Time series forecasting is essential across diverse domains. While MLP-based methods have gained attention for achieving Transformer-comparable performance with fewer parameters and better robustness, they face critical limitations including loss of weak seasonal signals, capacity constraints in weight-sharing MLPs, and insufficient channel fusion in channel-independent strategies. To address these challenges, we propose MDMLP-EIA (Multi-domain Dynamic MLPs with Energy Invariant Attention) with three key innovations. First, we develop an adaptive fused dual-domain seasonal MLP that categorizes seasonal signals into strong and weak components. It employs an adaptive zero-initialized channel fusion strategy to minimize noise interference while effectively integrating predictions. Second, we introduce an energy invariant attention mechanism that adaptively focuses on different feature channels within trend and seasonal predictions across time steps. This mechanism maintains constant total signal energy to align with the decomposition-prediction-reconstruction framework and enhance robustness against disturbances. Third, we propose a dynamic capacity adjustment mechanism for channel-independent MLPs. This mechanism scales neuron count with the square root of channel count, ensuring sufficient capacity as channels increase. Extensive experiments across nine benchmark datasets demonstrate that MDMLP-EIA achieves state-of-the-art performance in both prediction accuracy and computational efficiency.

Froth flotation is a complex industrial process involving multicell cascades. During the froth flotation process, a single-cell fault not only compromises its own functionality but may also propagate to adjacent cells, ultimately affecting the entire production line. Therefore, accurate and timely recognition of fault traces in the flotation process is critical for ensuring production stability. In this article, we propose a novel fault trace recognition framework using a dynamic edge weight-based cross-cell interaction graph Transformer and joint task learning. Initially, we propose a dynamic edge weighting method to update multicell node features, enhancing the model’s adaptability to dynamic industrial scenarios. Then, we introduce a cross-cell attention mechanism to decode the fault propagation path, explicitly capturing interaction-aware state features among multiple cells. Furthermore, we employ a two-stage joint task learning scheme, progressing from fault interval prediction to fault trace recognition, thereby significantly improving efficiency and accuracy. Finally, extensive experiments conducted on both benchmark datasets and real-world froth flotation processes demonstrate the effectiveness and robustness of the proposed method.

Accurate camera calibration is essential for obtaining precise three-dimensional information of a target. However, in the froth flotation process, it is challenging to position the calibration board support surfaces correctly. This difficulty makes it hard to capture high-quality calibration images from various angles, ultimately impacting the accuracy of the calibration results. To address this issue, we propose a planar template camera calibration method based on convolutional neural networks and synthetic data augmentation. Initially, we establish a virtual imaging scene to map the relationship between the feature map and camera parameters. Then, we conduct coarse camera calibration and apply synthetic data augmentation within specific range constraints to create a comprehensive calibration dataset. After that, we develop a deep calibration network named FSC-McCNN to facilitate the correspondence between the calibration feature map and camera parameters. This network comprises feature spatial coding (FSC) and multichannel convolutional neural networks (McCNN). The proposed approach effectively compensates for changes in camera focal length and requires only a single calibration image, thereby reducing the calibration workload at flotation sites. Experiments conducted on synthetic and real flotation datasets demonstrate the effectiveness and robustness of the proposed method.

In industrial scenarios, noise interference and feature overlap often result in blurred classification boundaries, compromising the reliability of rolling bearing fault diagnosis. An adaptive distribution-aware discriminative loss (ADADL) is introduced, through which intraclass thresholds are dynamically adjusted and interclass boundaries are optimized, thereby enhancing compactness and separability in the feature space. By integrating it with the cross-entropy loss, ADADL yields marked gains in diagnostic accuracy on both the Case Western Reserve University benchmark and real-world datasets, particularly under conditions of class imbalance and high noise. Visualization analyses further confirm its ability to sharpen clustering boundaries, suppress feature overlap, and effectively mitigate blurred decision regions.

