Online sequential extreme learning machine in nonstationary environments.

System identification in nonstationary environments represents a challenging problem to solve and lots of efforts have been put by the scientific community in the last decades to provide adequate solutions on purpose. Most of them are targeted to work under the system linearity assumption, but also some have been proposed to deal with the nonlinear case study. In particular the authors have recently advanced a neural architecture, namely time-varying neural networks (TV-NN), which has shown remarkable identification properties in the presence of nonlinear and nonstationary conditions. TV-NN training is an issue due to the high number of free parameters and the extreme learning machine (ELM) approach has been successfully used on purpose. ELM is a fast learning algorithm that has recently caught much attention within the neural networks (NNs) research community. Many variants of ELM have been appeared in recent literature, specially for the stationary case study. The reference one for TV-NN training is named ELM-TV and is of batch-learning type. In this contribution an online sequential version of ELM-TV is developed, in response to the need of dealing with applications where sequential arrival or large number of training data occurs. This algorithm generalizes the corresponding counterpart working under stationary conditions. Its performances have been evaluated in some nonstationary and nonlinear system identification tasks and related results show that the advanced technique produces comparable generalization performances to ELM-TV, ensuring at the same time all benefits of an online sequential approach.