1 Introduction
2 Materials and methods
2.1 Field experiment
2.2 Data
Material | C (%) | Mn (%) | Si (%) | Cr (%) | Ni (%) | Mo (%) | Al (%) | Mg (%) | V (%) | W (%) | Ti (%) |
---|---|---|---|---|---|---|---|---|---|---|---|
EN 41CrAlMo7 (1.8509) | 0.39 | 0.45 | 0.27 | 1.50 | 0.25 | 0.20 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 |
EN 42CrMo4 (1.7225) | 0.42 | 0.55 | 0.27 | 1.05 | 0.30 | 0.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
50HS (1.5026) | 0.5 | 0.45 | 1.00 | 1.05 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
PENTHOR 854 | 0.55 | 0.70 | 1.40 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
S14 | 3.5 | 0.60 | 2.55 | 0.30 | 1.20 | 0.50 | 0.00 | 0.05 | 0.00 | 0.00 | 0.00 |
L11 | 2.8 | 1.00 | 2.20 | 1.08 | 0.50 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
XTB | 3.05 | 1.25 | 1.95 | 0.55 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.75 | 0.23 |
Process no. | Temperature (oC) | Process organization |
---|---|---|
1 | 540 | 6A |
2 | 540 | 6A/2D |
3 | 540 | 8A/2D |
4 | 540 | 4A/2D/4A |
5 | 510 | 6A |
6 | 560 | 6A/2D |
7 | 560 | 4A/2D |
8 | 560 | 2A/2D/2A |
10 | 540 | 12A |
11 | 560 | 9A |
12 | 510 | 12A |
2.3 Data preprocessing
3 Artificial neural networks
3.1 Multilayer feed-forward (MLFF) ANN
3.2 RBF network
4 ANN training algorithms
4.1 Algorithm of backpropagation method
4.2 Broyden–Fletcher–Goldfarb–Shanno’s method
5 Experiments
5.1 ANN for predicting the properties of nitrided layers
Nitrided layer properties | Network architecture | Training quality | Testing quality | Validation quality | Training algorithm (iterations) | Error function | Hidden neurons activation | Output neurons activation |
---|---|---|---|---|---|---|---|---|
H
| MLP 11-9-1 | 0.9996 | 0.9979 | 0.8746 | BFGS 82 | SOS | Tanh | Linear |
ECD | MLP 11-4-1A | 0.9732 | 0.9885 | 0.9662 | BFGS 41 | SOS | Exponential | Logistic |
MLP 11-4-1B | 0.9707 | 0.9862 | 0.9739 | BFGS 45 | SOS | Exponential | Logistic | |
G
| MLP 11-12-1 | 0.9575 | 0.9916 | 0.8945 | BFGS 21 | SOS | Tanh | Linear |
MLP 11-4-1 | 0.9569 | 0.9981 | 0.9982 | BFGS 29 | SOS | Tanh | Tanh |
NHitrided layer properties | Network architecture | Training quality | Testing quality | Validation quality | Training algorithm (iterations) | Error function | Hidden neurons activation | Output neurons activation |
---|---|---|---|---|---|---|---|---|
H
| MLP 11-4-1 | 0.9993 | 0.9047 | 0.9998 | BFGS 65 | SOS | Tanh | Tanh |
ECD | MLP 11-4-1 | 0.9792 | 1.0000 | 1.0000 | BFGS 32 | SOS | Tanh | Linear |
G
| MLP 11-4-1 | 0.7810 | 0.9842 | 1.0000 | BFGS 9 | SOS | Logistic | Exponential |
5.2 Neural networks for determining process segmentation based on the technological requirements of the surface layer
