| Summary: | 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.
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