Table 4 Output results of neural networks optimized by different algorithms.
Algorithm | Parameters | Best | Worst | Mean | Standard deviation |
|---|---|---|---|---|---|
EDBO-BP-PID | \({K_p}\) | 30.0000 | 29.9309 | 29.9967 | 0.0117 |
\({K_i}\) | 6.0237 | 8.1161 | 7.1638 | 0.6725 | |
\({K_d}\) | 0.0171 | 0.1415 | 0.0421 | 0.0427 | |
\(\eta\) | 0.0491 | 0.0697 | 0.0626 | 0.0056 | |
\(\alpha\) | 0.0296 | 0.2883 | 0.0983 | 0.1292 | |
DBO-BP-PID | \({K_p}\) | 25.0000 | 20.9121 | 24.9591 | 0.4087 |
\({K_i}\) | 4.2536 | 3.3388 | 4.2387 | 0.1133 | |
\({K_d}\) | 0.0100 | 0.1986 | 0.0220 | 0.0364 | |
\(\eta\) | 0.0948 | 0.0394 | 0.0936 | 0.0083 | |
\(\alpha\) | 0.0025 | 0.0217 | 0.0046 | 0.0056 | |
PSO-BP-PID | \({K_p}\) | 25.0000 | 23.3558 | 24.9815 | 0.1654 |
\({K_i}\) | 4.1027 | 25.0000 | 24.9815 | 0.1654 | |
\({K_d}\) | 0.0100 | 25.0000 | 24.9815 | 0.1654 | |
\(\eta\) | 0.0014 | 0.0826 | 0.0045 | 0.0119 | |
\(\alpha\) | 0.0787 | 0.1661 | 0.0773 | 0.0136 | |
EDBO-PID | \({K_p}\) | 30.0000 | 26.5768 | 28.1226 | 0.4887 |
\({K_i}\) | 5.0018 | 5.2710 | 5.0037 | 0.0276 | |
\({K_d}\) | 0.1335 | 0.2000 | 0.1373 | 0.0102 | |
DBO-PID | \({K_p}\) | 30.0000 | 24.6680 | 29.9466 | 0.5331 |
\({K_i}\) | 5.1040 | 3.8568 | 5.0864 | 0.1301 | |
\({K_d}\) | 0.2000 | 0.1647 | 0.1996 | 0.0035 | |
PSO- PID | \({K_p}\) | 25.0000 | 22.5365 | 24.7527 | 0.7787 |
\({K_i}\) | 4.1674 | 3.7249 | 4.1275 | 0.1421 | |
\({K_d}\) | 0.0847 | 0.1048 | 0.0848 | 0.0076 | |
BP- PID | \({K_p}\) | 25.0000 | 19.5365 | 20.7527 | 0.8425 |
\({K_i}\) | 4.1971 | 3.2258 | 4.1985 | 0.2674 | |
\({K_d}\) | 0.1267 | 0.1022 | 0.0957 | 0.0121 |
