结合栈式监督AE与可变加权ELM的回归预测模型

在现代工业生产过程中，许多关键变量与产品质量或生产效率密切相关，关键变量的实时监测是实现利润最大化及节能降耗的有效途径。针对回归预测任务中目标特征提取不全面、预测精度较低等问题，提出一种基于栈式监督自编码器与可变加权极限学习机的回归预测模型。通过堆叠多层自编码器并在每层自编码器中添加回归网络，同时以有监督方式对栈式自编码器（SAE）进行逐层预训练，得到与输出变量相关的特征表示。利用反向传播算法对网络参数进行微调，优化自编码器模型参数。在分析提取特征与输出变量的相关性基础上，对极限学习机（ELM）的输入权值和偏置进行加权得到预测结果。实验结果表明，与基于ELM和SAE-ELM的回归预测模型相比，该模型在多晶硅铸锭的G6产品数据集上的均方根误差降低0.056 7和0.011 2、决定系数提高0.489 3和0.290 3，具有更高的回归预测准确性及更强的鲁棒性与泛化性能。

Regression Prediction Model Combining Stack Supervised AE and Variable Weighted ELM

Many key variables in the modern industrial production are closely related to the product quality or production efficiency.Monitoring such key variables on a regular basis is an effective method of maximizing profits, saving energy, and reducing consumption.This study presents a regression prediction model based on a Stack Supervised Auto-Encoder(SSupAE) and a variable weighted Extreme Learning Machine(vwELM) to address problems such as inaccurate feature extraction and low prediction accuracy in regression prediction tasks.First, the Stacked Auto-Encoder(SAE) is trained in a supervised manner by stacking multi-layer Auto-Encoders(AEs) and adding a regression network to each layer of the AEs, to obtain the output-related feature representation.Then, the parameters of the SSupAE network are fine-tuned by applying back-propagation to optimize the model parameters of the AEs.Finally, the correlation between the extracted features and the output variables are analyzed, and the input weight and bias of the Extreme Learning Machine(ELM) are weighted to obtain the predicted results.The experimental results show that compared with those of the regression prediction model based on the ELM and SAE-ELM, the Root Mean Square Error(RMSE) of the proposed model on the G6 product dataset of polycrystalline silicon ingots is reduced by 0.056 7 and 0.011 2 and the coefficient of determination(R²) is increased by 0.489 3 and 0.290 3, indicating that the proposed model has better regression prediction accuracy, robustness, and generalization performance.