Prediction of drilling pressure in bolting based on gaussian process time series regression optimal kernel function and historical points

Timely understanding of surrounding rock pressure bolting is crucial to enhance the service life of drilling rigs and ensure coal mine production safety. However, delayed feedback of drilling pressure, nonlinear distribution of coal and rock hardness,and inapplicability of existing methods in bolt support are common problems. To address these issues, a prediction method of drilling pressure in bolt support is proposed based on the optimal kernel function and historical points of Gaussian process time series regression. This is a machine learning method that is highly adaptabile to nonlinear problems and provides probabilistic output. It utilizes Gaussian stochastic process, kernel function, and Bayesian theory to predict the sequence coal rock pressure during bolt support. The optimal kernel function and historical points for the proposed prediction method were selected based on drilling pressure test data obtained during roadway excavation where the drill box was drilled 1000 mm. The parameters included 10 types of kernel functions (E, SE, RQ, Maten3/2, Maten5/2, ARDE, ARDSE, ARDRQ, ARDMatern3/2, ARDMatern5/2) and 7 different historical points (8, 10, 12, 14, 16, 18, 20). The optimal hyperparameter were adaptively determined through the negative logarithmic edge likelihood function as the minimization objective function. A total of 70 numerical calculations were performed using a single-step extrapolation method with a 7:3 ratio for the training and testing sets on the selected samples. Based on the evaluation indicators, such as determinability coefficient (R₂), root mean square error (RMSE), and the average absolute error (MAE) of the test set, the optimal kernel function and optimal combination of duration points for four bolt support drilling pressure prediction strategies were identified. The optimal combination includes Matern5/2 with historical points 10, ARDMatern5/2 with historical points 10, SE with historical points 18, and RQ with historical points 18. The optimal kernel function was selected as Matern5/2 and the optimal number of historical points was chosen as 10, considering the minimization of computational complexity. Drilling pressure test data obtained from drilling the drill box at 1200 mm, 2400 mm and 3000 mm during the tunnel excavation process were used for numerical calculations The predicted distribution of the drilling pressure supported by the anchor rod was given with a 95% confidence interval. The proposed method achieved an R₂ of 0.61317 and an MAE of 0.026957 for drilling pressure during drilling with a 1200 mm drill box, with an average width percentage of the interval of 3.072%. For the drilling pressure of 2400 mm drill box, the proposed method achieved an R₂ of 0.93118 and an MAE of 0.010895, with an average width percentage of the interval of 0.581%. For the drilling pressure of 3000 mm drill box, the proposed method achieved an R₂ of 0.99647 and an MAE of 0.0091847, with an average width percentage of the interval of 0.614%. The final conclusion found that the combination of different kernel functions and historical points has a significant difference in prediction performance,which is two important factors that cannot be ignored.The prediction results were excellent for the data bands with a uniform hardness distribution of the surrounding rock and acceptable for the data bands with abrupt hardness changes.