Coupling prediction of multi-stage axial turbine characteristics based on data-driven and change of flow angle
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摘要:
构建了一种基于数据驱动的涡轮性能多模型耦合预测方法。该方法融合了多个机器学习模型和级间气流角变化规律，利用熵权法综合量化分析预测结果，动态确定最优模型。经多级轴流涡轮特性变工况实例验证表明：在定转速下，相较于传统方法，该方法在质量流量-效率特性与质量流量-膨胀比特性上的计算精度分别提升了40.47%与18.26%，与三维仿真结果的最大误差不超过3%。在变转速预测中，基于网格超参数优化，成功构建了2～8 kg/s质量流量范围内的特性图谱，膨胀比最大误差接近3%，满足精度要求。
Abstract:A data-driven coupled prediction method for turbine performance was proposed by incorporating multiple machine learning models and inter-stage flow angle variation patterns. Multiple prediction analysis models were established based on fundamental data, and the entropy weighting method was used to perform comprehensive quantitative analysis of the model predictions. The optimal prediction model was dynamically determined based on data-driven approaches. Verification through multi-stage axial turbine characteristic variation examples demonstrated that under constant rotational speed conditions, compared with the traditional direct prediction method without considering changes in the flow angle, the computational accuracy of the flow-efficiency characteristic and the flow-expansion ratio characteristic was improved by 40.47% and 18.26%, respectively. Furthermore, the maximum error compared with the results of three-dimensional numerical simulations was less than 3%. For variable speed performance prediction, the construction of the turbine characteristic map within a wide flow range of 2 to 8 kg/s was achieved through grid hyper parameter optimization methods. Simulation testing of the constructed map validated that the maximum error in the expansion ratio was close to 3%, meeting the requirements for characteristic estimation accuracy.
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图 1 涡轮特性耦合预测分析方法框架
Figure 1. Framework of coupling predictive analysis method for turbine characteristics
图 6 定转速效率特性超参数优化
Figure 6. Constant speed efficiency characteristic hyper-parameter optimization
图 7 定转速气流角模型的效率特性得分
Figure 7. Efficiency characteristic score of constant speed flow angle model
图 8 定转速气流角模型的效率综合评价
Figure 8. Comprehensive evaluation of efficiency of constant speed flow angle model
图 9 定转速膨胀比特性超参数优化
Figure 9. Constant speed expansion ratio characteristic hyper-parameter optimization
图 10 定转速气流角模型的膨胀比特性得分
Figure 10. Expansion ratio characteristic score of constant speed flow angle model
图 11 定转速气流角模型综合评价结果
Figure 11. Comprehensive evaluation results of constant speed flow angle model
图 12 不同输入条件效率特性对比
Figure 12. Comparison of efficiency characteristics at different input conditions
图 13 不同输入条件膨胀比特性对比
Figure 13. Comparison of expansion ratio characteristics at different input conditions
图 14 定转速下不同输入方法误差比较
Figure 14. Error comparison of different input methods at constant speed
图 18 变转速预测模型综合评价结果
Figure 18. Comprehensive evaluation results of variable speed prediction model
表 1 模型评价指标
Table 1. Model evaluation indices
误差指标 量符号 计算公式 决定系数（R2） $ {X_1} $ $ {R^2} = 1 - \frac{{{{\displaystyle\sum\limits_0^{n - 1} { （{y_i} - {{\hat y}_i}） ^2} }}}}{{\displaystyle\sum\limits_0^{n - 1} {{{ （{y_i} - {{\bar y}_i}） ^2}}} }}\quad {\bar y_i} = \dfrac{1}{n}\displaystyle\sum\limits_0^{n - 1} {{y_i}} $ 解释方差（EVS） $ {X_2} $ $1 - \dfrac{{{\text{Var}} （ {{y_i} - {{\hat y}_i}} ） }}{{{\text{Var}} （ {{y_i}} ） }}$ 平均绝对误差（MAE） $ {X_3} $ $ \dfrac{1}{n}\displaystyle\sum\limits_0^{n - 1} {|{y_i} - } {\hat y_i}| $ 均方误差（MSE） $ {X_4} $ $ \dfrac{1}{n}\displaystyle\sum\limits_0^{n - 1} { （{y_i} - } {\hat y_i}{） ^2} $ 平均相对误差（MRE） $ {X_5} $ $ \dfrac{1}{n}\displaystyle\sum\limits_0^{n - 1} {\frac{{|{y_i} - {{\hat y}_i}|}}{{|{y_i}|}}} $ 最大误差（ME） $ {X_6} $ $ \max （|{y_i} - {\hat y_i}|） $ 中位绝对误差（MEAE） $ {X_7} $ $ {\text{median}} （|{y_i} - {\text{median}} （y） |） $ 
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