Multi-objective optimization method based on Black-Litterman model for ore grinding grading process and related device

Abstract

The invention discloses a multi-objective optimization method based on a Black-Litterman model for an ore grinding grading process, a multi-objective optimization device based on the Black-Litterman model for the ore grinding grading process, multi-objective optimization equipment and a computer readable storage medium. According to the method, the experience viewpoint of a process expert and historical data are organically fused by adopting the Black-Litterman model; the limitation that a traditional optimization method only depends on data driving or only depends on expert experience is overcome, and collaborative complementation of subjective knowledge and objective data is achieved. The deep learning technology is introduced to extract time series data features, and the convolutional neural network is combined to fuse expert viewpoints, so that the optimization model can fully excavate complex dynamic characteristics and inherent rules in the ore grinding classification process. Practical experience is fused into a prediction framework, so that the result is more suitable for practical operation, and the accuracy of ore grinding classification multi-objective optimization is improved.

Description

Technical Field

[0001] This invention belongs to the field of grinding optimization technology, and more specifically, relates to a multi-objective optimization method based on the Black-Litterman model for grinding and classification processes, a multi-objective optimization device based on the Black-Litterman model for grinding and classification processes, a multi-objective optimization equipment, and a computer-readable storage medium. Background Technology

[0002] Grinding and classification is a crucial step in mineral processing, involving grinding ore to a suitable particle size and classifying it to provide qualified feed for subsequent beneficiation processes. However, the grinding and classification process presents numerous challenges.

[0003] Grinding and classification is a crucial step in mineral processing, primarily responsible for crushing ore to a suitable particle size and classifying it to provide qualified feed for subsequent beneficiation operations. However, the grinding and classification process presents numerous challenges. First, the process involves multiple interdependent objectives, such as grinding efficiency, classification accuracy, and energy consumption. Increasing grinding efficiency may increase energy consumption, while reducing energy consumption may affect classification accuracy. Second, the grinding and classification process is influenced by various factors, including ore properties (such as hardness and particle size distribution), equipment parameters (such as mill speed and feed rate), and operating conditions (such as feed concentration and classifier overflow particle size). These factors are intertwined, making the optimization problem complex. Furthermore, the grinding and classification process exhibits strong coupling and nonlinear characteristics, making it difficult for traditional control methods to effectively handle such complex systems, resulting in poor optimization performance. Existing technologies have limitations in addressing these challenges. For example, some methods focus on single-objective optimization, neglecting the balance between multiple objectives; some methods based on precise mathematical models are limited in practical applications due to the difficulty in accurately obtaining model parameters. Therefore, it is of great significance to develop a grinding and classification optimization method that can comprehensively consider the balance of multiple objectives, is highly adaptable, and is applicable to actual production.

[0004] Wang Xiaoli et al. from Central South University proposed an uncertain multi-objective optimization method for the grinding and classification process. First, a deterministic multi-objective optimization model is constructed to maximize mill power to increase mill throughput and maximize the -0.075mm fineness content in the first-stage overflow to improve product quality. Considering the uncertainty of the feed particle size distribution during production, the ore particle size parameter is treated as a triangular fuzzy parameter to construct a fuzzy chance constraint model for the grinding and classification process. A hybrid NSGA-II algorithm based on reliability measures and fuzzy simulation is used to solve the model, obtaining the Pareto optimal frontier. Finally, the optimal setpoint is determined using the TOPSIS decision method. Practical results show that this method improves product quality by 3.52% and increases output by 7.56 t / h, demonstrating good performance.

[0005] Therefore, how to integrate practical experience into the prediction framework to make the results more in line with practical operations and improve the accuracy of multi-objective optimization of grinding and classification is a key issue of concern to those skilled in the art. Summary of the Invention

[0006] The purpose of this application is to provide a multi-objective optimization method based on the Black-Litterman model for grinding and classification processes, a multi-objective optimization device based on the Black-Litterman model for grinding and classification processes, a multi-objective optimization equipment, and a computer-readable storage medium, which integrates practical experience into the prediction framework, making the results more consistent with practical operations and improving the accuracy of multi-objective optimization for grinding and classification.

