Acta Metallurgica Sinica (English Letters) ›› 2015, Vol. 28 ›› Issue (2): 182-195.DOI: 10.1007/s40195-014-0184-6
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Temel Varol1, Aykut Canakci1(), Sukru Ozsahin2
Received:
2014-01-26
Revised:
2014-09-17
Online:
2015-02-10
Published:
2015-07-23
Temel Varol, Aykut Canakci, Sukru Ozsahin. Modeling of the Prediction of Densification Behavior of Powder Metallurgy Al-Cu-Mg/B4C Composites Using Artificial Neural Networks[J]. Acta Metallurgica Sinica (English Letters), 2015, 28(2): 182-195.
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Sample ID | Compact pressure (MPa) | Reinforcement ratio (wt%) | Reinforcement size (μm) | Milling time (h) | Density (g/cm3) | Porosity (%) | ||||
---|---|---|---|---|---|---|---|---|---|---|
Measured | Predicted | Error (%) | Measured | Predicted | Error (%) | |||||
1 | 200 | 0 | 0 | 0 | 2.675 | 2.673 | 0.07 | 4.46 | 4.275 | 4.14 |
3 | 200 | 0 | 0 | 1 | 2.645 | 2.641 | 0.16 | 5.54 | 5.392 | 2.67 |
5 | 200 | 0 | 0 | 5 | 2.621 | 2.619 | 0.08 | 6.39 | 6.125 | 4.15 |
7 | 200 | 0 | 0 | 10 | 2.603 | 2.599 | 0.17 | 7.04 | 6.827 | 3.02 |
9 | 200 | 5 | 49 | 0.5 | 2.645 | 2.647 | -0.06 | 5.1 | 5.206 | -2.07 |
10 | 200 | 5 | 49 | 1 | 2.63 | 2.637 | -0.28 | 5.6 | 5.529 | 1.27 |
14 | 200 | 5 | 49 | 10 | 2.566 | 2.563 | 0.12 | 7.9 | 8.078 | -2.25 |
17 | 200 | 10 | 49 | 1 | 2.587 | 2.580 | 0.26 | 6.67 | 6.792 | -1.83 |
19 | 200 | 10 | 49 | 5 | 2.54 | 2.533 | 0.29 | 8.37 | 8.610 | -2.87 |
22 | 200 | 20 | 49 | 0 | 2.583 | 2.581 | 0.09 | 5.87 | 6.048 | -3.03 |
23 | 200 | 20 | 49 | 0.5 | 2.551 | 2.554 | -0.12 | 7.04 | 6.976 | 0.91 |
25 | 200 | 20 | 49 | 2 | 2.53 | 2.534 | -0.14 | 7.8 | 7.709 | 1.17 |
27 | 200 | 20 | 49 | 7 | 2.42 | 2.415 | 0.21 | 11.81 | 11.930 | -1.01 |
28 | 200 | 20 | 49 | 10 | 2.415 | 2.403 | 0.49 | 12 | 12.348 | -2.90 |
31 | 200 | 5 | 5 | 1 | 2.624 | 2.626 | -0.08 | 5.81 | 5.905 | -1.64 |
33 | 200 | 5 | 5 | 5 | 2.585 | 2.593 | -0.30 | 7.21 | 7.036 | 2.41 |
35 | 200 | 5 | 5 | 10 | 2.554 | 2.556 | -0.07 | 8.33 | 8.325 | 0.06 |
36 | 200 | 10 | 5 | 0 | 2.598 | 2.598 | -0.01 | 6.28 | 6.084 | 3.12 |
39 | 200 | 10 | 5 | 2 | 2.56 | 2.557 | 0.11 | 7.65 | 7.571 | 1.03 |
41 | 200 | 10 | 5 | 7 | 2.455 | 2.454 | 0.05 | 11.44 | 11.401 | 0.34 |
43 | 200 | 20 | 5 | 0 | 2.565 | 2.566 | -0.05 | 6.53 | 6.548 | -0.28 |
44 | 200 | 20 | 5 | 0.5 | 2.539 | 2.539 | 0.00 | 7.47 | 7.489 | -0.26 |
45 | 200 | 20 | 5 | 1 | 2.532 | 2.531 | 0.06 | 7.73 | 7.784 | -0.70 |
49 | 200 | 20 | 5 | 10 | 2.385 | 2.399 | -0.57 | 13.08 | 12.511 | 4.35 |
50 | 400 | 0 | 0 | 0 | 2.725 | 2.723 | 0.08 | 2.68 | 2.535 | 5.39 |
51 | 400 | 0 | 0 | 0.5 | 2.709 | 2.703 | 0.23 | 3.25 | 3.238 | 0.36 |
53 | 400 | 0 | 0 | 2 | 2.687 | 2.685 | 0.09 | 4.04 | 3.877 | 4.03 |
54 | 400 | 0 | 0 | 5 | 2.67 | 2.660 | 0.37 | 4.64 | 4.680 | -0.86 |
57 | 400 | 5 | 49 | 0 | 2.71 | 2.716 | -0.22 | 2.73 | 2.772 | -1.55 |
58 | 400 | 5 | 49 | 0.5 | 2.693 | 2.696 | -0.13 | 3.34 | 3.458 | -3.52 |
