Discriminative and statistical transfer learning-based soft sensors under multiple working conditions

In industrial processes, the change in working conditions contributes to the distribution divergence between training data and test data. However, conventional soft sensor approaches follow the assumption that training data and test data follow the same data distribution. Consequently, the established soft sensor model is inapplicable to new working conditions. In order to tackle this challenge, a novel approach based on discriminative and statistical transfer learning (DSTL) is proposed for soft sensors under multiple working conditions. First, the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> </mml:math> -means clustering is applied to establish class pseudo labels. Besides, statistical distribution alignment is introduced to overcome marginal and conditional data distribution discrepancies between historical working conditions and new working conditions. Finally, by minimizing intra-class discrepancy and maximizing inter-class discrepancy, DSTL preserves discriminative information across multiple working conditions, which in turn enhances the performance of statistical distribution alignment. Comprehensive experiments on a fed-batch penicillin fermentation process are adopted to verify the effectiveness of the proposed model.