Flotation reagent formulation optimization method and system based on data analysis

Abstract

The application discloses a data analysis-based flotation reagent formula optimization method and system, which comprises the following steps: monitoring a flotation tank slurry in real time through an online detection device, obtaining a mineral grade, a reagent concentration and a froth thickness dataset, processing the dataset based on a time delay analysis algorithm to generate a reagent correlation feature library, clustering the feature library according to reagent types to construct an effect correlation graph, using a multi-objective optimization algorithm to calculate the graph to generate a candidate formula set, and screening and determining an optimal formula according to a cost constraint and controlling a reagent adding device to perform adjustment. The application solves the problem of lacking quantitative analysis of reagent synergistic effect and time sequence correlation modeling in the prior flotation reagent formula optimization technology, and improves the scientificity and accuracy of reagent formula optimization.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a method and system for optimizing flotation reagent formulations based on data analysis. Background Technology

[0002] Optimization of flotation reagent formulations is a core technology in the mineral processing field. Traditional reagent formulation design mainly relies on empirical formulas and small-scale experiments, adjusting the flotation effect by changing the dosage of collectors, frothers, and modifiers. Existing technologies use single-factor or orthogonal experimental methods to optimize reagent formulations, determining the optimal formulation by testing the concentrate grade and recovery rate under different reagent combinations. Some advanced beneficiation plants have begun to apply automated control technology, using online detection equipment to monitor flotation process parameters. However, the adjustment of reagent formulations is still mainly based on the experience judgment of operators and simple feedback control.

[0003] Existing technologies have significant shortcomings. First, they lack quantitative analysis of the synergistic effects between reagents, making it impossible to accurately describe the synergistic or antagonistic effects of different reagent combinations, leading to a high degree of blindness in the formulation optimization process. Second, they ignore the time lag of reagent action and fail to establish a correlation model between reagent addition time and flotation effect response time, resulting in inaccurate timing of formulation adjustments. In addition, existing methods lack multi-objective synergistic optimization capabilities, often focusing only on the improvement of a single indicator while ignoring the trade-off between grade, recovery rate, and cost, and lacking effective risk assessment and cost control mechanisms.

[0004] Based on the above analysis, the fundamental problem with existing technologies lies in the lack of systematic data analysis methods to reveal the inherent laws governing the action of reagents during the flotation process. Due to the inability to accurately quantify the synergistic effects and temporal relationships between reagents, formulation optimization lacks a scientific basis, leading to a series of technical problems such as difficulties in multi-objective optimization, insufficient cost control capabilities, and low precision in formulation adjustment. The essence of these problems is that existing technologies have failed to fully utilize the large amount of data information generated during the flotation process and lack effective algorithms and technical means to transform data into reagent formulation optimization decisions. Summary of the Invention

[0005] This application provides a data analysis-based method and system for optimizing flotation reagent formulations, which addresses the lack of quantitative analysis of reagent synergistic effects and time-series correlation modeling in existing flotation reagent formulation optimization technologies, thereby improving the scientific rigor and accuracy of reagent formulation optimization.

[0006] In a first aspect, this application provides a data analysis-based method for optimizing flotation reagent formulations, the data analysis-based method for optimizing flotation reagent formulations comprising:

[0007] Real-time monitoring of the slurry in the flotation cell is achieved using online detection equipment, resulting in a flotation process dataset that includes ore grade distribution, reagent concentration changes, and froth layer thickness.

[0008] The flotation process dataset is subjected to time-series correlation processing based on the reagent action time delay analysis algorithm to generate a reagent correlation feature library containing the collector synergy coefficient and the frother response delay;

[0009] The drug-related feature library was subjected to hierarchical cluster analysis according to drug type to construct drug effect correlation maps for collectors, foaming agents, and modifiers;

[0010] A multi-objective drug ratio optimization algorithm is used to calculate the drug effect correlation graph to generate a set of candidate drug formulations.

[0011] The candidate drug formulation set is screened and evaluated based on production cost constraints to determine the optimal drug dosing formulation and control the drug addition system to perform formulation adjustments.

[0012] Optionally, the step of real-time monitoring of the slurry in the flotation cell using online detection equipment to obtain a flotation process dataset including ore grade distribution, reagent concentration changes, and froth layer thickness includes:

[0013] X-ray fluorescence spectrometry was used to scan and detect the slurry in the flotation cell to obtain data on the percentage of mineral composition and the distribution of gangue minerals.

[0014] The concentration of added agents was monitored using an online concentration meter, and the concentration sequences of collectors, frothers, and modifiers were obtained.

[0015] The thickness values ​​collected by the foam layer thickness sensor are sorted according to the timestamp to generate time series data of foam layer thickness.

[0016] The mineral composition percentage data, reagent concentration sequence, and foam layer thickness time series data are time-aligned to obtain synchronized flotation monitoring data.

[0017] The synchronized flotation monitoring data is normalized based on a data standardization protocol to generate the flotation process dataset.

[0018] Optionally, the step of performing time-series correlation processing on the flotation process dataset according to the reagent action time delay analysis algorithm to generate a reagent correlation feature library containing collector synergy coefficients and frother response delays includes:

[0019] Correlation analysis was performed on the reagent concentration sequences in the flotation process dataset based on the Pearson correlation coefficient to obtain the inter-reagent correlation matrix.

[0020] The sliding time window technique is applied to the correlation matrix between the agents to calculate the time delay, thereby obtaining the time delay parameters between the collector and the frother and the time delay parameters between the modifier and the collector.

[0021] The time delay parameter is quantified according to the synergistic effect calculation formula to generate the synergistic coefficient of the collector and the synergistic coefficient of the foaming agent.

[0022] Based on the time-series analysis algorithm, the delay quantification of the reagent addition time and the flotation effect response time is performed to obtain the frother response delay value and the modifier response delay value.

[0023] The synergistic coefficients of the collectors, synergistic coefficients of the foaming agents, the response delay values ​​of the foaming agents, and the response delay values ​​of the modifiers are classified and stored according to the agent type to construct the agent-related feature library.

[0024] Optionally, the step of performing hierarchical cluster analysis on the drug-related feature library according to drug type to construct drug effect correlation maps for collectors, foaming agents, and modifiers includes:

[0025] Based on the classification criteria for drug types, the synergistic coefficients of collectors, synergistic coefficients of frothers, response delay values ​​of frothers, and response delay values ​​of modifiers in the drug-related feature library are grouped into feature groups to obtain the collector feature group, the frother feature group, and the modifier feature group.

[0026] Cluster analysis of the synergy coefficients within the collector feature group is performed based on Euclidean distance calculation to generate collector effect cluster centers and collector inter-class distance matrices.

[0027] The K-means clustering algorithm was applied to the foaming agent feature group and the modifier feature group for hierarchical clustering to obtain the cluster centers of foaming agent effect, the cluster centers of modifier effect, and the corresponding inter-class distance matrix.

[0028] Based on the principle of graph theory, the cluster centers of the collector effect, the foaming agent effect, and the modifier effect are connected by nodes to generate a drug effect association network topology.

[0029] The drug effect association network topology is mathematically described based on the adjacency matrix representation method, and the drug effect association graph is constructed.

[0030] Optionally, the step of performing cluster analysis on the synergy coefficients within the collector feature group based on Euclidean distance calculation to generate collector effect cluster centers and inter-class distance matrices includes:

[0031] Based on the Euclidean distance algorithm, the pairwise distance of each collector synergy coefficient in the collector feature group is calculated to obtain the collector synergy coefficient distance matrix.

[0032] The K-value initialization algorithm is applied to the collector synergy coefficient distance matrix to initialize the cluster centers, thereby obtaining the initial set of collector cluster center coordinates;

[0033] Based on the minimum distance criterion, the collector synergy coefficients are assigned to the corresponding initial cluster centers according to the principle of closest distance, generating the collector synergy coefficient grouping results;

[0034] Based on the centroid update algorithm, the centroid of the synergy coefficients in each group of the collector synergy coefficient grouping results is calculated, and new collector effect cluster centers are obtained by updating the centroid.

[0035] The Euclidean distances between the cluster centers of the new collector effects are stored in a matrix to construct the inter-cluster distance matrix of the collectors.

[0036] Optionally, the step of performing formulation calculations on the drug effect correlation graph using a multi-objective drug ratio optimization algorithm to generate a candidate drug formulation set includes:

[0037] Based on the objective function construction rules, the correlation graph of the agent effect is used to set multiple objective functions, and objective functions for concentrate grade, recovery rate and agent cost are established.

[0038] According to the weight allocation strategy, the weight coefficients of the objective function of concentrate grade, objective function of recovery rate and objective function of reagent cost are allocated to obtain the weighted multi-objective optimization function;

[0039] The non-dominated sorting algorithm is applied to the weighted multi-objective optimization function to perform Pareto solution set search, and the initial drug ratio solution space is obtained.

[0040] Based on the crossover and mutation operation, the dosage of collector, foaming agent and modifier in the initial drug ratio solution space are iteratively optimized to generate an optimized drug ratio solution set.

[0041] The optimized drug ratio solution set is screened and filtered according to feasibility constraints to construct the candidate drug formulation set.

[0042] Optionally, the step of screening and evaluating the candidate drug formulation set based on production cost constraints, determining the optimal drug dosing formulation, and controlling the drug addition system to perform formulation adjustments includes:

[0043] Based on the unit price parameter of the agent, the cost of the amount of collector, foaming agent and modifier added to each formulation in the candidate agent formulation set is calculated to obtain the total agent cost data corresponding to each formulation;

[0044] The total cost data of the drug is constrained and filtered according to the cost constraint threshold to generate a subset of feasible drug formulations that meet the cost requirements;

[0045] The confidence assessment algorithm is applied to the subset of feasible drug formulations to perform risk assessment calculations, and the predicted confidence values ​​and risk assessment indicators for each formulation are obtained.

