## 3 Application and Experiment Test
### Model Development  
Before predictive models for blast-induced ground vibration prediction were developed, the dataset underwent normalization to prevent data leakage, in which information from validation or test sets inadvertently influences the training process. In this study, the min-max normalization technique was utilized to scale the features (consisting of 11 variables from the blast-induced ground vibration dataset) to a similar range, aiding in the facilitation of learning.  
For the development of the CGO-ANN model predicting PPV, the collected dataset comprising 180 samples was partitioned into two parts. A total of 70% of the dataset was randomly selected as the training dataset to optimize the weights and biases of the ANN model. Meanwhile, the remaining 30% was reserved for testing the model's performance.  
It is important to highlight that this study not only proposes and develops the CGO-ANN model but also introduces the PSO-ANN, GA-ANN, single ANN, and USBM empirical models for comparison purposes, evaluating the superiority of the proposed CGO-ANN model. For the hybrid models like CGO-ANN, GA-ANN, and PSO-ANN, the initial parameters of the metaheuristic algorithms play a crucial role in enhancing the optimization processes for predicting PPV. These initial parameters are configured as follows:  
* GA: crossover coefficient = 0.85; mutation coefficient = 0.05.
* PSO: local coefficient = global coefficient = 1.2; weight min coefficient = 0.4; weight max coefficient = 0.9.
* CGO: using the number of populations and iterations.  
Furthermore, all these algorithms are implemented with varying initial population diversities (i.e., 100, 200, 300, 400, 500), and the optimization process spans 1000 iterations.  
An initial ANN structure with a single hidden layer containing 15 hidden neurons was chosen for this study, utilizing the ReLU activation function. MSE (mean-squared error) served as the objective function for these hybrid models during the training process. The development and optimization process of the CGO-ANN, PSO-ANN, and GA-ANN models are illustrated in Figure 6.  
Furthermore, alongside the hybrid models, a standalone ANN was developed for predicting PPV and contrasting it with the proposed CGO-ANN model. The identical datasets, encompassing both training and testing datasets, normalization technique, and structure, were employed in constructing the standalone ANN model. However, in this instance, the backpropagation algorithm was employed to train the ANN model, representing the most prevalent algorithm traditionally used for ANN model training. The performance of the ANN model development is depicted in Figure 7.  
Figure 6: _Cont._  
Figure 6: Optimization process of the hybrid models for PPV prediction under different population sizes. (**a**) CGO-ANN model; (**b**) GA-ANN model; (**c**) PSO-ANN model.  
Figure 7: Development process of the single ANN model for PPV prediction.  
The USBM (United States Bureau of Mines) empirical equation stands as one of the most frequently utilized equations for swiftly gauging the intensity of PPV in blasting. This equation was pioneered by [PERSON] and [PERSON] (2018) and relies on historical data and regression analysis for its computation. It is worth mentioning that the identical datasets will be employed in establishing the USBM empirical equation, which is ultimately formulated to estimate PPV in the following manner:  
\[\text{PPV}=1.684\bigg{(}\frac{\text{D}}{\sqrt{\text{Q}_{\text{max}}}}\bigg{)}^ {-0.337} \tag{8}\]  
According to the USBM equation, the horizontal distance (D) and maximum explosive charge per delay (\(\text{Q}_{\text{max}}\)) should be used to calculate PPV.