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. 2024 Jan 12;14:1219. doi: 10.1038/s41598-023-49839-y

Table 2.

Central composite design (CCD) with experimental responses and predicted responses.

S.No Parameters Experimental value* RSM prediction ANFIS prediction Machine learning algorithm prediction
X1 X2 X3 X4 X5 y1 y2 y3 y4 y5 y1 y2 y3 y4 y5 y1 y2 y3 y4 y5 y1 y2 y3 y4 y5
1 1 60 18 45 65 432.26 312.34 62.65 59.45 54.67 432.03 298.47 62.04 58.87 53.90 432 312 62.7 59.5 54.7 643.54 411.64 76.84 71.12 66.30
2 1 70 18 45 75 462.56 325.58 65.43 61.92 56.58 447.98 309.29 62.20 58.14 53.02 463 326 65.4 61.9 56.6 572.68 346.90 66.05 62.82 57.70
3 0.5 60 18 35 75 599.06 391.56 72.34 66.45 61.06 600.04 382.65 73.64 67.52 62.77 599 392 72.3 66.4 61.1 643.54 411.64 76.84 71.12 66.30
4 0.155 65 23 40 70 670.32 451.45 81.23 77.39 71.55 739.73 466.89 83.08 77.92 72.81 670 451 81.2 77.4 71.6 643.54 411.64 76.84 71.12 66.30
5 1 70 28 45 75 562.56 353.03 68.03 65.4 60.48 511.45 336.76 66.65 62.19 57.47 563 353 68 65.4 60.5 631.10 393.11 74.63 68.02 63.66
6 0.5 70 18 35 65 653.28 403.06 76.27 72.04 68.76 616.82 393.6 75.529 71.296 66.94 653 403 76.3 72 68.8 643.54 411.64 76.84 71.12 66.30
7 0.75 65 23 28.11 70 498.34 334.56 67.83 63.45 57.46 495.19 328.22 64.787 59.87 54.62 498 335 67.8 63.5 57.5 631.10 393.11 74.63 68.02 63.66
8 1 70 18 45 65 427.56 319.48 65.84 61.5 57.36 449.98 314.75 64.64 61.48 57.24 428 319 65.8 61.3 57.4 643.54 411.64 76.84 71.12 66.30
9 1 60 18 35 65 431.67 320.25 65.82 62.87 58.26 432.81 291.18 61.55 56.50 52.15 432 320 65.8 62.9 58.3 417.93 301.03 61.55 57.98 53.38
10 0.75 76.89 23 40 70 513.63 367.58 66.61 63.65 59.34 552.59 364.22 66. 4 63.330 59.21 514 368 66.6 63.7 59.3 631.10 393.11 74.63 68.02 63.66
11 1 60 28 45 75 423.78 321.25 61.64 57.72 52.08 458.15 311.1 60.17 55.92 51.12 424 321 61.6 57.7 52.1 572.68 346.90 66.05 62.82 57.70
12 0.5 70 18 45 75 659.43 413.76 77.59 73.04 68.56 629.26 401.48 78.11 73.21 68.54 659 414 77.6 73 68.6 643.54 411.64 76.84 71.12 66.30
13 0.5 60 18 45 65 642.57 396.56 76.06 71.43 65.33 647.3 399.68 73.18 69.23 63.91 643 397 76.1 71.4 65.3 417.93 301.03 61.55 57.98 53.38
14 0.5 60 28 45 65 660.12 422.6 63.45 59.93 55.52 629.26 401.58 66.50 62.43 57.43 660 423 63.5 59.9 55.6 631.10 393.11 74.63 68.02 63.66
15 1 70 18 35 75 414.56 299.39 52.02 48.93 43.78 408.63 284.88 55.78 51.62 47.28 415 299 52 48.9 43.8 417.93 301.03 61.55 57.98 53.38
