Estimation of the Edge Crush Resistance of Corrugated Board Using Artificial Intelligence
Abstract
:1. Introduction
2. Materials and Methods
2.1. Paperboard and Cardboard Laboratory Tests
2.2. Artificial Neural Networks–Training Data
2.3. Gaussian Processes
- Be symmetrical. That means that ;
- Be positively defined. That means that the kernel matrix induced by for any set of inputs should be a positive definite matrix.
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Corrugated Board | Component Papers | Corrugated Layers | ||||||
---|---|---|---|---|---|---|---|---|
Wave | Grammage | Height | Paper ID | Grammage | Thickness | Height | Period | Take-Up |
Type | (g/m2) | (mm) | (g/m2) | (mm) | (mm) | (mm) | Factor | |
B | 410 | 2.912 | TL3125 | 124 ± 6 | 0.27 ± 0.1 | - | - | - |
WS120 | 118 ± 6 | 0.25 ± 0.1 | 2.55 | 6.34 | 1.337 | |||
TL3125 | 126 ± 6 | 0.27 ± 0.1 | - | - | - | |||
C | 590 | 4.110 | KLB170 | 168 ± 8 | 0.36 ± 0.2 | - | - | - |
S.C.175 | 176 ± 8 | 0.36 ± 0.2 | 3.63 | 7.95 | 1.427 | |||
KLB170 | 169 ± 8 | 0.36 ± 0.2 | - | - | - | |||
E | 480 | 1.586 | TLWC160 | 158 ± 8 | 0.17 ± 0.1 | - | - | - |
WS135 | 133 ± 6 | 0.13 ± 0.1 | 1.16 | 3.50 | 1.236 | |||
TLW160 | 159 ± 8 | 0.17 ± 0.1 | - | - | - | |||
BC | 790 | 6.740 | KLB170 | 168 ± 8 | 0.28 ± 0.2 | - | - | - |
W135 | 136 ± 6 | 0.25 ± 0.1 | 2.55 | 6.34 | 1.337 | |||
WS80 | 79 ± 4 | 0.22 ± 0.1 | - | - | - | |||
WS135 | 133 ± 6 | 0.25 ± 0.1 | 3.63 | 7.95 | 1.427 | |||
KLB170 | 172 ± 8 | 0.28 ± 0.2 | - | - | - | |||
BE | 600 | 4.150 | TLW140 | 141 ± 7 | 0.28 ± 0.2 | - | - | - |
WS95 | 94 ± 5 | 0.22 ± 0.1 | 2.55 | 6.34 | 1.337 | |||
WS80 | 81 ± 4 | 0.22 ± 0.1 | - | - | - | |||
WS95 | 94 ± 5 | 0.22 ± 0.1 | 1.16 | 3.50 | 1.236 | |||
TL3125 | 124 ± 6 | 0.28 ± 0.2 | - | - | - | |||
BE | 590 | 4.120 | TL3125 | 125 ± 6 | 0.32 ± 0.2 | - | - | - |
WS95 | 94 ± 5 | 0.24 ± 0.1 | 2.55 | 6.34 | 1.337 | |||
W80 | 79 ± 5 | 0.22 ± 0.1 | - | - | - | |||
WS95 | 96 ± 5 | 0.24 ± 0.1 | 1.16 | 3.50 | 1.236 | |||
TL3125 | 124 ± 6 | 0.29 ± 0.2 | - | - | - |
Layer | SCT | Tensile Stiffness | Flute | GRM * | THK * | ANG * | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
CD | MD | 45 d | CD | MD | 45 d | Width | Height | TUF * | ||||
Liner | 1 | 2 | 3 | 4 | 5 | 6 | - | - | - | 7 | 8 | - |
Flute | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | - |
Liner | 20 | 21 | 22 | 23 | 24 | 25 | - | - | - | 26 | 27 | - |
- | - | - | - | - | - | - | - | - | - | - | - | 28 |
Layer | SCT | Tensile Stiffness | Flute | GRM * | THK * | ANG * | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
