###### Abstract
[18] and [PERSON] et al. [19] developed ICA-ANN models based on imperial competition algorithms and FFA-ANN models based on firefly algorithms for quarry blasting ground vibration prediction. Several scholars [20; 21; 22; 23] have proposed hybrid models integrating the firefly algorithm (FFA), genetic algorithm (GA), and particle swarm optimization (PSO) with Support Vector Regression (SVR) and artificial neural networks (ANNs) to enhance the accuracy of blasting vibration velocity predictions. [PERSON] et al. asserted that the PSO-SVR model provides a more precise estimation of blasting vibration intensity. [PERSON] et al. identified the GA-SVR-RBF model as the optimal method for estimating peak particle velocity (PPV). Additionally, [PERSON] et al. and [PERSON] et al. found the FFA-SVR model to be both efficient and reliable. [PERSON] et al. [24] employed feature selection methods to identify primary input variables and developed two prediction models, FS-RF and FS-BN, for predicting ground vibrations resulting from quarry blasting, and the FS-RF model exhibited marginally superior accuracy compared to the FS-BN model. [PERSON] [25] introduced a second-order polynomial intelligent committee machine (SPICM) for open-pit mine bench blasting vibration prediction, which proved to be more accurate and reliable than previous empirical formulas and neural network models. The SPICM model represents a novel advancement in machine learning technology for blasting vibration prediction. [PERSON] et al. [26] utilized PSO to optimize the hyperparameters of XGBoost for predicting ground vibration. Additionally, several researchers [27; 28; 29; 30] have integrated intelligent optimization algorithms with neural networks to build optimized network models for fly-rock distance prediction in blasting scenarios. [PERSON] [31] combined relevance vector regression (RVR) with grey wolf optimization (GWO) to establish the RVR-GWO model and incorporated the bat algorithm (BA) to create two intelligent models, RVR-GWO and RVR-BA, aiming to improve the efficiency of ground vibration prediction. However, it is noteworthy that there are limited studies focusing on the application of the particle swarm optimization algorithm in predicting the environmental effects of mine blasting, such as peak particle velocity. Additionally, there is a gap in the research landscape concerning the PSO-RF intelligent hybrid learning model. Innovative development in the domain of intelligent hybrid learning models based on the particle swarm optimization algorithm remains a crucial area for future exploration. The objective of this study is to forecast the peak vibration velocity of mass points in underground long hole blasting. This prediction is based on mathematical empirical formula regression, wherein the original blasting test data are partitioned into training and testing sets. Employing the particle swarm optimization (PSO) algorithm to optimize model hyperparameters, two machine learning models, PSO-SVR and PSO-RF, tailored for small sample datasets, are developed. These models are specifically designed for predicting the peak vibration velocity of mass points in underground long hole blasting, considering multiple parameter indicators. The reliability of these machine learning models is assessed using metrics such as the mean absolute error (MAE), mean squared error (MSE), and coefficient of determination (\(R^{2}\)).