图  1  热模拟试验流程示意

Figure  1.  Schematic illustration of thermal simulation experimental processes

图  2  神经网络结构示意

Figure  2.  Schematic diagram of the neural network architecture

图  3  隐藏层数量与单层神经元数量对人工神经网络性能的影响

Figure  3.  The influences of the hidden layer number and neuron number in each hidden layer on the performance of ANN

图  4  P650不同温度和应变速率下的真应力-应变曲线

Figure  4.  True stress-true stain curves of P650 steel at different temperatures and strain rate

(a) 0.01 s⁻¹; (b) 0.1 s⁻¹; (c) 1 s⁻¹; (d) 10 s⁻¹

图  5  各参数线性关系

Figure  5.  Linear relationships of various parameters

(a) $ {\text{ln}}\dot \varepsilon $-$ \ln \sigma $；(b) $ {\text{ln}}\dot \varepsilon $-$ \sigma $；(c) $ {\text{ln}}\dot \varepsilon $-$\ln [\sinh (\alpha \sigma )]$；(d) $\ln [\sinh (\alpha \sigma )]$-1/T

图  6  应变量0.1时ln Z与$\ln [\sinh (\alpha \sigma)]$关系

Figure  6.  Plot of lnZ and $\ln [\sinh (\alpha \sigma)]$ at strain of 0.1

图  7  材料常数与真应变关系曲线

Figure  7.  The relationships between material constants and true strain

(a) n; (b) ln A; (c) α; (d) ${\text{Q}}$

图  8  人工神经网络预测输出数据与实测输出数据对比

(a)训练数据；(b)测试数据

Figure  8.  Predicted output data from the ANN versus measured output data for the training data and testing data

图  9  应变补偿Arrhenius模型、ANN模型的实测与预测流变应力对比

Figure  9.  Comparisons between measured and predicted flow stress by strain-compensated Arrhenius model and ANN model of P650 steel

(a) 0.01 s⁻¹；(b) 0.1 s⁻¹；(c) 1 s⁻¹；(d) 10 s⁻¹

图  10  试验值与预测值之间的相关性

(a)人工神经网络；(b)应变补偿Arrhenius模型

Figure  10.  Correlation between the measured and predicted stress data

图  11  模型的相对误差分布

(a)人工神经网络模型；(b) 应变补偿Arrhenius模型；(c)各模型间的相对误差对比

Figure  11.  Relative error distribution diagram of the model