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The permeability index (PI) of a blast furnace (BF) is a key indicator of furnace performance, as it reflects the extent of indirect reduction, energy consumption, molten iron quality, and overall production efficiency. Accurate prediction of the PI is essential for ensuring stable and efficient BF performance. Due to the complex multi-time-scale characteristics of different operational parameters, this paper presents a multi-step prediction model based on multi-time-scale analysis to capture their long-term evolution trends. First, the multi-time-scale characteristics of BF operation are analyzed from both the smelting mechanism and data-driven perspectives. According to the characteristics, this paper constructs a single-step prediction model of PI on the long-time-scale, medium-time-scale, and short-time-scale, respectively, and introduces an iterative compensation strategy to extend each single-step model into a multi-step prediction framework, and then fuses the prediction results under the multi-time-scale to obtain the results of the future PI. Finally, the performance evaluation is shown based on actual industrial data, which verifies the significant advantages of the proposed multi-step prediction method based on iterative compensation in terms of accuracy and stability.

With the widespread deployment of intelligent sensors and advances in data storage, large volumes of process data are continuously collected, providing a foundation for developing soft sensors for multi-scale monitoring in complex industrial processes. This paper proposes an enhanced autoencoder-based temporal convolutional soft sensor model for industrial process monitoring, aiming to effectively capture multi-scale features and the dynamic evolution of process data. The proposed filter temporal convolutional network incorporates adaptive filter-response normalization, thereby enhancing multi-scale feature extraction and improving model generalization. Then, a multi-layer filter temporal convolutional autoencoder is developed to enable efficient multi-scale feature extraction and accurate process data reconstruction. Moreover, a multi-scale feature fusion module with a channel attention mechanism is designed to adaptively integrate temporal features and significantly enhance model robustness. Finally, a statistical metric based on reconstruction errors is established, and the Kullback-Leibler divergence is employed to determine control limits for fault detection. The superiority and effectiveness of the proposed method are validated through applications to the wastewater treatment process and the multiphase flow process.

Dynamic latent variable (DLV) models have been widely applied in industrial soft sensing due to their ability to extract features and capture dynamic behavior. However, conventional DLV models are limited to linear feature extraction and perform poorly with nonuniformly sampled data. Thus, this paper proposes a soft sensor for a nonuniform sampling nonlinear dynamic process using irregular-time-interval latent probabilistic predictability embedding supervised deep network (ILPPSDN). First, a prediction regularization term is added to the decoding loss of the target-related autoencoder to model latent temporal dependencies and enhance feature predictability. Furthermore, the internal state derivative in the proposed irregular-time-interval variational recurrent neural network is parameterized by an ordinary differential equation network, integrating hidden-state evolution with state updates. In addition, all network components are jointly optimized through unified training. Then, an ILPPSDN-based soft sensor is developed for nonuniformly sampled nonlinear dynamic processes via pre-training and supervised fine-tuning. Finally, the results indicate that the proposed ILPPSDN can reduce the root mean square error by at least 26.1 %, 21.1 %, and 26.1 % at the uneven sampling ratios of 1/2, 2/3, and 3/4 in the debutanizer column. Correspondingly, in the sulfur recovery unit, these values are 21.1 %, 26.1 %, and 26.1 %. Additionally, in the ablation studies, the proposed method reduced the root mean square error by at least 5 % and 6 % in the two industrial cases, respectively.

The high-speed train power traction system operates for extended periods of time in complex environments with high temperatures and vibrations, making the system susceptible to various types of incipient faults. In addition, coupled with missing sensor data under complex operating conditions, the diagnosis of incipient faults under practical conditions becomes even more challenging. To address the aforementioned issues, this paper proposes an innovative data imputation method that combines kernel functions with the modified Akima (Makima) interpolation algorithm. This method can effectively address the scenario of a large number of sensor signals continuously missing in high-speed train traction systems. Expanding on this, a real-time incipient fault diagnosis framework is proposed, which combines Deep-Principal Component Analysis (Deep-PCA) with Multi-scale Principal Component Analysis (MSPCA). This framework enhances the capability to extract fault features from both horizontal and vertical perspectives, thereby improving the accuracy of fault detection. Furthermore, the continuous wavelet transform (CWT) is employed to amplify fault-related information within the dataset. This enhanced dataset, combined with a fault isolation criterion based on the reconstructed cumulative contribution rate, enables the achievement of precise fault isolation.

Anomaly detection of converter valves via acoustic analysis has been a hot topic in the high-voltage direct current research field. However, several factors have significantly hindered the practical deployment of such acoustic anomaly detection methods, including the infrequency of valve anomalies leading to imbalanced distributions of acoustic samples, limitations in computational resources, and inherent class imbalance in acoustic signals. To address these challenges, this paper proposes a novel unsupervised anomaly detection framework, named lightweight transformer-based generative adversarial networks (LT-GAN). It introduces two lightweight modules, MobileNet V2 and D-MobileNet V2, to perform downsampling and upsampling of Mel-spectrograms derived from acoustic signals. Furthermore, it incorporates a K-ViT block to enhance global representation learning of spectral images and reduce network parameters. Experiments on real-world acoustic datasets show the superiority of the proposed LT-GAN, which achieves an AUC of 0.9806 on the ROC curve, significantly outperforming baseline methods. In the low false-positive regions [0, 0.1], [0, 0.2], and [0, 0.3], the p-AUCs reach 0.9295, 0.9122, and 0.9559, respectively. Moreover, LT-GAN exhibits exceptional lightweight characteristics, with model complexity metrics of 9.626 million parameters, 0.506 GFLOPs, and a model size of 37.48 MB. These results validate the effectiveness of the proposed approach in terms of anomaly detection performance and resource efficiency.

