A state-space approach to mathematical modeling and parameters identification of vehicle frontal crash

Figures & data

Figure 1. Vehicle crash experimental setup (Robbersmyr, 2004).

Figure 2. Vehicle undergoing deformation (Robbersmyr, 2004).

Figure 3. Measured and estimated outputs.

Figure 4. A double-spring–mass–damper model.

Table 1.  Parameters estimation.

		Estimated Parameters
Cases	Solution no.	k1(N/m)	k2(N/m)	c1(N s/m)	c2(N s/m)
Case1:m1=1/3 mt	1	3498.37	640,808	22,989	9440
m2=2/3 mt	2	15,324.66	6293.37	5247	96,1212.45
Case2:m1=2/3 mt	1	7720.9	440,070	33,306.4	13,746.15
m2=1/3 mt	2	11,102.14	33,162.72	458,205	1,320,210
Case3:m1=1/4 mt	1	475.68	606,207.28	20,541.68	8419.68
m2=3/4 mt	2	15,406.26	6314.76	634.24	808,276.38
Case4:m1=3/4 mt	1	6734.92	337,670.38	36,588.11	15,115.54
m2=1/4 mt	2	9147	3778.88	26,939.66	1,350,681.54

Figure 5. Comparative analysis between vehicle crash test and model results for m₁=⅓m_t.

Figure 6. Comparative analysis between vehicle crash test and model results for m₂=⅓m_t.

Figure 7. Comparative analysis between vehicle crash test and model results for m₁=¼m_t.

Figure 8. Comparative analysis between vehicle crash test and model results for m₂=¼m_t.

Figure 9. Comparative analysis between vehicle crash test and model results for m₂=¼m_t.

Figure 10. Comparative analysis between the vehicle crash test and model results for m₂=¼m_t.

Figure 11. Comparative analysis between the vehicle crash test and model results for m₂=¼m_t.

Figure 12. Comparative analysis between vehicle crash test and model results for m₂=¼m_t.

Table 2.  Dynamic crash and time of crash comparison.

CmExp (cm)	Tm−Exp (s)	Solution no.1	Masses	Cm (cm)	Tm (s)	Solution no.2	Masses	Cm (cm)	Tm (s)
50.63	0.075	Case1:m1=1/3 mt	m2	66.55	0.14	Case1:m1=1/3 mt	m2	∞	–
		m2=2/3 mt	m1	66.13	0.19	m2=2/3 mt	m1	∞	–
		Case2:m1=2/3 mt	m2	52.92	0.11	Case2:m1=2/3 mt	m2	50.16	0.16
		m2=1/3 mt	m1	51.05	0.16	m2=1/3 mt	m1	49.82	0.15
		Case3:m1=1/4 mt	m2	73.07	0.17	Case3:m1=1/4 mt	m2	∞	–
		m2=3/4 mt	m1	72.45	0.17	m2=3/4 mt	m1	∞	–
		Case4:m1=3/4 mt	m2	50.48	0.11	Case4:m1=3/4 mt	m2	60.24	0.24
		m2=1/4 mt	m1	48.14	0.16	m2=1/4 mt	m1	60.24	0.24

Robbersmyr, K. G. (2004). Calibration test of a standard Ford Fiesta 1.1l, model year 1987, according to NS-EN 12767 (Technical Report 43/2004). Grimstad, Norway: Agder Research.

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