A Mixed-Integer Formulation for the Simultaneous Input Selection and Outlier Filtering in Soft Sensor Training

Soft sensors are used to calculate the real-time values of process variables which can be measured in the laboratory only or require expensive online measurement tools. A set of mathematical expressions are developed and trained from historical data to exploit the statistical knowledge between online and offline measurements to ensure a reliable prediction performance, for optimization and control purposes. This study focuses on the development of a mixed-integer optimization problem to perform input selection and outlier filtering simultaneously using rigorous algorithms during the training procedure, unlike traditional heuristic and sequential methods. Nonlinearities and nonconvexities in the optimization problem is further tailored for global optimality and computational advancements by reformulations and piecewise linearizations to address the complexity of the task with additional binary variables, representing the selection of a particular input or data. The proposed approach is implemented on actual data from two different industrial plants and compared to traditional approach.