Nonlinear method of precrash velocity determination for Mini car class-B-spline tensors products with probabilistic weights

Adam Mrowicki,Przemysław Kubiak,Wojciech Zakrzewicz

doi:10.14669/am.vol87.art8

Abstract

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%.

Highlights

The three main factors deciding a road accident are: driver, vehicle and road conditions
The dependencies presented in prior section govern the crash site reconstruction and lay the base for the nonlinear method
B-spline tensor products is due to the fact, that mini vehicles are less of the data set and its validation is performed shed by comparing the velocity values of the Firstly, probabilistic weights are assigned to each case and introduced into the mathed introducedmianttoictahlemmoadtheelm

Summary

Introduction

The three main factors deciding a road accident are: driver, vehicle and road conditions. The most popular methods of precrash velocity determination utilize a linear model [6, 7, 37]. This approach is based on an assumption that bk coefficient is the slope of deformation coefficient Cs [20, 36] and vehicle mass m. Such simplification comes with a higher error of velocity estimation [18, 19]. An alternative method was deviseda nonlinear approach This new method is based on three main assumptions:. Bk slope of nonlinearly dependent on Cs deformation and vehicle mass m.

Nonlinear approach

Results of approximation of B-spline tensor products

Conclusions