[0046] Based on the comprehensive evaluation criteria, the predicted confidence scores and risk assessment indicators are ranked comprehensively to determine the optimal drug dosing formula with the highest comprehensive score.

[0047] According to the automatic control command, the reagent addition parameters in the optimal reagent addition formula are input into the reagent addition device for execution control, thereby completing the reagent formula adjustment for the flotation process.

[0048] Secondly, this application provides a data analysis-based flotation reagent formulation optimization system, the data analysis-based flotation reagent formulation optimization system comprising:

[0049] The monitoring module is used to monitor the slurry in the flotation cell in real time through online detection equipment, and obtain a flotation process dataset including ore grade distribution, reagent concentration changes and froth layer thickness;

[0050] The association module is used to perform time-series association processing on the flotation process dataset according to the reagent action time delay analysis algorithm, and generate a reagent association feature library containing the collector synergy coefficient and the frother response delay;

[0051] The clustering module is used to perform hierarchical clustering analysis on the drug-related feature library according to drug type, and construct drug effect correlation maps of collectors, foaming agents and modifiers;

[0052] The calculation module is used to perform formula calculation on the drug effect correlation graph through a multi-objective drug ratio optimization algorithm to generate a set of candidate drug formulas;

[0053] The screening module is used to screen and evaluate the candidate drug formulation set according to production cost constraints, determine the optimal drug addition formulation, and control the drug addition system to perform formulation adjustments.

[0054] Thirdly, a data analysis-based flotation reagent formulation optimization device is provided, comprising: a memory and at least one processor, wherein the memory stores instructions; the at least one processor invokes the instructions in the memory to cause the data analysis-based flotation reagent formulation optimization device to execute the aforementioned data analysis-based flotation reagent formulation optimization method.

[0055] Fourthly, a computer-readable storage medium is provided, wherein instructions are stored therein, which, when executed on a computer, cause the computer to perform the above-described data analysis-based flotation reagent formulation optimization method.

[0056] The technical solution provided in this application utilizes online detection equipment to monitor the technical characteristics of the slurry in the flotation cell in real time. Compared with traditional offline sampling and analysis methods, this approach has significant advantages. Real-time monitoring can capture dynamic changes in the flotation process, and the obtained datasets of mineral grade distribution, reagent concentration changes, and froth layer thickness have high temporal resolution and continuity, providing a reliable data foundation for subsequent time-series correlation analysis. The application of a reagent action time delay analysis algorithm addresses the technical deficiency of existing technologies that ignore reagent action time delays. By generating a reagent correlation feature library that includes collector synergy coefficients and frother response delays, accurate quantification of the synergistic effects and temporal relationships between reagents is achieved. The technical features enable formulation optimization to shift from experience-driven to data-driven, significantly improving the scientific rigor and reproducibility of the optimization results. The hierarchical clustering analysis constructs a drug effect correlation map, which expresses complex drug interactions in the form of a network topology, providing structured input information for multi-objective drug ratio optimization algorithms. The multi-objective drug ratio optimization algorithm can simultaneously consider multiple conflicting objectives such as concentrate grade, recovery rate, and drug cost. It finds the best trade-off solution through Pareto optimal solution set search, avoiding the local optimum problem that may be caused by traditional single-objective optimization. The introduction of production cost constraints ensures the economic feasibility and engineering practicality of the optimization results.

[0057] The algorithm accurately identifies the time delay relationship between reagent addition and effect response through sliding time window technology and Pearson correlation coefficient analysis. This feature makes a significant contribution to revealing the synergistic mechanism of collectors and frothers, enabling precise timing of reagent addition in formulation adjustments. The application of hierarchical clustering algorithm in constructing reagent effect correlation maps fully utilizes the differences in the mechanisms of action of different reagents. By using K-means clustering and Euclidean distance calculation, similar effect patterns are classified. The hierarchical processing feature of the algorithm ensures accurate identification and classification of different types of reagent effect patterns. The multi-objective reagent ratio optimization algorithm adopts non-dominated sorting and crossover mutation operations, which fully adapt to the characteristics of multi-objective conflicts in the flotation process. The evolutionary search mechanism of the algorithm can find the global optimum in the complex multi-dimensional objective space, avoiding getting trapped in the local optimum. The risk quantification function of the confidence assessment algorithm provides a safety guarantee for formulation selection. The algorithm assesses the risk level of formulation implementation through Bayesian inference and historical data statistical analysis. The organic combination of these algorithm features realizes the fundamental transformation of flotation reagent formulation optimization from qualitative experience to quantitative science, significantly improving the accuracy, stability and economy of formulation optimization. Attached Figure Description

[0058] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a schematic diagram of an embodiment of the flotation reagent formulation optimization method based on data analysis in this application.

[0060] Figure 2 This is a schematic diagram of an embodiment of the flotation reagent formulation optimization system based on data analysis in this application.

[0061] Figure 3 This is a schematic block diagram of the flotation reagent formulation optimization device based on data analysis in an embodiment of the present invention. Detailed Implementation

[0062] This application provides a data analysis-based method and system for optimizing flotation reagent formulations. The terms "first," "second," "third," "fourth," etc. (if present)," in the specification, claims, and accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such use of data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0063] For ease of understanding, the specific process of the embodiments of this application is described below. Please refer to [link / reference]. Figure 1 One embodiment of the flotation reagent formulation optimization method based on data analysis in this application includes:

[0064] Step S101: Monitor the slurry in the flotation cell in real time using online detection equipment to obtain a flotation process dataset including ore grade distribution, reagent concentration changes, and froth layer thickness;

[0065] Step S102: Perform time-series correlation processing on the flotation process dataset according to the reagent action time delay analysis algorithm to generate a reagent correlation feature library containing the collector synergy coefficient and the frother response delay;

[0066] Step S103: Perform hierarchical cluster analysis on the drug association feature library according to drug type to construct drug effect association maps for collectors, foaming agents, and modifiers;

[0067] Step S104: Calculate the formula of the drug effect correlation graph using a multi-objective drug ratio optimization algorithm to generate a set of candidate drug formulas;

[0068] Step S105: Screen and evaluate the candidate drug formulation set according to the production cost constraints, determine the optimal drug addition formulation, and control the drug addition system to perform formulation adjustment.

[0069] It is understood that the executing entity of this application can be a data analysis-based flotation reagent formulation optimization system, or it can be a terminal or a server; no specific limitation is made here. This application's embodiments use a server as an example for illustration.

[0070] Specifically, X-ray fluorescence spectrometry is used to scan and detect the slurry in the flotation cell to obtain the percentage data of mineral composition. This data reflects the content distribution of target minerals such as copper ore and iron ore in the slurry. At the same time, an online concentration meter monitors the concentration of the added collector, frother, and modifier to obtain the concentration sequence data of each reagent at different time points. A froth layer thickness sensor collects the thickness value and sorts it according to the timestamp to generate time-series data. These data are time-aligned to form synchronized flotation monitoring data. Finally, the data is normalized through a data standardization protocol to generate a flotation process dataset.

[0071] A reagent action time delay analysis algorithm was used to perform time-series correlation processing on the flotation process dataset. Pearson correlation coefficient analysis was used to analyze the correlation between reagent concentration sequences. By calculating the linear correlation between changes in different reagent concentrations, a reagent correlation matrix was obtained. The sliding time window technique was applied to this matrix to calculate time delays and identify the time delay parameters between collectors and frothers, and between modifiers and collectors. Synergistic effect calculation converted the time delay parameters into synergistic coefficients to quantify the synergistic effect strength between different reagents. The time-series analysis algorithm quantified the delay between reagent addition time and flotation effect response time to obtain the frother response delay value and modifier response delay value. These parameters were classified and stored according to reagent type to construct a reagent correlation feature library.

[0072] The drug-related feature library is subjected to hierarchical clustering analysis according to drug type. Based on the drug type classification criteria, the synergistic coefficients of collectors, synergistic coefficients of frothers, response delay values ​​of frothers, and response delay values ​​of modifiers are grouped into three feature groups: collector, frother, and modifier. Euclidean distance calculation is used to perform clustering analysis on the synergistic coefficients within the collector feature group. Similarity is determined by calculating the spatial distance between each synergistic coefficient, generating cluster centers and inter-cluster distance matrices for collector effects. The K-means clustering algorithm is applied to the frother and modifier feature groups for hierarchical clustering, obtaining their respective effect cluster centers and inter-cluster distance matrices. Graph theory is used to connect these cluster centers as nodes, forming a drug effect association network topology. The adjacency matrix representation is used to mathematically describe the network and construct a drug effect association graph.

[0073] A multi-objective reagent ratio optimization algorithm is used to calculate the formulation of the reagent effect correlation spectrum. The objective function construction rules set multi-objective functions for the spectrum, establishing objective functions for concentrate grade, recovery rate, and reagent cost. A weight allocation strategy is used to assign weight coefficients to these objective functions to obtain a weighted multi-objective optimization function. The non-dominated sorting algorithm is applied to this function to search for Pareto solution set, and the non-dominated solution set is found in the multi-dimensional objective space to obtain the initial reagent ratio solution space. Crossover and mutation operations are used to iteratively optimize the dosage of collector, frother, and modifier in the solution space. By simulating the biological evolution process, the formulation scheme is continuously improved to generate an optimized reagent ratio solution set. Feasibility constraints are used to screen and filter the solution set to construct a candidate reagent formulation set.

