井眼轨道的软着陆设计模型的改进解法

Improved Solution to Design Model of Soft Landing in Borehole Trajectory

摘要:

井眼轨道的软着陆设计模型的求解可以归结为一个七元非线性方程组的求解问题。前人给出了数值迭代求解算法，然而并没有证明该迭代算法的收敛性，并且该算法是否收敛严重依赖于用户给出的迭代初始值。通过一系列的消元、化简的数学技巧，将七元非线性方程组化简为一元多项式方程，并在此基础上给出了软着陆设计模型的一个新算法。理论分析和实际算例表明，新算法的主要计算工作量是求多项式方程的非负实数根，其他未知数与实数根是简单的函数关系，计算量很小。新算法克服了迭代算法的初值依赖性以及迭代过程可能发散等缺陷，并且在设计模型有多个解的情况下，可以同时求出这些解。

Abstract:

The solution for design model of soft landing in borehole trajectory can come down to the solution with 7-element nonlinear equations. The algorithm convergence of known numerical iterative algorithm has not been proved, and the convergence of this iterative algorithm severely depends on initial iteration value from the user. 7-element nonlinear equations are simplified to be onevariable polynomial equation by element elimination and simplification; and based on which, a new algorithm for design model of soft landing was developed. Theoretical analysis and practical calculation examples show that the new algorithm is mainly for the calculation of nonnegative real roots of polynomial equation, and calculation of functional relationship between other unknown number and real root is very less. The new algorithm overcomes the dependence on the initial value and probable iterative process divergence, and can get the solutions at the same time when there are several design model solutions.