[0007] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a multi-objective optimization method based on the Black-Litterman model for grinding and classification processes, comprising: Process data of the grinding and classification process are collected, and the process data are normalized using the Min-Max standardization method to obtain normalized historical data; wherein, the process data includes: ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, ball mill current and ball addition rate; Based on the normalized historical data, the average values ​​of ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, and ball addition are calculated to obtain the market equilibrium revenue vector. Construct an enterprise opinion matrix by combining the subjective opinion matrix of process experts and a deep learning model; Based on the volatility of the historical data, the variances of the ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, ball addition rate, and the corresponding coefficients between each target value are calculated to obtain the risk estimation covariance matrix. Based on the confidence level of each target in the grinding and classification production process, an error covariance matrix is ​​constructed; wherein, the error covariance matrix is ​​a diagonal matrix, and the diagonal elements of the diagonal matrix represent the influence levels of the variances of ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, and ball addition amount on the entire grinding and classification production process. Using the Black-Litterman model, combined with the market equilibrium payoff vector, the firm view matrix, the risk estimation covariance matrix, and the error covariance matrix, the posterior payoff and the posterior covariance matrix are calculated. A multi-objective genetic algorithm is used to optimize the posterior gain and the posterior covariance matrix to obtain the Pareto front solution set, and the optimal solution is selected from the Pareto front solution set according to actual production needs and preference data. In actual production, the optimal solution is applied to verify the deviation of the optimization effect. When the deviation exceeds the preset threshold, the model parameters are updated.

[0008] Optionally, a corporate opinion matrix can be constructed by combining the subjective opinion matrix of process experts and a deep learning model, including: Based on the production experience data of process experts, a K×6 matrix composed of K subjective viewpoints is determined, and corresponding weights are assigned according to the relationship between the parameters in each viewpoint, thus obtaining the process expert subjective viewpoint matrix. Time-series data is obtained from the historical data, and features are extracted from the time-series data using an RNN model to obtain a time-series data feature matrix; The subjective opinion matrix of the process experts is combined with the time-series data feature matrix, and the combined matrix is ​​convolved using a CNN model to obtain the enterprise opinion matrix.

[0009] Optionally, the risk estimation covariance matrix is ​​a symmetric matrix, with the diagonal elements representing the variance of each optimization objective and the off-diagonal elements representing the covariance between each optimization objective, calculated by multiplying the corresponding coefficients and standard deviations.

[0010] Optionally, the posterior return is calculated by adding the market equilibrium return vector to an adjustment based on the firm's viewpoint; wherein the adjustment is determined by the firm's viewpoint matrix, the risk estimation covariance matrix, the error covariance matrix, and the viewpoint influence weights; the posterior covariance matrix is ​​calculated by scaling the risk estimation covariance matrix and subtracting the adjustment term based on the firm's viewpoint.

