Fast Calculating Surrogate Models for Leg and Head Impact in Vehicle–Pedestrian Collision Simulations

Figures & data

Table 1 Degrees of freedom for leg and head impact

Degree of freedom	Vehicle–leg impactor	Vehicle–head impactor
Position in longitudinal direction (x)	Depends on y (based on bumper contour)	Variable
Position in lateral direction (y)	Variable	Variable
Position in vertical direction (z)	Depends on ry, set to constant	Depends on x, y (based on hood contour)
Rotation about x (rx)	Constant zero	Irrelevant for HIC
Rotation about y (ry)	Almost constant, set to constant	Irrelevant for HIC
Rotation about z (rz)	Constant zero	Irrelevant for HIC
Velocity in longitudinal direction (vx)	Variable	Variable
Velocity in lateral direction (vy)	Variable	Variable
Velocity in vertical direction (vz)	Constant zero	Variable
Rotational velocity about x (rx)	Constant zero	Irrelevant for HIC
Rotational velocity about y (ry)	Constant zero	Irrelevant for HIC
Rotational velocity about z (rz)	Constant zero	Irrelevant for HIC

Figure 1 Coordinate system definition and degrees of freedom for head and leg impact constellation.

Figure 2 Areas of assumed high nonlinearity in the output (i.e., leg injury criteria) of the leg surrogate models (dark gray) and areas of assumed low nonlinearity (light gray).

Figure 3 Partition of the hood into 16 areas for training data selection.

Figure 4 Local linear model tree structure.

Table 2 HIC15 mean average error results of training and test and relative change between test and training for the most relevant head impact models (no preprocessing)

Model	Training MAE	Test MAE	Relative change (%)
LOLIMOT	87.8	87.3	−1
SVR	76.5	84.0	10
Kriging	55.8	77.8	39

Table 3 Leg acceleration, knee bending, and shearing mean average error results of training and test and relative change between test and training for the most relevant leg impact models

		Max. leg acceleration (g)
Model	Training data set	Training MAE	Test MAE	Relative change (%)
LOLIMOT	LHS	14.14	15.92	13
SVR	LHS	12.53	10.83	−14
Kriging	LHS	8.91	12.10	36
	CLSTsimple	5.57	8.06	45
	CLSTcomplex	6.81	10.25	50
		Max. knee bending angle (°)
LOLIMOT	LHS	2.11	3.32	57
SVR	LHS	2.69	2.74	2
Kriging	LHS	0.97	1.59	63
	CLSTsimple	0.66	1.70	157
	CLSTcomplex	0.70	2.05	191
		Max. knee shearing (mm)
LOLIMOT	LHS	0.33	0.33	3
SVR	LHS	0.32	0.36	15
Kriging	LHS	0.28	0.35	26
	CLSTsimple	0.18	0.27	46
	CLSTcomplex	0.12	0.26	121

Figure 5 Results of the LOLIMOT head impact model on test data.