CD | MD | 45 d | CD | MD | 45 d | Width | Height | TUF * | ||||
Liner | 1 | 2 | 3 | 4 | 5 | 6 | - | - | - | 7 | 8 | - |
Flute | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | - |
Liner | 20 | 21 | 22 | 23 | 24 | 25 | - | - | - | 26 | 27 | - |
Flute | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | |
Liner | 39 | 40 | 41 | 42 | 43 | 44 | - | - | - | 45 | 46 | |
- | - | - | - | - | - | - | - | - | - | - | - | 47 |
Grade ID | Paper ID | Short-Span Compression Strength | Tensile Stiffness | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
CD | MD | 45 Deg | CD | MD | 45 Deg | ||||||||
(kN/m) | (kN/m) | ||||||||||||
TL3125 | 2.14 | ±0.12 | 3.97 | ±0.05 | 2.92 | ±0.05 | 373.3 | ±2.1 | 1012.7 | ±6.3 | 572.7 | ±10.8 | |
B-410 | WS120 | 2.09 | ±0.07 | 4.09 | ±0.15 | 3.14 | ±0.08 | 365.1 | ±8.8 | 1024.6 | ±8.5 | 516.5 | ±9.7 |
TL3125 | 2.09 | ±0.11 | 4.05 | ±0.11 | 3.11 | ±0.14 | 381.2 | ±11.2 | 1058.3 | ±9.8 | 595.1 | ±10.5 | |
KLB170 | 3.28 | ±0.18 | 5.96 | ±0.23 | 4.43 | ±0.19 | 527.8 | ±9.1 | 1472.1 | ±20.1 | 929.1 | ±20.3 | |
C-590 | S.C.175 | 4.18 | ±0.19 | 7.47 | ±0.18 | 5.84 | ±0.07 | 686.1 | ±13.9 | 1476.1 | ±10.9 | 924.7 | ±48.9 |
KLB170 | 3.19 | ±0.06 | 5.51 | ±0.18 | 4.65 | ±0.13 | 568.1 | ±14.8 | 1445.1 | ±31.7 | 956.2 | ±26.6 | |
TLWC160 | 2.75 | ±0.20 | 4.20 | ±0.15 | 3.49 | ±0.13 | 412.1 | ±6.8 | 1043.6 | ±11.1 | 635.0 | ±11.2 | |
E-480 | WS135 | 2.13 | ±0.10 | 4.25 | ±0.15 | 2.95 | ±0.07 | 365.0 | ±9.8 | 1067.5 | ±14.5 | 533.5 | ±8.5 |
TLW160 | 2.43 | ±0.11 | 4.09 | ±0.13 | 3.21 | ±0.11 | 443.9 | ±1.5 | 1102.1 | ±38.6 | 667.0 | ±5.4 | |
KLB170 | 3.39 | ±0.12 | 6.14 | ±0.19 | 4.69 | ±0.13 | 618.9 | ±17.6 | 1534.2 | ±6.7 | 990.0 | ±17.5 | |
W135 | 2.19 | ±0.09 | 4.27 | ±0.10 | 3.09 | ±0.13 | 369.1 | ±11.2 | 1113.5 | ±9.8 | 572.4 | ±22.6 | |
BC-790 | WS80 | 1.50 | ±0.08 | 2.30 | ±0.09 | 1.91 | ±0.04 | 317.1 | ±4.2 | 699.1 | ±3.3 | 445.0 | ±5.8 |
WS135 | 2.23 | ±0.04 | 4.37 | ±0.15 | 3.18 | ±0.06 | 385.9 | ±12.0 | 1147.4 | ±7.6 | 623.5 | ±8.0 | |
KLB170 | 3.30 | ±0.18 | 5.98 | ±0.32 | 4.66 | ±0.20 | 592.7 | ±8.3 | 1418.9 | ±23.6 | 838.2 | ±12.7 | |
TLW140 | 2.61 | ±0.13 | 3.92 | ±0.09 | 3.08 | ±0.11 | 506.0 | ±7.1 | 1000.0 | ±12.6 | 622.6 | ±11.7 | |
WS95 | 1.69 | ±0.09 | 2.99 | ±0.16 | 2.26 | ±0.09 | 331.9 | ±5.5 | 872.7 | ±6.0 | 498.6 | ±10.3 | |
BE-600 | WS80 | 1.42 | ±0.03 | 2.56 | ±0.17 | 1.88 | ±0.08 | 273.2 | ±3.8 | 812.8 | ±12.3 | 424.8 | ±7.2 |
WS95 | 1.52 | ±0.08 | 3.16 | ±0.13 | 2.46 | ±0.06 | 290.7 | ±6.7 | 885.5 | ±18.9 | 508.4 | ±14.7 | |
