# Open-Pit Bench Blasting Fragmentation Prediction Based on Stacking Integrated Strategy
## 1 Introduction
It is evident that random forest, XGBoost, SVM, and neural network algorithms are common choices among researchers for prediction. To ensure and improve prediction accuracy, many scholars choose to optimize the prediction process using optimization algorithms. For example, [PERSON] et al. [23] optimized the ANN model prediction process using the firefly algorithm, resulting in coefficients of determination \(R^{2}\) of 0.94 and 0.93 for the prediction of rock fragments and fly-rock. [PERSON] et al. [24] established an extreme learning machine model using Grey Wolf Optimization (GWO) and compared the prediction results of the average size of blast fragmentation before and after optimization, proving that the optimization algorithm can effectively improve the model's prediction accuracy. Some scholars have further improved optimization algorithms. [PERSON] et al. [25] conducted a study on the parameters of Convolutional Neural Network (CNN) and Multilayer Perceptron (MLP) for predicting the mean fragment size, and utilized the GWO algorithm to optimize the training process, further improving model performance. Rather than using a single algorithm to optimize the model, using multiple optimization algorithms and comparing the prediction quality can make the prediction results more convincing. [PERSON] et al. [26] used five optimization algorithms, including the Salp Swarm Algorithm, GWO, and Particle Swarm Optimization (PSO), to optimize the forecasting performance of the Support Vector Regression (SVR) model. They combined these algorithms with three mathematical indicators to compare and evaluate the best prediction model. Although the prediction method for optimizing the basic algorithm has gradually developed and matured, enhancing the model's accuracy and prediction ability, there are still some limitations of the single prediction method due to the relatively complex factors affecting the fragmentation produced by rock blasting. To improve the generalization ability of a single algorithm, some scholars have integrated algorithms to predict the blasting effect. [PERSON] et al. [27] established various integrated models, including the simple averaging ensemble, weighted averaging ensemble, separate stacking model, and Bayesian-eXtreme Gradient Boosting, filling the gap in predicting blasting fly-rock using integrated models. [PERSON] et al. [28] also introduced the AdaBoost algorithm in their study on predicting compressive strength. However, AdaBoost and XGBoost are essentially integrated models of homogeneous algorithms, with poor integration of the advantages of non-homogeneous algorithms. [PERSON] et al. [29] combined the different characteristics of four models and achieved the highest prediction accuracy for rock deformation using the stacking-tree-RF-KNN-MLP structure. [PERSON] et al. [30] utilized random forest, Gaussian Process (GP), and Gradient Boosting Machine (GBM) as base learners to establish a stacking ensemble model for predicting ground vibration, significantly improving the model's predictive performance. [PERSON] et al. [31] employed a stacking ensemble learning method that combined LightGBM, random forest, and XGBoost as base learners, and Ridge, Lasso, and Linear Regression as meta-learners to predict rock compressive strength (RCS). The model demonstrated excellent prediction accuracy, achieving an R\({}^{2}\) of 0.946. It can be seen that the stacking integrated model gives better prediction results than a single model in all cases. It also offers better performance in fusing different qualitative single models to combine their respective strengths, as well as in model generalization. Currently, the effectiveness of applying the stacking ensemble model to blast fragmentation prediction remains unknown, and this area requires further exploration. This study aims to improve prediction accuracy by applying a stacking ensemble model to blast fragmentation prediction. In this study, 97 samples of data collected from blasts conducted around the world by [PERSON] et al. [4] are used as datasets.