非线性函数参数的线性化率定方法

非线性函数参数率定基本上都是以误差平方和目标函数为信息依据的,其过程通常包括误差平方和目标函数构建和一阶函数求导为零得其参数优值解这两步操作.本文通过研究发现以上两步操作给非线性函数参数增加了不相关的局部极优值,提出了非线性函数参数的线性化率定方法.该方法对非线性函数以参数为自变量求导,再通过导函数差分线性化,并对线性化的参数用误差平方和目标函数进行率定,然后逐步迫近非线性函数参数的最优值.本文在理论上证明了该方法的收敛性,检验了此方法的合理性、优点和效果,解决了非线性函数参数以误差平方和为目标函数增加不相关的局部极优值的理论性问题,而且该方法的实用性和效果都比较好.

The linearized calibration method of non-linear function parameter

Non-linear function parameter calibration is usually based on the objective function of minimum error square sum,which including the construction of objective function and the first-order derivation of objective function.Since the traditional non-linear parameter calibration will introduce unrelated local optimums,a new non-linear parameter linearized calibration method was proposed in the paper.The new method obtained non-linear function derivation of parameters first and then the linear difference of the derivation function.Afterwards,linearized parameters calibration was accomplished using minimum error square sum as objective function,through these steps gradually approximating the optimal value of non-linear parameters.This new method was proved to be convergent,reasonable and effective in theory,and improved non-related local optimums problems of traditional calibration method based on minimum error square sum objective function.