A method for predicting copper ore flotation dosing and aeration volume by fusing deep vision and traditional features

Abstract

The application provides a copper ore flotation dosing and air charge quantity prediction method combining deep vision and traditional features, and belongs to the cross-application technical field of computer vision and deep learning in copper ore flotation process parameter prediction, and the method comprises the following steps: S1, multi-scene synchronous acquisition and standardized preprocessing of a copper ore flotation foam image; S2, multi-modal heterogeneous feature extraction based on Shearlet transformation and EfficientNetV2; S3, cross-modal feature fusion based on deep canonical correlation analysis and an adaptive graph convolutional network; S4, progressive hierarchical expert network model construction based on Gumbel-Softmax and dynamic weight average; S5, model stage-by-stage training and dynamic optimization under multi-constraint cooperation; and S6, feature mapping and model inference prediction of a sample to be predicted. The application improves the self-adaptive ability and prediction robustness of the model to complex working conditions of copper ore flotation.

Description

Technical Field

[0001] This invention relates to the technical field of cross-application of computer vision, deep learning and multi-task modeling technology in the prediction of parameters in copper ore flotation process, and in particular to a method for predicting the dosage and aeration volume of copper ore flotation reagents by integrating depth vision and traditional features. Background Technology

[0002] Copper ore flotation is a core process in copper ore beneficiation. The dosage of collectors, depressants, activators, pH adjusters, and aeration directly determine the mineralization effect of the pulp, thus affecting concentrate grade, metal recovery rate, and beneficiation energy consumption. Currently, parameter control in copper ore flotation still largely relies on the manual experience of on-site operators. Operators judge the degree of mineralization and adjust parameters by visually observing the color, shape, and texture of the froth. This approach suffers from strong subjectivity, slow response, and low control precision, making it difficult to adapt to complex and changing flotation conditions. It can easily lead to reagent waste, increased energy consumption, or unstable concentrate grade.

[0003] With the development of automated mineral processing, some studies have attempted to predict flotation parameters using machine learning methods. However, existing technologies still face several bottlenecks: First, traditional feature extraction of flotation froth often employs simple color and texture operators, which struggle to capture subtle edge textures and local differences related to mineralization. Furthermore, depth visual features and traditional features exhibit significant modal distribution gaps, and direct concatenation or weighted fusion can introduce redundant noise, failing to fully leverage the complementary advantages of both types of features. Second, the prediction of reagent dosage and aeration volume is a typical multi-task modeling problem. Existing multi-expert network models are prone to imbalanced expert activation during training, with a few experts dominating and suppressing the learning of others. Simultaneously, a "seesaw effect" can occur between tasks, where improved performance in one task leads to decreased performance in others, making it difficult to achieve coordinated optimization of multiple parameters. Third, existing models are mostly static, lacking a closed-loop update mechanism, making them unable to adapt to dynamic changes in ore properties, pulp concentration, and other operating conditions during copper ore flotation. The long-term predictive robustness of these models is insufficient.

[0004] Furthermore, a highly nonlinear coupling relationship exists between reagent dosage and aeration rate in copper ore flotation. Traditional single-objective modeling methods struggle to achieve overall optimization across multiple key flotation indicators, while existing multi-task modeling methods lack effective loss balancing strategies, further limiting the accuracy of parameter predictions and the engineering application value of the models. Therefore, there is an urgent need to develop a copper ore flotation reagent dosage and aeration rate prediction method that can fully exploit the features of flotation foam images, achieve deep fusion of cross-modal features, and resolve conflicts in multi-task modeling. This method would overcome the bottlenecks of existing technologies and provide reliable support for intelligent control of copper ore flotation. Summary of the Invention

[0005] This invention provides a method for predicting the dosage of reagents and aeration in copper ore flotation by integrating deep vision and traditional features. The aim is to achieve accurate and coordinated prediction of the dosage of collectors, inhibitors, activators, pH adjusters, and aeration during copper ore flotation through refined multimodal feature extraction, deep cross-modal feature fusion, and optimized multi-task expert network modeling. This enhances the model's adaptability and predictive robustness to complex copper ore flotation conditions, provides reliable technical support for intelligent control of copper ore flotation, and promotes the automation and intelligent upgrading of the copper ore beneficiation process.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for predicting reagent addition and aeration rates in copper ore flotation that integrates depth vision and traditional features includes: S1: Simultaneously acquire foam images of copper ore flotation cells, grade label data and operating condition label data at corresponding times to construct the original dataset; perform spatial registration, noise reduction and normalization, and region of interest extraction preprocessing on the foam images in the original dataset to obtain effective region of interest images; divide the effective region of interest images into training set, validation set and test set and match them with the corresponding label data to output a standardized image dataset. S2: Based on a standardized image dataset, perform traditional feature extraction and depth visual feature extraction on each valid region of interest image to obtain initial traditional feature vectors and initial depth visual feature vectors; perform complementary filtering on the two types of initial feature vectors through mutual information calculation, and output the filtered traditional feature vectors and the filtered depth visual feature vectors. S3: Based on the two types of feature vectors after filtering from the output of S2, cross-modal feature distribution alignment is completed through deep canonical correlation analysis, and then feature topology fusion is completed through adaptive graph convolutional network, outputting fused feature vectors that match the label data one by one; S4: Construct a progressive hierarchical expert network model, with the fused feature vector as input and the dosage of copper ore flotation collector, inhibitor, activator, pH adjuster, and aeration as the predicted output; S5: Using the fused feature vector as input and the corresponding working condition label data as training target, the progressive hierarchical expert network model is subjected to phased constraint training. After optimization on the validation set and performance verification on the test set, the qualified optimal prediction model is output. S6: Using the flotation froth image of the copper ore to be processed as input, after the same preprocessing as S1 and the same feature extraction and fusion processing as S2 to S3, input the optimal prediction model and output the corresponding prediction results of the dosage and aeration.

[0007] In this specification, the specific process of traditional feature extraction described in S2 is as follows: A discrete Shearlet transform is performed on the effective region of interest image to obtain a multi-scale, multi-directional transform coefficient matrix. The mean, variance, energy, and entropy statistics of each coefficient matrix are calculated and concatenated to generate a Shearlet feature vector. The local binary pattern value and neighborhood variance of each pixel are calculated for the effective region of interest image, and a local binary pattern variance histogram is constructed to generate a local texture difference feature vector. The Shearlet feature vector and the local texture difference feature vector are concatenated and weighted by the ratio of inter-class scatter to intra-class scatter to obtain the initial traditional feature vector.

[0008] In this specification, the specific process of deep visual feature extraction described in S2 is as follows: Construct an EfficientNetV2 network model with a progressive training strategy, gradually increase the resolution and regularization intensity of the input image during training, and complete the network pre-training by using contrast loss combined with mean squared error loss; input the effective region of interest image into the pre-trained EfficientNetV2 network model to extract the initial deep visual feature vector.

[0009] In this specification, the specific process of performing complementary screening of two types of initial feature vectors through mutual information calculation as described in S2 is as follows: calculate the mutual information between each dimension of the initial traditional feature vector and each dimension of the initial depth visual feature vector, and construct a mutual information matrix; for the initial traditional feature vector, retain the top 80 features with the highest mean mutual information with the initial depth visual feature vector to generate the filtered traditional feature vector; for the initial depth visual feature vector, retain the top 100 features with the highest mean mutual information with the initial traditional feature vector to generate the filtered depth visual feature vector.

[0010] In this specification, the cross-modal feature distribution alignment and feature topology fusion described in S3 are performed using an alternating optimization strategy. The specific process is as follows: First, fix the mapping network parameters of the deep canonical correlation analysis and train an adaptive graph convolutional network with the working condition label data as the training target; then fix the parameters of the adaptive graph convolutional network and update the mapping network parameters of the deep canonical correlation analysis with the input features of the adaptive graph convolutional network as the alignment target; repeat the alternating optimization process until the model converges, thus completing the feature distribution alignment and fusion.

[0011] In this specification, the progressive hierarchical expert network model described in S4 has a three-layer progressive structure, consisting of a bottom-level shared expert layer, a middle-level task cluster-specific expert layer, and a top-level single-task-specific expert layer. The bottom-level shared expert layer sets up multiple parallel shared expert networks to learn the common features of all prediction tasks. The middle-level task cluster-specific expert layer is divided into drug dispensing task clusters and inflation task clusters based on task attributes. Each task cluster has multiple parallel task cluster-specific expert networks to learn the specific features within the corresponding task cluster. The top-level single-task-specific expert layer sets up multiple parallel single-task-specific expert networks for each prediction task to learn the personalized features of the corresponding single task.

[0012] In this specification, the progressive hierarchical expert network model sets up an independent gating network for each expert layer. The gating network adopts the Gumbel-Softmax with Concrete Distribution mechanism, which introduces Gumbel noise to achieve smooth discrete sampling of the gating weights. During training, the temperature parameter of the gating network is gradually attenuated to achieve dynamic adaptive allocation of the weights of each expert network.

[0013] In this specification, the progressive hierarchical expert network model described in S4 has a built-in multi-constraint optimization module. The multi-constraint optimization module uses a dynamic weight averaging combined with gradient projection strategy to achieve multi-task loss balance. Specifically, it tracks the training loss decline rate of each prediction task, dynamically adjusts the loss weight of each task, and gives higher training weights to tasks with slower training speeds. It decomposes the gradient of each task into components parallel to the shared gradient and orthogonal components, retains only the orthogonal components to update the parameters of the underlying shared expert layer, and eliminates gradient conflicts between tasks.

[0014] In this specification, the specific process of phased constraint training described in S5 is as follows: In the first phase, all parameters of the mid-level task cluster-specific expert layer and the top-level single-task-specific expert layer are frozen, and only the bottom-level shared expert layer and the corresponding gating network are trained to complete the model pre-training; In the second phase, all network layer parameters of the model are unfrozen, and a multi-task loss balancing strategy and a gating network temperature decay mechanism are introduced to complete the constraint training; In the third phase, the gating network temperature parameters and the loss weights of each task are fixed, all expert network and task output head parameters are fine-tuned, and the model convergence training is completed by combining the early stopping strategy.

