Identification of finite-time delay and regressors for the design of soft sensors in the presence of input collinearity

Soft sensors (SSs) play an important role in Industry 4.0 by providing estimates of process variables when conventional sensors are impractical or unavailable. The design of SSs requires estimating the possible output finite-time delay, e.g. due to the measurement process or transport phenomena, and selecting the correct model regressors. In this context, this paper presents a new method called multiple correlation delay and regressor selection (MC-DRS), which can be used to simultaneously identify the output finite-time delay and the regressors for dynamic models in the class of finite impulse-response models. The method, which belongs to the class of filter approaches, uses data stored in historical databases and solves problems caused by the collinearity of the inputs. The MC-DRS has a low computational complexity and outperforms existing model-agnostic methods such as correlation-based methods (Pearson, Kendall, Spearman and distance correlations), maximal information coefficient, Lipshitz quotients and minimum redundancy maximum relevance algorithm. Synthetic case studies and an industrial benchmark validate its effectiveness and underline its advantages in SS design for Industry 4.0 applications. In detail, the results obtained show that the proposed method was able to detect the correct finite-time delay and the number of regressors in 100% of the case studies. None of the other methods were able to correctly identify both system parameters. Among these methods, the distance correlation was able to detect the finite-time delay in 50% of the cases, while the Lipshitz quotients were able to detect the number of regressors in 50% of the cases. • The MC-DRS determines both the model order and the finite-time delay in soft sensors. • The proposed approach works also in the presence of input collinearity. • It uses data stored in historical databases and does not require ad-hoc experiments. • The MC-DRS is model agnostic and has a low computational complexity. • The MC-DRS outperforms other model-agnostic state-of-the-art methods.