Froth flotation is a critical mineral processing technique for separating and recovering valuable minerals from ore. To provide guidance for flotation process control, monitoring models must continuously adapt to unpredictable feed fluctuations. However, traditional computer vision methods struggle with data distribution shifts caused by varying feed conditions, leading to severe performance degradation in long-term industrial deployment. This article proposes the continual learning visual sensing network (CLVS), a framework that continuously updates sensing models from streaming industrial data while mitigating catastrophic forgetting. CLVS incorporates two key innovations: 1) A froth visual Transformer developed according to froth formation principles, which explicitly models cluster motion patterns across frames to improve representation robustness under varying feed conditions; and 2) a memory-attention-distillation-based continual learning strategy that exploits memory attention for rehearsal sample selection and knowledge transfer, enabling stable continual adaptation without relying on class-probability-based dark knowledge. Experiments on an industrial lead-zinc flotation dataset containing 32 971 input-output pairs across four distribution shifts demonstrate that CLVS consistently outperforms six state-of-the-art continual learning methods, achieving up to 14.04%, 20.51%, and 7.90% improvements in average R2 accuracy for Zn, Pb, and Fe tailing grade estimation, respectively. These results demonstrate the effectiveness of CLVS in maintaining reliable monitoring performance under nonstationary conditions, highlighting its practical potential for real-time industrial flotation monitoring.

Froth flotation is a widely used mineral beneficiation technique, where effective process monitoring is essential for optimizing mineral separation. However, in practical industry, manual labeling suffers from noises, leading to a significant portion of incorrectly labeled data. Though deep learning monitoring models are powerful in capturing complex visual patterns, their high capacity makes them vulnerable to overfitting noisy labels, hindering robust model development. To address this challenge, this study proposes a noise-robust contrastive ensemble learning method for practical industrial process monitoring. The method first constructs multiple diverse monitoring models in distinct representation spaces using a novel disparity contrastive learning strategy. Then, clean and mislabeled data for each sub-model are distinguished by measuring the inter-model consensus and intra-model uncertainty of its peer models. Finally, a structure-consistency-based semi-supervised learning strategy is proposed to refine these sub-models by treating mislabeled data as unlabeled, encouraging representation-aligned predictions through mutual information maximization. Through iterative noisy-label identification and semi-supervised refinement, robust monitoring model are obtained even with heavily corrupted training data. Extensive experiments on industrial froth flotation data demonstrate the effectiveness and advantages of the proposed method compared to existing state-of-the-art noise-robust learning techniques.

Froth flotation is an important mineral processing technique for separating and recovering valuable minerals from ore. However, developing image-based monitoring models for industrial flotation is hindered by the high cost and scarcity of labeled data. To overcome this challenge, we propose a memory-network-based data-efficient framework for predicting key performance indicator (KPI) in flotation monitoring. Our approach integrates two key innovations: 1) a novel froth image representation model that captures both macroscopic visual patterns of the froth layer and correlations among localized froth patterns across the image and 2) a hybrid self-supervised and semi-supervised learning strategy that leverages the short-term stationarity (STS) of flotation processes for label-free pretraining, followed by memory attention distillation (MAD) to refine predictions using limited labeled data. Experiments on an industrial flotation dataset comprising 32 971 input-output pairs demonstrate that our method surpasses state-of-the-art semi-supervised regression techniques by 7.97% in R-squared accuracy and achieves performance comparable to fully supervised models while using 80% fewer labeled samples.

Froth flotation is a widely employed mineral beneficiation technique, and effective process monitoring is critical for optimizing mineral separation. However, in the industrial process, labeling froth images to create large labeled datasets is both expensive and time-consuming. Semi-supervised deep learning offers a promising solution, but leveraging unlabeled data remains a significant challenge. To this aim, we propose an uncertainty-aware semi-supervised contrastive learning method. Our approach employs a pseudo-labeling module with dropout to generate pseudo labels and estimate uncertainty. Based on the uncertainty scores, the pseudo-labeled data are split into reliable and unreliable sets. A semi-supervised contrastive learning module is developed to exploit pseudo-label information and learn class-aware representations from the reliable set. Additionally, a dynamically weighted consistency learning module is introduced to explore potential classification information in the unreliable data while preventing the model from being misled by low-confidence predictions. Comparison experiments on industrial zinc flotation data show our method achieves 88.12% classification accuracy, surpassing the best alternative by a margin of 5.11%. These results demonstrate that our method generalizes well to unseen test data and outperforms state-of-the-art methods.