[0074] The candidate reagent formulation set is screened and evaluated based on production cost constraints. The reagent unit price parameter is used to calculate the cost of the reagent dosage for each formulation. The total reagent cost data for each formulation is obtained by multiplying the dosage by the corresponding reagent unit price and summing the results. The cost constraint threshold is used to constrain and screen the total cost data to generate a subset of feasible reagent formulations that meet the cost requirements. The confidence assessment algorithm performs risk assessment calculations on the subset of feasible formulations. Based on historical data and statistical analysis methods, the predicted confidence value and risk assessment index of each formulation are calculated. The comprehensive evaluation criteria are used to comprehensively rank the confidence values ​​and risk indicators to determine the optimal reagent dosage formulation with the highest comprehensive score. The automatic control command inputs the reagent dosage parameters of the optimal formulation into the reagent addition device for execution control to complete the reagent formulation adjustment of the flotation process.

[0075] In one specific embodiment, the process of performing step S101 may specifically include the following steps:

[0076] X-ray fluorescence spectrometry was used to scan and detect the slurry in the flotation cell to obtain data on the percentage of mineral composition and the distribution of gangue minerals.

[0077] The concentration of added agents was monitored using an online concentration meter, and the concentration sequences of collectors, frothers, and modifiers were obtained.

[0078] The thickness values ​​collected by the foam layer thickness sensor are sorted according to the timestamp to generate time series data of foam layer thickness.

[0079] Time alignment processing was performed on mineral composition percentage data, reagent concentration sequence, and foam layer thickness time series data to obtain synchronized flotation monitoring data;

[0080] Based on a data standardization protocol, synchronized flotation monitoring data is normalized to generate a flotation process dataset.

[0081] Specifically, the process of scanning and detecting slurry in a flotation cell using an X-ray fluorescence spectrometer involves complex physicochemical analysis. The X-ray tube inside the X-ray fluorescence spectrometer generates a high-energy X-ray beam. When these X-rays irradiate the slurry sample, the atoms in the sample are excited, inner-shell electrons are ejected to form holes, and outer-shell electrons emit characteristic X-ray fluorescence when they jump to fill the holes. The fluorescence emitted by different elements has specific energy and wavelength. The spectrometer's built-in energy spectrum detector captures these fluorescence signals and converts them into electrical signals. The signal processing circuit converts the electrical signals into digital signals and transmits them to the data processing unit. The data processing unit matches and identifies the detected fluorescence spectra with the built-in standard spectral library, and determines the content of each element by calculating the peak area integral. The percentage data of mineral composition is obtained through stoichiometry conversion of element content, and the distribution data of gangue minerals is obtained by scanning slurry samples at different locations to obtain spatial distribution information. The entire detection process adopts a continuous scanning mode, completing a complete elemental analysis cycle every 30 seconds, generating time-series mineral composition data.

[0082] Online concentration monitoring of added reagents utilizes the principle of electrochemical sensing. The online concentration meter contains a specific electrode system. When the reagent solution flows across the electrode surface, the conductivity of the solution changes. Conductivity and reagent concentration have a linear relationship; the concentration meter calculates the reagent concentration by measuring the change in solution conductivity. During collector concentration sequence monitoring, xanthate-type collector molecules undergo redox reactions on the electrode surface, generating characteristic current signals. The intensity of these current signals is proportional to the collector concentration. Foaming agent concentration sequence monitoring utilizes the surface activity of foaming agent molecules, indirectly determining the foaming agent concentration by measuring changes in solution surface tension. For alkaline adjusters such as lime, a composite measurement method combining a pH electrode and an ion-selective electrode is used. The pH electrode measures changes in solution acidity / alkalinity, while the ion-selective electrode detects the concentration of specific ions. The actual concentration of the adjuster is calculated by combining these two signals. Concentration monitoring employs a real-time continuous measurement mode, with data acquisition frequency once per minute, forming a high-density time series of reagent concentrations.

[0083] The process of sorting the thickness values ​​collected by the foam layer thickness sensor according to the timestamp solves the data time sequence problem. The foam layer thickness sensor uses ultrasonic ranging technology. The sensor emits high-frequency ultrasonic pulses. The ultrasonic waves propagate in the air and are reflected when they encounter the foam layer surface. The reflected waves return to the sensor and are captured by the receiver. The time measurement circuit built into the sensor accurately calculates the round-trip time of the ultrasonic waves. The distance between the sensor and the foam layer surface is calculated according to the sound velocity formula. The foam layer thickness value is obtained by converting it with preset flotation cell geometric parameters. Each measurement is recorded with a precise timestamp. The timestamp uses the standard Unix time format to ensure time accuracy. Since the sensor may be affected by environmental interference or equipment failure, resulting in irregular data acquisition time, the sorting process arranges all thickness values ​​in ascending order according to the value of the timestamp, eliminating the time sequence problem that may occur during data storage. The sorted data forms a strictly chronological foam layer thickness time series data, which reflects the continuous change trend of foam stability and flotation effect during the flotation process.

[0084] To address the synchronization issue of multi-source data, time alignment processing was performed on mineral composition percentage data, reagent concentration sequences, and foam layer thickness time series data. Since the sampling frequencies and times of different sensors are not entirely consistent, the original data exhibited time misalignment. Time alignment processing first established a unified time reference, selecting the smallest sampling interval among all sensors as the standard time step, and establishing a standard time axis. The standard time axis is divided into time points according to the standard time step, starting from the data acquisition start time. For missing data at standard time points, linear interpolation was used to supplement the data. Linear interpolation uses the values ​​of two adjacent actual sampling points to calculate the estimated value of the intermediate time point through a linear equation. The interpolation calculation ensures data continuity and temporal consistency. For time points outside the interpolation range, the nearest neighbor value filling method was used. After time alignment processing, all types of data have corresponding values ​​at the same time points, forming a time-synchronized multidimensional data matrix. The rows of the matrix represent standard time points, and the columns represent different monitoring parameters, resulting in synchronized flotation monitoring data.

[0085] Based on a data standardization protocol, synchronized flotation monitoring data is normalized to eliminate differences in dimensions and numerical ranges among different parameters. The data standardization protocol adopts the Z-score standardization method, which uses statistical principles to convert data with different distributions into a standard normal distribution. The standardization process first calculates the statistical characteristics of each monitoring parameter, including descriptive statistics such as arithmetic mean, standard deviation, maximum value, and minimum value. The arithmetic mean reflects the central tendency of the parameter, and the standard deviation describes the dispersion of the data. The Z-score calculation formula subtracts the mean of the corresponding parameter from each original value and then divides by the standard deviation to obtain the standardized value. The standardized value distribution has a mean of 0 and a standard deviation of 1, eliminating the influence of different physical dimensions such as mineral content percentage, reagent concentration in milligrams per liter, and foam thickness in centimeters in the original data, so that all parameters can be compared and analyzed on the same numerical scale. The standardization process can also reduce the interference of extreme values ​​on subsequent analysis algorithms. After normalization, a flotation process dataset containing the standardized values ​​of all monitoring parameters is generated.

[0086] In one specific embodiment, the process of performing step S102 may specifically include the following steps:

[0087] Correlation analysis was performed on the reagent concentration sequences in the flotation process dataset based on the Pearson correlation coefficient to obtain the inter-reagent correlation matrix.

[0088] The sliding time window technique was applied to the correlation matrix between agents to calculate the time delay, and the time delay parameters of collectors and frothers and modifiers and collectors were obtained.

[0089] Based on the synergistic effect calculation formula, the time delay parameter is quantified by the synergistic coefficient to generate the synergistic coefficient of the collector and the synergistic coefficient of the foaming agent.

[0090] Based on the time-series analysis algorithm, the delay quantification of the reagent addition time and the flotation effect response time is performed to obtain the frother response delay value and the modifier response delay value.

[0091] Collector synergy coefficient, foaming agent synergy coefficient, foaming agent response delay value, and modifier response delay value are classified and stored according to agent type to construct an agent association feature library.

[0092] Specifically, correlation analysis of reagent concentration sequences in the flotation process dataset based on the Pearson correlation coefficient involves complex statistical calculations. The Pearson correlation coefficient is a statistical indicator that measures the degree of linear correlation between two continuous variables. Its calculation requires paired analysis of the reagent concentration sequences. The correlation analysis first extracts the collector, frother, and modifier concentration sequences from the flotation process dataset. Each sequence contains concentration values ​​arranged in chronological order. The calculation process requires determining the sample mean of each sequence by summing all values ​​in the sequence and dividing by the sample size to obtain the arithmetic mean. Subsequently, the variance and standard deviation of each sequence are calculated. The Pearson correlation coefficient is obtained by dividing the sum of the squares of the differences between each value and the mean by the sample size minus one. The standard deviation is the square root of the variance. The calculation of the Pearson correlation coefficient involves calculating the covariance of the corresponding time point values ​​of the two sequences. The covariance is equal to the sum of the products of the differences between the corresponding values ​​of the two sequences and their respective means, divided by the sample size minus one. Finally, the correlation coefficient is equal to the covariance divided by the product of the standard deviations of the two sequences. The correlation coefficient ranges from negative one to positive one. A positive value indicates a positive correlation, and a negative value indicates a negative correlation. The absolute value reflects the strength of the correlation. By calculating the correlation coefficients between the collector and the foaming agent, the collector and the modifier, and the foaming agent and the modifier, a three-by-three symmetric matrix structure is formed to obtain the correlation matrix between the agents.

