Dynamical Soft Sensors from Scarce and Irregularly Sampled Outputs Using Sparse Optimization Techniques

In process industries, quality variables such as concentrations and viscosity usually require offline laboratory analysis due to difficulties associated with online sensing and are often sampled slowly or irregularly compared to other variables such as temperatures and flow rates. Dynamical soft sensors, which relate the uniformly fast sampled variables to irregularly sampled quality variables, are crucial in control and process monitoring applications. Most identification approaches for soft sensing assume that all the variables are sampled regularly and uniformly. The existing auxiliary model (AM)-based approaches for dealing with irregular sampling suffer from drawbacks such as nonconvex optimization, lack of model parsimony and require prior information about the system dynamics. This work addresses a few of these issues by developing a flexible AM that can accommodate complex linear process dynamics without assuming any prior knowledge and compromising on model parsimony by using redundant Laguerre filters and casting the model learning in the sparse optimization framework. The developed AM is utilized to efficiently reconstruct the measurements at the base sampling interval, which further serves as a foreground for the traditional parametric model identification techniques or the expectation maximization algorithm to obtain optimal parameter estimates. The efficacy of the proposed AM-based soft sensor algorithm is demonstrated through synthetic as well as industrial simulation case studies. Finally, a few guidelines on effective sampling of quality variables to generate informative experiments for soft sensor development are also presented.