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. 2023 Dec 2;15(23):4605. doi: 10.3390/polym15234605

Table 3.

The elements E1Nλ^, v1Nλ^, E2Nλ^, v2Nλ^, E3Nλ^, v3Nλ^ and ENλ^ of the vector gNλ^ solving optimization task (13) for regularization parameter λ^=1.27×103, the mean-square identification indices QN(gNλ^), Equation (8), the integral quadratic indices Q(gNλ^), Equation (5), and the relative square errors ERR (39) of the measurement-independent parameters gλ, approximation for seven-parameter Maxwell model (26) and N relaxation modulus measurements corrupted by additive independent noises of normal distribution with standard deviation σ=0.001 [Pa].

N QN(gNλ^) [Pa2] Q(gNλ^) [Pa2] ERR [%] E1Nλ^ [Pa] v1Nλ^ [s1] E2Nλ^ [Pa] v2Nλ^ [s1] E3Nλ^ [Pa] v3Nλ^ [s1] ENλ^ [Pa]
50 1.6 × 10−5 1.08569 × 10−3 3.66 × 10−2 0.91380 3.496 × 10−3 0.83143 2.7811 × 10−2 0.82996 2.7811 × 10−2 7.603 × 10−3
100 2.25694 × 10−5 4.38001 × 10−5 7.83 × 10−4 0.96972 3.695 × 10−3 1.0064 2.832 × 10−2 1.05894 5.5844 × 10−2 1.0765 × 10−2
250 1.39206 × 10−5 1.13403 × 10−5 1.53 × 10−5 0.96278 3.675 × 10−3 1.04195 2.7757 × 10−2 1.10192 6.3315 × 10−2 1.0623 × 10−2
500 1.62056 × 10−5 1.96741 × 10−5 2.63 × 10−5 0.95898 3.665 × 10−3 1.03016 2.7044 × 10−2 1.09224 6.3563 × 10−2 1.045 × 10−2
1000 1.23718 × 10−5 9.7523 × 10−6 5.82 × 10−5 0.96012 3.664 × 10−3 1.04663 2.7517 × 10−2 1.10631 6.428 × 10−2 1.0313 × 10−2
2500 1.33721 × 10−5 1.09919 × 10−5 2.17 × 10−5 0.96250 3.67 × 10−3 1.04209 2.7724 × 10−2 1.10388 6.3365 × 10−2 1.0324 × 10−2
5000 1.36971 × 10−5 1.15176 × 10−5 1.82 × 10−5 0.96271 3.673 × 10−3 1.03686 2.7685 × 10−2 1.10569 6.3398 × 10−2 1.0428 × 10−2
7500 1.35309 × 10−5 1.12970 × 10−5 1.95 × 10−5 0.96231 3.67 × 10−3 1.03806 2.7636 × 10−2 1.10573 6.3676 × 10−2 1.0362 × 10−2
10,000 1.35952 × 10−5 1.14719 × 10−5 1.29 × 10−5 0.96236 3.67 × 10−3 1.04048 2.7686 × 10−2 1.10274 6.3591 × 10−2 1.033 × 10−2
20,000 1.58069 × 10−5 1.60772 × 10−5 1.19 × 10−5 0.963075 3.672 × 10−3 1.03044 2.7711 × 10−2 1.09572 6.2326 × 10−2 1.0375 × 10−2
50,000 1.53858 × 10−5 1.50425 × 10−5 2.82 × 10−6 0.96263 3.671 × 10−3 1.03389 2.7724 × 10−2 1.09609 6.2494 × 10−2 1.0336 × 10−2
100,000 1.45691 × 10−5 1.33615 × 10−5 2.62 × 10−7 0.96311 3.674 × 10−3 1.03655 2.7767 × 10−2 1.09878 6.2832 × 10−2 1.0407 × 10−2