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为探究神经网络在预测超临界传热方面的有效性, 建立了水平直管内超临界R1234ze(E)冷却传热的神经网络预测模型, 并与修正的Dittus-Boelter (D-B)型传热关联式进行比较分析. 研究表明, 输入参数对于反向传播神经网络(BPNN)预测精度的影响很大, 且并非所有BPNN输入参数组合都能带来比传热关联式更好的预测结果. 输入参数组合
$ {{Re} _{\text{b}}} $ ,$ {Pr _{\text{b}}} $ ,$ {{{\rho _{\text{b}}}} \mathord{\left/ {\vphantom {{{\rho _{\text{b}}}} {{\rho _{\text{w}}}}}} \right. } {{\rho _{\text{w}}}}} $ ,$ {{{{\overline C }_{\text{p}}}} \mathord{\left/ {\vphantom {{{{\overline C }_{\text{p}}}} {{C_{{\text{pw}}}}}}} \right. } {{C_{{\text{pw}}}}}} $ ,$ {{{\lambda _{\text{b}}}} \mathord{\left/ {\vphantom {{{\lambda _{\text{b}}}} {{\lambda _{\text{w}}}}}} \right. } {{\lambda _{\text{w}}}}} $ ,$ {{{\mu _{\text{b}}}} \mathord{\left/ {\vphantom {{{\mu _{\text{b}}}} {{\mu _{\text{w}}}}}} \right. } {{\mu _{\text{w}}}}} $ 的预测表现最好, 对于试验集的预测结果的平均绝对偏差和最大偏差仅为2.02%和9.34%, 远低于传热关联式预测偏差, 且对于高温段 h的趋势、 h最大值以及 h峰值位置的预测比关联式更加准确. 此外, 将遗传算法优化的BP (GA-BP)模型与BP模型在两种不同的适应度值计算方式下进行比较, 揭示GA-BP在提高超临界传热预测精度方面的有效性. 研究表明, 当网络训练与适应度值计算采用相同数据时, 将引起过拟合, 并不能进一步提高预测精度; 当网络训练与适应度值计算采用不同数据时, 可使得网络泛化性能提高, 预测结果的均方根偏差和最大偏差均有进一步的降低.-
关键词:
- R1234ze(E)/
- 超临界传热/
- 传热预测/
- 神经网络
The prediction of heat transfer coefficients or wall temperatures of heat exchanger tubes is an important research topic in supercritical heat transfer, which is extremely significant for the application of supercritical fluids in industrial production and the design of the entire thermal system. At present, the empirical correlation method is the most widely adopted prediction method, but its predicted heat transfer coefficient still has significant difference from the actual data near the pseudo-critical temperature. Therefore, some scholars proposed using artificial neural networks to predict the heat transfer performance of supercritical fluids in tubes. On the basis of previous researches, this work further explores the effectiveness of artificial neural network in predicting supercritical heat transfer, focusing on the influence of input parameters on neural network prediction results and the influence of genetic algorithm optimization on the prediction results. In this research, a neural network prediction model for supercritical R1234ze(E) cooled in horizontal straight tubes is established and compared with the modified D-B heat transfer correlation. The result shows that the input parameter has great influence on the prediction accuracy of BPNN, and not all BPNN input parameter combinations can bring better prediction results than heat transfer correlation. The combination of $ {{Re} _{\text{b}}} $ ,$ {Pr _{\text{b}}} $ ,$ {{{\rho _{\text{b}}}} \mathord{\left/ {\vphantom {{{\rho _{\text{b}}}} {{\rho _{\text{w}}}}}} \right. } {{\rho _{\text{w}}}}} $ ,$ {{{{\overline C }_{\text{p}}}} \mathord{\left/ {\vphantom {{{{\overline C }_{\text{p}}}} {{C_{{\text{pw}}}}}}} \right. } {{C_{{\text{pw}}}}}} $ ,$ {{{\lambda _{\text{b}}}} \mathord{\left/ {\vphantom {{{\lambda _{\text{b}}}} {{\lambda _{\text{w}}}}}} \right. } {{\lambda _{\text{w}}}}} $ ,$ {{{\mu _{\text{b}}}} \mathord{\left/ {\vphantom {{{\mu _{\text{b}}}} {{\mu _{\text{w}}}}}} \right. } {{\mu _{\text{w}}}}} $ features the best prediction performance. The AAD and Error maxof the prediction result for the trial set are only 2.02% and 9.34%, which are far lower than the prediction deviation of the heat transfer correlation, and the predictions of the trend of hin the high temperature region, the maximum value of hand the position of the peak value of hare more precise than heat transfer correlation. Moreover, this research compares GA-BP model with BP model under two different fitness value calculation methods to reveal the effectiveness of GA-BP in enhancing the prediction accuracy of supercritical heat transfer, concluding that when the same dataset is adopted for network training and fitness value calculation, over-fitting will occur and the GA-BP cannot further improve the prediction accuracy; when different datasets are used to train the network and calculate the fitness value, the generalization ability of the network will be strengthened, and the root mean square deviation and the maximum deviation of the prediction result can be further reduced.This work will provide a practical tool for predicting the cooling convection heat transfer of supercritical R1234ze(E) in horizontal tubes, laying the foundation for its application in trans-critical heat pump systems, and providing inspiration for potential research directions of ANN in supercritical heat transfer prediction. 
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Case d/mm G/(kg·m–2·s–1) q/(kW·m–2) P/MPa Tb/K 1—12 3, 4, 5, 6, 7, 8, 9, 10,
11, 12, 13, 14320 –40 4.0 370—420 13—24 6 160, 200, 240, 280, 320, 360,
400, 440, 480, 520, 560, 600–40 4.0 370—420 25—34 6 320 –10, –20, –30, –40, –50, –60,
–70, –80, –90, –1004.0 370—420 35—44 6 320 –40 3.8, 4.0, 4.2, 4.4,
4.6, 4.8, 5.0, 5.2,370—420 
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序号 项目 值或选择 1 隐藏层神经元数目 由测试集的预测结果确定 2 隐藏层传递函数 tansig 3 输出层传递函数 purelin 4 训练函数类型 由测试集的预测结果确定 5 学习函数类型 learngdm 6 最大迭代次数 20000 7 训练目标误差 10–10 8 网络学习速率 0.1 9 验证集最大确认失败数 6 下载:
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d/mm G/(kg·m–2·s–1) q/(kW·m–2) P/MPa Case 1 8 250 –75 3.9 Case 2 5 460 –55 3.9 Case 3 8 220 –65 4.5 Case 4 7 300 –25 4.5 下载:
