A Novel Assisted Artificial Neural Network Modeling Approach for Improved Accuracy Using Small Datasets: Application in Residual Strength Evaluation of Panels with Multiple Site Damage Cracks
Abstract
:1. Introduction
2. Background
2.1. Residual Strength of Panels with MSD
- σ: The remote applied stress.
- a: Lead crack half-length.
- βW: Finite width correction factor.
- βa/ℓ: Cracks interaction correction factor for the effect of MSD cracks on the lead crack.
- L: Length of the ligament between the lead crack and MSD crack.
- ℓ: MSD crack half-length.
- βa: The overall SIF correction factor for the lead crack tip.
- βℓ: The overall SIF correction factor for the adjacent MSD crack tip.
- βH: Correction factor for the effect of the hole.
- βℓ/a: The cracks interaction correction factor for the effect of the lead crack on MSD cracks.
2.2. ANN Input Parameters Selection
3. The Experimental Dataset
4. ANN Modeling Procedure
4.1. Traditional ANN Modeling Approach
4.2. Assisted-ANN Modeling Approach
- First assistance level: here, the panel configuration SIF correction factor (βP-config) is used as an assistance parameter. This correction factor corrects the SIF of the lead crack for all effects related to the panel configuration, where the unstiffened panel configuration (seen in Figure 1) is taken as a reference configuration. Therefore, the value of βP-config for the unstiffened panels (listed in Table A1) is unity (βP-config = 1) since this is the reference configuration. For the stiffened panels, the panel configuration correction factor is basically the stiffeners’ effect correction factor (βP-config = βstf), and its value for each of the different cracks/stiffeners configurations is given in Table A2. This stiffeners’ effect correction factor accounts not only for the presence of the stiffeners and their arrangement, but it also accounts for their cross-sectional area and spacing, the fasteners stiffness and spacing, and the crack location and length. Finally, for the lap-joint panels, the panel configuration correction factor is the lap-joint effect correction factor (βP-config = βLJ), and its value for each of the different cracks configurations is given in Table A3. This factor mainly accounts for the fasteners arrangement, stiffness and spacing, and for the point loads induced by the fasteners along the crack plane.
- Second assistance level: here, instead of using the panel configuration SIF correction factor (βP-config), the overall lead crack SIF correction factor () is used. The βa includes both the finite width correction and the cracks interaction correction (as seen in Equation (5)), and it also includes the panel configuration correction factor (βstf or βLJ). The values of for all the 113 data points are given in Table A1, Table A2 and Table A3.
- Third assistance level: here, instead of using one assistance parameter as in the previous assistance levels, two assistance parameters are used simultaneously. In addition to the overall lead crack SIF correction factor (), which is used in the second assistance level, the overall SIF correction factor for the adjacent MSD crack () is also used. The mainly accounts for the cracks interaction effect and the hole effect (as seen in Equation (6)) and its values are also given in the tables.
- Fourth assistance level: here, instead of using the SIF correction factors, the residual strength value calculated by the linkup model (Equation (4)) is used as the assistance parameter. As can be seen form the linkup model equation, it includes the SIF geometric correction factors as well as the lead and MSD crack lengths, the ligament length and the material’s yield strength. Therefore, the inclusion of the linkup model’s residual strength predictions provides the highest level of assistance since it combines the effects of many of the input parameters together.
4.3. Reduced Size Training Datasets
4.4. ANN Optimization and Performance Evaluation
5. Results and Discussion
5.1. Assisted-ANN Performance for Different Learning Algorithms
5.2. Effect of Smaller Training Dataset Size
5.3. ANN Inputs Relative Importance
6. Concluding Remarks
- Different types of parameters can be used as assistance parameters, and one or more assistance parameters can be used at the same time. The assistance parameters can be obtained using any well-established relation that partially or fully relate some (or all) of the inputs with the output (e.g., the SIF correction factors are partial relations while the linkup model is a full relation). The amount of the achieved accuracy improvement depends on the level and the accuracy of the assistance parameter(s) being used.
- The fact that the SIF correction factors can be successfully used as assistance input parameters makes the proposed assisted-ANN approach to be useful in a very wide variety of fracture mechanics applications (both for fatigue crack growth and static fracture). The assisted-ANN approach should prove to be very helpful in cases where the number of data points available for training the ANN is limited, which is generally the case in many experimental investigations in the fracture mechanics field.