TL3125 | 2.13 | ±0.09 | 3.83 | ±0.13 | 2.93 | ±0.10 | 440.6 | ±3.4 | 1082.2 | ±13.3 | 623.3 | ±35.4 | |
TL3125 | 2.26 | ±0.13 | 3.64 | ±0.08 | 3.06 | ±0.11 | 412.9 | ±11.6 | 961.3 | ±10.0 | 587.0 | ±3.4 | |
WS95 | 1.50 | ±0.06 | 2.69 | ±0.13 | 2.01 | ±0.09 | 294.3 | ±8.6 | 756.4 | ±13.8 | 427.4 | ±8.8 | |
BE-590 | W80 | 1.47 | ±0.08 | 2.34 | ±0.06 | 1.94 | ±0.08 | 343.5 | ±5.8 | 696.5 | ±14.5 | 459.8 | ±5.0 |
WS95 | 1.75 | ±0.10 | 2.96 | ±0.18 | 2.15 | ±0.06 | 332.0 | ±4.0 | 854.7 | ±4.2 | 474.4 | ±11.0 | |
TL3125 | 2.32 | ±0.07 | 3.75 | ±0.06 | 2.87 | ±0.17 | 413.8 | ±4.7 | 883.1 | ±20.9 | 588.3 | ±14.5 |
Board ID | Edge Crush Resistance | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
CD (0 Deg) | 15 Deg | 30 Deg | 45 Deg | 60 Deg | 75 Deg | |||||||
(kN/m) | ||||||||||||
B-410 | 5.48 | ±0.09 | 5.17 | ±0.12 | 4.40 | ±0.03 | 3.88 | ±0.10 | 3.05 | ±0.10 | 2.29 | ±0.13 |
C-590 | 9.68 | ±0.10 | 9.07 | ±0.14 | 7.60 | ±0.02 | 6.24 | ±0.12 | 4.83 | ±0.10 | 3.49 | ±0.23 |
E-480 | 6.37 | ±0.17 | 5.92 | ±0.08 | 5.99 | ±0.26 | 5.47 | ±0.27 | 5.16 | ±0.17 | 4.56 | ±0.18 |
BC-790 | 10.41 | ±0.13 | 9.56 | ±0.37 | 8.38 | ±0.29 | 6.96 | ±0.10 | 6.00 | ±0.17 | 4.31 | ±0.16 |
BE-600 | 8.95 | ±0.14 | 8.39 | ±0.06 | 7.76 | ±0.14 | 6.46 | ±0.18 | 5.66 | ±0.32 | 4.30 | ±0.35 |
BE-590 | 9.68 | ±0.10 | 9.07 | ±0.14 | 7.60 | ±0.02 | 6.24 | ±0.12 | 4.83 | ±0.10 | 3.49 | ±0.22 |
Model | Mean Absolute Error (%) | ||
Method | 3-Layer Cardboard | 5-Layer Cardboard | |
FF (full) | 3.163 | 1.575 | |
FF (small) | 2.273 | 1.921 | |
DL (full) | 2.985 | 3.093 | |
DL (small) | 3.948 | 2.916 | |
GP (full) | 2.484 | 1.317 | |
GP (small) | 2.260 | 2.150 | |
Analytical [78] | 1.760 | 2.987 | |
FEM-1 [78] | 1.640 | 2.260 | |
FEM-2 [78] | 4.010 | 4.227 | |
Empirical-1 [78] | 3.547 | 10.60 | |
Empirical-2 [78] | 1.997 | 9.800 |
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Garbowski, T.; Knitter-Piątkowska, A.; Grabski, J.K. Estimation of the Edge Crush Resistance of Corrugated Board Using Artificial Intelligence. Materials 2023, 16, 1631. https://doi.org/10.3390/ma16041631
Garbowski T, Knitter-Piątkowska A, Grabski JK. Estimation of the Edge Crush Resistance of Corrugated Board Using Artificial Intelligence. Materials. 2023; 16(4):1631. https://doi.org/10.3390/ma16041631
Chicago/Turabian StyleGarbowski, Tomasz, Anna Knitter-Piątkowska, and Jakub Krzysztof Grabski. 2023. "Estimation of the Edge Crush Resistance of Corrugated Board Using Artificial Intelligence" Materials 16, no. 4: 1631. https://doi.org/10.3390/ma16041631