Abstract: A new method for the non-linear least square estimation was proposed on the basis of the characteristics of Casson rheological formula.It is unnecessary to artificially give an initial iteration value.The iteration process of this method can converge steadily to a unique minimum point in the domain of parameter and can not fall into the trap of the minimum point.This method requires a little storage and can converge rapidly.This is a globally optimized algorithm and can derive a rheological parameter estimation,showing superior statistic features including near unbiasedness of fitting residual error and almost least variance.The calculation cases,using a large amount of practical drilling fluid dada,indicate that the new method has smaller fitting variance,more similar mean value and more superior statistical feature of fitting residual error than the linear regression.This method can be used to determine the rheological parameter in Casson model of drilling fluid,optimize rheological model,adjust and evaluate the performance of drilling fluid.

Key words: drilling fluid, Casson rheological model, rheological parameter, fitting residual error, non-linear least square estimation method

摘要： 针对卡森流变方程的特点,提出了一种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,迭代过程稳定的收敛到参数允许区域中的唯一最小点,不会陷入极小点陷阱,存储需求量小,收敛速度快.新算法是一个全局优化算法,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为最小的特征.利用实际钻井液数据计算的实例表明,新方法具有比线性回归方法更小的拟合方差、相近的均值及优良的拟合残差统计特性.该方法可以应用到钻井液卡森流变模式流变参数的确定、钻井液流变模式优选及钻井液性能调整和评价等方面.

关键词: 钻井液, 卡森流变模式, 流变参数, 拟合方差, 非线性最小二乘估计算法