Timely and reliable estimation of Ferrous Oxide (FeO) in sintered ore is increasingly critical for blast furnace control under tightening energy and emission constraints. Offline chemical assays incur substantial delays and high costs, depriving operators of the rapid feedback needed for timely set-point correction. Meanwhile, the sintering process is strongly nonlinear and heterogeneous across sensing modalities, making single-source soft sensors brittle in production. To address this, we present a multimodal fusion Transformer for online FeO soft sensing that couples mechanistic models with data-driven learning: thermodynamic state variables from a temperature-field model are fused with process time series at the data level to inject physics-informed context, and a dual-stream encoder performs deep fusion of time series and image sequences via cross-attention to achieve fine-grained temporal–spatial alignment. Experimental results on a real-world sintering dataset demonstrate that the proposed model significantly outperforms baseline methods in terms of RMSE and R2. Furthermore, the fusion strategy generalizes to stronger Transformer backbones, indicating architectural portability and robustness. The results highlight that incorporating domain knowledge with attention-based multimodal fusion is an effective route to industrial soft sensing under real-world constraints.

Modern industrial plants generally demonstrate the characteristics of large scale, long process, and multiunit collaborative operation, which makes the spatio-temporal distribution an inherent nature, and the quality stability is usually hard to be guaranteed. A quality-related spatio-temporal information analytics based multiunit synergetic monitoring framework is presented in this paper. In this framework, the spatio-temporal properties are analyzed from the unit level and the process level, respectively. Firstly, for each operation unit, the quality supervised spatio-temporal support region is constructed with a concurrent feature extraction strategy. In this strategy, temporal dynamic features are extracted by a long short term memory (LSTM) network with attention mechanism. Concurrently, the spatial feature is extracted with the mutual information-kernel principal component analysis approach. Secondly, for the plant-wide process, a third order multiunit-spatio-temporal feature tensor is constructed for feature fusions. Via tensor decomposition, the interconnected associations among units and the quality inheritance along the process are explored, and the original feature space is decomposed into several subspaces. Finally, a multiunit synergetic monitoring model is developed over subspaces and the comprehensive monitoring results are given by Bayesian fusion. Reasonable interpretations can be provided in the monitoring results. The effectiveness of the proposed framework is verified on a real hot strip mill process.Note to Practitioners—This paper intends to provide a spatio-temporal information analytics and fusion framework for multiunit processes and to develop a quality-related process monitoring method for industrial plants. Different from the existing works, the monitoring model built in this paper is based on the multiunit-spatio-temporal sensitive information, which is extracted by a concurrent strategy and fused by the tensor model. In addition, the quality inheritance among multiunits is considered in this framework and the monitoring results in each subspace can provide helpful instructions for the field technicians. In detail, the fault-relevant unit can be located by the relatively independent subspace monitoring, and the quality-related anomaly propagation tendency can be indicated by the strong associative subspace monitoring.

Anomaly detection is a cornerstone of industrial safety, enabling real-time monitoring of process operations by identifying deviations from normal conditions through statistical analysis. In real-world industrial scenarios, the nonstationary properties of multivariate time-series data present a common and substantial challenge. Existing methods for extracting stationary sources $(\mathcal {SS}s)$ mainly rely on weak stationarity (i.e., mean and variance), but their performance is limited by the long-tailed distributions common in industrial datasets. Higher-order moments, in contrast, provide a more comprehensive statistical description, capturing complex data characteristics that the mean and variance overlook. To bridge this significant gap, we propose a continuous stationary moment analysis (Co-SMA) anomaly detection framework. Its core innovation is the SMA algorithm, which introduces a novel objective function to minimize cumulative sum of the differences in multiorder moments between each epoch and the overall data, effectively fulfilling the $\mathcal {SS}$ estimation task. Furthermore, to overcome the inefficiencies of traditional model updating methods, we develop an event-triggered model updating framework based on the model bias index and first-order perturbation theory. Within this framework, we introduce a convex hull coverage metric, which enables the model to be adjusted efficiently according to the data distribution drift. The framework also incorporates iterative refinement of detection statistics and thresholds, establishing a dynamic adjustment mechanism that ensures optimal performance across diverse operating conditions. The theoretical basis of Co-SMA's properties is rigorously established. Experimental evaluations on numerical simulations and real-world datasets from the ironmaking process demonstrate Co-SMA's superior capabilities in $\mathcal {SS}$ estimation and anomaly detection.

Broad learning system (BLS), a tri-layer feedforward neural network, has gained widespread recognition for its exceptional scalability and computational efficiency. However, BLS and its derivatives encounter several challenges: 1) overlooking the uncertainty introduced by numerous nonlinear random mappings; 2) failing to cope with the misalignment of model inputs with the output sampling rate; 3) lack of attention to nonstationary scenarios; and 4) absence of theoretical optimization for incremental learning. To overcome these obstacles, we propose a regression modeling and anomaly detection scheme rooted in a temporal kernel stationary BLS (TKS-BLS). We first create a nonlinear kernel broad representation (NKBR) extraction strategy, providing a robust nonlinear foundation for random feature mapping via kernel technology. Following this, we probe the mechanism of temporal matching between model inputs and outputs through a temporal alignment parameter, interpretable under a latent variable relationship. In the integration phase, we establish a Kullback-Leibler divergence objective function to facilitate the capture of stationary relationships within time-series data, in conjunction with the regression error. Subsequently, a double-loop parameter optimization algorithm and an independent incremental learning mechanism are put forth, both backed by comprehensive theoretical analyses. Our method’s superiority is thoroughly confirmed by experimental outcomes from extensive case studies across seven real ironmaking process datasets.