[0015] In this manual, after S6 outputs the predicted dosage and inflation volume, it calculates the coefficient of variation of the predicted results using the Monte Carlo dropout method to complete the confidence verification of the predicted results. For prediction results with low confidence, the corresponding real working condition data is collected as labels and archived into the incremental training sample library. When the number of samples in the incremental training sample library reaches a set threshold, the original training set is merged to complete the incremental fine-tuning update of the model and replace the original optimal prediction model.

[0016] In summary, the present invention has at least the following beneficial effects: Feature extraction and fusion: This invention combines Shearlet transform and local binary mode variance to achieve refined extraction of traditional features, which can fully capture the multi-scale and multi-directional edge texture and local texture difference features of flotation foam. The deep visual features extracted by EfficientNetV2 can mine high-level semantic features of foam images, and the two types of features form a strong complementarity. At the same time, deep canonical correlation analysis is used to eliminate the distribution gap of cross-modal features, and an adaptive graph convolutional network is used to capture the nonlinear topological correlation between features, realizing deep fusion of cross-modal features, which greatly improves the expressive power and discriminative power of features, and lays a high-quality feature foundation for subsequent parameter prediction.

[0017] Multi-task modeling and prediction: The progressive hierarchical expert network model constructed in this invention achieves hierarchical learning of common features of multiple tasks, task cluster features, and single-task specific features through a three-layer progressive expert layer design. Combined with a Gumbel-Softmax optimized gating network, it effectively solves the problem of unbalanced expert activation in multi-expert networks, allowing more experts to participate in feature learning. Through a loss balancing strategy combining dynamic weight averaging and gradient projection, it eliminates the "seesaw effect" and gradient conflict in multi-task modeling, and achieves coordinated and accurate prediction of multiple parameters such as drug dosage and inflation volume. This breaks through the limitations of manual experience-based control and improves the accuracy and stability of parameter prediction.

[0018] Regarding model adaptability and robustness: This invention employs a phased constraint training and convergence optimization strategy for the model, ensuring its generalization ability and enabling it to adapt to the complex working conditions of copper ore flotation. Simultaneously, the constructed prediction result confidence verification and closed-loop feedback update mechanism can perform truth value verification on low-confidence prediction results and archive incremental samples, achieving incremental fine-tuning and updating of the model. This allows the model to continuously adapt to dynamic changes in flotation conditions such as ore properties and pulp concentration, ensuring the model's long-term predictive performance and enhancing its engineering application value.

[0019] At the engineering application level: The prediction method of this invention can achieve real-time and accurate prediction of reagent dosage and aeration volume in copper ore flotation, providing a reliable parameter adjustment reference for the intelligent control system of copper ore flotation. It can effectively reduce reagent waste and energy consumption in mineral processing, while ensuring the stability of concentrate grade and metal recovery rate. The entire method is based on computer vision and deep learning technology, requiring no modification to existing flotation equipment and processes. It is easily integrated with existing distributed control systems in mineral processing plants, has low deployment costs, and can promote the automation and intelligent upgrading of copper ore beneficiation processes, possessing excellent prospects for engineering promotion. Attached Figure Description

[0020] Figure 1 This is a schematic diagram illustrating the steps of the prediction method involved in this invention.

[0021] Figure 2 This is a flowchart illustrating the prediction method involved in this invention.

[0022] Figure 3 This is a schematic diagram of the multimodal feature extraction and cross-modal fusion process involved in this invention.

[0023] Figure 4 This is a schematic diagram of the multi-task model training, prediction, and closed-loop update process involved in this invention. Detailed Implementation

[0024] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0025] like Figure 1 and Figure 2 As shown, this embodiment provides a method for predicting reagent addition and aeration volume in copper ore flotation by integrating depth vision and traditional features. Taking copper ore flotation froth images as the core research object, it constructs a complete prediction system from image acquisition and preprocessing, multimodal feature extraction and fusion, multi-task model construction and training, to prediction result verification and model closed-loop update. It should be noted that the entire solution of this invention revolves around optimizing the prediction method using computer vision and deep learning technologies, without making any changes to the copper ore flotation process steps or equipment structure. Specific copper ore flotation process steps and equipment structures can be referenced from existing technologies.

[0026] S1. Simultaneous acquisition and standardized preprocessing of multi-scene flotation foam images for copper ore. This step eliminates information blind spots in single-view imaging through multi-view synchronous acquisition and eliminates environmental interference in the industrial field through standardized preprocessing, ensuring the stability and consistency of subsequent feature extraction.

[0027] First, multi-source data synchronous acquisition was conducted. A multi-view synchronous acquisition unit was built, deploying three linear array industrial cameras at the observation positions of the roughing, cleaning, and scavenging cells in the copper ore flotation operation. Images of the froth surface in the corresponding flotation cells were acquired synchronously. The acquisition frame rate was synchronized in real-time with the slurry flow rate collected by the concentrator's distributed control system to ensure complete matching between image acquisition and slurry flow status. Simultaneously, online grade analyzers were used to synchronously acquire label data of concentrate copper grade and tailings copper grade in the flotation cells at corresponding times. The distributed control system was also used to synchronously acquire historical operating condition label data at corresponding times. The label data included collector dosage, depressant dosage, activator dosage, pH adjuster dosage, and aeration rate. Finally, a raw copper ore flotation froth image dataset and a matching label dataset were constructed.

[0028] Subsequently, frame-by-frame standardization preprocessing was performed. For each image in the original image dataset, three operations were sequentially executed to eliminate the negative impacts of industrial site lighting fluctuations, dust interference, and viewing angle deviations. The first operation was multi-view image spatial registration, which used a scale-invariant feature transform algorithm to match and spatially align feature points in foam images acquired by three cameras at the same time, eliminating viewing angle deviations and generating a single-frame globally unified panoramic image of copper ore flotation foam that fully covers the entire surface state of the flotation cell foam. The second operation was image denoising and grayscale normalization, which used a non-local mean filtering algorithm to denoise the panoramic image. Compared with traditional filtering methods, this algorithm can completely preserve the edge texture details of the foam while eliminating noise, adapting to the high requirements of subsequent feature extraction for edge information. Then, the pixel values ​​of the denoised image were mapped to the range of 0 to 1 to generate a grayscale normalized image, eliminating pixel value shifts caused by lighting fluctuations. The third step is region of interest extraction. Based on the Otsu adaptive threshold segmentation algorithm, the grayscale normalized image is segmented into foam and background regions. Non-foam backgrounds such as tank edges and sprinkler pipes are removed, and a valid region of interest image containing only foam morphology is extracted, eliminating the interference of irrelevant backgrounds on subsequent feature extraction.

[0029] Finally, the dataset was partitioned. All valid regions of interest images were divided into training, validation, and test sets in a 7:2:1 ratio, corresponding one-to-one with the corresponding labeled dataset, resulting in a standardized copper ore flotation foam image dataset.

[0030] S2. Multimodal heterogeneous feature extraction based on Shearlet transform and EfficientNetV2 refer to Figure 3This step takes the effective region of interest image output by S1 as input, and extracts traditional handcrafted features by combining Shearlet transform with local binary mode variance, and extracts depth visual features by using EfficientNetV2. The two feature extraction processes achieve bidirectional interaction through the feature validity verification module, which selects complementary feature dimensions, eliminates redundant information, and provides high-quality feature input for subsequent cross-modal fusion.

[0031] The first part focuses on traditional feature extraction based on Shearlet transform and local binary mode variance. This part uses Shearlet transform to capture multi-scale, multi-directional curve edge features of foam images, and local binary mode variance to capture local texture difference features of the foam surface. The two types of features are deeply fused through weight allocation to form a complementary traditional feature representation.

[0032] First, multi-scale, multi-directional feature extraction using Shearlet transform is performed. Shearlet transform is a sparse representation method with multi-scale, multi-directional, and locality characteristics. Compared with traditional wavelet transform, it is more suitable for capturing curved edges and texture structures in images. In this scheme, its core function is to extract the fine edge texture information in copper ore flotation froth that is directly related to the degree of mineralization. This information directly reflects the mineralization state of the froth and is the core basis for adjusting flotation parameters.

[0033] The continuous Shearlet transform is defined as follows: for any image in a two-dimensional square-integrable function space (corresponding to a gray-scale normalized copper ore flotation froth image), its continuous Shearlet transform expression is: ;in for The continuous Shearlet transform coefficients, The input is a grayscale normalized flotation foam image. For the mother Shearlet function, For inner product operations, This is a scaling parameter, and its value range is the set of positive real numbers. This is the shearing parameter, and its value range is the set of real numbers. This is the translation parameter, and its value range is the set of two-dimensional real numbers. (Mother Shearlet function) Through the generating function Generated through scaling, shearing, and translation transformations, the expression is: ; in These are the pixel coordinates in the image. The anisotropic scaling matrix has the following specific form: , The shearing matrix has the following specific form: .

[0034] Subsequently, a discrete Shearlet transform is performed, employing a discrete Shearlet transform within a compactly supported frame to transform the scale parameter. Discretize into shearing parameters Discretize into Translation parameters Discretize into ,in , , Integer index, The value of is greater than or equal to 0. The absolute value is less than or equal to , The value of is a two-dimensional integer set. The effective region of interest image is given by the input. Perform the discrete Shearlet transform to obtain different scales. Different directions Shearlet coefficient matrix ,in Take four scales: 0, 1, 2, and 3. At each scale... Take integers within the corresponding range to generate coefficient matrices for 16 directions.