A novel dynamic inner manifold learning algorithm based on forward selection component variables (FSV-DiML) is proposed for industrial process monitoring. The method begins with forward selection component analysis (FSCA) to select monitoring variables, effectively removing redundancies while preserving critical information. DiML is then used to construct a new objective function designed to extract dynamic latent variables (DLVs) with manifold structures from high-dimensional and nonlinear data. This approach enables the separation of process data into dynamic and static subspaces. However, since high-dimensional data often contain low-dimensional manifold structures, neighborhood preserving embedding (NPE) is applied to reduce the dimensionality of each subspace while preserving its manifold structure. Finally, Bayesian inference and fusion techniques are employed to merge various monitoring statistics into a unified monitoring index, further improving fault detection performance. The proposed FSV-DiML model is validated on the Tennessee Eastman (TE) and multiphase flow facility processes, demonstrating significant improvements over existing methods in accurately detecting faults in complex industrial processes.

Temperature prediction in the tin chemical process (TCP) is crucial for implementing production process monitoring and predictive control. However, TCP’s discrete-continuous hybrid structure, incorporating both binary and continuous variables, poses challenges for traditional prediction models. To overcome these limitations, this study introduces a TCP temperature prediction approach using a trapezoidal rule (TR) and improved stochastic configuration networks (TR-ISCNs). First, the TR transforms discrete variables into continuous forms. Next, the continuous data are used to train improved stochastic configuration networks (ISCNs) to develop a temperature prediction model. Finally, a TR-ISCNs-based model update framework is implemented, enabling the prediction model to leverage recent window data for real-time parameter updates and temperature forecasts as new data becomes available. The proposed method’s effectiveness is demonstrated through application in a real TCP.

Probabilistic Principal Component Analysis (PPCA) is widely used in process monitoring. However, its underlying assumption that data follows a Gaussian distribution limits its effectiveness in handling Low Probability Events (LPEs), which often deviate from this assumption. To address this challenge, we propose a novel method called Sparse Filtering-based Improved Mixed-Gaussian Probabilistic Principal Component Analysis (SFIMPPCA) for enhanced LPEs detection. First, a Sparse Filtering (SF) preprocessing technique with an incremental structure is employed to extract the most discriminative features. Second, to address the distortion caused by LPEs, a dynamic ratio correction mechanism based on statistical variability is introduced, followed by a newly designed Mixed-Gaussian Probabilistic Principal Component Analysis (MPPCA). Third, a Bayesian Optimization Algorithm (BOA) is applied to automatically adjust control limits, enhancing the accuracy and reliability of fault detection. The effectiveness of the proposed method is validated using the Tennessee Eastman (TE) process and the Tin Chemical Process (TCP). Experimental results demonstrate that the proposed method significantly improves performance under LPEs conditions, achieving a 10%-12% improvement in most cases.

In dynamic industrial environments, effective soft-sensing methods need adapt to real-time variations in process conditions. Though recent efforts have integrated deep learning and handcrafted features to design hybrid feature methods while reducing reliance on diverse training data, existing approaches often rely on fixed fusion strategies, limiting their adaptability. In this study, we propose a sentinel-based adaptive hybrid soft sensing (SAHSS) method, which dynamically shifts between deep learning and handcrafted features to enhance representation adaptability under changing conditions. The sensing model consists of a deep learning monitoring branch, a handcrafted monitoring branch, and a sentinel. The sentinel serves as a decision-making unit that dynamically selects between the deep learning and handcrafted branches based on image reconstruction error. To extract sensitive image features for the deep learning branch and evaluate their reliability for the sentinel, we develop a mixup bidirectional adversarial autoencoder (MixBiAAE). This autoencoder leverages feature interpolation to smooth and stabilize the learned latent space, thereby enhancing the invertible relationship between the image encoder and generator. Additionally, to help the hybrid sensing model adapt to fluctuating working conditions, a momentum memory network (MoMN) -based regression module is designed for both branches, allowing incremental updates with new data without retraining the model. Extensive experiments on an industrial flotation dataset demonstrate that our method outperforms existing hybrid soft sensing techniques, offering a robust and adaptive solution for industrial process monitoring.

In complex industrial process monitoring, prevalent challenges include high dimensionality, extensive redundancies, and dynamic characteristics. In this paper, a Multimodal Extended Kalman Filtering–Mixture Probabilistic Principal Component Analyzers (Multi-modal EKF–MPPCA) algorithm is designed to tackle these issues. The proposed approach begins with multimodal data selection via extended Kalman filtering and dynamic lag embedding to enhance variable expressiveness. A feature extraction module then employs a Laplace mixture model to generate modality-specific weighted features, which are projected using PPCA to capture dominant dynamic patterns. Finally, a covariance-based dimensionality reduction framework computes T2 and SPE statistics for comprehensive monitoring of latent deviations and residual anomalies. Verification results on the Tennessee Eastman (TE) process confirm that the multimode EKF–MPPCA algorithm achieves higher fault detection rate and stronger dynamic adaptability compared with the traditional single-mode monitoring method. 1

Multivariate statistical process monitoring has been widely used in industry process. However, traditional algorithms often ignore the complexity dynamic features of actual industry process. This study proposes a novel algorithm based on Approximate Entropy and Slow Feature Analysis (AE-SFA), which has completed the full-condition monitoring of a dynamic complexity system and quantitative divided static components and dynamic components. The algorithm achieves the optimal detection rate under T 2 and SPE control limits. To enrich the experiment, we used the Tennessee Eastman process dataset to demonstrate the superiority of our algorithm. From the comprehensive score of the optimal detection rate, the accuracy of the proposed method is improved by 3.24% and 10.50% of T 2 and SPE statistics, respectively.