[0011] This application also provides a multi-objective optimization device based on the Black-Litterman model for grinding and classification processes, comprising: The process data acquisition module is used to collect process data of the grinding and classification process, and to normalize the process data using the Min-Max standardization method to obtain normalized historical data; wherein, the process data includes: ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, ball mill current and ball addition rate; The market equilibrium revenue calculation module is used to calculate the average value of ball mill feed rate, average value of overflow flow rate, average value of overflow particle size, average value of grinding noise, average value of energy consumption, and average value of ball addition amount based on the normalized historical data, so as to obtain the market equilibrium revenue vector. The Enterprise Perspective Matrix Construction Module is used to construct an enterprise perspective matrix by combining the subjective perspective matrix of process experts and a deep learning model. The risk estimation matrix construction module is used to calculate the variance of ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, ball addition amount and corresponding coefficients between each target value based on the volatility of the historical data, so as to obtain the risk estimation covariance matrix. The error covariance matrix construction module is used to construct an error covariance matrix based on the confidence level of each target in the grinding and classification production process. The error covariance matrix is ​​a diagonal matrix, and the diagonal elements of the diagonal matrix represent the influence levels of the variances of the ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, and ball addition amount on the entire grinding and classification production process. The posterior return calculation module is used to calculate the posterior return and the posterior covariance matrix using the Black-Litterman model, combined with the market equilibrium return vector, the firm view matrix, the risk estimation covariance matrix, and the error covariance matrix. The optimization solution module is used to optimize the posterior benefit and the posterior covariance matrix using a multi-objective genetic algorithm to obtain the Pareto front solution set, and select the optimal solution from the Pareto front solution set according to actual production needs and preference data. The optimal solution application module is used to apply the optimal solution in actual production, verify the deviation of the optimization effect, and update the model parameters when the deviation exceeds a preset threshold.

[0012] This application also provides a multi-objective optimization device, including: Memory, used to store computer programs; A processor is used to implement the steps of the multi-objective optimization method described above when executing the computer program.

[0013] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the multi-objective optimization method described above.

[0014] It has the following beneficial effects: By employing the Black-Litterman model, this invention organically integrates the experience and insights of process experts with historical data, overcoming the limitations of traditional optimization methods that rely solely on data-driven approaches or expert experience. This achieves a synergistic complementarity between subjective knowledge and objective data. By introducing deep learning technology to extract time-series data features and combining it with convolutional neural networks to fuse expert opinions, the optimization model can fully explore the complex dynamic characteristics and inherent laws of the grinding and classification process. Based on a multi-objective genetic algorithm optimization using posterior revenue and posterior covariance matrices, it can find the optimal balance between multiple conflicting objectives such as throughput, product quality, and energy consumption, generating diverse Pareto optimal solution sets for decision-makers to choose from. This method exhibits good adaptability and robustness; through continuous monitoring and model update mechanisms, it can promptly respond to changes in production conditions and maintain the stability of the optimization results. Overall, this invention provides a scientific, efficient, and reliable solution for the intelligent optimization of the grinding and classification process, contributing to improved overall production efficiency and automation levels in mineral processing plants. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of this application. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0016] Figure 1 A flowchart illustrating a multi-objective optimization method based on the Black-Litterman model for a grinding and classification process, provided as an embodiment of this application; Figure 2 A schematic diagram of a multi-objective optimization device based on the Black-Litterman model for grinding and classification processes provided in an embodiment of this application; Figure 3 This is a schematic diagram of the structure of the multi-objective optimization device provided in the embodiments of this application. Detailed Implementation

[0017] The purpose of this application is to provide a multi-objective optimization method based on the Black-Litterman model for grinding and classification processes, a multi-objective optimization device based on the Black-Litterman model for grinding and classification processes, a multi-objective optimization equipment, and a computer-readable storage medium, which integrates practical experience into the prediction framework, making the results more consistent with practical operations and improving the accuracy of multi-objective optimization for grinding and classification.

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0019] The following example illustrates a multi-objective optimization method based on the Black-Litterman model for grinding and classification processes provided in this application.

[0020] Please refer to Figure 1 , Figure 1 The flowchart illustrates a multi-objective optimization method based on the Black-Litterman model for grinding and classifying processes, provided in an embodiment of this application.

[0021] In this embodiment, the method may include: S101, collect process data of the grinding and classification process, and normalize the process data using the Min-Max standardization method to obtain normalized historical data; the process data includes: ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, ball mill current and ball addition rate. This step uses a sensor system installed on the grinding and classification production line to collect real-time process data of the grinding and classification process. The process data includes: Ball mill feed rate: measured by a weighing sensor, in tons per hour; Overflow flow rate: Measured by a flow meter, in cubic meters per hour; Overflow particle size: The content of particles in the -0.075 mm size range is measured by an online particle size analyzer, and the unit is percentage; Grinding sound: The vibration signal of the ball mill is measured by a vibration sensor, and the unit is decibels; Ball mill current: Measured by a current sensor, in amperes; Ball addition rate: Recorded manually or by an automatic ball addition system, in kilograms per hour.