60 | 400 | 5 | 49 | 2 | 2.673 | 2.674 | -0.04 | 4.06 | 4.244 | -4.52 |
62 | 400 | 5 | 49 | 7 | 2.623 | 2.620 | 0.12 | 5.85 | 6.081 | -3.94 |
64 | 400 | 10 | 49 | 0 | 2.663 | 2.667 | -0.16 | 3.93 | 3.704 | 5.75 |
65 | 400 | 10 | 49 | 0.5 | 2.641 | 2.647 | -0.21 | 4.73 | 4.457 | 5.77 |
69 | 400 | 10 | 49 | 7 | 2.517 | 2.526 | -0.34 | 9.2 | 9.014 | 2.02 |
71 | 400 | 20 | 49 | 0 | 2.625 | 2.629 | -0.14 | 4.34 | 4.317 | 0.52 |
72 | 400 | 20 | 49 | 0.5 | 2.6 | 2.605 | -0.19 | 5.25 | 5.155 | 1.80 |
75 | 400 | 20 | 49 | 5 | 2.563 | 2.552 | 0.43 | 6.6 | 7.083 | -7.32 |
77 | 400 | 20 | 49 | 10 | 2.46 | 2.449 | 0.45 | 10.35 | 10.705 | -3.43 |
79 | 400 | 5 | 5 | 0.5 | 2.682 | 2.686 | -0.16 | 3.73 | 3.817 | -2.34 |
80 | 400 | 5 | 5 | 1 | 2.675 | 2.673 | 0.06 | 3.98 | 4.264 | -7.13 |
83 | 400 | 5 | 5 | 7 | 2.61 | 2.611 | -0.05 | 6.32 | 6.385 | -1.02 |
85 | 400 | 10 | 5 | 0 | 2.658 | 2.652 | 0.23 | 4.11 | 4.240 | -3.17 |
87 | 400 | 10 | 5 | 1 | 2.625 | 2.619 | 0.23 | 5.3 | 5.451 | -2.86 |
89 | 400 | 10 | 5 | 5 | 2.59 | 2.583 | 0.29 | 6.57 | 6.902 | -5.05 |
91 | 400 | 10 | 5 | 10 | 2.491 | 2.501 | -0.42 | 10.14 | 9.932 | 2.05 |
92 | 400 | 20 | 5 | 0 | 2.62 | 2.618 | 0.08 | 4.52 | 4.705 | -4.10 |
95 | 400 | 20 | 5 | 2 | 2.561 | 2.562 | -0.03 | 6.67 | 6.676 | -0.10 |
96 | 400 | 20 | 5 | 5 | 2.524 | 2.541 | -0.67 | 8.02 | 7.480 | 6.73 |
99 | 600 | 0 | 0 | 0 | 2.766 | 2.760 | 0.22 | 1.21 | 1.233 | -1.92 |
101 | 600 | 0 | 0 | 1 | 2.741 | 2.734 | 0.27 | 2.11 | 2.152 | -1.98 |
102 | 600 | 0 | 0 | 2 | 2.728 | 2.722 | 0.22 | 2.57 | 2.565 | 0.19 |
105 | 600 | 0 | 0 | 10 | 2.688 | 2.682 | 0.21 | 4 | 3.893 | 2.67 |
107 | 600 | 5 | 49 | 0.5 | 2.735 | 2.741 | -0.22 | 1.83 | 1.898 | -3.73 |
110 | 600 | 5 | 49 | 5 | 2.685 | 2.692 | -0.25 | 3.63 | 3.571 | 1.63 |
112 | 600 | 5 | 49 | 10 | 2.659 | 2.663 | -0.15 | 4.56 | 4.571 | -0.25 |
115 | 600 | 10 | 49 | 1 | 2.7 | 2.698 | 0.06 | 2.6 | 2.595 | 0.18 |
117 | 600 | 10 | 49 | 5 | 2.665 | 2.665 | 0.01 | 3.86 | 3.945 | -2.19 |
118 | 600 | 10 | 49 | 7 | 2.622 | 2.619 | 0.12 | 5.41 | 5.629 | -4.06 |
120 | 600 | 20 | 49 | 0 | 2.687 | 2.685 | 0.09 | 2.08 | 2.136 | -2.68 |
123 | 600 | 20 | 49 | 2 | 2.625 | 2.632 | -0.26 | 4.34 | 4.075 | 6.10 |
125 | 600 | 20 | 49 | 7 | 2.525 | 2.536 | -0.42 | 7.98 | 7.599 | 4.78 |
126 | 600 | 20 | 49 | 10 | 2.512 | 2.508 | 0.15 | 8.45 | 8.569 | -1.41 |
129 | 600 | 5 | 5 | 1 | 2.711 | 2.720 | -0.32 | 2.69 | 2.648 | 1.55 |
131 | 600 | 5 | 5 | 5 | 2.679 | 2.685 | -0.24 | 3.84 | 3.790 | 1.31 |
133 | 600 | 5 | 5 | 10 | 2.652 | 2.656 | -0.16 | 4.81 | 4.808 | 0.04 |
134 | 600 | 10 | 5 | 0 | 2.713 | 2.716 | -0.11 | 2.13 | 1.886 | 11.48 |
137 | 600 | 10 | 5 | 2 | 2.68 | 2.679 | 0.03 | 3.32 | 3.274 | 1.40 |
139 | 600 | 10 | 5 | 7 | 2.611 | 2.606 | 0.19 | 5.81 | 6.038 | -3.93 |
141 | 600 | 20 | 5 | 0 | 2.678 | 2.672 | 0.24 | 2.41 | 2.652 | -10.03 |
143 | 600 | 20 | 5 | 1 | 2.641 | 2.636 | 0.20 | 3.75 | 3.939 | -5.05 |
144 | 600 | 20 | 5 | 2 | 2.617 | 2.621 | -0.16 | 4.63 | 4.513 | 2.54 |
