在井下锚杆支护过程中，及时了解工作压力对提高钻机使用寿命、保障煤矿生产安全具有重要的意义。针对目前锚杆支护中钻进压力反馈滞后、煤岩硬度分布非线性、现有方法不适用等问题，提出了一种基于高斯过程时间序列回归最优核函数和历史点数的锚杆支护钻进压力预测方法。这种方法通过高斯随机过程、核函数以及贝叶斯理论进行锚杆支护时间序列煤岩压力预测，是一种对非线性问题适应性高、具有概率意义输出的机器学习方法。以巷道掘进过程中钻箱钻进1 000 mm时的钻进压力试验数据作为最优核函数和历史点数的筛选样本，以10种核函数(E、SE、RQ、Matern3/2、Matern5/2、ARDE、ARDSE、ARDRQ、ARDMatern3/2、ARDMatern5/2)和7种历史点数(8、10、12、14、16、18、20)作为筛选对象，通过负对数边缘似然函数为极小化目标函数自适应获取最优超参数，以单步外推的方式和训练集、测试集7∶3的比例对筛选样本进行了70次数值解算。分别以测试集可决系数(R₂)、测试集均方根误差(RMSE)、测试集平均绝对误差(MAE)为数值解算评价指标，获取了4种锚杆支护钻进压力预测策略的最优核函数和最优历时点数组合(Matern5/2+历时点数10、ARDMatern5/2+历史点数10、SE+历时点数18、RQ+历史点数18)。基于最小化计算量，选取最优核函数为Matern5/2、最优历史点数为10，再次分别对巷道掘进过程中钻箱钻进1 200、2 400、3 000 mm的钻进压力试验数据进行数值解算，给出95%置信区间下锚杆支护钻进压力预测分布。所提出的方法对于钻箱钻进1 200 mm的钻进压力的预测数据，R₂为0.61317，MAE为0.026957，区间平均宽度百分比为3.072%；所提出的方法对于钻箱钻进2 400 mm的钻进压力的预测数据，R₂为0.931 18，MAE为0.010 895，区间平均宽度百分比为0.581%；所提出的方法对于钻箱钻进3 000 mm的钻进压力的预测数据，R₂为0.996 47，MAE为0.009 184 7，区间平均宽度百分比为0.614%。最终发现，不同核函数和历史点数的组合选择会有较大差距的预测效果，是不可忽略的两个重要因素，本研究方法对围岩硬度分布均匀的数据波段预测结果优秀，对围岩硬度突变的数据波段预测结果在可接受范围内。

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.