非线性混合回归演化算法研究

STUDY ON HYBRID EVOLUTIONARY NONLINEAR REGRESSION ALGORITHM

关键词:  液体推进剂火箭发动机  非线性方程  回归分析  计算数学

Key words:  Liguid propellant rocket engine  Nonlinear equation  Regression analysis computational mathematics

摘要:

基于最小二乘法的常规非线性回归算法的缺点，提出了方程结构与系数的混合回归演化策略方法。在指定最大回归项数的前提下，该混合回归演化策略先找到一些基本满足拟合要求（回归项数与精度）的初始种子回归方程，再以回归项数逐步减少、拟合精度逐步提高为准则，对初始种子回归方程进一步混合回归演化，最后得到回归项数最少、拟合精度最高的最佳回归方程。此外，利用该混合回归演化策略对液体火箭发动机常见的几个经验关系式进行了非线性回归拟合实例分析，拟合残差分布表明该混合回归演化策略方法是有效的。

Abstract:

Due to the shortcomings of conventional regression algorithm based on MQE(mean squared error)that can not be easily overcomed,a hybrid evolutionary regression algorithm to this problem presented and the structure and coefficients of the nonlinear regression equations can be regressed with this algorithm simultaneously By setting the maximal number limit of nonlinear items for the regression equation,this hybrid algorithm is firstly used to obtain some initial seeded regression equations,which basically meet the requirements on the regression accuracy and the number limit of nonlinear items,then these initial seeded equations can be simplified and optimized progressively through Evolution Strategies to form a parsimonious nonlinear regression equation,this simplification and optimization process is under the supervision of a criterion:to minimize the residual and the number of nonlinear items.Different cross over and mutation operators are specially designed for the Evolution Strategies to make the hybrid nonlinear regression of structure and coefficients possible and efficient In addition,several kinds of statistieal nonlinear relationship in liquid rocket engine are regressed based on experimental data samples,the residual distributions show that this hybrid evolutionary nonlinear regression algorithm is effective and pragmatic.