A variable selection method for soft sensor development through mixed integer quadratic programming

•A variable selection method is proposed by formulating as a nested optimization problem.•A mixed integer quadratic programming with warm start technique is developed for selecting the best variable subset.•An industrial application to distillation column is presented with the proposed variable selection method.

Soft sensors are widely employed in industry to predict quality variables, which are difficult to measure online, by using secondary variables. To build an accurate soft sensor, a proper variable selection is critical. In this project, a method of selecting the optimal secondary variables for a soft sensor model is proposed. It is formulated as a nested optimization problem. In each iteration, a mixed integer quadratic programming (MIQP) is conducted with the Bayesian information criterion (BIC) to estimate the prediction error. A warm start (WS) technique is developed to speed up the convergence. The proposed method is evaluated using a number of instances from the UCI Machine Learning Repository. The computational results demonstrate that this method is well suited for finding the best variable subsets. The method is successfully applied to build soft sensors for an industrial distillation column. The results show that the proposed method can effectively select feature variables that will improve the model prediction performance and reduce the model complexity. Comparisons with other methods, including the traditional partial least square technique, are also presented.