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浙江大学学报(工学版)  2019, Vol. 53 Issue (2): 382-387    DOI: 10.3785/j.issn.1008-973X.2019.02.022
计算机与控制工程     
基于误差均值与方差最小化的鲁棒T-S模糊建模方法
隋昊(),覃高峰,崔祥波,陆新江*()
中南大学 机电工程学院 高性能复杂制造国家重点实验室,湖南 长沙 410083
Robust fuzzy T-S modeling method based on minimizing mean and variance of modeling error
Hao SUI(),Gao-feng QIN,Xiang-bo CUI,Xin-jiang LU*()
State Key Laboratory of High Performance Complex Manufacturing, School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China
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摘要:

传统T-S模糊建模方法在非线性系统建模方面已有大量的成功应用,但其现有的参数辨识方法没有考虑模型的结构风险项,因此模型的泛化性不强. 同时,尽管传统T-S模糊建模方法能够在高斯噪声下取得较好的辨识效果,但没有综合考虑误差的均值与方差项,导致在非高斯噪声或者异常值下辨识效果较差. 针对传统T-S模糊建模方法的这些不足,提出基于误差均值与方差最小化的鲁棒T-S模糊建模方法. 该方法通过构建全新的参数辨识目标函数,将结构风险项及误差的均值和方差最小化,从而提高T-S建模的泛化性和鲁棒性. 仿真与试验结果表明,在噪声干扰下,鲁棒T-S模糊建模方法能够对非线性系统进行有效建模,且建模效果优于传统T-S模糊建模方法.

关键词: T-S模糊建模结构风险泛化性鲁棒性非线性系统    
Abstract:

Traditional T-S fuzzy modeling method has been widely and successfully used to model nonlinear systems with noise. However, most of the existing parameters identification methods for T-S model do not consider structural risk item, which would lead to poor generalization. Although traditional T-S fuzzy modeling method could achieve good recognition effect under Gaussian noise, the identification effect under non-Gaussian noise or outliers is poor, because the mean and variance items of error are not comprehensively considered. The robust fuzzy T-S modeling method was proposed to overcome the weakness of the traditional modeling method. The new modeling method constructed a new objective function to identify the parameters. The new objective function not only considered structural risk, but also minimized the mean and variance of error, which would lead to better generalization and robustness. Simulation and experiment results showed that the new modeling method can effectively model the nonlinear system under the noise interference, and the modeling effect was superior to that of the traditional T-S fuzzy modeling method.

Key words: T-S fuzzy modeling method    structural risk    generalization    robustness    nonlinear system
收稿日期: 2018-01-24 出版日期: 2019-02-21
CLC:  TP 301  
通讯作者: 陆新江     E-mail: suihao@csu.edu.cn;luxj@csu.edu.cn
作者简介: 隋昊(1993—),男,硕士生,从事数据建模理论研究. orcid.org/0000-0002-2030-8315. E-mail: suihao@csu.edu.cn
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隋昊
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引用本文:

隋昊,覃高峰,崔祥波,陆新江. 基于误差均值与方差最小化的鲁棒T-S模糊建模方法[J]. 浙江大学学报(工学版), 2019, 53(2): 382-387.

Hao SUI,Gao-feng QIN,Xiang-bo CUI,Xin-jiang LU. Robust fuzzy T-S modeling method based on minimizing mean and variance of modeling error. Journal of ZheJiang University (Engineering Science), 2019, 53(2): 382-387.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2019.02.022        http://www.zjujournals.com/eng/CN/Y2019/V53/I2/382

图 1  鲁棒T-S模糊建模方法思想
图 2  鲁棒T-S模糊建模方法目标函数
图 3  鲁棒T-S模糊建模方法流程图
图 4  鲁棒T-S模糊建模方法对含异常值数学算例的建模结果
方法 R RMSE R-square
训练 测试 训练 测试
NFCRMA模型[11] 8 0.526 8 0.210 7 0.941 2 0.957 7
FCRSM模型[12] 8 0.513 6 0.194 5 0.943 0 0.960 5
WLS-SVM[16] ? 0.509 3 0.193 8 0.946 2 0.963 5
新方法 8 0.588 5 0.139 5 0.937 5 0.994 3
表 1  不同建模方法对数学算例拟合结果对比
图 5  液压缸试验台
名称 符号 数值 单位
运动部件质量 $M$ 109.5 kg
柱塞有效面积 $A$ 0.012 3 m2
粘性阻尼系数 $c$ 2.1×106 N/(m·s?1
最大静摩擦力 ${F_{\rm{s}}}$ 3.914 9×103 N
库仑摩擦力 ${F_{\rm{c}}}$ 3.473 2×103 N
临界Stribeck速度 ${v_{\rm{s}}}$ 0.001 02 m/s
粘滞摩擦系数 ${\sigma _2}$ 23 063 N/(m·s?1
表 2  液压缸试验台系统参数
图 6  液压系统主、从动缸体积流量训练及测试样本
图 7  鲁棒T-S模糊建模方法对含异常值液压系统的训练结果
图 8  鲁棒T-S模糊建模方法对液压系统的测试结果
方法 R RMSE R-square
训练 测试 训练 测试
NFCRMA模型[11] 10 0.0633 0.041 6 0.892 1 0.935 6
FCRSM模型[12] 10 0.0655 0.036 5 0.882 6 0.947 8
WLS-SVM[16] ? 0.0606 0.037 0 0.912 6 0.941 8
新方法 10 0.0671 0.031 2 0.876 4 0.980 3
表 3  不同模型对液压系统的训练和测试结果对比
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