Table 4 Calculated values (MSE, R) of NARX NN models with LMA, for Number of Hidden Neurons 10 with number of delays d2 – d10.

d2

\(1.425 \cdot 10^{-4}\)

99.681

\(3.642 \cdot 10^{-5}\)

99.912

\(7.933 \cdot 10^{-5}\)

99.798

d3

\(\mathbf {2.553} \cdot \textbf{10}^{-\textbf{5}}\)

99.933

\(6.807 \cdot 10^{-5}\)

99.842

\(1.574 \cdot 10^{-4}\)

99.636

d4

\(2.418 \cdot 10^{-4}\)

99.396

\(3.832 \cdot 10^{-5}\)

99.899

\(7.910 \cdot 10^{-4}\)

98.235

d5

\(1.240 \cdot 10^{-4}\)

99.713

\(5.452 \cdot 10^{-5}\)

99.864

\(3.823 \cdot 10^{-4}\)

99.057

d6

\(1.435 \cdot 10^{-4}\)

99.659

\(5.959 \cdot 10^{-5}\)

99.833

\(1.267 \cdot 10^{-4}\)

99.708

d7

\(2.837 \cdot 10^{-5}\)

99.925

\(1.648 \cdot 10^{-5}\)

99.615

\(1.201 \cdot 10^{-4}\)

99.647

d8

\(4.641 \cdot 10^{-5}\)

99.894

\(6.847 \cdot 10^{-5}\)

99.823

\(1.989 \cdot 10^{-4}\)

99.523

d9

\(4.679 \cdot 10^{-5}\)

99.868

\(8.771 \cdot 10^{-5}\)

99.778

\(7.887 \cdot 10^{-4}\)

98.004

d10

\(3.984 \cdot 10^{-5}\)

99.905

\(3.520 \cdot 10^{-5}\)

99.916

\(3.874 \cdot 10^{-4}\)

99.067