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输入参数 试验集预测结果 AAD/% RMSE/% Errormax/% 传热关联式 — 5.58 7.72 29.40 BP神经网络 1) $ {{Re} _{\text{b}}} $, $ {Pr _{\text{b}}} $, $ {{{\rho _{\text{b}}}} \mathord{\left/ {\vphantom {{{\rho _{\text{b}}}} {{\rho _{\text{w}}}}}} \right. } {{\rho _{\text{w}}}}} $, $ {{{{\overline C }_{\text{p}}}} \mathord{\left/ {\vphantom {{{{\overline C }_{\text{p}}}} {{C_{{\text{pw}}}}}}} \right. } {{C_{{\text{pw}}}}}} $, $ {{Gr} \mathord{\left/ {\vphantom {{Gr} {{Re} _{\text{b}}^{2}}}} \right. } {{Re} _{\text{b}}^{2}}} $ 8.24 12.40 43.98 2) $ {{Re} _{\text{b}}} $, $ {Pr _{\text{b}}} $, $ {{{\rho _{\text{b}}}} \mathord{\left/ {\vphantom {{{\rho _{\text{b}}}} {{\rho _{\text{w}}}}}} \right. } {{\rho _{\text{w}}}}} $, $ {{{{\overline C }_{\text{p}}}} \mathord{\left/ {\vphantom {{{{\overline C }_{\text{p}}}} {{C_{{\text{pw}}}}}}} \right. } {{C_{{\text{pw}}}}}} $ 3.51 5.07 15.19 3) $ {{Re} _{\text{b}}} $, $ {Pr _{\text{b}}} $, $ {{{\rho _{\text{b}}}} \mathord{\left/ {\vphantom {{{\rho _{\text{b}}}} {{\rho _{\text{w}}}}}} \right. } {{\rho _{\text{w}}}}} $, $ {{{{\overline C }_{\text{p}}}} \mathord{\left/ {\vphantom {{{{\overline C }_{\text{p}}}} {{C_{{\text{pw}}}}}}} \right. } {{C_{{\text{pw}}}}}} $, $ {{{\lambda _{\text{b}}}} \mathord{\left/ {\vphantom {{{\lambda _{\text{b}}}} {{\lambda _{\text{w}}}}}} \right. } {{\lambda _{\text{w}}}}} $, $ {{{\mu _{\text{b}}}} \mathord{\left/ {\vphantom {{{\mu _{\text{b}}}} {{\mu _{\text{w}}}}}} \right. } {{\mu _{\text{w}}}}} $ 2.02 3.01 9.34 4) G,q,d,Tb, $ {\rho _{\text{b}}} $ 9.89 15.52 73.24 5) G,q,d,Tb, $ {\rho _{\text{b}}} $, $ {C_{{\text{pb}}}} $, $ {\lambda _{\text{b}}} $, $ {\mu _{\text{b}}} $, 4.58 5.35 11.35 6) G,q,d,Tb, $ {\rho _{\text{b}}} $, $ {{{\rho _{\text{b}}}} \mathord{\left/ {\vphantom {{{\rho _{\text{b}}}} {{\rho _{\text{w}}}}}} \right. } {{\rho _{\text{w}}}}} $, $ {{{{\overline C }_{\text{p}}}} \mathord{\left/ {\vphantom {{{{\overline C }_{\text{p}}}} {{C_{{\text{pw}}}}}}} \right. } {{C_{{\text{pw}}}}}} $, $ {{{\lambda _{\text{b}}}} \mathord{\left/ {\vphantom {{{\lambda _{\text{b}}}} {{\lambda _{\text{w}}}}}} \right. } {{\lambda _{\text{w}}}}} $, $ {{{\mu _{\text{b}}}} \mathord{\left/ {\vphantom {{{\mu _{\text{b}}}} {{\mu _{\text{w}}}}}} \right. } {{\mu _{\text{w}}}}} $ 47.24 63.17 224.89 7) G,q,d,Tb, $ {\rho _{\text{b}}} $, $ {C_{{\text{pb}}}} $, $ {\lambda _{\text{b}}} $, $ {\mu _{\text{b}}} $, $ {{{\rho _{\text{b}}}} \mathord{\left/ {\vphantom {{{\rho _{\text{b}}}} {{\rho _{\text{w}}}}}} \right. } {{\rho _{\text{w}}}}} $, $ {{{{\overline C }_{\text{p}}}} \mathord{\left/ {\vphantom {{{{\overline C }_{\text{p}}}} {{C_{{\text{pw}}}}}}} \right. } {{C_{{\text{pw}}}}}} $, $ {{{\lambda _{\text{b}}}} \mathord{\left/ {\vphantom {{{\lambda _{\text{b}}}} {{\lambda _{\text{w}}}}}} \right. } {{\lambda _{\text{w}}}}} $, $ {{{\mu _{\text{b}}}} \mathord{\left/ {\vphantom {{{\mu _{\text{b}}}} {{\mu _{\text{w}}}}}} \right. } {{\mu _{\text{w}}}}} $ 52.52 63.15 151.79 下载:
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