Network name | Training quality | Testing quality | Validation quality | Training algorithm (iterations) | Error function | Hidden neurons activation | Output neurons activation |
---|---|---|---|---|---|---|---|
MLP 11-4-3A | 0.9092 | 0.6260 | 0.6484 | BFGS 84 | SOS | Logistic | Linear |
MLP 11-4-3B | 0.8944 | 0.6232 | 0.6516 | BFGS 56 | SOS | Logistic | Linear |
Network name | Training quality | Testing quality | Validation quality | Training algorithm (iterations) | Error function | Hidden neurons activation | Output neurons activation |
---|---|---|---|---|---|---|---|
MLP 11-4-3 | 0.9028 | 0.6228 | 1.0000 | BFGS 102 | SOS | Logistic | Tanh |
MLP 11-8-3 | 0.8812 | 0.6220 | 1.0000 | BFGS 1050 | SOS | Tanh | Logistic |
6 Results
Layer thickness H (HV) | ||||||
---|---|---|---|---|---|---|
Construction steels | Cast irons | |||||
Real | ANN | Abs. difference | Real | ANN | Abs. difference | |
1 | 996 | 998 | 2 | 345.6 | 344.0 | 1.6 |
2 | 439 | 442 | 3 | 375.6 | 378.2 | 2.6 |
3 | 549 | 545 | 3 | 344.4 | 342.6 | 1.8 |
4 | 695 | 696 | 1 | 338.8 | 338.5 | 0.3 |
5 | 436 | 437 | 1 | 300.2 | 301.0 | 0.8 |
6 | 320 | 320 | 0 | 330.0 | 327.0 | 3.0 |
7 | 821 | 806 | 15 | 398.0 | 398.4 | 0.4 |
8 | 838 | 844 | 5 | 384.2 | 392.8 | 8.6 |
9 | 506 | 607 | 101 | 372.4 | 372.8 | 0.4 |
10 | 683 | 684 | 0 | 399.8 | 409.9 | 10.1 |
Diffusion layer thickness (α) ECD (µm) | ||||||||
---|---|---|---|---|---|---|---|---|
Construction steels | Cast irons | |||||||
Real | ANN1 | ANN2 | ANN group | Abs. difference | Real | ANN | Abs. difference | |
1 | 140 | 156 | 167 | 161 | 21 | 45.0 | 44.8 | 0.2 |
2 | 100 | 72 | 75 | 74 | 26 | 40.0 | 40.1 | 0.1 |
3 | 70 | 78 | 86 | 82 | 12 | 50.0 | 42.8 | 7.2 |
4 | 90 | 92 | 92 | 92 | 2 | 45.0 | 47.0 | 2.0 |
5 | 90 | 96 | 94 | 95 | 5 | 50.0 | 50.5 | 0.5 |
6 | 80 | 85 | 82 | 84 | 4 | 55.0 | 56.6 | 1.6 |
7 | 170 | 166 | 171 | 168 | 2 | 65.0 | 61.4 | 3.6 |
8 | 220 | 184 | 181 | 182 | 38 | 40.0 | 41.3 | 1.3 |
9 | 110 | 53 | 68 | 60 | 50 | 50.0 | 49.9 | 0.1 |
10 | 170 | 172 | 173 | 173 | 3 | 40.0 | 37.9 | 2.1 |
Nitride phase thickness (γ′) G (µm) | ||||||||
---|---|---|---|---|---|---|---|---|
Construction steels | Cast irons | |||||||
Real | ANN1 | ANN2 | ANN group | Abs. difference | Real | ANN | Abs. difference | |
1 | 8.0 | 8.0 | 7.2 | 7.6 | 0.4 | 3.4 | 3.0 | 0.4 |
2 | 1.0 | 2.3 | 1.0 | 1.6 | 0.6 | 0.6 | 0.5 | 0.1 |
3 | 3.0 | 3.3 | 2.5 | 2.9 | 0.1 | 0.6 | 0.5 | 0.1 |
4 | 4.0 | 3.4 | 3.4 | 3.4 | 0.6 | 1.7 | 4.0 | 2.3 |
5 | 0.5 | 1.6 | 2.0 | 1.8 | 1.3 | 0.6 | 0.5 | 0.1 |
6 | 2.0 | 0.6 | 1.4 | 1.0 | 1.0 | 3.1 | 5.0 | 1.9 |
7 | 8.0 | 7.7 | 7.8 | 7.7 | 0.3 | 3.9 | 3.0 | 0.9 |