[0093] This paper applies the sliding time window technique to the correlation matrix between drugs to solve the problem of time lag in drug action by calculating time delays. The sliding time window technique sets a fixed-length observation window on the time series, which slides along the time axis according to a preset step size. Statistical characteristics of the data within each window are calculated. In the time delay calculation, the window length is set to 60 minutes and the step size to 5 minutes to ensure sufficient time resolution to capture the delayed effects between drugs. The delay calculation is achieved by performing correlation analysis on the concentration sequences of one drug with the concentration sequences of another drug after time shifting. The process involves shifting the frother concentration sequence forward by 5 minutes, 10 minutes, 15 minutes, up to 60 minutes. After each shift, the Pearson correlation coefficient with the collector concentration sequence is calculated. The time shift corresponding to the maximum correlation coefficient is the time delay parameter between the collector and the frother. The same method is used to calculate the time delay between the modifier concentration sequence and the collector concentration sequence. By traversing different time shifts, the delay time with the strongest correlation is found, thus obtaining the time delay parameters between the collector and the frother, and the time delay parameters between the modifier and the collector. These parameters quantify the optimal configuration of the order and timing of agent addition.

[0094] The synergy coefficient is quantified based on the synergy calculation formula to convert time information into a numerical representation of the synergy effect. The synergy calculation formula is based on the comparison principle of combined and individual effects of reagents. Calculating the synergy coefficient requires obtaining the flotation effect index under combined reagent action and the effect index of each reagent acting alone. The combined effect is represented by the concentrate recovery rate or grade measured under optimal time delay conditions with simultaneous addition of two reagents. The individual effects are represented by the flotation effect values ​​when only the collector or only the frother is added, respectively. The synergy coefficient calculation formula is: [Formula omitted for brevity]. The synergy coefficient is calculated by dividing the combined effect of the collector and frother by the sum of the individual effects. A synergy coefficient greater than 1 indicates a positive synergistic effect between the agents, less than 1 indicates an antagonistic effect, and equal to 1 indicates that the agents are independent of each other. The synergy coefficient of the collector is calculated by dividing the combined effect of the collector and frother by the sum of the individual effects of the collector and frother. The synergy coefficient of the frother is calculated by dividing the combined effect of the frother and modifier by the sum of the individual effects of the frother and modifier. The synergy coefficient quantifies the strength of the mutual enhancement or inhibition between the agents, providing a quantitative basis for subsequent optimization of the agent formulation.

[0095] Based on a time-series analysis algorithm, the delay quantification of reagent dosing time and flotation effect response time is performed. Dynamic time warping technology is used to identify the response pattern of reagent action. The time-series analysis algorithm determines the response delay by establishing a time mapping relationship between reagent dosing events and flotation effect change events. The algorithm first identifies dosing events in the reagent concentration sequence, defined as the time point when the concentration value shows a significant increase. Dosing events are identified by calculating the first difference of the concentration sequence and setting a threshold. Flotation effect response events are determined by monitoring the changing trend of concentrate grade or recovery rate. The response event is manifested as an increase in the effect index after reagent dosing. The delay quantification process is achieved by calculating the difference between the time of the addition event and the time of the corresponding response event. The frother response delay value is calculated by identifying the change time of the foam layer thickness or foam stability index after the addition of the frother. The modifier response delay value is determined by monitoring the impact time of the change in mineral surface properties after pH adjustment on the flotation effect. The time series analysis algorithm uses moving average filtering to eliminate random noise interference. By setting a response amplitude threshold, it is ensured that the detected response events are statistically significant. The frother response delay value and the modifier response delay value are obtained. These delay values ​​reflect the time characteristics of the agent action mechanism.

[0096] The synergistic coefficients of collectors, synergistic coefficients of frothers, response delay values ​​of frothers, and response delay values ​​of modifiers are classified and stored according to agent type to construct an agent-related feature library. A structured data organization method is adopted. The classification and storage process assigns feature parameters to corresponding categories based on the chemical properties and mechanisms of action of the agents. The collector category stores the synergistic coefficients of collectors and time delay parameters related to collectors; the frother category stores the synergistic coefficients of frothers and response delay values ​​of frothers; and the modifier category stores the response delay values ​​of modifiers and synergistic parameters related to pH adjustment. The storage structure adopts a multi-dimensional array format, with the first dimension representing the agent type, the second dimension representing the feature parameter type, and the third dimension representing the time series. Each storage unit contains metadata such as parameter values, calculation timestamps, and data quality identifiers. The feature library construction process also includes data indexing. By establishing a multi-level index structure based on agent type, time range, and parameter type, data query and retrieval are accelerated. The feature library supports incremental updates; newly collected data can be dynamically added to the corresponding storage location after undergoing the same calculation process. The completed agent-related feature library contains information on the strength of synergistic effects and time response characteristics between agents.

[0097] In one specific embodiment, the process of performing step S103 may specifically include the following steps:

[0098] Based on the classification criteria of drug types, the synergistic coefficients of collectors, synergistic coefficients of frothers, response delay values ​​of frothers and response delay values ​​of modifiers in the drug association feature library are grouped into feature groups, namely collector feature group, frother feature group and modifier feature group;

[0099] Cluster analysis of the synergy coefficients within the characteristic groups of collectors is performed based on Euclidean distance calculation, generating cluster centers of collector effects and inter-class distance matrices of collectors.

[0100] The K-means clustering algorithm was applied to the foaming agent feature group and the modifier feature group for hierarchical clustering to obtain the cluster centers of foaming agent effect, the cluster centers of modifier effect, and the corresponding inter-class distance matrix.

[0101] Based on the principle of graph theory, nodes are connected to the cluster centers of the effects of the collector, the effects of the foaming agent, and the effects of the modifier to generate a network topology structure for the association of drug effects.

[0102] The adjacency matrix representation method is used to mathematically describe the topology of the drug effect association network and construct a drug effect association graph.

[0103] Specifically, based on the reagent type classification standard, the feature parameters in the reagent-related feature library are grouped. Based on the differences in the mechanism of action and chemical properties of reagents in the flotation process, the reagent type classification standard divides flotation reagents into three major categories: collectors, frothers, and modifiers. Each category of reagents has a specific mechanism of action and effect characteristics. The classification standard first performs primary classification based on the main function of the reagents. Collectors are mainly responsible for binding with the target mineral surface to form a hydrophobic film; frothers are responsible for generating stable foam to support mineral particles; and modifiers are responsible for adjusting the chemical environment of the pulp and influencing the surface properties of minerals. The feature grouping process extracts various feature parameters from the reagent-related feature library. The collector synergy coefficient reflects the effectiveness of collectors when used in combination with other reagents. The degree of effect enhancement is calculated by the ratio of the effect of the collector acting alone to the combined effect. The frother synergy coefficient characterizes the strength of the synergistic effect between the frother and the modifier or collector. The frother response delay value records the time characteristics of foam formation and stabilization after the frother is added. The modifier response delay value describes the time interval at which the modifier affects the flotation effect after changing the pulp environment. The grouping process assigns the collector synergy coefficient and its related time delay parameters to the collector feature group, the frother synergy coefficient and the frother response delay value to the frother feature group, and the modifier response delay value and its parameters related to pH changes to the modifier feature group. These three independent feature groups provide a data basis for subsequent cluster analysis.

[0104] Cluster analysis of synergy coefficients within a collector feature group is performed based on Euclidean distance calculation. Geometric distance is used to measure the similarity between data points. Euclidean distance calculation is based on the formula for the straight-line distance between two points in multidimensional space. In the analysis of the collector feature group, each synergy coefficient value is considered a point in the multidimensional feature space. The distance calculation process first maps the synergy coefficient data to a standardized feature space to eliminate the influence of different numerical ranges on the distance calculation. The Euclidean distance between two synergy coefficients is equal to the square root of the sum of the squares of the differences in each dimension. The cluster analysis process constructs a distance matrix by calculating the pairwise distances between all synergy coefficient data points. The distance matrix is ​​a symmetric matrix with diagonals... Elements are zero, and off-diagonal elements represent the Euclidean distance between corresponding data points. The clustering process uses a hierarchical clustering method. In the initial state, each synergy coefficient data point forms an independent cluster. The algorithm repeatedly merges the two closest clusters until the preset number of clusters is reached. The minimum distance criterion is used in the cluster merging process, that is, the new cluster center after merging is determined by calculating the geometric center of the original data points. The coordinates of the cluster center are equal to the arithmetic mean of the coordinates of all data points in the cluster. The generated collector effect cluster centers represent the typical characteristics of different synergy effect modes. The collector inter-cluster distance matrix records the Euclidean distance between each cluster center, providing connection strength information for subsequent network construction.

[0105] The K-means clustering algorithm was applied to the foaming agent feature group and the modifier feature group for hierarchical clustering. An iterative optimization method was used to determine the optimal cluster partitioning. The K-means algorithm achieves cluster optimization by minimizing the sum of squared distances from data points within a cluster to the cluster centers. The algorithm first randomly initializes K cluster centers, with the K value determined based on the distribution characteristics of the feature group data and domain knowledge. Different K values ​​were assigned to the foaming agent and modifier feature groups to suit their respective data characteristics. The iterative process includes two alternating steps: the first step assigns each data point to the nearest cluster center using the Euclidean distance formula; the second step recalculates the sum of squared distances from each cluster center. The new cluster center coordinates are equal to the mean of the coordinates of all data points in the cluster. The iterative process continues until the change in the cluster center position is less than a preset threshold or the maximum number of iterations is reached. During the hierarchical clustering process, the cluster analysis of the foaming agent feature group focuses on the combination pattern of foaming agent synergy coefficient and response delay value, and identifies the feature patterns corresponding to different foaming effect types. The cluster analysis of the modifier feature group focuses on the correlation between modifier response delay value and pH change rate, and obtains the foaming agent effect cluster center, modifier effect cluster center and the corresponding inter-class distance matrix. The inter-class distance matrix calculates the Euclidean distance between each cluster center, reflecting the degree of similarity between different effect patterns.

