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
APA StyleGarbowski, T., Knitter-Piątkowska, A., & Grabski, J. K. (2023). Estimation of the Edge Crush Resistance of Corrugated Board Using Artificial Intelligence. Materials, 16(4), 1631. https://doi.org/10.3390/ma16041631