Data-Driven Soft Sensor Modelling with Time Delay Estimation through Bayesian Optimization

The soft sensor technology is an effective solution to online estimation of primary variable that is difficult to measure via hardware sensors in industrial processes. By selecting several easy-to-measure auxiliary variables that are closely related to the primary variable, a mathematical model can be established to predict the primary variable online. However, there is typically a time-delayed correlation between auxiliary variables and primary variable, which is usually neglected in state-of-the-art soft sensing approaches. In this study, we propose a new data-driven soft sensing approach by considering time-delayed inputs in Support Vector Machine (i.e. TD-SVM). Both discrete-valued time delays and hyperparameters of SVM are jointly optimized by using Bayesian Optimization (BO) algorithm based on Gaussian process. We carry out case studies on process data from a real-world methanol plant in China, which demonstrate the usefulness of the proposed soft sensor model and parameter optimization strategy. It is shown that the BO can effectively optimize the estimation of time delays and hyperparameters of SVM jointly, thereby helping to improve the model accuracy.