To deal with the highly nonlinear and time-varying characteristics of Batch Process, a model named adaptive stacking approximate kernel based broad learning system is proposed in this paper. This model innovatively introduces the approximate kernel based broad learning system (AKBLS) algorithm and the Adaptive Stacking framework, giving it strong nonlinear fitting ability, excellent generalization ability, and adaptive ability. The Broad Learning System (BLS) is known for its shorter training time for effective nonlinear processing, but the uncertainty brought by its double random mapping results in poor resistance to noisy data and unpredictable impact on performance. To address this issue, this paper proposes an AKBLS algorithm that reduces uncertainty, eliminates redundant features, and improves prediction accuracy by projecting feature nodes into the kernel space. It also significantly reduces the computation time of the kernel matrix by searching for approximate kernels to enhance its ability in industrial online applications. Extensive comparative experiments on various public datasets of different sizes validate this. The Adaptive Stacking framework utilizes the Stacking ensemble learning method, which integrates predictions from multiple AKBLS models using a meta-learner to improve generalization. Additionally, by employing the moving window method—where a fixed-length window slides through the database over time—the model gains adaptive ability, allowing it to better respond to gradual changes in industrial Batch Process. Experiments on a substantial dataset of penicillin simulations demonstrate that the proposed model significantly improves predictive accuracy compared to other common algorithms.

Aiming at the lack of reliable gradual fault detection and abnormal condition alarm and evaluation ability in the plasticizing process of single-base gun propellant, a fault detection and diagnosis method based on normalized mutual information weighted multiway principal component analysis (NMI-WMPCA) under limited batch samples modelling was proposed. In this method, the differences of coupling correlation among multi-dimensional process variables and the coupling characteristics of linear and nonlinear relationships in the process are considered. NMI-WMPCA utilizes the generalization ability of a multi-model to establish an accurate fault detection model in limited batch samples, and adopts fault diagnosis methods based on a multi-model SPE statistic contribution plot to identify the fault source. The experimental results demonstrate that the proposed method is effective, which can realize the rapid detection and diagnosis of multiple faults in the plasticizing process.

Single-step tightening is simple and fast compared to multi-step tightening, and it is therefore frequently used during the tightening of bolts in flange structures. However, single-step tightening to maintain uniformity is more difficult to achieve. To address this problem, existing methods such as the Elastic Interaction Coefficient Method (EICM) and Tetraparametric Assembly Method (TAM) have been investigated for load uniformity in single-step tightening. In order to improve the computational efficiency and accuracy of the traditional methods, a new single-step tightening method is proposed in this paper. This method can realize the design of the initial preload force simply by measuring the change in bolt load in a specific sequence. It is verified by numerical simulation that this method can realize the uniform distribution of bolt load. In addition, this paper will provide suggestions for the optimal tightening sequence for the single-step tightening method.

In industrial processes, accurate quality prediction is essential for optimizing operations and ensuring product consistency. However, the inherent complexity of industrial processes typically involves a large number of monitoring variables, accompanied by significant challenges such as high nonlinearity and data redundancy. To address this issue, this article proposes the broad learning system combined with feature-weighted stacked target-related Laplacian autoencoder (BLS-FW-STLapAE). The proposed model innovatively incorporates hidden-layer features extracted by the stacked target-related Laplacian autoencoder (STLapAE) into the feature nodes of the broad learning system (BLS). This approach addresses the issue of insufficient feature extraction caused by random mapping in BLS. This integration enables the model to capture both local geometric structures and key target-related features, significantly enhancing predictive performance in complex industrial environments. In addition, mutual information (MI) is introduced in STLapAE to evaluate the correlation between features and the target variable, further improving the model’s ability to capture relevant information about the target variable and ensuring that all relevant information is effectively utilized. Finally, the feasibility and practical value of the proposed algorithm were validated on benchmark public datasets and two real-world industrial applications: penicillin fermentation and solid propellant manufacturing. The superior predictive performance demonstrated across these tests enables operators to proactively adjust process parameters and prevent quality deviations, thereby significantly improving production safety and reducing operational costs in such high-risk chemical engineering domains.

The core quality data, such as interior ballistic performance, are seriously unbalanced in the plasticizing and molding process, which makes it difficult for traditional supervised learning methods to accurately predict this kind of index. A Tri-training weighted ensemble JITL-RVM model based on an integrated confidence evaluation strategy is proposed to solve the above problem. The method is based on Tri-training semi-supervised regression architecture and uses both labeled and unlabeled data for modeling. First of all, the traditional single similarity measure method is difficult to use to evaluate the real similarity between data samples reliably and stably. This method realizes diversity enhancement and data expansion of the data set for modelling through ensemble just-in-time modelling based on three homologous and heterogeneous mixed similarity measures. Secondly, a new integrated confidence evaluation strategy is used to select the unlabeled samples, and the pseudo-labeled data, which can improve the prediction performance of the model, can be selected. To improve the prediction effect of the model, the pseudo-label value of the data is revised continuously. The integrated confidence evaluation strategy can overcome many shortcomings of the traditional confidence evaluation method based on Co-training regression (Coreg). Finally, the final quality prediction value is obtained through weighted integration fusion, which reflects the difference between different models and further improves the prediction accuracy. The experimental results of interior ballistic performance prediction of single-base gun propellant show the effectiveness and superiority of the proposed method, and it can improve the RMSE, R², and PHR to 0.8074, 0.9644, and 93.3%, respectively.