Prediction model of slope deformation in open pit mines based on GJO-MLP
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摘要: 露天矿边坡变形受地质结构、水文地质条件、采矿活动等多种因素影响，使得预测模型复杂，难以准确捕捉所有影响因素。目前，大量监测设备部署在露天矿边坡周围，用于实时记录露天矿边坡位移数据，这些数据具有高维度、时序关联性及非线性等特性。如果在其他条件未知而只有数据的情况下，使用传统的边坡稳定性分析方法无法有效进行边坡变形预测，而采用仅基于数据的模型对露天矿边坡位移数据进行预测对边坡稳定性的事前分析十分必要。针对上述问题，提出了一种基于金豺优化多层感知机（GJO−MLP）的露天矿边坡变形预测模型。GJO中各智能体间相互独立，可以通过并行计算加速优化MLP的训练过程；GJO能够结合MLP的非线性建模和特征提取能力，使得优化后的MLP在处理复杂问题时更具优势。为检验GJO−MLP的可行性和有效性，将GJO−MLP分别与基于蚁群算法优化的MLP（ACO−MLP）、基于引力搜索算法优化的MLP（GSA−MLP）及基于差分进化算法优化的MLP（DE−MLP）进行对比分析，在6个数据集上的仿真实验结果表明：在相同实验条件下，相较于其他3种算法，GJO−MLP表现出更好的寻优性能。将基于GJO−MLP的边坡变形预测模型应用于宝日希勒露天矿边坡变形预测和花坪子边坡变形预测中，结果表明：在相同条件下，相较于其他3种算法，基于GJO−MLP的边坡变形预测模型在对边坡变形数据进行预测时不仅表现出更好的预测求解性能，而且还具有更好的可行性和鲁棒性。Abstract: The deformation of open-pit mine slopes is influenced by various factors such as geological structure, hydrogeological conditions, mining activities, etc., making the prediction model complex. It is difficult to accurately capture all influencing factors. At present, a large number of monitoring devices are deployed around the slope of open-pit mines to record real-time displacement data of open-pit mine slopes. The data has the features of high-dimensional, temporal correlation, and nonlinear. Traditional slope stability analysis methods cannot effectively predict slope deformation without knowing other conditions and only data, it is necessary to use a data-based model to predict the displacement data of open-pit mine slopes in advance for slope stability analysis. In order to solve the above problems, a deformation prediction model for open-pit mine slopes based on the golden jackal optimized multilayer perception machine (GJO-MLP) is proposed. Each agent in GJO is independent of each other and can accelerate the training process of optimizing MLP through parallel computing. GJO can combine the nonlinear modeling and feature extraction capabilities of MLP, making the optimized MLP more advantageous in dealing with complex problems. To test the feasibility and effectiveness of GJO-MLP, GJO-MLP is compared and analyzed with ant colony algorithm optimization based MLP (ACO-MLP), gravity search algorithm optimization based MLP (GSA-MLP), and differential evolution algorithm optimization based MLP (DE-MLP). The simulation results on six datasets show that under the same experimental conditions, GJO-MLP shows better optimization performance compared to the other three algorithms. The slope deformation prediction model based on GJO-MLP is applied to the slope deformation prediction of Baorixile open-pit mine and Huapingzi slope deformation prediction. The results show that under the same conditions, compared to the other three algorithms, the slope deformation prediction model based on GJO-MLP not only show better predictive performance in predicting slope deformation data, but also has better feasibility and robustness.