16 1 60 28 35 75 398.76 286.48 51.72 46.67 41.37 420.15 291.17 56.39 52.79 47.56 399 286 51.7 46.7 41.4 643.54 411.64 76.84 71.12 66.30
17 0.5 70 28 35 65 656.45 412.92 77.54 73.85 68.67 619.4 400.83 75.90 72.02 67.17 656 413 77.5 73.9 68.7 572.68 346.90 66.05 62.82 57.70
18 0.75 65 23 51.89 70 556.34 366.45 69.6 65.73 61.32 553.18 366.19 69.89 65.54 60.56 556 366 69.6 65.7 56.1 572.68 346.90 66.05 62.82 57.70
19 0.75 65 23 40 70 482.67 325.67 72.74 68.63 63.65 483.67 324.5 72.28 67.22 62.85 484 325 72.5 67.5 63.1 643.54 411.64 76.84 71.12 66.30
20 0.75 65 34.89 40 70 536.32 367.34 69.43 65.91 61.27 559.71 360 66.64 63.10 58.07 536 367 69.4 65.9 61.3 631.10 393.11 74.63 68.02 63.66
21 1 60 18 45 75 404.45 278.31 56.71 51.76 46.64 447.98 309.3 62.20 58.14 53.02 404 278 56.7 51.8 46.6 643.54 411.64 76.84 71.12 66.30
22 1 60 28 45 65 395.67 264.37 53.56 47.62 42.27 403.45 277.84 54.12 49.77 44.72 396 264 53.6 47.7 42.3 572.68 346.90 66.05 62.82 57.70
23 0.75 65 23 40 70 481.36 326.54 74.75 70.74 64.18 483.67 324.5 72.28 67.22 62.85 484 325 72.5 67.5 63.1 631.10 393.11 74.63 68.02 63.66
24 0.5 70 28 45 65 654.34 432.64 78.56 74.74 70.46 626.1 412.88 72.99 69.27 64.96 654 433 78.6 74.7 70.5 643.54 411.64 76.84 71.12 66.30
25 1 70 28 35 65 422.53 293.08 58.93 53.41 48.45 419.15 276.39 57.47 52.18 47.54 423 293 58.9 53.4 48.4 417.93 301.03 61.55 57.98 53.38
26 0.75 65 23 40 81.892 602.37 399.45 73.72 69.86 65.78 573.3 379.18 69.72 65.10 60.9 602 399 73.7 69.9 65.8 572.68 346.91 66.05 62.82 57.70
27 0.75 65 11.11 40 70 574.32 348.52 68.56 65.82 60.43 544.66 349.29 68.60 64.88 60.04 574 349 68.6 65.8 60.4 631.10 393.11 74.63 68.02 63.66
28 0.75 65 23 40 70 484.65 324.07 71.85 64.74 59.78 483.67 324.5 72.28 67.22 62.85 484 325 72.5 67.5 63.1 631.10 393.11 74.63 68.02 63.66
29 0.5 70 18 35 75 562.12 371.74 73.54 67.84 63.28 575.57 376.85 70.90 66.44 61.67 562 372 73.5 67.8 63.3 631.10 393.11 74.63 68.02 63.66
30 0.75 65 23 40 70 485.34 325.94 69.93 65.34 62.54 483.67 324.5 72.28 67.22 62.85 484 325 72.5 67.5 63.1 572.68 346.90 66.05 62.82 57.70
31 0.5 60 28 35 75 660.12 418.6 79.45 74.93 70.52 624.86 406.96 76.26 71.99 67.21 660 419 79.4 74.9 70.5 631.10 393.11 74.63 68.02 63.66
32 0.5 70 18 45 65 641.32 401.83 75.34 73.32 68.56 627.62 405.62 76.03 72.93 68.37 641 402 75.3 73.3 68.6 643.54 411.64 76.84 71.12 66.30
33 0.5 70 28 35 75 633.35 401.162 72.23 70.89 66.28 616.9 406.52 77.16 74.04 69.19 633 401 72.2 70.9 66.3 631.10 393.11 74.63 68.02 63.66