[0022] Data was collected every 5 minutes for 30 consecutive days, resulting in 8640 data sets. Missing values ​​were filled using linear interpolation. Specifically, if data was missing at time i, it was filled using the average of the data from time i-1 and time i-1.

[0023] The process data is normalized using the Min-Max normalization method, with a mapping range of -1 to +1. Normalization scales the original data proportionally to fit it into a specific range, facilitating subsequent data processing and model calculations.

[0024] In this embodiment, the normalized range of each parameter is as follows: Ball mill feed rate: Original range 150 to 200 tons per hour, normalized to -1 to +1; Overflow flow rate: Original range 80 to 120 cubic meters per hour, normalized to -1 to +1; Overflow particle size: original range 60% to 75%, normalized to -1 to +1; Grinding tone: Original range 75 to 95 dB, normalized to -1 to +1; Ball mill current: original range 280 to 350 amperes, normalized to -1 to +1; Ball addition rate: Original range 100 to 200 kg / hour, normalized to -1 to +1.

[0025] S102. Based on the normalized historical data, calculate the average value of ball mill feed rate, average value of overflow flow rate, average value of overflow particle size, average value of grinding noise, average value of energy consumption, and average value of ball addition to obtain the market equilibrium revenue vector. This step first calculates the average value of each optimization objective based on the normalized historical data. Since the main power consumption of grinding and classification is the power consumption of the ball mill, the energy consumption is calculated using the ball mill's energy consumption, which is obtained by multiplying the ball mill's current and voltage.

[0026] In this embodiment, assuming the ball mill's operating voltage is 380 volts, the energy consumption is equal to the ball mill's current multiplied by 380 and then divided by 1000, in kilowatts.

[0027] The calculated market equilibrium payoff vector contains the average of six parameters, after normalization: The average feed rate of the ball mill is 0.12. The average overflow flow rate is -0.05. The average overflow particle size is 0.08. The average value of the grinding sound was -0.03; The average energy consumption is 0.15; The average number of balls added was 0.06.

[0028] The market equilibrium return vector reflects the expected performance of each optimization objective in the absence of additional perspectives, serving as a benchmark for optimization.

[0029] S103, combining the subjective viewpoint matrix of process experts and deep learning models to construct the enterprise viewpoint matrix; Building upon S102, this step combines the subjective viewpoint matrix of process experts with a deep learning model to construct the enterprise viewpoint matrix.

[0030] Furthermore, this step may include: Step S103.1: Construct a matrix of subjective opinions of process experts.

[0031] Five senior process experts from the ore dressing plant were organized to provide their subjective opinions on optimizing the grinding and classification process based on their years of production experience. In this embodiment, the experts provided three subjective opinions, forming a 3x6 matrix: Viewpoint 1: Appropriately reducing the feed rate can improve the fineness of the overflow particle size, but it will reduce the output. Experts believe that the feed rate should be reduced, with a weight of -0.8; the overflow particle size should be increased, with a weight of 0.6; other parameters should remain unaffected, with a weight of 0.

[0032] Viewpoint 2: Increasing the ball loading can improve grinding efficiency, thereby reducing grinding noise and increasing overflow particle size, but it will increase energy consumption. Experts believe that increasing overflow particle size has a weight of 0.5, reducing grinding noise has a weight of -0.6, increasing energy consumption has a weight of 0.4, increasing ball loading has a weight of 0.7, and other parameters have a weight of 0.

[0033] Viewpoint 3: By optimizing the overflow flow rate of the classifier, the classification accuracy can be improved while maintaining output. Experts believe that a slight increase in feed rate has a weight of 0.3, an increase in overflow flow rate has a weight of 0.8, an increase in overflow particle size has a weight of 0.5, and other parameters have a weight of 0.

