基于灵敏度的条件目标函数构建方法研究

Construction of weighed objective functions based on sensitivity analysis

分析了非线性模型参数率定研究的现状与存在的问题,剖析了以误差平方和为基础的目标函数特点与不足,定义了模型参数灵敏度、目标函数参数灵敏度和样本信息量概念,证明了样本信息量与模型参数灵敏度间关系的存在并导出了其函数关系,通过模型参数灵敏度与样本信息量的因果合理性分析设计了模型参数灵敏度的B条件,提出了基于模型参数灵敏度的条件目标函数构建思想和定义于模型参数灵敏度B条件域的目标函数式,从多方分析论证了基于灵敏度的条件目标函数比较传统目标函数的优点,以线性模型为例初步证明了基于灵敏度的条件目标函数在灵敏度上的提高和参数间关联度的降低,研究了模型参数灵敏度与自变量间的相关性对构建灵敏度条件域的作用,为非线性模型局部优值问题的解决找到了一种途径。最后初步尝试将其运用到理想模型的参数率定中,取得了一定成果。

This paper analyzes the state-of-the-art and problems in calibration of nonlinear models,and points out the features and shortages of the traditional objective functions.Then we develop a concept of sensitivity in model parameters,objective functions and samples,and proves a relationship of parameter sensitivity versus information content of sample.Based on these sensitivity concepts,weighed objective functions are introduced and compared with the traditional ones,and a linear model is used as an example to test the advantages of these new functions.Application to calibration of an ideal model shows reasonable results and effectiveness of this method.