一种基于固定截距多元线性回归的涡轮叶片冷却效果经验公式推导方法

An Empirical Formula Derivation Method of Turbine Blade Cooling Effectiveness Based on Fixed Intercept Multiple Linear Regression

为综合考量三个常见因素(冷气与燃气流量比、温比及燃气雷诺数)对航空发动机涡轮叶片冷却性能的影响,推导并发展了一种新型的多元线性回归分析方法,即固定截距的多元线性回归分析方法。通过对试验数据分别采用三种回归分析方法(即单因素非线性回归分析、常规多元线性回归分析和固定截距多元线性回归分析)处理分析后对比发现,运用固定截距多元线性回归分析方法处理的结果中确定系数更高,残差平方和令人满意,可见该方法更适合于当前试验方法下的冷却效果试验数据经验公式的拟合。

To understand the influence of three common factors(flow ratio of cooling air and gas,temperature ratio,and gas Reynolds number)on the cooling performance of aero engine turbine blades,a new multiple linear regression analysis method with a fixed intercept was derived and introduced.By comparing the test data processed by different regression methods(single factor nonlinear regression,ordinary multiple linear regression,and fixed intercept multiple linear regression).It is found that the coefficient of determination is higher and the sum of residual square is satisfactory in the new method,and the method shall be more suitable for fitting the empirical formula of cooling effectiveness test.