【摘要】 为提高非线性自回归神经网络(NARX-NN)的多步预测性能，提出了一种预测值反馈再训练(FR)策略.首先采用常规训练策略对NARX-NN进行训练，然后利用模型的单步预测结果替换实测值，得到重构训练集，并指导网络再次训练.为验证FR的有效性，将其应用于3种典型的NARX-NN模型：非线性自回归深度神经网络(NARX-DNN)、基于长短期记忆网络的编码器-解码器(LSTMED)和深度自回归网络(DeepAR),以预测燃煤锅炉NO_x质量浓度或综合能源系统电负荷.与常规训练策略和计划采样的对比结果表明，采用FR的NARX-NN具有最高的多步预测精度，其中，LSTMED对NO_x质量浓度前向15步预测的平均绝对百分比误差(MAPE)为4.01%;DeepAR对电负荷前向24步预测的平均MAPE为4.34%.配对样本T检验结果表明，FR对NARX-NN的多步预测性能提升具有显著性.通过保持训练阶段和预测阶段输入的一致性，FR有效提升了NARX-NN模型的多步预测精度.更多还原

【Abstract】 To improve the multi-step prediction performance of nonlinear autoregressive neural network(NARX-NN), a predictive value feedback retraining(FR) strategy was proposed. Initially, the NARX-NN was trained using conventional training strategies. Then, the training samples were reconstructed by replacing the measured values with the one-step predicted values, which were used to train the network again. To validate the effectiveness of FR, it was applied to three typical NARX-NN models: nonlinear autoregressive deep neural network(NARX-DNN), encoder-decoder based on long short-term memory network(LSTMED) and deep autoregressive network(DeepAR) for predicting the NO_x mass concentration of coal-fired boilers or the electrical load of integrated energy system. Comparison results with conventional training strategies and scheduled sampling show that NARX-NN with FR has the highest multi-step prediction accuracy, with a mean absolute percentage error(MAPE) of 4.01% for LSTMED for 15-step forward prediction of NO_x mass concentration and 4.34% for DeepAR for 24-step forward prediction of electrical loads. The results of paired-sample T-test indicate that FR improves the multi-step prediction performance of NARX-NN significantly. By keeping the consistency of the inputs in the training and prediction phases, FR effectively improves the multi-step prediction accuracy of the NARX-NN model.更多还原