A Mineral Flotation Performance Prediction Method and System Based on Graph Neural Networks

Abstract

This invention relates to the field of intelligent mineral processing technology, and discloses a method and system for predicting mineral flotation performance based on graph neural networks. The method includes: Step 1, acquiring multi-source flotation data and aligning it according to discrete time points to obtain standardized flotation input samples; Step 2, constructing a dynamic heterogeneous flotation relationship graph containing multiple types of nodes, process edges, and time-series edges; Step 3, establishing relationship conservation constraints and filtering propagation paths to obtain a constraint propagation graph; Step 4, calculating the structural ambiguity index and identifying ambiguous sample pairs; Step 5, performing graph neural network message passing to obtain the final depth features of the nodes; Step 6, performing ambiguity separation and obtaining predicted values ​​for grade, recovery rate, and overall performance; Step 7, constructing a joint objective function to obtain a prediction model and outputting the prediction results and ambiguity metric. This invention achieves effective modeling of complex process relationships in mineral flotation and high-precision prediction of flotation performance.

Description

Technical Field

[0001] This invention belongs to the field of intelligent mineral processing technology, specifically relating to a method and system for predicting mineral flotation performance based on graph neural networks. Background Technology

[0002] In the field of mineral processing, flotation is a crucial step in achieving mineral separation and enrichment, and its operational performance directly impacts important production indicators such as concentrate grade and mineral recovery rate. Because the flotation process involves the coupled effects of multiple factors, including ore properties, reagent formulation, equipment structure, and operating parameters, and is accompanied by complex multiphase reactions involving gas, liquid, and solid phases, its operating state exhibits significant nonlinearity, dynamics, and uncertainty. Therefore, accurately modeling the flotation process and predicting its performance has always been a significant challenge in mineral processing production.

[0003] In existing technologies, flotation performance prediction largely relies on empirical models, statistical methods, or machine learning methods based on a single data source. These methods typically treat various process parameters as independent input variables, making it difficult to effectively express the correlations between different variables and the transmission mechanisms within the process flow. Furthermore, traditional methods often neglect the time-dependent characteristics and structural constraints in the flotation process, leading to poor stability of prediction results under complex operating conditions or fluctuations in ore properties. In addition, in actual production, there are often situations where local observation conditions are similar but the final flotation results differ significantly; existing methods struggle to effectively distinguish such samples, easily causing prediction bias. Summary of the Invention

[0004] This invention provides a method and system for predicting mineral flotation performance based on graph neural networks, which solves the technical problems in related technologies such as difficulty in effectively integrating multi-source heterogeneous flotation data, difficulty in expressing structural correlations and temporal transmission relationships in the process, and insufficient prediction accuracy and stability when local observations are similar but results differ.

[0005] This invention provides a method for predicting mineral flotation performance based on graph neural networks, comprising the following steps:

[0006] Step 1: Obtain ore slurry property data, reagent addition and operating condition data, flotation cell section connection data, froth state characterization data, and flotation performance label data, and align them according to discrete time points to obtain standardized flotation input samples;

[0007] Step 2: Construct a dynamic heterogeneous flotation relationship diagram based on the standardized flotation input samples. The dynamic heterogeneous flotation relationship diagram includes mineral attribute nodes, operating condition nodes, tank segment nodes, foam state nodes, performance target nodes, and process edges and timing edges between each node.

[0008] Step 3: Establish relationship conservation constraints based on the dynamic heterogeneous flotation relationship diagram, and filter the propagation paths to obtain the constraint propagation diagram;

[0009] Step 4: Calculate the structural ambiguity index and identify ambiguous sample pairs based on the constraint propagation diagram, standardized flotation input samples, and flotation performance label data.

[0010] Step 5: Based on the constraint propagation graph and ambiguous sample pairs, perform graph neural network message passing to obtain the final depth features of the nodes;

[0011] Step 6: Based on the final depth characteristics of the nodes and ambiguous sample pairs, perform ambiguity separation to obtain the predicted values ​​of concentrate grade, mineral recovery rate, and comprehensive flotation performance.

[0012] Step 7: Based on the predicted values ​​of concentrate grade, mineral recovery rate, comprehensive flotation performance, flotation performance label data, node final depth characteristics, and structural ambiguity index, construct a joint objective function to obtain the flotation performance prediction model, and output the mineral flotation performance prediction results and ambiguity measurement value.

[0013] This invention also provides a mineral flotation performance prediction system based on graph neural networks, comprising:

[0014] The data acquisition and preprocessing module is used to acquire ore slurry property data, reagent addition and operating condition data, flotation cell section connection data, foam state characterization data and flotation performance label data, and align them according to discrete time points to obtain standardized flotation input samples;

[0015] The heterogeneous relationship modeling module is used to construct a dynamic heterogeneous flotation relationship diagram based on standardized flotation input samples. The dynamic heterogeneous flotation relationship diagram includes mineral attribute nodes, operating condition nodes, tank segment nodes, foam state nodes, performance target nodes, and process edges and timing edges between each node.

[0016] The propagation constraint construction module is used to establish relationship conservation constraints based on the dynamic heterogeneous flotation relationship graph, and to filter propagation paths to obtain a constraint propagation graph;

[0017] The ambiguity identification calculation module is used to calculate the structural ambiguity index and identify ambiguous sample pairs based on the constraint propagation diagram, standardized flotation input samples, and flotation performance label data.

[0018] The gated propagation learning module is used to perform graph neural network message passing based on the constraint propagation graph and ambiguous sample pairs to obtain the final depth features of the nodes;

[0019] The ambiguity separation prediction module is used to separate ambiguities based on the final depth characteristics of nodes and ambiguous sample pairs, and obtain the predicted values ​​of concentrate grade, mineral recovery rate and comprehensive flotation performance.

[0020] The joint optimization output module is used to construct a joint objective function based on the predicted values ​​of concentrate grade, mineral recovery rate, comprehensive flotation performance, flotation performance label data, node final depth characteristics, and structural ambiguity index, to obtain the flotation performance prediction model, and output the mineral flotation performance prediction results and ambiguity metric values.