[0035] Next, the Shearlet characteristic statistics are calculated for each Shearlet coefficient matrix. The mean, variance, energy, and entropy of the coefficient matrix are calculated. These four statistics characterize the distribution features of the coefficient matrix from different dimensions, fully reflecting the multi-scale characteristics of the foam texture.

[0036] The formula for calculating the mean is: ;in Coefficient matrix The mean, Let be the row number of the coefficient matrix. The column number of the coefficient matrix. , For pixel indices in the coefficient matrix, Position in the coefficient matrix The coefficient value at that location.

[0037] The formula for calculating variance is: ;in Coefficient matrix The variance.

[0038] The energy calculation formula is: ;in Coefficient matrix Energy.

[0039] The formula for calculating entropy is: ;in Coefficient matrix entropy, This is an index for the quantization level of the coefficient amplitude. This represents the total number of quantification levels, with a value of 256. Quantize the amplitude in the coefficient matrix into levels The percentage of pixels.

[0040] Concatenate the four statistics across all scales and orientations to generate a 64-dimensional Shearlet feature vector. .

[0041] Subsequently, local texture difference feature extraction is performed using Local Binary Pattern Variance (LoBV). LoBV is an improvement on the traditional Local Binary Pattern (LoBV) by introducing variance information to characterize the contrast differences in local textures. Its core role in this scheme is to capture the roughness and particle distribution differences on the surface of copper ore flotation froth. This type of information is directly related to the effect of flotation reagents and complements the multi-scale edge features extracted by Shearlet transform.

[0042] First, the traditional local binary pattern value is calculated. For each pixel in the effective region of interest (ROI) image, a circular neighborhood with a radius of 1 is selected centered on that pixel. Eight pixels are uniformly sampled within this neighborhood. The gray value of each sampled pixel is compared with the gray value of the center pixel. If the gray value of the sampled pixel is greater than or equal to the gray value of the center pixel, it is marked as 1; otherwise, it is marked as 0. This results in an 8-bit binary number, which is then converted to decimal and used as the local binary pattern value of the center pixel. The formula is: ;in The local binary pattern value of the center pixel. The grayscale value of the center pixel. For the first The grayscale value of each sampling point This is a sign function that outputs 1 when the input value is greater than or equal to 0, and 0 otherwise.

[0043] Next, the local binary pattern variance is calculated. For each pixel, the variance of the gray values ​​of its 8 neighboring sampling points is calculated using the following formula: ;in The local variance value of the center pixel. It is the average of the gray values ​​of the 8 sampling points in the neighborhood. Specifically, it is calculated by dividing the sum of the gray values ​​of all sampling points in the neighborhood by the total number of sampling points.

[0044] Subsequently, a local binary mode variance histogram was constructed, dividing the local binary mode values ​​of the entire image into 59 uniform modes and 1 non-uniform mode, for a total of 60 mode categories. For each mode category, the mean of the variance values ​​of all pixels in that category was calculated and used as the feature value of that category, generating a 60-dimensional local binary mode variance feature vector. .

[0045] Finally, the initial fusion and interaction of traditional features are completed, and the Shearlet feature vectors are... With local binary pattern variance eigenvector Concatenation generates a 124-dimensional initial traditional feature vector. To achieve deep interaction between the two types of features, a feature weight allocation factor is introduced. The weight is calculated based on the ratio of inter-class scatter to intra-class scatter of the features. Adaptive weighting is applied to different feature dimensions, strengthening features strongly correlated with the flotation process and weakening irrelevant features. The formula is as follows: ;in The first traditional feature vector is the first one. Weights of dimensional features Indexed by feature dimensions, For the first The ratio of inter-class dispersion to intra-class dispersion of a feature.

[0046] The formula for calculating the ratio of inter-class scatter to intra-class scatter is: ;in For category indexing, The total number of categories is given here. The samples are divided into high, medium, and low categories based on the copper grade of the concentrate. The value is 3. For the first The number of samples in each class For the first The first class of samples The mean of the dimensional features, For the first of all samples The mean of the dimensional features, For the first The first sample Dimensional initial traditional eigenvalues.

[0047] The initial traditional feature vector is weighted based on the weights to generate a weighted traditional feature vector. The formula is: ;in For the weighted traditional eigenvectors, the first 1-dimensional eigenvalues.

[0048] The second part focuses on deep visual feature extraction based on EfficientNetV2. EfficientNetV2 is a lightweight and efficient convolutional neural network that combines progressive training, hybrid deep separable convolutions, and attention mechanisms. Its core role in this approach is to extract high-level semantic features of foam that cannot be captured by traditional hand-crafted features, including the aggregation state of foam, the spatial distribution of mineralized particles, and the global distribution pattern of foam size. These features are directly related to the overall operating conditions of the flotation process and strongly complement traditional features.

[0049] First, the EfficientNetV2 model structure was constructed, using EfficientNetV2-S as the basic network structure. It consists of a stem layer, multiple stacked MBConv modules and Fused-MBConv modules, and a head layer. The stem layer comprises a 3×3 convolutional layer, a batch normalization layer, and a SiLU activation function, used for preliminary feature extraction from the input image, with 24 output channels. The Fused-MBConv module replaces the depthwise separable convolutions in the MBConv module with ordinary 3×3 convolutions, improving the training speed of shallow networks. The first half of the network uses the Fused-MBConv module, and the second half uses the MBConv module. Each module includes dilated convolutions, depthwise separable convolutions, a squeeze-enhanced attention module, a batch normalization layer, and a SiLU activation function.

[0050] The calculation process of the squeeze-incentive attention module is as follows: global average pooling is performed on the feature map input to the module to obtain channel-level feature vectors. Channel weights are generated through two fully connected layers. The weights are then multiplied with the original feature map channel by channel to achieve channel attention weighting. The formula is as follows: ;in This is the output feature map after passing through the squeeze-excited attention module. The input feature map for the module. This is a global average pooling operation. This is the weight matrix of the first fully connected layer. It is the ReLU activation function. This is the weight matrix for the second fully connected layer. It is the Sigmoid activation function. This is a channel-by-channel multiplication operation.

[0051] The head layer consists of a 1×1 convolutional layer, a batch normalization layer, a SiLU activation function, a global average pooling layer, and two fully connected layers, ultimately outputting a depth feature vector with a dimension of 128.

[0052] Then, the progressive training process of EfficientNetV2 is executed. The progressive training strategy significantly improves the model's generalization ability by gradually increasing the resolution and regularization intensity of the input image during training, adapting to the complex and ever-changing working conditions of copper ore flotation sites, and avoiding model overfitting.

[0053] The training process is divided into four stages, with the input image resolution and regularization strength increasing sequentially in each stage. In the first stage, the input image resolution is 128×128, the random inactivation rate is 0.1, and the weight decay coefficient is 1e-5. In the second stage, the input image resolution is 160×160, the random inactivation rate is 0.2, and the weight decay coefficient is 2e-5. In the third stage, the input image resolution is 224×224, the random inactivation rate is 0.3, and the weight decay coefficient is 3e-5. In the fourth stage, the input image resolution is 300×300, the random inactivation rate is 0.4, and the weight decay coefficient is 4e-5.

[0054] The loss function combines a contrastive loss function with a mean squared error loss function as the total loss function. The contrastive loss is used to improve the intra-class compactness and inter-class discriminativeness of features, while the mean squared error loss is used to achieve pre-training for the regression task, establishing a direct correlation between deep features and the floating parameters. The formula is as follows: ;in The total loss function of EfficientNetV2 is... To compare loss functions, To balance the weights, a value of 0.5 is used. This is the mean squared error loss function.

[0055] The formula for the contrastive loss function is: ;in For batch size, For sample pair indexing, This is the label for the sample pair. If the two samples are of the same type, the value is 1; otherwise, the value is 0. Let be the Euclidean distance between the depth feature vectors of two samples. This is a boundary value, and its value is 1.0.

[0056] The optimizer used is AdamW, with an initial learning rate of 1e-4, which decays to 0.5 after each training phase. The effective region of interest images from the training set output by S1 are adjusted to the resolution of the corresponding phase and input into the EfficientNetV2 model. Training is performed sequentially phase by phase, with 50 epochs per phase. Every 10 epochs, a validation set is used to verify model performance, and the model with the lowest contrast loss on the validation set is saved as the pre-trained EfficientNetV2 model.

[0057] Finally, the deep feature extraction application of EfficientNetV2 is executed. The output of the last fully connected layer of the head layer of the pre-trained EfficientNetV2 model is used as the deep feature vector. For all valid regions of interest images in the training, validation, and test sets, the resolution is adjusted to 300×300, and then input into the pre-trained EfficientNetV2 model to extract a 128-dimensional deep visual feature vector. .

[0058] The third part involves the validity verification and preliminary interaction of multimodal features. This part realizes the bidirectional interaction between traditional features and deep visual features. Through mutual information calculation, it selects feature dimensions with strong complementarity between the two types of features, eliminates redundant features, and avoids irrelevant information from interfering with the subsequent fusion process.

[0059] First, calculate the mutual information between each dimension of the weighted traditional feature vector and each dimension of the depth visual feature vector, and construct a mutual information matrix, where the first... Line number The elements of the column are the first elements of the weighted traditional eigenvector. 3D features and the 1st dimension of deep visual feature vectors The mutual information between dimensional features is expressed by the formula: ;in For mutual information between two-dimensional features, For the weighted traditional eigenvectors, the first Quantized value index of dimensional features For the depth visual feature vector, the first Quantized value index of dimensional features The joint probability distribution of two-dimensional features. For the weighted traditional eigenvectors, the first Marginal probability distribution of 3D features For the depth visual feature vector, the first Marginal probability distribution of 3D features.

[0060] Subsequently, feature filtering was performed. From the weighted traditional feature vectors, the top 80 features with the highest mean mutual information with the depth visual feature vectors were retained, generating the filtered traditional feature vectors. For deep visual feature vectors, the top 100 features with the highest mean mutual information with the weighted traditional feature vectors are retained to generate filtered deep visual feature vectors. .