[0106] Based on graph theory principles, node connections are established between cluster centers representing the effects of various drugs. A topological structure for the relationships between drug effects is constructed using network theory. Graph theory treats cluster centers as nodes in a network, and the connections between nodes reflect the degree of mutual influence between drug effects. The connection construction process first determines the node set, including cluster centers representing the effects of harvesters, foaming agents, and modifiers. Each cluster center is considered an independent node in the network. Node connection determination is based on the distance values ​​in the inter-class distance matrix. When the distance between two cluster centers is less than a preset threshold, a connection is established between the corresponding nodes. The connection threshold is determined by analyzing the statistical characteristics of the distance distribution, usually by selecting a specific percentile of the distance distribution as the threshold. The connection weight is calculated based on the reciprocal of the distance between cluster centers. The closer the cluster centers are, the greater the connection weight, indicating a stronger correlation between drug effects. The network construction process also considers the temporal relationship of drug action, adjusting the directionality of connections according to the drug administration order and response delay time to form a directed network structure. The generated drug effect association network topology includes node attributes and edge attributes. Node attributes record the feature vector of the cluster center and the drug type it belongs to, while edge attributes record the connection weight and direction information.

[0107] This paper uses adjacency matrix representation to mathematically describe the topology of the drug effect association network, transforming the graph structure into a computable numerical matrix. Adjacency matrix is ​​a standard mathematical tool in graph theory used to describe network connections. The rows and columns of the matrix correspond to nodes in the network, and the matrix element values ​​represent the connection state and strength between the corresponding nodes. The adjacency matrix construction process first determines the matrix dimension, which is equal to the total number of nodes in the network, including the cluster center nodes of all drug types. The matrix is ​​initialized to zero. Then, the matrix elements are filled according to the connection information in the network topology. For node pairs with connections, the corresponding positions in the adjacency matrix are filled with... The adjacency matrix of a directed network is an asymmetric matrix, reflecting the directional characteristics of the connections. The magnitude of the matrix elements reflects the connection strength; the larger the value, the stronger the correlation between drug effects. The mathematical properties of the adjacency matrix support various network analysis algorithms, including path analysis, centrality calculation, and community detection. The constructed drug effect correlation graph is stored in the form of an adjacency matrix, supporting subsequent formulation calculation and optimization analysis. The connection patterns contained in the graph reflect the synergistic and competitive relationships between different drug effects, providing network structure constraints for multi-objective drug ratio optimization.

[0108] In one specific embodiment, the process of performing cluster analysis on the synergistic coefficients within the collector feature group based on Euclidean distance calculation can specifically include the following steps:

[0109] Based on the Euclidean distance algorithm, the pairwise distance of each collector synergy coefficient in the collector feature group is calculated to obtain the collector synergy coefficient distance matrix.

[0110] The K-value initialization algorithm is applied to the collector synergy coefficient distance matrix to initialize the cluster centers, thereby obtaining the initial set of collector cluster center coordinates;

[0111] Based on the minimum distance criterion, the collector synergy coefficients are assigned to the corresponding initial cluster centers according to the principle of closest distance, generating the grouping results of the collector synergy coefficients;

[0112] Based on the centroid update algorithm, the centroid of the synergy coefficients in each group of the collector synergy coefficient grouping results is calculated and updated to obtain new collector effect cluster centers.

[0113] The Euclidean distances between the new collector effect cluster centers are stored in a matrix to construct the inter-collector class distance matrix.

[0114] Specifically, the pairwise distance calculation of each collector synergy coefficient within the collector feature group is based on the Euclidean distance algorithm. This algorithm employs the principle of geometric spatial distance measurement. The Euclidean distance algorithm, based on a multidimensional extension of the Pythagorean theorem, is used to calculate the straight-line distance between any two points in a multidimensional space. In the analysis of collector synergy coefficients, each synergy coefficient value is treated as a point coordinate in one-dimensional space. Although the synergy coefficient itself is one-dimensional data, in actual calculations, it is usually combined with multiple dimensions such as the time characteristics, intensity, and duration of the synergy coefficient to form a multidimensional feature vector. The distance calculation process first extracts all synergy coefficients within the collector feature group as a numerical sequence. Assuming the feature group contains n synergy coefficient values, then n multiplied by n minus one divided by 2 distance calculations are required. The Euclidean distance between synergistic coefficients is calculated using the formula of the square root of the sum of squares of the differences in each dimension. For one-dimensional cases, the distance equals the absolute difference between the two values; for multi-dimensional cases, the distance equals the square root of the sum of squares of the differences in each dimension. During the calculation, it is necessary to ensure that all dimensions of data use the same numerical scale to avoid interference from different units of measurement in the distance calculation. The results of pairwise distance calculations are organized into a symmetric matrix structure. The row and column indices of the matrix correspond to the numbers of the synergistic coefficients, and the matrix element values ​​represent the Euclidean distance between corresponding synergistic coefficients. A diagonal element of zero indicates that the distance between the synergistic coefficient and itself is zero. Off-diagonal elements record the actual distance values ​​between different synergistic coefficients. The resulting collector synergistic coefficient distance matrix provides basic distance information for subsequent cluster center initialization.

[0115] This paper applies a K-value initialization algorithm to the distance matrix of collector synergy coefficients to initialize cluster centers, addressing the starting point selection problem in clustering algorithms. The goal of the K-value initialization algorithm is to select suitable initial cluster center locations from the distance matrix, ensuring that the distribution of initial centers represents the overall structural characteristics of the data. The algorithm first determines the value of the number of clusters, K. The selection of K is based on the elbow rule, silhouette coefficient analysis, or domain expert knowledge. For collector synergy coefficients, K is typically determined based on the expected classification of collector types, quantities, and effect patterns. The initialization process employs an improved strategy of the K-means++ algorithm. The first cluster center is randomly selected from any synergy coefficient in the distance matrix as the starting point, and subsequent cluster centers... The selection is based on the principle of maximizing distance, that is, selecting the synergy coefficient that is farthest from the existing cluster centers as the new cluster centers. Maximizing distance ensures that the initial cluster centers are relatively evenly distributed in the data space, avoiding the local optimum problem caused by the cluster centers being too concentrated. During the selection process, the pre-calculated distance values ​​in the distance matrix are used to determine the next center position by comparing the minimum distance between the candidate point and the selected center. The selection process is repeated until K initial cluster centers are obtained. Each cluster center corresponds to a specific synergy coefficient value and its coordinate information in the collector feature group, and the initial collector cluster center coordinate set is obtained. This set contains the multi-dimensional coordinate vectors of K cluster centers, providing a starting benchmark for subsequent data allocation and iterative optimization.

[0116] Based on the minimum distance criterion, the collector synergy coefficients are assigned to their corresponding initial cluster centers according to the principle of proximity. A greedy strategy is used to determine the cluster affiliation of data points. The minimum distance criterion determines the optimal affiliation by comparing the distances of each synergy coefficient to each cluster center. The assignment process iterates through each synergy coefficient value in the collector feature group. For each synergy coefficient, its Euclidean distance to all K cluster centers is calculated. The distance calculation uses the previously constructed distance matrix or directly applies the Euclidean distance formula. The comparison process finds the cluster center with the smallest distance value, and the current synergy coefficient is assigned to the cluster group corresponding to that cluster center. The assignment result records the cluster label of each synergy coefficient. The labels, ranging from 1 to K, represent different cluster groups. The allocation process also needs to handle boundary cases. When the distances from the synergy coefficients to multiple cluster centers are equal, a preset decision rule is used, usually selecting the cluster center with the smaller number to ensure the determinism of the algorithm. After allocation, the number of synergy coefficients in each cluster group is counted to ensure that there are no empty clusters. Empty clusters are handled by randomly selecting cluster centers again or merging similar clusters. The generated collector synergy coefficient grouping results include a member list of each cluster group and the corresponding synergy coefficient values. The grouping results provide a data basis for centroid update calculation, ensuring that subsequent cluster center optimization can be based on accurate data grouping.

[0117] The centroid update algorithm is used to calculate the centroids of the synergy coefficients within each group of the collector synergy coefficient grouping results. The geometric center optimization principle is then applied to update the cluster center positions. The centroid update algorithm is based on the objective function of minimizing the sum of squared distances from data points within a cluster to the cluster center. The new cluster center coordinates are determined by calculating the geometric mean of all synergy coefficients within each cluster. The centroid calculation process first extracts all synergy coefficient values ​​within each cluster. For a cluster containing m synergy coefficients, the new cluster center coordinates are equal to the arithmetic mean of the coordinate vectors of these m synergy coefficients. In the one-dimensional case, the cluster center is equal to the arithmetic mean of all synergy coefficient values ​​within the group. In the multi-dimensional case, the average values ​​of each dimension need to be calculated separately to construct the new center coordinate vector. The average value calculation involves calculating the average values ​​of all synergy coefficients within the group. The centroid update process is performed simultaneously on all K clusters, generating K new cluster center coordinates. The positions of the new cluster centers are more representative of the distribution characteristics of each group's data compared to the initial centers. The updated cluster centers can minimize the dispersion of data points within the group. The centroid update algorithm also includes a convergence test, which judges whether the algorithm has converged by comparing the changes in the positions of the cluster centers before and after the update. The algorithm terminates when the changes in the positions of all cluster centers are less than a preset threshold. Otherwise, the data allocation and iterative process of centroid update are carried out based on the new cluster centers. The newly obtained collector effect cluster centers represent the typical characteristics of different synergistic effect modes, providing optimized center point coordinates for subsequent inter-class distance calculations.