Fault detection in industrial processes is essential for enhancing production safety. Despite the application of the neighborhood preserving embedding (NPE) algorithm in fault detection as a manifold learning technique, a notable limitation exists-NPE overlooks local geometric structure, leading to suboptimal fault detection and occasional false alarms. This paper introduces the Gaussian kernel weighted NPE (KW-NPE) algorithm to address this challenge. Specifically designed for precise weight assignment in local structures, KW-NPE strategically employs the Gaussian kernel method to project the spatial neighborhood set and capture comprehensive local structural characteristics. The weight assignment, dependent on feature values, enhances the retention of intrinsic structure during dimensionality reduction. A novel objective function further augments this process.To assess performance, a comprehensive composite index is introduced in a case study, amalgamating the false alarm rate and fault detection rate. The effectiveness of the KW-NPE algorithm is demonstrated through extensive simulations and its application to the Tennessee Eastman process dataset, highlighting its superiority over conventional approaches.

Bearing fault diagnosis is of great significance to the normal operation of machinery, and its performance and life span directly affect the operational efficiency and safety of the whole equipment. For existing image coding methods which detecting the bearing fault with a large number of training samples and complex neural networks to achieve the desired detection performance, the Multiscale Permutation Entropy Gray Image Coding (MPEGIC) method is proposed. In order to fully extract the feature information of the time series signal, this paper uses the Multiscale Permutation Entropy (MPE) method to construct a new image coding method by calculating the alignment information of the time series to reflect the complexity and randomness of the time series at different scales, and dividing the obtained feature matrix and mapping it to the gray-scale image domain. And it is experimentally verified by Case Western Reserve University (CWRU) bearing dataset and self-made rotor experimental platform bearing dataset. The results show that the method in this paper effectively reduces the number of training samples and the number of model parameters, and maintains a better detection performance even in a strong noise background.

Timely and accurate recognition of flotation working conditions plays a crucial role in stabilizing process indicators and formulating production operation strategies. Soft sensing methods based on deep learning allow for automatic learning of features from input froth images directly, and is considered a promising flotation monitoring approach. However, the high demand for a large number of labeled samples severely hinders the application of such methods because acquiring froth videos is easily in flotation plants, but manually adding labels to video frames is often expensive. Therefore, a representation-enhanced semi-supervised learning method for flotation working condition recognition is proposed in this paper. Firstly, based on the consistency assumption, a student-teacher network is developed. It leverages massive unlabeled froth image data by ensuring the consistency of model outputs under variations in the input space. Secondly, to guide the student-teacher network learn class-aware cluster representation from unlabeled data, a novel prototypical contrastive learning method with hard negative mixing is proposed. Comparative and ablation experiments on industrial flotation dataset show the effectiveness of the proposed method.

Froth flotation is a widely used beneficiation method in mineral processing. Accurate grade monitoring is crucial for efficient minerals separation. However, despite recent developments highlighting the potential of deep learning in flotation monitoring, these methods face limitations in application due to the lack of reliable feature extraction and the scarcity of large datasets related to target task. To address these issues, we propose a self-supervised dynamic and static feature collaborative representation learning method. It extracts the spatiotemporal information from froth videos based on a two-stream convolutional architecture and is trained on a video frame prediction task without labeled data until both appearance and motion constraints are satisfied. Experiments on industrial zinc flotation data demonstrate that the learned representations transfer well to downstream grade monitoring tasks. This approach not only solves the label shortage problem when training large-scale deep learning models but also outperforms the state-of-the-art methods in flotation monitoring.

To address the instability issue caused by time-delay and nonlinear characteristics of intermittent reactions in batch reactors, a temperature control method for batch reactors based on adaptive delay compensation was proposed. By integrating the chemical reaction mechanism inside the reactor with graphical analysis and actual production data, a time-varying second-order delayed transfer function model for the reactor is established. The adaptive rate for controlling the time-varying delayed system is designed based on the control error between the actual controlled object and the nominal model. Furthermore, standard Smith predictor is employed to compensate for the delay in the error term. When applied to temperature control in batch reactors, experimental results demonstrate that this method effectively reduces the temperature control errors caused by time-varying delays, significantly accelerates the convergence speed and diminishes the oscillation amplitude of the temperature curve.

