单因变量的偏最小二乘法在双曲递减中的应用

二元回归法是一种重要的求解油气产量双曲递减参数的方法，但在二元回归方程中，2个自变量的相关系数较大，存在严重的多重相关性，这样会使最小二乘法失效，得到的回归模型的拟合效果不好．为了较好地解决多重相关性问题，基于陈元千教授提出的二元回归方程，提出了用偏最小二乘法来求解递减参数．介绍了偏最小二乘法的基本原理、建模基本思想和交叉有效性判别法并讨论了该方法在双曲递减方程中的应用．实例表明偏最小二乘法解决了二元回归方程中的多重相关性问题，得到了较好的拟合效果．

Application of simple partial least squares regression to hyperbolic decline curve

Binary line regression is an important method to calculate Arps hyperbolic decline parameters,but in the regression function the relativity of two independent variables Q and Qt is high, which will bring about the problem of serious multicollinearity.Generally least-squares regression method can not deal with multicollinearity.To resolve this problem, Partial Least Squares(PLS)to obtain the decline parameters based on the binary line regression function proposed by Prof. Chen Yuanqian is adopted .The basic principle ,the basic modeling method and the cross validation of PLS regression are introduced and the application of simple PLSs regression to hyperbolic decline curve is discussd .It is shown that the PLS regression can be used to the binary line regression function of Arps hyperbolic decline to solve multicolnearity perfectly.