轴流泵装置调速性能的非线性回归模型研究

Nonlinear Regression Model of Speed-governing Performance of Axial Flow Pump Device

利用理论推导和试验数据相结合的方法,通过多元非线性回归分析得出轴流泵装置调速性能模型。根据水泵基本方程,结合假定条件推导出轴流泵装置扬程、效率关于转速、流量的特性方程。利用高精度水力机械试验台分别对2种不同类型的轴流泵装置试验测试,分析得出效率和扬程特性曲线随转速变化呈非线性变化的结论。利用试验数据作为观测值,特性方程作为预测模型,利用nlinfit函数和遗传算法相结合的多元非线性回归算法计算得出特性方程的待定系数。对2个算法的分析比较发现,单独利用多元非线性回归算法所求得的系数解趋于局部最优,而结合遗传算法后能得到全局最优解。将所求待定系数代入预测模型,分别将2种轴流泵装置的扬程、效率调速特性试验数据与预测值进行比较,得出:全流量范围内扬程误差绝对值在0~0.8 m之间,效率误差绝对值在0~8%之间;设计工况点附近扬程误差绝对值在0~0.5 m之间,效率误差绝对值在0~5%之间。

The model of speed-governing performance of axial flow pump device was deduced by combining theory with experimental data,and by using multiple nonlinear regression analysis method.The study of the model was aimed at a present situation that there was no speed-governing performance model with clear physical meaning. With this model,the study of speed control strategy can go further.Firstly,the characteristic equation of head,efficiency about speed and flow was deduced by the basic equation of water pump,combined with some assumptions. And then a conclusion that the efficiency and head characteristic curve was shown to be nonlinearly variable by the change of speed which was given by the test of two different types axial flow pump devices on the high-precision hydraulic machinery test bed.The undetermined coefficients of characteristic equation were concluded by multivariate nonlinear regression algorithm combined by ‘nlinfit＇function and genetic algorithm,using experimental data as the observation value,and using the characteristic equation as the predictive model. By comparing ‘nlinfit＇function with genetic algorithm,it was clear that the coefficient solution tended to locally optimum by using ‘nlinfit＇function only. And it tended to globally optimum by combining with genetic algorithm. By comparing the experimental data with prediction model,both of which are of two different types axial flow pump devices＇ speed-governing performance of head and efficiency,it showed that on the whole area,the head error between prediction model and measured value was 0 ～ 0. 8 m,and the efficiency error was 0 ～ 8%.On the area nearby the design point,the head error between prediction model and measured value was 0 ～0. 5 m,and the efficiency error was 0 ～ 5%.