Multilayer feedforward networks are universal approximators
Neural Networks
A finite-difference method for linearization in nonlinear estimation algorithms
Automatica (Journal of IFAC)
Nonlinear Bayesian Filters for Training Recurrent Neural Networks
MICAI '08 Proceedings of the 7th Mexican International Conference on Artificial Intelligence: Advances in Artificial Intelligence
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Multi-reservoir echo state network with sparse bayesian learning
ISNN'10 Proceedings of the 7th international conference on Advances in Neural Networks - Volume Part I
An Augmented Echo State Network for Nonlinear Adaptive Filtering of Complex Noncircular Signals
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Adaptive fuzzy clustering based anomaly data detection in energy system of steel industry
Information Sciences: an International Journal
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When using echo state networks (ESNs) to establish a regression model for noisy nonlinear time series, only the output uncertainty was usually concerned in some literature. However, the unconsidered internal states uncertainty is actually important as well. In this study, an improved ESN model with noise addition is proposed, in which the additive noises describe the internal state uncertainty and the output uncertainty. In terms of the parameters determination of this prediction model, a nonlinear/linear dual estimation consisting of a nonlinear Kalman filter and a linear one is proposed to perform the supervised learning. For verifying the effectiveness of the proposed method, the noisy Mackey Glass time series and the generation flow of blast furnace gas (BFG) in steel industry practice are both employed. The experimental results demonstrate that the proposed method is effective and robust for noisy nonlinear time series prediction.