Assessment of rockburst risk using multivariate adaptive regression splines and deep forest model

Rockburst is a major instability issue faced by underground excavation projects, which is induced by the instantaneous release of a large amount of strain energy stored in rock mass. Because of its disastrous damage to infrastructures and facilities, more and more studies have been focused on rockburst prediction. However, due to highly nonlinear relationships between the occurrence of rockburst and potential triggering factors, traditional mechanism-based prediction methods have great difficulties in providing the reliable results. In this study, a multivariate adaptive regression splines (MARS) model and a novel deep forest algorithm were applied to predict and classify rockburst intensity of a database including 344 rockburst cases collected worldwide. The t-distributed stochastic neighbor embedding method (t-SNE) was utilized for nonlinear dimensionality reduction and visualization of the original input features. After that, the Gaussian mixture model was adopted to relabel original data to determine relative intensity of these rockburst cases. Then, the MARS model and deep forest model were constructed with these newly labeled data. Their performances were compared with some widely used machine learning methods, such as random forest, extreme gradient boost, and ANN model. The results clearly proved the capability of the proposed models to assess and forecast rockburst risk. It also proved that these approaches should be used as cross-validation against each other. The Shapley additive explanations method was adopted to investigate the relative importance of input features of the developed MARS model. The result shows that σθ and σc are the most important features for rockburst intensity prediction, where σθ is the tangential stress around underground opening and σc refers to uniaxial compressive strength of the rock.