# Optimization of BP Neural Network Model for Rockburst Prediction under Multiple Influence Factors
## 1 Introduction  
Construction activities (drilling and blasting) of large underground caverns and tunnel excavations, etc., inevitably cause internal damage and redistribution of in situ stress rock masses, which are easy to induce brittle failures, such as spalling, cracking and rockburst [1, 2]. Rockburst is a phenomenon in which the elastic energy gathered in a rockmass is released suddenly and violently under external influence, resulting in rockbursting or ejection. In 1900, rockburst was first observed in the Kolar gold mine of India, which has frequently occurred in the construction of mines, hydraulic works, tunnels and other projects in many countries [3; 4; 5; 6].  
The prediction and evaluation of rockburst are important prerequisites for formulating prevention and control measures. In recent years, machine learning techniques have been applied well in the field of classification and recognition, and they have become promising methods in rockburst prediction, such as support vector machine [7; 8], neural network [9; 10], random forest [11; 12], cloud model [13; 14], extreme learning machine [15; 16], Bayesian classifier [17; 18], decision tree [19; 20], fuzzy C-means clustering [21] and logistic regression model [22]. As a classical supervised learning algorithm, the BP (ack propagation) neural network has been widely used in rockburst prediction [23; 24; 25]. Most of the existing studies used a standard BP neural network, that is, using a gradient descent algorithm to train the model, which has some disadvantages, including sensitive initial weight setting, local extreme value prone to occur, slow convergence speed, difficult selection of network structure, etc. Given these deficiencies, [PERSON] et al. [26] used Levenberg-Marquardt algorithm to train a BP network and improve the efficiency of the standard model. [PERSON] [27] optimized the network by adding linear transfer functions, momentum terms and introducing a new training method (Resilient BP). [PERSON] [28] adjusted the weight and threshold of the algorithm structure by increasing the self-adaptability and momentum term coefficient. [PERSON] et al. [29] used particle swarm optimization, and [PERSON] et al. [30] used a genetic algorithm to optimize the initial weights and thresholds of a BP network, which improved the prediction accuracy of the model. [PERSON] et al. [31] established an improved BP neural network adopting an adaptive learning rate algorithm and an algorithm based on numerical optimization technology. Existing studies have used different optimization algorithms to improve the standard BP network model and achieved good results. However, a comparative analysis of optimization effects among multiple different algorithms has not been carried out, and the influence of different index dimensionless methods on the prediction accuracy of the BP model has not been discussed.  
Therefore, based on three sample sizes of rockburst examples (40, 70 and 100), this paper selects a standard gradient descent algorithm, four typical optimization algorithms (momentum gradient descent algorithm, quasi-Newton algorithm, conjugate gradient algorithm and Levenberg-Marquardt algorithm) and four commonly used index dimensionless methods (unified extreme value processing method, differentiated extreme value processing method, data averaging processing method and normalization processing method). Additionally, it establishes sixty BP prediction models, systematically carries out comparative research on model prediction effect, optimizes the best rockburst prediction model and applies it to engineering cases.  
This manuscript is an extension of the conference paper _BP neural network model optimization for rockburst prediction considering sample sizes, optimization algorithms and dimensionless methods._ No copyright issue is involved.