基于混合矩的多输出模型确认指标研究

针对随机不确定性条件下多输出计算模型与物理实验数据之间一致性难以量化度量这一问题,本文提出一组新的基于混合矩的多输出模型确认指标。在不确定情况下,同时考虑到多维输出之间的相关关系和单输出的均值,构建了由多输出数学期望列阵和协方差矩阵组成的多输出模型确认局部混合矩指标和全局混合矩指标。其中局部混合矩指标包括绝对指标(LA-3M)和相对指标(LR-3M),它们适合固定位置的多输出局部模型确认；全局混合矩指标也包括绝对指标(GA-3M)和相对指标(GR-3M),它们适合多点位置的多输出全局模型确认。通过数字算例和工程算例,并与PIT和t-pooling 面积指标进行对比,结果表明本文所提指标可行有效,能够方便地度量计算模型和物理实验之间的差异程度。

Mixed moment based validation metric for modelswith multivariate output

In order to provide a quantitative measure that characterizes the agreement between multiple output calculation models and experimental observations,a new set of mixed moment based validation metrics for models is proposed in this paper. Considering both uncertainties among multiple responses from model and physical observations, the mathematical expectation of single dimensional variable and covariance matric of multi-dimensional variables are introduced to the validation metrics for models. Two new metrics LA-3M and LR-3M are proposed for validating multi-responses at a single validation site. The other two new metrics are GA-3M and GR-3M which assess the global agreement according to collecting data of multiple responses observed at multiple validation sites. These metrics are examined and compared with the PIT area metric and the t-pooling metric respectively through a numerical test case and an engineering example to illustrate their feasibility and effectiveness, and they can easily measure the difference between multiple responses obtained from the simulation results and that obtained from experimental measurements.