考虑模糊不确定性情况的模型确认指标方法

doi:10.12305/j.issn.1001-506X.2026.10.18

摘要/Abstract

摘要：

针对实际工程中存在的模糊不确定性情况下的模型确认问题，提出一种新的模型确认指标，以量化考虑模糊不确定性情况的计算仿真模型与实验测量结果的差异性程度。该方法首先基于模糊不确定性的数学性质，引入服从标准均匀分布的随机变量，将隶属水平视为标准均匀分布空间对应的累积分布值，从而实现模糊不确定性隶属函数向随机变量累积分布函数的转换；然后，将实验测量数据转化到标准均匀分布空间中，从而获得经验累积分布函数；最后，定义计算仿真模型对应的累积分布函数与实验测量结果的经验累积分布函数之间的面积差为模糊不确定性模型确认指标。数值算例和工程算例的结果表明，所提指标能够有效处理单确认点和多确认点的模型确认问题，验证了该指标的正确性和工程适用性。

关键词: 模糊不确定性, 模型确认, 计算仿真模型, 隶属函数, 确认指标

Abstract:

For the model validation under fuzzy uncertainties in practical engineering, a novel model validation metric is proposed to quantify the degree of consistency between the computational simulation model and experimental measurements considering the fuzzy uncertainty. Based on the mathematical properties of fuzzy uncertainty, the method firstly introduces a random variable following the standard uniform distribution and interprets the membership level as the corresponding cumulative distribution value in the standard uniform space, thereby transforming fuzzy membership function into the cumulative distribution function of this random variable. Experimental measurement data are then mapped into the standard uniform space to obtain an empirical cumulative distribution function. Finally, the area difference between the cumulative distribution function corresponding to the computational simulation model and the empirical cumulative distribution function of the experimental measurements is defined as the fuzzy uncertainty model validation metric. Numerical examples and engineering case studies demonstrate that the proposed metric effectively handles model validation at both single and multiple validation points, confirming its correctness and practical applicability.

Key words: fuzzy uncertainty, model validation, computational simulation model, membership function, validation metric

中图分类号:

V241
O235

李贵杰, 朱苗苗, 秦强. 考虑模糊不确定性情况的模型确认指标方法[J]. 系统工程与电子技术, 2026, 48(10): 3460-3472.

Guijie Li, Miaomiao Zhu, Qiang Qin. Model validation metric method considering fuzzy uncertainty[J]. Systems Engineering and Electronics, 2026, 48(10): 3460-3472.

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测试场景	模型编号	模型形式	模型描述
测试1	模型1	$ y_{1}^{{m}_{1}}(x)=y_{}^{e}(x,{\theta }^{1}=1.5) $	与实验输出完全相同
测试1	模型2	$ y_{2}^{{m}_{2}}(x)=y_{}^{e}(x,{\theta }^{2}=1.2) $	模型参数不正确
测试2	模型3	$ y_{3}^{{m}_{3}}(x)=y_{}^{e}(x,{\theta }^{3}\sim (1.48,1.5,1.52)) $	模型参数中心值准确，不确定性小
测试2	模型4	$ y_{4}^{{m}_{4}}(x)=y_{}^{e}(x,{\theta }^{4}\sim (1.46,1.5,1.54)) $	模型参数中心值准确，不确定性大

指标	模型1	模型2
模糊不确定性确认指标	0.012	0.307
U-pooling指标	0.041	0.471

指标	模型1	模型2
模糊不确定性确认指标	0.002	0.482
U-pooling指标	0.003	0.083

指标/模型	模型3	模型4
模糊不确定性确认指标	0.113	0.235
U-pooling指标	0.048	0.117

指标	模型3	模型4
模糊不确定性确认指标	0.032	0.061
U-pooling指标	0.039	0.080