[0034] Therefore, the process expert subjective opinion matrix is ​​a 3x6 matrix, where each row represents an expert opinion and each column represents the weight of an optimization parameter.

[0035] Step S103.2: Extract time series data features.

[0036] From the normalized historical data, data from 7 consecutive days were selected as time series data samples. Each sample contains 2016 time steps, which is 7 days multiplied by 24 hours and then multiplied by 12 sampling points per hour.

[0037] A recurrent neural network (RNN) model is used to extract features from time-series data. RNNs can process sequential data and capture the patterns and trends of data changes over time. In this embodiment, the specific parameter settings of the RNN model are as follows: The input dimension is 6, corresponding to 6 process parameters; the number of hidden layer units is 128; the output dimension is 6; the activation function is the hyperbolic tangent function; the learning rate is set to 0.001; and the training batch is 100 epochs.

[0038] After processing by a recurrent neural network model, a time-series data feature matrix with dimensions of 128 rows and 6 columns is obtained. This matrix captures the dynamic characteristics of each parameter changing over time and reflects the temporal pattern of the grinding and classification process.

[0039] Step S103.3: Integrate expert opinions with temporal characteristics.

[0040] The process expert subjective opinion matrix is ​​combined with the time series data feature matrix. First, the expert opinion matrix is ​​expanded by copying it to a 128-row, 6-column matrix to match the time series feature matrix in spatial dimension.

[0041] Then, the expanded expert opinion matrix and the time-series feature matrix are stacked along the channel dimension to form a 128-row, 6-column, 2-channel three-dimensional tensor, which serves as the input to the convolutional neural network. The convolutional neural network can automatically learn feature patterns in the input data and extract the fused features of expert experience and historical data.

[0042] The specific parameter settings for the convolutional neural network model are as follows: kernel size is 3x3; number of kernels is 32; stride is 1; padding uses the same mode to keep the output size unchanged; activation function is ReLU; pooling method is max pooling, pooling window is 2x2; fully connected layer output dimension is 3 rows and 6 columns.

[0043] By employing convolutional processing through a convolutional neural network model, a fusion feature of expert opinions and temporal data is extracted, ultimately outputting a corporate opinion matrix with 3 rows and 6 columns. The values ​​in this matrix have been adjusted compared to the expert subjective opinion matrix, incorporating temporal features from historical data to make the opinions more accurate and adaptable.

[0044] For example, in the first viewpoint, the weight of the ore feed rate was adjusted from -0.8 to -0.75, and the weight of the overflow particle size was adjusted from 0.6 to 0.65. These adjustments are based on the actual correlation reflected by historical data.

[0045] S104. Based on the volatility of historical data, the variances of ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, ball addition amount, and correlation coefficients between each target value are calculated to obtain the risk estimation covariance matrix. Based on S103, the variance and correlation coefficient of each optimization objective are calculated using the volatility of the normalized historical data. Variance reflects the dispersion of the data for each objective, while correlation coefficient reflects the degree of correlation between different objectives.

[0046] First, calculate the variance of each objective separately. Assume the calculated variances are as follows: ball mill feed rate variance is 0.042; overflow flow rate variance is 0.035; overflow particle size variance is 0.028; grinding noise variance is 0.031; energy consumption variance is 0.038; and ball addition variance is 0.045.

[0047] Next, calculate the correlation coefficient between each objective. The correlation coefficient ranges from -1 to +1, with positive values ​​indicating a positive correlation and negative values ​​indicating a negative correlation. A larger absolute value indicates a stronger correlation. For example: The correlation coefficient between feed rate and overflow flow rate is 0.72, indicating a strong positive correlation; when the feed rate increases, the overflow flow rate also tends to increase. The correlation coefficient between feed rate and overflow particle size is -0.45, indicating a moderate negative correlation. When the feed rate increases, the overflow particle size tends to decrease. The correlation coefficient between ore feed rate and energy consumption is 0.85, indicating a strong positive correlation. The correlation coefficient between overflow flow rate and overflow particle size is 0.38; The correlation coefficient between overflow particle size and grinding sound is -0.52; The correlation coefficient between energy consumption and the amount of pellets added is 0.68.