147 | 600 | 20 | 5 | 10 | 2.5 | 2.500 | -0.01 | 8.89 | 8.854 | 0.40 |
MAPE | 0.093 | 1.400 | ||||||||
RMSE | 0.004 | 0.136 |
Table 1 Experimental data and predicted output from the ANN network for training set
Sample ID | Compact pressure (MPa) | Reinforcement ratio (wt%) | Reinforcement size (μm) | Milling time (h) | Density (g/cm3) | Porosity (%) | ||||
---|---|---|---|---|---|---|---|---|---|---|
Measured | Predicted | Error (%) | Measured | Predicted | Error (%) | |||||
1 | 200 | 0 | 0 | 0 | 2.675 | 2.673 | 0.07 | 4.46 | 4.275 | 4.14 |
3 | 200 | 0 | 0 | 1 | 2.645 | 2.641 | 0.16 | 5.54 | 5.392 | 2.67 |
5 | 200 | 0 | 0 | 5 | 2.621 | 2.619 | 0.08 | 6.39 | 6.125 | 4.15 |
7 | 200 | 0 | 0 | 10 | 2.603 | 2.599 | 0.17 | 7.04 | 6.827 | 3.02 |
9 | 200 | 5 | 49 | 0.5 | 2.645 | 2.647 | -0.06 | 5.1 | 5.206 | -2.07 |
10 | 200 | 5 | 49 | 1 | 2.63 | 2.637 | -0.28 | 5.6 | 5.529 | 1.27 |
14 | 200 | 5 | 49 | 10 | 2.566 | 2.563 | 0.12 | 7.9 | 8.078 | -2.25 |
17 | 200 | 10 | 49 | 1 | 2.587 | 2.580 | 0.26 | 6.67 | 6.792 | -1.83 |
19 | 200 | 10 | 49 | 5 | 2.54 | 2.533 | 0.29 | 8.37 | 8.610 | -2.87 |
22 | 200 | 20 | 49 | 0 | 2.583 | 2.581 | 0.09 | 5.87 | 6.048 | -3.03 |
23 | 200 | 20 | 49 | 0.5 | 2.551 | 2.554 | -0.12 | 7.04 | 6.976 | 0.91 |
25 | 200 | 20 | 49 | 2 | 2.53 | 2.534 | -0.14 | 7.8 | 7.709 | 1.17 |
27 | 200 | 20 | 49 | 7 | 2.42 | 2.415 | 0.21 | 11.81 | 11.930 | -1.01 |
28 | 200 | 20 | 49 | 10 | 2.415 | 2.403 | 0.49 | 12 | 12.348 | -2.90 |
31 | 200 | 5 | 5 | 1 | 2.624 | 2.626 | -0.08 | 5.81 | 5.905 | -1.64 |
33 | 200 | 5 | 5 | 5 | 2.585 | 2.593 | -0.30 | 7.21 | 7.036 | 2.41 |
35 | 200 | 5 | 5 | 10 | 2.554 | 2.556 | -0.07 | 8.33 | 8.325 | 0.06 |
36 | 200 | 10 | 5 | 0 | 2.598 | 2.598 | -0.01 | 6.28 | 6.084 | 3.12 |
39 | 200 | 10 | 5 | 2 | 2.56 | 2.557 | 0.11 | 7.65 | 7.571 | 1.03 |
41 | 200 | 10 | 5 | 7 | 2.455 | 2.454 | 0.05 | 11.44 | 11.401 | 0.34 |
43 | 200 | 20 | 5 | 0 | 2.565 | 2.566 | -0.05 | 6.53 | 6.548 | -0.28 |
44 | 200 | 20 | 5 | 0.5 | 2.539 | 2.539 | 0.00 | 7.47 | 7.489 | -0.26 |
45 | 200 | 20 | 5 | 1 | 2.532 | 2.531 | 0.06 | 7.73 | 7.784 | -0.70 |
49 | 200 | 20 | 5 | 10 | 2.385 | 2.399 | -0.57 | 13.08 | 12.511 | 4.35 |
50 | 400 | 0 | 0 | 0 | 2.725 | 2.723 | 0.08 | 2.68 | 2.535 | 5.39 |
51 | 400 | 0 | 0 | 0.5 | 2.709 | 2.703 | 0.23 | 3.25 | 3.238 | 0.36 |
53 | 400 | 0 | 0 | 2 | 2.687 | 2.685 | 0.09 | 4.04 | 3.877 | 4.03 |
54 | 400 | 0 | 0 | 5 | 2.67 | 2.660 | 0.37 | 4.64 | 4.680 | -0.86 |
57 | 400 | 5 | 49 | 0 | 2.71 | 2.716 | -0.22 | 2.73 | 2.772 | -1.55 |
58 | 400 | 5 | 49 | 0.5 | 2.693 | 2.696 | -0.13 | 3.34 | 3.458 | -3.52 |
60 | 400 | 5 | 49 | 2 | 2.673 | 2.674 | -0.04 | 4.06 | 4.244 | -4.52 |
62 | 400 | 5 | 49 | 7 | 2.623 | 2.620 | 0.12 | 5.85 | 6.081 | -3.94 |
64 | 400 | 10 | 49 | 0 | 2.663 | 2.667 | -0.16 | 3.93 | 3.704 | 5.75 |
65 | 400 | 10 | 49 | 0.5 | 2.641 | 2.647 | -0.21 | 4.73 | 4.457 | 5.77 |
69 | 400 | 10 | 49 | 7 | 2.517 | 2.526 | -0.34 | 9.2 | 9.014 | 2.02 |
71 | 400 | 20 | 49 | 0 | 2.625 | 2.629 | -0.14 | 4.34 | 4.317 | 0.52 |
