Prediction of free bending forming result of TP2 pipe based on POA-BP
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摘要: 将壁厚减薄率和椭圆率作为管材自由弯曲成形结果的评价指标，选取弯曲模与管材间隙值、弯曲模圆角半径值、管材弯曲变形区长度、导向机构圆角半径值、导向机构与管材间隙值作为影响因子。利用数值模拟方法对管材自由弯曲成形结果的评价指标和影响因子建立样本库，并随机选取6组作为测试样本，其余的作为训练样本，结合BP神经网络和鹈鹕优化算法对预测模型进行训练，构建POA-BP神经网络预测模型对管材自由弯曲成形结果进行预测。结果表明，POA-BP预测模型的壁厚减薄率和椭圆率的最大预测误差不超过2%，故POA-BP预测模型能够有效预测管材成形结果。Abstract: The wall thickness thinning rate and ellipticity are selected as evaluation criteria for the free bending forming results of the pipe. The influencing factors include the gap between the bending die and the pipe, the radius of the corner of the bending die, the length of the bending deformation zone of the pipe, the radius of the corner of the guide mechanism, and the gap between the guide mechanism and the pipe. A sample library for the evaluation criteria and influencing factors of free bending of pipes is established using numerical simulation method. Six random groups are selected as test samples, while the remaining samples are used for training. The POA-BP neural network prediction model is constructed by combining the BP neural network and the Pelican optimization algorithm to predict the free bending forming results of pipes. The results show that the maximum prediction error of the wall thickness reduction rate and ellipticity of the POA-BP prediction model does not exceed 2%. Therefore, the POA-BP prediction model can effectively predict the pipe forming results.
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Key words:
- pipe /
- free bending /
- evaluation criteria /
- neural network /
- prediction
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表 1 TP2铜管材料参数
密度/
（g/cm3）抗拉强度/
MPa弹性模量
E/GPa屈服强度/
MPa泊松比$ \varepsilon $ 8.930 367.87 115 33.48 0.32 
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表 2 模拟和实验结果对比
弯曲段 δ/（%） ε/（%） 1 模拟 1.83 1.02 实验 1.66 1.81 偏差 0.17 0.79 2 模拟 2.66 3.04 实验 2.02 3.77 偏差 0.64 0.73 3 模拟 5.22 4.61 实验 4.82 5.76 偏差 0.4 1.15
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表 3 不同隐含层节点数训练得到的MSE
节点数 MSE 4 0.137 5 0.086 6 0.029 7 0.023 8 0.019 9 0.014 10 0.012 11 0.012 12 0.018 13 0.009
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表 4 鹈鹕优化算法基本参数
参数类型 数值 说明 鹈鹕种群数量 30 - 学习因子 0.4 - 邻域半径 由0.2趋近至0 R为常数0.2 POA最大迭代次数 50 - 搜索空间维度 72 由各层节点数决定
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表 5 BP模型、POA-BP模型的预测结果与数值模拟结果对比
序号 A1/
mmA2/
mmA3/
mmA4/
mmA5/
mm数值模拟 BP预测模型 POA-BP
预测模型δ/
（%）ε/
（%）It /
（%）Id /
（%）It /
（%）Id /
（%）1 0.1 2.5 24 2.5 0.4 3.98 6.03 1.181 2.405 0.854 0.713 2 0.2 2.5 21 2 0.2 5.24 5.33 1.947 1.707 1.107 0.694 3 0.2 1.5 23 2.5 0.3 4.41 5.54 1.361 2.852 0.295 1.318 4 0.3 2.5 23 1.5 0.3 4.23 5.98 3.357 0.017 0.615 1.121 5 0.2 2 25 1.5 0.2 4.28 5.67 0.187 0.071 0.771 0.882 6 0.2 2 25 1.5 0.4 3.65 7.65 3.891 2.418 1.726 0.745
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表 6 实际加工与POA-BP预测模型结果对比
序号 实际加工 POA-BP预测模型 δ/（%） ε/（%） δ/（%） ε/（%） 1 3.84 6.23 3.946 5.987 2 4.98 5.45 5.182 5.293 3 4.56 5.25 4.423 5.467 4 4.38 5.69 4.204 5.913 5 4.08 5.97 4.247 5.62 6 3.44 7.87 3.587 7.593
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