34 1 70 28 45 65 421.65 274.92 55.63 51.62 47.31 437.91 299.48 60.36 55.51 51.13 422 275 55.6 51.6 47.3 631.10 393.11 74.63 68.02 63.66
35 0.5 60 18 35 65 636.45 392.43 74.98 67.56 63.45 660.13 403.42 78.5 72.92 67.96 636 392 75 67.6 63.5 643.54 411.64 76.84 71.12 66.30
36 0.75 53.11 23 40 70 586.05 348.65 64.76 61.43 56.34 540.82 345.43 62.22 57.88 52.87 586 349 64.8 61.4 56.3 572.68 346.90 66.05 62.82 57.70
37 1 70 18 35 65 418.9 268.06 53.78 48.04 44.36 427.11 291.69 58.33 53.76 50.01 419 268 53.8 48 44.4 643.54 411.64 76.84 71.12 66.30
38 0.75 65 23 40 70 485.76 323.54 75.89 70.05 66.88 483.67 324.5 72.28 67.22 62.85 484 325 72.5 67.5 63.1 643.54 411.64 76.84 71.12 66.30
39 0.5 70 28 45 75 645.34 404.72 77.84 69.42 65.24 666.48 431.18 80.95 76.42 72.43 645 405 77.8 69.4 65.2 631.10 393.11 74.63 68.02 63.66
40 1 70 28 35 75 423.76 278.43 55.58 51.56 46.65 449.81 301.07 57.05 53.74 48.43 424 278 55.6 51.6 46.7 417.93 301.03 61.55 57.98 53.38
41 0.75 65 23 40 70 483.72 324.65 72.86 66.83 62.41 483.67 324.5 72.28 67.22 62.85 484 325 72.5 67.5 63.1 417.93 301.03 61.55 57.98 53.38
42 0.5 60 18 45 75 638.34 401.61 76.45 69.49 65.56 630.09 391.51 75.03 68.95 64.16 638 402 76.4 69.5 65.6 572.68 346.90 66.05 62.82 57.70
43 1.35 65 23 40 70 360.76 243.17 50.51 45.76 41.07 286.35 221.78 46.18 41.73 36.48 361 243 50.5 45.8 41.1 643.54 411.64 76.84 71.12 66.30
44 0.75 65 23 40 58.11 534.63 345.92 66.76 62.56 58.26 557.44 359.62 68.01 63.56 59.54 535 346 66.8 62.6 58.3 643.54 411.64 76.84 71.12 66.30
45 0.75 65 23 40 70 485.65 325.73 71.03 68.45 64.07 483.67 324.5 72.28 67.22 62.85 484 325 72.5 67.5 63.1 572.68 346.90 66.05 62.83 57.70
46 0.75 65 23 40 70 484.38 324.23 70.98 65.43 61.68 483.67 324.5 72.28 67.22 62.85 484 325 72.5 67.5 63.1 417.93 301.02 61.55 57.98 53.38
47 1 60 28 35 65 396.06 256.34 54.76 50.56 45.56 522.2 334.46 67.52 62.47 57.34 396 256 54.8 50.6 45.6 631.10 393.11 74.63 68.02 63.66
48 1 60 18 35 75 380.76 268.04 52.56 47.58 43.34 497.88 332.57 65.7 60.41 55.77 381 268 52.6 47.6 43.3 417.93 301.02 61.55 57.98 53.38
49 0.5 60 28 45 75 642.82 402.63 73.67 69.67 65.34 650.8 415.85 74.23 69.04 64.97 643 403 73.7 69.7 65.3 643.54 411.64 76.84 71.12 66.30
50 0.5 60 28 35 65 636.42 393.95 74.76 68.72 63.34 646.2 405.29 75.24 70.51 65.12 636 394 74.8 68.7 63.3 631.10 393.11 74.63 68.02 63.66

*All the experiments repeated three times.