Process Data Analytics via Probabilistic Latent Variable Models: A Tutorial Review

Abstract

Dimensionality reduction is important for the high-dimensional nature of data in the process industry, which has made latent variable modeling methods popular in recent years. By projecting high-dimensional data into a lower-dimensional space, latent variables models are able to extract key information from process data while simultaneously improving the efficiency of data analytics. Through a probabilistic viewpoint, this paper carries out a tutorial review of probabilistic latent variable models on process data analytics. Detailed illustrations of different kinds of basic probabilistic latent variable models (PLVM) are provided, as well as their research statuses. Additionally, more counterparts of those basic PLVMs are introduced and discussed for process data analytics. Several perspectives are highlighted for future research on this topic.

Modern Soft-Sensing Modeling Methods for Fermentation Processes

“…There are different probabilistic methods have been reviewed in the literature such as probabilistic PCA, probabilistic independent component analysis (ICA), probabilistic PLS, and factor analysis. A more detail discussion and research status of different kinds of PLVMs is provided in [32].…”

“…This can be seen in the subject of published applications for soft sensors, where several researchers concentrate strongly on a model type in their field of expertise. Just to give a few examples, if the process variables are non-Gaussianly distributed or they have a non-linear relationship with each other, a non-linear probabilistic latent variable modeling method needs to be utilized; If the process variables are Gaussianly distributed or they have a linear correlation with each other, then a linear Gaussian probabilistic/PCA should be employed [32]. Deep neural network models demonstrate great performance in complicated highly-non-linear processes, comprising richer information in deep layers of network and large training datasets [33].…”

“…The tools and methods reviewed here are ones that have proved to be useful with a sensor system. Currently, with profound studies into the theory of soft sensor control and the ongoing advancement of engineering technology, some modern methods have appeared and developed rapidly to solve the problems which are hard to measure for soft sensor models, such as FL [43], partial least squares (PLS) [44], SVM [45], support vector regression (SVR), radial basis function (RBF), NN [23], GA [46], and PLVMs [32]. Some important soft-sensing modeling methods, shown in Figure 4 are used for the prediction of quality variables.…”

Heats and input variables selection for designing a water detection framework applicable to industrial electric arc furnaces

“…[11] Latent variable methods such as MPCA (multiway principal component analysis) and MPLS (multiway projection to latent structures) are well-known techniques in dealing with high-dimensional batch data with many, noisy, and collinear variables. [12][13][14] MPCA first unfolds the three dimensions batch data into two dimensions. Then, it is used on the unfolded heat to capture the correlation structure on the measured variables (ie, X array) and projects the array into a lower dimensional latent structure.…”

A Label Noise Robust Stacked Auto‐Encoder Algorithm for Inaccurate Supervised Classification Problems

“…References [16,17] adopt a probabilistic model of kernel Fisher Discriminate, where the probability of the incorrectly labeled data point will be updated. Other methods [18][19][20] also adopt a probabilistic framework, treating each sample's label as a latent variable. The current label is taken as the prior to estimate the posterior label possibility, based on which weights of samples are updated.…”