Accurately forecasting the short-term traction load of railways is of great significance for optimizing the operation and dispatching of railway departments and ensuring the safety of power grids. The strong volatility and randomness of railway load signals make it difficult for traditional short-term load forecasting models to achieve high-precision predictions. To this end, this paper proposes a hybrid deep learning model with high temporal resolution characteristics to improve the accuracy of railway load forecasting. Variational mode decomposition (VMD) is used to decompose the original load sequence to reduce its volatility and forecasting difficulty, and its parameters are optimized by the improved beluga whale optimization (IBWO) algorithm. The Kolomogorov-Arnold Network (KAN) model is used to extract intricate spatial features from load data, aiming to enhance the efficiency and precision of feature extraction. The Informer model is used to extract long-term dependencies of sequences, aiming to improve the shortcomings of traditional methods that are difficult to effectively achieve modeling of ultra long time series. The advantage of the proposed forecasting method is to improve forecasting accuracy while reducing the difficulty of model deployment. The experimental results based on a real dataset from a substation on the Longhai Railway show that the VMD algorithm optimized by IBWO effectively improves the forecasting accuracy of the proposed method. Compared to traditional methods, the KAN model enhances the operational efficiency of the hybrid model. Furthermore, the proposed method significantly outperforms some traditional baseline models and the Transformer model in terms of both forecasting accuracy and operational efficiency.

Reagent addition control performance of zinc first rougher significantly affects the quality of the final product. It is common to control visual features to satisfactory feature setpoints, in order to realize satisfactory reagent addition control. However, existing methods usually use the historical data under the desired production state to generate the feature setpoint, and the historical data under the undesired production state are ignored. Moreover, the number of feed grade categories for feature setpoint generation is settled, and thus the richness of corresponding query rules for presetting the reagent addition rate is limited. In this situation, a reagent addition control strategy with a dual frequent pattern tree (dual FP tree)-based feature setpoint generator and knowledge core-based reagent fine presetting is proposed for zinc first rougher. First, a dual FP tree-based feature setpoint generator with the complementary input is constructed to fully utilize the dataset, where the main tree is designed to construct the knowledge repository and the secondary tree is established for optimization. Second, the optimized knowledge rules are taken as cores to construct an optimal operational pattern base for reagent fine presetting. Then, a designed feedback controller based on a fuzzy logic system with a three-way decision mechanism is explored to adjust reagent addition rates and try to make visual features track prescribed feature setpoints. The ablation results show effectiveness of the dual FP tree-based feature setpoint generator, reagent fine presetting and feedback controller. The comparative experimental results demonstrate the potential of the proposed control strategy. Note to Practitioners—This article is motivated by the problem of reagent addition control in the zinc flotation process. This article focuses on making visual features track prescribed feature setpoints by adjusting reagent addition rates, aiming to achieve the goal of controlling the zinc concentrate grade within its acceptable range. However, two challenges exist for control: the historical data under the desired production state are usually used during feature setpoint generation, while latent process knowledge in the historical data under the undesired production state is ignored; the number of feed grade categories for feature setpoint generation is settled during reagent presetting, which means the richness of corresponding query rules for presetting the reagent addition rate is limited. Therefore, this article suggests a reagent addition control strategy with a dual FP tree-based feature setpoint generator and knowledge core-based reagent fine presetting to address those problems. A suitable feedback controller is designed for outputting reagent addition adjustment values to qualify the concentrate grade, which is based on feature setpoint generation and reagent fine presetting. The experiments are carried out for evaluation. The evaluation shows the potential and superiority of the proposed approach in terms of decision-making and automation control in froth flotation.

In order to integrate the advantages of Model Predictive Control (MPC) and artificial neural networks, this paper proposes a control framework based on sequence generation (SGCF). The main idea of SGCF is to first generate an ideal subsequent state trajectory conditioned on the current working condition, and then infer feasible control sequences accordingly. To achieve implicit optimization of the performance metric during sequence generation, different learning weights are assigned to labeled samples. A confidence score based on model interaction is further introduced to evaluate the reliability of each inference and assist training. Theoretical analysis is provided to explain how the sequence generation network learns under performance guidance, promoting better trajectories. The effectiveness of SGCF is validated through experiments on inverted pendulum control and lead-zinc rougher flotation reagent control. Multiple baseline methods are considered, including state feedback control (SFC) models and data-driven MPC approaches. Results demonstrate that SGCF achieves advantages in both control performance and cost, while maintaining favorable inference efficiency. Moreover, SGCF exhibits potential for interpretable reasoning.