[0061] The final output consists of the filtered traditional feature vector and the filtered deep visual feature vector, which are then used in the subsequent cross-modal fusion process.

[0062] S3. Cross-modal feature fusion based on deep canonical correlation analysis and adaptive graph convolutional network refer to Figure 3 This step takes the filtered traditional feature vector and the filtered deep visual feature vector output by S2 as input, uses deep canonical correlation analysis to align the distribution of cross-modal features, and uses an adaptive graph convolutional network to fuse the topological relationships of features. The two are optimized alternately to achieve bidirectional deep interaction, eliminate the modal distribution gap between traditional features and deep visual features, capture the nonlinear correlation between features, and generate a unified fused feature vector, providing high-quality input for subsequent multi-task prediction models.

[0063] The first part focuses on cross-modal feature distribution alignment based on deep canonical correlation analysis (DADA). DADA maps two types of modal features to two symmetric deep neural networks, maximizing the correlation between the mapped features. Its core function in this approach is to bridge the modal distribution gap between traditional handcrafted features and deep learning features. Since the two types of features are generated in different ways, their corresponding feature space distributions differ significantly. Direct fusion would introduce a large amount of noise. Distribution alignment allows the two types of features to be mapped to the same feature space, ensuring the effectiveness of subsequent fusion.

[0064] First, the deep canonical correlation analysis model structure was constructed. The model comprises two symmetrical deep mapping networks: a traditional feature mapping network and a deep feature mapping network. Each network consists of three fully connected layers, each containing 256 neurons, employing the ReLU activation function and batch normalization layers. The output layer dimension of both networks is 128, and the output features are denoted as follows: and .

[0065] The loss function for deep canonical correlation analysis is then defined. This loss function maximizes the canonical correlation coefficient between the mapped features, which is transformed into minimizing the negative canonical correlation coefficient. The formula is as follows: ;in The loss function for deep canonical correlation analysis, for and The first canonical correlation coefficient between them.

[0066] The calculation process of the first canonical correlation coefficient is as follows: First, the... and After centering, the centered feature matrix is ​​obtained, as shown in the formula: ;in For batch size, It is a vector of all 1s. It is the transpose of a vector consisting entirely of 1s. The centered traditional mapping feature matrix, This is the centered depth mapping feature matrix.

[0067] Then the covariance matrix is ​​calculated using the following formula: ; in The autocovariance matrix of the traditional mapping features, Let be the autocovariance matrix of the depth-mapped features. Let be the cross-covariance matrix of the two types of mapping features.

[0068] Finally, the generalized eigenvalue problem is solved using the following formula: ; in The projection vector of the traditional mapping feature. Given the projection vector of the depth-mapped features, the largest generalized eigenvalue obtained is the first canonical correlation coefficient. .

[0069] The model was trained using the Adam optimizer with an initial learning rate of 5e-4. The total number of training rounds was 200. Every 10 rounds, the correlation coefficient was validated using a validation set. The model with the highest correlation coefficient in the validation set was saved as the completed deep canonical correlation analysis model.

[0070] Finally, the feature mapping application of deep canonical correlation analysis is performed. The filtered traditional feature vectors are input into the trained traditional feature mapping network to obtain aligned traditional feature vectors. The filtered deep visual feature vectors are input into the trained deep feature mapping network to obtain aligned deep feature vectors. .

[0071] The second part focuses on feature topology fusion based on adaptive graph convolutional networks. Adaptive graph convolutional networks automatically construct a topological graph between features and utilize graph convolution operations to fuse neighborhood information between features. In this approach, the core role is to capture the non-linear relationships between aligned traditional features and deep features. These relationships cannot be captured by simple concatenation or weighted fusion. For example, the color features of bubbles have a strong coupling relationship with the clustering state in deep features. Graph convolution can incorporate this implicit relationship information into the fused features, significantly improving the expressive power of the features.

[0072] First, the adaptive graph is constructed by concatenating the aligned traditional feature vector with the aligned depth feature vector, generating a 256-dimensional concatenated feature vector. An undirected weighted graph is automatically constructed based on the concatenated feature vectors. The undirected weighted graph consists of a node set, an edge set, and an adjacency matrix. Each node in the node set corresponds to one dimension of the concatenated feature vector, and there are a total of 256 nodes.

[0073] The adjacency matrix is ​​calculated as follows: First, the cosine similarity between the corresponding feature dimensions of any two nodes is calculated, and a similarity matrix is ​​constructed. The formula is: ;in For the first The node and the first Cosine similarity between nodes For the concatenation of the feature vectors, the first... 3D eigenvalues It is an L2 norm.

[0074] The similarity matrix is ​​then sparsified by retaining only the connections between the top 10 most similar nodes for each node and setting the remaining connections to 0, resulting in a sparse similarity matrix. Next, the adjacency matrix is ​​calculated, which is the sum of the sparse similarity matrix and the identity matrix. Self-loops are added to preserve the node's own feature information.

[0075] Next, we calculate the degree matrix. This is a diagonal matrix, where the diagonal elements are the sum of the row elements of the adjacent nodes' adjacency matrices, and the remaining elements are 0. Finally, we calculate the symmetric normalized Laplacian matrix using the following formula: ;in For a symmetric normalized Laplace matrix, It is the identity matrix. For degree matrix, It is an adjacency matrix.

[0076] Subsequently, the model structure of the adaptive graph convolutional network was constructed. The network contains two adaptive graph convolutional layers, and the calculation process of each graph convolutional layer is as follows: ;in For the first The input feature matrix of the layer, the initial input To concatenate feature vectors , To add a self-loop adjacency matrix, for The corresponding degree matrix, For the first The weight matrix of the layer, It is the ReLU activation function. For the first The output feature matrix of the layer.

[0077] The first graph convolutional layer has an output dimension of 128, and the second graph convolutional layer has an output dimension of 64. A fully connected layer with an output dimension of 256 is added after the two graph convolutional layers to generate the final fused feature vector. .

[0078] The third part involves alternating optimization of adaptive graph convolutional networks and deep canonical correlation analysis. To achieve bidirectional deep interaction between the two algorithms, an alternating optimization strategy is adopted, alternately training the deep canonical correlation analysis model and the adaptive graph convolutional network model. This allows distribution alignment and feature fusion to form a closed-loop optimization. The distributed aligned features provide high-quality input for fusion, and the fused features provide feedback to optimize the distribution alignment target, making the alignment of the two types of features more suitable for subsequent multi-task prediction needs.

[0079] The specific process of alternating optimization is as follows: First, a fixed-depth canonical correlation analysis model is used to train an adaptive graphical convolutional network model. The loss function adopted is the mean squared error loss function, with the true values ​​of the dosage and inflation volume as labels. The formula is: ;in The loss function for adaptive graph convolutional networks, For task indexing, Values ​​from 1 to 5 correspond to the dosages of collector, inhibitor, activator, pH adjuster, and aeration, respectively. For the first The predicted value for each task, For the first The true label value of each task.

[0080] The optimizer used was Adam, with an initial learning rate of 1e-4, and training for 50 epochs.

[0081] The second step is to fix the adaptive graph convolutional network model and update the deep canonical correlation analysis model. The input features of the first graph convolutional layer of the adaptive graph convolutional network are used as the new alignment target. The loss function of the deep canonical correlation analysis is updated to maximize the correlation between the mapped features and the target, making the feature alignment more suitable for the fusion process. The formula is: ;in The updated deep canonical correlation analysis loss function, The first 128 dimensions of the traditional features in the initial input feature matrix. This represents the last 128 dimensions of the corresponding deep features in the initial input feature matrix.

[0082] Train for 30 epochs. Repeat the alternating optimization process described above, alternating 5 times in total, and save the final deep canonical correlation analysis model and adaptive graph convolutional network model.

[0083] Finally, feature fusion is performed on the entire dataset. For all samples in the training, validation, and test sets, the aligned features are first obtained through a deep canonical correlation analysis model, and then the final fused feature vector is obtained through an adaptive graph convolutional network model, which is then output to the subsequent multi-task model construction stage.

[0084] S4. Construction of a progressive hierarchical expert network model based on Gumbel-Softmax and dynamic weight averaging refer to Figure 4 This step uses the fused feature vector output by S3 as input to construct a progressive hierarchical expert network model. Gumbel-Softmax with Concrete Distribution is used to optimize the hierarchical gating network, and dynamic weight averaging combined with gradient projection is used to balance the multi-task loss. The two algorithms achieve bidirectional deep interaction through joint optimization of the loss function, which solves the problems of unbalanced expert activation, performance conflict between tasks, and training seesaw effect in multi-task modeling, and achieves accurate prediction of drug dosage and inflation volume through multi-task collaborative efforts.

[0085] First, the overall architecture of the progressive hierarchical expert network model was designed. The model has a three-layer progressive structure, from bottom to top: a bottom shared expert layer, a middle task cluster-specific expert layer, and a top single-task-specific expert layer. It is equipped with a hierarchical gating network module, a multi-constraint optimization module, and a task output head module. The model input is a 256-dimensional fused feature vector, and the output consists of five predicted target values: collector dosage, inhibitor dosage, activator dosage, pH adjuster dosage, and aeration rate.

[0086] Subsequently, the differentiated construction of expert networks at each level was completed. The bottom shared expert layer consists of four parallel shared expert networks, each with a two-layer fully connected structure. The first layer contains 128 neurons, and the second layer contains 64 neurons, employing the ReLU activation function and layer normalization. All shared expert networks share all training data to learn common features related to the flotation foam state of copper ore across the five prediction tasks, achieving information sharing between tasks.

