ELM weighted hybrid modeling and its online modification

Extreme learning machine (ELM) is a fast online learning algorithm for single hidden layer feed-forward neural networks (SLFN), which keeps the fast learning speed with good performance. And it has been widely used on function approximation and prediction classification. However, the parameters in hidden layer of ELM are randomly determined which leads to the unstable prediction performance. So the ELM weighted hybrid modeling method is proposed. Firstly, several ELM sub-models of high precision are trained and stored in the model base. When a new sample needs to be predicted, those ELM sub-models are combined with weight as the hybrid model to output the prediction result. The hybrid model reduces the randomness of prediction with single ELM, and improves the accuracy and ensures the relative stability of the prediction results. Due to the time-varying in process, the model modification conditions and sliding window sample length are set. And the sub-models in model base which prediction error exceeds the threshold will be retrained online, so as to modify the hybrid model online. Four simulation examples verify the effectiveness of the proposed method.