PREDICTION OF STRESS CONCENTRATION FACTORS OF STAINLESS STEEL ROUND SQUARE MIXECD TUBE JOINTS BASED ON INTERPRETABLE MACHINE LEARNING
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摘要:
不锈钢圆方混合管在循环荷载下可能发生疲劳破坏。提出一种预测精度高并可解释机理的“应力集中系数预测模型”，从而定量评价不锈钢圆方混合管节点的抗疲劳性能。创建了包含615个不锈钢管节点(T型、Y型、X型和K型节点)的数据库，并确定关键输入特征，继而选取九种典型回归算法建立模型，并将每种模型的预测值和试验值进行比较，从而获得优选应力集中系数的预测模型。在此基础上，使用Shapley方法从全局、个体和特征依赖性进行解释。结果表明：XGBoost模型测试集与训练集的预测精度均大于0.98，特征选取有效；XGBoost模型在预测圆方混合管不锈钢节点SCF时具有较高的预测精度和泛化能力；在不锈钢混合管节点SCF预测公式中应考虑是否搭接和搭接率的影响，截面尺寸特征之间存在高度依赖性；建立的人机交互GUI模块可实现不锈钢圆方混合管节点应力集中系数的精准预测。
Abstract:The fatigue failure of stainless steel round square mixed tubes may occur under cyclic load. A " prediction model of stress concentration factor" with high prediction accuracy and explanation mechanism was proposed to quantitatively evaluate the fatigue resistance of stainless steel round square mixed tube joints. A database of 615 stainless steel tube joints (T-, Y-, X- and K-joints) was created and key input characteristics were identified. Then, nine typical regression algorithms were selected to establish the model, and the predicted values of each model were compared with the test values, so as to obtain the optimal prediction model of stress concentration factor. On this basis, Shapley method was used to explain the global, individual and feature dependencies. The results showed that the prediction accuracies of both test set and training set of XGBoost model were greater than 0.98, and the feature selection was effective. The XGBoost model had high prediction accuracy and generalization ability when predicting the SCF of stainless steel round square mixed tube joints. The influence of overlap and overlap rate should be considered in SCF prediction formula and there was a high dependence between the dimensional features of the section. The human-computer interactive GUI module can accurately predict the stress concentration coefficient of stainless steel round square mixed tube joints.
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Keywords:
- stainless steel /
- square pipe /
- stress concentration factor /
- interpretability /
- XGBoost /
- SHAP /
- GUI
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图 9 XGBoost模型与已有预测方程预测结果对比
Figure 9. Comparison between prediction results of XGBoost model and existing prediction equations
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图 10 XGBoost模型和已有预测方程对SCFc的k值统计分布
Figure 10. Statistical distribution of k-values of SCFc by XGBoost model and existing prediction equations
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图 11 XGBoost模型和已有预测方程对SCFb的k值统计分布
Figure 11. The XGBoost model and existing prediction equations support the statistical distribution of k-values of SCFb
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图 12 XGBoost模型与已有预测方程预测结果对比的泰勒图
Figure 12. Taylor diagram comparing the prediction results of the XGBoost model and the existing prediction equations
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图 16 样本309号K型节点的个体解释
Figure 16. Individual explanations for selected samples of different joint types
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图 20 试验与有限元的荷载-位移曲线对比
Figure 20. Verification of the baseline model load-displacement curve
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图 21 有限元/试验结果与GUI模块预测结果对比
