基于FEEMD-AE与反馈极限学习机组合模型预测研究与应用

针对现有工业过程非平稳时间序列中的特征提取及预测问题，提出了基于快速集合经验模态分解（fast ensemble empirical mode decomposition，FEEMD）、近似熵（approximate entropy，AE）和反馈极限学习机（feedback extreme learning machine，FELM）的组合模型。首先，针对复杂非平稳时序数据，采用FEEMD方法将其分解为从高频到低频的相对平稳的本征模态函数分量和余项；其次，为解决经过FEEMD分解出来的分量复杂度问题，运用近似熵（AE）计算分量复杂度并进行特征重构，以降低分量复杂性；然后，基于传统ELM结构，通过引入反馈机制，在输出层与隐含层之间增加反馈层用来记忆隐含层输出数据，并计算数据趋势变化率动态更新反馈层输出，形成反馈极限学习机（FELM），对非线性动态系统的下一时刻输出进行预测；最后，将所提出的组合预测模型通过UCI标准数据集与精对苯二甲酸（PTA）溶剂系统进行建模仿真，仿真结果表明，提出的组合模型预测方法能够得到较高的预测精度，为实际生产操作优化提供了一定的指导。

Prediction research and application of a combination model based on FEEMD-AE and feedback extreme learning machine

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.