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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。
Based on the shortcoming of the conventional nonlinear regression algorithm based on the least square method, a hybrid regression evolution strategy method of the equation structure and the coefficient is proposed. Under the premise of specifying the maximum number of regressions, the hybrid regression evolutionary strategy first finds some initial seed regression equations that basically meet the fitting requirements (regression terms and precision), then gradually reduces the number of regression items and gradually increases the fitting accuracy to Criteria, the initial seed regression equation further mixed regression evolution, and finally get the least regression number, the best fitting accuracy of the best regression equation. In addition, several empirical empirical relationships of liquid rocket motors were simulated by using nonlinear regression. The fitting residuals distribution shows that the hybrid regression evolution strategy is effective.