Developing accurate data-driven soft-sensors through integrating dynamic kernel slow feature analysis with neural networks

Abstract

A data-driven soft-sensor modelling approach based on dynamic kernel slow feature analysis (KSFA) is proposed in this paper. Slow feature analysis is a feature extraction method that aims to extract slowly varying features that can capture the driving forces behind data. However, there are situations where linear SFA (LSFA) cannot capture the driving forces due to nonlinear relationships between the driving forces and input signals. KSFA is a nonlinear extension of LSFA that utilises the kernel trick to map the inputs into a higher-dimensional feature space. Extracting the nonlinear driving forces can improve soft-sensor performance by utilising the nonlinear slow features as inputs to a neural network, which provides information on the key underlying trends, with the added benefit of noise reduction. Combining KSFA with a neural network further improves soft-sensor performance for cases where nonlinear relationships between the driving forces and soft-sensor outputs are present. The effectiveness of the proposed method is first demonstrated on a numerical example, where the theoretical advantages of KSFA can be easily observed. It is then applied to a benchmark simulated industrial fed-batch penicillin process.