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图 4 各算法在不同数据集上的迭代收敛曲线
Figure 4. Iterative convergence curve of each algorithm under different datasets
图 5 4种算法对东帮685观测点变形监测预测误差
Figure 5. Prediction error of deformation monitoring of 685 observation points in Dongbang by four algorithms
图 6 4种算法对花坪子边坡观测点TP02−HPZ的预测结果
Figure 6. Prediction results of TP02-HPZ of Huapingzi slope observation point by four algorithms
图 7 4种算法对观测点TP02−HPZ的预测绝对误差和
Figure 7. The sum of the forecast absolute errors of the four algorithms for the observation point TP02-HPZ
表 1 数据集详细信息
Table 1. Datasets details
数据集 训练样本数 测试样本数 类别 Balloon 16 16 2 Iris 150 150 3 Breast cancer 599 100 2 Heart 80 187 2 Cosine 31 38 — Sine 126 252 — 
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表 2 算法参数设置
Table 2. Algorithm parameter settings
算法 参数 值 GJO−MLP 种群规模
最大迭代次数30
200ACO−MLP 种群规模
最大迭代次数
初始信息素
信息素指数权重
蒸发率30
200
10
0.3
0.1GSA−MLP 种群规模
最大迭代次数
Rnorm30
200
2DE−MLP 种群规模
最大迭代次数
交叉概率30
200
0.2
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表 3 MLP初始模型结构
Table 3. MLP initial model structure
数据集 属性 MLP结构 Balloon 4 4−9−1 Iris 4 4−9−3 Breast cancer 9 9−19−1 Heart 22 22−45−1 Cosine 1 1−15−1 Sine 1 1−15−1
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表 4 数据集实验结果
Table 4. Classification datasets experimental results
数据集 算法 MSE（AVE±STD） 分类精度/% 测试误差 Balloon GJO−MLP 0.135 2±0.001 5 34.00 — ACO−MLP 0.600 0±1.17×10−16 40.00 — GSA−MLP 0.200 4±0.057 9 6.00 — DE−MLP 0.160 7±0.009 5 13.50 — Iris GJO−MLP 0.056 4±0.017 4 51.67 — ACO−MLP 1.845 7±0.011 8 0 — GSA−MLP 0.286 9±0.139 0 21.87 — DE−MLP 0.146 8±0.024 9 38.33 — Breast cancer GJO−MLP 0.001 7±2.53×10−4 98.00 — ACO−MLP 0.663 2±1.17×10−16 0 — GSA−MLP 0.016 1±0.007 4 50.00 — DE−MLP 0.024 2±0.024 9 6.10 — Heart GJO−MLP 0.112 0±0.013 2 73.75 — ACO−MLP 0.500 0±0 50.00 — GSA−MLP 0.160 3±0.019 4 41.25 — DE−MLP 0.177 3±0.011 2 69.50 — Cosine GJO−MLP 0.177 8±6.151×10−4 — 4.971 6 ACO−MLP 1.080 1±2.62×10−6 — 14.504 2 GSA−MLP 0.296 3±0.070 0 — 7.924 1 DE−MLP 0.181 1±0.001 2 — 6.356 9 Sine GJO−MLP 0.455 3±0.002 4 — 149.421 7 ACO−MLP 1.498 9±8.83×10−7 — 251.958 8 GSA−MLP 0.463 6±0.004 4 — 152.154 0 DE−MLP 0.442 2±0.007 7 — 150.004 5
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表 5 东帮685观测点变形监测数据
Table 5. Deformation monitoring data of Dongbang 685
mm 监测时间 北方向位移 东方向位移 竖直位移 2022−10−01T08:00:00 −55.800 −160.100 −63.500 2022−10−01T16:00:00 −54.700 −159.700 −68.600 2022−10−02T00:00:00 −57.400 −159.000 −64.400 2022−10−02T08:00:00 −54.800 −159.200 −60.900 2022−10−02T16:00:00 −55.900 −160.100 −63.400 2022−10−03T00:00:00 −55.600 −157.800 −63.000 2022−10−03T08:00:00 −54.400 −157.800 −62.800 2022−10−03T16:00:00 −53.600 −158.700 −63.900 2022−10−04T00:00:00 −55.900 −157.400 −63.700 2022−10−04T08:00:00 −56.500 −158.100 −64.800 