Input variable scaling for statistical modeling

• Input variable scaling has a large effect on the accuracy of soft sensors.
• Two input-variable-scaling methods are proposed that reflect the variables’ importance.
• One scaling method is data-driven, while the other is knowledge-driven.
• A numerical simulation examined the theoretical properties of the method.
• The effectiveness of the proposed methods is confirmed in two industrial processes.

Input variable scaling is one of the most important steps in statistical modeling. However, it has not been actively investigated, and autoscaling is mostly used. This paper proposes two input variable scaling methods for improving the accuracy of soft sensors. One method statistically derives the input variable scaling factors; the other one uses spectroscopic data of a material whose content is estimated by the soft sensor. The proposed methods can determine the scales of the input variables based on their importance in output estimation. Thus, it can reduce the negative effects of input variables which are not related to an output variable. The effectiveness of the proposed methods was confirmed through a numerical example and industrial applications to a pharmaceutical and a distillation processes. In the industrial applications, the proposed methods improved the estimation accuracy by up to 63% compared to conventional methods such as autoscaling with input variable selection.