Three-dimensional thermal stress prediction method in double-wall structure using convolutional neural networks
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摘要:
为实现三维物理场的预测，提出一种利用卷积神经网络（CNN）对双层壁冷却结构外壁三维热应力快速评估方法。针对双层壁冷却结构外壁平板状的结构特征，沿壁厚方向将温度场切分为多个切片。将温度作为卷积网络输入张量的基本元素，不同厚度位置的切片对应输入张量的通道维度，从而实现将三维温度场输入进网络，并输出在热载荷作用下的三维等效应力场。结果表明：训练收敛后的网络在测试集上的平均绝对误差为1.23 MPa，平均相对误差为15.10%，对峰值应力的平均绝对误差为16.10 MPa，平均相对误差为11.81%。对于双层壁冷却结构的热应力预测问题，CNN能够很好地完成温度到应力的映射。使用深度学习方法探究热弹性问题的潜在机理有望实现。
Abstract:To realize the prediction of 3D physical field, a method for rapid evaluation of 3D thermal stress on the outer wall of double-wall cooling structure using convolutional neural network (CNN) was presented. For the structural characteristics of the flat plate shape of the double-wall cooling structure outer wall, the temperature field was sliced into multiple sections along the wall thickness direction. The temperature was used as the basic element of the input tensor of the CNN, and the sections at different thickness positions corresponded to channel dimensions of the input tensor. The 3D temperature field was input into the CNN for output of the 3D von-Mises stress field under thermal load. The average absolute error of the trained converged network on the testing set was 1.23 MPa, with an average relative error of 15.10%, and the average absolute error for peak stresses was 16.10 MPa, with an average relative error of 11.81%. Results showed that for the thermal stress prediction problem of double-wall cooling structures, CNN can complete the temperature-to-stress mapping well. Exploring potential mechanisms of the thermoelasticity problems by using deep learning methods is expected to be realized.
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图 10 训练集和测试集上的绝对误差分布
Figure 10. Absolute error distribution on the training set and testing set
图 11 训练集和测试集上预测应力场峰值应力回归分析
Figure 11. Peak stress regression analysis of predicted stress field on training set and testing set
表 1 变量参数范围
Table 1. Range of variable parameters
参数 数值 气膜孔直径Df /mm 0.4～0.9 气膜孔倾斜角α/（°） 20～70 气膜孔展向间距P/mm 3Df～5Df 气膜孔流向间距S/mm 3Df～13Df 外壁厚度Ho/mm 0.7～1.2 冲击距离H/mm 0.7～1.2 主流燃气温度Tm/K 1 700, 1 900, 2 100 主流燃气速度Vm/（m/s） 400, 800 吹风比M 0.75, 1.25 
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表 2 训练集和测试集各项指标结果
Table 2. Indexes results of the training set and testing set
参数 训练集 测试集 EMSE/MPa2 0.40 3.49 EMAE/MPa 0.43 1.23 EMRE/% 6.75 15.10 EPMAE/MPa 2.63 16.10 EPMRE/% 2.39 11.81
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表 3 样本各项变量的具体取值
Table 3. Values of each variable in the sample
样本 训练集样本
ID1-CD1测试集样本
ID1-CD7Df/mm 0.85 α/（°） 30.16 P/mm 4.09Df S/mm 12.84Df Ho/mm 0.75 Tm/K 1700 Vm/（m/s） 400 M 0.75 1.25
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