A new methodology of nonlinear parameter approximation used for rheological model of drilling fluids

This paper proposes an effective way of searching for initial value, which is based on Gauss-Newton iteration and combined with the common features of nonlinear rheological equation of drilling fluids. With this method, we can find a fine initial value, which can be applied to the parameter estimation of nonlinear rheological model of drilling fluids. This method overcomes the shortcomings of Gauss-Newton method which strongly depends on the initial value and the iteration may not be convergent in practical application and fully exerts the advantages of Gauss-Newton method which has smaller workload in each step and faster pace of convergence. Large quantities of measured drilling fluids examples show that the rheological parameters estimated by this method have a fine statistical characteristic, that is, fitting residual is nearly unbiased and variance is almost minimum. Besides, the fitting residual is smaller than the one of traditional linear regression and has excellent statistical properties.