To facilitate feature extraction and prediction of nonstable time series in industrial processes

a combination model was proposed from fast ensemble empirical mode decomposition (FEEMD)

approximate entropy (AE)

and feedback extreme learning machine (FELM). First

the FEEMD method was used to decompose complex non-stable time series data into relatively stable intrinsic model function components and residuals from high to low frequency. Secondly

complexity of these components by FEEMD decomposition was reduced by AE complexity degree calculation and feature reconstruction. Thirdly

a feedback mechanism based on traditional ELM structure was introduced to create a feedback layer between output layer and hidden layer for memorizing output data of the hidden layer

calculating trending change rate of output data

and dynamically updating output of the feedback layer

such that a feedback extreme learning machine (FELM) was formed to predict the next timepoint output for nonlinear dynamic system. Finally

the combination model was used to simulate purified terephthalic acid (PTA) solvent system with UCI standard data set. The simulation results show that the proposed method can obtain high prediction accuracy

which will provide guidance for operation optimization of actual production processes.