Integrating Autoencoder and Heteroscedastic Noise Neural Networks for the Batch Process Soft-Sensor Design

Abstract

Viscosity represents a key product quality indicator but has been difficult to measure in-process in real-time. This is particularly true if the process involves complex mixing phenomena operated at dynamic conditions. To address this challenge, in this study, we developed an innovative soft sensor by integrating advanced artificial neural networks. The soft sensor first employs a deep learning autoencoder to extract information-rich process features by compressing high-dimensional industrial data and then adopts a heteroscedastic noise neural network to simultaneously predict product viscosity and associated uncertainty. To evaluate its performance, predictions of product viscosity were made for a number of industrial batches operated over different seasons. Furthermore, probabilistic machine learning techniques, including the Gaussian process and the Bayesian neural network, were selected to benchmark against the heteroscedastic noise neural network. Through comparison, it is found that the proposed soft-sensor has both high accuracy and high reliability, indicating its potential for process monitoring and quality control.

Constructing a Symbolic Regression-Based Interpretable Soft Sensor for Industrial Data Analytics and Product Quality Control

“…Therefore, it is concluded to accurately characterize process uncertainty, and it is necessary to use a complex architecture of a nonlinear estimator such as an HNN or a Gaussian process (GP) so that more process information can be captured. 6 Lastly, we can conclude that it was possible to extract physically meaningful correlations from a complex mixing process of a non-Newtonian fluid using minimal process variables. All statistical expressions generated through symbolic regression used low-dimensional representations of one shared process sensor.…”

“…This is a consequence of the parsimony of the developed models in order to capture the overarching correlations. Therefore, it is concluded to accurately characterize process uncertainty, and it is necessary to use a complex architecture of a nonlinear estimator such as an HNN or a Gaussian process (GP) so that more process information can be captured …”

“…This is primarily expected to be due to the simple nature of the expressions defined by symbolic regression, which do not fully capture the process information. Evidence to support this can be found in ref , when the use of a more complex data-driven model structure such as a heteroscedastic neural network (HNN) to approximate uncertainty provided significantly more realistic estimates. The HNN model is defined by the use of many parameters, allowing representative estimation of the process uncertainty, indicating that the underestimations provided by using the symbolic regression models are predominantly caused by a lack of parameters.…”

“…Importantly, the interpretable nature of expressions generated via symbolic regression provides a direct advantage over more traditional data-driven models such as neural networks and GPs, for which gain in process understanding is limited. Furthermore, when compared with previous work using more complex data-driven models, it is shown that equivalent accuracy is achieved even with the increased interpretability and simpler model structure. Another significant advantage of the proposed models is the ease of being implemented into new or existing process plants, which is not true for more complex machine learning models, since they lack symbolic form.…”

“…Case study 1 describes the more complex formulation and so is used to test the robustness of the proposed symbolic regression framework. The data for this is detailed in ref 16.…”