Key performance indicator (KPI) reflects the quality and efficiency of manufacturing operations, and KPI forecasting enables proper operations or controls in many industrial processes. However, existing KPI forecasting methods are inadequate for managing the advance prediction of KPI across multiple cycles effectively, which impedes precise and timely control in complex industrial processes. Therefore, we propose an adaptive encoder-decoder framework with partial teacher forcing strategy (PTF-ED) to enable flexible multihorizon KPI forecasting. First, we employ an encoder that processes the input time series and an attention layer to generate the context vectors. Then, we divide the measured KPIs into delayed and current time series, and design a delayed decoder and a current decoder in series to make the delayed and current time series correspond to the input time series. Especially, we propose a partial teacher forcing strategy to utilize the measured KPI efficiently and tackle the challenge of exposure bias in the current time series between training and inference phases. Moreover, we introduce a weighted multihorizon forecasting constraint in the model training loss to constrain the input-output correspondence across different sample intervals. The effectiveness of the proposed model has been validated through both a numerical simulation study and a case study in a real-world zinc flotation process.

Accurate and stable feed-grade monitoring is essential for flotation and reagent control. Although some monitoring models for feed grade have been developed in recent years, they always use a group of time-series data with a fixed time step as input, and neglect the roles of models at different training steps. Therefore, to enhance the stability and accuracy of the feed-grade monitoring model, we propose a feature-ensemble model with an adaptive self-ensemble module. First, we use multiple groups of input vectors with different time steps as inputs to the monitoring model. Then, we introduce an adaptive self-ensemble module (ASE module) to fully use the models at different training steps with an adaptive adjustment mechanism and a self-ensemble module. After that, we construct a feature-ensemble model (FE model) embedding the ASE module to handle the multiple time series with different time steps. Effectiveness of the proposed monitoring model is validated both on a numerical example and an industrial example in froth flotation. In the numerical example, the root mean squared error (RMSE) of the three FE models with the ASE module decreases by 0.0090 to 0.0159, and the R-squared ($R^{2}$) score increases by 0.0013 to 0.0035, compared with the three single models. In industrial application, the RMSE of the three FE models with the ASE module decreases by 7.20% to 9.70%, and the$R^{2}$increases by 6.71% to 7.34%, compared with the three single models. This shows our framework can improve the feed-grade monitoring performance.

Accurate grade monitoring in froth flotation is crucial for improving process efficiency and mineral recovery. Current grade monitoring models typically use mean video features and fail to capture feature variations within individual videos. Furthermore, they usually embed the most recently available feed grade into the visual feature vector without providing a refined embedding of feed grade. Therefore, we propose a flotation grade monitoring model with feed grade refined embedding (FGRE) and nonoverlapping patch encoding (NOPE). First, we develop an FGRE module to generate fine-grained feed grade representations. This module extracts the time series of critical feed grade elements by physical topology of the flotation process, and it employs a grouped weight-sharing time-lagged-recurrent neural network (RNN) to fuse multisource temporal data. Then, we introduce an RNN with NOPE to encode video patches and extract dynamic information from each froth video. This network enables the capture of subtle visual feature variations within each individual video. After that, we implement a multivideo temporal extraction strategy to capture dynamic temporal features across multiple videos for grade monitoring. Experiments are conducted on a real-world zinc flotation process. Our proposed approach can be integrated into most existing flotation grade monitoring models, significantly enhancing their monitoring performance.

Complex imaging environments and conditions in real-world scenes pose significant challenges for stereo matching tasks. Models are susceptible to underperformance in non-Lambertian surfaces, weakly textured regions, and occluded regions, due to the difficulty in establishing accurate matching relationships between pixels. To alleviate these problems, we propose a multi-scale geometrically enhanced stereo matching model that exploits the geometric structural relationships of the objects in the scene to mitigate these problems. Firstly, a geometric structure perception module is designed to extract geometric information from the reference view. Secondly, a geometric structure-adaptive embedding module is proposed to integrate geometric information with matching similarity information. This module integrates multi-source features dynamically to predict disparity residuals in different regions. Third, a geometric-based normalized disparity correction module is proposed to improve matching robustness for pathological regions in realistic complex scenes. Extensive evaluations on popular benchmarks demonstrate that our method achieves competitive performance against leading approaches. Notably, our model provides robust and accurate predictions in challenging regions containing edges, occlusions, reflective, and non-Lambertian surfaces. Our source code will be publicly available.

