An Evaluation of Objective Rating Methods for Full-Body Finite Element Model Comparison to PMHS Tests

Figures & data

Table 1 Comparison of objective evaluation methods used in the study

Study name	Evaluation metric	Best match value	Worst match value	Notes
Sprague and Geers (2004)	Magnitude, SGM	SGM = 0, equal magnitude of experiment	SGM = −1 (much less than experiment) SGM = ∞ (much greater than experiment)	Mean comparison only
	Phase, SGP	SGP = 0, no phase differences between simulation and experiment	SGP = 1 (180° out of phase of experiment)	Mean comparison only Result is normalized by π
Rhule et al. (2002)	CSD	CSD = 0, sum of squared difference between experiment and simulation is zero	Positive valued only CSD = n (n standard deviations from the mean) CSD = ∞ (many standard deviations from the mean)	Accounts for standard deviation, CSD = , square root used to report results in terms of a cumulative standard deviation rather than cumulative variance. BioRank utilizes
Gehre et al. (2009)	CORA corridor, C cor	C cor = 1, with inner corridor	C cor = 0, outside of outer corridor	Comparison based on user-provided inner and outer corridors
	CORA phase, C phase	C phase = 1, required shift is less than user-defined δmin	C phase = 0, required shift is greater than user-defined δmax	Mean comparison only Phase shift value is interpolated between a min and max permissible shift
	CORA size, C size	C size = 1, area under the curve of simulated and experimental results are equal	C size → 0, area under the curve of simulated and experimental results are very different	Mean comparison only
	CORA shape, C shape	C shape = 1, shape of curves is similar	C shape → 0, shape of curves is very different	Mean comparison only Utilizes a normalized cross-correlation

Fig. 1 Study flowchart. Results from 53 channels of data were applied to each of the methods above. Therefore, at the end of this part of the study there was a value of each of the 7 metrics listed above for 53 time-valued signals (color figure available online).

Fig. 2 Time lapse images showing the kinematics of the GHBMC M50 model. The top row indicates overall body motion and the second and third rows show spine kinematics from the side and back, respectively (color figure available online).

Table 2 Cross-plot matrix for comparison study

	Sprague and Geers (2004)		Rhule et al. (2002)	Gehre et al. (2009)
	SGM	SGP	CSD	C cor	C phase	C size	C shape
SGM		√	√	√	√	√	√
SGP			√	√	√	√	√
CSD				√	√	√	√
C cor					√	√	√
C phase						√	√
C size							√
C shape

Fig. 3 Cross-plots of the 3 best correlated metric pairs.

Table 3 Results from the 21 regressions conducted with the statistically significant correlations highlighted

	Sprague and Geers (2004)		Rhule et al. (2002)	Gehre et al. (2009)
	SGM	SGP	CSD	C cor	C shape	C size	C phase
SGM		0.00	0.09	0.06	0.02	0.73	0.01
SGP			0.00	0.00	0.82	0.03	0.31
CSD				0.59	0.01	0.09	0.01
C cor					0.02	0.08	0.02
C shape						0.04	0.21
C size							0.01
C phase
Coefficients in bold demonstrate R ^2 values greater than 0.5.

Fig. 4 Left: Bar chart showing that SGM can be less than zero while CORA size is always positive. Right: (A) a case where SGM is negative because, on average, the model response is smaller than the experimental mean; (B) a case where both SGM and CORA size are positive. Both the SGM and CORA size factor do not consider the phase shift that is apparent in either A or B.

Fig. 5 Histogram comparing the range of CSD to the range of CORA corridor.

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Gehre , C , Gades , H and Wernicke , P . Objective rating of signals using test and simulation responses . Paper presented at: 21st ESV Conference; June 15–18 , Stuttgart, Germany

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