[0048] Based on the variance and correlation coefficient, a risk estimation covariance matrix is ​​constructed, which is a 6-row, 6-column symmetric matrix. The diagonal elements represent the variance of each objective, and the off-diagonal elements represent the covariance between the objectives. The covariance is calculated by multiplying the correlation coefficient by the standard deviation of the corresponding two objectives.

[0049] For example, the covariance between the feed rate and the overflow rate is equal to 0.72 multiplied by the standard deviation of the feed rate and then multiplied by the standard deviation of the overflow rate, resulting in a value of 0.0276.

[0050] The risk estimation covariance matrix describes the uncertainty of each optimization objective and their interrelationships, providing a risk assessment basis for subsequent optimization calculations.

[0051] S105, construct the error covariance matrix based on the confidence level of each target in the grinding and classification production process; wherein, the error covariance matrix is ​​a diagonal matrix, and the diagonal elements of the diagonal matrix represent the influence levels of the variances of ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, and ball addition amount on the entire grinding and classification production process. Building upon S104, this step determines the confidence level of each optimization objective's impact on the entire production process, based on the actual conditions of the grinding and classification production process and expert evaluation. A higher confidence level indicates a more certain impact of the objective on production, greater expert confidence in the assessment, and a smaller corresponding error variance.

[0052] In this embodiment, the confidence level and corresponding error variance of each target can be determined, for example, based on expert evaluation results, as follows: Ball mill feed rate: 90% confidence level, error variance 0.005; Overflow flow rate: 85% confidence level, error variance 0.008; Overflow particle size: 95% confidence level, error variance 0.003; Grinding sound: 75% confidence level, error variance 0.012; Energy consumption: Confidence level 92%, error variance 0.004; Ball quantity added: Confidence level 80%, error variance 0.010.

[0053] Construct an error covariance matrix, which is a 6x6 diagonal matrix. The diagonal elements represent the aforementioned error variance values, while the off-diagonal elements are all 0. The smaller the diagonal elements, the more certain the impact of the objective on the overall grinding and classification production, and the higher the credibility of the viewpoint.

[0054] S106 uses the Black-Litterman model, combined with the market equilibrium payoff vector, firm view matrix, risk estimation covariance matrix and error covariance matrix, to calculate the posterior payoff and posterior covariance matrix; Using the Black-Litterman model, combined with the market equilibrium payoff vector, firm view matrix, risk estimation covariance matrix, and error covariance matrix, the posterior payoff and posterior covariance matrix are calculated.

[0055] The opinion influence weight is set to 0.025. This parameter controls the degree of influence of expert opinions on the final result. The larger the weight value, the greater the influence of expert opinions; the smaller the weight value, the greater the market equilibrium influence of historical data.

[0056] The enterprise opinion vector is defined as the target return that experts expect to achieve. In this embodiment, it includes three values, namely 0.15, 0.20 and 0.18, which correspond to the expected return levels of the three expert opinions.

[0057] The posterior benefit is calculated as follows.

[0058] Posterior returns are obtained by adding the market equilibrium return vector to an adjustment based on firm perspectives. The calculation of the adjustment involves a comprehensive operation of the firm perspective matrix, the risk estimation covariance matrix, the error covariance matrix, and the weights of perspective influence.

[0059] In the specific calculation process, an intermediate matrix is ​​first constructed, which comprehensively considers the interaction between the firm's view and risk estimation, as well as the error level of the view. Then, an adjustment is calculated, which reflects the impact of the difference between expert opinion and market equilibrium after being weighted by risk and confidence level.

