钻井液流变参数的非线性最小二乘估计算法

A new method of non-linear least square estimation of rheological parameter for drilling fluid

摘要:

钻井液流变模式的参数估计问题大多使用线性回归方法进行求解，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。针对三种非线性流变方程(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。

关键词:钻井液;流变方程;参数估计;线性回归;非线性回归

Abstract:

The estimation problem of rheological parameter for drilling fluid usually requires the linear regression method to get the solution. However, it changes the statistic feature of measurement error, resulting that the derived rheological parameter estimation has no unbiasedness and the least variance. A new method of non-linear least square estimation is proposed in according to the characteristics of three none-linear rheological equations. It is unnecessary to artificially give an initial iteration value. The iteration process can converge steadily to a unique minimum point, and can not fall into the minimum point trap. The method requires little storage and converges rapidly. This is a algorithm which can derive a rheological parameter estimation that shows superior statistic features of near unbiasedness of fitting residual error and almost least variance. A large amount of practical drilling fluid cases indicate that, the new method has smaller fitting variance, similar mean, and more superior statistical feature of fitting residual error than linear regression.

Key words:drilling fluid; rheological equation; parameter estimation; linear regression; non-linear regression