Echo State Network(ESN) is a recurrent neural network with a large, randomly generated recurrent part called the dynamic reservoir. Only the output weights are modified during training. However, proper balancing of the trade-off between the structure and performance for ESN remains a difficult task. In this paper, a structure optimized method for ESN based on contribution is proposed to simplify its network structure and improve its performance.First, we evaluate the contribution of reservoir neurons. Second, we present a pruning mechanism to remove the unimportant connection weights of reservoir neurons with low contribution. Finally, the new output weights are learned with the pseudo inverse method. The novel optimized ESN, named C-ESN, is tested on a Lorenz chaotic time-series prediction and an actual municipal sewage treatment system. The simulation results show that the C-ESN can have better prediction and generalization performance than ESN.
It is difficult to measure the online values of biochemical oxygen demand(BOD) due to the characteristics of nonlinear dynamics, large lag and uncertainty in wastewater treatment process. In this paper, based on the knowledge representation ability and learning capability, an improved T–S fuzzy neural network(TSFNN) is introduced to predict BOD values by the soft computing method. In this improved TSFNN, a K-means clustering is used to initialize the structure of TSFNN, including the number of fuzzy rules and parameters of membership function. For training TSFNN, a gradient descent method with the momentum item is used to adjust antecedent parameters and consequent parameters. This improved TSFNN is applied to predict the BOD values in effluent of the wastewater treatment process. The simulation results show that the TSFNN with K-means clustering algorithm can measure the BOD values accurately. The algorithm presents better approximation performance than some other methods.