[0060] Finally, the market equilibrium payoff vector is added to the adjustment amount to obtain the posterior payoff. The calculated posterior payoff in this embodiment contains six values: 0.135, 0.168, 0.095, -0.042, 0.162, and 0.078.

[0061] These figures indicate that, after incorporating expert opinions, the expected performance of each optimization objective has been adjusted to better align with expert experience and actual production needs.

[0062] The posterior covariance matrix is ​​calculated as follows: The posterior covariance matrix is ​​obtained by scaling the risk estimation covariance matrix and subtracting an adjustment term based on firm perspectives. The scaling factor is related to the weight of perspective influence, and the adjustment term reflects the impact of firm perspectives on uncertainty.

[0063] The posterior covariance matrix was calculated, resulting in a 6-row, 6-column symmetric matrix. Its element values ​​were adjusted compared to the original risk estimation covariance matrix, reflecting the changes in uncertainty after incorporating expert opinions. Typically, expert opinions can reduce the uncertainty of certain objectives, making the optimization more robust.

[0064] S107 uses a multi-objective genetic algorithm to optimize the posterior gain and posterior covariance matrix, obtains the Pareto front solution set, and selects the optimal solution from the Pareto front solution set based on actual production needs and preference data. Building upon S106, this step utilizes a multi-objective genetic algorithm to optimize the posterior gain and posterior covariance matrix, yielding the Pareto front solution set. The multi-objective genetic algorithm is a heuristic optimization algorithm capable of simultaneously optimizing multiple conflicting objectives to find a set of non-dominated solutions.

[0065] For example, optimization objectives are set as follows: Objective 1, maximize mill throughput, including maximizing feed rate and overflow flow rate; Objective 2, maximize product quality, i.e., maximize the content of negative 0.075 mm fineness in overflow particles; Objective 3, minimize energy consumption; Objective 4, optimize grinding noise to keep grinding noise within a reasonable range.

[0066] Constraints: Ball mill feed rate, 150 to 200 tons per hour; overflow flow rate, 80 to 120 cubic meters per hour; overflow particle size, 60% to 75%; grinding noise, 75 to 95 dB; ball mill current, 280 to 350 amperes; ball feed rate, 100 to 200 kilograms per hour.

[0067] Multi-objective genetic algorithm parameter settings: population size 100 individuals; number of generations 200; crossover probability 0.9, i.e., a 90% probability of crossover; mutation probability 0.1, i.e., a 10% probability of mutation; selection method tournament selection, where several individuals are randomly selected from the population each time to compete.

[0068] After 200 generations of evolution, the algorithm converged, yielding a Pareto front solution set containing 58 non-dominated solutions. These solutions represent different optimization schemes that achieve different balances among multiple objectives, allowing decision-makers to choose from them based on actual needs.

[0069] Based on the actual production needs and preferences of the ore processing plant, the decision-makers prioritize increasing throughput while ensuring product quality, and also consider energy consumption. After comprehensive consideration, the following optimal solution is selected from the Pareto front solution set: The ball mill has a feed rate of 185 tons per hour; an overflow flow rate of 105 cubic meters per hour; an overflow particle size of 68%; a grinding noise level of 82 decibels; a ball mill current of 315 amperes, corresponding to an energy consumption of 119.7 kilowatts; and a ball loading rate of 145 kilograms per hour.

[0070] S108 applies the optimal solution in actual production, verifies the deviation of the optimization effect, and updates the model parameters when the deviation exceeds the preset threshold.

[0071] The optimal solution selected in S107 was applied to actual production. After running for 72 hours, the optimization effect was verified by adjusting parameters such as the ball mill feed rate to 185 tons per hour and the ball addition rate to 145 kilograms per hour.