[0021] The beneficial effects of this invention are as follows: Addressing the complex, time-series-dependent, and highly fluctuating relationships among ore properties, reagent formulations, tank structure, froth state, and performance results in mineral flotation, this invention employs a graph neural network to uniformly model multi-source heterogeneous data. This transforms the originally scattered production data into a graph structure representation with process correlations and time dependencies. Furthermore, it introduces relation conservation constraints and ambiguous sample identification and separation mechanisms, enabling the model to more accurately characterize key transmission paths and complex coupling relationships in the flotation process. Compared to traditional methods, this invention not only improves the prediction accuracy and stability of concentrate grade, mineral recovery rate, and overall flotation performance, but also outputs ambiguous measurement information, enhancing the interpretability of the results. This provides more reliable support for flotation production process analysis, parameter optimization, and operational decision-making. Attached Figure Description

[0022] Figure 1 This is a flowchart of the mineral flotation performance prediction method based on graph neural networks of the present invention. Detailed Implementation

[0023] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0024] It should be noted that, unless otherwise defined, the technical or scientific terms used in one or more embodiments of the present invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in one or more embodiments of the present invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0025] like Figure 1 As shown, the mineral flotation performance prediction method based on graph neural networks includes the following steps:

[0026] Step 1: Obtain ore slurry property data, reagent addition and operating condition data, flotation cell section connection data, froth state characterization data, and flotation performance label data, and align them according to discrete time points to obtain standardized flotation input samples;

[0027] Step 2: Construct a dynamic heterogeneous flotation relationship diagram based on the standardized flotation input samples. The dynamic heterogeneous flotation relationship diagram includes mineral attribute nodes, operating condition nodes, tank segment nodes, foam state nodes, performance target nodes, and process edges and timing edges between each node.

[0028] Step 3: Establish relationship conservation constraints based on the dynamic heterogeneous flotation relationship diagram, and filter the propagation paths to obtain the constraint propagation diagram;

[0029] Step 4: Calculate the structural ambiguity index and identify ambiguous sample pairs based on the constraint propagation diagram, standardized flotation input samples, and flotation performance label data.

[0030] Step 5: Based on the constraint propagation graph and ambiguous sample pairs, perform graph neural network message passing to obtain the final depth features of the nodes;

[0031] Step 6: Based on the final depth characteristics of the nodes and ambiguous sample pairs, perform ambiguity separation to obtain the predicted values ​​of concentrate grade, mineral recovery rate, and comprehensive flotation performance.

[0032] Step 7: Based on the predicted values ​​of concentrate grade, mineral recovery rate, comprehensive flotation performance, flotation performance label data, node final depth characteristics, and structural ambiguity index, construct a joint objective function to obtain the flotation performance prediction model, and output the mineral flotation performance prediction results and ambiguity measurement value.

[0033] In one embodiment of the present invention, firstly, multi-source heterogeneous data for modeling the mineral flotation process is acquired, including ore pulp property data, reagent addition and operating condition data, flotation cell section connection data, foam state characterization data, and flotation performance label data.

[0034] The ore pulp attribute data is used to reflect the characteristics of the raw materials entering the flotation system, including but not limited to parameters such as ore grade, particle size distribution, mineral composition, pulp concentration, and pH value; the reagent addition and operating condition data is used to describe the control variables in the flotation process, including the amount of collector, frother, and modifier added, as well as operating parameters such as aeration rate, stirring intensity, and liquid level; the flotation cell section connection data is used to represent the process connection relationship between flotation equipment and the flow path of the pulp between each cell section; the foam state characterization data is used to reflect the characteristics of the flotation interface, including information such as foam size distribution, stability, color characteristics, or image extraction characteristics; and the flotation performance label data is used to represent the flotation results at the corresponding time, including concentrate grade, recovery rate, and comprehensive performance indicators.

[0035] Furthermore, the aforementioned multi-source data are aligned according to a unified time benchmark, mapping data with different sampling frequencies and from different sources to discrete time series to form time-consistent data samples. During the alignment process, continuous data can be resampled, interpolated, or aggregated according to a preset time window to eliminate the impact of time deviations.

[0036] After time alignment is completed, various types of data are standardized, including normalization or standard deviation standardization for continuous variables, encoding of categorical data, and completion or removal of missing data, in order to improve data consistency and usability.

[0037] Through the above processing, standardized flotation input samples are constructed in discrete time units. Each sample contains at least the ore slurry property characteristics, operating condition characteristics, structural connection information, foam state characteristics, and corresponding flotation performance labels at the corresponding time, providing a unified input basis for subsequent modeling and prediction based on graph neural networks.

[0038] In one embodiment of the present invention, after obtaining standardized flotation input samples, a dynamic heterogeneous flotation relationship diagram is further constructed based on the standardized flotation input samples to represent the structural relationships between multiple source elements in the mineral flotation process and their evolution over time. The dynamic heterogeneous flotation relationship diagram includes mineral attribute nodes, operating condition nodes, tank segment nodes, foam state nodes, performance target nodes, and process edges and timing edges connecting various nodes.

[0039] Specifically, in step 21, corresponding nodes are generated based on different types of data in the standardized flotation input samples. Mineral attribute nodes are generated based on ore and pulp attribute data to represent the physicochemical properties of the raw materials; operating condition nodes are generated based on reagent addition and operating condition data to represent the control conditions during the flotation process; flotation cell segment nodes are generated based on flotation cell segment connection data to represent the structure of the flotation equipment and the position of the pulp flow; foam state nodes are generated based on foam state characterization data to reflect the characteristics of the flotation interface; and performance target nodes are generated based on flotation performance label data to represent the flotation results at the corresponding time point.

[0040] Step 22: After generating various nodes, further establish the relationships between nodes based on the flotation process flow and variable action paths. Specifically, establish connections between mineral property nodes and tank segment nodes to represent the influence of raw material properties on the processing behavior of each tank segment; establish connections between operating condition nodes and tank segment nodes to represent the regulatory effect of operating conditions on the operating state of the tank segment; establish connections between tank segment nodes and froth state nodes to represent the influence of equipment operation on froth interface characteristics; establish connections between froth state nodes and performance target nodes to represent the determining role of froth behavior on the final flotation indicators; and simultaneously, establish connections between upstream tank segment nodes and downstream tank segment nodes according to the material flow direction in the flotation process to represent the transfer path of the slurry between different tank segments.