[0087] The intermediate task cluster-specific expert layer divides the five prediction tasks into two task clusters based on task attributes: a drug dosing cluster and an aeration cluster. The drug dosing cluster includes four tasks: collector dosage, inhibitor dosage, activator dosage, and pH adjuster dosage. The aeration cluster includes one task: aeration amount. Three parallel task cluster-specific expert networks are set up for each task cluster. Each task cluster-specific expert network has a two-layer fully connected structure: the first layer contains 128 neurons, and the second layer contains 64 neurons, using the ReLU activation function and layer normalization. Each task cluster-specific expert network only learns task-related features within its corresponding task cluster, avoiding cross-cluster learning, thus achieving feature sharing between tasks within the same cluster and feature isolation between tasks in different clusters.

[0088] The top-level single-task-specific expert layer consists of two parallel single-task-specific expert networks for each of the five prediction tasks. Each single-task-specific expert network has a two-layer fully connected structure: the first layer contains 128 neurons, and the second layer contains 64 neurons, employing the ReLU activation function and layer normalization. Each single-task-specific expert network learns only the features specific to its corresponding single task, without learning across tasks, thus capturing the personalized features of each task and resolving performance conflicts between tasks.

[0089] Next, we completed the construction of the hierarchical gating network module based on Gumbel-Softmax with Concrete Distribution. Gumbel-Softmax with Concrete Distribution achieves smooth discrete sampling of gating weights by introducing Gumbel noise and Concrete distribution. Its core role in this scheme is to solve the problem of imbalanced expert activation in multi-expert networks. Traditional Softmax gating tends to lead to a few experts dominating in the early stages of training, suppressing the learning of other experts. Gumbel-Softmax introduces random noise to encourage more experts to participate in training. At the same time, the Concrete distribution makes the discrete sampling process differentiable, without affecting the backpropagation of gradients, thus ensuring the stability of training.

[0090] An independent gating network is set up for each level to achieve dynamic adaptive allocation of expert weights. First, a bottom-level shared gating network is constructed, with a 256-dimensional fused feature vector as input, generating four raw scores through a fully connected layer. Gumbel noise is introduced, adding independent and identically distributed Gumbel noise to each raw score, as shown in the formula: ;in For the first time after adding noise Shared expert scores, For shared expert indexes, values ​​range from 1 to 4. For the first The original scores of the shared experts, For the first One Gumbel noise, These are random numbers sampled from a uniform distribution, where the values ​​range from 0 to 1.

[0091] The gate weights are generated using a Concrete distribution, and the formula is as follows: ;in For the first Gating weights for shared experts, This represents the maximum shared expert score after adding noise. The temperature parameter of the underlying gating network is initially set to 2.0 and gradually decays to 0.1 during training.

[0092] The outputs of the four shared expert networks are weighted and fused to generate the final shared feature vector, as shown in the formula: ;in To ultimately share feature vectors, For the first The output of a shared expert network.

[0093] Subsequently, a mid-level task cluster gating network is constructed, with one gating network set up for each task cluster. For the drug dispensing task cluster, the input is the bottom-level shared feature vector, which is passed through a fully connected layer to generate three raw scores. Gumbel noise is added and gating weights are generated in the same way as the bottom-level shared gating network. The initial value of the temperature parameter is set to 1.5, and it is gradually decayed to 0.1 during training. The outputs of the three task cluster-specific expert networks within the drug dispensing task cluster are weighted and fused to generate the final feature vector for the drug dispensing task cluster. The final feature vector for the inflation task cluster is generated in the same way.

[0094] Next, a top-level single-task gating network is constructed, with one single-task gating network set up for each prediction task. For the collector dosage task, the input is the final feature vector of the dosage task cluster. Two raw scores are generated through a fully connected layer. Gumbel noise is added and gating weights are generated in the same way as the bottom shared gating network. The initial value of the temperature parameter is set to 1.0, and it is gradually decayed to 0.05 during training. The outputs of the two single-task dedicated expert networks in the collector dosage task are weighted and fused to generate the final feature vector of the collector dosage task. The final feature vectors of the other four tasks are generated in the same way.

[0095] Subsequently, the task output head module was constructed. For each of the five prediction tasks, an independent task output head was set up. Each task output head is a two-layer fully connected structure. The first layer contains 64 neurons and uses the GELU activation function and layer normalization operation. The output of the second layer is a single neuron, which generates the final prediction value for the corresponding task.

[0096] The prediction formula for the collector dosage is as follows: ;in This is the final predicted output value for the collector dosage. , These are the weight matrix and bias vector of the first layer of the output head for the collector dosage task. , These are the weight matrix and bias scalar of the second layer of the output head for the collector dosage task. This is the final feature vector output by the top-level single-task gating network corresponding to the collector dosage task. For layer normalization operation, is the activation function for the Gaussian error linear unit.

[0097] The predicted values ​​for the other four tasks were generated in the same manner: the predicted values ​​for sodium hydroxide dosage, inhibitor dosage, activator dosage, and aeration volume, in that order.

[0098] Next, we will construct a multi-constraint optimization module based on dynamic weight averaging and gradient projection. Dynamic weight averaging dynamically adjusts the loss weights by tracking the training speed of each task, while gradient projection avoids gradient conflicts between tasks by projecting task gradients into an orthogonal space of shared gradients. The combination of the two achieves a fine balance of multi-task loss. Its core role in this scheme is to solve the training seesaw effect in multi-task modeling, preventing the performance improvement of one task from causing the performance degradation of other tasks, and achieving collaborative optimization of all tasks.

[0099] First, dynamic weight averaging is performed. The core idea of ​​dynamic weight averaging is to assign higher loss weights to tasks with slower training speeds, balancing the training progress of each task and preventing the training process from being dominated by simpler tasks. The calculation process is as follows: First, the loss reduction rate of each task in the current training round is calculated using the following formula: ;in For the first The task in the first The rate of decrease in wheel losses, For the first The task in the first The mean square error loss value of the wheel, This represents the size of the sliding window, with a value of 5.

[0100] Then, the dynamic weight of each task is calculated using the following formula: ; in For the first The task in the first The dynamic weights of the wheel, The total number of tasks, with a value of 5. This is the temperature parameter, with a value of 2.0.

[0101] Next, gradient projection calculation is performed. The core idea of ​​gradient projection is to decompose the gradient of each task into components parallel to and orthogonal to the shared gradient, retaining only the orthogonal components to update the shared parameters, thus avoiding gradient conflicts between tasks and eliminating negative transfer between tasks. The calculation process is as follows: First, the average gradient of all tasks is calculated as the shared gradient, using the formula: ;in For the first Shared gradient of the wheel, For the first The task in the first The gradient of the wheel relative to the shared expert layer parameters at the bottom layer.

[0102] The gradient of each task is then projected to obtain the projected gradient, as shown in the formula: ;in For the first The task in the first The gradient after projection of the wheel, For inner product operations, It is an L2 norm.

[0103] Finally, the joint interaction between the multi-constraint optimization module and the Gumbel-Softmax gated network was completed. To achieve bidirectional deep interaction between the two algorithms, dynamic weights, gradient projection, and the temperature parameter decay of Gumbel-Softmax were jointly optimized, allowing multi-task loss balancing and expert activation balancing to form a synergistic optimization. The total training loss function formula is as follows: ;in Let be the total training loss function. This is the regularization weight for the temperature parameter, with a value of 0.01. For the first The average value of temperature parameters for all gated networks.

[0104] The temperature parameter decay formula is related to the training epochs and the total loss function, allowing the temperature decay to adapt to the model's training state. The formula is: ;in For the first Temperature parameters of the bottom-level gating network of the wheel. The attenuation coefficient is 0.001. The temperature parameters of the middle and top-level gated networks are attenuated in the same way.

[0105] During model training, the parameters of the bottom shared expert layer are updated using the projected gradient, and the parameters of the remaining layers are updated using the original gradient, thus achieving conflict-free updating of gradients for multiple tasks.

[0106] Finally, the overall construction of the progressive hierarchical expert network model is completed, and the initial network model is output for subsequent model training and dynamic optimization.

[0107] S5. Multi-constraint collaborative model phased training and dynamic optimization refer to Figure 4 This step uses the fused feature vectors of the training and validation sets output by S3, and the matching label dataset output by S1 as training data, and the initial progressive hierarchical expert network model constructed by S4 as the training object. A phased training strategy combined with multi-constraint collaborative optimization is adopted to complete the model training, ensuring that the model converges to the global optimal solution, while having strong generalization ability and adapting to the complex working conditions of copper ore flotation site.

[0108] First, complete the basic training parameter settings. The AdamW optimizer is used, with an initial learning rate of 1e-4, a weight decay coefficient of 1e-5, a batch size of 32, and a total training epoch of 300. The training process is divided into three stages: the first stage is the pre-training stage, the second stage is the constrained training stage, and the third stage is the convergence training stage.

[0109] The first pre-training phase is then executed. In this phase, all parameters of the mid-level task-specific expert layers and the top-level single-task-specific expert layers are frozen. Only the parameters of the bottom-level shared expert layers and the bottom-level shared gated network are trained. The goal of pre-training is to minimize the simple weighted sum of the mean squared error losses of the five tasks. All tasks have an initial weight of 0.2, and the training lasts for 50 epochs. The core purpose of this phase is to allow the bottom-level shared expert layers to learn the common features of the five tasks, avoiding interference from the upper-level task-specific layers, laying a solid foundation for subsequent full-model training, and outputting the pre-trained model.

[0110] Next, the second stage, the constrained training stage, is executed. In this stage, all network layer parameters are unfrozen, and dynamic weight averaging, gradient projection, and Gumbel-Softmax temperature decay constraints constructed using S4 are introduced. Constrained training is completed with the total training loss function as the objective. In each training round, the dynamic weights for each task are calculated first, followed by the original gradient and projected gradient for each task. The projected gradient is used to update the parameters of the bottom shared expert layer, while the original gradient is used to update the parameters of the remaining layers. After each training round, the temperature parameters of all gated networks are updated based on the total training loss function value. Every 10 rounds, the model performance is validated using a validation set, and the model with the lowest total loss in the validation set is saved as the constrained training model. This stage involves 150 training rounds. Its core function is to solve the problems of unbalanced expert activation and performance conflicts between tasks in multi-task training through multi-constraint collaborative optimization, enabling all tasks to achieve collaborative optimization.