This study explores linear encryption techniques to protect against information-based stealthy attacks on re-mote state estimation. Utilizing smart sensors equipped with local Kalman filters, the system transmits innovations rather than raw measurements via wireless networks. However, this transmission is susceptible to malicious data interception and manipulation by attackers. To safeguard against these stealthy threats, encryption and decryption modules are integrated into the system. This research aims to assess the effectiveness of the encryption strategy when faced with information-based stealthy attacks. A key contribution of this paper is the adoption of the most comprehensive attack models, moving away from the conventional reliance on innovation-based linear attack models. Our results demonstrate that the proposed linear encryption approach effectively mitigates stealthy attacks under certain mild conditions. The efficacy of the encryption is further validated through numerical examples, corroborating the theoretical advancements presented in this paper.

In this article, a novel time-constrained global and local nonlinear analytic stationary subspace analysis (Tc-GLNASSA) is proposed to enhance blast furnace ironmaking process (BFIP) monitoring. Although the existing analytic stationary subspace analysis method has been available for deriving process consistent relationships. However, the presence of complex nonlinear, periodic nonstationary, and time-varying smelting conditions renders the satisfactory estimation of stationary projections unattainable. To this end, we leverage multiple kernel functions and manifold learning methods to establish a global and local nonlinear structure with time constraints, which will identify the unique nonlinearities excited by periodic nonstationarity. Meanwhile, a singular value decomposition-based modeling efficiency promotion strategy is constructed to reduce the proposed Tc-GLNASSA's computational complexity significantly. The orthogonality of model update scheme is analyzed theoretically, and an overall BFIP monitoring framework is given. Ultimately, practical BFIP case studies fully demonstrate the effectiveness of our proposal.

As the infrastructure industry continues to evolve toward digitalization, ongoing development of spatial and temporal data-based intelligent sensing guarantees safe operation. However, blast furnace ironmaking processes (BFIP) encounter a tricky dilemma in this revolution. Data-driven multivariate statistical analysis always fails for expected diagnosis performance due to complex dynamic, nonlinear, and nonstationary characteristics. To address this issue, we propose a novel method named modified mixed kernel-aided canonical stationary variate analysis (M2KCSVA). To start with, the past and future matrices and multiview nonlinear mapping of mixed kernel are properly considered to explore canonical stationary variables (CSVs) for both temporal correlation and weak stationarity. Especially, efficiency improvement procedures based on singular value decomposition and iterative modeling flow are deployed to reduce the computational cost and estimate accurate CSVs. In addition, we retain the smooth information without autocorrelation in the residuals for further analysis using stationary subspace analysis to generate static stationary variables. The corresponding two statistics and exponential difference contributions are computed for simultaneous fault detection and identification with an intuitive interpretation of dynamic and static stationary information. Experiments through an actual BFIP demonstrate that M2KCSVA surpasses comparison methods in terms of efficiency and accuracy.

For some practical industrial systems or components, such as blast furnaces and Li-ion batteries, there are two important factors to model the degradation processes. One is the long-range dependence, which can reflect the non-Markovian nature of the degradation processes. The other factor is the existence of multiple modes, because the operating conditions and external environments inevitably change during the whole lifetime of these systems. In this paper, we first propose a fractional Brownian motion (FBM) based degradation model with long-range dependence and multiple modes, and then consider the prediction of remaining useful life. To identify the multiple modes in the degradation process, we propose a two-step method, including change-points detection and linear segments clustering. In each degradation mode, the degradation rate is assumed to be normally distributed. The means and variances of these distributions can be obtained by the maximum likelihood estimation. To describe the switching between different modes, the continuous-time Markov chain is applied, and its transition rate matrix can be estimated by the historical switching time. An approximation of the first passage time with a predefined threshold can be obtained by a weak convergence theorem and a time-space transformation. A numerical simulation and a practical case of a blast furnace wall are provided to demonstrate the effectiveness of the proposed method.

A prerequisite for the existing remaining useful life prediction methods based on stochastic processes is the assumption of independent increments. However, this is in sharp contrast to some practical systems including batteries and blast furnace walls, in which the degradation processes have the property of long-range dependence. Based on the fractional Brownian motion, we adopt a degradation process with long-range dependence to predict the remaining useful life of the above systems. Because the degradation process with long-range dependence is neither a Markovian process nor a semimartingale, the exact analytical first passage time is difficult to derive directly. To address this problem, a weak convergence theorem is first adopted to approximately transform a fractional Brownian motion-based degradation process into a Brownian motion-based one with a time-varying coefficient. Then, with a space-time transformation, the first passage time of the degradation process with long-range dependence can be obtained in a closed form. Unknown parameters in the degradation model can be identified using discrete dyadic wavelet transform and maximum likelihood estimation. Numerical simulations and a practical example of a blast furnace wall are given to verify the effectiveness of the proposed method.