Non-linear method of determining vehicle pre-crash speed based on tensor B-spline products with probabilistic weights — Intermediate Car Class. (December 2018) - Krukowski, Mateusz; Kubiak, Przemysław; Mrowicki, Adam; Siczek, Krzysztof; Gralewski, Jacek
Highlights: The tensor B-spline product approximation shows advantage over the linear model. The weighted relative error for B-spline approximation equals to 4.6459% whereas in the linear model it amounts to 5.5644%. If developed further, the method can be used to improve the precision of energy method up to several percent. Abstract: In the following study we consider the Intermediate Car Class. We apply a novel non-linear method, where the work W of car deformation is defined as an algebraic function of deformation ratio Cs . We use the data from the NHTSA (National Highway Traffic Safety Administration) database comprising numerous frontal crash tests. On the basis of this database, we determine the mathematical model parameters. In the so-called energetic approach, collisions are treated as non-elastic. The velocity threshold that defines the elastic collision was set to be 11 km/h. Such an approach, which greatly simplifies our considerations, determines the linear dependence of energy lost during deformation on deformation coefficient Cs . The coefficient Cs is calculated as a weighted mean value of deformation points C1 –C6 . In this paper, the authors suggest a more precise non-linear method in order to determine the work of deformation.