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The pivotal factor to regulate and enhance within an operating batch is the quality process, a challenging variable to monitor online. Soft sensors offer an immediate alternative for providing real-time insights into process quality, yet persisting issues include the imbalance between process and quality measurements, noisy measurements, and the intricate 3-dimensional dynamic batch data structure. This paper introduces the Robust Semi-Supervised Dual-Attention Latent Dynamic Conditional State-Space Model (RS2DA-LDCSSM) to address these challenges for within-batch quality prediction. Given the frequent absence of quality data due to measurement inconveniences, an imputation network is embedded within the RS2DA-LDCSSM to facilitate the prediction of future quality. To prevent information distortion during data unfolding, the Attentional Sequence-to-Sequence RNN Encoder-Decoder (AS2S-RNNED) is employed to process the 3-dimensional batch data. The proposed method integrates AS2S-RNNED with a probability state-space model to filter out noisy process data and stabilize the probability prediction of quality data, extracting spatial and temporal latent data from past process and quality data while minimizing the loss in multi-step prediction. This work represents a novel approach to dynamic nonlinear batch processes through probabilistic semi-supervised learning. The RS2DA-LDCSSM is adaptable to any batch process for within-batch quality prediction, as evidenced by numerical cases demonstrating its reliability, achieving an R2 value of 0.87, surpassing comparison methods. In an industrial penicillin fermentation batch process, the RS2DA-LDCSSM exhibits remarkable robustness with a high R2 index value of 0.99 in practical quality prediction scenarios, showcasing its efficacy. • Semi-supervised model training utilizes unlabeled process data. • Separate networks are crafted for process and quality feature extraction. • The state-space model with the encoder-decoder is used to extract latent features. • A multi-step-ahead prediction learning scheme yields favorable prediction results. [ABSTRACT FROM AUTHOR]

The pivotal factor to regulate and enhance within an operating batch is the quality process, a challenging variable to monitor online. Soft sensors offer an immediate alternative for providing real-time insights into process quality, yet persisting issues include the imbalance between process and quality measurements, noisy measurements, and the intricate 3-dimensional dynamic batch data structure. This paper introduces the Robust Semi-Supervised Dual-Attention Latent Dynamic Conditional State-Space Model (RS2DA-LDCSSM) to address these challenges for within-batch quality prediction. Given the frequent absence of quality data due to measurement inconveniences, an imputation network is embedded within the RS2DA-LDCSSM to facilitate the prediction of future quality. To prevent information distortion during data unfolding, the Attentional Sequence-to-Sequence RNN Encoder-Decoder (AS2S-RNNED) is employed to process the 3-dimensional batch data. The proposed method integrates AS2S-RNNED with a probability state-space model to filter out noisy process data and stabilize the probability prediction of quality data, extracting spatial and temporal latent data from past process and quality data while minimizing the loss in multi-step prediction. This work represents a novel approach to dynamic nonlinear batch processes through probabilistic semi-supervised learning. The RS2DA-LDCSSM is adaptable to any batch process for within-batch quality prediction, as evidenced by numerical cases demonstrating its reliability, achieving an R2 value of 0.87, surpassing comparison methods. In an industrial penicillin fermentation batch process, the RS2DA-LDCSSM exhibits remarkable robustness with a high R2 index value of 0.99 in practical quality prediction scenarios, showcasing its efficacy. • Semi-supervised model training utilizes unlabeled process data. • Separate networks are crafted for process and quality feature extraction. • The state-space model with the encoder-decoder is used to extract latent features. • A multi-step-ahead prediction learning scheme yields favorable prediction results. [ABSTRACT FROM AUTHOR]