Reagent addition control level of the zinc first rougher has a significant impact on quality of the zinc concentrate. As froth visual features are important indicators of working states in froth flotation, they are usually controlled to optimal setpoints by reagent addition for the desired concentrate. Existing methods usually construct a rule base for feature setpoint generation and design an error-driven feedback controller for reagent addition. However, there are still some issues: 1) a portion of data is used for rule base establishment and knowledge in remaining data is ignored; 2) as the rule base is sparse, it may lead to match failures caused by insufficient knowledge; 3) existing controllers only consider the error at the current time, while ignore the temporal information in error sequences. Therefore, we propose a reagent addition control strategy with the dual rule-based weighted fuzzy interpolative reasoning module and temporal encoder-decoder Bayesian network. Firstly, we design a dual rule base with complementary data to fully mine knowledge. Then, we explore a weighted fuzzy interpolative reasoning module for feature setpoint generation. This module selects several nearest neighbor rules in a positive rule base as interpolative candidates and determines rule weights via the nearest neighbor rules in the negative rule base. After that, we introduce a temporal encoder-decoder network by taking temporal error sequences as the input to recognize working states, and use a Bayesian network to realize reagent adjustment. Ablations and comparative experiments on industrial data show the effectiveness of the proposed control strategy.

Accurate and timely foam grade prediction plays an important role in the flotation foam industry process. However, the information between foam characteristic series and foam grade series at different sampling times often does not match, making the prediction result lagging behind. A multistep fusion transformer (MSFT) model is designed in this article. First, we extract multiple froth time series as input to correlate feature information and grade information under multiple time series, then, a self-attention structure is designed to fuse at multiple scales, which enhances the degree of information correlation under different time series, finally, the information matrix is passed through the fully connected layer to obtain the final prediction result. Compared with the existing froth grade network recurrent neural networks (RNN), long short-term memory (LSTM), gated recurrent unit, Transformer, Enc–Dec (RNN), feature reconstruction–regression, Siamese time series and difference (LSTM), and FlotationNet models, the MSFT model has reduced the baseline by 30.3%, 30.3%, 30%, 66.9%, 30%, 45.8%, 55.2%, and 52.5%, respectively, among all indicators.

To prevent industrial fault propagation, it is important to clarify the relationship between industrial system components and identify the fault propagation path efficiently and timely, aiming at the problems in fault propagation path identification, this article presents an equipment fault propagation analysis approach based on unstable points identification to solve such issues. First, the fault propagation diagram is created by analyzing the industrial complex system components. Furthermore, to address the issues of traditional interpretative structural modeling (ISM), the bilateral rotation interpretative structural modeling (BRISM) method is proposed to stratify the components and detect the unstable points. Finally, the fault propagation graph is analyzed using the PageRank algorithm to update the unstable points and edge weights between different nodes to identify the fault propagation paths. The results indicate that the proposed method can effectively identify fault propagation paths between components and can be applied to various industrial systems.

In contemporary industries, diagnosing bearing faults is crucial, yet the complexity and diversity of these faults pose challenges to traditional methods. Existing algorithms typically treat compound faults as independent events, overlooking the interrelations among different faults, which constrains the performance in diagnosing the faults with diverse semantic complexities. Also, the research on leveraging multimodal data to enhance fault diagnosis accuracy is limited. To overcome the weakness mentioned above, a multimodal knowledge graph (MKG) construction method based on multimodel data, including time series vibration signals, spectrum, and description text of datasets, is proposed. Subsequently, a fault diagnosis method utilizing a MKG completion model based on a relation cascade graph attention network is designed to capture the relationship between various faults. Experimental results on an MKG constructed from seven bearing datasets demonstrate the robustness of the proposed method.

3D froth information is a significant indicator of working condition recognition in froth flotation. To extract it accurately, the first and key step is camera calibration. Although there have been many camera calibration methods proposed in these years, they cannot handle well for binocular camera calibration in froth flotation. The main reason is that there is an open environment without support surface or special geometric shapes for camera calibration in froth flotation. Therefore, we propose a novel binocular camera calibration method based on key frame sequences and weighted normalized tilt difference. First, we extract a high-quality frame sequence by filtering out incomplete and out-of-focus images from the froth video. Then, we propose a method to measure the tilt degree of the planar plate and extract the key frame sequences of the planar plate based on the tilt difference. After that, we calculate the camera parameters by weighted normalized tilt difference under various poses. The proposed binocular camera calibration method uses the froth video to obtain accurate and robust camera parameters, and does not require auxiliary equipment. Experiments have demonstrated the effectiveness and flexibility of the proposed method in froth flotation.