72 | 400 | 20 | 49 | 0.5 | 2.6 | 2.605 | -0.19 | 5.25 | 5.155 | 1.80 |
75 | 400 | 20 | 49 | 5 | 2.563 | 2.552 | 0.43 | 6.6 | 7.083 | -7.32 |
77 | 400 | 20 | 49 | 10 | 2.46 | 2.449 | 0.45 | 10.35 | 10.705 | -3.43 |
79 | 400 | 5 | 5 | 0.5 | 2.682 | 2.686 | -0.16 | 3.73 | 3.817 | -2.34 |
80 | 400 | 5 | 5 | 1 | 2.675 | 2.673 | 0.06 | 3.98 | 4.264 | -7.13 |
83 | 400 | 5 | 5 | 7 | 2.61 | 2.611 | -0.05 | 6.32 | 6.385 | -1.02 |
85 | 400 | 10 | 5 | 0 | 2.658 | 2.652 | 0.23 | 4.11 | 4.240 | -3.17 |
87 | 400 | 10 | 5 | 1 | 2.625 | 2.619 | 0.23 | 5.3 | 5.451 | -2.86 |
89 | 400 | 10 | 5 | 5 | 2.59 | 2.583 | 0.29 | 6.57 | 6.902 | -5.05 |
91 | 400 | 10 | 5 | 10 | 2.491 | 2.501 | -0.42 | 10.14 | 9.932 | 2.05 |
92 | 400 | 20 | 5 | 0 | 2.62 | 2.618 | 0.08 | 4.52 | 4.705 | -4.10 |
95 | 400 | 20 | 5 | 2 | 2.561 | 2.562 | -0.03 | 6.67 | 6.676 | -0.10 |
96 | 400 | 20 | 5 | 5 | 2.524 | 2.541 | -0.67 | 8.02 | 7.480 | 6.73 |
99 | 600 | 0 | 0 | 0 | 2.766 | 2.760 | 0.22 | 1.21 | 1.233 | -1.92 |
101 | 600 | 0 | 0 | 1 | 2.741 | 2.734 | 0.27 | 2.11 | 2.152 | -1.98 |
102 | 600 | 0 | 0 | 2 | 2.728 | 2.722 | 0.22 | 2.57 | 2.565 | 0.19 |
105 | 600 | 0 | 0 | 10 | 2.688 | 2.682 | 0.21 | 4 | 3.893 | 2.67 |
107 | 600 | 5 | 49 | 0.5 | 2.735 | 2.741 | -0.22 | 1.83 | 1.898 | -3.73 |
110 | 600 | 5 | 49 | 5 | 2.685 | 2.692 | -0.25 | 3.63 | 3.571 | 1.63 |
112 | 600 | 5 | 49 | 10 | 2.659 | 2.663 | -0.15 | 4.56 | 4.571 | -0.25 |
115 | 600 | 10 | 49 | 1 | 2.7 | 2.698 | 0.06 | 2.6 | 2.595 | 0.18 |
117 | 600 | 10 | 49 | 5 | 2.665 | 2.665 | 0.01 | 3.86 | 3.945 | -2.19 |
118 | 600 | 10 | 49 | 7 | 2.622 | 2.619 | 0.12 | 5.41 | 5.629 | -4.06 |
120 | 600 | 20 | 49 | 0 | 2.687 | 2.685 | 0.09 | 2.08 | 2.136 | -2.68 |
123 | 600 | 20 | 49 | 2 | 2.625 | 2.632 | -0.26 | 4.34 | 4.075 | 6.10 |
125 | 600 | 20 | 49 | 7 | 2.525 | 2.536 | -0.42 | 7.98 | 7.599 | 4.78 |
126 | 600 | 20 | 49 | 10 | 2.512 | 2.508 | 0.15 | 8.45 | 8.569 | -1.41 |
129 | 600 | 5 | 5 | 1 | 2.711 | 2.720 | -0.32 | 2.69 | 2.648 | 1.55 |
131 | 600 | 5 | 5 | 5 | 2.679 | 2.685 | -0.24 | 3.84 | 3.790 | 1.31 |
133 | 600 | 5 | 5 | 10 | 2.652 | 2.656 | -0.16 | 4.81 | 4.808 | 0.04 |
134 | 600 | 10 | 5 | 0 | 2.713 | 2.716 | -0.11 | 2.13 | 1.886 | 11.48 |
137 | 600 | 10 | 5 | 2 | 2.68 | 2.679 | 0.03 | 3.32 | 3.274 | 1.40 |
139 | 600 | 10 | 5 | 7 | 2.611 | 2.606 | 0.19 | 5.81 | 6.038 | -3.93 |
141 | 600 | 20 | 5 | 0 | 2.678 | 2.672 | 0.24 | 2.41 | 2.652 | -10.03 |
143 | 600 | 20 | 5 | 1 | 2.641 | 2.636 | 0.20 | 3.75 | 3.939 | -5.05 |
144 | 600 | 20 | 5 | 2 | 2.617 | 2.621 | -0.16 | 4.63 | 4.513 | 2.54 |
147 | 600 | 20 | 5 | 10 | 2.5 | 2.500 | -0.01 | 8.89 | 8.854 | 0.40 |
MAPE | 0.093 | 1.400 | ||||||||
RMSE | 0.004 | 0.136 |
Sample ID | Compact pressure (MPa) | Reinforcement ratio (%) | Reinforcement size (μm) | Milling time (h) | Density (g/cm3) | Porosity (%) | ||||
---|---|---|---|---|---|---|---|---|---|---|
Measured | Predicted | Error (%) | Measured | Predicted | Error (%) | |||||