In complex industrial process monitoring, prevalent challenges include high dimensionality, extensive redundancies, and dynamic characteristics. In this paper, we propose an Improved Dynamic Latent Variable-Neighborhood Preserving Embedding (DLV -NPE) algorithm specifically designed to tackle these issues. The methodology begins with the implementation of a variance-covariance feature selection method to minimize redundancies among monitoring variables. This is followed using a dynamic latent variable algorithm to extract dynamic regression properties from the selected variables. Subsequently, the NPE algorithm is employed to preserve the residuals of high-dimensional dynamic latent variables and the high-dimensional residuals of selected variables, thereby preserving the integrity of the low-dimensional manifold structure. Finally, Bayesian inference is applied to develop comprehensive monitoring indicators. The efficacy of the DL V -NPE algorithm is validated through its application to the Tennessee Eastman (TE) process, where it demonstrates superior fault detection capabilities compared to other algorithms.

To ensure the reliability and safety of modern industrial process monitoring, computer vision-based soft measurement has received considerable attention due to its nonintrusive property. State-of-the-art computer vision-based approaches mostly rely on feature embedding from deep neural networks. However, this kind of feature extraction suffers from noise effects and limitation of labeled training instances, leading to unsatisfactory performance in real industrial process monitoring. In this article, we develop a novel hybrid learning framework for feature representation based on knowledge distillation and supervised contrastive learning. First, we attempt to transfer the abundant semantic information in handcrafted features to deep learning feature-based network by knowledge distillation. Then, to enhance the feature discrimination, supervised contrastive learning is proposed to contrast many positive pairs against many negative pairs per anchor. Meanwhile, two important mechanisms, memory queue-based negative sample augmentation and hard negative sampling, are added into the supervised contrastive learning model to assist the proper selection of negative samples. Finally, a flotation process monitoring problem is considered to illustrate and demonstrate the effectiveness of the proposed method.

Computer vision is now being used more frequently to monitor working conditions in various industries. However, labeling data for this purpose can be costly, which often leads to partially labeled datasets. To overcome this issue, there is a growing demand for semisupervised data-driven models that can utilize the abundance of unlabeled data available to improve monitoring performance. While there have been many methods developed to improve data efficiency, there has been limited focus on utilizing information from past iterations to further enhance performance. To this end, a semisupervised contrastive memory network is developed. The network guides embedding functions to map inputs to match its supporting memories learned in past iterations, and a mix-up unsupervised learning strategy, which integrates consistency regularization with mutual information, is designed to enable training of the network with unlabeled data. The experimental results show that the proposed method produces more discriminative representation and is beneficial to semisupervised learning. Notably, on froth flotation process monitoring with Inception-V3 as the backbone, it achieves 90.03% top-1 accuracy with 16% labeled data, which is comparable to the fully supervised method trained with the 100% labeled data, and largely outperforms existing semisupervised methods.

Froth flotation is a vital mineral concentration process. Because of fluctuations in feed conditions of flotation processes, adaptively adjusting the setpoint in computer vision-based flotation reagent control is important to maintain the economic optimum in production. However, due to the high-dimension property of deep learning image features, it may be difficult to calculate a deep learning image feature-based setpoint that can satisfy the kinetic of flotation processes. Different from existing feature-level setpoint calculation methods, this study investigates image-level optimal setpoint calculation, and a generative adversarial network-based setpoint calculation model (SetpointGAN) is developed. Besides the widely used generative adversarial loss, we propose a feature consistency loss to encourage the visual consistency between synthesized setpoints and the ground-truth setpoint, and a feed consistency loss to guarantee the control attainable of calculated setpoints. Compared to feature-level setpoint calculation methods, the results of SetpointGAN can be intuitively evaluated by comparing it to collected real froth images of optimal flotation statuses. Experiments evaluated using real zinc flotation data demonstrate the effectiveness of the proposed SetpointGAN and its advantages over existing works.

Froth flotation is an important mineral concentration technique. Faulty conditions in flotation processes may cause the huge waste of mineral resources and reagents, and consequently, may lead to deterioration in terms of benefits of flotation plants. In this paper, we propose a computer vision-aided fault detection and diagnosis approach for froth flotation. Specifically, a joint Gabor texture feature based on the Copula model is designed to describe froth images; a rejection sampling technique is developed to generate training sets from the quality distribution of real flotation products, and then an isolation forest-based fault detector is learned; and a fault diagnosis model based on spline regression is developed for root cause identification. Simulation experiments conducted on the historical industry data show that the proposed strategy has better performance than the alternative methods. Thereafter, the entire framework has been tested on a lead-zinc flotation plant in China. Experimental results have demonstrated the effectiveness of the proposed method.