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.

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.

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.

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.

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.

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.

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.

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.