-
摘要: 针对具有不确定性非线性系统的机理模型难以建立的问题，提出了基于模糊灰色认知网络（Fuzzy grey cognitive networks，FGCN）的非线性系统建模方法.该方法将模糊认知网络和灰色系统理论相结合，把模糊认知网络的节点状态值和权值扩展为灰色区间，引入灰度来评判可靠性.采用一种带终端约束的非线性Hebbian学习算法（Nonlinear hebbian learning，NHL）辨识FGCN的模型参数，引入了与FGCN模型中节点的系统实际测量值对应的灰数值，在更新机制中增加了包含系统测量值与预测值之差的修正项，对权值进行有监督的修正.利用水箱控制系统进行的仿真实验结果表明，本文提出的建模方法能解决对数据存在不确定性或缺失的复杂系统建模的难题，所建的模型能做出接近人类智能的控制决策，所采用的权值学习方法具有收敛速度快、学习结果精准等优点，并克服了传统非线性Hebbian算法对初始值依赖性强的缺点，对不确定性系统的建模具有广泛适用性.
-
关键词:
- 模糊认知网络 /
- 灰色系统理论 /
- Hebbian学习算法 /
- 终端约束
Abstract: For nonlinear systems with uncertainty, a method of nonlinear system modeling based on fuzzy grey cognitive networks (FGCN) is proposed. By combining fuzzy cognitive networks modeling method and grey system theory, the state value of fuzzy cognitive networks (FCN) node is extended to grey interval. The concept of grey level is introduced to judge the accuracy of the results. This method has the advantages of fuzzy cognitive networks graphical representation and the features of grey system theory that are effective and reliable in the scene of small data, poor information. Moreover, nonlinear Hebbian learning (NHL) with terminal constraint is adopted to identify the system parameters. In the process of weights learning, the algorithm introduces the actual value of the node in the system and increases the difference between measured values and predicted values to amend the weights on the basis of the original update mechanism, then the final value iteration formula is obtained after normalization. The proposed modeling method and the weight learning method are verified in the water tank control system. The algorithm has the advantages of fast convergence rate and accurate study results, and overcomes the traditional shortcoming of nonlinear Hebbian learning, i.e., strong dependence of initial value. Simulation results illustrate the applicability of the FGCN and the algorithm to model uncertain systems.1) 本文责任编委 刘艳军 -
图 1 基于FGCN带终端约束的非线性Hebbian算法流程图
Fig. 1 Flowchart of NHL with terminal constraints based on FGCN
图 5 带终端约束的NHL学习的FGCN仿真结果
Fig. 5 FGCN simulation results trained by NHL with terminal constraints
表 1 NHL算法学习的仿真结果
Table 1 Simulation results trained by NHL
概念节点 FGCN模型(灰度为零) FGCN模型(灰度不为零) 灰色稳态值$\otimes{{\mathit{\boldsymbol A}}}_i$ 灰度$ \varphi ( \otimes{{\mathit{\boldsymbol A}}}_i )$ 白化值$\hat A_i$ 灰色稳态值$\otimes{{\mathit{\boldsymbol A}}}_i$ 灰度$ \varphi ( \otimes{{\mathit{\boldsymbol A}}}_i )$ 白化值$\hat A_i$ 1 [0.728, 0.728] 0 0.728 [0.7279, 0.7280] 0.0001 0.72795 2 [0.6663, 0.6663] 0 0.6663 [0.6662, 0.6663] 0.0001 0.66625 3 [0.7523, 0.7523] 0 0.7523 [0.7522, 0.7523] 0.0001 0.75225 4 [0.6608, 0.6608] 0 0.6608 [0.6608, 0.6609] 0.0001 0.66085 5 [0.799, 0.799] 0 0.799 [0.7989, 0.7991] 0.0002 0.799 6 [0.835, 0.835] 0 0.835 [0.8349, 0.8351] 0.0002 0.835 7 [0.7826, 0.7826] 0 0.7826 [0.7826. 0.7827] 0.0001 0.75265 8 [0.6399, 0.6399] 0 0.6399 [0.6397, 0.6399] 0.0002 0.6398 
下载: 导出CSV
表 2 带终端约束非线性Hebbian算法学习仿真结果
Table 2 Simulation results trained by NHL with terminal constraints