[0041] In addition, to represent the time dynamics of the flotation process, temporal edges of the same type of nodes are established between adjacent discrete moments, connecting the nodes of the previous discrete moment with the corresponding nodes of the current discrete moment, thereby constructing cross-time dependencies and enabling the model to capture the lag effect of variable evolution on subsequent flotation results.

[0042] Step 23: After completing the construction of nodes and edges, a dynamic heterogeneous flotation relationship diagram structure is formed based on mineral attribute nodes, working condition nodes, tank segment nodes, foam state nodes, performance target nodes, and the process edges and timing edges.

[0043] Furthermore, to achieve effective modeling of the aforementioned relationship graph by the graph neural network, various types of raw data are mapped into feature representations of a unified dimension. Specifically, this includes: converting ore slurry attribute data, reagent addition and operating condition data, flotation cell segment connection data, froth state characterization data, and flotation performance label data into equal-dimensional feature vectors; concatenating these feature vectors with the node type identifier and discrete time identifier of the corresponding nodes to generate a composite representation vector; and determining the initial feature representation of each node based on the composite representation vector, which serves as the input for subsequent graph neural network propagation and updates.

[0044] The dynamic heterogeneous flotation relationship graph constructed in the above manner unifies multi-source heterogeneous data into a graph representation with structural constraints and time dependencies, capable of simultaneously representing the complex relationships between variables and their temporal evolution characteristics. Compared with traditional methods based on independent features or sequence modeling, this invention improves the model's ability to express the actual flotation mechanism by introducing node type differentiation, process path constraints, and cross-temporal connection mechanisms. Simultaneously, by unifying feature dimensions and integrating type and temporal information, it enhances the model's collaborative modeling capability for heterogeneous data, thereby improving prediction accuracy and model stability.

[0045] In one embodiment of the present invention, after constructing a dynamic heterogeneous flotation relationship graph, relationship conservation constraints are further established based on the actual process mechanism in the flotation process, and information propagation paths are filtered to obtain a constraint propagation graph for subsequent graph neural network modeling.

[0046] Specifically, in step 31, relationship conservation constraints are established based on the dynamic heterogeneous flotation relationship diagram to limit the directionality and reachability of information propagation between different types of nodes. These relationship conservation constraints are determined based on the physical and technological causal relationships in the flotation process and include two categories: permitted propagation paths and prohibited propagation paths.

[0047] The permitted propagation paths include: propagation paths from mineral property nodes to tank segment nodes, representing the influence of raw material properties on equipment processing behavior; propagation paths from operating condition nodes to tank segment nodes, representing the regulatory effect of operating conditions on the tank segment's operating state; propagation paths from tank segment nodes to foam state nodes, representing the influence of equipment operating state on the foam interface; propagation paths from foam state nodes to performance target nodes, representing the influence of interface behavior on the final flotation index; propagation paths from upstream tank segment nodes to downstream tank segment nodes, representing the transmission relationship of slurry in the process flow; and propagation paths from nodes of the same type at the previous discrete time step to the corresponding nodes at the current discrete time step, representing the continuity and lag effect of variables evolving over time.

[0048] Prohibited propagation paths include: reverse propagation paths from performance target nodes to mineral attribute nodes to prevent non-causal interference from the resulting information on the original input; for example, the obtained recovery rate is not allowed to negatively influence ore grade. Reverse time propagation paths from later discrete-time nodes to earlier discrete-time nodes to avoid violating temporal dependencies; for example, the current operating condition information is not allowed to influence the state at past times. Direct propagation paths between dissimilar nodes without clear process associations are also prohibited to prevent the mixed propagation of physically meaningless information; for example, mineral attribute nodes are not allowed to directly establish skip connections with performance target nodes, bypassing intermediate processes.

[0049] Step 32: After establishing the aforementioned relationship conservation constraints, all process edges and timing edges in the dynamic heterogeneous flotation relationship graph are screened one by one. Specifically, each edge is matched with the allowed and prohibited propagation paths. Edges that do not conform to the relationship conservation constraints are deleted, while edges that do conform are retained, thereby obtaining a set of information propagation paths that satisfy the causal logic of the process.

[0050] After completing the edge screening, a constraint propagation graph is constructed based on mineral attribute nodes, operating condition nodes, tank segment nodes, foam state nodes, performance target nodes, and the effective propagation paths obtained through screening. This constraint propagation graph is a subgraph structure formed after constraint screening based on the original dynamic heterogeneous flotation relationship graph, and it only contains information transmission paths that conform to the flotation process mechanism.

[0051] By introducing propagation constraints based on process mechanisms, invalid connections and non-causal paths in the original graph structure are eliminated, making the information propagation process more consistent with the actual mechanisms of industrial processes. This reduces noise interference and misleading propagation during model training, improving the physical consistency and semantic reliability of the graph structure. Compared to unconstrained graph modeling, this invention, through explicit filtering and restriction of propagation paths, effectively avoids the diffusion of information between irrelevant nodes and temporal inverse dependencies. This makes the subsequent message passing process of the graph neural network more stable and controllable, thereby improving the model's ability to identify key process relationships and further enhancing the accuracy and robustness of prediction results.

[0052] In one embodiment of the present invention, after obtaining the constraint propagation map, the structural ambiguity index is further calculated based on the constraint propagation map, standardized flotation input samples, and flotation performance label data, and ambiguous sample pairs are identified to reflect the complex phenomenon of similar local observations but large differences in results under different operating conditions.

[0053] Specifically, in step 41, based on the standardized flotation input samples, samples from two different time points are selected, and their respective flotation cell segment connection data and foam state characterization data are extracted. The flotation cell segment connection data is aggregated to obtain cell segment state aggregated features; the foam state characterization data is aggregated to obtain foam state aggregated features; wherein the aggregation process is used to compress similar multi-source data into a fixed-dimensional feature representation; further, the cell segment state aggregated features and the foam state aggregated features are combined to obtain local observation features; the combined representation fuses different types of features to form a unified feature vector that can comprehensively characterize the local flotation state; and the Euclidean distance between the local observation features corresponding to the samples from two different time points is calculated, and the Euclidean distance is subjected to exponential mapping to obtain local observation similarity. Local observation similarity can be expressed as: , This represents the local observation similarity, where t and s represent two different time points. and These represent the local observation features at the corresponding time points. express and The Euclidean distance; through the above method, the similarity of local states can be transformed into a quantifiable numerical index, where the smaller the Euclidean distance, the higher the corresponding local observation similarity.