[0118] The Euclidean distances between cluster centers of the new collector effect are stored in a matrix to construct a numerical description of the relationships between clusters. The matrix storage process organizes the distance relationships between cluster centers into a standard mathematical matrix format, facilitating subsequent network construction and association analysis. The distance calculation uses the same Euclidean distance algorithm as the synergy coefficient distance calculation. For K cluster centers, the pairwise distances K multiplied by K minus one and divided by 2 need to be calculated. The distance between each pair of cluster centers is calculated using the Euclidean distance formula. The distance matrix is ​​a K multiplied by K symmetric square matrix. The row and column indices of the matrix correspond to different cluster center numbers. Diagonal elements of zero represent the distance between a cluster center and itself, while off-diagonal elements record the actual distances between different cluster centers. The distance matrix, where the numerical values ​​of the matrix elements reflect the degree of similarity between cluster centers, indicates that the smaller the distance, the more similar the corresponding synergistic effect patterns, and the larger the distance, the more significant the differences in synergistic effects. The matrix storage also includes metadata information, recording auxiliary information such as the characteristic attributes of the cluster centers, the number of synergistic coefficients, and cluster quality indicators. The storage format uses either a sparse matrix or a dense matrix, determined by the sparsity of the distance distribution. The constructed inter-cluster distance matrix provides connection weight information for subsequent graph theory network construction. The distance values ​​in the matrix are used to determine the connection strength and network topology between cluster centers. The distance matrix also supports cluster quality evaluation, assessing the quality of clustering by analyzing the ratio of inter-cluster distance to intra-cluster distance.

[0119] In one specific embodiment, the process of executing step S105 may specifically include the following steps:

[0120] Based on the objective function construction rules, multiple objective functions are set for the correlation graph of reagent effect, and objective functions for concentrate grade, recovery rate and reagent cost are established.

[0121] Based on the weight allocation strategy, weight coefficients are assigned to the objective functions of concentrate grade, recovery rate, and reagent cost to obtain a weighted multi-objective optimization function.

[0122] The non-dominated sorting algorithm is applied to the Pareto solution set search of the weighted multi-objective optimization function to obtain the initial solution space of the drug ratio.

[0123] Based on the crossover and mutation operation, the dosage of collector, frother and modifier in the initial solution space of the drug ratio are iteratively optimized to generate the optimized solution set of the drug ratio.

[0124] The optimized drug ratio solution set is screened and filtered according to feasibility constraints to construct a candidate drug formulation set.

[0125] Specifically, based on the objective function construction rules, a multi-objective function is set for the reagent effect correlation graph to transform the key performance indicators of the flotation process into calculable mathematical expressions. The objective function construction rules are based on the technical requirements and economic benefits of the flotation process. The concentrate grade objective function reflects the enrichment degree of the target mineral in the flotation product. The function construction process first extracts the mapping relationship between the cluster centers of each reagent effect and the concentrate grade from the reagent effect correlation graph. By analyzing historical production data, a mathematical model between reagent dosage and concentrate grade is established. The concentrate grade objective function is expressed as a multivariate nonlinear function of collector dosage, frother dosage, and modifier dosage. The function parameters are extracted from the connection weights and node attributes of the correlation graph through regression analysis. The recovery rate objective function describes the efficiency of separating and recovering the target mineral from the raw ore. The function construction is based on material balance. Based on the principle of equilibrium and flotation kinetics, the relationship between reagent dosage and mineral recovery rate is modeled as an exponentially decaying or logarithmically growing function. The function coefficients are determined by analyzing the response delay parameter and synergy coefficient in the reagent effect correlation graph. The reagent cost objective function quantifies the economic cost of reagent consumption. The function construction process linearly combines the unit price of various reagents with the dosage. The cost function is a linear sum of the costs of collectors, frothers, and modifiers. The cost of each type of reagent is equal to the dosage multiplied by the corresponding unit price. The unit price information is obtained from market data or purchase records. The process of setting the multi-objective function also needs to consider the interrelationship between objectives. There is usually a trade-off between concentrate grade and recovery rate. High grade often corresponds to a relatively low recovery rate. Reagent cost and treatment effect are positively correlated. The three objective functions established form the mathematical framework of the multi-objective optimization problem.

[0126] The multi-objective optimization problem is transformed into a single-objective optimization problem by assigning weight coefficients to the three objective functions according to a weight allocation strategy. The weight allocation strategy, based on the analytic hierarchy process (AHP) and an expert evaluation system, determines the relative importance of each objective. The weight coefficient allocation process first constructs an objective importance comparison matrix. A judgment matrix is ​​established by comparing the relative importance of concentrate grade, recovery rate, and reagent cost pairwise. The elements of the judgment matrix use a scoring standard from 1 to 9, where 1 represents equal importance, 9 represents extreme importance, and intermediate values ​​represent different degrees of importance. During the matrix construction process, experts from different fields, including flotation process experts, production managers, and economic analysts, were invited to score the results. The consistency of the expert scores was tested by calculating the consistency ratio; a consistency ratio less than 0.1 was considered acceptable. The weights were calculated using... The eigenvector method determines weight coefficients by calculating the eigenvector corresponding to the largest eigenvalue of the judgment matrix. Each component of the eigenvector, after normalization, serves as the weight coefficient for each objective function. The sum of the weight coefficients equals 1 to ensure the numerical rationality of the weighted result. Weight allocation also considers dynamic changes in production stages and market conditions. During periods of mineral resource scarcity, the recovery rate weight is increased; during periods of high product prices, the concentrate grade weight is increased; and during periods of significant cost control pressure, the cost weight is increased. Dynamic weight adjustment is achieved by establishing a weight correction factor, which is calculated in real-time based on changes in external environmental indicators. The resulting weighted multi-objective optimization function is a linear weighted combination of three single-objective functions. The numerical value of the weighted function represents the comprehensive optimization effect, providing a unified evaluation standard for subsequent Pareto solution set search.

[0127] This paper applies the non-dominated sorting algorithm to Pareto solution set search for weighted multi-objective optimization functions. It employs evolutionary computation principles to find the optimal solution set for multi-objective optimization problems. Based on Pareto optimality theory, the non-dominated sorting algorithm determines the relative merits of solutions by comparing their performance across different objective functions. The Pareto solution set search process first generates an initial solution population. Each solution vector contains three decision variables: collector dosage, frother dosage, and modifier dosage. The initial solution generation uses Latin hypercube sampling to ensure a uniform distribution of solutions in the decision space. The number of solutions is determined based on problem complexity and computational resources, typically ranging from 100 to 500 solution vectors. The non-dominated sorting process divides the solution population into different front layers according to Pareto dominance. The first front layer contains non-dominated solutions, i.e., solutions that are not strictly dominated by other solutions across all objective functions. The solution is dominated by the first front layer. The second front layer contains solutions dominated only by the solutions in the first front layer, and so on until all solutions are assigned to the corresponding front layer. The sorting process uses a fast non-dominated sorting algorithm, which determines the dominance relationship by comparing the values ​​of each pair of solutions on each objective function. Solution A dominates solution B if and only if A is not inferior to B on all objectives and is strictly superior to B on at least one objective. The time complexity of the sorting algorithm is the square of the solution population size. After sorting, the crowding distance of each solution is calculated. The crowding distance measures the distribution density of the solution in the objective space. Solutions with larger distances have better diversity. Pareto solution set search combines the sorting results and crowding distances to select and eliminate solutions, retaining solutions with lower front layers and larger crowding distances, to obtain the initial drug ratio solution space. This solution space contains multiple drug ratio vectors representing different trade-off schemes.

[0128] The initial drug ratio solution space is iteratively optimized based on crossover and mutation operations. The evolutionary mechanism of a genetic algorithm is used to improve the quality of the solution. Crossover and mutation operations simulate the genetic and mutation phenomena in biological evolution, generating new candidate solutions through information exchange and random perturbation between solution vectors. The crossover process randomly selects two parent solution vectors from the solution space using roulette wheel selection or tournament selection methods. The selection probability is proportional to the fitness of the solution, which is calculated by combining the weighted multi-objective function value and the Pareto front hierarchy. The crossover operation employs a simulated binary crossover method, controlling the randomness and locality of the crossover process by calculating the crossover probability and distribution index. The crossover probability is typically set between 0.7 and 0.9, and the distribution index controls the similarity between the offspring solutions and the parent solutions. The crossover operation generates two offspring solution vectors. The decision variables of the offspring solutions are determined by the crossover process through the parent solutions. The weighted combination of the corresponding variables in the alternative solution is calculated. The mutation operation randomly perturbs the child solutions generated by the crossover, with the mutation probability set between 0.01 and 0.1. The mutation operation adopts the multinomial mutation method, which fine-tunes the variable values ​​by adding random numbers that follow a specific probability distribution. The mutation intensity is controlled by the distribution index parameter. A smaller distribution index produces a larger mutation amplitude. The iterative optimization process repeatedly executes the selection, crossover, and mutation operations. Each iteration generates a new solution population. After the new population is merged with the original population, non-dominated sorting and crowding distance calculation are performed. Excellent solutions are retained and inferior solutions are eliminated. The iterative process continues until the convergence condition is met or the maximum number of iterations is reached. The convergence condition is determined by monitoring the diversity index of the solution population and the degree of improvement of the objective function. The generated optimized drug ratio solution set contains multiple high-quality solution vectors that have been iteratively improved.