2 | 200 | 0 | 0 | 0.5 | 2.659 | 2.654 | 0.19 | 5.04 | 4.948 | 1.82 |
8 | 200 | 5 | 49 | 0 | 2.658 | 2.668 | -0.38 | 4.6 | 4.452 | 3.22 |
11 | 200 | 5 | 49 | 2 | 2.622 | 2.616 | 0.23 | 5.89 | 6.225 | -5.69 |
13 | 200 | 5 | 49 | 7 | 2.571 | 2.567 | 0.17 | 7.72 | 7.946 | -2.92 |
16 | 200 | 10 | 49 | 0.5 | 2.595 | 2.590 | 0.20 | 6.39 | 6.439 | -0.77 |
20 | 200 | 10 | 49 | 7 | 2.465 | 2.463 | 0.10 | 11.08 | 11.137 | -0.52 |
26 | 200 | 20 | 49 | 5 | 2.511 | 2.492 | 0.75 | 8.49 | 9.228 | -8.70 |
30 | 200 | 5 | 5 | 0.5 | 2.633 | 2.638 | -0.19 | 5.49 | 5.502 | -0.22 |
34 | 200 | 5 | 5 | 7 | 2.562 | 2.559 | 0.13 | 8.04 | 8.230 | -2.36 |
38 | 200 | 10 | 5 | 1 | 2.572 | 2.565 | 0.27 | 7.22 | 7.263 | -0.60 |
42 | 200 | 10 | 5 | 10 | 2.438 | 2.447 | -0.35 | 12.05 | 11.768 | 2.34 |
47 | 200 | 20 | 5 | 5 | 2.473 | 2.477 | -0.17 | 9.88 | 9.756 | 1.26 |
55 | 400 | 0 | 0 | 7 | 2.66 | 2.646 | 0.52 | 5 | 5.167 | -3.34 |
59 | 400 | 5 | 49 | 1 | 2.681 | 2.681 | -0.01 | 3.77 | 3.991 | -5.86 |
61 | 400 | 5 | 49 | 5 | 2.647 | 2.649 | -0.09 | 4.99 | 5.054 | -1.28 |
63 | 400 | 5 | 49 | 10 | 2.615 | 2.612 | 0.10 | 6.14 | 6.343 | -3.31 |
67 | 400 | 10 | 49 | 2 | 2.615 | 2.622 | -0.28 | 5.66 | 5.418 | 4.27 |
70 | 400 | 10 | 49 | 10 | 2.503 | 2.511 | -0.30 | 9.7 | 9.652 | 0.49 |
73 | 400 | 20 | 49 | 1 | 2.59 | 2.589 | 0.04 | 5.62 | 5.721 | -1.79 |
78 | 400 | 5 | 5 | 0 | 2.702 | 2.706 | -0.15 | 3.02 | 3.119 | -3.29 |
81 | 400 | 5 | 5 | 2 | 2.668 | 2.669 | -0.03 | 4.24 | 4.423 | -4.31 |
86 | 400 | 10 | 5 | 0.5 | 2.632 | 2.631 | 0.02 | 5.45 | 4.984 | 8.55 |
93 | 400 | 20 | 5 | 0.5 | 2.591 | 2.595 | -0.14 | 5.58 | 5.521 | 1.05 |
97 | 400 | 20 | 5 | 7 | 2.45 | 2.459 | -0.36 | 10.71 | 10.356 | 3.30 |
100 | 600 | 0 | 0 | 0.5 | 2.754 | 2.747 | 0.24 | 1.64 | 1.677 | -2.28 |
103 | 600 | 0 | 0 | 5 | 2.705 | 2.699 | 0.21 | 3.39 | 3.303 | 2.57 |
106 | 600 | 5 | 49 | 0 | 2.745 | 2.752 | -0.26 | 1.47 | 1.504 | -2.34 |
109 | 600 | 5 | 49 | 2 | 2.705 | 2.713 | -0.30 | 2.91 | 2.870 | 1.38 |
111 | 600 | 5 | 49 | 7 | 2.667 | 2.673 | -0.21 | 4.27 | 4.236 | 0.78 |
114 | 600 | 10 | 49 | 0.5 | 2.715 | 2.712 | 0.12 | 2.06 | 2.104 | -2.12 |
121 | 600 | 20 | 49 | 0.5 | 2.661 | 2.668 | -0.28 | 3.02 | 2.714 | 10.13 |
124 | 600 | 20 | 49 | 5 | 2.592 | 2.599 | -0.28 | 5.54 | 5.360 | 3.25 |
128 | 600 | 5 | 5 | 0.5 | 2.73 | 2.733 | -0.11 | 2.01 | 2.175 | -8.19 |
132 | 600 | 5 | 5 | 7 | 2.655 | 2.665 | -0.37 | 4.7 | 4.505 | 4.16 |
136 | 600 | 10 | 5 | 1 | 2.692 | 2.689 | 0.10 | 2.89 | 2.869 | 0.74 |
140 | 600 | 10 | 5 | 10 | 2.606 | 2.588 | 0.68 | 6 | 6.783 | -13.05 |
145 | 600 | 20 | 5 | 5 | 2.582 | 2.593 | -0.41 | 5.9 | 5.602 | 5.06 |
MAPE | 0.119 | 1.720 | ||||||||
RMSE | 0.005 | 0.179 |
Table 2 Validation data and predicted output from the ANN network for the validation data set
Sample ID | Compact pressure (MPa) | Reinforcement ratio (%) | Reinforcement size (μm) | Milling time (h) | Density (g/cm3) | Porosity (%) | ||||
---|---|---|---|---|---|---|---|---|---|---|