[0054] Step 42: Based on the constraint propagation diagrams corresponding to two different time points, the initial node features of mineral attribute nodes, operating condition nodes, tank segment nodes, foam state nodes, and performance target nodes in each diagram are aggregated, and information is converged by combining effective propagation paths to obtain the overall structural features of each of the two time points. The Euclidean distance between the two overall structural features is further calculated to obtain the global structural difference; simultaneously, based on the flotation performance label data corresponding to the two different time points, the Euclidean distance between the corresponding performance labels is calculated to obtain the performance label difference. The overall structural features reflect the comprehensive state formed after propagation of various factors under process constraints. Compared with the local observation features in Step 41, it not only includes local measurement information but also integrates upstream conditions and cross-node propagation effects, thus characterizing a more complete system structural difference.

[0055] Step 43: Multiply the local observation similarity, global structural difference, and performance label difference to obtain the structural ambiguity index. Further, compare the structural ambiguity index with a preset ambiguity threshold. When the structural ambiguity index is higher than the ambiguity threshold, the corresponding sample pair is identified as an ambiguous sample pair. The structural ambiguity index represents the degree of local similarity but significant differences in overall structure or result. For example, at two different times, the tank state and foam performance may be similar, indicating high local observation similarity. However, due to differences in ore properties or upstream operating conditions, the final recovery rate or grade may differ significantly, resulting in a high structural ambiguity index, thus identifying it as an ambiguous sample pair.

[0056] Furthermore, the ambiguity determination threshold is adaptively determined based on the structural ambiguity index distribution corresponding to the training samples. Specifically, this includes: statistically analyzing the structural ambiguity indices corresponding to the training samples and sorting them according to their numerical values; selecting the corresponding structural ambiguity index value based on a preset quantile position; and using the selected structural ambiguity index as the ambiguity determination threshold. Through this method, the threshold can be adaptively adjusted according to the data distribution, thereby improving the stability and adaptability of ambiguity recognition.

[0057] By using the above method, complex samples that are difficult to distinguish through a single feature during the flotation process can be explicitly identified, enabling the model to focus on modeling data with structural ambiguity. This avoids prediction bias caused by sample mixing under different mechanistic conditions and improves the model's ability to distinguish complex working conditions and its prediction accuracy.

[0058] In one embodiment of the present invention, after obtaining the constraint propagation graph and ambiguous sample pairs, graph neural network message passing is further performed based on the constraint propagation graph to obtain the final depth features of each node, thereby realizing a deep characterization of the complex structural relationships in the flotation process.

[0059] Specifically, in step 51, based on the constraint propagation graph corresponding to each sample in the ambiguous sample pair, for all allowed propagation neighbors of the same receiving node, combining the current round node characteristics of each allowed propagation neighbor and the corresponding edge type bias term, the propagation score of each effective propagation path is calculated, and the propagation score is normalized to obtain the path gating edge weight. Here, the allowed propagation neighbor refers to the adjacent node in the constraint propagation graph that has an effective propagation path with the current node; the edge type bias term is used to represent the differential impact of different process relationship types on information propagation; process relationship types include mineral attributes to tank segment, working condition to tank segment, tank segment to foam state, foam state to performance target, and inter-tank segment transmission relationships, etc.; the propagation score is used to represent the degree of contribution of neighboring nodes to the current node through the corresponding path; the path gating edge weight is a weight normalized to the contribution degree of each propagation path, used to adjust the information propagation intensity of different paths.

[0060] In one specific implementation, the path gating edge weight can be represented as: , Let represent the path gate weight propagating from neighbor node j to node i in layer l, used to characterize the influence weight of this propagation path on node i; i represents the target node currently receiving information, j represents a neighbor node with an allowed propagation path to node i, and m represents the index of any allowed propagation neighbor node of node i. This represents the set of allowed propagation neighbors of node i, that is, the set of nodes in the constrained propagation graph that have a valid propagation path with node i; Let T represent the query vector of node i at level l, and let T denote the transpose operation. This represents the key vector of node j at layer l. This represents the bias term corresponding to the edge type between node j and node i, used to distinguish the differences in the impact of different process relationship types on information propagation. This represents the dot product of the query vector and the key vector. The bias term corresponding to the edge type between node m and node i.

[0061] Step 52: Based on the path gating edge weights, perform a weighted summation of the current round node features of the neighboring nodes that are allowed to propagate in the constraint propagation graph to obtain the aggregated message of each node.

[0062] Step 53: Update the node features based on the current round node features of each node and the aggregated message to obtain the updated node features of each node. Specifically, the node update process can be represented as follows: , This represents the updated node characteristics of node i at level l+1. This represents the current node characteristics of node i at layer l. A mapping matrix representing the characteristics of a node itself. This represents the aggregated message of node i at layer l. Represents a nonlinear activation function;

[0063] Step 54: Set the current node feature of the first round as the initial feature representation of the node, set the current node feature of the remaining rounds as the updated node feature of the previous round, and repeat steps 51 to 53 for the constraint propagation graph corresponding to each sample in the ambiguous sample pair according to the preset propagation layer, so as to realize multi-round information propagation and finally obtain the final depth feature of each node.

[0064] Through the above process, within the effective propagation path defined by the constraint of relationship conservation, multi-source information such as mineral properties, operating conditions, tank structure, and foam state is propagated and fused layer by layer. A path gating mechanism is used to differentiate the weighting of different propagation paths, enabling node characteristics to more accurately reflect the key influencing relationships in the flotation process. By combining process-constrained propagation path screening with path gating weighting, the information propagation process conforms to the causal relationships in the actual flotation process, effectively reducing information interference from irrelevant paths. Simultaneously, multi-layer propagation enhances the ability of node characteristics to express complex process coupling relationships, thereby improving the accuracy and stability of flotation performance prediction and providing a reliable decision-making basis for the analysis and control of the flotation production process.

