Structure Design for Recurrent Fuzzy Neural Network Based on Wavelet Transform Fuzzy Markov Chain
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摘要: 针对递归模糊神经网络(Recurrent fuzzy neural network, RFNN)的递归量难以自适应的问题, 提出一种基于小波变换–模糊马尔科夫链(Wavelet transform fuzzy Markov chain, WTFMC)算法的RFNN模型.首先, 在时间维度上记录隐含层神经元的模糊隶属度, 并采用小波变换将该时间序列进行分解, 通过模糊马尔科夫链对子序列的未来时段进行预测, 之后将各预测量合并后代入递归函数中得到具有自适应性的递归量.其次, 利用梯度下降算法更新RFNN的参数来保证神经网络的精度.最后, 通过非线性系统建模中几个基准问题和实际污水处理中关键水质参数的预测实验, 证明了该神经网络模型的可行性和有效性.Abstract: Aiming to solve the problem that the recursive variable in the recurrent fuzzy neural network (RFNN) is difficult to be self-adaptive, this paper proposes an RFNN structure model based on wavelet transform fuzzy Markov chain (WTFMC). Firstly, it records the fuzzy membership degree of hidden layer neurons in time dimension, and decomposes the time series by wavelet transform. The future period of the subsequence is predicted by fuzzy Markov chain, and the adaptive recursive variables are obtained by combining the predictors into the recursive function. Secondly, the gradient descent algorithm is utilized to update the parameters of RFNN in order to ensure the accuracy of neural network. Finally, the feasibility and validity of the neural network model are demonstrated by several benchmark problems in nonlinear system modeling and the prediction of key water quality parameters in the practical wastewater treatment.
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Key words:
- Recurrent fuzzy neural network /
- wavelet transform /
- fuzzy Markov chain /
- dynamic modeling /
- wastewater treatment
1) 本文责任编委 刘艳军 -
图 2 Henon混沌系统训练样本RMSE
Fig. 2 RMSE values in the training process of the Henon chaotic system
图 3 Henon混沌系统测试样本拟合效果
Fig. 3 Desired and predicted outputs of the Henon chaotic system
图 4 Henon混沌系统测试样本的预测误差
Fig. 4 Prediction error in the testing process of the Henon chaotic system
图 8 Mackey-Glass时间序列训练样本RMSE
Fig. 8 RMSE values in the training process of Mackey-Glass time series
图 10 Mackey-Glass时间序列测试样本的预测误差
Fig. 10 Prediction error in the testing process of Mackey-Glass time series
图 13 非线性系统测试样本的预测误差
Fig. 13 Prediction error in the testing process of nonlinear system
图 16 出水氨氮测试样本的预测误差
Fig. 16 Prediction error in the testing process of effluent NH$_4$-N
表 1 不同网络对Henon混沌时间序列的预测结果
Table 1 Prediction results of Henon chaotic time series with different networks
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表 3 不同网络对Mackey-Glass时间序列的预测结果
Table 3 Prediction results of Mackey-Glass time series with different networks
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表 4 不同网络对非线性系统的预测结果
Table 4 Prediction results of nonlinear system identification with different networks
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表 5 不同网络对出水氨氮的预测结果
Table 5 Prediction results of effluent NH$_4$-N with different networks with different networks
网络 规则数 训练RMSE 测试RMSE WTFMC-RFNN 12 0.0041 0.0351 IRSFNN (TSK) 16 0.0052 0.0468 RSEFNN-LF 12 0.0048 0.0404 TRFN-S 14 0.0045 0.0394 WRFNN 15 0.0053 0.0529 HO-RNFS 15 0.0047 0.0458 RFNN 12 0.0041 0.0437
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