Measured | Predicted | Error (%) | Measured | Predicted | Error (%) | |||||
2 | 200 | 0 | 0 | 0.5 | 2.659 | 2.654 | 0.19 | 5.04 | 4.948 | 1.82 |
8 | 200 | 5 | 49 | 0 | 2.658 | 2.668 | -0.38 | 4.6 | 4.452 | 3.22 |
11 | 200 | 5 | 49 | 2 | 2.622 | 2.616 | 0.23 | 5.89 | 6.225 | -5.69 |
13 | 200 | 5 | 49 | 7 | 2.571 | 2.567 | 0.17 | 7.72 | 7.946 | -2.92 |
16 | 200 | 10 | 49 | 0.5 | 2.595 | 2.590 | 0.20 | 6.39 | 6.439 | -0.77 |
20 | 200 | 10 | 49 | 7 | 2.465 | 2.463 | 0.10 | 11.08 | 11.137 | -0.52 |
26 | 200 | 20 | 49 | 5 | 2.511 | 2.492 | 0.75 | 8.49 | 9.228 | -8.70 |
30 | 200 | 5 | 5 | 0.5 | 2.633 | 2.638 | -0.19 | 5.49 | 5.502 | -0.22 |
34 | 200 | 5 | 5 | 7 | 2.562 | 2.559 | 0.13 | 8.04 | 8.230 | -2.36 |
38 | 200 | 10 | 5 | 1 | 2.572 | 2.565 | 0.27 | 7.22 | 7.263 | -0.60 |
42 | 200 | 10 | 5 | 10 | 2.438 | 2.447 | -0.35 | 12.05 | 11.768 | 2.34 |
47 | 200 | 20 | 5 | 5 | 2.473 | 2.477 | -0.17 | 9.88 | 9.756 | 1.26 |
55 | 400 | 0 | 0 | 7 | 2.66 | 2.646 | 0.52 | 5 | 5.167 | -3.34 |
59 | 400 | 5 | 49 | 1 | 2.681 | 2.681 | -0.01 | 3.77 | 3.991 | -5.86 |
61 | 400 | 5 | 49 | 5 | 2.647 | 2.649 | -0.09 | 4.99 | 5.054 | -1.28 |
63 | 400 | 5 | 49 | 10 | 2.615 | 2.612 | 0.10 | 6.14 | 6.343 | -3.31 |
67 | 400 | 10 | 49 | 2 | 2.615 | 2.622 | -0.28 | 5.66 | 5.418 | 4.27 |
70 | 400 | 10 | 49 | 10 | 2.503 | 2.511 | -0.30 | 9.7 | 9.652 | 0.49 |
73 | 400 | 20 | 49 | 1 | 2.59 | 2.589 | 0.04 | 5.62 | 5.721 | -1.79 |
78 | 400 | 5 | 5 | 0 | 2.702 | 2.706 | -0.15 | 3.02 | 3.119 | -3.29 |
81 | 400 | 5 | 5 | 2 | 2.668 | 2.669 | -0.03 | 4.24 | 4.423 | -4.31 |
86 | 400 | 10 | 5 | 0.5 | 2.632 | 2.631 | 0.02 | 5.45 | 4.984 | 8.55 |
93 | 400 | 20 | 5 | 0.5 | 2.591 | 2.595 | -0.14 | 5.58 | 5.521 | 1.05 |
97 | 400 | 20 | 5 | 7 | 2.45 | 2.459 | -0.36 | 10.71 | 10.356 | 3.30 |
100 | 600 | 0 | 0 | 0.5 | 2.754 | 2.747 | 0.24 | 1.64 | 1.677 | -2.28 |
103 | 600 | 0 | 0 | 5 | 2.705 | 2.699 | 0.21 | 3.39 | 3.303 | 2.57 |
106 | 600 | 5 | 49 | 0 | 2.745 | 2.752 | -0.26 | 1.47 | 1.504 | -2.34 |
109 | 600 | 5 | 49 | 2 | 2.705 | 2.713 | -0.30 | 2.91 | 2.870 | 1.38 |
111 | 600 | 5 | 49 | 7 | 2.667 | 2.673 | -0.21 | 4.27 | 4.236 | 0.78 |
114 | 600 | 10 | 49 | 0.5 | 2.715 | 2.712 | 0.12 | 2.06 | 2.104 | -2.12 |
121 | 600 | 20 | 49 | 0.5 | 2.661 | 2.668 | -0.28 | 3.02 | 2.714 | 10.13 |
124 | 600 | 20 | 49 | 5 | 2.592 | 2.599 | -0.28 | 5.54 | 5.360 | 3.25 |
128 | 600 | 5 | 5 | 0.5 | 2.73 | 2.733 | -0.11 | 2.01 | 2.175 | -8.19 |
132 | 600 | 5 | 5 | 7 | 2.655 | 2.665 | -0.37 | 4.7 | 4.505 | 4.16 |
136 | 600 | 10 | 5 | 1 | 2.692 | 2.689 | 0.10 | 2.89 | 2.869 | 0.74 |
140 | 600 | 10 | 5 | 10 | 2.606 | 2.588 | 0.68 | 6 | 6.783 | -13.05 |
145 | 600 | 20 | 5 | 5 | 2.582 | 2.593 | -0.41 | 5.9 | 5.602 | 5.06 |
MAPE | 0.119 | 1.720 | ||||||||
RMSE | 0.005 | 0.179 |
Fig. 7 The change of porosity with milling time and compaction pressure for unreinforced Al2024 alloy (a) and Al2024-20 wt% B4C (D50:49 µm) (b) composite
