Industrial Process Soft Sensing Based on Bidirectional Optimization Learning of Data Augmentation and Prediction Models Under Limited Data

Soft sensing techniques are crucial for predicting key quality indicators in industrial processes. Despite the widespread application of deep learning in the soft sensing domain, challenges such as limited sampling and the complex nonlinear relationships among process variables limit the accuracy and adaptability of soft sensing models. Consequently, this study develops a bidirectional optimization learning of data augmentation and prediction modeling framework (BOL-DAPM). Considering that the generated samples must adhere to specific distribution characteristics and maintain the relationship between feature and target variables, a regression-constrained autoencoder (R-CAE) is developed that is capable of generating higher-quality new samples. To address the lack of consideration for maintaining intervariable correlation during the feature extraction process of soft sensing models, a nonlinear correlation index-constrained stacked target-related autoencoder (NC-STAE) is established, enhancing the accuracy of the predictive model. Considering the strong dependency between data generation and predictive models, a bidirectional optimization strategy is implemented through the loss function flow between the two models. This approach further improves the predictive accuracy of soft sensing with limited data. Experimental validation on datasets from the debutanizer column and concrete compressive strength confirmed that the proposed methods surpass recent comparative approaches in reducing prediction error, improving the coefficient of determination (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula>) and lowering the mean absolute error (MAE), with an average precision performance increase of 35%.