A variable-structure online sequential extreme learning machine for time-varying system prediction

Abstract

A variable-structure online sequential extreme learning machine (OS-ELM) is proposed by incorporating a hidden units pruning strategy. As conventional OS-ELM increases network dimensionality by adding newly-received samples as hidden units, the hidden layer dimension would expand and result in “dimensionality curse” finally. Furthermore, the vast number of hidden units cannot represent time-varying dynamics adaptively and would deteriorate the network generalization capability. Therefore, there is a practical need to adjust the dimension of OS-ELM not only by adding hidden units but also by simultaneously pruning superfluous units which contribute less to the output. To evaluate the individual contribution of existing hidden units, an index is proposed referred to as normalized error reduction ratio. The variable structure OS-ELM adds newly received samples in hidden units, and prunes those units contribute less to current dynamics from network simultaneously, thus the resulted network possesses parsimonious structure which can represent current system dynamics more efficiently. The online network structure adjustment approach can handle samples which are presented one-by-one or chuck-by-chuck. The variable-structure OS-ELM (VS-OSELM) can be implemented for online identification and prediction of time-varying systems. In this study, to evaluate the efficiency of VS-OSELM, it was implemented for real-time prediction of tidal level change which is a complex time-varying process. Online tidal prediction simulations is conducted based on the real measured tidal and meteorological data of Old Port Tampa in Florida, United States. Simulation results demonstrate that the proposed variable-structure OS-ELM is suitable for identification and prediction of complex time-varying systems with high prediction accuracy and fast computation speed.