Abstract
Soft-sensors are widely utilized for predictions of important but hard-to-measure variables in industrial processes. However, significant variations, process uncertainties, negative influence of external environment and insufficient use of unlabeled data always cause the attenuation of prediction performance. Thus, this paper proposed an adaptive semi-supervised multi-output soft-sensor by co-training recursive heterogeneous models. In the proposed strategy, a linear multi-output model, called recursive partial least square (MRPLS), and a nonlinear multi-output, called long short-term memory recurrent neural network (MLSTM), are co-trained to deal with inefficient use of label data adaptively. Ensemble of both models are not only able to address the linear and nonlinear hybrid behaviors in different time scale, but also able to deal with multiple tasks learning issues. In addition, the model proposed an odd-even grouping strategy to equalize two parts of the labeled data, which is able to capture the global variations of a process. To validate the prediction performance of the proposed soft-sensor, it was verified through a simulation benchmark platform (BSM1) and a real sewage treatment plant (UCI database). The results meant that co-training MRPLS-MLSTM achieved better performance compared with other existing co-training models in terms of the hard-to-measure variables.
Highlights
In the process industries, soft-sensors are proposed to predict the hard-to-measure variables on the basis of easy-to-measure variables
Based on the above co-training regression model, an adaptive semi-supervised multi-output soft-sensor is proposed in this paper, termed as co-training MRPLS-MLSTM
By comparing with the adaptive soft-sensors, we found co-training MRRPLS-MLSTM can better track the change trend of the target
Summary
Soft-sensors are proposed to predict the hard-to-measure variables on the basis of easy-to-measure variables. D. Li et al.: Learning Adaptive Semi-Supervised Multi-Output Soft-Sensors With Co-Training of Heterogeneous Models data, while those only with input variables are referred as unlabeled data. The grouping method tends to converge into local data selection, thereby reducing the model prediction performance In this light, Zhou et al proposed a tri-training algorithm to improve the generalization ability of the model by establishing three mutually independent labeled data sets and regression models [19]. Multi-output linear models, such as multivariate linear regression (MLR), are used to build a soft-sensor model [21] Despite their advantages, nonlinearity in the industrial processes could degrade their prediction performance. ADAPTIVE SEMI-SUPERVISED MULTI-OUTPUT SOFT-SENSORS The purpose of co-training algorithm is to select appropriate unlabeled data with high confidence and to optimize the performance of prediction model. The proposed softsensor can deal with dynamic multi-output learning in industrial process, and be able to approach the hybrid behaviors of linearity and nonlinearity
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