钻井液流变参数的非线性最小二乘估计算法

钻井液流变模式的参数估计问题大多使用线性回归方法求解,然而,线性回归方法改变了测量误差的统计特征,使得所得到的流变参数估计不具有无偏性和方差最小等特点.针对3种非线性流变方程(幂律模式、赫巴模式和卡森模式)的特点,分别提出了非线性最小二乘估计的新算法.该算法不需要人工给定迭代初始值,迭代过程稳定收敛到最小点,不会陷入极小点陷阱,存储需求小,收敛速度很快,所得到的流变参数估计具有拟合残差近似无偏性和方差几乎最小的优良统计特征.大量的实际钻井液算例表明,新方法具有比线性回归方法更小的拟合方差,拟合残差统计特性优于线性回归方法.

A New Method of Non linear Least Square Estimation of Rheological Parameter for Drilling Fluid

The estimation problem of rheological parameter for drilling fluid usually resorts to the linear regression method to get the solution.As a result, the statistic feature of measurement error becomes different,and the derived rheological parameter estimation tends to be no unbiasedness and with the least variance.A new method of non linear least square estimation is proposed according to the characteristics of three non linear rheological equations.There is no need to give an initial iteration value artificially.The iteration process can converge steadily to a unique minimum point without falling into the minimum point trap.Little storage space is in need but with a rapid convergence.A rheological parameter estimation derived on the basis of the algorithm presents superior statistic features of near unbiasedness of fitting residual error and with almost the least variance.Lots of practical drilling fluid cases validate that the new method is of smaller fitting variance with the similar mean,and a superior statistical feature of fitting residual error over that of linear regression.