# Predicting the Loose Zone of Roadway Surrounding Rock Using Wavelet Relevance Vector Machine
## 1 Introduction  
A surrounding rock loose zone refers to the stress redistribution of surrounding rock after excavation and the stress variation in surrounding rock, which leads to stress concentration. When the stress value exceeds the strength limit or yield limit, the roadway surrounding rock mass breaks up and forms a certain range of rupture area [1]. For many years, rock bolts are commonly used to enhance the stability of surrounding rock [2; 3; 4; 5]. However, rock bolts are subjected to the loose zone of pre-load [6; 7; 8] or corrosion [9; 10; 11] and may fail [12]. The thickness determination of loose zone is not only a significant factor for the roadway surrounding rock's stability, but also an important basis for the design of roadway support. Therefore, the accurate determination for the thickness of loose zone of roadway surrounding rock makes a great difference to improve the stability of underground engineering rock mass [13; 14; 15; 16]. With the development of structural health monitoring [17; 18; 19], the methods to determine the loose zone thickness of roadway surrounding rock generally include acoustic wave test, numerical simulation and, support vector machine prediction [20; 21]. The acoustic wave test method [22] can directly and accurately determine the range of loose zone, however the field operation is cumbersomeand the cost is high. The numerical simulation method [23] is low cost and easy to realize. Nevertheless, it is obviously affected by the parameters of surrounding rock, and the result sometime has a large margin of error. Due to the nonlinearity of loose zone for surrounding rock and uncertainty of state and parameter measurement, the prediction of surrounding rock loose zone can be regarded as a typical complex and fuzziness problem. In recent decades, various intelligent methods, such as artificial neural network (ANN) [24; 25; 26], fuzzy logic [27; 28; 29], genetic algorithm (GA) [30; 31], wavelet packet analysis (WPA) [32; 33; 34], supporting vector machine (SVM) [35; 36; 37], among others [38; 39; 40], have been developed to deal with nonlinearities and uncertainties. The support vector machine prediction method [41] can solve the problems of nonlinearity and small samples, and has achieved some success in the prediction of roadway surrounding rock loose zone. Nevertheless, the prediction accuracy and generalization ability of the model are affected by parameters. Relevant vector machine (RVM) [42; 43; 44; 45] is a sparse probability model alike support vector machine (SVM) proposed by [PERSON] in 2001. Its training process is based on Bayesian framework [47; 48]. RVM can be used for regression estimation and prediction to obtain the distribution of predicted values. It not only has excellent nonlinear fitting and generalization ability, but also makes up for the defect that SVM needs to estimate regularization parameters and cannot get the prediction results based on probability [49; 50]. RVM combines the advantages of core-based method and Bayesian theory, and establishes the relationship between a group of input vectors and its required output. Therefore, the selection of kernel functions plays an important role in RVM achieving good performance. In practical applications, the commonly used kernels are Gauss kernels and polynomial kernels [51], however they cannot generate a complete set of bases in a space (such as square integrable space) by translation. The incomplete base will result in RVM not approaching any objective function in the kernel space. Wavelet is a function approximation tool in square integrable space [52; 53]. Wavelet kernel function has been applied to SVM function approximation, which effectively improves the accuracy of the model [51]. Wavelet technology has great potential in dealing with approximation and classification of non-stationary signals [54; 55]. Wavelet function is a group of bases [56], which can approximate any function.