[0129] The optimized reagent ratio solution set was screened and filtered based on feasibility constraints to ensure its practical operability. Feasibility constraints were established based on the technical limitations and safety requirements of flotation production, including upper and lower limits for reagent dosage, rationality of reagent ratio, equipment processing capacity, and environmental standards. Reagent dosage constraints set minimum and maximum dosage limits based on reagent solubility, storage capacity, and economic considerations. Collector dosage was typically limited to 20-100 mg / L, frother dosage to 5-30 mg / L, and adjuster dosage to the appropriate range based on pH adjustment requirements. Reagent ratio constraints, based on flotation chemistry principles, ensured compatibility between different reagents and prevented chemical precipitation. The process involves considering the ratios of antagonistic reactions, equipment processing capacity constraints such as the volume of the flotation machine, stirring power, and aeration capacity, which limit the addition of reagents. Environmental standards ensure that the concentration of residual reagents in the wastewater meets emission requirements. The screening and filtration process checks each reagent ratio vector in the solution set to see if it meets all constraints. Solution vectors that do not meet the constraints are removed from the solution set. The constraint check uses a combination of numerical comparison and logical judgment. For continuous variable constraints, numerical comparison is used, and for discrete constraints, logical judgment is used. The screening process also includes an assessment of the engineering feasibility of the solution, considering the ease of operation and control accuracy requirements of the production site. After filtration, a candidate reagent formulation set is constructed, which contains all feasible reagent ratio schemes that meet the constraints.

[0130] In one specific embodiment, the process of executing step S106 may specifically include the following steps:

[0131] Based on the unit price parameter of the agent, the cost of the dosage of the collector, the dosage of the foaming agent and the dosage of the modifier in each formulation in the candidate agent formulation set is calculated to obtain the total agent cost data corresponding to each formulation;

[0132] The total cost data of the pharmaceutical agents is constrained and filtered based on the cost constraint threshold to generate a subset of feasible pharmaceutical formulations that meet the cost requirements.

[0133] The confidence assessment algorithm is applied to a subset of feasible drug formulations to perform risk assessment calculations, and the predicted confidence values ​​and risk assessment indicators for each formulation are obtained.

[0134] Based on the comprehensive evaluation criteria, the predicted confidence scores and risk assessment indicators are ranked to determine the optimal drug dosing formula with the highest comprehensive score.

[0135] According to the automatic control instructions, the reagent addition parameters in the optimal reagent addition formula are input into the reagent addition device for execution control, thereby completing the reagent formula adjustment for the flotation process.

[0136] Specifically, a linear cost calculation model is used to perform cost accounting on the candidate reagent formulation set based on the reagent unit price parameter. The reagent unit price parameter is obtained from a market procurement price database and includes three types of basic data: collector unit price, frother unit price, and modifier unit price. The cost accounting process extracts the dosage data of each formulation from the candidate reagent formulation set. The collector dosage is expressed in milligrams per liter (mg / L) to represent the concentration of the collector in the slurry. The frother and modifier dosages are expressed in the same unit. The cost is calculated by multiplying the dosage of each reagent by its corresponding unit price. The total cost of the formulation is obtained by summing the results. During the calculation, unit conversion is required to convert the dosage in milligrams per liter into the actual weight of reagent consumed. The conversion is based on the volumetric flow rate and density parameters of the treated slurry. The total reagent cost data is expressed in yuan per ton of ore, reflecting the reagent cost required to process a unit of ore. The cost accounting also considers the effective utilization rate of the reagent. The actual consumption is corrected by the reagent loss coefficient, which is determined based on the equipment conveying efficiency and the completeness of the chemical reaction. The obtained total reagent cost data for each formulation forms the basis for cost analysis.

[0137] The total cost data of the pharmaceutical formulation is constrained and screened using a numerical filtering method based on a cost constraint threshold. The cost constraint threshold is determined according to the company's budget control requirements and market competition pressure. The threshold setting process comprehensively considers economic factors such as the proportion of raw material costs, profit margins, and product prices. The constraint screening process compares the total cost of each formulation with the preset threshold one by one. Formulations exceeding the threshold are removed from the candidate set. The screening process uses strict inequality judgment to retain only formulations with costs strictly less than the threshold. The screening algorithm also includes cost distribution analysis, which evaluates the rationality of cost distribution by calculating the mean, standard deviation, maximum, and minimum costs of candidate formulations. Abnormally high-cost formulations are identified and eliminated using outlier detection methods. Outlier judgment is based on the interquartile range and standardized residual calculation of cost data. The generated feasible pharmaceutical formulation subset contains all formulation schemes that meet the cost constraints. The size of the subset is determined according to the strictness of the constraints and the cost distribution characteristics of the original candidate set.

[0138] The confidence assessment algorithm was applied to a subset of feasible reagent formulations for risk assessment using Bayesian inference and historical data statistical analysis. The algorithm is based on a comprehensive evaluation of the formulation prediction accuracy and production stability. First, a formulation effect prediction model is established. Predictive relationships are constructed by analyzing the correlation between formulation parameters and actual flotation effects in historical production data. The prediction model uses regression analysis, with the reagent dosage as input variables and concentrate grade and recovery rate as output variables. The regression coefficients are determined using the least squares method during model training. Prediction confidence is determined by calculating the statistical deviation between predicted and actual values; a smaller deviation indicates higher prediction confidence. Risk assessment indicators include three dimensions: technical risk, economic risk, and operational risk. Technical risk is calculated using the historical success rate of formulation parameters; economic risk is determined based on the standard deviation of cost fluctuations; and operational risk is assessed based on formulation complexity and operational difficulty. The risk indicators of each dimension are synthesized into a comprehensive risk assessment value using a weighted average method. The weight allocation is determined based on the product of the risk impact degree and the probability of occurrence. Obtaining the prediction confidence values ​​and risk assessment indicators for each formulation lays the data foundation for the comprehensive evaluation.

[0139] Based on comprehensive evaluation criteria, a multi-attribute decision analysis method is used to comprehensively rank the predicted confidence scores and risk assessment indicators. The comprehensive evaluation criteria establish a trade-off mechanism between confidence scores and risk indicators. The evaluation process first standardizes the confidence scores and risk indicators to eliminate the influence of different indicator dimensions and numerical ranges. Standardization adopts the maximum-minimum value normalization method to map the original values ​​to the range of zero to one. The comprehensive score is calculated using a weighted summation method. The confidence score weight and risk weight are determined according to decision preferences. Risk-averse decisions tend to increase the risk indicator weight, while risk-neutral decisions use equal weights. The ranking process arranges the comprehensive scores of all formulations in descending order of numerical value. The formulation with the highest score is determined as the optimal drug dosing formulation. The ranking algorithm also includes sensitivity analysis, which observes the stability of the ranking results by adjusting the weight parameters to ensure the robustness of the optimal formulation selection. The formulation with the highest comprehensive score represents the best choice in terms of confidence and risk balance.

[0140] The optimal reagent dosing formula parameters are input into the reagent addition device according to the automatic control instructions. The execution control adopts a digital control interface and feedback adjustment mechanism. The control instruction generation process converts the dosage of collector, frother, and modifier in the optimal formula into control signals that the equipment can recognize. The signal conversion is based on the technical specifications and control protocol of the reagent addition device, including specific control quantities such as the opening setting of the flow control valve, the speed adjustment of the metering pump, and the stirring parameters of the mixer. The execution control process adopts a closed-loop control strategy, adjusting the control parameters by real-time monitoring of reagent concentration and flotation effect indicators. The feedback control is based on the proportional-integral-derivative control algorithm, calculating the correction range of the control quantity according to the deviation between the set value and the actual value. The control execution also includes a safety protection mechanism, which automatically switches to the preset safety formula when an abnormality is detected. The reagent formula adjustment of the flotation process realizes closed-loop optimization from data analysis to production execution.

[0141] The above describes the data analysis-based flotation reagent formulation optimization method in the embodiments of this application. The following describes the data analysis-based flotation reagent formulation optimization system in the embodiments of this application. Please refer to [link to relevant documentation]. Figure 2 One embodiment of the flotation reagent formulation optimization system based on data analysis in this application includes:

[0142] The monitoring module is used to monitor the slurry in the flotation cell in real time through online detection equipment, and obtain a flotation process dataset including ore grade distribution, reagent concentration changes and froth layer thickness;

[0143] The association module is used to perform time-series association processing on the flotation process dataset according to the reagent action time delay analysis algorithm, and generate a reagent association feature library containing the collector synergy coefficient and the frother response delay;

[0144] The clustering module is used to perform hierarchical clustering analysis on the drug-related feature library according to drug type, and construct drug effect correlation maps of collectors, foaming agents and modifiers;

[0145] The calculation module is used to perform formula calculation on the drug effect correlation graph through a multi-objective drug ratio optimization algorithm to generate a set of candidate drug formulas;

[0146] The screening module is used to screen and evaluate the candidate drug formulation set according to production cost constraints, determine the optimal drug addition formulation, and control the drug addition system to perform formulation adjustments.

[0147] above Figure 2 The flotation reagent formulation optimization system based on data analysis in this embodiment of the invention will be described in detail from the perspective of modular functional entities. The flotation reagent formulation optimization device based on data analysis in this embodiment of the invention will be described in detail from the perspective of hardware processing.

