Prediction of the maximum ground settlement caused by shield tunneling based on the improved limit learning machine model
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摘要:
城市地铁盾构施工引发的地面过大变形会严重影响周边构筑物的正常使用，甚至引发工程事故。针对传统预测方法中的数据维度过大容易导致精度降低、计算复杂等问题，提出了一种基于主成分分析（principal component analysis，PCA）算法和哈里斯鹰优化（Harris Hawks optimization，HHO）算法的极限学习机（extreme learning machine，ELM）预测模型。在地质、几何及盾构参数中初选14个影响因子，利用PCA算法在14维数组中分离和提取5个主成分变量作为模型的输入，利用HHO优化ELM模型的输入层权值和隐含层阈值参数，得到预测模型的最优解。以昆明轨道交通五号线怡心桥站—广福路站隧道区间监测数据进行仿真验证，并将该模型与BP神经网络、RBF、未优化的ELM模型进行对比分析。结果表明：PCA-HHO-ELM预测模型的均方根误差为0.143 5、平均绝对误差为0.026 2、决定系数为0.959 6，相较于其他模型，该模型具有更优的预测性能；与未优化的ELM模型相比，HHO算法能够提高ELM模型的预测精度和泛化能力。PCA-HHO-ELM模型能可靠预测盾构诱发的地表最大沉降，可为类似变形预测提供一种更为可行的新思路。
Abstract:Excessive ground deformation caused by shield tunneling of urban metro will seriously affect the normal use of surrounding structures, and even cause engineering accidents. In view of the problems that the data dimension in traditional prediction methods is too large, which easily leads to lower accuracy and complex calculation, this study proposes an extreme learning machine (ELM) prediction model based on the principal component analysis (PCA) algorithm and Harris Hawk optimization algorithm (HHO). Ten influence factors are preliminarily selected from the geological, geometric and shield parameters. PCA is used to separate and extract five principal component variables from the 10 dimensional arrays as the input of the model. HHO is used to optimize the input layer weights and hidden layer threshold parameters of the ELM model, and the optimal solution of the prediction model is obtained. The monitoring data of the Yiguang section of Kunming Rail Transit Line 5 are used for simulation verification, and the model is compared with the BP neural network, RBF and non-optimized ELM model. The results show that the root mean square error of the PCA-HHO-ELM prediction model is 0.1435, the average absolute error is 0.0262, and the determination coefficient R2 is 0.9596. Compared with other models, this model has better prediction performance. Compared with the non-optimized ELM, HHO can improve the prediction accuracy and generalization ability of ELM. The PCA-HHO-ELM model can reliably predict the maximum ground settlement induced by shield, and can provide a more feasible new idea for similar deformation prediction.
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表 1 数据集数据统计信息表
Table 1. Data set statistics table
参数 最小值 最大值 地质参数 地下水位（A1）/m 1.50 1.92 浮密度（A2）/（g·cm–3） 0.54 0.77 压缩模量（A3）/MPa 3.37 4.42 泊松比（A4） 0.28 0.33 侧压力系数（A5） 0.49 0.59 几何参数 埋深（A6）/m 18.4 25.3 盾构参数 土压力（A7）/MPa 1.8 2.7 总推力（A8）/kN 8 760 16 280 掘进速度（A9）/（mm·min–1） 61 94 出土量（A10）/ m3 45.8 48.0 刀盘扭矩（A11）/（N·m） 1 200 2 275 拼装时间（A12）/h 0.35 0.85 注浆量（A13）/m3 3.60 4.40 注浆压力（A14）/bar 3.0 3.8 地表最大沉降/mm −15.69 10.44 
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表 2 主成分系数矩阵
Table 2. Principal component coefficient matrix
影响因子 主成分 1 2 3 4 5 A1 0.897 0.023 0.086 0.077 0.052 A2 0.937 −0.077 0.043 0.041 0.051 A3 −0.228 0.586 0.376 −0.460 −0.163 A4 −0.271 −0.259 −0.724 0.340 0.105 A5 0.956 −0.068 −0.130 −0.007 −0.028 A6 0.376 0.335 0.365 0.492 0.315 A7 0.683 −0.093 −0.116 −0.520 0.060 A8 −0.078 0.310 0.425 −0.053 0.748 A9 −0.474 0.530 −0.582 0.019 0.216 A10 −0.227 0.867 −0.247 0.123 −0.128 A11 −0.809 −0.112 −0.056 −0.256 0.188 A12 −0.790 −0.464 0.277 −0.071 0.080 A13 −0.201 −0.636 0.046 0.019 0.247 A14 −0.445 −0.011 0.622 0.384 −0.365
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表 3 4类模型预测结果
Table 3. Prediction results of four types of models
组号 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 实测值/mm 2.89 9.86 5.03 4.45 2.07 10.44 0.82 3.64 0.44 13.42 9.69 4.96 2.54 1.93 1.43 BP预测值/mm 1.62 −8.49 3.61 −8.92 −0.56 12.08 −0.97 3.51 0.12 −13.78 10.10 −3.74 2.53 2.24 0.70 RBF预测值/mm 5.04 0.49 2.12 2.00 −2.86 2.81 0.31 4.48 0.50 −11.03 5.07 −11.39 2.03 2.01 0.50 ELM预测值/mm −0.24 −6.17 4.21 0.11 −0.94 12.90 0.27 −0.51 −1.51 −11.13 11.95 −4.05 2.63 2.12 0.26 PCA-HHO-ELM预测值/mm 2.11 −7.83 4.93 −5.25 0.14 9.38 −1.90 7.34 −1.23 −12.66 12.93 −4.72 3.83 3.46 −0.82 组号 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 实测值/mm 0.01 6.33 5.22 14.19 13.74 1.14 4.17 5.31 1.61 0.08 9.90 1.24 10.84 2.24 12.35 BP预测值/mm −0.06 4.85 4.89 −14.13 −14.25 0.49 4.10 5.93 1.73 −0.05 −9.73 −0.01 −10.46 1.30 −11.83 RBF预测值/mm 0.50 3.59 2.56 −11.32 −7.45 0.50 4.47 5.07 0.50 0.50 −9.67 0.50 −8.02 0.58 −7.45 ELM预测值/mm −0.53 5.72 5.79 −11.76 −15.91 1.34 2.90 5.71 1.65 −0.58 −9.78 0.70 −8.43 −0.12 −14.09 PCA-HHO-ELM预测值/mm −1.33 6.50 6.89 −13.27 −14.07 2.16 4.35 2.43 4.00 −0.99 −9.01 0.13 −10.76 1.18 −12.41
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表 4 模型性能评价结果
Table 4. Performance evaluation results of the model
评价指标 RMSE MAE R2 最大误差/mm 平均误差/mm PCA-HHO-ELM模型 0.143 5 0.026 2 0.959 6 3.70 1.29 BP预测模型 0.232 3 0.042 4 0.894 3 4.48 0.82 RBF模型 0.392 1 0.071 6 0.698 6 10.35 2.52 ELM预测模型 0.571 8 0.104 4 0.359 2 4.56 1.48
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