- The lower the accuracy of the predictions obtained using the traditional approach, the more the improvement that is achieved using the assisted approach. For the SGC algorithm (it gives the least accurate results), the relative error reduction achieved by the assisted approach reached −46%; whereas for the BR algorithm (it gives the most accurate results), the relative error reduction achieved by the assisted approach reached −22% only.
- As the size of the training dataset gets smaller, the assistance input parameters will play a more significant role in improving the ANN performance. The results show that the relative error reduction generally increases as the size of the training dataset gets smaller. For the 22 data points training dataset, the achieved relative error reduction by the assisted approach reached −37%; whereas for the 75 data points training dataset, the achieved relative error reduction by the assisted approach reached −22% only.
- In the proposed assisted approach, all the direct independent inputs used in the traditional approach are still used and the assistance parameter(s) is/are used as additional input(s). The added assistance parameter(s) will influence the internal configuration of the ANN, especially the neurons’ connection weights. When an assistance parameter is added to the inputs, its relative weight becomes clearly higher than most (or all) of the other direct independent inputs. This shows the importance of adding the assistance parameter and the significant role it plays in the internal ANN structure. Also, when an assistance parameter is added, the relative weight of some of the inputs is reduced significantly, which means that the assistance parameter is taking over their role. Usually, the inputs with very small relative weights are deleted; however, our results show that to be not necessary since the ANN can recognize the importance of each of the inputs and give it its appropriate weight. Furthermore, the results show that the ANN is able to efficiently handle all the different types of inputs whether they are independent or dependent.
Author Contributions
Funding
Conflicts of Interest
Appendix A
Panel ID | σy MPa | W mm | a mm | ℓ mm | L mm | σExp MPa | βa | βℓ | σLU MPa |
---|---|---|---|---|---|---|---|---|---|
U-1 a | 310.3 | 610 | 93.35 | 4.45 | 3.81 | 79.84 | 1.190 | 3.380 | 63.33 |
U-2 a | 310.3 | 610 | 90.81 | 4.45 | 6.35 | 97.15 | 1.126 | 2.714 | 90.90 |
U-3 a | 310.3 | 610 | 88.27 | 4.45 | 8.89 | 112.18 | 1.102 | 2.350 | 114.02 |
U-4 a | 275.8 | 610 | 84.46 | 8.26 | 8.89 | 94.25 | 1.146 | 2.100 | 95.80 |
U-5 a | 275.8 | 610 | 83.19 | 6.99 | 11.43 | 110.04 | 1.103 | 1.989 | 116.25 |
U-6 a | 275.8 | 610 | 81.92 | 5.72 | 13.97 | 120.04 | 1.085 | 1.903 | 134.84 |
U-7 a | 275.8 | 610 | 80.65 | 4.45 | 16.51 | 132.52 | 1.063 | 1.789 | 154.39 |
U-8 a | 275.8 | 610 | 118.75 | 4.45 | 3.81 | 67.57 | 1.238 | 3.536 | 49.41 |
U-9 a | 275.8 | 610 | 116.21 | 4.45 | 6.35 | 83.36 | 1.166 | 2.985 | 69.93 |
U-10 a | 275.8 | 610 | 113.67 | 4.45 | 8.89 | 94.94 | 1.141 | 2.600 | 87.15 |
U-11 a | 275.8 | 610 | 109.86 | 8.26 | 8.89 | 82.33 | 1.184 | 2.360 | 82.20 |
U-12 a | 275.8 | 610 | 108.59 | 6.99 | 11.43 | 97.15 | 1.139 | 2.224 | 99.60 |
U-13 a | 275.8 | 610 | 107.32 | 5.72 | 13.97 | 105.7 | 1.117 | 2.122 | 115.52 |
U-14 a | 275.8 | 610 | 106.05 | 4.45 | 16.51 | 119.77 | 1.098 | 1.997 | 131.35 |
U-15 a | 310.3 | 610 | 144.15 | 4.45 | 3.81 | 59.02 | 1.305 | 3.900 | 48.39 |
U-16 a | 310.3 | 610 | 141.61 | 4.45 | 6.35 | 73.98 | 1.228 | 3.255 | 68.48 |
U-17 a | 310.3 | 610 | 139.07 | 4.45 | 8.89 | 83.71 | 1.198 | 2.798 | 85.45 |
U-18 a | 275.8 | 610 | 135.26 | 8.26 | 8.89 | 71.23 | 1.239 | 2.590 | 71.70 |
U-19 a | 275.8 | 610 | 133.99 | 6.99 | 11.43 | 83.50 | 1.191 | 2.438 | 86.71 |
U-20 a | 275.8 | 610 | 132.72 | 5.72 | 13.97 | 93.91 | 1.174 | 2.319 | 99.79 |
U-21 a | 275.8 | 610 | 131.45 | 4.45 | 16.51 | 108.73 | 1.149 | 2.194 | 113.58 |
U-22 a | 275.8 | 610 | 160.66 | 8.26 | 8.89 | 71.23 | 1.314 | 2.770 | 63.00 |
U-23 b | 324.1 | 2286 | 254 | 6.35 | 6.35 | 61.50 | 1.104 | 3.570 | 58.51 |
U-24 b | 324.1 | 2286 | 177.8 | 5.08 | 7.62 | 84.12 | 1.066 | 3.224 | 79.31 |
U-25 b | 324.1 | 2286 | 71.12 | 7.62 | 10.16 | 137.9 | 1.070 | 1.880 | 140.43 |
U-26 b | 324.1 | 2286 | 195.58 | 5.08 | 15.24 | 97.91 | 1.040 | 2.631 | 113.98 |
U-27 b | 324.1 | 2286 | 241.3 | 6.35 | 19.05 | 88.95 | 1.050 | 2.560 | 114.11 |
U-28 b | 324.1 | 2286 | 96.52 | 7.62 | 22.86 | 161.34 | 1.035 | 1.620 | 197.38 |
U-29 b | 324.1 | 2286 | 273.05 | 6.35 | 25.4 | 91.29 | 1.049 | 2.428 | 125.70 |
U-30 b | 324.1 | 2286 | 127 | 5.08 | 33.02 | 151.69 | 1.015 | 1.664 | 218.90 |
U-31 c | 268.9 | 508 | 101.6 | 3.81 | 8.89 | 97.43 | 1.140 | 2.390 | 91.46 |
U-32 c | 268.9 | 508 | 96.52 | 6.35 | 11.43 | 99.98 | 1.147 | 2.080 | 103.46 |
U-33 c | 268.9 | 508 | 40.64 | 10.16 | 12.7 | 144.8 | 1.094 | 1.420 | 162.97 |
U-34 c | 268.9 | 508 | 63.5 | 12.7 | 12.7 | 106.05 | 1.141 | 1.620 | 125.81 |
U-35 c | 268.9 | 508 | 93.98 | 6.35 | 13.97 | 110.32 | 1.130 | 1.910 | 118.80 |
U-36 c | 268.9 | 508 | 40.64 | 6.35 | 16.51 | 171.55 | 1.054 | 1.361 | 204.87 |
U-37 c | 268.9 | 508 | 91.44 | 6.35 | 16.51 | 118.94 | 1.123 | 1.780 | 132.76 |
U-38 c | 268.9 | 508 | 76.2 | 6.35 | 31.75 | 155.14 | 1.077 | 1.370 | 213.88 |
U-39 c | 268.9 | 508 | 38.1 | 12.7 | 38.1 | 194.78 | 1.049 | 1.130 | 307.93 |
U-40 d | 303.4 | 600 | 90 | 7.5 | 8 | 106.83 | 1.144 | 2.150 | 98.28 |
U-41 d | 303.4 | 600 | 90 | 7.5 | 12 | 120.83 | 1.107 | 1.950 | 126.15 |
U-42 d | 303.4 | 600 | 90 | 7.5 | 18 | 132 | 1.086 | 1.700 | 161.03 |
U-43 d | 303.4 | 600 | 111 | 7.5 | 10 | 103 | 1.159 | 2.300 | 98.72 |
U-44 d | 303.4 | 600 | 111 | 7.5 | 15 | 107.83 | 1.128 | 1.970 | 127.35 |
U-45 d | 303.4 | 600 | 113 | 7.5 | 15 | 113.33 | 1.131 | 1.980 | 126.04 |
U-46 d | 303.4 | 600 | 113 | 7.5 | 20 | 119.67 | 1.120 | 1.800 | 148.96 |
U-47 d | 303.4 | 600 | 136 | 7.5 | 20 | 99 | 1.172 | 1.920 | 131.00 |
U-48 d | 303.4 | 600 | 138 | 7.5 | 30 | 110.67 | 1.166 | 1.680 | 162.62 |
U-49 d | 303.4 | 600 | 143 | 7.5 | 20 | 100 | 1.192 | 1.960 | 126.00 |
U-50 d | 303.4 | 600 | 148 | 7.5 | 30 | 106.67 | 1.195 | 1.740 | 153.63 |
Panel ID | Stiff. Config. | σy MPa | Astf mm2 | W mm | a mm | ℓ mm | L mm | σExp MPa | βP-config (β s) | βa | β ℓ | σLU MPa |
---|---|---|---|---|---|---|---|---|---|---|---|---|
S-1 | One-Bay | 275.8 | 105 | 610 | 118.75 | 4.45 | 3.81 | 73.09 | 0.882 | 1.077 | 3.594 | 54.51 |
S-2 | One-Bay | 275.8 | 105 | 610 | 116.21 | 4.45 | 6.35 | 86.95 | 0.890 | 1.034 | 2.935 | 77.09 |
S-3 | One-Bay | 275.8 | 105 | 610 | 113.67 | 4.45 | 8.89 | 99.91 | 0.897 | 1.018 | 2.559 | 95.93 |
S-4 | One-Bay | 275.8 | 105 | 610 | 108.59 | 6.99 | 11.43 | 95.43 | 0.911 | 1.034 | 2.186 | 107.83 |
S-5 | One-Bay | 275.8 | 105 | 610 | 107.32 | 5.72 | 13.97 | 110.66 | 0.914 | 1.018 | 2.082 | 125.06 |
S-6 | One-Bay | 275.8 | 105 | 610 | 106.05 | 4.45 | 16.51 | 122.18 | 0.917 | 1.006 | 1.981 | 141.89 |
S-7 | One-Bay | 275.8 | 105 | 610 | 144.15 | 4.45 | 3.81 | 74.67 | 0.711 | 0.915 | 3.936 | 55.30 |
S-8 | One-Bay | 275.8 | 105 | 610 | 141.61 | 4.45 | 6.35 | 88.67 | 0.736 | 0.900 | 3.210 | 77.56 |
S-9 | One-Bay | 275.8 | 105 | 610 | 139.07 | 4.45 | 8.89 | 97.08 | 0.761 | 0.907 | 2.797 | 95.18 |
S-10 | One-Bay | 275.8 | 105 | 610 | 133.99 | 6.99 | 11.43 | 96.25 | 0.800 | 0.952 | 2.388 | 103.83 |
S-11 | One-Bay | 275.8 | 105 | 610 | 132.72 | 5.72 | 13.97 | 112.66 | 0.811 | 0.946 | 2.271 | 119.73 |
S-12 | One-Bay | 275.8 | 105 | 610 | 131.45 | 4.45 | 16.51 | 127.83 | 0.819 | 0.940 | 2.159 | 135.43 |
S-13 | One-Bay | 310.3 | 161.3 | 610 | 113.67 | 4.45 | 8.89 | 107.08 | 0.875 | 0.993 | 2.559 | 110.08 |
S-14 | One-Bay | 310.3 | 151.6 | 610 | 108.59 | 6.99 | 11.43 | 108.6 | 0.895 | 1.016 | 2.186 | 122.98 |
S-15 | One-Bay | 310.3 | 151.6 | 610 | 107.32 | 5.72 | 13.97 | 119.9 | 0.898 | 1.000 | 2.082 | 142.73 |
S-16 | One-Bay | 310.3 | 151.6 | 610 | 106.05 | 4.45 | 16.51 | 130.8 | 0.900 | 0.987 | 1.981 | 162.21 |
S-17 | One-Bay | 310.3 | 161.3 | 610 | 144.15 | 4.45 | 3.81 | 81.5 | 0.661 | 0.851 | 3.936 | 65.09 |
S-18 | One-Bay | 310.3 | 151.6 | 610 | 133.99 | 6.99 | 11.43 | 114.04 | 0.774 | 0.921 | 2.388 | 119.72 |
S-19 | One-Bay | 310.3 | 161.3 | 610 | 132.72 | 5.72 | 13.97 | 120.32 | 0.783 | 0.913 | 2.271 | 138.51 |
S-20 | One-Bay | 310.3 | 161.3 | 610 | 131.45 | 4.45 | 16.51 | 139.35 | 0.793 | 0.911 | 2.159 | 156.56 |
S-21 | One-Bay | 303.4 | 105 | 610 | 81.92 | 5.72 | 13.97 | 130.73 | 0.953 | 1.026 | 1.873 | 155.60 |
S-22 | Two-Bay * | 275.8 | 105 | 610 | 107.32 | 5.72 | 13.97 | 80.53 | 1.247 | 1.388 | 2.082 | 95.79 |
S-23 | Two-Bay * | 275.8 | 105 | 610 | 108.59 | 6.99 | 11.43 | 70.88 | 1.244 | 1.412 | 2.186 | 83.42 |
S-24 | Two-Bay * | 275.8 | 105 | 610 | 109.86 | 8.26 | 8.89 | 58.68 | 1.240 | 1.451 | 2.343 | 69.93 |
S-25 | Two-Bay * | 275.8 | 105 | 610 | 132.72 | 5.72 | 13.97 | 75.85 | 1.181 | 1.378 | 2.271 | 86.91 |
S-26 | Two-Bay * | 275.8 | 105 | 610 | 133.99 | 6.99 | 11.43 | 67.85 | 1.177 | 1.401 | 2.388 | 75.79 |
S-27 | Two-Bay * | 275.8 | 105 | 610 | 135.26 | 8.26 | 8.89 | 56.75 | 1.174 | 1.440 | 2.563 | 63.57 |
S-28 | Two-Bay * | 275.8 | 105 | 610 | 158.12 | 5.72 | 13.97 | 72.26 | 1.110 | 1.375 | 2.446 | 79.87 |
S-29 | Two-Bay * | 275.8 | 105 | 610 | 159.39 | 6.99 | 11.43 | 63.92 | 1.106 | 1.399 | 2.574 | 69.67 |
S-30 | Two-Bay * | 275.8 | 105 | 610 | 160.66 | 8.26 | 8.89 | 54.75 | 1.102 | 1.438 | 2.767 | 58.49 |
S-31 | Two-Bay * | 275.8 | 105 | 610 | 183.52 | 5.72 | 13.97 | 68.74 | 1.005 | 1.348 | 2.610 | 75.55 |
S-32 | Two-Bay * | 275.8 | 105 | 610 | 184.79 | 6.99 | 11.43 | 60.95 | 0.997 | 1.367 | 2.748 | 66.10 |
S-33 | Two-Bay * | 275.8 | 105 | 610 | 186.06 | 8.26 | 8.89 | 51.85 | 0.989 | 1.400 | 2.957 | 55.64 |
S-34 | Two-Bay * | 310.3 | 105 | 610 | 107.32 | 5.72 | 13.97 | 97.01 | 1.247 | 1.388 | 2.082 | 107.77 |
S-35 | Two-Bay * | 310.3 | 105 | 610 | 132.72 | 5.72 | 13.97 | 84.26 | 1.181 | 1.378 | 2.271 | 97.77 |
S-36 | Two-Bay * | 310.3 | 105 | 610 | 158.12 | 5.72 | 13.97 | 82.33 | 1.110 | 1.375 | 2.446 | 89.85 |
Panel ID | σy MPa | W mm | a mm | ℓ mm | L mm | σExp MPa | βP-config (β LJ) | βa | β ℓ | σLU MPa |
---|---|---|---|---|---|---|---|---|---|---|
LJ-1 | 268.9 | 610 | 106.52 | 3.65 | 16.83 | 126.73 | 0.843 | 0.922 | 2.506 | 146.46 |
LJ-2 | 268.9 | 610 | 106.52 | 4.92 | 15.56 | 115.77 | 0.846 | 0.935 | 2.323 | 137.17 |
LJ-3 | 268.9 | 610 | 107.79 | 3.65 | 15.56 | 126.73 | 0.821 | 0.904 | 2.574 | 141.51 |
