# Open-Pit Bench Blasting Fragmentation Prediction Based on Stacking Integrated Strategy
## 1 Introduction  
The proper fragmentation of blasting has always been the goal of rock mining production. Many subsequent operations after blasting, including loading, transport, and grinding, are affected by the degree of fragmentation [1]. High-quality breakage can avoid the need for the secondary blasting of large rock pieces, reduce the energy consumed by crushers and grinders, increase digging capacity and loading productivity, and reduce production costs [2, 3]. The breakage of rock is a complex and dynamic process, and rock fragmentation can be affected by a number of variables. Numerous previous studies have shown that the parameters that determine fragmentation can be categorized into controllable and uncontrollable. The design parameters of blasting and explosive-related parameters are controllable, whereas uncontrollable parameters include the physical and mechanical properties of the rock and its structure [4, 5]. When establishing the prediction model for the blasting situation, the controllable and uncontrollable parameters should be considered comprehensively. However, due to the difficulty in obtaining parameters in actual projects, ensuring the validity of collected parameters is challenging. Therefore, itis urgent to establish a feasible model considering a variety of factors to predict the size of fragmentation. As early as the last century, attempts have been made to establish empirical formulas for predicting blasting fragmentation by summarizing and analyzing data. [PERSON] and [PERSON] [6] proposed the Rosin-Rammler semi-empirical formula, which provides a rough judgment of block size through the relationship between characteristic bulkiness and the cumulative passing percentage. The Kuznetsov formula combines factors such as explosive quality and rock strength for block size prediction [7]. [PERSON] further developed the Kuz-Ram model based on the [PERSON] and Kuznetsov formulations [8]. Due to the shortcomings of the Kuz-Ram model in fine fragment prediction, many scholars have subsequently continued to modify and improve it. [PERSON] et al. [9] developed the Kuznetsov-Cunningham-Ouchterlony (KCO) model based on the Kuz-Ram model, which compensates for its shortcomings in predicting fine fragments and its limitations regarding the upper limit of block size. During blasting, uncontrolled parameters affect rock fragmentation to a greater extent compared to controlled parameters [10], making it difficult to propose a fitting equation for fragmentation that accounts for all blasting influences. With the extensive development and application of AI technology in many fields, it has gradually become an effective method for solving complex prediction problems [11; 12; 13; 14; 15; 16; 17; 18]. [PERSON] et al. [19] used a Back Propagation Neural Network (BPNN) model to predict the average particle size of blast fragmentation, training it with four learning algorithms. Its predictive ability was confirmed to be superior to multiple regression models used by previous scholars. [PERSON] et al. [20] constructed an artificial neural network (ANN) to predict the degree of rock fragmentation by comparing several methods. He pointed out through sensitivity analysis that the most influential parameters in the fragmentation process were powder factor, burden, and bench height. In addition to neural networks, there are multiple other methods for prediction. For example, [PERSON] et al. [21] established the XGBoost model to predict rock fragmentation and compared it with the prediction results of BPNN, confirming that XGBoost has better prediction ability and faster prediction speed. [PERSON] et al. [22] constructed a Support Vector Machine (SVM) model and an Adaptive Network-based Fuzzy Inference System (ANFIS) based on Principal Component Analysis (PCA) and compared the prediction results with the Kuz-Ram method. Their findings further proved that the accuracy of AI methods is better compared to previous empirical formulas.