[0065] In one embodiment of the present invention, after obtaining the final depth features of the nodes and ambiguous sample pairs, further ambiguity separation processing is performed, and flotation performance prediction is realized based on the separated features, thereby obtaining the predicted values ​​of concentrate grade, mineral recovery rate and comprehensive flotation performance.

[0066] Specifically, in step 61, based on the final depth features of the nodes, the final depth features of all nodes in the same constraint propagation graph are summed dimension by dimension, and the summation result is compared with the total number of nodes in the constraint propagation graph to obtain graph-level features. Here, the final depth features of the nodes refer to the node representations obtained after propagation through a multi-layer graph neural network; the dimension-by-dimensional summation refers to the accumulation of the feature vectors of each node in the corresponding dimension; and the graph-level features refer to the vector representations used to comprehensively characterize the current flotation system state, which can comprehensively reflect the fusion result of multi-source information such as mineral properties, operating conditions, tank structure, and foam state in the graph structure.

[0067] Step 62: Calculate the Euclidean distance between two graph-level features based on the ambiguous sample pairs, and compare the preset ambiguous sample separation interval threshold with the Euclidean distance. When the Euclidean distance is less than the preset ambiguous sample separation interval threshold, the difference between the threshold and the Euclidean distance is determined as the ambiguous separation loss; the ambiguous separation loss can be expressed as:

[0068] , Indicates the loss of ambiguity separation. This represents two samples at different times in an ambiguous sample pair, where t and s are the two different times. This represents the preset threshold for separating ambiguous samples. and These represent the graph-level features at two different times. This represents the set of ambiguous sample pairs, and max represents the function that takes the maximum value.

[0069] When the Euclidean distance is not less than the threshold, the ambiguity separation loss is set to zero. Based on this ambiguity separation loss, separation constraints are applied to the two graph-level features to obtain the ambiguity-separated graph-level features. The ambiguous sample pair refers to a pair of samples that are similar in local observations but differ in overall structure or performance results. The ambiguity separation loss is used to constrain the distance between such samples in the feature space, ensuring sufficient discriminative power in the representation space. The separation constraint refers to adjusting the graph-level features through an optimization process so that the distance between sample pairs with ambiguous features in the feature space is not less than a preset interval, thereby avoiding sample overlap under different process mechanisms.

[0070] Step 63: Based on the graph-level features after ambiguity separation, input them into the concentrate grade prediction layer to obtain the concentrate grade prediction value; simultaneously, input the graph-level features into the mineral recovery rate prediction layer to obtain the mineral recovery rate prediction value. Further, the product of the comprehensive performance weight parameter and the concentrate grade prediction value is used as the first fusion term, and the product of the comprehensive performance weight parameter and the mineral recovery rate prediction value is subtracted from the product of the comprehensive performance weight parameter and the mineral recovery rate prediction value as the second fusion term. The first and second fusion terms are then added to obtain the comprehensive flotation performance prediction value. The concentrate grade prediction layer and the mineral recovery rate prediction layer can be regression models based on graph-level features, used to output the prediction results of corresponding indicators respectively; the comprehensive performance weight parameter is a preset or adjustable parameter used to balance the weights of concentrate grade and recovery rate in the comprehensive evaluation; the comprehensive flotation performance prediction value is used to reflect the overall flotation effect.

[0071] Through the above process, this invention, based on graph neural network modeling, further introduces a feature separation mechanism for ambiguous samples. This enables the model to effectively distinguish different process states in the feature space when local observations are similar but results differ, thereby improving the discriminative ability of the prediction results. By constructing graph-level features and introducing ambiguity separation constraints, the model can avoid feature aliasing between different production states, improving its adaptability to complex operating conditions. Simultaneously, by modeling and weighting the concentrate grade and recovery rate separately, a more comprehensive performance evaluation result can be provided for the flotation production process. This is beneficial for supporting parameter optimization and decision-making during production, thereby improving the overall operating efficiency and economic benefits of mineral flotation production.

[0072] In one embodiment of the present invention, after obtaining the predicted values ​​of concentrate grade, mineral recovery rate, comprehensive flotation performance, flotation performance label data, node final depth characteristics, and structural ambiguity index, a joint objective function is further constructed, the model is optimized and trained to obtain a flotation performance prediction model, and the mineral flotation performance prediction results and ambiguity measurement values ​​are output based on the flotation performance prediction model.

[0073] Specifically, in step 71, based on the predicted concentrate grade and the actual concentrate grade labels in the flotation performance label data, the squared deviation between the predicted concentrate grade and the actual concentrate grade labels is calculated, and the average of the squared deviations for all samples is obtained to get the grade prediction deviation loss. Simultaneously, based on the predicted mineral recovery and the actual mineral recovery labels in the flotation performance label data, the squared deviation between the predicted mineral recovery and the actual mineral recovery labels is calculated, and the average of the squared deviations for all samples is obtained to get the recovery prediction deviation loss. Here, the flotation performance label data refers to the actual result data used to supervise model training, including at least actual concentrate grade labels and actual mineral recovery labels; the squared deviation refers to the square of the difference between the predicted value and the actual label, used to amplify the impact of larger prediction errors on the loss result. By constructing grade prediction deviation losses and recovery prediction deviation losses separately, the model can simultaneously consider both concentrate grade prediction and recovery prediction tasks, avoiding optimization of only one indicator leading to a decrease in the predictive ability of the other indicator.

[0074] Step 72: Based on the final depth features of the nodes, extract the final depth features of the nodes at both ends of the effective propagation path along the constraint propagation graph. Calculate the squared Euclidean distance between the final depth features of the two ends of the path, and multiply the squared Euclidean distance by the corresponding edge weights and sum them to obtain the graph structure smoothing loss. Here, the effective propagation path refers to the process edges and timing edges retained after being filtered by relation conservation constraints; the nodes at both ends of the path refer to the starting and ending nodes connected by the same effective propagation path; the edge weights represent the connection strength or influence of the corresponding effective propagation path in the graph structure; the graph structure smoothing loss constrains the representation differences in the feature space of interconnected nodes with effective propagation relationships to avoid excessive differences, thereby maintaining the continuity and consistency of representations between adjacent nodes in the graph structure. This loss term illustrates that, under the premise of conforming to process transfer relationships, the information propagated along the effective path should have a certain degree of smoothness, so that the node representation obtained by the model more conforms to the continuous transfer law in the actual flotation process.