8 | 10.0 | 10.8 | 10.3 | 10.6 | 0.6 | 2.3 | 2.0 | 0.3 |
9 | 1.0 | 2.7 | 2.6 | 2.6 | 1.6 | 2.5 | 4.0 | 1.5 |
10 | 10.0 | 9.6 | 9.3 | 9.5 | 0.5 | 0.5 | 0.5 | 0.0 |
Construction steels | Cast irons | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Real | ANN1 | ANN2 | ANN group | Abs. difference | Real | ANN1 | ANN2 | ANN group | Abs. difference | |
First saturation segment time A1 (h) | ||||||||||
1 | 6.0 | 9.2 | 9.2 | 9.2 | 3.2 | 6.0 | 9.0 | 4.0 | 6.5 | 0.5 |
2 | 6.0 | 6.8 | 6.2 | 6.5 | 0.5 | 6.0 | 6.0 | 6.0 | 6.0 | 0.0 |
3 | 8.0 | 6.8 | 6.2 | 6.5 | 1.5 | 8.0 | 8.0 | 8.0 | 8.0 | 0.0 |
4 | 4.0 | 3.7 | 2.9 | 3.3 | 0.7 | 4.0 | 4.0 | 4.0 | 4.0 | 0.0 |
5 | 6.0 | 5.3 | 6.2 | 5.8 | 0.2 | 6.0 | 6.0 | 6.0 | 6.0 | 0.0 |
6 | 2.0 | 5.4 | 6.2 | 5.8 | 3.8 | 12.0 | 9.0 | 12.0 | 10.5 | 1.5 |
7 | 12.0 | 9.2 | 9.2 | 9.2 | 2.8 | 9.0 | 9.0 | 4.0 | 6.5 | 2.5 |
8 | 9.0 | 9.2 | 9.2 | 9.2 | 0.2 | 12.0 | 9.0 | 12.0 | 10.5 | 1.5 |
9 | 12.0 | 48.5 | 103.0 | 75.7 | 63.7 | 6.0 | 9.0 | 4.0 | 6.5 | 0.5 |
10 | 6.0 | 9.3 | 9.2 | 9.3 | 3.3 | 6.0 | 6.0 | 4.0 | 5.0 | 1.0 |
Annealing segment time D1 (h) | ||||||||||
1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
2 | 2.0 | 1.7 | 1.9 | 1.8 | 0.2 | 2.0 | 2.0 | 2.0 | 2.0 | 0.0 |
3 | 2.0 | 1.7 | 1.9 | 1.8 | 0.2 | 2.0 | 2.0 | 2.0 | 2.0 | 0.0 |
4 | 2.0 | 2.2 | 2.5 | 2.4 | 0.4 | 2.0 | 2.0 | 2.0 | 2.0 | 0.0 |
5 | 2.0 | 2.2 | 1.9 | 2.0 | 0.0 | 2.0 | 2.0 | 2.0 | 2.0 | 0.0 |
6 | 2.0 | 2.2 | 1.9 | 2.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
7 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
8 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
9 | 0.0 | − 10.2 | − 22.6 | − 16.4 | 16.4 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
10 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 2.0 | 2.0 | 2.0 | 2.0 | 0.0 |
Second saturation segment time A2 (h) | ||||||||||
1 | 0.0 | − 0.1 | − 0.1 | − 0.1 | 0.1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
2 | 0.0 | 0.0 | 0.5 | 0.3 | 0.3 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
3 | 0.0 | 0.1 | 0.5 | 0.3 | 0.3 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
4 | 4.0 | 3.7 | 3.3 | 3.5 | 0.5 | 4.0 | 4.0 | 4.0 | 4.0 | 0.0 |
5 | 0.0 | 0.9 | 0.5 | 0.7 | 0.7 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
6 | 2.0 | 0.9 | 0.5 | 0.7 | 1.3 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
7 | 0.0 | − 0.2 | − 0.1 | − 0.1 | 0.1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
8 | 0.0 | − 0.2 | − 0.1 | − 0.1 | 0.1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
9 | 0.0 | − 23.7 | − 52.5 | − 38.1 | 38.1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
10 | 0.0 | − 0.1 | − 0.1 | − 0.1 | 0.1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |