# Application of Artificial Neural Network (ANN) in Predicting Box Compression Strength (BCS)
## 3 Result
### Model Accuracy Verification Using Physical Testing  
To further evaluate the capability of the ANN model in predicting BCS values, physical test data from the lab in the School of Packaging at Michigan State University were used to verify the model's accuracy. The BCS values of 10 single-wall B-flute RCS boxes with varying dimensions, provided by the Packaging Corporation of America (PCA), were measured using a Lansmont Squeezer (S/N 13455) (Monterey, CA, USA). These values were then used as test data for the ANN model that had been previously trained on 395 real-world data samples. For each box dimension, at least 10 samples were tested to calculate the average BCS value, which was used as the representative input for the model. All box samples were preconditioned at a temperature of 23.0 \(\pm\) 1.0 \({}^{\circ}\)C (73.4 \(\pm\) 1.8 \({}^{\circ}\)F) and a relative humidity of 50.0 \(\pm\) 2.0% for at least 24 h, in accordance with TAPPI T 402, \"Standard Conditioning and Testing Atmospheres for Paper, Board, Pulp Handsheets, and Related Products\" [27].  
Based on the optimal modeling parameters identified above--four inputs (ECT, Box length, Width and Depth), 24 neurons in the hidden layer, and 70 modeling cycles (with the number of epochs extended to 200 epochs for a more conservative result)--the ANN model was further evaluated using BCS data from an additional set of 10 box dimensions tested in the lab. When the BCS data from the 10 box dimensions were used as test data, the model achieved an average prediction error of 3.2% across the 70 cycles--a much lower error rate compared with the test data's error of 10.5% during the ANN model training process. The results show that the average tested BCS values for all 10 dimensions fall within the range of the minimum and maximum predicted BCS values, as illustrated in Figure 14. These findings suggest that the ANN model can reliably predict BCS for most of the tested box dimensions, demonstrating its accuracy and underscoring its potential for industrial applications. The code used to train the model is provided in Supplementary Python code S1 and S2.  
Figure 13: Residual distribution histogram (for test data) of the trained ANN model for BCS prediction across 70 modeling cycles.  
To assess the agreement between the ANN model predictions and the experimentally tested BCS values, a Bland-Altman analysis was performed. The Bland-Altman plot displays the differences between predicted and tested BCS values against their mean. For all the 10 dimensions of the box samples tested, most of the data points fell within the 95% limits of agreement (mean difference \(\pm\) 1.96 \(\times\) standard deviation), suggesting good consistency between the model predictions and experimental results. This analysis supports the reliability of the ANN model in predicting BCS values for box samples within the studied range. The Bland-Altman plot of each box sample is shown in Figure 15, from left to right, top to bottom, the box dimensions are: 12 \(\times\) 8 \(\times\) 8 in, 16 \(\times\) 14 \(\times\) 8 in, 16 \(\times\) 16 \(\times\) 8 in, 12 \(\times\) 12 \(\times\) 12 in, 14 \(\times\) 10 \(\times\) 12 in, 16 \(\times\) 8 \(\times\) 6 in, 16 \(\times\) 10 \(\times\) 6 in, 16 \(\times\) 16 \(\times\) 12 in, 14 \(\times\) 12 \(\times\) 10 in, and 12 \(\times\) 12 \(\times\) 10 in, respectively.  
Figure 14: Comparison of tested BCS average and ANN predicted BCS average values of 10-dimension boxes tested in the lab.  
Figure 15: _Cont._