[0075] Step 73: Based on the grade prediction deviation loss, recovery rate prediction deviation loss, ambiguity separation loss, and graph structure smoothing loss, multiply each loss by its corresponding preset loss weight coefficient and sum them to obtain the joint objective function. Then, optimize the model parameters based on the joint objective function to obtain the flotation performance prediction model. The joint objective function can be expressed as:

[0076] Where F represents the joint objective function, , , and Let represent the preset loss weight coefficients corresponding to the grade prediction bias loss, recovery rate prediction bias loss, ambiguity separation loss, and graph structure smoothing loss, respectively. N represents the total number of samples participating in training, and t represents the t-th sample. This represents the predicted concentrate grade of the t-th sample. This represents the true concentrate grade label for the t-th sample. This represents the predicted mineral recovery value for the t-th sample. This represents the true mineral recovery label for the t-th sample. This represents the two nodes connected by a valid propagation path. This represents the weight of the corresponding edge between node i and node j. This represents the final depth feature obtained after node i has passed through the Lth layer of the graph neural network. This represents the final depth feature obtained by node j after propagation through the Lth layer of the graph neural network, where L represents the preset number of propagation layers. This indicates the loss due to grade prediction bias. This indicates the loss due to the bias in recovery rate prediction. This represents the graph structure smoothing loss.

[0077] The ambiguity separation loss is used to separate samples that are similar in local observations but have significant differences in overall structure or results in the feature space, thereby enhancing the model's ability to distinguish ambiguous samples. The preset loss weight coefficient is used to adjust the relative influence of each loss term during model training. By constructing a joint objective function, the model can not only fit target indicators such as concentrate grade and mineral recovery rate, but also simultaneously take into account the identification of ambiguous samples and the preservation of graph structure relationships, thereby improving the model's overall performance in complex flotation scenarios.

[0078] Step 74: Process the sample to be predicted according to the flotation performance prediction model, and output the final predicted values ​​of concentrate grade, mineral recovery rate, and overall flotation performance; and determine the maximum value of the structural ambiguity index of the sample to be predicted relative to the reference sample set as the ambiguity metric. Here, the sample to be predicted refers to a new sample that has not yet participated in the model's supervised training and needs to be predicted for performance; the reference sample set refers to the set of samples used for structural ambiguity comparison with the sample to be predicted, which can be a training sample set, a validation sample set, or a pre-selected benchmark sample set; the ambiguity metric is used to represent the maximum degree of structural ambiguity exhibited by the sample to be predicted compared with the reference sample set. The higher the ambiguity metric, the more likely the sample to be predicted is in a state of local observational similarity but significant differences in internal structural relationships or performance results, thus indicating that this sample needs to be given higher attention in prediction interpretation, operating condition analysis, or production decision-making.

[0079] By constructing a joint objective function, this invention unifies and optimizes grade prediction, recovery rate prediction, ambiguity separation, and graph structure constraints, enabling the model to simultaneously improve prediction accuracy and stability under complex operating conditions, and effectively distinguish between samples with similar structures but different results. Compared to traditional methods, this invention not only outputs flotation performance prediction results but also provides ambiguity measurement information, thereby enhancing the interpretability of the results and providing a more reliable basis for flotation process optimization and production decisions.

[0080] In one embodiment of the present invention, a mineral flotation performance prediction system based on graph neural networks is also provided, comprising:

[0081] The data acquisition and preprocessing module is used to acquire ore slurry property data, reagent addition and operating condition data, flotation cell section connection data, foam state characterization data and flotation performance label data, and align them according to discrete time points to obtain standardized flotation input samples;

[0082] The heterogeneous relationship modeling module is used to construct a dynamic heterogeneous flotation relationship diagram based on standardized flotation input samples. The dynamic heterogeneous flotation relationship diagram includes mineral attribute nodes, operating condition nodes, tank segment nodes, foam state nodes, performance target nodes, and process edges and timing edges between each node.

[0083] The propagation constraint construction module is used to establish relationship conservation constraints based on the dynamic heterogeneous flotation relationship graph, and to filter propagation paths to obtain a constraint propagation graph;

[0084] The ambiguity identification calculation module is used to calculate the structural ambiguity index and identify ambiguous sample pairs based on the constraint propagation diagram, standardized flotation input samples, and flotation performance label data.

[0085] The gated propagation learning module is used to perform graph neural network message passing based on the constraint propagation graph and ambiguous sample pairs to obtain the final depth features of the nodes;

[0086] The ambiguity separation prediction module is used to separate ambiguities based on the final depth characteristics of nodes and ambiguous sample pairs, and obtain the predicted values ​​of concentrate grade, mineral recovery rate and comprehensive flotation performance.

[0087] The joint optimization output module is used to construct a joint objective function based on the predicted values ​​of concentrate grade, mineral recovery rate, comprehensive flotation performance, flotation performance label data, node final depth characteristics, and structural ambiguity index, to obtain the flotation performance prediction model, and output the mineral flotation performance prediction results and ambiguity metric values.

[0088] It should be noted that the interval and threshold sizes are set for ease of comparison. The size of the threshold depends on the amount of sample data and the base number set by those skilled in the art for each set of sample data, as long as it does not affect the proportional relationship between the parameter and the quantized value. Furthermore, the above formulas are all dimensionless calculations, and the formulas are derived from software simulations using a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0089] The embodiments of the present invention have been described above, but the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms based on the guidance of the present embodiments, all of which are within the protection scope of the present embodiments.

