卡森模式流变参数非线性估计的改进算法  

An improved algorithm of nonlinear estimation for the Casson model rheological parameter

作　　者：闫吉曾[1] 罗懿[1] 邓红琳[1] 

机构地区：[1]中国石化华北分公司工程技术研究院,河南郑州450006

出　　处：《石油学报》2013年第1期184-187,共4页Acta Petrolei Sinica

基　　金：国家重大科技专项(2011ZX05045-03)资助

摘　　要：通常对卡森模式流变参数进行非线性估计的求解过程相当复杂,针对这一问题,提出了一种基于非线性回归的改进算法。该算法不仅将流变参数估计转化为求一元函数的最小值问题,而且还给出了目标函数搜索区间上界和下界的确定方法。通过大量实测数据对一元目标函数进行计算的结果显示,其为搜索区间上的单峰函数,可采用二分法、黄金分割法及Fibonacci法等一维搜索法求解。改进算法计算稳定,无须设初始值,收敛速度快,且易于计算机编程。经实例计算验证,该算法所得的流变参数是基于最小二乘意义下的最优估计。The nonlinear estimation of Casson model rheological parameters is usually a complex process. To solve this problem, an improved algorithm which is based on nonlinear regression is proposed. Then rheological parameters estimation algorithm is turned into seeking the minimization of one variable function and a method for determining the upper and lower bounds of the search interval is given. The test results based on a large amount of practical data showed that the object function is a unimodal function in the search interval, which can he solved with one-dimensional search method such as dichotomy, the golden section and Fibonacci meth- od. This algorithm has such advantages as calculation stability, no need to set initial values, fast convergence and easy for computer programming. Through example tests, the proposed rheological parameter estimation was proved to be the optimal estimation based on the least squares method.

关 键 词：卡森模式 流变参数 Fibonacci法 非线性估计 最小二乘法 

分 类 号：TE254.1[石油与天然气工程—油气井工程]