# Application of Artificial Neural Network (ANN) in Predicting Box Compression Strength (BCS)
## 2 Method
### Development of ANN Model Architecture
#### 2.2.1 Determination of ANN Hidden Neuron Number Configuration  
To construct the ANN model, the hidden layer neuron configuration was determined by balancing model accuracy and computational efficiency. Five optimization methods were evaluated to optimize the hidden layer configuration, aiming to maximize accuracy while minimizing computational cost. The selected optimization methods included the Akaike Information Criterion (AIC) [21], the Bayesian Information Criterion (BIC) [21], Hebb's rule [22], the Optimal Brain Damage (OBD) algorithm [23; 24], and Bayesian Optimization (BO) [25; 26]. The number of neurons ranged from 1 to 145, with the number of hidden layers varying from 1 to 2 for the first four methods, and from 1 to 3 for the Bayesian Optimization method. The optimized configurations for the number of hidden neurons, derived from the five methods, were recorded along with the corresponding ANN model's prediction errors. The final hidden neuron configuration was determined by comparing model errors across all five methods, selecting the configuration that minimized model error while maximizing computational efficiency. An exhaustive search was used as a validation technique to assess the effectiveness of these methods and to help identify the global minimum of model error during hidden neuron optimization. The exhaustive search method not only prevents the model from becoming trapped in local minima of the BCS prediction error but also serves as a reference for balancing model complexity and accuracy, thereby reducing the risk of overfitting.  
The five methods mentioned above--namely, the AIC, the BIC, Hebb's rule, the OBD rule, and BO--were evaluated for optimizing the number of hidden neurons in the ANN. The model errors for the test data obtained using each method were calculated and compared, as shown in Figure 5.  
Among the five optimization methods, the Bayesian Optimization approach achieved the lowest model error of 10.3% with three hidden layers, each containing 145 neurons. In comparison, the AIC method (1 HL) produced a slightly higher error of 10.5% using a single hidden layer with only 24 neurons--a significantly simpler architecture. This suggests that increasing the number of neurons to 145 in three layers did not yield a  
Figure 5: ANN model error average with their optimized hidden neuron numbers using the six selected methods.  
substantial improvement in prediction accuracy over the simpler configuration. To verify this observation, an exhaustive grid search was performed, evaluating hidden layer sizes from 20 to 40 neurons (in increments of 1). The lowest average BCS prediction error of 10.5% was observed with 24 neurons in a single hidden layer, matching the result from the AIC method (1 HL), as shown in Figure 5 (the last column). Considering these results and aiming to balance computational efficiency with predictive accuracy, a single hidden layer with 24 neurons was selected as the final optimal ANN architecture, minimizing unnecessary neuron connections.  
Based on the research above on ANN architecture, the structure of the generalized ANN model developed for BCS prediction is outlined in Figure 6. The model consists of four BCS features as inputs, featuring one hidden layer with 24 neurons.