Figure 21. Comparison of finite element/test results with GUI module predictions
表 1 487个不锈钢管节点SCF样本的统计数据
Table 1 Statistical data of SCF samples of 487 stainless steel pipe joints
文献 支撑弦杆
宽径比β支撑弦杆
厚度比τ弦杆
径厚比2γ截面形式
Tube-type截面形式
Joint-type是否搭接
overlapSCFt,c SCFt,b 文献[13] 0.54~0.88 0.76~1.01 49.63~52.37 CS T N 5.53~33.17 11.79~32.61 0.54~0.88 0.76~1.02 49.93~51.81 CS Y N 0.64~33.24 10.70~18.96 0.54~0.88 0.76~1.03 50.17~50.63 CS X N 0.29~34.99 6.29~34.99 文献[14, 28 − 29] 0.20~0.60 0.30~0.90 20~50 CS T N 4.24~84.51 4.34~42.71 0.20~0.60 0.30~0.90 20~50 CS T N 3.43~91.62 4.56~45.98 文献[31] 0.25~1.00 0.50~2.00 10~70 CS T N 0.58~230.32 1.90~113.42 0.25~1.00 0.50~2.00 10~70 CS Y N 3.25~133.55 1.82~74.37 0.25~1.00 0.50~2.00 10~70 CS X N 8.12~257.93 1.95~133.15 文献[32] 0.61~0.91 0.75~1.01 40.39~45.48 SC K Y 5.55~8.31 2.08~5.22 0.51~0.76 0.74~1.00 39.60~45.09 SC K N 0.92~4.80 1.14~5.09 0.54~0.88 0.74~1.00 50.19~50.56 CS K Y 2.64~15.66 1.95~5.07 0.54~0.88 0.71~1.02 50.52~51.04 CS K N 1.17~8.34 0.52~4.82 文献[30] 0.40~0.60 0.40~1.00 33.33~66.67 SC K N 1.21~5.58 2.76~43.13 0.40~0.80 0.40~1.00 33.33~66.67 SC K Y 3.00~16.38 3.50~19.67 0.40~0.80 0.40~0.90 31.25~62.50 CS K N 1.43~16.25 0.45~1.38 0.40~0.80 0.40~0.90 31.25~62.50 CS K Y 1.27~13.31 2.86~34.67 注：SCFt,c为试验获得的不锈钢节点弦杆的应力集中系数；SCFt,b为试验获得的不锈钢节点支撑的应力集中系数。 
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表 2 ML模型的最优超参数
Table 2 Optimal hyperparameters of the ML models
弦杆/支撑 模型 最优超参数 弦杆/支撑 模型 最优超参数 弦杆 LR None 支撑 LR None Ridge alpha=1, solver="sag" Ridge alpha=1, solver="sag" Lasso alpha=0.1, l1_ratio=0.2 Lasso alpha=0.1, l1_ratio=0.3 KNN Algorithm='brute', n_neighbors=6,weights='distance' KNN Algorithm='brute', n_neighbors=7,weights='uniform' DT max_depth=14, splitter='best' DT max_depth=15, splitter='best' RF n_estimators=300, max_depth=16,
min_samples_leaf=3, min_samples_split=3RF n_estimators=400, max_depth=18,
min_samples_leaf=4, min_samples_split=3GBDT learning_rate=0.1, max_depth=6,
n_estimators=450, tol=0.0001GBDT learning_rate=0.01,max_depth=4,
n_estimators=300,tol=0.001AdaBoost max_depth=7, min_samples_leaf=1,
min_samples_split=2, splitter="best"AdaBoost max_depth=9, min_samples_leaf=1,
min_samples_split=2, splitter="random"XGBoost learning_rate=0.1, max_depth=5,
n_estimators=300, gamma=0.2,l1=0, l2=1XGBoost learning_rate=0.001, n_estimators=400,
max_depth=7, gamma=0.3, l1=0, l2=1
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表 3 各模型的预测精度及误差指标
Table 3 The prediction accuracy of each model and the error index
模型 训练集数据 测试集数据 总数据 R2 MAE RMSE MdAE R2 MAE RMSE MdAE R2 MAE RMSE MdAE LR 弦杆 0.65 14.12 17.33 10.07 0.64 14.32 19.29 14.40 0.64 14.16 18.47 12.21 支撑 0.64 15.23 17.32 10.36 0.63 16.81 20.50 10.01 0.63 16.09 19.57 10.11 Ridge 弦杆 0.66 14.94 19.97 10.71 0.64 16.61 17.33 12.94 0.65 13.70 21.54 11.51 支撑 0.65 14.10 20.25 11.08 0.63 16.31 18.32 11.96 0.64 15.75 19.58 11.42 Lasso 弦杆 0.62 14.03 23.74 12.04 0.61 14.41 18.32 13.15 0.61 14.16 22.49 12.98 支撑 0.55 14.94 20.11 9.56 0.54 15.62 21.33 10.59 0.54 15.07 20.59 10.07 KNN 弦杆 0.86 6.29 13.57 1.44 0.82 8.72 17.32 1.99 0.84 6.39 15.52 1.77 支撑 0.87 6.02 12.54 2.66 0.86 7.64 14.31 3.33 0.86 6.27 13.92 3.04 DT 弦杆 0.95 4.82 15.62 1.01 0.94 5.15 17.33 4.00 0.94 3.57 16.16 2.45 支撑 0.95 3.72 13.19 1.56 0.94 5.71 17.33 3.66 0.94 4.71 15.34 2.86 RF 弦杆 0.97 2.14 6.20 0.94 0.95 4.87 8.46 2.44 0.96 2.69 7.33 1.97 支撑 0.97 2.32 7.54 0.96 0.94 4.77 8.95 2.09 0.95 3.75 7.61 1.87 GBDT 弦杆 0.96 2.11 6.45 0.94 0.95 4.04 7.12 2.00 0.96 2.93 7.01 1.26 支撑 0.97 2.55 5.73 1.46 0.96 3.83 6.32 2.72 0.96 2.95 6.07 2.48 AdaBoost 弦杆 0.98 2.95 5.74 1.02 0.96 3.73 6.52 2.00 0.97 2.91 6.23 1.17 支撑 0.98 2.21 5.02 1.00 0.96 3.41 5.64 2.69 0.97 2.85 5.32 1.71 XGBoost 弦杆 0.99 2.03 4.27 0.81 0.98 3.17 5.18 1.71 0.98 2.26 4.73 1.29 支撑 0.99 1.79 3.83 0.98 0.98 3.71 4.88 2.34 0.98 2.18 4.35 1.81
