Nonlinear method of precrash velocity determination for Mini car class-B-spline tensors products with probabilistic weights
More details
Hide details
Institute of Machine Design and Operation, Wrocław University of Technology
Institute of Vehicles, Warsaw University of Technology, Polska
Submission date: 2020-02-05
Final revision date: 2020-03-15
Acceptance date: 2020-03-24
Publication date: 2020-03-30
Corresponding author
Adam Mrowicki   

Institute of Machine Design and Operation, Wrocław University of Technology
The Archives of Automotive Engineering – Archiwum Motoryzacji 2020;87(1):97-108
Following research paper introduces a nonlinear method of determining the velocity of a vehicle before the impact-the Equivalent Energy Speed (EES) for mini car class. To estimate the magnitude of EES, this method utilizes the deformation work Wdef of the vehicle, defined by the quotient of deformation coefficient Cs and plastic deformation. Currently used methods assume linear relationship between velocity, deformation and mass of the vehicle. New approach estimates such relation by means of three dimensional surfaces. Such mathematical model is based on data provided by National Highway Traffic Safety Administration (NHTSA) that covers full frontal collisions with a rigid barrier. Vehicles take part in a standardized collision and are being crashed at a known velocity. Then the deformation is measured in six control points. Method introduces the B-spline tensor products and least square approximation with probabilistic weights that shows promising results. Linear approach generates relative error of 18.2% whereas the nonlinear approach reduces it down to 11.2%.
Axler S.: Linear Algebra Done Right. Springer, New York, 1997.
Campbell B.J.: The traffic accident data project scale. InCollision Investigation Methodology Symposium, Warrenton, 1969.
Cheney W., Kincaid D.: Numerical Analysis. Mathematics of Scientific Computing, Wadsworth Group, 2002.
Cromack J.R., Lee S.N.: Consistency study for vehicle deformation index. SAE Technical Paper. 1974, DOI: 10.4271/740299.
Faraj R., Holnicki-Szulc J., Knap L., Seńko J.: Adaptive inertial shock-absorber. Smart Materials and Structures. 2016, 25(3), 035031, DOI: 10.1088/0964-1726/25/3/035031.
Foret-Bruno J.Y., Trosseille X., Le Coz J.Y., Bendjellal F., Steyer C., Phalempin T., et al.: Thoracic injury risk in frontal car crashes with occupant restrained with belt load limiter. SAE Technical Paper. 1998, DOI: 10.4271/983166.
Geigl B.C., Hoschopf H., Steffan H., Moser A.: Reconstruction of occupant kinematics and kinetics for real world accidents. International journal of crashworthiness. 2003, 8(1), 17–27, DOI: 10.1533/ijcr.2003.0217.
Gidlewski M., Żardecki D.: Linearization of the lateral dynamics reference model for the motion control of vehicles. Mechanics Research Communications. 2017, 82, 49–54, DOI: 10.1016/j.mechrescom.2016.09.001.
Gidlewski M., Jemioł L., Żardecki D.: Sensitivity investigations of lane change automated process. 23rd International Conference Engineering Mechanics 2017, Location: Svratka, Czech Republic. Engineering Mechanics. 2017, 23, 330–333, 361–362.
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), Krakow, Poland. Materials Science and Engineering. 2016, 148, 012039, DOI: 10.1088/1757-899X/148/1/012039.
Gidlewski M., Żardecki D.: Simulation-Based Sensitivity Studies of a Vehicle Motion Model. 20th International Scientific Conference Transport Means 2016, Juodkrante, Lithuania, Transport Means –Proceedings of the International Conference. 2016, 236-240.
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, 13(4), 363–373, DOI: 10.1080/13588260801976120.
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), 254–262, DOI: 10.7467/KSAE.2015.23.3.254.
Han I.: Analysis of vehicle collision accidents based on qualitative mechanics. Forensic Science International. 2018, 291, 53–61, DOI: 10.1016/j.forsciint.2018.08.004.
Han I.: Vehicle collision analysis from estimated crush volume for accident reconstruction. International Journal of Crashworthiness. 2019, 24(1), 100–105, DOI: 10.1080/13588265.2018.1440499.
