基于变分推理回声状态网络集成模型的工业数据区间预测
Variational inference-based echo state network ensemble model for intervals prediction of industrial data

针对含噪声工业时间序列数据的区间预测问题, 本文提出了一种使用变分推理来数值求解回声状态网络 (echo state network, ESN)集成模型参数的区间预测方法. 在模型构建上, 将ESN集成模型中各个ESN单元输出权值 向量的先验分布方差设置为相互独立形式, 相比较非独立形式更有利于模型稳定性; 在模型参数求解上, 本文提出 用变分推理来近似推导出集成模型中所有不确定参数的联合后验概率分布, 以分布中的参数均值作为模型参数值, 相对于已有ESN集成模型使用最大化边缘似然度的参数估计方法效果更好. 为验证提出方法的有效性, 测试了人工 数据集和钢铁企业真实煤气数据集. 实验结果表明本文方法参数估计更为准确, 在预测精度, 区间质量和模型稳定 性以及耗时方面表现优秀.
Pointing at interval prediction of industrial noisy time series, an interval prediction method based on an echo state network (ESN) ensemble optimized by variational inference is proposed. In the stage of model construction, the prior distribution variance of each ESN’s output weight matrix is set to be independent, which could be more stable than the non-independent form; In the stage of parameter solution, the paper uses variational inference to approximate posterior distribution of uncertain parameters, and get the parameters from the posterior distribution, thus the parameter estimation can be more accurate than the existing ESN ensemble optimized by marginal maximum likelihood estimation. In order to demonstrate the availability of the method, an artificial data set and two gas data sets from iron and steel enterprise are tested in this paper. The results show that the parameters estimated by variational inference are more accurate, and the method has relatively excellent performance in prediction accuracy , interval mass, model stability, and time cost.