Sample ID | Compact pressure (MPa) | Reinforcement ratio (%) | Reinforcement size (μm) | Milling time (h) | Density (g/cm3) | Porosity (%) | ||||
---|---|---|---|---|---|---|---|---|---|---|
Measured | Predicted | Error (%) | Measured | Predicted | Error (%) | |||||
4 | 200 | 0 | 0 | 2 | 2.634 | 2.627 | 0.28 | 5.9 | 5.849 | 0.87 |
6 | 200 | 0 | 0 | 7 | 2.612 | 2.604 | 0.32 | 6.71 | 6.658 | 0.78 |
12 | 200 | 5 | 49 | 5 | 2.594 | 2.602 | -0.32 | 6.9 | 6.699 | 2.91 |
15 | 200 | 10 | 49 | 0 | 2.615 | 2.610 | 0.17 | 5.67 | 5.694 | -0.42 |
18 | 200 | 10 | 49 | 2 | 2.572 | 2.562 | 0.40 | 7.22 | 7.454 | -3.24 |
21 | 200 | 10 | 49 | 10 | 2.45 | 2.454 | -0.15 | 11.62 | 11.559 | 0.53 |
24 | 200 | 20 | 49 | 1 | 2.542 | 2.535 | 0.27 | 7.36 | 7.619 | -3.52 |
29 | 200 | 5 | 5 | 0 | 2.652 | 2.656 | -0.15 | 4.81 | 4.871 | -1.27 |
32 | 200 | 5 | 5 | 2 | 2.613 | 2.612 | 0.05 | 6.21 | 6.372 | -2.62 |
37 | 200 | 10 | 5 | 0.5 | 2.58 | 2.581 | -0.04 | 6.93 | 6.709 | 3.19 |
40 | 200 | 10 | 5 | 5 | 2.533 | 2.518 | 0.60 | 8.63 | 9.097 | -5.41 |
46 | 200 | 20 | 5 | 2 | 2.51 | 2.531 | -0.83 | 8.53 | 7.817 | 8.36 |
48 | 200 | 20 | 5 | 7 | 2.402 | 2.409 | -0.28 | 12.47 | 12.153 | 2.54 |
52 | 400 | 0 | 0 | 1 | 2.693 | 2.690 | 0.13 | 3.82 | 3.702 | 3.10 |
56 | 400 | 0 | 0 | 10 | 2.657 | 2.640 | 0.65 | 5.11 | 5.391 | -5.50 |
66 | 400 | 10 | 49 | 1 | 2.638 | 2.631 | 0.27 | 4.94 | 5.039 | -2.00 |
68 | 400 | 10 | 49 | 5 | 2.592 | 2.593 | -0.05 | 6.49 | 6.569 | -1.22 |
74 | 400 | 20 | 49 | 2 | 2.578 | 2.580 | -0.06 | 6.05 | 6.074 | -0.39 |
76 | 400 | 20 | 49 | 7 | 2.471 | 2.468 | 0.11 | 9.95 | 10.026 | -0.76 |
82 | 400 | 5 | 5 | 5 | 2.635 | 2.642 | -0.28 | 5.42 | 5.296 | 2.28 |
84 | 400 | 5 | 5 | 10 | 2.605 | 2.605 | 0.01 | 6.5 | 6.610 | -1.69 |
88 | 400 | 10 | 5 | 2 | 2.603 | 2.614 | -0.43 | 6.1 | 5.681 | 6.88 |
90 | 400 | 10 | 5 | 7 | 2.505 | 2.514 | -0.37 | 9.63 | 9.369 | 2.71 |
94 | 400 | 20 | 5 | 1 | 2.583 | 2.582 | 0.03 | 5.87 | 5.964 | -1.61 |
98 | 400 | 20 | 5 | 10 | 2.437 | 2.442 | -0.22 | 11.19 | 10.943 | 2.20 |
104 | 600 | 0 | 0 | 7 | 2.692 | 2.689 | 0.11 | 3.86 | 3.656 | 5.29 |
108 | 600 | 5 | 49 | 1 | 2.719 | 2.728 | -0.32 | 2.4 | 2.364 | 1.50 |
113 | 600 | 10 | 49 | 0 | 2.722 | 2.723 | -0.05 | 1.8 | 1.674 | 7.01 |
116 | 600 | 10 | 49 | 2 | 2.685 | 2.685 | 0.00 | 3.14 | 3.109 | 0.99 |
119 | 600 | 10 | 49 | 10 | 2.614 | 2.598 | 0.60 | 5.7 | 6.457 | -13.28 |
122 | 600 | 20 | 49 | 1 | 2.653 | 2.651 | 0.09 | 3.32 | 3.353 | -0.99 |
127 | 600 | 5 | 5 | 0 | 2.735 | 2.746 | -0.40 | 1.83 | 1.724 | 5.77 |
130 | 600 | 5 | 5 | 2 | 2.697 | 2.708 | -0.42 | 3.19 | 3.045 | 4.55 |
135 | 600 | 10 | 5 | 0.5 | 2.709 | 2.703 | 0.23 | 2.27 | 2.373 | -4.54 |
138 | 600 | 10 | 5 | 5 | 2.653 | 2.657 | -0.15 | 4.29 | 4.179 | 2.59 |
142 | 600 | 20 | 5 | 0.5 | 2.65 | 2.653 | -0.12 | 3.43 | 3.304 | 3.67 |
146 | 600 | 20 | 5 | 7 | 2.515 | 2.524 | -0.37 | 8.35 | 8.005 | 4.13 |
MAPE | 0.126 | 1.625 | ||||||||
RMSE | 0.006 | 0.179 |
Table 3 Experimental data and predicted output from the ANN network for the testing data set
