Refining data-driven soft sensor modeling framework with variable time reconstruction

Due to the difference of variable positions brought by process structure, time-delay exists between process variables and quality variables. In this paper, this commonly overlooked problem in data-driven soft sensor modeling is illustrated and solved. The main idea in this paper is to take the variable time-delay (VTD) as a model parameter to reconstruct the dataset and then solve it through optimizing the objective function of models. However, the combination of VTD would lead to an intractable high computational complexity, then it is proposed to use an efficient population-based Integer Differential Evolution (IDE) algorithm to select the optimal VTD values and cooperatively learn model parameters. With the help of IDE algorithm, a Variable Time Reconstruction (VTR) modeling framework is then formulated for soft sensor development. As examples, three types of VTR-based soft sensors are developed under this framework to cope with different cases of data features. The presented numerical and industrial cases demonstrate that the proposed VTR-based model can effectively learn the VTD values, which can reconstruct and recover the original data pattern, and thus significantly help increase the generalization performance of soft sensor models. (C) 2020 Elsevier Ltd. All rights reserved.