Please wait a minute...
浙江大学学报(工学版)
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
 全文: PDF(1015 KB)   HTML
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
服务　　
把本文推荐给朋友
加入引用管理器
E-mail Alert
作者相关文章　　
隋昊
覃高峰
崔祥波
陆新江

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    或    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
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.
[1] 沈麒,赵琰,周晓炜,袁晓冉. 结合结构与梯度的图像哈希算法[J]. 浙江大学学报(工学版), 2020, 54(8): 1525-1533.
[2] 杨春宁, 方家为, 李春, 葛晖. 基于稳定性判据的高超声速复合控制方法[J]. 浙江大学学报(工学版), 2017, 51(2): 422-428.
[3] 李滔, 王士同. 增量式0阶TSK模糊分类器及鲁棒改进[J]. 浙江大学学报(工学版), 2017, 51(10): 1901-1911.
[4] 杨慧琳, 黄智刚, 刘久文, 杜元锋. 基于核模糊C均值指纹库管理的WIFI室内定位方法[J]. 浙江大学学报(工学版), 2016, 50(6): 1126-1133.
[5] 赵婵媛, 陆志强, 崔维伟. 考虑随机故障的流水线调度问题前摄优化方法[J]. 浙江大学学报(工学版), 2016, 50(4): 641-649.
[6] 朱光明, 蒋荣欣, 周凡, 田翔, 陈耀武. 带测量偏置估计的鲁棒卡尔曼滤波算法[J]. 浙江大学学报(工学版), 2015, 49(7): 1343-1349.
[7] 马腾, 赵兴忠, 高博青, 吴慧. 自由曲面形状和拓扑联合优化研究[J]. 浙江大学学报(工学版), 2015, 49(10): 1946-1951.
[8] 张成,李志安,高博青,董石麟. 基于H∞理论的网壳结构鲁棒性分析[J]. J4, 2013, 47(5): 818-823.
[9] 单艳玲, 高博青. 基于连续体拓扑优化的网壳结构鲁棒构型分析[J]. J4, 2013, 47(12): 2118-2124.
[10] 王秀君, 胡协和. 一种改进的单神经元PID控制策略[J]. J4, 2011, 45(8): 1498-1501.
[11] 段斌, 梁军, 费正顺, 杨敏, 胡斌. 基于GA-ANN的非线性半参数建模方法[J]. J4, 2011, 45(6): 977-983.
[12] 金良, 王维锐, 刘哲, 石浩然. 集成干扰观测器的BP-PID在炉温控制上的应用[J]. J4, 2011, 45(10): 1761-1765.
[13] 王晔, 刘山. 期望轨迹可变的非线性时变系统迭代学习控制[J]. J4, 2009, 43(5): 839-843.
[14] 蒋凯 陈杭 周怀阳 蒋春跃 叶树明. 非线性系统的梯度变分迭代自学习控制[J]. J4, 2008, 42(8): 1365-1369.
[15] 茅僰 应祖光 朱位秋. 不确定结构非线性随机最优控制的鲁棒性[J]. J4, 2008, 42(7): 1101-1105.