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

Deriving physical models for key performance indicators (KPIs) has been a challenge for industries developing accurate control and optimization schemes. As a result, data-driven models have seen a rise in application within recent literature; however, commonly used “black-box” data-driven models suffer from a lack of interpretability, limiting their uptake within industrial settings. To address this challenge, we developed an interpretable soft sensor by integrating symbolic regression among dimensionality reduction, statistical feature engineering, and latent variable modeling. Through this approach, symbolic regression can effectively extract important statistical relations between the KPI and key process variables. To investigate their performance and compare against existing machine learning models, two industrial case studies were presented focusing on formulation product quality control. It is concluded that symbolic regression-generated soft sensors are of high accuracy, and their expressions can provide meaningful physical insights into the underlying processes, highlighting their great potential for future applications.