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• Under the JITL framework, GMVAE is utilized to extract latent representations with multimode characteristics by considering Gaussian mixture models in the latent space. • Each latent variable can be described through a Gaussian mixture distribution. Subsequently, a MSKL divergence is utilized to measure its similarity. • Based on the MSKL divergence, weighted input and output historical data are obtained, and then a local model is established. • The effectiveness of the proposed method is validated through a numerical example along with simulation on the TE benchmark process. Industrial data are often high-dimensional, nonlinear and multiple-modal. This paper develops a soft sensor model based on Gaussian mixture Variational Autoencoder (GMVAE) under the just-in-time learning (JITL) framework. To extract latent representations with multimode characteristics, GMVAE as a deep neural network model is utilized by considering Gaussian mixture models (GMM) in the latent space. After training the GMVAE model, each latent (or feature) variable can be described through a Gaussian mixture distribution. Subsequently, when a new sample arrives, a mixture symmetric Kullback-Leibler (MSKL) divergence is utilized to measure its similarity with historical data samples. MSKL divergence can measure similarity between two Gaussian mixture probability density functions. Based on the MSKL divergence, weighted input and output historical data are obtained, and then a local model is established. The effectiveness of the proposed soft sensor modeling method is validated through a numerical example along with simulation on the Tennessee Eastman benchmark process. [ABSTRACT FROM AUTHOR]

Considering industrial process with high-dimensional, intrinsic nonlinearities and possibly abnormal observations, a robust deep learning soft sensor model is developed under the just-in-time learning framework. As an unsupervised deep learning approach, Variational Autoencoder (VAE) has been successfully applied to soft sensing problems owing to its ability to describe the latent representations by probability distributions. In this work, to construct high performance soft sensor model, mutual information (MI) is first introduced for input variable selection. By further incorporating MI as weights on variable of the traditional VAE model, a MI-based output-relevant VAE is developed. For each new sample that arrives, by utilizing Symmetric Kullback-Leibler (SKL) divergence, its relevance with historical samples is determined. Based on the SKL divergence, the input samples that are most relevant to the query sample can be collected. The selected historical input samples and corresponding output samples are employed to build a Gaussian process regression (GPR) local model. Expectation maximation (EM) algorithm is utilized to deal with the nonlinearity and abnormal output observations in GPR local model simultaneously for robustness of the soft sensors. Numerical simulations and a benchmark process are employed to validate the effectiveness of the proposed soft sensor, which demonstrates its superior performance over traditional approaches. • A MI-based output-relevant VAE is presented by incorporating MI as weights on variable of the traditional VAE model. • The selected historical samples through SKL divergence are employed to build a GPR local model. • The abnormal output observations in GPR local model for robustness of the soft sensors is dealt with the EM algorithm. • Numerical simulations and a benchmark process are employed to validate the effectiveness of the proposed soft sensor. [ABSTRACT FROM AUTHOR]

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. • Variational autoencoder is employed to extract the distribution of each feature variable. • Kullback-Leibler divergence is employed to evaluate the similarity between the historical samples and a query sample. • Gaussian process regression is used to build model based on the selected samples, and then make a prediction. • The effectiveness of the proposed method is demonstrated through a numerical example and an industrial process. [ABSTRACT FROM AUTHOR]