[0148] Reference Figure 3 This invention also provides a data analysis-based flotation reagent formulation optimization device, which can be a server, and its internal structure can be as follows: Figure 3 As shown, the data analysis-based flotation reagent formulation optimization device includes a processor, memory, display screen, input device, network interface, and database connected via a system bus. The processor, designed as a computer, provides computational and control capabilities. The memory of the data analysis-based flotation reagent formulation optimization device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores the operating system, computer programs, and database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database of the data analysis-based flotation reagent formulation optimization device stores the data corresponding to this embodiment. The network interface of the data analysis-based flotation reagent formulation optimization device is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements the above-described method.

[0149] Those skilled in the art will understand that Figure 3 The structure shown is merely a block diagram of a portion of the structure related to the present invention and does not constitute a limitation on the data analysis-based flotation reagent formulation optimization device to which the present invention is applied.

[0150] The present invention also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when the instructions are executed on a computer, cause the computer to perform the steps of the data analysis-based flotation reagent formulation optimization method.

[0151] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0152] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a data analysis-based flotation reagent formulation optimization device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0153] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing flotation reagent formulation based on data analysis, characterized in that, The method includes: Real-time monitoring of the slurry in the flotation cell is achieved using online detection equipment, resulting in a flotation process dataset that includes ore grade distribution, reagent concentration changes, and froth layer thickness. The flotation process dataset is subjected to time-series correlation processing based on the reagent action time delay analysis algorithm to generate a reagent correlation feature library containing the collector synergy coefficient and the frother response delay; The drug-related feature library was subjected to hierarchical cluster analysis according to drug type to construct drug effect correlation maps for collectors, foaming agents, and modifiers; A multi-objective drug ratio optimization algorithm is used to calculate the drug effect correlation graph to generate a set of candidate drug formulations. The candidate drug formulation set is screened and evaluated based on production cost constraints to determine the optimal drug dosing formulation and control the drug addition system to perform formulation adjustments. The step involves performing time-series correlation processing on the flotation process dataset using a reagent action time-delay analysis algorithm to generate a reagent correlation feature library containing collector synergy coefficients and frother response delays, including: Correlation analysis was performed on the reagent concentration sequences in the flotation process dataset based on the Pearson correlation coefficient to obtain the inter-reagent correlation matrix. The sliding time window technique is applied to the correlation matrix between the agents to calculate the time delay, thereby obtaining the time delay parameters between the collector and the frother and the time delay parameters between the modifier and the collector. The time delay parameter is quantified according to the synergistic effect calculation formula to generate the synergistic coefficient of the collector and the synergistic coefficient of the foaming agent. Based on the time-series analysis algorithm, the delay quantification of the reagent addition time and the flotation effect response time is performed to obtain the frother response delay value and the modifier response delay value. The synergistic coefficients of the collectors, synergistic coefficients of the foaming agents, the response delay values ​​of the foaming agents, and the response delay values ​​of the modifiers are classified and stored according to the agent type to construct the agent-related feature library.

2. The method for optimizing flotation reagent formulation based on data analysis according to claim 1, characterized in that, The process involves real-time monitoring of the slurry in the flotation cell using online detection equipment to obtain a flotation process dataset containing mineral grade distribution, reagent concentration changes, and froth layer thickness, including: X-ray fluorescence spectrometry was used to scan and detect the slurry in the flotation cell to obtain data on the percentage of mineral composition and the distribution of gangue minerals. The concentration of added agents was monitored using an online concentration meter, and the concentration sequences of collectors, frothers, and modifiers were obtained. The thickness values ​​collected by the foam layer thickness sensor are sorted according to the timestamp to generate time series data of foam layer thickness. The mineral composition percentage data, reagent concentration sequence, and foam layer thickness time series data are time-aligned to obtain synchronized flotation monitoring data. The synchronized flotation monitoring data is normalized based on a data standardization protocol to generate the flotation process dataset.

3. The method for optimizing flotation reagent formulation based on data analysis according to claim 1, characterized in that, The step of performing hierarchical cluster analysis on the drug-related feature library according to drug type to construct drug effect correlation maps for collectors, foaming agents, and modifiers includes: Based on the classification criteria for drug types, the synergistic coefficients of collectors, synergistic coefficients of frothers, response delay values ​​of frothers, and response delay values ​​of modifiers in the drug-related feature library are grouped into feature groups to obtain the collector feature group, the frother feature group, and the modifier feature group. Cluster analysis of the synergy coefficients within the collector feature group is performed based on Euclidean distance calculation to generate collector effect cluster centers and collector inter-class distance matrices. The K-means clustering algorithm was applied to the foaming agent feature group and the modifier feature group for hierarchical clustering to obtain the cluster centers of foaming agent effect, the cluster centers of modifier effect, and the corresponding inter-class distance matrix. Based on the principle of graph theory, the cluster centers of the collector effect, the foaming agent effect, and the modifier effect are connected by nodes to generate a drug effect association network topology. The drug effect association network topology is mathematically described based on the adjacency matrix representation method, and the drug effect association graph is constructed.

4. The method for optimizing flotation reagent formulation based on data analysis according to claim 3, characterized in that, The clustering analysis of the synergy coefficients within the collector feature group based on Euclidean distance calculation, generating collector effect cluster centers and inter-class distance matrices, includes: Based on the Euclidean distance algorithm, the pairwise distance of each collector synergy coefficient in the collector feature group is calculated to obtain the collector synergy coefficient distance matrix. The K-value initialization algorithm is applied to the collector synergy coefficient distance matrix to initialize the cluster centers, thereby obtaining the initial set of collector cluster center coordinates; Based on the minimum distance criterion, the collector synergy coefficients are assigned to the corresponding initial cluster centers according to the principle of closest distance, generating the collector synergy coefficient grouping results; Based on the centroid update algorithm, the centroid of the synergy coefficients in each group of the collector synergy coefficient grouping results is calculated, and new collector effect cluster centers are obtained by updating the centroid. The Euclidean distances between the cluster centers of the new collector effects are stored in a matrix to construct the inter-cluster distance matrix of the collectors.

5. The method for optimizing flotation reagent formulation based on data analysis according to claim 1, characterized in that, The step of performing formulation calculations on the drug effect correlation graph using a multi-objective drug ratio optimization algorithm to generate a candidate drug formulation set includes: Based on the objective function construction rules, the correlation graph of the agent effect is used to set multiple objective functions, and objective functions for concentrate grade, recovery rate and agent cost are established. According to the weight allocation strategy, the weight coefficients of the objective function of concentrate grade, objective function of recovery rate and objective function of reagent cost are allocated to obtain the weighted multi-objective optimization function; The non-dominated sorting algorithm is applied to the weighted multi-objective optimization function to perform Pareto solution set search, and the initial drug ratio solution space is obtained. Based on the crossover and mutation operation, the dosage of collector, foaming agent and modifier in the initial drug ratio solution space are iteratively optimized to generate an optimized drug ratio solution set. The optimized drug ratio solution set is screened and filtered according to feasibility constraints to construct the candidate drug formulation set.

6. The method for optimizing flotation reagent formulation based on data analysis according to claim 1, characterized in that, The step of screening and evaluating the candidate drug formulation set based on production cost constraints, determining the optimal drug dosing formulation, and controlling the drug addition system to perform formulation adjustments includes: Based on the unit price parameter of the agent, the cost of the amount of collector, foaming agent and modifier added to each formulation in the candidate agent formulation set is calculated to obtain the total agent cost data corresponding to each formulation; The total cost data of the drug is constrained and filtered according to the cost constraint threshold to generate a subset of feasible drug formulations that meet the cost requirements; The confidence assessment algorithm is applied to the subset of feasible drug formulations to perform risk assessment calculations, and the predicted confidence values ​​and risk assessment indicators for each formulation are obtained. Based on the comprehensive evaluation criteria, the predicted confidence scores and risk assessment indicators are ranked comprehensively to determine the optimal drug dosing formula with the highest comprehensive score. According to the automatic control command, the reagent addition parameters in the optimal reagent addition formula are input into the reagent addition device for execution control, thereby completing the reagent formula adjustment for the flotation process.

7. A flotation reagent formulation optimization system based on data analysis, characterized in that, For implementing the data analysis-based flotation reagent formulation optimization method as described in any one of claims 1-6, the data analysis-based flotation reagent formulation optimization system comprises: The monitoring module is used to monitor the slurry in the flotation cell in real time through online detection equipment, and obtain a flotation process dataset including ore grade distribution, reagent concentration changes and froth layer thickness; The association module is used to perform time-series association processing on the flotation process dataset according to the reagent action time delay analysis algorithm, and generate a reagent association feature library containing the collector synergy coefficient and the frother response delay; The clustering module is used to perform hierarchical clustering analysis on the drug-related feature library according to drug type, and construct drug effect correlation maps of collectors, foaming agents and modifiers; The calculation module is used to perform formula calculation on the drug effect correlation graph through a multi-objective drug ratio optimization algorithm to generate a set of candidate drug formulas; The screening module is used to screen and evaluate the candidate drug formulation set according to production cost constraints, determine the optimal drug addition formulation, and control the drug addition system to perform formulation adjustments.

8. A flotation reagent formulation optimization device based on data analysis, characterized in that, It includes a memory and a processor, the memory storing a computer program that can run on the processor, and the processor executing the computer program to implement the data analysis-based flotation reagent formulation optimization method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is run by the processor, it causes the processor to perform the data analysis-based flotation reagent formulation optimization method as described in any one of claims 1 to 7.

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