概念节点 FGCN模型(灰度为零) FGCN模型(灰度不为零) 灰色稳态值$\otimes{{\mathit{\boldsymbol A}}}_i$ 灰度$ \varphi ( \otimes{{\mathit{\boldsymbol A}}}_i )$ 白化值$\hat A_i$ 灰色稳态值$\otimes{{\mathit{\boldsymbol A}}}_i$ 灰度$ \varphi ( \otimes{{\mathit{\boldsymbol A}}}_i )$ 白化值$\hat A_i$ 1 [0.73, 0.73] 0 0.73 [0.7300, 0.7301] 0 0.73005 2 [0.67, 0.67] 0 0.67 [0.6700, 0.6701] 0.0001 0.67005 3 [0.75, 0.75] 0 0.75 [0.7500, 0.7500] 0.0001 0.75005 4 [0.66, 0.66] 0 0.66 [0.6599, 0.6600] 0.0001 0.65995 5 [0.80, 0.80] 0 0.8 [0.8000, 0.8001] 0.0001 0.80005 6 [0.8304, 0.8304] 0 0.8304 [0.8304, 0.8305] 0.0001 0.83045 7 [0.7799, 0.7799] 0 0.7799 [0.7798, 0.7799] 0.0001 0.77985 8 [0.6290, 0.6290] 0 0.629 [0.6290, 0.6291] 0.0001 0.62905
下载: 导出CSV
-
[1] Maffi T, Sommariva S, Ranzi E, Faravelli T. A predictive kinetic model of sulfur release from coal. Fuel, 2012, 91(1):213-223 doi: 10.1016/j.fuel.2011.08.017 [2] Kosko B. Fuzzy cognitive maps. International Journal of Man-Machine Studies, 1986, 24(1):65-75 doi: 10.1016/S0020-7373(86)80040-2 [3] Abe S. Neural networks and fuzzy systems. Journal of the Acoustical Society of America, 1998, 103(6):49-71 http://cn.bing.com/academic/profile?id=e80ce6127b4eabe34504df8cbd762fc2&encoded=0&v=paper_preview&mkt=zh-cn [4] Stylios C D, Groumpos P P. Fuzzy cognitive maps: a soft computing technique for intelligent control. In: Proceedings of the 2000 IEEE International Symposium on Intelligent Control. Rio Patras, Greece: IEEE, 2000. 97-102 https://ieeexplore.ieee.org/document/882906/ [5] Papageorgiou E I, Aggelopoulou K D, Gemtos T A, Nanos G D. Yield prediction in apples using Fuzzy Cognitive Map learning approach. Computers & Electronics in Agriculture, 2013, 91(2):19-29 http://cn.bing.com/academic/profile?id=ec1ab0dcd05b08cd918133540df03b06&encoded=0&v=paper_preview&mkt=zh-cn [6] Antigoni P, Anninou, Groumpos P P. Modeling of parkinson's disease using fuzzy cognitive maps and non-linear hebbian learning. International Journal on Artificial Intelligence Tools, 2014, 23(5):17. http://cn.bing.com/academic/profile?id=3fd5f3cc7cdc99f485868e2febdcc872&encoded=0&v=paper_preview&mkt=zh-cn [7] Fatahi S, Moradi H. A fuzzy cognitive map model to calculate a user's desirability based on personality in e-learning environments. Computers in Human Behavior, 2016, 63:272-281. doi: 10.1016/j.chb.2016.05.041 [8] Kreinovich V, Stylios C D. Why fuzzy cognitive maps are efficient. International Journal of Computers Communications & Control, 2015, 10(6):825-833 http://cn.bing.com/academic/profile?id=729e7f2c3a861f633d0ca9dee7c01db3&encoded=0&v=paper_preview&mkt=zh-cn [9] Obiedat M, Samarasinghe S. A novel semi-quantitative Fuzzy Cognitive Map model for complex systems for addressing challenging participatory real life problems. Applied Soft Computing, 2016, 48:91-110 doi: 10.1016/j.asoc.2016.06.001 [10] Christen B, Kjeldsen C, Dalgaard T, Martin-Ortega J. Can fuzzy cognitive mapping help in agricultural policy design and communication? Land Use Policy, 2015, 45:64-75 doi: 10.1016/j.landusepol.2015.01.001 [11] 张燕丽. 基于模糊认知图的动态系统的建模与控制[博士学位论文], 大连理工大学, 中国, 2012 http://cdmd.cnki.com.cn/Article/CDMD-10141-1012393394.htmZhang Yan-Li. The Modeling and Control of Dynamic System Based on Fuzzy Cognitive Maps[Ph. D. dissertation], Dalian University of Technology, China, 2012 http://cdmd.cnki.com.cn/Article/CDMD-10141-1012393394.htm [12] Kottas T, Stimoniaris D, Tsiamitros D, Kikis V, Boutalis Y, Dialynas E. New operation scheme and control of Smart Grids using Fuzzy Cognitive Networks. In: Proceedings of the 2015 IEEE Eindhoven on PowerTech. Eindhoven, Netherlands: IEEE, 2015. 