# Research on Hard Rock Pillar Stability Prediction Based on SABO-LSSVM Model
## 1 Introduction
The reliability analysis method differs from the safety factor method in that it establishes a stochastic model for reliability assessment, treats the input variables of the pillar as random variables, and describes them using distribution functions. [PERSON] and [PERSON] [17] proposed a reliability design method to overcome the shortcomings of the safety factor method, which neglects the influence of the inherent joint and fracture characteristics of the rock mass in pillar design. The reliability design method fully considers the non-uniformity and discontinuity of the rock mass and has a greater practical value. Statistical learning theory involves analyzing the mine pillar stability through reverse analysis based on a large number of actual cases. [PERSON] and [PERSON] et al. [14] proposed the application of multivariate mathematical statistical methods from nonlinear science in the analysis of mine pillar stability using quantization theory II (QTII) for pillar state discrimination models. [PERSON] et al. [18] applied fuzzy logic to predict the safe sizes of mine pillars based on a dataset of 399 coal mine pillar samples. Although statistical learning theory can provide guidance for engineering practice, it also has limitations in terms of interpretability and the inability to explain the essence of the problem [2]. The numerical simulation method involved establishing a pillar model using computer simulation software and conducting simulation calculations based on reasonable mechanical principles. [PERSON] et al. [19] conducted instability mechanism analyses for different types of underground mine pillar failures, performed three-dimensional numerical simulations using the Drucker-Prager yield criterion for various mining scenarios, and evaluated the sensitivity of the factors affecting pillar stability using orthogonal range analysis. The stability analysis of mine pillars is a complex nonlinear problem that involves indicators, such as pillar size, rock mass strength, and their interrelationships [14]. Despite attempts by many scholars to use classical methods, such as the safety factor approach and reliability analysis, to comprehensively evaluate pillar stability, there have always been limitations in terms of accuracy and applicability. In recent years, with the advancement of computer technology, neural networks and intelligent algorithms have been widely applied in various fields. Machine learning statistical analysis methods based on monitoring information have become a research hotspot owing to their high accuracy and efficiency [20]. These methods have been applied in studies related to rock-burst prediction, blast casting effect prediction, mine pillar stability prediction, and other mining safety issues. Researchers such as [PERSON] and [PERSON] et al. [21; 22] have successfully applied machine learning models, such as support vector machines (SVM) and GA-XGB for rock-burstgrade prediction, achieving good prediction accuracy. [PERSON] et al. (2020) combined the Weibull model with a BP neural network for blast pile shape prediction. [PERSON] (2020) compared the prediction performance of BP, SVM, and radial basis function (RBF) models in predicting the blasting effect in open-pit mines. In addition to the aforementioned areas, scholars have continuously explored the application of machine learning for predicting the stability grade of mine pillars. [PERSON] et al. (2020) evaluated the performance of SVM and Fisher's discriminant analysis (FDA) in mine pillar stability prediction, and the results showed that the SVM model performed better. [PERSON] and [PERSON] et al. (2020) used a large number of measured pillar samples to compare ten prediction models, including distance discriminant analysis (DDA), Bayesian discriminant analysis (BDA), extreme learning machine (ELM), and least-squares support vector machine (LSSVM), for mine pillar state recognition from various perspectives. In summary, the application of machine learning methods to the prediction of mine pillar stability has become a research hotspot.