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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. • An output-relevant VAE is proposed for extracting output-relevant features by using correlation between process variables. • With symmetric Kullback–Leibler 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. • 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. [ABSTRACT FROM AUTHOR]

• Traditional Gaussian Process Regression models typically assume independent identically distributed noises for all observations. However, applications with colored noises/disturbances frequently arise in modeling of complex processes. • We modeled the colored noise by an ARMA time series model and determined its covariance for subsequent Gaussian Process modeling. • A novel approach based on hybrid kernels is proposed, thereby avoiding parametric modeling of the colored noises. • A synthetic data, a simulated example and a polyester polymerization process were used to demonstrate the effectiveness of the proposed approach. Traditional Gaussian Process Regression (TGPR) models typically assume independent identically distributed (i.i.d.) noises for all observations. However, applications with colored noises/disturbances frequently arise in modeling of complex processes. In this work, first, we consider to model noise by an ARMA time series model and determine its covariance for subsequent Gaussian Process (GP) modeling. Then a novel approach based on hybrid kernels is proposed, thereby avoiding parametric modeling of the colored noises. Moreover, all hyper-parameters are estimated simultaneously by using a particle swarm optimization (PSO) algorithm. Finally, a synthetic data, a simulated example, as well as a polyester polymerization process are used to demonstrate the effectiveness of the proposed approach. [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]