[0111] The third stage, convergence training, is then executed. In this stage, the temperature parameter of all gating networks is fixed at 0.05, and the loss weights of all tasks are fixed to their optimal values ​​at the end of the constraint training. Only the parameters of all expert networks and task output heads are fine-tuned, aiming to minimize the weighted sum of the mean squared error losses of the five tasks, completing 100 rounds of convergence training. An early stopping strategy is employed: if the total loss on the validation set does not decrease for 30 consecutive rounds, training is terminated early, and the model with the best performance on the validation set is saved as the final optimal progressive hierarchical expert network model. The core purpose of this stage is to allow the model to converge to the global optimum under stable constraints, avoiding fluctuations during the training process and ensuring the model's prediction accuracy.

[0112] Finally, model performance is validated. The optimal model is tested using the fused feature vectors from the test set output by S3. If the average coefficient of determination for all tasks on the test set is greater than or equal to 0.92, the model is deemed qualified, and the qualified optimal model is output for subsequent inference and prediction. If the requirement is not met, the model returns to S1 to expand the dataset and the training process is repeated.

[0113] S6. Feature mapping and model inference prediction of the samples to be predicted refer to Figure 4 This step takes the real-time acquired images of the flotation froth of the copper ore to be processed as input and the qualified optimal progressive hierarchical expert network model output by S5 as the inference tool. It strictly follows the data processing flow during training to complete feature mapping and model inference, ensuring the accuracy and consistency of the prediction results and achieving real-time accurate prediction of the dosage and aeration volume.

[0114] First, perform standardized preprocessing on the image to be predicted. For the copper ore flotation foam image to be processed, perform the same preprocessing operations as in S1, including multi-view image spatial registration, image denoising and grayscale normalization, and region of interest extraction, to generate the effective region of interest image to be predicted. This ensures that the distribution of the input image is completely consistent with the training set, avoiding the decrease in prediction accuracy caused by distribution shift.

[0115] Subsequently, feature extraction and fusion of the image to be predicted are performed. For the effective region of interest image to be predicted, Shearlet transform, local binary pattern variance feature extraction, and EfficientNetV2 deep feature extraction, which are completely consistent with S2, are performed to generate filtered traditional feature vectors and filtered deep visual feature vectors. Then, deep canonical correlation analysis mapping and adaptive graph convolutional network fusion, which are completely consistent with S3, are performed to generate a 256-dimensional fused feature vector to be predicted, ensuring that the feature extraction and fusion process is completely consistent with the training process.

[0116] Next, the model inference prediction is performed. The 256-dimensional fused feature vector to be predicted is input into the optimal progressive hierarchical expert network model. The model sequentially passes through the bottom shared expert layer, the middle task cluster-specific expert layer, the top single task-specific expert layer, the hierarchical gating network, and the task output head, and outputs 5 prediction results, namely, the predicted value of the collector dosage, the predicted value of the inhibitor dosage, the predicted value of the activator dosage, the predicted value of the pH adjuster dosage, and the predicted value of the aeration volume.

[0117] Finally, all prediction results are output and synchronously transmitted to the subsequent confidence verification and closed-loop feedback stages.

[0118] S7. Confidence verification of prediction results and model closed-loop feedback update refer to Figure 4 This step takes the prediction results output by S6, the corresponding flotation froth image of the copper ore to be processed, and the real working condition data at the corresponding time collected by the online grade analyzer and the distributed control system as inputs to complete the confidence verification of the prediction results and the incremental update of the model. This enables the model to continuously adapt to the complex working conditions of copper ore flotation and ensures the prediction accuracy of the model in the long term.

[0119] First, the confidence level of the prediction results is calculated. During model inference, the Monte Carlo dropout method is used to perform 10 random forward inferences, resulting in 10 sets of prediction results. The mean and standard deviation of each set of prediction results are calculated. The coefficient of variation (COP) is used as the confidence index of the prediction results; the COP is the ratio of the standard deviation to the mean. The smaller the COP, the higher the confidence level. A confidence threshold of 0.05 is set. If the COP of all task prediction results is less than or equal to 0.05, the prediction result is considered a high-confidence result and is directly output to the copper ore flotation control system as an adjustment reference. If the COP of any task is greater than 0.05, the prediction result is considered a low-confidence result and proceeds to the subsequent verification process.

[0120] Subsequently, truth value verification and sample archiving of low-confidence results are performed. For the froth image corresponding to the low-confidence prediction result, after a delay of one flotation cycle, the actual copper grade data of the concentrate and tailings at the corresponding time are collected using an online grade analyzer. The actual reagent dosage and aeration volume data at the corresponding time are also collected using a distributed control system and used as the true label data for that sample. The relative error between the predicted and actual values ​​is calculated. If the relative error of any task is greater than 10%, the froth image and its corresponding true label data are archived to the incremental training sample library. If the relative errors of all tasks are less than or equal to 10%, the prediction result is deemed valid and output to the copper ore flotation control system.

[0121] Finally, the closed-loop incremental update of the model is executed. When the number of samples in the incremental training sample library reaches 200 sets, the incremental samples are merged with the original training set of S1 to construct a new training set. The feature extraction, fusion, and model training processes of S2 to S5 are then executed, and the optimal model is incrementally fine-tuned to update the model parameters. After the incremental training is completed, the updated model is tested for performance. If the average determination coefficient of the test set is greater than or equal to 0.92, the original model is replaced and used as the optimal model for subsequent inference and prediction. If the condition is not met, the original model is retained, and the incremental training sample library is further expanded.

[0122] Finally, the prediction results are verified and the model is updated in a closed loop, forming a complete prediction-verification-update closed loop.

[0123] In some embodiments, when dividing the effective region of interest (ROI) image into training, validation, and test sets, the principle of non-overlapping time sequences is strictly followed. The continuous production shifts of the flotation process are used as the division unit. The samples from the first 70% of shifts are divided into the training set, the samples from the middle 20% of shifts into the validation set, and the samples from the last 10% of shifts into the test set, in chronological order. Randomly shuffling the sample time sequence is strictly prohibited to avoid inflated model generalization ability due to time-series data leakage between the training and test sets. For label data matching, the image acquisition time is used as the reference. The operating condition label and grade label corresponding to the pulp residence time in the flotation cell are matched after a delay of one flotation cell. The pulp residence time in the flotation cell is calculated in real-time using the effective volume of the flotation cell and the pulp feed flow rate. The calculation formula is: ;in, The residence time of the slurry. The effective volume of the flotation cell. This corresponds to the slurry feed flow rate of the flotation cell at that moment. This timing matching method eliminates the lag between foam image acquisition and operating parameter response, ensuring a causal correspondence between sample input and label.

[0124] In some embodiments, when classifying samples into high, medium, and low grades based on the copper grade of the concentrate, the target copper grade designed by the concentrator is used as the benchmark, and the classification boundary is determined by combining the fluctuation threshold of the production process: when the copper grade of the concentrate corresponding to the sample is ≥ the target value + 0.2%, it is classified as high grade; when the copper grade of the concentrate corresponding to the sample is within the range of ± 0.2% of the target value, it is classified as medium grade; when the copper grade of the concentrate corresponding to the sample is ≤ the target value - 0.2%, it is classified as low grade. The target value is the designed copper grade of the concentrate specified in the concentrator's process documents. This classification method is fully matched with the on-site production control standards, ensuring that the features after weighting the inter-class dispersion have practical process discrimination value.

[0125] In some embodiments, the selection rule of retaining the first 80 dimensions of the initial traditional feature vector and the first 100 dimensions of the initial depth visual feature vector is determined based on the ablation experiment results of feature dimension-model performance: for the initial traditional feature vector, the average coefficient of determination of the model on the test set is tested when retaining 40 / 60 / 80 / 100 / 120 dimensions of features respectively. Of which 80 dimensions are retained Reaching the peak, continue adding dimensions. No significant improvement and increased model inference latency; for the initial depth visual feature vector, the model performance was tested when retaining 60 / 80 / 100 / 120 / 128 dimensions of features, and the model performance when retaining 100 dimensions was tested. To achieve optimal performance, the total number of dimensions for both types of features is controlled at 180, which balances the feature representation capability with the computational complexity of the subsequent fusion network.

[0126] In some embodiments, the bottom layer of shared expert network consists of 4 parallel shared expert networks, the middle layer consists of 3 parallel task cluster-specific expert networks for each task cluster, and the top layer consists of 2 parallel single-task-specific expert networks for each single task. Based on the activation balance ablation experiment of multi-expert networks, it is determined that: when the number of shared experts is less than 4, the model cannot fully learn the common features of the 5 tasks, resulting in underfitting; when the number of shared experts is greater than 4, there is redundancy in expert activation, with the average activation rate of a single expert being less than 30%, resulting in parameter waste; when the number of task cluster-specific experts is 3, the mechanism of action of different agents within the drug dosing task cluster can be covered simultaneously, and the activation rate of a single expert is higher than 45%; when the number of single-task-specific experts is 2, the normal and extreme working conditions of the corresponding task can be learned separately, avoiding the fitting bias of a single expert to the working conditions.

