###### Abstract  
Obtaining accurate basic parameters for long hole blasting is challenging, and the resulting vibration damage significantly impacts key surface facilities. Predicting ground vibration velocity accurately and mitigating the harmful effects of blasting are crucial aspects of controlled blasting technology. This study focuses on the prediction of ground vibration velocity induced by underground long hole blasting tests. Utilizing the fitting equation based on the US Bureau of Mines (USBM) formula as a baseline for predicting peak particle velocity, two machine learning models suitable for small sample data, Support Vector Regression (SVR) machine and Random Forest (RF), were employed. The models were optimized using the particle swarm optimization algorithm (PSO) to predict peak particle velocity with multiple parameters specific to long hole blasting. Mean absolute error (MAE), mean Squared error (MSE), and coefficient of determination (\(R^{2}\)) were used to assess the model predictions. Compared with the fitting equation based on the USBM model, both the Support Vector Regression (SVR) and Random Forest (RF) models accurately and effectively predict peak particle velocity, enhancing prediction accuracy and efficiency. The SVR model exhibited slightly superior predictive performance compared to the RF model. rock blasting; long hole blasting; peak particle velocity prediction; particle swarm optimization (PSO); Support Vector Regression (SVR); Random Forest (RF)  
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to establish empirical equations [5; 6; 7; 8] based on the relationship between PPV measurement distance (D) and the amount of explosive charge per delay (W) for each blast, including the Sadowsky formula, USBM formula, U-B formula, Indian formula, and Japanese formula. Although empirical formulas for PPV prediction are convenient and quick, they may not accurately predict under certain specific conditions and may fail to provide high-quality prediction results. The rapid advancement of artificial intelligence technologies, including genetic algorithms, fuzzy mathematics, neural networks, classification and regression tree methods, and intelligence committee machines, has significantly enhanced the prediction of production blasting vibration velocity in the field of blasting ground vibration analysis. These methods have notably improved prediction accuracy and efficiency. [PERSON] et al. [9; 10; 11] and [PERSON] et al. [12] utilized various mathematical empirical formulas and BP neural networks to predict on-site blasting-induced ground vibrations, finding the ANN model to be more accurate. In the context of open-pit mines in India, [PERSON] et al. [13; 14] conducted research on blasting vibrations, considering factors such as the maximum single-segment charge and distance from the blasting working face to the test point. They utilized the support vector machine (SVM) model, demonstrating its superior accuracy. The SVM model, when based on dual input parameters, outperformed its counterpart utilizing single-input parameters. [PERSON] et al. [15] applied SVM to predict ground vibrations from blasting at the Bakhtiari Dam in Iran, highlighting the superior predictive performance of the method, particularly concerning peak particle vibration velocity. [PERSON] [16] established blasting vibration prediction models using generalized regression neural networks and support vector machines. Through an analysis of signals from underground long hole blasting vibrations, the peak particle vibration velocity and main vibration frequency and duration were predicted, finding that the SVM model exhibited the best predictive performance. [PERSON] [17] conducted principal component analysis on multiple factors influencing blasting safety. Utilizing support vector machines, a vibration velocity prediction model was developed. The generalization ability of the model was enhanced by reducing input information dimensions, and the feasibility of increasing blasting charge experiments was assessed. Additionally, [PERSON] et al.