An Adaptive Online Sequential Extreme Learning Machine for Real-Time Tidal Level Prediction

Abstract

An adaptive variable-structure online sequential extreme learning machine (OS-ELM) is proposed by incorporating a hidden nodes pruning strategy. As conventional OS-ELM increases network dimensionality by adding newly-received data samples, the resulted dimension would expand dramatically and result in phenomenon of “dimensionality curse” finally. As the measurement samples may come endlessly, there is a practical need to adjust the dimension of OS-ELM not only by adding hidden units but also by pruning superfluous units simultaneously. To evaluate the contribution of existing hidden units and locate the superfluous units, an index is implemented referred to as normalized error reduction ratio. As the OS-ELM adds new samples in hidden units, those existing units contribute less to current dynamics would be deleted from network, thus the resulted parsimonious network can represent current system dynamics more efficiently. This online dimension adjustment approach can handle samples which are presented one-by-one or chuck-by-chuck with variable chuck size. The adaptive variable-structure OS-ELM was implemented for online tidal level prediction purpose. To evaluate the efficiency of the adaptive variable structure OS-ELM, tidal prediction simulations was conducted based on the actual measured tidal data and meteorological data of Old Port Tampa in the United States. Simulation results reveal that the proposed variable-structure OS-ELM demonstrates its effectiveness in short term tidal predictions in respect of accuracy and rapidness.