A time series context self-supervised learning for soft measurement of the f-CaO content

Abstract The content of free calcium oxide (f-CaO) in cement clinker is an important index for cement quality. In the production of cement clinker, the number of unlabeled samples is excessive and there is an interplay between the variables in time. A time series context self-supervised learning (TS-CSSL) is proposed. This method constructs pretextual tasks based on the temporal relationships between different variables from a large amount of unlabeled time series data. Considering the process of cement production and the residence time of materials in each piece of equipment, the method designs the segmentation of periods for different variables in the context-based self-supervised pretextual task. On this basis, a soft sensor for f-CaO content was implemented. After the experimental validation, the evaluation metrics root means square errors ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mtext>RMSE</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> of the TS-CSSL model decreased by 2.41% and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:mrow> </mml:math> improved by 10.93% compared to the random initialization model. Compared to the model with 8 sets of temporal relationships, the TS-CSSL model showed a decrease in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mtext>RMSE</mml:mtext> </mml:mrow> </mml:mrow> </mml:math> of 5.33% and an increase in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:mrow> </mml:math> of 21.9%. The experimental results demonstrate that the feature representation learned by the model can be used in a CNN framework and the effectiveness of the proposed self-supervised assistance task.