Sample ID | Compact pressure (MPa) | Reinforcement ratio (%) | Reinforcement size (μm) | Milling time (h) | Density (g/cm3) | Porosity (%) | ||||
---|---|---|---|---|---|---|---|---|---|---|
Measured | Predicted | Error (%) | Measured | Predicted | Error (%) | |||||
4 | 200 | 0 | 0 | 2 | 2.634 | 2.627 | 0.28 | 5.9 | 5.849 | 0.87 |
6 | 200 | 0 | 0 | 7 | 2.612 | 2.604 | 0.32 | 6.71 | 6.658 | 0.78 |
12 | 200 | 5 | 49 | 5 | 2.594 | 2.602 | -0.32 | 6.9 | 6.699 | 2.91 |
15 | 200 | 10 | 49 | 0 | 2.615 | 2.610 | 0.17 | 5.67 | 5.694 | -0.42 |
18 | 200 | 10 | 49 | 2 | 2.572 | 2.562 | 0.40 | 7.22 | 7.454 | -3.24 |
21 | 200 | 10 | 49 | 10 | 2.45 | 2.454 | -0.15 | 11.62 | 11.559 | 0.53 |
24 | 200 | 20 | 49 | 1 | 2.542 | 2.535 | 0.27 | 7.36 | 7.619 | -3.52 |
29 | 200 | 5 | 5 | 0 | 2.652 | 2.656 | -0.15 | 4.81 | 4.871 | -1.27 |
32 | 200 | 5 | 5 | 2 | 2.613 | 2.612 | 0.05 | 6.21 | 6.372 | -2.62 |
37 | 200 | 10 | 5 | 0.5 | 2.58 | 2.581 | -0.04 | 6.93 | 6.709 | 3.19 |
40 | 200 | 10 | 5 | 5 | 2.533 | 2.518 | 0.60 | 8.63 | 9.097 | -5.41 |
46 | 200 | 20 | 5 | 2 | 2.51 | 2.531 | -0.83 | 8.53 | 7.817 | 8.36 |
48 | 200 | 20 | 5 | 7 | 2.402 | 2.409 | -0.28 | 12.47 | 12.153 | 2.54 |
52 | 400 | 0 | 0 | 1 | 2.693 | 2.690 | 0.13 | 3.82 | 3.702 | 3.10 |
56 | 400 | 0 | 0 | 10 | 2.657 | 2.640 | 0.65 | 5.11 | 5.391 | -5.50 |
66 | 400 | 10 | 49 | 1 | 2.638 | 2.631 | 0.27 | 4.94 | 5.039 | -2.00 |
68 | 400 | 10 | 49 | 5 | 2.592 | 2.593 | -0.05 | 6.49 | 6.569 | -1.22 |
74 | 400 | 20 | 49 | 2 | 2.578 | 2.580 | -0.06 | 6.05 | 6.074 | -0.39 |
76 | 400 | 20 | 49 | 7 | 2.471 | 2.468 | 0.11 | 9.95 | 10.026 | -0.76 |
82 | 400 | 5 | 5 | 5 | 2.635 | 2.642 | -0.28 | 5.42 | 5.296 | 2.28 |
84 | 400 | 5 | 5 | 10 | 2.605 | 2.605 | 0.01 | 6.5 | 6.610 | -1.69 |
88 | 400 | 10 | 5 | 2 | 2.603 | 2.614 | -0.43 | 6.1 | 5.681 | 6.88 |
90 | 400 | 10 | 5 | 7 | 2.505 | 2.514 | -0.37 | 9.63 | 9.369 | 2.71 |
94 | 400 | 20 | 5 | 1 | 2.583 | 2.582 | 0.03 | 5.87 | 5.964 | -1.61 |
98 | 400 | 20 | 5 | 10 | 2.437 | 2.442 | -0.22 | 11.19 | 10.943 | 2.20 |
104 | 600 | 0 | 0 | 7 | 2.692 | 2.689 | 0.11 | 3.86 | 3.656 | 5.29 |
108 | 600 | 5 | 49 | 1 | 2.719 | 2.728 | -0.32 | 2.4 | 2.364 | 1.50 |
113 | 600 | 10 | 49 | 0 | 2.722 | 2.723 | -0.05 | 1.8 | 1.674 | 7.01 |
116 | 600 | 10 | 49 | 2 | 2.685 | 2.685 | 0.00 | 3.14 | 3.109 | 0.99 |
119 | 600 | 10 | 49 | 10 | 2.614 | 2.598 | 0.60 | 5.7 | 6.457 | -13.28 |
122 | 600 | 20 | 49 | 1 | 2.653 | 2.651 | 0.09 | 3.32 | 3.353 | -0.99 |
127 | 600 | 5 | 5 | 0 | 2.735 | 2.746 | -0.40 | 1.83 | 1.724 | 5.77 |
130 | 600 | 5 | 5 | 2 | 2.697 | 2.708 | -0.42 | 3.19 | 3.045 | 4.55 |
135 | 600 | 10 | 5 | 0.5 | 2.709 | 2.703 | 0.23 | 2.27 | 2.373 | -4.54 |
138 | 600 | 10 | 5 | 5 | 2.653 | 2.657 | -0.15 | 4.29 | 4.179 | 2.59 |
142 | 600 | 20 | 5 | 0.5 | 2.65 | 2.653 | -0.12 | 3.43 | 3.304 | 3.67 |
146 | 600 | 20 | 5 | 7 | 2.515 | 2.524 | -0.37 | 8.35 | 8.005 | 4.13 |
MAPE | 0.126 | 1.625 | ||||||||
RMSE | 0.006 | 0.179 |
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