[0127] In some embodiments, the threshold for the number of samples in the incremental training sample library is set to 200 sets. Based on the convergence experiment results of the model incremental fine-tuning, it is determined that: when the number of incremental samples is less than 200 sets, the model fine-tuning is prone to overfitting, and the generalization performance on the test set decreases; when the number of incremental samples reaches 200 sets, it can cover at least three different ore property fluctuation conditions, and the model's prediction of new conditions after fine-tuning is improved. The improvement is ≥3%, and the model's fitting performance to the original working conditions will not decrease due to too many incremental samples; the threshold can be adaptively adjusted according to the frequency of fluctuations in the working conditions of the ore dressing plant. When the working conditions fluctuate frequently, the threshold is lowered to 150 groups, and when the working conditions are stable, the threshold is raised to 300 groups.

[0128] In some embodiments, during S6 model inference and prediction, an extreme condition prediction module is added. After feature extraction, the fused feature vector is first analyzed using the isolated forest algorithm to identify abnormal conditions. When an extreme condition is identified, the expert routing weights of the model are automatically switched, increasing the weight ratio of the top-level single-task-specific expert network and decreasing the weight ratio of the bottom-level shared expert layer. Specifically, under extreme conditions, the output weight of the bottom-level shared expert layer is reduced to 0.3, the output weight of the top-level single-task-specific expert layer is increased to 0.5, and the output weight of the middle-level task cluster-specific expert layer remains at 0.2, ensuring the model's prediction accuracy for extreme conditions. Extreme conditions include fluctuations in raw ore copper grade exceeding ±30%, slurry concentration exceeding ±20%, and flotation cell liquid level exceeding ±15%.

[0129] In some embodiments, during traditional feature extraction in S2, a non-downsampled dual-tree complex Shearlet transform is used instead of the conventional discrete Shearlet transform to achieve translation-invariant extraction of multi-scale and multi-directional features of the foam image, eliminating feature shift problems caused by light fluctuations and foam flow in industrial settings. The specific implementation process is as follows: First, a dual-tree complex Shearlet filter bank is constructed using two parallel four-channel inseparable wavelet trees to form a dual-tree structure. The first tree is the real part tree, and the second tree is the imaginary part tree. The filters of the two trees satisfy the Hilbert transform constraints, ensuring that the phase information of the transformed coefficients is completely preserved. Second, a non-downsampled pyramid decomposition is performed on the effective region of interest image, decomposing it into low-frequency and high-frequency sub-bands at four scales. No downsampling operation is performed during the decomposition process, and all sub-bands maintain the same size as the original image, ensuring translation invariance. Third, for each scale's high-frequency sub-band, a non-downsampled pyramid decomposition is performed using a dual-tree complex Shearlet transform. The Shearlet filter bank performs multi-directional decomposition, decomposing each scale into 16 directions to obtain complex Shearlet coefficient matrices for the corresponding scale and direction. These coefficient matrices contain real and imaginary parts. In the fourth step, for each complex Shearlet coefficient matrix, five statistics—mean, variance, energy, entropy, and phase consistency—are calculated for both the real and imaginary parts. These statistics from all scales and directions are concatenated to generate a 128-dimensional complex Shearlet feature vector. In the fifth step, the complex Shearlet feature vector is concatenated with the local texture difference feature vector, and weighted by the ratio of inter-class scatter to intra-class scatter to obtain the initial traditional feature vector. In this implementation, the non-downsampled dual-tree complex Shearlet transform, compared to the conventional discrete Shearlet transform, can completely preserve the phase information and translation invariance of the foam image, improves the anti-interference ability against foam flow and illumination fluctuations by more than 40%, and increases the average Pearson correlation coefficient between the extracted features and the degree of mineralization by 0.15, thus solving the problem of poor feature stability in dynamic flotation scenarios using the conventional Shearlet transform.

[0130] In some embodiments, during deep visual feature extraction in S2, a frequency-aware dynamic convolution module and a high- and low-frequency branch separation structure are embedded into the EfficientNetV2 network model to achieve differentiated extraction of low-frequency global morphological features and high-frequency edge texture features of the foam image, thereby strengthening the correlation between depth features and flotation conditions. The specific implementation process is as follows: First, the feature map output from the stem layer of EfficientNetV2 is decomposed into a low-frequency feature map and a high-frequency feature map using a learnable Gaussian low-pass filter and a high-pass filter. The low-frequency feature map corresponds to global semantic features such as the overall size and aggregation state of the foam, while the high-frequency feature map corresponds to detailed features such as the edge texture and particle attachment state of the foam. Second, a high- and low-frequency dual-branch structure is constructed. The low-frequency branch uses a large-kernel convolution (7×7) and a global attention mechanism to capture long-distance global dependencies. The high-frequency branch uses a dynamic convolution kernel, and the weights of the convolution kernel are adaptively adjusted according to the texture complexity of the input image. The calculation method of the dynamic convolution kernel is as follows: ;in, The final weights of the dynamic convolution kernel. This represents the number of parallel convolution kernels, with a value of 4. For the first The adaptive weights of each convolutional kernel are generated through global average pooling of the input high-frequency feature map and a fully connected layer. For the first The weights of the basic convolutional kernels are determined; thirdly, a frequency interaction module is embedded in each MBConv module, which weights the global semantic information of the low-frequency branch to the high-frequency branch through channel attention, and simultaneously weights the texture detail information of the high-frequency branch to the low-frequency branch through spatial attention, realizing bidirectional interaction between high- and low-frequency features; fourthly, during network pre-training, independent loss functions are set for the low-frequency and high-frequency branches respectively. The low-frequency branch uses mean squared error loss to fit the global working parameters, and the high-frequency branch uses contrast loss to enhance the inter-class discriminative power of texture features. The total loss function is: ;in, The mean square error loss for the low-frequency branch. The frequency balancing weight is set to 0.3. In the fifth step, after pre-training, the features output from the high- and low-frequency branches of the network are concatenated and then dimensionality-reduced through a fully connected layer to obtain the initial depth visual feature vector. This implementation breaks away from the conventional approach of EfficientNetV2, which indiscriminately processes high- and low-frequency features of images. It designs differentiated extraction branches based on the characteristic features of flotation foam images, significantly improving the discriminative power of depth features for different working conditions.

[0131] In some embodiments, when performing complementarity screening on the two types of initial feature vectors in S2, a two-step screening strategy combining maximum information coefficient (MIC) and conditional mutual information is adopted to replace the conventional mutual information screening. This retains complementary features while eliminating redundant information within the features, further improving the effectiveness of the features. The specific implementation process is as follows: First, calculate the maximum information coefficient between each dimension of the initial traditional feature vector and each dimension of the initial depth visual feature vector to construct the MIC matrix. The formula for calculating the maximum information coefficient is: ;in, , These are random variables with two feature dimensions, The number of divisions in a two-dimensional grid. This represents the maximum number of grid divisions, and its value is 0.6 times the total number of samples. The first step involves calculating the mutual information of two features within a grid partition. The second step involves preliminary screening based on the MIC matrix. For the initial traditional feature vector, the top 100 features with the highest MIC mean relative to the initial depth visual feature vector are retained. For the initial depth visual feature vector, the top 120 features with the highest MIC mean relative to the initial traditional feature vector are retained. The third step involves redundant removal of the pre-screened features based on conditional mutual information. For features within the same modality, the conditional mutual information of any two feature dimensions relative to the label data is calculated using the following formula: ;in, , For two feature dimensions within the same modality, For the corresponding working condition label data; when When the value is less than a set threshold of 0.05, it is determined that two features are redundant, and the feature dimension with the lower mean MIC is removed. In the fourth step, after completing the redundancy removal, the final output is the traditional feature vector after 80-dimensional filtering and the depth visual feature vector after 100-dimensional filtering. In this implementation, the maximum information coefficient can capture any form of nonlinear dependency between features, and has a stronger ability to characterize nonlinear associations than conventional mutual information. Conditional mutual information can accurately remove redundant features within a modality, solving the problem that conventional mutual information filtering easily retains redundant features.

[0132] In some embodiments, during cross-modal feature distribution alignment and topological fusion in S3, a deep canonical correlation analysis with embedded manifold regularization constraints is adopted, combined with a dynamic adjacency adaptive graph convolutional network. Through alternating optimization, the manifold structure of cross-modal features is preserved and deep fusion is achieved, solving the problems of conventional DCCA easily losing local manifold structure and the inability of the fixed adjacency matrix of conventional graph convolution to adapt to dynamic feature associations. The specific implementation process is as follows: First, a deep canonical correlation analysis model with manifold regularization constraints is constructed. Based on the original DCCA loss function, a manifold regularization term is added, and the total loss function is: ;in, This is the manifold regularization weight, with a value of 0.01. , These are the manifold regularization terms for traditional features and depth visual features, respectively. The formula for calculating the manifold regularization term is: ;in, , For the first batch , Mapping features of each sample Let be the nearest neighbor weight matrix between samples. When two samples are k nearest neighbors, The value of k is the Gaussian kernel similarity between samples, otherwise it is 0, and the value of k is 10. The second step involves constructing a dynamic adjacency adaptive graph convolutional network. For the concatenated aligned feature vectors, the adjacency matrix is ​​recalculated in each graph convolutional layer, achieving dynamic updates to the adjacency matrix rather than keeping it fixed. The dynamic adjacency matrix is ​​calculated as follows: ;in, For the first The dynamic adjacency matrix of a layer graph convolutional layer. For the first The input feature matrix of the layer, It is the sigmoid activation function. For Hadama accumulation, For the first The sparse mask matrix of the layer retains only the connections of the top 10 most similar nodes for each node; The third step, during the alternating optimization process, first fixes the mapping network parameters of the manifold constraint DCCA and trains the dynamic adjacency graph convolutional network with the working condition label data as the target; then fixes the parameters of the dynamic adjacency graph convolutional network and updates the mapping network parameters of the manifold constraint DCCA with the first layer input features of the graph convolutional network as the alignment target; repeats the alternating optimization until the model converges.

[0133] In this implementation, the manifold regularization constraint can preserve the local geometric structure of features in the original space and avoid the loss of discriminative power of features after DCCA mapping. The dynamic adjacency graph convolution can adaptively capture the topological associations between features at different levels. Compared with conventional graph convolution with a fixed adjacency matrix, the feature fusion effect is significantly improved.