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表 5 试验、有限元及GUI模块结果对比
Table 5 Comparison of experimental, finite element and GUI module results
试件 支撑弦杆
宽径比β支撑弦杆
厚度比τ弦杆
径厚比2γ弦杆 支撑 SCFt SCFFE SCFGUI 误差/(%) SCFt SCFFE SCFGUI 误差/(%) CS-C150×3-B108×3-G72.20(S1) 0.72 0.96 51.04 1.17 1.13 1.21 3.40 2.08 2.11 2.03 −2.40 CS-C200×4-B108×3-O34.50(S2) 0.54 0.74 50.19 4.92 4.89 4.83 −1.80 5.07 4.96 5.14 1.40 SC-C160×4-B80×3-G45.86 (S3) 0.51 0.74 40.91 3.45 3.43 3.63 5.20 1.89 1.97 1.84 2.60 SC-C133×3- B80×3-O41.20 (S4) 0.60 1.00 44.33 8.31 8.16 8.03 −3.40 2.59 2.43 2.56 1.20 CS-C180×4- B140×3-G60 0.78 0.75 45.00 − 3.03 3.19 5.02 − 1.63 1.58 −3.06 CS-C200×4- B140×3-G80 0.70 0.75 50.00 − 3.82 4.01 4.90 − 2.57 2.49 −3.11 CS-C240×5- B160×4-G80 0.67 0.80 48.00 − 2.94 3.02 2.72 − 2.94 3.07 4.42 CS-C260×5- B180×4-G80 0.69 0.80 52.00 − 4.07 3.96 −2.70 − 2.69 2.74 1.86 CS-C220×5- B180×4-G80 0.82 0.80 44.00 − 2.36 2.13 −9.74 − 2.93 2.70 −7.84 CS-C280×6- B140×3-G80 0.50 0.50 46.67 − 5.32 4.96 −6.76 − 1.83 1.85 1.09 CS-C180×4- B140×3-O30.31 0.78 0.75 45.00 − 4.04 4.05 0.26 − 3.00 3.12 4.00 CS-C200×4- B140×3-O25.57 0.70 0.75 50.00 − 4.50 4.37 −2.97 − 3.34 3.51 5.08 CS-C240×5- B160×4-O40.41 0.67 0.80 48.00 − 4.10 4.07 −0.73 − 3.06 3.16 3.26 CS-C260×5- B180×4-O31.43 0.69 0.80 52.00 − 4.75 4.69 −1.26 − 3.50 3.45 −1.43 CS-C220×5- B180×4-O39.78 0.82 0.80 44.00 − 3.52 3.61 2.55 − 2.88 2.95 2.43 CS-C280×6- B140×3-O45.45 0.50 0.50 46.67 − 8.13 7.98 −1.84 − 2.57 2.63 2.33 SC-C180×4- B140×3-G60 0.78 0.75 45.00 − 3.44 3.55 3.19 − 2.12 2.13 0.47 SC -C200×4- B140×3-G80 0.70 0.75 50.00 − 10.86 10.98 1.10 − 10.31 10.37 0.58 SC -C240×5- B160×4-G80 0.67 0.80 48.00 − 10.26 10.37 1.07 − 8.92 9.03 1.23 SC -C260×5- B180×4-G80 0.69 0.80 52.00 − 9.80 9.68 −1.22 − 8.72 8.62 1.14 SC -C220×5- B180×4-G80 0.82 0.80 44.00 − 8.84 8.83 0.11 − 9.47 9.57 1.05 SC -C280×6- B140×3-G80 0.50 0.50 46.67 − 12.78 12.65 −1.02 − 11.06 11.21 1.36 SC -C180×4- B140×3-O30.31 0.78 0.75 45.00 − 7.03 7.02 −0.14 − 2.54 2.46 −3.14 SC -C200×4- B140×3-O25.57 0.70 0.75 50.00 − 7.39 7.45 0.81 − 2.38 2.31 −2.94 SC -C240×5- B160×4-O40.41 0.67 0.80 48.00 − 7.42 7.68 3.54 − 2.69 2.71 0.74 SC -C260×5- B180×4-O31.43 0.69 0.80 52.00 − 9.58 9.26 −3.34 − 2.84 3.11 9.51 SC -C220×5- B180×4-O39.78 0.82 0.80 44.00 − 6.65 6.71 0.90 − 2.95 2.84 −3.73 SC -C280×6- B140×3-O45.45 0.50 0.50 46.67 − 8.62 8.20 −4.87 − 2.95 3.02 2.37 注：CS表示支撑为圆管，弦杆为方管；SC表示支撑为方管，弦杆为圆管；C表示弦杆；B表示支撑；G表示间隙节点；O表示搭接节点。
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表 6 流程图各参数计算结果
Table 6 Calculation results of each parameter of the flow chart
参数 结果 截面参数 β=0.57, τ=22.5, 2γ=0.5, Θ=38.7, A0=5410, A1=1480 结构计算参数 σb=18/mm2, σc=59/mm2 SCF结果 SCFb=4.13, SCFc=8.51 实际热点参数 Sb=243.62 N/mm2, Sc=149.00 N/mm2 设计热点参数 Srhs,b=304.51 N/mm2, Srhs,c=186.25 N/mm2 疲劳寿命 Nf,b=218762次, Nf,c=204174次 注：下标b表示支撑；c表示弦杆。
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