In recent years, deep learning techniques have been increasingly adopted in soft sensor modeling, with the transformer architecture demonstrating notable advantages not only in natural language processing and image analysis but also in time-series modeling. Autoencoders, known for their ability to learn compact representations of process data, have also been widely applied for feature extraction in soft sensors. However, when dealing with multivariate process data, conventional autoencoder-based models often suffer from underfitting due to persistent reconstruction errors or overfitting when the reconstruction loss converges prematurely. These issues hinder effective feature learning and limit the model's generalization capability in real-world applications. To address these challenges, this paper proposes Resformer, a novel transformer-based architecture that incorporates residual feature compensation. Resformer employs a two-stage autoencoding structure to extract both primary and secondary features and fuses them via a cross-attention mechanism to enhance representation completeness. Time tokens are used as the basic modeling units to capture spatiotemporal dependencies among process variables, which are then mapped to the target quality variable through a dedicated decoding structure. Experimental results on the Tennessee Eastman (TE) process and an industrial alkylation process dataset demonstrate that Resformer, with residual compensation and spatiotemporal feature learning, significantly outperforms recent transformer-based variants while maintaining comparable architectural complexity suitable for practical deployment.

Satellites are vital for communication and navigation, yet delayed or incomplete telemetry data hinder the evaluation of degradation processes and system reliability. As the core of satellite power systems, lithium batteries ensure operational stability. This study focuses on lithium batteries in low Earth orbit satellites and addresses telemetry delay-induced data loss. A data recovery method, termed the FAST Model, based on feature acquisition and short-sequence prediction, is proposed. The method effectively captures degradation trends and capacity fluctuations, including regeneration effects, with minimal data. In the satellite battery dataset with approximately 70 % missing data, the proposed model reduces recovery errors by more than 50 % compared with existing methods. Furthermore, the data recovered by the FAST Model enables more accurate estimation of the remaining useful life of batteries. Under the same prediction framework, the use of FAST-recovered data leads to a reduction of prediction errors by about 5 %-30 %, as evaluated by metrics such as MAE and RMSE, compared with other recovery approaches.

Climate change mitigation necessitates significant reductions in carbon emissions from traditional refining industries. However, accurately attributing renewable bio-feedstock contributions to CO₂ emissions in refinery co-processing remains challenging due to dynamic feedstock variability and complex nonlinear process interactions. Existing static and linear methodologies inadequately address these real-time adaptive demands and intricate nonlinearities. To overcome these shortcomings, we propose a hybrid adaptive modeling framework integrating constrained Recursive Least Squares (RLS) with sparse Generalized Additive Models (GAM), complemented by conformal prediction for uncertainty quantification. Our method adaptively tracks feedstock contributions, ensures physical interpretability through non-negativity constraints. Validated on an industrial dataset of over 86,000 samples, the proposed framework achieves superior predictive accuracy (RMSE: 345.4, R²: 0.950), outperforming 15 baseline methods. More importantly, it delivers interpretable and uncertainty-aware estimates of renewable CO₂ emissions in real time, establishing a practical pathway for transparent and data-driven refinery decarbonization.

The air quality monitoring system (AQMS) has attracted considerable attention due to its environmental significance and impact on human health. AQMS are critical for facilitating early-warning mechanisms to implement policies and protect urban communities. However, existing frameworks rely on physical sensors compromised by degradation, leading to unreliable decision-making. To overcome this limitation, this study introduces a region-wide soft sensor validation using a memory-integrated graph convolutional autoencoder (LSTM-GCN-AE). Results indicate that the relevance-embedded LSTM-GCN-AE outperforms the traditional GCN, achieving a 43.4 % improvement in reconstruction accuracy under precision faults and a 50.2 % enhancement in imputation performance for PM_2.5 sensor, identified through interpretability analysis of relevant nodes in the GCN. Moreover, the proposed framework successfully maintained consistency between predicted and actual environmental conditions, thereby enhancing the reliability of real-time AQMS data, health risk assessment, and early-warning mechanisms for urban air quality management.

In industrial process monitoring, factors such as production schedule changes, equipment aging, and environmental disturbances often lead to shifts in the underlying data distribution. These distributional changes tend to increase false alarm rates and undermine the reliability and adaptability of traditional fault detection methods, thereby compromising the safe and stable operation of industrial facilities. To address these critical challenges, a lifelong fault detection strategy that integrates a Kolmogorov-Arnold Network (KAN) with a novel test-time training (TTT) mechanism is proposed in this paper. Unlike conventional hybrid models, the proposed method introduces a new adaptation framework, in which reconstruction errors dynamically guide selective parameter updates. This allows the model to continuously adapt to distributional shifts without requiring retraining or labeled target data. During online test operation, the model automatically refines its hidden representations using trusted normal samples through a lightweight online update mechanism, thereby improving generalization and robustness under nonstationary conditions. Comprehensive experiments on a widely recognised benchmark dataset from the chemical industry demonstrate that the proposed method significantly outperforms existing state-of-the-art approaches, achieving 92.7 % correct monitoring rate with 0 % false alarm rate under nonstationary conditions.