LJ-4 | 268.9 | 610 | 107.79 | 4.92 | 14.29 | 113.35 | 0.826 | 0.918 | 2.393 | 131.79 |
LJ-5 | 268.9 | 610 | 107.79 | 6.19 | 13.02 | 106.53 | 0.834 | 0.934 | 2.268 | 122.30 |
LJ-6 | 268.9 | 610 | 109.06 | 3.65 | 14.29 | 119.84 | 0.810 | 0.889 | 2.656 | 135.86 |
LJ-7 | 268.9 | 610 | 109.06 | 4.92 | 13.02 | 113.56 | 0.815 | 0.905 | 2.466 | 125.64 |
LJ-8 | 268.9 | 610 | 109.06 | 6.19 | 11.75 | 105.77 | 0.818 | 0.923 | 2.346 | 115.69 |
LJ-9 | 268.9 | 610 | 109.06 | 7.46 | 10.48 | 101.49 | 0.821 | 0.944 | 2.294 | 105.38 |
LJ-10 | 268.9 | 610 | 131.92 | 3.65 | 16.83 | 107.29 | 0.828 | 0.948 | 2.853 | 128.10 |
LJ-11 | 268.9 | 610 | 131.92 | 4.92 | 15.56 | 102.6 | 0.831 | 0.961 | 2.642 | 120.00 |
LJ-12 | 268.9 | 610 | 133.19 | 3.65 | 15.56 | 105.91 | 0.810 | 0.930 | 2.930 | 123.87 |
LJ-13 | 268.9 | 610 | 133.19 | 4.92 | 14.29 | 97.29 | 0.812 | 0.941 | 2.720 | 115.66 |
LJ-14 | 268.9 | 610 | 133.19 | 6.19 | 13.02 | 90.32 | 0.816 | 0.958 | 2.572 | 107.41 |
LJ-15 | 268.9 | 610 | 134.46 | 3.65 | 14.29 | 102.18 | 0.793 | 0.915 | 3.034 | 118.92 |
LJ-16 | 268.9 | 610 | 134.46 | 4.92 | 13.02 | 96.25 | 0.799 | 0.930 | 2.799 | 110.25 |
LJ-17 | 268.9 | 610 | 134.46 | 6.19 | 11.75 | 88.26 | 0.802 | 0.949 | 2.663 | 101.50 |
LJ-18 | 268.9 | 610 | 134.46 | 7.46 | 10.48 | 81.91 | 0.807 | 0.971 | 2.613 | 92.34 |
LJ-19 | 268.9 | 610 | 157.32 | 3.65 | 16.83 | 89.29 | 0.816 | 0.992 | 3.314 | 111.70 |
LJ-20 | 268.9 | 610 | 157.32 | 4.92 | 15.56 | 86.26 | 0.820 | 1.007 | 3.028 | 104.84 |
LJ-21 | 268.9 | 610 | 158.59 | 3.65 | 15.56 | 87.84 | 0.802 | 0.979 | 3.403 | 107.63 |
LJ-22 | 268.9 | 610 | 158.59 | 4.92 | 14.29 | 81.29 | 0.806 | 0.994 | 3.113 | 100.53 |
LJ-23 | 268.9 | 610 | 158.59 | 6.19 | 13.02 | 75.02 | 0.812 | 1.012 | 2.952 | 93.26 |
LJ-24 | 268.9 | 610 | 159.86 | 3.65 | 14.29 | 84.46 | 0.787 | 0.964 | 3.503 | 103.38 |
LJ-25 | 268.9 | 610 | 159.86 | 4.92 | 13.02 | 79.78 | 0.793 | 0.981 | 3.218 | 95.89 |
LJ-26 | 268.9 | 610 | 159.86 | 6.19 | 11.75 | 74.12 | 0.796 | 1.001 | 3.059 | 88.26 |
LJ-27 | 268.9 | 610 | 159.86 | 7.46 | 10.48 | 69.23 | 0.801 | 1.025 | 2.988 | 80.39 |
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Assistance Level | AP1 | AP2 |
---|---|---|
1 | βP-config | - |
2 | βa | - |
3 | βa | βℓ |
4 | σLU | - |
Scenario | BR | LM | SGC | ||||||
---|---|---|---|---|---|---|---|---|---|
MAEP [%] | RSMEP [%] | R2 [%] | MAEP [%] | RSMEP [%] | R2 [%] | MAEP [%] | RSMEP [%] | R2 [%] | |
Traditional | 3.8 | 5.51 | 92.39 | 5.59 | 7.89 | 81.19 | 7.65 | 10.33 | 75.94 |
Assisted 1 | 3.76 | 5.42 | 92.61 | 5.56 | 7.92 | 84.56 | 6.41 | 8.67 | 83.32 |
