RESEARCH PAPER
NONLINEAR METHOD OF VEHICLE VELOCITY DETERMINATION BASED ON INVERSE SYSTEM AND TENSOR PRODUCT OF LEGENDRE POLYNOMIALS - INTERMEDIATE CLASS
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
Submission date: 2019-02-05
Final revision date: 2019-03-06
Acceptance date: 2019-03-15
Publication date: 2019-03-29
Corresponding author
Przemyslaw Kubiak
Department of Vehicles and Fundamentals of Machine Design, Lodz University of Technology, 1/15 Stefanowskiego Str.,, 90-924, Lodz, Polska
Department of Vehicles and Fundamentals of Machine Design, Lodz University of Technology, 1/15 Stefanowskiego Str.,, 90-924, Lodz, Polska
The Archives of Automotive Engineering – Archiwum Motoryzacji 2019;83(1):133-149
KEYWORDS
TOPICS
ABSTRACT
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%.
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