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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]

• Common features are extracted from the source domain for the target-scare system. • The extracted feature knowledge in transfer learning avoids information loss. • Semi-supervised mechanism is designed to use the information of unlabeled data. • The designed objective functions enhance step-ahead prediction for target grades. • Dynamic characteristics of processes are represented by latent state-space models. In response to the dynamic demands of the market, this study addresses the challenge of frequent operational adjustments in a production line to accommodate diverse product grades. The resulting scarcity of data in the new operating conditions (target grade) impedes the development of reliable soft-sensor prediction models. A two-step learning method, termed S2-LGMNSSM-TS-T, is proposed. This method employs a semi-supervised latent Gaussian mixture nonlinear state space model (S2-LGMNSSM-TS) trained on both target and source data, providing a dynamic, one-step-ahead predictive soft sensor. To overcome data scarcity in the target grade, insights from the source are utilized. With a Gaussian mixture prior distribution, S2-LGMNSSM-TS identifies dynamic behaviors in both target and source grades. The enhanced S2-LGMNSSM-TS-T configuration focuses on target-grade predictions, leveraging source knowledge and mitigating data scarcity issues. A numerical example and an industrial case study demonstrate the model's effectiveness in improving target-grade predictions through source knowledge utilization. [ABSTRACT FROM AUTHOR]

• Abnormal data are used to augment the deviation of the fault from the normal. • Non-negative information sharing and transferring improve model accuracy. • Normal-relevant common features are extracted and assimilated in one step. • The proposed model is updated by diagnosing a new fault to lift model tenacity. In this new era of Industry 4.0, manufacturers tend to store process data from the entire production, regardless of whether they are "normal" or "faulty" for further data analysis. However, almost all the existing monitoring models are constructed based on normal data instead of abnormal data. In fact, the "normal" and some of the "faulty" data originate from the same production line. Thus, not only the normal data but also the abnormal ones can be used to improve the monitoring performance of conventional monitoring performance by simultaneously sharing and extracting common knowledge. In this paper, a fault assistant Gaussian mixture prior variational autoencoder (FA-GMPVAE) is proposed to perform information sharing and enhance the statistic model for the normal operating region. Unlike an ordinary variational autoencoder (VAE) and an ordinary Gaussian mixture prior variational autoencoder (GMPVAE), the structure of FA-GMPVAE is a combination of a "normal" based VAE network and a "normal-relevant" based GMPVAE (NR-GMPVAE) network. FA-GMPVAE can make the shared information non-negative to prevent information loss because only the normal-relevant common information is shared by the one-step transfer learning procedure. In addition, fault diagnosis of NR-GMPVAE can be flexibly updated with the new type of fault. Correspondingly, the probability density estimates of latent variables and residuals instead of point estimates are then given so that distribution-based monitoring indices of the normal data can be designed and the fault detection decisions can be made opportunely. To show the effectiveness of the proposed method, a numerical and a real industrial example are presented. [ABSTRACT FROM AUTHOR]