## 4 Results and Discussion  
In this section, we present the results and discuss the findings of our study aimed at predicting blast-induced ground vibration. Our study focused on developing and evaluating predictive models to estimate PPV, which is a crucial parameter for assessing the potential impact of blasting operations on nearby structures and the surrounding environment. We specifically investigated the performance of the CGO-ANN, GA-ANN, PSO-ANN, single ANN, and USBM models, with a particular emphasis on the proposed novel CGO-ANN model. The outcome predictions of the CGO-ANN, GA-ANN, PSO-ANN, single ANN, and USBM models are shown in Figure 8 for both training and testing datasets. The outcomes depicted in Figure 8 showcased diverse performance levels among various algorithms, with certain models demonstrating superior accuracy and predictive capability over others. Notably, the CGO-ANN model, introduced as a novel approach in this study, exhibited particularly promising results, surpassing other models in terms of accuracy and predictive capacity. Conversely, the USBM model displayed the weakest performance in predicting PPV across both training and testing datasets. Figure 9 illustrates a scatter plot correlating the measured PPVs with the predicted PPVs to assess the accuracy of each model in predicting blast-induced ground vibration. The findings revealed that the CGO-ANN and GA-ANN models offered greater accuracy in PPV prediction compared to the other models. Furthermore, the hybrid models, including CGO-ANN, GA-ANN, and PSO-ANN, demonstrated enhancements over the single ANN model in predicting PPV within the Tonglushan Copper Mine of China. Conversely, the empirical model (USBM) exhibited the highest errors in regards to PPV estimation. To delve deeper into the predictive capabilities of each model in forecasting PPV, in our study, we undertook a regression analysis using both measured and predicted PPV values, as depicted in Figure 10. Our analyses revealed that the hybrid ANN models exhibited superior convergence compared to the single ANN model, with particular emphasis on the CGO-ANN model. Notably, the predicted data points from the CGO-ANN model clustered closer to the regression line than did those from the other models. Additionally, as depicted in Figure 10, the confidence level of the developed models is illustrated with a 95% confidence interval (highlighted by the grey areas). Notably, the majority of the predicted datasets from the CGO-ANN model fall within this interval, surpassing the performance of the GA-ANN model and other models showcased in the figure. It is significant that the USBM empirical model displayed the least accuracy and convergence, indicating a notable disparity between its predicted and actual values. To precisely assess the performance of the developed models, we computed various performance metrics, including mean squared error (MSE), root mean squared error (RMSE), mean absolute error (MAE), and determination coefficient (\(\mathbb{R}^{2}\)) based on both the measured and predicted PPV values. These metrics are presented in Table 2 for comprehensive evaluation. Figure 8: The outcome predictions of PPV under the models developed: (**a**) training samples; (**b**) testing samples. The performance evaluation of the PPV predictive models provides compelling evidence supporting the superiority of the CGO-ANN model. Across both the training and testing datasets, the CGO-ANN model consistently yields lower MSE, RMSE, and MAE values compared to the other models. For instance, in the testing dataset, the CGO-ANN model exhibits an MSE of 0.259, whereas the GA-ANN, PSO-ANN, single ANN, and USBM models record MSE values of 0.637, 0.720, 0.770, and 2.672, respectively. Similarly, the CGO-ANN model achieves an RMSE of 0.508 and an MAE of 0.425 in the testing dataset, outperforming all other models. Moreover, the R\({}^{2}\) values further reinforce the superiority of the CGO-ANN model in explaining the variance in PPV.