基于混合评价指标的自组织模糊神经网络设计研究

doi:10.11949/j.issn.0438-1157.20190180

摘要/Abstract

摘要：

针对在无增长和修剪阈值时模糊神经网络结构难以自适应问题，提出一种基于混合评价指标(hybrid evaluation index, HEI)的结构设计方法。首先，通过模糊C均值聚类算法(fuzzy C-means clustering, FCM)确定初始规则层神经元数目及其中心与宽度。其次，基于戴维森堡丁指数(Davies bouldin index, DBI)和邓恩指数(Dunn index, DI)提出一种新的相关性评价指标(relevance evaluation index, REI)来计算规则层各神经元输出之间的相关性，同时根据训练过程中网络输出均方根误差(root mean square error， RMSE)的变化情况来确定网络的学习能力，然后基于REI和RMSE提出了HEI。通过HEI来调整模糊神经网络的拓扑结构，有效解决了在无增长和修剪阈值时网络结构难以动态自调整的问题且避免了网络结构冗余。最后，通过对Mackey-Glass时间序列预测、非线性系统辨识和大气中PM_2.5浓度预测，证明了该结构设计方法的可行性和有效性。

关键词: 自组织模糊神经网络, 混合评价指标, 优化设计, 动态建模, 预测

Abstract:

Aiming at the problem that the fuzzy neural network structure is difficult to adapt when there is no growth and pruning thresholds, this paper proposes a structure design method based on hybrid evaluation index (HEI). First, the initial number, centers and widths of rule neurons are determined by the fuzzy C-means clustering algorithm. Next, a novel relevance evaluation index (REI), which is composed of the Davies bouldin index (DBI) and the Dunn index (DI), is presented to calculate the correlation among the outputs of rule neurons. The learning ability of neural network will be determined by the change of root mean square error (RMSE) during the training process. Then, the HEI is presented based on REI and RMSE. The topology structure of the fuzzy neural network is adjusted according to the HEI. Finally, the feasibility and effectiveness of the structure design method are proved by using the Mackey-Glass time series prediction, nonlinear system identification and PM_2.5 concentration prediction.

Key words: self-organizing fuzzy neural network, hybrid evaluation index (HEI), optimal design, dynamic modeling, prediction

中图分类号:

TP 183

乔俊飞, 贺增增, 杜胜利. 基于混合评价指标的自组织模糊神经网络设计研究[J]. 化工学报, 2019, 70(7): 2606-2615.

Junfei QIAO, Zengzeng HE, Shengli DU. Design of self-organizing fuzzy neural network based on hybrid evaluation index[J]. CIESC Journal, 2019, 70(7): 2606-2615.

图/表 13

图1 模糊神经网络结构

Fig.1 Structure of fuzzy neural network

图2 Mackey-Glass时间预测测试结果

Fig.2 Testing results for Mackey-Glass time series prediction

图3 Mackey-Glass时间预测测试误差

Fig.3 Testing errors for Mackey-Glass time series prediction

图4 Mackey-Glass时间预测规则层神经元个数

Fig.4 Number of rule neurons for Mackey-Glass time series prediction

表1 Mackey-Glass时间序列预测中

Table 1 Performance comparisons of different methods for Mackey-Glass time series prediction

Method	Number of rule nurons	Testing RMSE	Training time/s
HEI-SOFNN	5	0.0093	10.71
SOFNN-AGA ^[17]	6	0.0119	21.20
GPFNN ^[34]	7	0.0107	27.33
NFN-FOESA^[16]	7	0.0132	168.35
FAOS-PFNN ^[9]	7	0.0201	27.33

图5 测试结果

Fig.5 Testing results

图6 非线性系统辨识测试误差

Fig.6 Testing errors for nonlinear system identification

图7 非线性系统辨识规则层神经元个数

Fig.7 Number of rule neurons for nonlinear system identification

表2 非线性系统辨识中不同方法的性能对比

Table 2 Performance comparisons of different methods for nonlinear system identification

Method	Number of rule nurons	Testing RMSE	Training time/s
HEI-SOFNN	5	0.0089	7.34
SOFNN-AGA^[17]	7	0.0090	13.10
GDFNN^[6]	8	0.0121	6.56
GPFNN^[34]	8	0.0067	17.26
NFN-FOESA ^[16]	9	0.0060	21.72

图8 PM2.5浓度预测测试结果

Fig.8 Testing results for PM2.5 concentration prediction

图9 PM2.5浓度预测测试误差

Fig.9 Testing errors for PM2.5 concentration prediction

图10 PM2.5浓度预测规则层神经元个数

Fig.10 Number of rule neurons for PM2.5 concentration prediction

表3 PM2.5浓度预测中不同方法的性能对比

Table 3 Performance comparisons of different methods for PM2.5 concentration prediction

Method	Testing RMSE	R²	Number of rule nurons
HEI-SOFNN	14.945	0.8823	6
FNN	36.687	0.7991	8
SOG-SOFNN^[35]	17.900	0.8400	10
RFNN^[36]	35.848	0.8052	9

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