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

Table 2.

The elements E1Nλ^, v1Nλ^, E2Nλ^, v2Nλ^ and ENλ^ of the vector gNλ^ solving optimization task (13) for regularization parameter λ^=2.51×103, 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 five-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] ENλ^ [Pa]
50 5.0 × 10−6 6.8155 × 10−4 2.07 0.94119 3.57829 × 10−3 1.73538 3.09241 × 10−2 8.412 × 10−3
100 3.6965 × 10−5 5.4636 × 10−5 1.75 × 10−2 1.01745 3.85167 × 10−3 2.02555 4.15854 × 10−2 1.2639 × 10−2
250 4.5229 × 10−5 5.5365 × 10−5 1.06 × 10−2 1.01928 3.85649 × 10−3 2.07666 4.22544 × 10−2 1.2885 × 10−2
500 5.1215 × 10−5 5.0257 × 10−5 3.05 × 10−3 1.02616 3.89451 × 10−3 2.06699 4.28871 × 10−2 1.2885 × 10−2
1000 5.1036 × 10−5 5.0021 × 10−5 5.5 × 10−3 1.02949 3.88211 × 10−3 2.07118 4.33627 × 10−2 1.2897 × 10−2
2500 5.0049 × 10−5 4.9049 × 10−5 1.02 × 10−3 1.02709 3.87612 × 10−3 2.06167 4.30789 × 10−2 1.27968 × 10−2
5000 5.1942 × 10−5 4.8581 × 10−5 1.89 × 10−4 1.02982 3.88972 × 10−3 2.05571 4.31916 × 10−2 1.31245 × 10−2
7500 5.1596 × 10−5 4.8712 × 10−5 1.89 × 10−4 1.03037 3.89006 × 10−3 2.05869 4.32779 × 10−2 1.30726 × 10−2
10,000 5.1276 × 10−5 4.8781 × 10−5 5.62 × 10−4 1.02979 3.88757 × 10−3 2.05899 4.32133 × 10−2 1.29740 × 10−2
20,000 4.8846 × 10−5 4.8995 × 10−5 1.20 × 10−4 1.02589 3.87391 × 10−3 2.05207 4.29263 × 10−2 1.28128 × 10−2
50,000 4.9066 × 10−5 4.8934 × 10−5 7.72 × 10−5 1.02631 3.87501 × 10−3 2.05244 4.29290 × 10−2 1.27937 × 10−2
100,000 4.9971 × 10−5 4.8738 × 10−5 6.42 × 10−6 1.02757 3.88095 × 10−3 2.05430 4.29902 × 10−2 1.29231 × 10−2