Assisted 2 | 3.45 | 5.04 | 93.16 | 4.86 | 6.8 | 87.89 | 6.05 | 8.16 | 84.49 |
Assisted 3 | 3.13 | 4.26 | 95.14 | 4.42 | 6.17 | 89.85 | 5.52 | 7.22 | 87.96 |
Assisted 4 | 2.97 | 4.07 | 96.21 | 3.31 | 4.2 | 96.04 | 4.13 | 5.48 | 92.9 |
Scenario | Reduced 1 (48) | Reduced 2 (35) | Reduced 3 (22) | ||||||
---|---|---|---|---|---|---|---|---|---|
MAEP [%] | RSMEP [%] | R2 [%] | MAEP [%] | RSMEP [%] | R2 [%] | MAEP [%] | RSMEP [%] | R2 [%] | |
Traditional | 4.68 | 6.52 | 88.73 | 5.55 | 7.52 | 85.77 | 6.86 | 9.54 | 80.97 |
Assisted 1 | 4.67 | 6.61 | 89.59 | 5.1 | 7.01 | 87.65 | 4.51 | 5.93 | 90.24 |
Assisted 2 | 4.16 | 5.82 | 91.46 | 4.65 | 6.32 | 90.2 | 4.52 | 5.92 | 90.97 |
Assisted 3 | 3.55 | 4.88 | 93.91 | 3.84 | 5.33 | 92.85 | 4.63 | 6.21 | 91.64 |
Assisted 4 | 3.46 | 4.54 | 95.21 | 3.46 | 4.52 | 95.16 | 4.26 | 5.83 | 92.81 |
Scenario | Direct Independent Inputs | Assistance Input Parameters | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
a | l | L | W | Astf | σy | Config ID | βP-config | βa | βℓ | σLU | |
Traditional | 2 | 4 | 1 | 7 | 6 | 5 | 3 | - | - | - | - |
Assisted 1 | 1 | 4 | 2 | 6 | 8 | 5 | 7 | 3 | - | - | - |
Assisted 2 | 1 | 6 | 2 | 7 | 8 | 4 | 5 | - | 3 | - | - |
Assisted 3 | 3 | 5 | 4 | 9 | 7 | 6 | 8 | - | 1 | 2 | - |
Assisted 4 | 8 | 4 | 2 | 5 | 6 | 7 | 3 | - | - | - | 1 |
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Hijazi, A.; Al-Dahidi, S.; Altarazi, S. A Novel Assisted Artificial Neural Network Modeling Approach for Improved Accuracy Using Small Datasets: Application in Residual Strength Evaluation of Panels with Multiple Site Damage Cracks. Appl. Sci. 2020, 10, 8255. https://doi.org/10.3390/app10228255
Hijazi A, Al-Dahidi S, Altarazi S. A Novel Assisted Artificial Neural Network Modeling Approach for Improved Accuracy Using Small Datasets: Application in Residual Strength Evaluation of Panels with Multiple Site Damage Cracks. Applied Sciences. 2020; 10(22):8255. https://doi.org/10.3390/app10228255
Chicago/Turabian StyleHijazi, Ala, Sameer Al-Dahidi, and Safwan Altarazi. 2020. "A Novel Assisted Artificial Neural Network Modeling Approach for Improved Accuracy Using Small Datasets: Application in Residual Strength Evaluation of Panels with Multiple Site Damage Cracks" Applied Sciences 10, no. 22: 8255. https://doi.org/10.3390/app10228255
APA StyleHijazi, A., Al-Dahidi, S., & Altarazi, S. (2020). A Novel Assisted Artificial Neural Network Modeling Approach for Improved Accuracy Using Small Datasets: Application in Residual Strength Evaluation of Panels with Multiple Site Damage Cracks. Applied Sciences, 10(22), 8255. https://doi.org/10.3390/app10228255