Semi-supervised selective ensemble learning based on distance to model for nonlinear soft sensor development

Data-driven soft sensors have been widely used in process systems for delivering online estimations of hard-to-measure yet important quality-related variables. However, in many data-driven soft sensor applications, the process may be strongly nonlinear, and the number of labeled samples is limited, which are two major difficulties in developing high-accuracy soft sensors. To cope with this issue, a novel soft sensing method based on semi-supervised selective ensemble learning strategy is proposed. In the proposed method, the process is initially localized by an adaptive process state partition approach, where the information of unlabeled samples can be incorporated. Subsequently, a new distance to model (DM) criterion is defined for selective ensemble learning, which can overcome the drawback of the k nearest neighbor method. The newly defined DM criterion along with the incorporation of unlabeled samples can help to describe the relationships between query samples and local models more accurately, and therefore is able to provide higher estimation accuracy. The parameters of the proposed method are finalized automatically by the particle swarm optimization technique. The proposed method is investigated using three real-life benchmark datasets, and the simulation results demonstrate the effectiveness of the proposed method in dealing with nonlinear regression problems in the process system and in the urban pollutant monitoring area.