Hight P.V., Fugger T.F., Marcosky J.: Automobile damage scales and the effect on injury analysis. SAE Technical Paper. 1992, DOI: 10.4271/920602.
Iraeus J., Lindquist M.: Pulse shape analysis and data reduction of real-life frontal crashes with modern passenger cars. International Journal of Crashworthiness. 2015, 20(6), 535–546, DOI: 10.1080/13588265.2015.1057005.
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, 293, 7–16, DOI: 10.1016/j.forsciint.2018.10.011.
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, 287, 47–53, DOI: 10.1016 / j.forsciint.2018.03.033.
Lindquist M., Hall A., Björnstig U.: Real world car crash investigations - A new approach. International Journal of Crashworthiness. 2003, 8(4), 375–384, DOI: 10.1533/ijcr.2003.0245.
Mackay G.M., Hill J., Parkin S., Munns J.A.: Restrained occupants on the nonstruck side in lateral collisions. Accident Analysis & Prevention. 1993, 25(2), 147–152, DOI: 10.1016/0001-4575(93)90054-Z.
Mannering F.L., Bhat C.R.: Analytic methods in accident research: Methodological frontier and future directions. Analytic Methods In Accident Research. 2014, 1, 1–22, DOI: 10.1016/j.amar.2013.09.001.
McHenry B.G.: The algorithms of CRASH. InSoutheast Coast Collision Conference, 2001, 1–34.
McHenry R.: Computer Program for Reconstruction of Highway Accidents. SAE Technical Paper. 1973, 730980, DOI: 10.4271/730980.
Nelson W.D.: The History and Evolution of the Collision Deformation Classification SAE J224 MAR80. SAE Technical Paper. 1981, 810213, DOI: 10.4271/810213.
Neptune J.A.: Crush stiffness coefficients, restitution constants, and a revision of CRASH3 & SMAC. SAE Technical Paper. 1998, 980029, DOI: 10.4271/980029.
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, 12, 48–65, DOI: 10.1016/j.amar.2016.10.002.
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, France.
Siddall D.E., Day T.D.: Updating the vehicle class categories. SAE Technical Paper. 1996, 960897, DOI: 10.4271/960897.
Vangi D., Cialdai C.: Evaluation of energy loss in motorcycle-to-car collisions. International Journal of Crashworthiness. 2014, 19(4), 361–370, DOI: 10.1080/13588265.2014.899072.
Vangi D.: Simplified method for evaluating energy loss in vehicle collisions. Accident Analysis & Prevention. 2009, 41(3), 633–641, DOI: 10.1016/j.aap.2009.02.012.
Wach W., Unarski J.: Determination of vehicle velocities and collision location by means of Monte Carlo simulation method. SAE Technical Paper. 2006, DOI: 10.4271/2006-01-0907.
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, Juodkrante, Lithuania. Transport Means – Proceedings of the International Conference. 2016, 693–698.
Wang W., Sun X., Wei X.: Integration of the forming effects into vehicle front rail crash simulation. International Journal of Crashworthiness. 2016, 21(1), 9–21, DOI: 10.1080/13588265.2015.1091170.
Wasik M., Skarka W.: Simulation of Crash Tests for Electrically Propelled Flying Exploratory Autonomous Robot. Advances in Transdisciplinary Engineering. 2016, 4, 937–946, DOI: 10.3233/978-1-61499-703-0-937.
Wood D.P., Simms C.K.: Car size and injury risk: a model for injury risk in frontal collisions. Accident Analysis & Prevention. 2002, 34(1), 93–99, DOI: 10.1016/S0001-4575(01)00003-3.
Żuchowski A.: The use of energy methods at the calculation of vehicle impact velocity. Archiwum Motoryzacji. 2015, 68, 85–111, 197–222.
Improvement of the Autodriver Algorithm for Autonomous Vehicles Using Roll Dynamics
Ching To, Sina Milani, Hormoz Marzbani, Reza Jazar
The Archives of Automotive Engineering – Archiwum Motoryzacji
Declaration of availability
Journals System - logo
Scroll to top