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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2019, Vol. 53 Issue (2): 382-387    DOI: 10.3785/j.issn.1008-973X.2019.02.022
Computer and Control Engineering     
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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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     
Received: 24 January 2018      Published: 21 February 2019
CLC:  TP 301  
Corresponding Authors: Xin-jiang LU     E-mail: suihao@csu.edu.cn;luxj@csu.edu.cn
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Hao SUI
Gao-feng QIN
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Xin-jiang LU
Cite this article:

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.

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


基于误差均值与方差最小化的鲁棒T-S模糊建模方法

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 
Fig.1 Idea of robust T-S fuzzy modeling method
Fig.2 Objective function of robust T-S fuzzy modeling method
Fig.3 Flow chart of robust T-S fuzzy modeling method
Fig.4 Modeling result of robust T-S fuzzy modeling method on mathematic case with outliers
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
Tab.1 Fitting results comparison of different modeling methods on mathematic case
Fig.5 Hydraulic experiment platform
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）
Tab.2 System parameters of hydraulic experiment platform
Fig.6 Training and test samples of hydraulic system master and slave cylinder flow
Fig.7 Training results of robust T-S fuzzy modeling method for hydraulic system with outliers
Fig.8 Test results of robust T-S fuzzy modeling method for hydraulic system
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
Tab.3 Comparison of training and testing results of different models on hydraulic system
[1]   LU X J, HUANG M H Two-level modeling based intelligent integration control for time-varying forging processes[J]. Industrial and Engineering Chemistry Research, 2015, 54 (21): 5690- 5696
[2]   马嘉跃, 高嵩, 黄姣茹, 等 一类非线性系统的扇区模糊建模方法[J]. 科学技术与工程, 2017, 17 (18): 84- 88
MA Jia-yue, GAO Song, HUANG Jiao-ru, et al Fuzzy modeling approach for a class of sector nonlinear system[J]. Science Technology and Engineering, 2017, 17 (18): 84- 88
doi: 10.3969/j.issn.1671-1815.2017.18.013
[3]   PáRAMO-CARRANZA L A, MEDA-CAMPA?A J A, DE JESúS RUBIO J, et al Discrete-time Kalman filter for Takagi-Sugeno fuzzy models[J]. Evolving Systems, 2017, 8 (3): 211- 219
doi: 10.1007/s12530-017-9181-0
[4]   LU X J, LI H X, DUAN J A, et al Integrated design and control under uncertainty: a fuzzy modeling approach[J]. Industrial and Engineering Chemistry Research, 2009, 49 (3): 1312- 1324
[5]   LAN J, PATTON R J Integrated design of fault-tolerant control for nonlinear systems based on fault estimation and T–S fuzzy modeling[J]. IEEE Transactions on Fuzzy Systems, 2017, 25 (5): 1141- 1154
doi: 10.1109/TFUZZ.2016.2598849
[6]   BOULKAIBET I, BELARBI K, BOUOUDEN S, et al A new TS fuzzy model predictive control for nonlinear processes[J]. Expert Systems with Applications, 2017, 88: 132- 151
doi: 10.1016/j.eswa.2017.06.039
[7]   SAMADI M F, SAIF M State-space modeling and observer design of Li-Ion batteries using Takagi-Sugeno fuzzy system[J]. IEEE Transactions on Control Systems Technology, 2017, 25 (1): 301- 308
doi: 10.1109/TCST.2016.2549270
[8]   PAL N R, SAHA S Simultaneous structure identification and fuzzy rule generation for Takagi-ugeno models[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2008, 38 (6): 1626- 1638
doi: 10.1109/TSMCB.2008.2006367
[9]   DOV?AN D, ?KRJANC I Recursive fuzzy c-means clustering for recursive fuzzy identification of time-varying processes[J]. ISA Transactions, 2011, 50 (2): 159- 169
doi: 10.1016/j.isatra.2011.01.004
[10]   SETNES M, BABUSKA R, VERBRUGGEN H B Rule-based modeling: precision and transparency[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 1998, 28 (1): 165- 169
doi: 10.1109/5326.661100
[11]   LI C, ZHOU J, XIANG X, et al T-S fuzzy model identification based on a novel fuzzy c-regression model clustering algorithm[J]. Engineering Applications of Artificial Intelligence, 2009, 22 (4): 646- 653
[12]   CHANG C W, TAO C W A novel approach to implement Takagi-Sugeno fuzzy models[J]. IEEE Transactions on Cybernetics, 2017, 47 (9): 2353- 2361
doi: 10.1109/TCYB.2017.2701900
[13]   DAM T, DEB A K A clustering algorithm based TS fuzzy model for tracking dynamical system data[J]. Journal of the Franklin Institute, 2017, 354 (13): 5617- 5645
doi: 10.1016/j.jfranklin.2017.06.014
[14]   TSAI S H, CHEN Y W A novel fuzzy identification method based on ant colony optimization algorithm[J]. IEEE Access, 2016, 4: 3747- 3756
doi: 10.1109/ACCESS.2016.2585670
[15]   李鹏程. 新的求解超大规模最小二乘问题的随机算法[D]. 西安: 西安电子科技大学, 2013.
LI Peng-cheng. New random algorithm for very large scale linear least-squares problems [D]. Xi’an: Xidian University, 2013.
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