# Application of Artificial Neural Network (ANN) in Predicting Box Compression Strength (BCS)
## 5 Conclusions  
In this study, a generalized ANN model for BCS prediction, designed for industrial applications, was developed. A dataset derived from real-world data was used, covering 90% of commonly used box dimensions in the industry. To optimize the hidden neuron configuration for the ANN model, five methods--the Information Criteria using the AIC method, Hebb's rule, the Information Criteria using the BIC method, the Optimal Brain Damage rule, and the Bayesian Optimization method--were investigated along with the exhaustive search method. Training results and corresponding model errors were compared to determine the optimal configuration. It was found that a hidden layer with 24 neurons provided the best balance between minimizing model error and reducing computational training time. The optimal epoch number and minimum modeling cycle count were determined to be 50 and 70, respectively, after the training error reduction plateaued. Across 70 modeling cycles, the average BCS error for the test data using the selected configuration was around 10%. Analysis of the BCS value distribution revealed that data points with BCS values between 347 lbs and 427 lbs, as well as those between 1999 and 2172 lbs, consistently showed higher prediction errors. This indicates that boundary data points--those at the extremes of the dataset--are more challenging for the ANN model to predict accurately. Moreover, the limited size of the extracted real-world dataset constrained the model's overall predictive accuracy. Further research is recommendedto expand the dataset and explore data augmentation techniques to enhance the model's performance. In conclusion, the developed ANN model demonstrates strong capability in predicting BCS values for commonly used box dimensions at an industrially applicable level. It achieved an average prediction error of approximately 10% and was validated by the physical tested data, confirming its practical reliability. This study provides valuable insights into the application of ANN for predicting BCS in corrugated packaging at an industrially applicable level, highlighting its potential to address key challenges in the packaging industry.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app15147722/s1](https://www.mdpi.com/article/10.3390/app15147722/s1)]([https://www.mdpi.com/article/10.3390/app15147722/s1](https://www.mdpi.com/article/10.3390/app15147722/s1)), Python code SI: 395 dp_ann_for_bcs_prediction(ect_l_w_d)_200 epoch; Python code SI: 395+10 dp_ann_for_bcs_prediction(ect_l_w_d)_200 epoch.  
Conceptualization, E.L.; Methodology, [PERSON] and [PERSON]; Software, J.G.; Validation, J.G.; Formal analysis, J.G.; Investigation, J.G.; Resources, E.L.; Data curation, E.L.; Writing--original draft, J.G.; Writing--review & editing, [PERSON]; Visualization, J.G.; Supervision, E.L. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.  
The authors declare no conflict of interest.