This article proposes a robust end-to-end deep learning-induced fault recognition scheme by stacking multiple sparse-denoising autoencoders with a Softmax classifier, called stacked spare-denoising autoencoder (SSDAE)-Softmax, for the fault identification of complex industrial processes (CIPs). Specifically, sparse denoising autoencoder (SDAE) is established by integrating a sparse AE (SAE) with a denoising AE (DAE) for the low-dimensional but intrinsic feature representation of the CIP monitoring data (CIPMD) with possible noise contamination. SSDAE-Softmax is established by stacking multiple SDAEs with a layerwise pretraining procedure, and a Softmax classifier with a global fine-tuning strategy. Furthermore, SSDAE-Softmax hyperparameters are optimized by a relatively new global optimization algorithm, referred to as the state transition algorithm (STA). Benefiting from the deep learning-based feature representation scheme with the STA-based hyperparameter optimization, the underlying intrinsic characteristics of CIPMD can be learned automatically and adaptively for accurate fault identification. A numeric simulation system, the benchmark Tennessee Eastman process (TEP), and a real industrial process, that is, the continuous casting process (CCP) from a top steel plant of China, are used to validate the performance of the proposed method. Experimental results show that the proposed SSDAE-Softmax model can effectively identify various process faults, and has stronger robustness and adaptability against the noise interference in CIPMD for the process monitoring of CIPs.

Concerning the problems of harrowing extraction and poor classification accuracy of fault features in rolling bearing vibration signals, a fault feature selection and classification method based on multi-indicator fusion is proposed. First, the original signal is decomposed through the improved complementary ensemble local mean decomposition method into several physically meaningful product functions (PF) and single residual components; then, the three indicators of kurtosis, correlation coefficient, and Kulback–Leibler divergence are combined to extract the most suitable PF components for signal reconstruction. Ultimately, the reconstructed signal's multidomain characteristics and entropy value features are retrieved and fed into the LightGBM classifier for classification in order to achieve an intelligent diagnosis of rolling bearing problems. The statistical results demonstrate that the proposed method can efficiently identify the functional PF components and has notable benefits in extracting features from diverse experimental datasets and detecting faults.

Abstract The accurate segmentation of blood vessels plays a crucial role in screening, diagnosis and treatment of multiple diseases. However, current automated segmentation approaches do not pay enough attention to the vascular topology errors (such as mistaking vessel‐breakpoints), resulting in considerable scattered vessel‐fragments in segmentation results. This article proposes a retinal vessel segmentation model using multi‐scale context gating and breakpoint attention mechanism, called MCG&BA‐Net. Specifically, it obtains a feature map containing contextual information of vessels through an introduced multi‐scale context module, and then filters the redundant features and noises by a gated structure to highlight target features. Furthermore, a kind of breakpoint attention module is proposed, which can locate and focus on potential breakpoint areas, thereby facilitating accurate segmentation results of tree‐like fine vessels. Extensive confirmatory and comparative experiments have been conducted on five public datasets, including three benchmark datasets, that is, DRIVE, CHASDB1 and SATRE, and two clinical datasets, that is, fundusimage1000 and RFMID. The AUC scores on the benchmark datasets are 0.9878, 0.9923 and 0.9942, respectively. Among them, the AUC score on CHADEDB1 and STARE outperforms the state‐of‐the‐art results. In addition, experimental results on the two clinical datasets demonstrate strong generalization capability of the propose method, indicating high clinical application values.

Accurate and in-time performance monitoring plays a great role in industrial processes. However, since the labeled performances are usually measured by some special devices with a relatively long-time interval, the current deep neural networks for the performance monitoring always treat them only as an output. But actually, in the industrial process like froth flotation, labeled performance at the previous moment could also offer valuable information for performance monitoring at the current moment, especially under unstable working conditions. Therefore, we propose a Siamese time series and difference network (STS-D net), which integrates input features at different time steps and labeled performance at the previous moment effectively. In this article, the proposed STS-D net includes two sub-networks. One is the Siamese time series network, which aims to extract effective and uniform feature representations for the input time series at the current and previous moments; the other is the difference network, which integrates the feature representations of the two input time series with labeled performance at the previous moment to predict the performance at the current moment in an incremental way. Effectiveness of the proposed STS-D net is validated in a real-world froth flotation process.