Claims

1. A method for predicting mineral flotation performance based on a graph neural network, characterized in that, Includes the following steps: Step 1: Obtain ore slurry property data, reagent addition and operating condition data, flotation cell section connection data, froth state characterization data, and flotation performance label data, and align them according to discrete time points to obtain standardized flotation input samples; Step 2: Construct a dynamic heterogeneous flotation relationship diagram based on the standardized flotation input samples. The dynamic heterogeneous flotation relationship diagram includes mineral attribute nodes, operating condition nodes, tank segment nodes, foam state nodes, performance target nodes, and process edges and timing edges between each node. Step 3: Establish relationship conservation constraints based on the dynamic heterogeneous flotation relationship diagram, and filter the propagation paths to obtain the constraint propagation diagram; Step 4: Calculate the structural ambiguity index based on the constraint propagation diagram, standardized flotation input samples, and flotation performance label data, and identify ambiguous sample pairs; whereby the structural ambiguity index is used to represent the degree of local similarity but large differences in overall structure or results; Step 4 includes: Step 41: Based on the standardized flotation input samples, extract the flotation cell segment connection data and foam state characterization data of the samples at two different times. Aggregate the flotation cell segment connection data to obtain the cell segment state aggregation feature, and aggregate the foam state characterization data to obtain the foam state aggregation feature. Combine the cell segment state aggregation feature and the foam state aggregation feature to obtain the local observation feature. Calculate the Euclidean distance between the two local observation features, and perform exponential mapping on the Euclidean distance to obtain the local observation similarity. Step 42: Based on the constraint propagation diagrams corresponding to the two different time points, aggregate the initial node features of the mineral attribute nodes, working condition nodes, tank segment nodes, foam state nodes, and performance target nodes in their respective constraint propagation diagrams, and combine them with the effective propagation path to obtain the overall structural features of the two different time points. Calculate the Euclidean distance between the two overall structural features to obtain the global structural difference. Based on the flotation performance label data corresponding to the two different time points, calculate the Euclidean distance between the two flotation performance label data to obtain the performance label difference. Step 43: Multiply the local observation similarity, global structural difference, and performance label difference to obtain the structural ambiguity index, and compare the structural ambiguity index with the preset ambiguity judgment threshold. According to the comparison results where the structural ambiguity index is higher than the preset ambiguity judgment threshold, identify ambiguous sample pairs. Step 5: Based on the constraint propagation graph and ambiguous sample pairs, perform graph neural network message passing to obtain the final depth features of the nodes; Step 6: Based on the final depth characteristics of the nodes and ambiguous sample pairs, perform ambiguity separation to obtain the predicted values ​​of concentrate grade, mineral recovery rate, and comprehensive flotation performance. Step 7: Based on the predicted values ​​of concentrate grade, mineral recovery rate, comprehensive flotation performance, flotation performance label data, node final depth characteristics, and structural ambiguity index, construct a joint objective function to obtain the flotation performance prediction model, and output the mineral flotation performance prediction results and ambiguity measurement value.

2. The graph neural network-based mineral flotation performance prediction method according to claim 1, characterized in that, A dynamic heterogeneous flotation relationship diagram is constructed based on standardized flotation input samples. This diagram includes mineral attribute nodes, operating condition nodes, tank segment nodes, foam state nodes, performance target nodes, and process edges and timing edges between these nodes. Step 21: Generate mineral attribute nodes based on ore pulp attribute data in standardized flotation input samples; generate operating condition nodes based on reagent addition and operating condition data; generate cell segment nodes based on flotation cell segment connection data; generate foam state nodes based on foam state characterization data; and generate performance target nodes based on flotation performance label data. Step 22: Based on the mineral attribute node, working condition node, tank segment node, foam state node, and performance target node, establish process edges from the mineral attribute node to the tank segment node, working condition node to the tank segment node, tank segment node to the foam state node, foam state node to the performance target node, and upstream tank segment node to downstream tank segment node, and establish time sequence edges from the same type of node in the previous discrete time to the corresponding node in the current discrete time. Step 23: Construct a dynamic heterogeneous flotation relationship diagram based on mineral attribute nodes, operating condition nodes, cell segment nodes, froth state nodes, performance target nodes, process edges, and time sequence edges. Then, convert the ore pulp attribute data, reagent addition and operating condition data, flotation cell segment connection segment data, froth state characterization data, and flotation performance label data into the initial node features of the corresponding nodes.

3. The graph neural network-based mineral flotation performance prediction method according to claim 2, characterized in that, The process involves converting ore and slurry property data, reagent addition and operating condition data, flotation cell segment connection data, froth state characterization data, and flotation performance label data into initial node features for their respective nodes. This includes mapping the ore and slurry property data, reagent addition and operating condition data, flotation cell segment connection data, froth state characterization data, and flotation performance label data into equal-dimensional feature vectors; concatenating each equal-dimensional feature vector with the node type identifier and discrete time identifier of the corresponding node; and generating the initial node features for the corresponding node based on the concatenation result.

4. The graph neural network-based mineral flotation performance prediction method of claim 1, wherein, Based on the dynamic heterogeneous flotation relationship diagram, relationship conservation constraints are established, and propagation paths are selected to obtain the constraint propagation diagram, including: Step 31: Based on the dynamic heterogeneous flotation relationship diagram, establish relationship conservation constraints, clarify the allowed propagation paths from mineral attribute nodes to tank segment nodes, operating condition nodes to tank segment nodes, tank segment nodes to foam state nodes, foam state nodes to performance target nodes, upstream tank segment nodes to downstream tank segment nodes, and nodes of the same type from the previous discrete time step to the corresponding node at the current discrete time step, and clarify the prohibited propagation paths from performance target nodes to mineral attribute nodes, nodes from the next discrete time step to the previous discrete time step, and nodes of different types without process associations. Step 32: Based on the relationship conservation constraint, filter the process edges and timing edges in the dynamic heterogeneous flotation relationship graph one by one, delete the process edges and timing edges that do not conform to the relationship conservation constraint, and retain the process edges and timing edges that conform to the relationship conservation constraint to obtain the effective propagation path; Step 33: Construct a constraint propagation graph based on mineral attribute nodes, working condition nodes, tank segment nodes, foam state nodes, performance target nodes, and effective propagation paths. The effective propagation paths include the process edges and timing edges retained in step 32.

5. The graph neural network-based mineral flotation performance prediction method of claim 1, wherein, The preset ambiguity determination threshold in step 43 is determined based on the distribution of structural ambiguity indices corresponding to the training samples, including: sorting the structural ambiguity indices corresponding to the training samples according to their size; selecting the corresponding structural ambiguity index according to the preset quantile position; and determining the selected structural ambiguity index as the ambiguity determination threshold.

