逼近误差的范数最小化的区间模糊模型建模

doi:10.16182/j.issn1004731x.joss.201803054

系统仿真学报 ›› 2018, Vol. 30 ›› Issue (3): 1203-1209.doi: 10.16182/j.issn1004731x.joss.201803054

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逼近误差的范数最小化的区间模糊模型建模

刘小雍, 熊中刚, 阎昌国

遵义师范学院工学院,贵州遵义 563002

收稿日期:2016-02-29 出版日期:2018-03-08 发布日期:2019-01-02
作者简介:刘小雍(1982-),男,贵州遵义,博士,讲师,研究方向为机器学习与故障检测。
基金资助:
遵义师范学院博士基金(遵师BS(2015)04号),贵州省教育厅项目(黔教合KY字[2015]457号,黔教合KY字[2016]254),省科技厅项目(黔科合LH字[2015]7054号)

Interval Fuzzy Modeling Based on Minimizing-norm on Approximation Error

Liu Xiaoyong, Xiong Zhonggang, Yan Changguo

College of engineering and technology, Zunyi Normal College, Zunyi 563002, China

Received:2016-02-29 Online:2018-03-08 Published:2019-01-02

摘要/Abstract

摘要： 实际应用中所获取到的数据往往呈现出不确定性或不准确性,传统的确定性建模方法很难对这一类型的数据进行描述。通过将线性规划与TS模糊模型相结合,应用逼近误差的范数最小化原理,研究了基于TS模糊模型的区间建模方法,其中区间模型分别由上界和下界TS模型构成。为了求解上、下界TS模型,基于逼近误差的范数最小化被用于建立各自的优化问题,将其转化为标准的线性规划对其求解得到区间模糊模型。提出的方法较好地解决了传统方法建模带有不确定性数据的非线性系统时得到的是确定性模型问题,不能很好的描述不确定或不准确的数据。论证了该方法具有较好的鲁棒性。

关键词: 逼近误差的范数, 区间模糊模型, 线性规划, TS模糊模型

Abstract: As the obtained data in many practical applications tend to be uncertain or inaccurate, conventional modeling methods characterized by deterministic model for this type of data have become undesirable. Taking linear programming and TS fuzzy model and some ideas from norm minimization into consideration, a novel method identifying interval fuzzy model (INFUMO) consisting of upper and lower TS fuzzy model (referred to as f_U and f_L) has been studied. In order to solve INFUMO, optimization problems based on minimizing-norm with respect to approximation error corresponding to f_U and f_L are constructed. Finally, optimization problems are solved by linear programming and INFUMO is thus constructed. The proposed method not only can deal with the problem that the conventional modeling method of uncertain data usually results in deterministic model, but also has better robustness.

Key words: norm on approximation error, INFUMO, linear programming, TS fuzzy model

中图分类号:

TP391.9

刘小雍, 熊中刚, 阎昌国. 逼近误差的范数最小化的区间模糊模型建模[J]. 系统仿真学报, 2018, 30(3): 1203-1209.

Liu Xiaoyong, Xiong Zhonggang, Yan Changguo. Interval Fuzzy Modeling Based on Minimizing-norm on Approximation Error[J]. Journal of System Simulation, 2018, 30(3): 1203-1209.

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逼近误差的范数最小化的区间模糊模型建模

Interval Fuzzy Modeling Based on Minimizing-norm on Approximation Error

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