An Prediction Method for Determining the Maximum von Mises Stress in Casing Based on SVM
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摘要:
为了预测非均匀地应力条件下不居中套管的最大应力，提高套管安全性，研究了基于支持向量机（SVM）的套管最大von Mises应力预测方法。首先确定了影响套管最大应力的关键因素，包括非均匀地应力、水泥环的弹性模量及泊松比、套管偏心距等8个因素；然后利用ANSYS软件构建了套管应力实验样本；最后建立了
ε−SVR 模型，实现了套管最大应力的预测。通过自学习，基于径向基核函数的SVM回归方法对于训练样本达到了很好的精度，5个测试样本的平均相对误差仅为1.32%，具有较好的预测精度，满足工程需求，且可以实现非均匀地应力条件下不居中套管最大应力的快速求解。研究结果为现场安全施工提供了理论依据。-
关键词:
- 支持向量机 /
- 非均匀地应力 /
- 套管偏心距 /
- von Mises应力
Abstract:In order to predict the maximum stress of uncentered casing under non-uniform in-situ stress and improve the safety of casing, a prediction method of casing’s maximum von Mises stress based on artificial intelligence SVM is studied. First, the key factors affecting the maximum stress of casing are determined, including non-uniform geologic stress, elastic modulus and Poisson's ratio of cement sheath, eccentricity of casing, etc. Then the "experimental" samples of casing stress are constructed by using ANSYS software. Finally the
ε−SVR model is established to realize the prediction of casing’s maximum stress. Through self-learning, the SVM regression method based on RBF kernel achieves good accuracy for training samples. For the five test samples, the average relative error is only 1.32%, which means that this method can meet the needs of engineering application. In particular, this method can be used to quickly solve the maximum stress of uncentered casing under non-uniform in-situ stress.The research results provide theoretical basis for site safety construction. -
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图 4 套管–水泥环–地层系统有限元模型
Figure 4. Finite element model for casing, cement sheath and formation
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图 5 套管内壁von Mises应力云图
Figure 5. von Mises stress cloud diagram on the casing inner wall
表 1 主要影响因素及取值范围
Table 1 Main influencing factors and range of values
影响因素 取值范围 最大水平主应力σH/MPa 80～135 最小水平主应力σh/MPa 30～80 钻井液密度ρf/（kg∙L–1） 1.15～2.05 水泥环的弹性模量Ec/GPa 10～60 水泥环的泊松比μc 0.15～0.35 地层的弹性模量Es/GPa 1～30 地层的泊松比μs 0.10～0.30 套管偏心距δ/mm 1.5～25.7 
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表 2 SVM“实验样本”数据
Table 2 Data of the SVM “experimental samples”
序号 ρf/（kg∙L–1） Ec/GPa μc Es/GPa μs σH/MPa σh/MPa δ/mm σv/MPa 1 1.73 35.00 0.26 15.70 0.25 55.00 107.50 25.7 642.24 2 1.48 38.57 0.18 25.91 0.23 40.71 123.21 1.5 766.62 3 1.48 38.57 0.18 25.91 0.23 40.71 123.21 11.2 768.59 4 1.23 38.57 0.18 17.74 0.31 37.14 80.00 1.5 458.83 5 1.48 20.71 0.32 25.91 0.23 51.43 127.14 20.8 754.53 6 1.48 38.57 0.18 25.91 0.23 40.71 123.21 6.3 767.72 7 1.48 20.71 0.32 25.91 0.23 51.43 127.14 11.2 754.29 8 2.05 42.14 0.35 23.87 0.16 65.71 111.43 1.5 487.51 9 1.73 35.00 0.26 9.57 0.40 51.43 127.14 25.7 1 008.85 10 1.81 27.86 0.17 7.53 0.34 44.29 103.57 1.5 835.23 … … … … … … … … … … 91 1.89 24.29 0.24 21.83 0.10 33.57 99.64 16.0 550.76 92 1.15 56.43 0.29 11.61 0.12 76.43 115.36 25.7 957.12 93 1.73 35.00 0.26 9.57 0.40 51.43 127.14 6.3 1 006.05 94 1.48 38.57 0.18 25.91 0.23 40.71 123.21 16.0 769.33 95 1.23 17.14 0.15 30.00 0.36 65.71 111.43 6.3 468.30 96 1.73 10.00 0.30 21.83 0.10 55.00 107.50 25.7 586.98 97 1.48 60.00 0.21 7.53 0.34 62.14 131.07 16.0 1 192.18 98 1.48 60.00 0.21 7.53 0.34 62.14 131.07 20.8 1 195.77 99 1.40 38.57 0.18 13.66 0.19 37.14 80.00 20.8 531.50 100 1.97 24.29 0.24 5.49 0.27 76.43 115.36 25.7 862.73
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表 3 测试样本的预测结果
Table 3 Predictive effect of test samples
样本序号 模型参数 最大von Mises应力/MPa 绝对误差/MPa 相对误差，% 平均相对误差，% 样本值 预测值 96 σ=2.01
ε=0.01
C=3.00586.98 603.21 16.23 2.76 1.32 97 1 192.18 1 200.54 8.36 0.70 98 1 195.77 1 207.74 11.97 1.00 99 531.50 530.85 –0.65 –0.12 100 862.73 845.36 –17.37 –2.01
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