6. The mineral flotation performance prediction method based on graph neural networks according to claim 1, characterized in that, Based on the constraint propagation graph and ambiguous sample pairs, graph neural network message passing is performed to obtain the final depth features of the nodes, including: Step 51: Based on the constraint propagation graph corresponding to each sample in the ambiguous sample pair, for all allowed propagation neighbors of the same receiving node, combine the current round node features of each allowed propagation neighbor and the corresponding edge type bias term, calculate the propagation score of each effective propagation path, and normalize each propagation score to obtain the path gating edge weight. Step 52: Based on the path gating edge weights, perform a weighted summation of the current round node features of the neighbor nodes that are allowed to propagate in the constraint propagation graph to obtain the aggregated message of each node; Step 53: Based on the current round node characteristics and aggregated messages of each node, update the updated node characteristics of each node. Step 54: Set the current node features of the first round as the initial node feature representation, set the current node features of the remaining rounds as the updated node features of the previous round, and repeat steps 51 to 53 for the constraint propagation graph corresponding to each sample in the ambiguous sample pair according to the preset propagation layer number to obtain the final depth features of the node.

7. The mineral flotation performance prediction method based on graph neural networks according to claim 1, characterized in that, Based on the final depth characteristics of the nodes and ambiguous sample pairs, ambiguity separation is performed to obtain predicted values ​​for concentrate grade, mineral recovery rate, and overall flotation performance, including: Step 61: Based on the final depth features of the nodes, sum the final depth features of all nodes in the same constraint propagation graph dimension by dimension, and compare the summation result with the total number of nodes in the same constraint propagation graph to obtain the graph-level features; Step 62: Calculate the Euclidean distance between two graph-level features based on the ambiguous sample pairs. Subtract the preset ambiguous sample separation interval threshold from the Euclidean distance. If the Euclidean distance is less than the preset ambiguous sample separation interval threshold, the difference is determined as the ambiguity separation loss. If the Euclidean distance is not less than the preset ambiguous sample separation interval threshold, the ambiguity separation loss is determined to be zero. Separation constraints are applied to the two graph-level features based on the ambiguity separation loss to obtain the ambiguity-separated graph-level features. Step 63: Input the graph-level features after ambiguity separation into the concentrate grade prediction layer to obtain the concentrate grade prediction value; input the graph-level features after ambiguity separation into the mineral recovery prediction layer to obtain the mineral recovery prediction value; multiply the comprehensive performance weight parameter and the concentrate grade prediction value as the first fusion term, and subtract the comprehensive performance weight parameter from the mineral recovery prediction value as the second fusion term; add the first fusion term and the second fusion term to obtain the comprehensive flotation performance prediction value.

8. The method for predicting mineral flotation performance based on graph neural networks according to claim 1, characterized in that, Based on the predicted values ​​of concentrate grade, mineral recovery rate, overall flotation performance, flotation performance label data, node final depth characteristics, and structural ambiguity index, a joint objective function is constructed to obtain the flotation performance prediction model. The model outputs the mineral flotation performance prediction results and ambiguity metrics, including: Step 71: Based on the predicted concentrate grade and the actual concentrate grade label in the flotation performance label data, calculate the squared deviation between the predicted concentrate grade and the actual concentrate grade label, and average the squared deviations of all samples to obtain the grade prediction deviation loss; Based on the predicted mineral recovery and the actual mineral recovery label in the flotation performance label data, calculate the squared deviation between the predicted mineral recovery and the actual mineral recovery label, and average the squared deviations of all samples to obtain the recovery prediction deviation loss. Step 72: Based on the final depth features of the nodes, extract the final depth features of the nodes at both ends of the effective propagation path of the constraint propagation graph, calculate the squared Euclidean distance between the final depth features of the nodes at both ends, and multiply the squared Euclidean distance by the corresponding edge weights and sum them to obtain the graph structure smoothing loss. Step 73: Multiply the grade prediction deviation loss, recovery rate prediction deviation loss, ambiguity separation loss and graph structure smoothing loss by the corresponding preset loss weight coefficients and sum them to obtain the joint objective function. Then, optimize the flotation performance prediction model based on the joint objective function. Step 74: Process the sample to be predicted according to the flotation performance prediction model, and output the final predicted value of concentrate grade, the final predicted value of mineral recovery rate and the final predicted value of comprehensive flotation performance; and determine the maximum value of the structural ambiguity index of the sample to be predicted relative to the reference sample set as the ambiguity metric value.

9. A mineral flotation performance prediction system based on graph neural networks, characterized in that, The mineral flotation performance prediction method based on graph neural networks as described in any one of claims 1-8 includes: The data acquisition and preprocessing module is used to acquire ore slurry property data, reagent addition and operating condition data, flotation cell section connection data, foam state characterization data and flotation performance label data, and align them according to discrete time points to obtain standardized flotation input samples; The heterogeneous relationship modeling module is used to construct a dynamic heterogeneous flotation relationship diagram based on standardized flotation input samples. The dynamic heterogeneous flotation relationship diagram includes mineral attribute nodes, operating condition nodes, tank segment nodes, foam state nodes, performance target nodes, and process edges and timing edges between each node. The propagation constraint construction module is used to establish relationship conservation constraints based on the dynamic heterogeneous flotation relationship graph, and to filter propagation paths to obtain a constraint propagation graph; The ambiguity identification calculation module is used to calculate the structural ambiguity index and identify ambiguous sample pairs based on the constraint propagation diagram, standardized flotation input samples, and flotation performance label data. The gated propagation learning module is used to perform graph neural network message passing based on the constraint propagation graph and ambiguous sample pairs to obtain the final depth features of the nodes; The ambiguity separation prediction module is used to separate ambiguities based on the final depth characteristics of nodes and ambiguous sample pairs, and obtain the predicted values ​​of concentrate grade, mineral recovery rate and comprehensive flotation performance. The joint optimization output module is used to construct a joint objective function based on the predicted values ​​of concentrate grade, mineral recovery rate, comprehensive flotation performance, flotation performance label data, node final depth characteristics, and structural ambiguity index, to obtain the flotation performance prediction model, and output the mineral flotation performance prediction results and ambiguity metric values.

Images