During chemical production, the different sampling frequencies of different variables generate a substantial amount of unlabeled data, which is challenging to use effectively, resulting in data waste. Additionally, distributed control systems frequently produce noisy data due to environmental interference and aging measurement instruments, complicating soft sensing modeling. Furthermore, in semi-supervised tasks, unsupervised components can undermine the accuracy of supervised tasks. To address these issues, this study proposes a semi-supervised soft sensing method for product quality based on a ladder network, enabling accurate, timely determination of key product quality and enhancing operational efficiency.

A two-step variable screening method—maximum mutual information (MIC) followed by minimum redundancy maximum relevance (mRMR)—was used to screen auxiliary variables. MIC was first applied to eliminate low-correlation variables, and mRMR was then used to remove redundant variables among the auxiliary set, yielding an optimal selection for modeling. The ladder network-based soft sensing method was then established, improving noise resistance by injecting disturbances into each encoder layer and reconstructing noise-free features layer by layer through the decoder. Skip connections were added between encoders and decoders to extract more information from unlabeled data, enhancing focus on supervised tasks and strengthening the model's robustness and generalization.

This method was applied to the methanol-to-olefin (MTO) process, termed DMTO. The MIC and mRMR screening reduced 203 auxiliary variables to an optimal 50. After preprocessing, several soft sensor models were established to compare outcomes. Results showed that unlabeled samples improved the effectiveness of supervised soft sensing tasks, with the proposed method enhancing various evaluation metrics. Residual analysis further indicated that the predicted residuals of the ladder network-based semi-supervised method closely aligned with a standard normal distribution, validating the method's superiority.

Compared with supervised and other semi-supervised learning methods, the ladder network demonstrates superior prediction accuracy and generalization in soft sensing ethylene products in the DMTO process. The proposed approach offers promising applications for real-time monitoring and control of product quality in chemical production.