考虑相关性的多元输出仿真模型验证方法

Multivariate Validation Method Under Correlation for Simulation Model

复杂仿真模型一般具有多个不同类型且带有相关性的输出,现有验证方法存在变量信息缺失、变量相关性度量不准确等问题.为此,提出基于变量选择和概率分布差异相结合的多变量仿真结果验证方法,考虑不确定性的影响,对选取到具有相关性的多个变量进行联合验证.首先,引入分形维数和互信息方法对多元异类输出进行相关性分析,提取相关变量子集.而后对相关变量子集中的各变量提取数据特征,进而计算各相关变量子集关于数据特征的联合概率分布,采用概率分布差异法度量仿真输出和参考输出联合概率分布的差异,并将其转化为一致性程度;在此基础上综合多个验证结果得到模型可信度.通过实例应用及对比实验,验证了方法的有效性.

Complex simulation models often generate the multivariate and different types of output, some problems such as the lacking variables information and the inaccuracy correlation measurement are involved in the existing validation methods. A novel validation method combining variables selection with area metric is proposed, the multiple outputs with correlation are selected for the associated validation under uncertainty. The fractal dimension and mutual information methods are primarily applied to analyze the correlation among multivariate and divise responses and extract the correlated variable subsets. Next, the interesting data characteristics of all variables are extracted in subset and the corresponding joint cumulative distribution function (JCDF) of each subset related to any characteristic is calculated. The area metric is used to measure the difference between the simulation and reference output JCDFs of multivariate characteristics in each subset, and the differences are transformed into the consistency degrees. Then the multiple validation results are integrated to obtain the model credibility. Finally, the method is validated through the application case and comparison experiments.