Back-Analysis Method for Stope Displacements Using Gradient-Boosted Regression Tree and Firefly Algorithm

It is essential to determine the properties of the rock mass surrounding underground excavations to facilitate stability analysis and engineering design. In this paper, a novel displacement back-analysis method was proposed based on gradient-boosted regression tree (GBRT) and firefly algorithm (FA). The proposed method, the GBRT-FA, utilized GBRT as an instance-based learning approach to substitute numerical modeling. Furthermore, FA was used for the hyperparameters tuning and the rock mass properties searching. The input variables in the numerical modeling were chosen to be deformation modulus, Poisson's ratio, cohesion, and internal friction angle, which were back-analysed using the GBRT-FA. A total of 13,310 numerical models were conducted to provide the dataset for the training and testing of GBRT models. A parametric study of back-analysis performance was also conducted. The results show that FA was efficient in the hyperparameters tuning of GBRT with stabilized results being obtained within six iterations. The average median absolute percentage error (APE) between displacement values from numerical modeling and the optimum GBRT model was 5.4%, denoting that numerical modeling could be well substituted by the optimum GBRT model. The overall performance of the GBRT-FA was reasonably good, with the average APE value for all input variables being 6.3%. The substitution performance of GBRT models, the dataset size, and the number of displacement measurements were found to have a significant influence on the performance of the displacement back-analysis method. Suggestions for the engineering applications of back-analysis methods were made based on the results, which have a guiding significance for underground mines.