Due to technical or economic limitations, timely measuring quality-relevant key performance indicators (KPIs) of complex industrial processes (CIPs), especially the chemical composition-related indexes, is intractable. Process monitoring image sequences (PMISs) usually involve significant information about the operation states and KPIs. Thus, soft sensor-based online KPI inference by incorporating process monitoring variables (TPMVs) and PMISs is more promising. However, the extremely inconsistent sampling rates with different expression forms and concerning aspects between PMISs and TPMVs lead to a great challenge in the soft sensor modeling by combining PMISs and TPMVs. In this article, a self-attention dual-channel deep network (SADCDN)-based soft sensor model for the end-to-end online KPI detection/prediction is proposed. Specifically, one channel adopts the gated recurrent unit (GRU) network to extract intrinsic time-series features in TPMVs, and simultaneously the other channel introduces a novel frame-dilated convolution fusion neural network (FDCFNN) to extract intrinsic spatiotemporal features from PMISs to address the sampling inconsistence between PMISs and TPMVs. Successively, dual-channel network features with different concerning aspects are weighted and fused based on an introduced self-attention mechanism to bridge the gap of sampling rates and concerning aspects between PMISs and TPMVs for the soft sensor modeling. Practical application results on two real industrial processes, the bauxite flotation process and the sintering process of a cement rotary kiln, have demonstrated the effectiveness and superiority of the proposed dual-channel model, laying a foundation for the process optimization of CIPs.

The control reliability of model predictive control is largely determined by the accuracy of the process model. The Hammerstein–Wiener (HW) model is an important nonlinear process modeling technique that has obtained great success in some process industries. Disturbances result in model mismatch and steady-state deviation, but little effort has been devoted to the coupling effects and inertial information in measured disturbances. In addition, few studies try to construct a disturbance observer (DO) to alleviate unmeasured disturbances. The present work proposes prompt disturbance rejection. First, a spatial–temporal long short-term memory-based measurable disturbance encoder is devised to analyze time-series information from measured disturbances and their coupling effects. The encoder can further clarify the status of inertial interference components and the disturbance intensity. Second, a DO is designed to estimate and attenuate unmeasured disturbances. Third, to create the new HW network, which is improved by integrating the disturbance encoder and observer differential, neural networks are used as nonlinear parts. Finally, a model predictive controller based on this improved model is constructed for real-time industrial process control. Simulation comparison experiments have demonstrated the superiority of the proposed methods. Real industry application in the country’s largest lead-zinc froth flotation plant in China validated the proposed model’s effectiveness in controlling chemical reagents.

Froth color can be referred to as a direct and instant indicator to the key flotation production index, for example, concentrate grade. However, it is intractable to measure the froth color robustly due to the adverse interference of time-varying and uncontrollable multisource illuminations in the flotation process monitoring. In this article, we proposed an illumination-invariant froth color measuring method by solving a structure-preserved image-to-image color translation task via an introduced Wasserstein distance-based structure-preserving CycleGAN, called WDSPCGAN. WDSPCGAN is comprised of two generative adversarial networks (GANs), which have their own discriminators but share two generators, using an improved U-net-like full convolution network to conduct the spatial structure-preserved color translation. By an adversarial game training of the two GANs, WDSPCGAN can map the color domain of froth images under any illumination to that of the referencing illumination, while maintaining the structure and texture invariance. The proposed method is validated on two public benchmark color constancy datasets and applied to an industrial bauxite flotation process. The experimental results show that WDSPCGAN can achieve illumination-invariant color features of froth images under various unknown lighting conditions while keeping their structures and textures unchanged. In addition, WDSPCGAN can be updated online to ensure its adaptability to any operational conditions. Hence, it has the potential for being popularized to the online monitoring of the flotation concentrate grade.