1-5 https://ieeexplore.ieee.org/document/7232563/ [13] Zhang J Y, Liu Z Q, Zhou S. Dynamic domination in fuzzy causal networks. IEEE Transactions on Fuzzy Systems, 2006, 14(1):42-57 doi: 10.1109/TFUZZ.2005.861606 [14] Liu Z Q, Zhang J Y. Interrogating the structure of fuzzy cognitive maps. Soft Computing, 2003, 7(3):148-153 doi: 10.1007/s00500-002-0202-x [15] Kottas T L, Boutalis Y S, Christodoulou M A. Fuzzy cognitive network:a general framework. Intelligent Decision Technologies, 2007, 1(4):183-196 doi: 10.3233/IDT-2007-1402 [16] 吉培荣, 黄巍松, 胡翔勇.无偏灰色预测模型.系统工程与电子技术, 2000, 22(6):78-80 http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=Y329621Ji Pei-Rong, Huang Wei-Song, Hu Xiang-Yong. Unbiased gray prediction model. Systems Engineering and Electronic, 2000, 22(6):78-80 http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=Y329621 [17] 吉培荣, 黄巍松, 胡翔勇.灰色预测模型特性的研究.系统工程理论与实践, 2001, (9):105-108 http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=Y329621Ji Pei-Rong, Huang Wei-Song, Hu Xiang-Yong. A Study on the properties of grey forecasting model. System Engineering Theory and Practice, 2001, (9):105-108 http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=Y329621 [18] Wu W Y, Chen S P. A prediction method using the grey model GMC(1, n) combined with the grey relational analysis:a case study on Internet access population forecast. Applied Mathematics and Computation, 2005, 169(1):198-217 doi: 10.1016/j.amc.2004.10.087 [19] Lian R J, Lin B F, Huang J H. A grey prediction fuzzy controller for constant cutting force in turning. International Journal of Machine Tool & Manufacture, 2005, 45(9):1047-1056 http://cn.bing.com/academic/profile?id=56bd0cfd79ed870e6229b9b9e7096033&encoded=0&v=paper_preview&mkt=zh-cn [20] Dickerson J A, Kosko B. Virtual worlds as fuzzy cognitive maps. Presence:Teleoperators and Virtual Environments, 1994:3(2):173-189 doi: 10.1162/pres.1994.3.2.173 [21] Papageorgiou E, Stylios C, Groumpos P. Fuzzy cognitive map learning based on nonlinear hebbian rule. In: Proceedings of the 2003 Australian Conference on Artificial Intelligence. Berlin, Germany: Springer 2003. 256-268 [22] Wu K, Liu J. Robust learning of large-scale fuzzy cognitive maps via the lasso from noisy time series. Knowledge-Based Systems, 2016, 113:23-38 doi: 10.1016/j.knosys.2016.09.010 [23] Natarajan R, Subramanian J, Papageorgiou E I. Hybrid learning of fuzzy cognitive maps for sugarcane yield classification. Computers & Electronics in Agriculture, 2016, 127:147-157 http://cn.bing.com/academic/profile?id=1bef7e064e95ea52374b4b864081bd96&encoded=0&v=paper_preview&mkt=zh-cn [24] Baykasoglu A, Durmusoglu Z D U, Kaplanoglu V. Training fuzzy cognitive maps via extended great deluge algorithm with applications. Computers in Industry, 2011, 62(2):187-195 doi: 10.1016/j.compind.2010.10.011 -
图(5) / 表(2)
计量
- 文章访问数: 2270
- HTML全文浏览量: 269
- PDF下载量: 773
- 被引次数: 0
