优化非线性回归目标函数的数值实验

Numerical tests for better objective function in non-linear data fitting

最小二乘法在化工中广泛用于数据拟合的线性和非线性回归及模型参数估值。为了从实验和生产现场数据中得到更接近真实函数的关联式,用数值实验的方法,对一系列目标函数形式与传统的最小二乘法进行比较。所测试的真实函数包括单调函数、单极值函数和双极值函数。数据所带的误差包括高斯分布和均匀分布的误差。结果表明,若数据误差遵从高斯分布时,以实验值与回归预测值间绝对偏差的1.5次幂之和为目标函数,优化所得的回归模型与真实的函数最接近。

The least square method is popularly used in linear and non-linear regressions for data fitting and estimating model parameters.To improve the efficiency,a series of objective function are proposed and compared with the traditional objective function of least squares.By numerical tests,it is found that the objective function of summing up the deviation raised to 1.5 power shows in overall the best performance in retrieving the true functional relationship underlying the raw data superimposed with random Gaussian error.