Abstract This paper presents a variational autoencoder-based just-in-time (JIT) learning framework for soft sensor modeling. Just-in-Time learning is often applied for soft sensor modeling in industrial processes. However, traditional just-in-time learning methods measure the similarity based on Euclidean distance, which has not taken into consideration the uncertainty in variables. To improve traditional just-in-time learning methods, in the proposed approach, the variational autoencoder is employed to extract features from input data set containing noise. Each feature variable is expressed by a Gaussian distribution. Then, by using the distribution of each feature variable, Kullback-Leibler divergence is employed to evaluate the similarity between the historical samples and a query sample. Furthermore, historical samples that are most similar to the query samples based on the values of the Kullback-Leibler divergence are selected for modeling. Finally, Gaussian process regression as a nonlinear regression model, is used to model the relationship between the selected input samples and the corresponding output samples, and then make a prediction. A numerical example as well as application on a practical debutanizer industrial process demonstrates the effectiveness of the proposed method.

中文翻译：

---

基于变分自编码器的软传感器深度学习实时建模方法

摘要 本文提出了一种用于软传感器建模的基于变分自编码器的即时 (JIT) 学习框架。即时学习通常用于工业过程中的软传感器建模。然而，传统的即时学习方法基于欧几里德距离来衡量相似性，没有考虑变量的不确定性。为了改进传统的即时学习方法，在所提出的方法中，采用变分自编码器从包含噪声的输入数据集中提取特征。每个特征变量都由高斯分布表示。然后，通过使用每个特征变量的分布，采用 Kullback-Leibler 散度来评估历史样本和查询样本之间的相似性。此外，选择与基于 Kullback-Leibler 散度值的查询样本最相似的历史样本进行建模。最后，高斯过程回归作为非线性回归模型，用于对选定的输入样本与对应的输出样本之间的关系进行建模，然后进行预测。一个数值例子以及在实际脱丁烷工业过程中的应用证明了所提出方法的有效性。