一类模糊模型的结构优化问题研究

Model Construction Optimization for A Class of Fuzzy Models

提出了将模糊模型统计信息准则 (FSIC)、基于奇异值分解 (SVD)的模糊模型结构分析、模糊规则删除与合并、参数估计等方法集成的模糊模型结构迭代优化 .研究表明 ,将 SVD引入到模糊模型结构分析、结合 FSIC指导模糊规则删除和合并 ,可从模型结构精简性、模型拟合和泛化性能等方面综合地确定最优模型结构 ;文中提出了实用可行的基于聚类加权组合和多重模糊聚类的规则合并算法 .该迭代优化方法已成功地应用于非线性函数逼近和航空煤油干点估计器的模糊模型构造 .仿真结果表明文中提出的方法简单实用 ,优化的模型结构比文献中给出的模型结构更加精简 .

One of the important issues in fuzzy model constructing requires finding a good trade-off between fitting the training data and keeping the model simple. This paper proposes a novel iterative approach for fuzzy model construction optimization or simplification, which includes fuzzy statistical information criteria (FSIC), fuzzy model structure analysis based on singular-value-decomposition and QR decomposition (SVD-QR), redundant or less important rule elimination, compatible rule merging and consequent parameter estimation. The redundant or less important rules are detected by the SVD-QR and the FSIC, and then eliminated. For the compatible rule merging, the weighted cluster combination algorithm and the multiple fuzzy clustering algorithm in the neighboring fuzzification sub-regions of the input space are developed respectively. The novel approach has been successfully applied to the construction of the fuzzy model for a nonlinear function approximator and the design of the fuzzy model for a product quality estimator of jet fuel oil in an oil refining plant. The simulation results show that the optimization approach of the fuzzy model structure is simple and feasible, and the resultant structures of the fuzzy models in this paper are more parsimonious than the structures of fuzzy models presented in the literatures.