改进的RSA方法在参数全局灵敏度分析中的应用

灵敏度分析是模型参数识别的重要方法.参照一维情形,采用统计分布特征值,对传统意义上的参数灵敏度分析进行了扩展,将参数灵敏度定义从一维扩展到多维,为在多维情形下分析参数的灵敏度提供思路.RSA方法是全局灵敏度分析的重要方法,但其对参数的二元划分具有一定的局限性,因此对其进行一定的改进:①将RSA方法对参数集的二元划分扩展为多元划分.②分析对象不局限于对模型参数值的分布,也包括模型目标函数的分布,即研究在函数各取值区间,参数的分布是否具有明显的变化;研究在参数各取值区间,函数的响应是否具有明显的变化.以,n=2的Rosenbrock函数作测试函数,对改进的RSA方法进行了检验.以模型参数为基础的分析结果和以模型目标函数为基础的分析结果均表明,模型的2个参数的全局灵敏度都非常高,二者的分析结论一致.

Application of Improved RSA Method in the Global Sensitivity Analysis of Model Parameters

The sensitivity analysis is an important method for parameter identification. By reference to the one-dimension case, the traditional sensitivity analysis is extended to multi-dimension with the statistical theory, which may bea solution to sensitivity analysis under multi-dimension condition. RSA is an important method for global sensitivity analysis, but it is necessary to be improved because of its limitation of dual categorization of the parameter values. Thetraditional RSA method can be improved from two aspects. Firstly, the dual categorization of the parameter values is extended to multi-categorization. Secondly,the analysis object is not limited to the parameter values, the object function can also be used for sensitivity analysis. That is, it is studied that whether the object function has distinct change within the parameter intervals and whetherthe parameters have distinct change within the object function intervals. Taking the classical Rosenbrock function (n2) as an example, the improved RSA method is tested. It shows that both the results based on the object function and theresults on the parameters are highly sensitive, so these two conclusions are consistent.