 
26.
McHenry R. Computer Program for Reconstruction of Highway Accidents, SAE Technical Paper 730980, Society of Automotive Engineers, 1973, doi: 10.4271/730980.
 
27.
Nelson W.D. The History and Evolution of the Collision Deformation Classification SAE J224 MAR80. SAE Technical Paper; 1981.
 
28.
Neptune J.A. Crush stiffness coefficients, restitution constants, and a revision of CRASH3 & SMAC. SAE Technical Paper; 1998 Feb 23.
 
29.
Norros I., Kuusela P., Innamaa S., Pilli-Sihvola E., Rajamäki R. The Palm distribution of traffic conditions and its application to accident risk assessment. Analytic methods in accident research. 2016 Dec 1;12:48-65., doi: 10.1016/j.amar.2016.10.002.
 
30.
Sharma D., Stern S., Brophy J., Choi E. An overview of NHTSA’s crash reconstruction software WinSMASH. InProceedings of the 20th International Technical Conference on Enhanced Safety of Vehicles 2007 Jun 18.
 
31.
Siddall D.E. Day TD. Updating the vehicle class categories. SAE Technical Paper; 1996 Feb 1., doi: 10,4271/960897.
 
32.
Vangi D., Cialdai C. Evaluation of energy loss in motorcycle-to-car collisions. International Journal of Crashworthiness. 2014 Jul 4;19(4):361-70., doi: 10.1080 / 13588265.2014.899072.
 
33.
Vangi D. Simplified method for evaluating energy loss in vehicle collisions. Accident Analysis & Prevention. 2009 May 1;41(3):633-41., doi: 10.1016 / j.aap.2009.02.012.
 
34.
Wach W., Unarski J. Determination of vehicle velocities and collision location by means of Monte Carlo simulation method. SAE Technical Paper; 2006 Apr 3., doi: 10.4271/2006-01-0907.
 
35.
Wach W., Gidlewski M., Prochowski L. Modelling reliability of vehicle collision reconstruction based on the law of conservation of momentum and Burg equations. 20th International Scientific Conference TRANSPORT MEANS 2016, Location: Juodkrante, Lithuania, Date: OCT 05- 07, 2016. Book Series: Transport Means – Proceedings of the International Conference, Pages: 693-698.
 
36.
Wang W., Sun X., Wei X. Integration of the forming effects into vehicle front rail crash simulation. International Journal of Crashworthiness. 2016. Jan 2;21(1)., pp. 9-21., doi: 10.1080/13588265.2015.1091170.
 
37.
Wąsik M., Skarka W. Simulation of Crash Tests for Electrically Propelled Flying Exploratory Autonomous Robot, Transdisciplinary Engineering: Crossing Boundaries Proceedings of the 23rd ISPE Inc. International Conference on Transdisciplinary Engineering October 3–7, 2016. Nel Wognum, Milton Borsato, Margherita Peruzzini, Josip Stjepandić and Wim J.C. Verhagen. Amsterdam: IOS Press, 2016.
 
38.
Wood D.P., Simms C.K. Car size and injury risk: a model for injury risk in frontal collisions. Accident Analysis & Prevention. 2002 Jan 1;34(1):93-9., doi: 10.1016/S0001-4575(01)00003-3.
 
39.
Żuchowski A. The use of energy methods at the calculation of vehicle impact velocity. The Archives of Automotive Engineering – Archiwum Motoryzacji. 2015;68(2):85-111.
 
eISSN:2084-476X