Table 4.

Identified material parameters by using two-stage and combined optimization for two back-stress terms.

	Two-Stage Optimization			Combined Optimization
Parameters	Min	Mid	Max	Min	Mid	Max
C1 (MPa)	87,646	94,140	90,260	64,193	87,366	148,784
γ1	210	221	210	138	171	434
C2 (MPa)	4000	4005	4011	3722	3616	4227
γ2	0	0	0	0	0	0
Q (MPa)	−136	−189	−107	−252	−251	−55
b	4.12	3.19	8.92	3.31	8.39	7.87
${\dot{\epsilon }}_0$ (s−1)	7.96 × 10−7	1.38 × 10−6	1.23 × 10−6	1.54 × 10−6	9.46 × 10−7	2.87 × 10−7
n	11.83	10.7	10.95	10	11	9.8
m	−0.99	−0.99	−0.99	−0.96	−0.92	−0.67
NMSE	1.02 × 10−4	1.16 × 10−4	1.01 × 10−4	9.73 × 10−5	1.10 × 10−4	1.27 × 10−4