基于Fibonacci法求幂律模式流变参数最优值

Seeking rheological parameter optimal solutions of power law model based on Fibonacci method

幂律模式属两参数流变模式,流变参数具有明确的物理意义,应用范围广泛,其值一般采用线性回归法计算,但在转换为线性方程过程中破坏了Gauss-Markov假定,所得参数估计值是近似解而非最优解,导致计算精度降低。针对幂律模式流变方程的特点,基于最小二乘法,通过数学变换,将流变参数估计过程转化为求解一元函数最小值问题。大量测试结果表明,该一元函数在求解区间是单峰函数。文中给出求解区间的上限和下限,并基于Fibonacci法求解。该算法稳定,无需设初始值,收敛速度快,易于计算机编程。经实例验证,所得流变参数估计值是最小二乘意义下的最优值。

The power law model is a two-parameter rheological model and its parameters have clear physical meaning and wide application range. The estimation of rheological parameter for drilling fluid usually resorts to the linear regression method. Due to the destruction of the Gauss-Markov assumptions in linear equation translation process, the result is usually approximate solution, instead of optimum solution, which reduces the computational accuracy. According to the characteristics of the power law rheological equation and based on the least squares method, a new algorithm is proposed about power law model rheologieal parameters estimation, and mainly, rheological parameters estimation is translated into one variable function minimum problem. The upper and lower bounds of the search interval are given. The test results, using a large amount of practical data, show that the one variable function is a unimodal function on the search range. Fibonacci method is proposed. The algorithm needs not to give an initial value artificially, the process is steady and the smaller storage space be needed with a rapid convergence and easy computer programing. Through example test, the rheological parameter estimation is the optimal estimation based on the least squares.