[0134] In some embodiments, when constructing the progressive hierarchical expert network model in S4, an expert sparse activation regularization constraint is added to the gating network. Simultaneously, a gradient surgical strategy is used instead of the conventional gradient projection strategy to fundamentally solve the problems of unbalanced expert activation and negative transfer between tasks in multi-expert networks. The specific implementation process is as follows: First, an expert sparse activation regularization term is added to the loss function of each layer of the gating network. The total loss function of the bottom shared gating network is: ;in, For mission losses, This is the sparse regularization weight, with a value of 0.005. Let L1 be the L1 norm of the gate weight vector. Through L1 sparse regularization, each sample is constrained to activate only 2-3 shared experts, avoiding feature learning ambiguity caused by average activation of all experts, and preventing a single expert from monopolizing activation. In the second step, during the Gumbel-Softmax sampling process of the gated network, an expert load balancing constraint is added. After each training round, the average activation rate of each expert is calculated. When the average activation rate of an expert exceeds 60%, a penalty term is added to the original gate score of that expert, using the following formula: ;in, The expert score after the penalty. For the first The average activation rate of each expert The average activation rate of all experts. The load balancing penalty coefficient is set to 0.1. The third step employs a gradient surgery strategy to achieve conflict-free gradient updates across multiple tasks, replacing the conventional gradient projection strategy. Specifically, for each task's gradient, its cosine similarity to the gradients of other tasks is calculated. When the cosine similarity is positive, the gradient is considered a positive transfer gradient and is fully retained for updating shared parameters. When the cosine similarity is negative, the gradient is considered a negative transfer gradient and is projected onto a space orthogonal to conflicting gradients, retaining only the orthogonal components for updating shared parameters. The calculation formula is as follows: ;in, For the first Postoperative gradient of each task In order to be with the first The fourth step involves combining a sparse regularization term, load balancing constraints, and multi-task dynamic weights into the overall training loss function to achieve joint optimization. In this implementation, sparse regularized expert routing solves the expert collapse and activation imbalance problems of conventional multi-expert networks. The gradient surgery strategy can accurately distinguish between positive and negative transfer gradients between tasks. Compared with the conventional gradient projection strategy, multi-task collaborative optimization has better results, and the model's average performance across all tasks is higher. It can increase by more than 2%.

Claims

1. A method for predicting reagent addition and aeration volume in copper ore flotation by integrating depth vision and traditional features, characterized in that, include: S1: Synchronously collect foam images, grade label data and operating condition label data of copper ore flotation cells at corresponding times to construct the original dataset; Spatial registration, denoising and normalization, and region of interest extraction preprocessing are performed sequentially on the bubble images in the original dataset to obtain effective region of interest images. The effective region of interest images are divided into training set, validation set, and test set and matched with the corresponding label data to output a standardized image dataset. S2: Based on a standardized image dataset, perform traditional feature extraction and depth visual feature extraction on each valid region of interest image to obtain initial traditional feature vectors and initial depth visual feature vectors; perform complementary filtering on the two types of initial feature vectors through mutual information calculation, and output the filtered traditional feature vectors and the filtered depth visual feature vectors. S3: Based on the two types of feature vectors after filtering from the output of S2, cross-modal feature distribution alignment is completed through deep canonical correlation analysis, and then feature topology fusion is completed through adaptive graph convolutional network, outputting fused feature vectors that match the label data one by one; S4: Construct a progressive hierarchical expert network model, with the fused feature vector as input and the dosage of copper ore flotation collector, inhibitor, activator, pH adjuster, and aeration as the predicted output; S5: Using the fused feature vector as input and the corresponding working condition label data as training target, the progressive hierarchical expert network model is subjected to phased constraint training. After optimization on the validation set and performance verification on the test set, the qualified optimal prediction model is output. S6: Using the flotation froth image of the copper ore to be processed as input, after the same preprocessing as S1 and the same feature extraction and fusion processing as S2 to S3, input the optimal prediction model and output the corresponding prediction results of the dosage and aeration.

2. The method for predicting reagent addition and aeration volume in copper ore flotation by integrating depth vision and traditional features according to claim 1, characterized in that, The specific process of traditional feature extraction described in S2 is as follows: Perform a discrete Shearlet transform on the effective region of interest image to obtain a multi-scale, multi-directional transform coefficient matrix; calculate the mean, variance, energy, and entropy statistics of each coefficient matrix and concatenate them to generate a Shearlet feature vector; calculate the local binary pattern value and neighborhood variance of each pixel on the effective region of interest image, construct a local binary pattern variance histogram to generate a local texture difference feature vector; concatenate the Shearlet feature vector and the local texture difference feature vector, and after weighting by the ratio of inter-class scatter to intra-class scatter, obtain the initial traditional feature vector.

3. The method for predicting reagent addition and aeration volume in copper ore flotation by integrating depth vision and traditional features according to claim 1, characterized in that, The specific process of deep visual feature extraction described in S2 is as follows: Construct an EfficientNetV2 network model with a progressive training strategy, gradually increase the resolution and regularization intensity of the input image during training, and complete the network pre-training by using contrast loss combined with mean square error loss; input the effective region of interest image into the pre-trained EfficientNetV2 network model to extract the initial deep visual feature vector.

4. The method for predicting reagent addition and aeration volume in copper ore flotation by integrating depth vision and traditional features according to claim 1, characterized in that, The specific process of complementary screening of two types of initial feature vectors by mutual information calculation as described in S2 is as follows: calculate the mutual information between each dimension of the initial traditional feature vector and each dimension of the initial depth visual feature vector, and construct a mutual information matrix; for the initial traditional feature vector, retain the top 80 features with the highest mean mutual information with the initial depth visual feature vector to generate the filtered traditional feature vector; for the initial depth visual feature vector, retain the top 100 features with the highest mean mutual information with the initial traditional feature vector to generate the filtered depth visual feature vector.

5. The method for predicting reagent addition and aeration volume in copper ore flotation by integrating depth vision and traditional features according to claim 1, characterized in that, The cross-modal feature distribution alignment and feature topology fusion described in S3 are performed using an alternating optimization strategy. The specific process is as follows: First, fix the mapping network parameters of the deep canonical correlation analysis and train an adaptive graph convolutional network with the working condition label data as the training target; then fix the parameters of the adaptive graph convolutional network and update the mapping network parameters of the deep canonical correlation analysis with the input features of the adaptive graph convolutional network as the alignment target; repeat the alternating optimization process until the model converges, thus completing the feature distribution alignment and fusion.

6. The method for predicting reagent addition and aeration volume in copper ore flotation by integrating depth vision and traditional features according to claim 1, characterized in that, The progressive hierarchical expert network model described in S4 has a three-layer progressive structure, consisting of a bottom-level shared expert layer, a middle-level task cluster-specific expert layer, and a top-level single-task-specific expert layer. The bottom-level shared expert layer sets up multiple parallel shared expert networks to learn the common features of all prediction tasks. The middle-level task cluster-specific expert layer is divided into drug dispensing task clusters and inflation task clusters based on task attributes. Each task cluster sets up multiple parallel task cluster-specific expert networks to learn the specific features within the corresponding task cluster. The top-level single-task dedicated expert layer sets up multiple parallel single-task dedicated expert networks for each prediction task, which are used to learn the personalized features of the corresponding single task.

7. The method for predicting reagent addition and aeration volume in copper ore flotation by integrating depth vision and traditional features according to claim 6, characterized in that, The progressive hierarchical expert network model sets up an independent gating network for each expert layer. The gating network adopts the Gumbel-Softmax with Concrete Distribution mechanism, which introduces Gumbel noise to achieve smooth discrete sampling of the gating weights. During training, the temperature parameter of the gating network is gradually attenuated to achieve dynamic adaptive allocation of the weights of each expert network.

8. The method for predicting reagent addition and aeration volume in copper ore flotation by integrating depth vision and traditional features according to claim 1, characterized in that, The progressive hierarchical expert network model described in S4 incorporates a multi-constraint optimization module. This module employs a dynamic weight averaging combined with a gradient projection strategy to achieve multi-task loss balance. Specifically, it tracks the training loss decline rate of each prediction task, dynamically adjusts the loss weight of each task, and ensures that tasks with slower training speeds receive higher training weights. The gradient of each task is decomposed into components parallel to and orthogonal to the shared gradient. Only the orthogonal components are retained to update the parameters of the underlying shared expert layer, thus eliminating gradient conflicts between tasks.

9. The method for predicting reagent addition and aeration volume in copper ore flotation by integrating depth vision and traditional features according to claim 1, characterized in that, The specific process of phased constraint training described in S5 is as follows: In the first phase, all parameters of the mid-level task cluster-specific expert layer and the top-level single-task-specific expert layer are frozen, and only the bottom-level shared expert layer and the corresponding gating network are trained to complete the model pre-training; In the second phase, all network layer parameters of the model are unfrozen, and a multi-task loss balancing strategy and a gating network temperature decay mechanism are introduced to complete the constraint training; In the third phase, the gating network temperature parameters and the loss weights of each task are fixed, all expert network and task output head parameters are fine-tuned, and the model convergence training is completed by combining the early stopping strategy.

10. The method for predicting reagent addition and aeration volume in copper ore flotation by integrating depth vision and traditional features according to claim 1, characterized in that, After S6 outputs the predicted dosage and inflation volume, it calculates the coefficient of variation of the predicted results using the Monte Carlo dropout method to verify the confidence level of the predicted results. For prediction results with low confidence, it collects the real working condition data at the corresponding time as labels and archives them into the incremental training sample library. When the number of samples in the incremental training sample library reaches a set threshold, it merges the original training set to complete the incremental fine-tuning update of the model and replaces the original optimal prediction model.

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