2022−10−04T16:00:00 −54.700 −161.800 −64.600 2022−10−23T00:00:00 −53.700 −157.400 −65.000 2022−10−23T08:00:00 −56.100 −158.500 −67.600 2022−10−23T16:00:00 −53.800 −161.600 −69.300 2022−10−24T00:00:00 −52.600 −156.700 −63.500 2022−10−24T08:00:00 −55.400 −160.400 −69.100 2022−10−24T16:00:00 −54.400 −160.400 −69.500 2022−10−25T00:00:00 −51.700 −159.600 −67.900 2022−10−25T08:00:00 −55.700 −157.700 −69.300 2022−10−25T16:00:00 −53.000 −159.800 −69.600 2022−10−26T00:00:00 −51.000 −159.000 −65.200 2022−10−26T08:00:00 −54.600 −157.200 −66.500
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表 6 4种算法对东帮685观测点变形监测数据的预测结果
Table 6. Prediction results of deformation monitoring data of 685 observation points in Dongbang by four algorithms
mm 监测时间 实际监测值 GJO−MLP ACO−MLP GSA−MLP DE−MLP 预测值 绝对误差 预测值 绝对误差 预测值 绝对误差 预测值 绝对误差 2022−10−01T08:00:00 55.800 56.873 1.073 60.500 4.700 58.902 3.102 58.105 2.305 2022−10−01T16:00:00 54.700 57.013 2.313 60.500 5.800 58.369 3.669 58.187 3.487 2022−10−02T00:00:00 57.400 56.238 1.162 60.500 3.100 59.067 1.667 57.941 0.541 2022−10−02T08:00:00 54.800 57.011 2.211 60.500 5.700 58.439 3.639 58.169 3.369 2022−10−02T16:00:00 55.900 56.845 0.945 60.500 4.600 58.918 3.018 58.102 2.202 2022−10−03T00:00:00 55.600 56.920 1.320 60.500 4.900 58.871 3.271 58.111 2.511 2022−10−03T08:00:00 54.400 57.013 2.613 60.500 6.100 58.293 3.893 58.264 3.864 2022−10−03T16:00:00 53.600 56.966 3.366 60.500 6.900 58.203 4.603 58.486 4.886 2022−10−25T00:00:00 51.700 56.571 4.871 60.500 8.800 57.918 6.218 58.597 6.897 2022−10−25T08:00:00 55.700 56.897 1.197 60.500 4.800 58.886 3.186 58.108 2.408 2022−10−25T16:00:00 53.000 56.886 3.886 60.500 7.500 58.118 5.118 58.560 5.560 2022−10−26T00:00:00 51.000 56.431 5.431 60.500 9.500 57.887 6.887 58.599 7.599 2022−10−26T08:00:00 54.600 57.014 2.414 60.500 5.900 58.330 3.730 58.209 3.609
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表 7 4种算法对花坪子边坡TP02−HPZ的预测结果
Table 7. Prediction results of TP02-HPZ of Huapingzi slope by four algorithms
mm 期号 实际监测值 GJO−MLP ACO−MLP GSA−MLP DE−MLP 预测值 绝对误差 预测值 绝对误差 预测值 绝对误差 预测值 绝对误差 111 53.800 53.754 0.046 54.000 0.200 53.655 0.145 53.716 0.084 112 53.900 53.803 0.097 54.000 0.100 53.688 0.212 53.763 0.137 113 53.900 53.803 0.097 54.000 0.100 53.688 0.212 53.763 0.137 114 53.400 53.443 0.043 54.000 0.600 53.460 0.060 53.439 0.039 115 53.300 53.341 0.041 54.000 0.700 53.391 0.091 53.339 0.039 116 53.200 53.231 0.031 54.000 0.800 53.312 0.112 53.235 0.035 117 53.000 53.021 0.021 54.000 1.000 53.120 0.120 53.016 0.016 118 53.300 53.341 0.041 54.000 0.700 53.391 0.091 53.339 0.039 119 53.200 53.231 0.031 54.000 0.800 53.312 0.112 53.235 0.035 120 53.100 53.124 0.024 54.000 0.900 53.222 0.122 53.126 0.026
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