Abstract Main challenges for developing data-based models lie in the existence of high-dimensional and possibly missing observations that exist in stored data from industry process. Variational autoencoder (VAE) as one of the deep learning methods has been applied for extracting useful information or features from high-dimensional dataset. Considering that existing VAE is unsupervised, an output-relevant VAE is proposed for extracting output-relevant features in this work. By using correlation between process variables, different weight is correspondingly assigned to each input variable. With symmetric Kullback–Leibler (SKL) divergence, the similarity is evaluated between the stored samples and a query sample. According to the values of the SKL divergence, data relevant for modeling are selected. Subsequently, Gaussian process regression (GPR) is utilized to establish a model between the input and the corresponding output at the query sample. In addition, owing to the common existence of missing data in output data set, the parameters and missing data in the GPR are estimated simultaneously. A practical debutanizer industrial process is utilized to illustrate the effectiveness of the proposed method.

中文翻译：

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输出相关变分自动编码器，用于具有缺失数据的即时软传感器建模

摘要 开发基于数据的模型的主要挑战在于存在高维且可能缺失的观察，这些观察存在于来自工业过程的存储数据中。变分自编码器（VAE）作为深度学习方法之一已被应用于从高维数据集中提取有用的信息或特征。考虑到现有的 VAE 是无监督的，本文提出了一种与输出相关的 VAE 来提取与输出相关的特征。通过使用过程变量之间的相关性，为每个输入变量对应分配不同的权重。使用对称 Kullback–Leibler (SKL) 散度，评估存储样本和查询样本之间的相似性。根据 SKL 散度的值，选择与建模相关的数据。随后，高斯过程回归（GPR）用于在查询样本的输入和相应输出之间建立模型。此外，由于输出数据集中缺失数据的普遍存在，探地雷达中的参数和缺失数据是同时估计的。一个实用的脱丁烷工业过程被用来说明所提出方法的有效性。