This article presents a simple yet powerful online flotation process working condition (FPWC) discrimination approach based on the sparse representation of froth images. It learns a local Gabor pattern-based discriminative dictionary with a linear classification model simultaneously for the FPWC identification by solving a sparsity-constrained optimization problem. The proposed method tends to achieve similar and distinct sparse codes of froth images for the same and different FPWCs, respectively, facilitating the accurate FPWC identification. To ensure the adaptability of the FPWC discrimination model, an incremental learning-based online model updating procedure is further derived to monitor the dynamically changing characteristics of FPWCs based on an introduced sparsity discrimination index. The proposed method was validated on an industrial preferential lead-flotation subcircuit process. The prototype monitoring system with extensive confirmatory and comparative experiments shows the effectiveness and superiority of the proposed method, which lays a foundation for the optimal control of industrial flotation processes.

With the rapid development of deep neural network (DNN), many DNN-based models for performance monitoring have been developed recently. However, some challenges still exist in the industrial performance monitoring: 1) different sample rates and time delays between the inputs and labeled performance; 2) a light-weight DNN architecture. Under this circumstance, we design a DNN named feature reconstruction-regression network (FR-R net) in this article. First, we extract the feature vector series as the input feature in order to capture the dynamic temporal information of the input data. Then, we design a feature reconstruction network with a weight-shared kernel network and fixed positional encoding to generate a reconstructed feature vector. Finally, we send the reconstructed feature vector into fully connected layers as a regression network to link the labeled performance. The effectiveness of the proposed FR-R net is validated on both a simulation case and an industrial froth flotation process.

This paper presents a froth image statistical modeling-based online flotation process operation-state identification method by introducing a biologically inspired Gabor wavelet transform in accordance with the physiological findings in the biological vision system. It derived the latent probabilistic density models of these biologically inspired Gabor filtering responses (GFRs) based on a versatile intermediate probability modeling frame, Gaussian scale mixture model. It has demonstrated that both the real and the imaginary representation of GFR obey a Laplace distribution. Accordingly, the amplitude representation of GFR obeys a Gamma distribution. Whereas the phase representation of GFR is an important yet frequently ignored aspect in Gabor-based signal analysis; it is demonstrated to be a periodic distribution and can be expressed by a von Mises-like distribution model. Successively, a local spline regression (LSR)-based classifier that the maps scattered statistical feature points of froth images directly to the operation-state labels smoothly is introduced for the operation-state recognition. Extensive confirmatory and comparative experiments on an industrial-scale bauxite flotation process demonstrate the effectiveness and superiority of the proposed method. Performance effects on different parameter settings, e.g., parameters of Gabor kernel and dimensionalities of multivariate statistical models, are further discussed.

The burst bubble rate has been strongly linked to froth stability, and thus, it is always used for performance prediction or modeling in the froth flotation. Due to different bubble motions and intensity changes as the bubbles move, the current burst bubble recognition methods are ineffective. Therefore, in this article, a similarity-based method for burst bubble recognition is proposed. The proposed method uses the local motion correction to deal with the different motion cases, and it selects the chamfer distance and the weighted normalized cross correlation as the similarity to decrease the influence of the intensity changes by the convex shape. Furthermore, the weighted normalized cross correlation is flexibly integrated with the template mask matching and the partial template matching. Extensive experiments have validated the effectiveness and robustness of the proposed method, where the precision and F1-score have been increased by at least 7.41% and 4.36%, respectively, compared with the current methods.

To achieve fine segmentation of complex natural images, people often resort to an interactive segmentation paradigm, since fully automatic methods often fail to obtain a result consistent with the ground truth. However, when the foreground and background share some similar areas in color, the fine segmentation result of conventional interactive methods usually relies on the increase of manual labels. This paper presents a novel interactive image segmentation method via a regression-based ensemble model with semi-supervised learning. The task is formulated as a non-linear problem integrating two complementary spline regressors and strengthening the robustness of each regressor via semi-supervised learning. First, two spline regressors with a complementary nature are constructed based on multivariate adaptive regression splines (MARS) and smooth thin plate spline regression (TPSR). Then, a regressor boosting method based on a clustering hypothesis and semi-supervised learning is proposed to assist the training of MARS and TPSR by using the region segmentation information contained in unlabeled pixels. Next, a support vector regression (SVR) based decision fusion model is adopted to integrate the results of MARS and TPSR. Finally, the GraphCut is introduced and combined with the SVR ensemble results to achieve image segmentation. Extensive experimental results on benchmark datasets of BSDS500 and Pascal VOC have demonstrated the effectiveness of our method, and the comparison with experiment results has validated that the proposed method is comparable with the state-of-the-art methods for interactive natural image segmentation.