[0072] The metrics for deviation verification can be, for example: The actual ore feed rate was 183.5 tons per hour, a deviation of 0.81% from the target value of 185 tons per hour. The actual overflow flow rate was 103.8 cubic meters per hour, which deviated from the target value of 105 by 1.14%. The actual overflow particle size was 67.2%, which deviated from the target value of 68% by 1.18%. The actual grinding noise was 83.5 dB, which deviated from the target value of 82 dB by 1.83%. The actual energy consumption was 121.2 kilowatts, which deviated from the target value of 119.7 by 1.25%. The actual ball loading rate was 143 kg / hour, which is 1.38% lower than the target value of 145 kg / hour.

[0073] With a preset threshold of 5%, the deviations of all parameters did not exceed the preset threshold, indicating that the optimization effect was good and the model parameters did not need to be updated.

[0074] The optimization effect can be evaluated as follows: Compared with the average data of the 30 days before optimization: the throughput increased from an average of 172 tons per hour to 183.5 tons per hour, an increase of 6.69%; the product quality improved, with the overflow particle size of -0.075 mm increasing from an average of 65% to 67.2%, an increase of 3.38%; and the energy consumption was optimized, with the energy consumption per unit throughput decreasing from 0.72 kW per ton per hour to 0.66 kW per ton per hour, a decrease of 8.33%.

[0075] The optimized solution has achieved significant results in actual production, verifying the effectiveness and practicality of the method of the present invention.

[0076] In summary, this embodiment organically integrates the experience and insights of process experts with historical data using the Black-Litterman model, overcoming the limitations of traditional optimization methods that rely solely on data-driven approaches or expert experience, and achieving synergistic complementarity between subjective knowledge and objective data. By introducing deep learning technology to extract time-series data features and combining it with convolutional neural networks to fuse expert opinions, the optimization model can fully explore the complex dynamic characteristics and inherent laws of the grinding and classification process. Based on a multi-objective genetic algorithm optimization using posterior revenue and posterior covariance matrices, it can find the optimal balance between multiple conflicting objectives such as throughput, product quality, and energy consumption, generating diverse Pareto optimal solution sets for decision-makers to choose from. This method exhibits good adaptability and robustness; through continuous monitoring and model update mechanisms, it can promptly respond to changes in production conditions and maintain the stability of the optimization effect. Overall, this invention provides a scientific, efficient, and reliable solution for the intelligent optimization of the grinding and classification process, contributing to improving the comprehensive production efficiency and automation level of concentrators.

[0077] Furthermore, another specific embodiment is provided.

[0078] The difference in this embodiment is that when the optimal solution is applied and verified 72 hours later, it is found that the deviation of some parameters exceeds the preset threshold, and the model parameters need to be updated.

[0079] During the verification phase of step S108, the following deviation was detected: The actual overflow particle size was 63.5%, which deviated from the target value of 68% by 6.62%, exceeding the 5% threshold. The actual energy consumption was 127.8 kilowatts, which is 6.77% lower than the target value of 119.7 kilowatts, exceeding the 5% threshold.

[0080] Analysis revealed that the ore properties had changed, with a coarser particle size distribution in the feed, leading to deviations in model predictions. Due to these changes in raw material properties, existing historical data and expert opinions may no longer be entirely applicable to current production conditions.

[0081] The model parameter update process may include: The first step is to re-collect data. Collect process data from the past 7 days, including data after changes in ore properties, as a new historical data sample to replace some of the original historical data.

[0082] The second step is to update the market equilibrium revenue vector. Based on the new historical data, the average value of each optimization objective is recalculated to obtain the updated market equilibrium revenue vector. Since the ore is coarser, the new average feed rate may need to be reduced, while the pellet loading rate may need to be increased.

[0083] The third step is to update the risk estimation covariance matrix. Based on the new historical data, the variance and correlation coefficient of each objective are recalculated to obtain the updated risk estimation covariance matrix. Changes in ore properties may lead to increased volatility in certain parameters, resulting in a corresponding increase in variance.

[0084] The fourth step is to update the enterprise perspective matrix. Consult process experts to adjust subjective perspectives in response to changes in ore properties. For example, experts might suggest increasing the ball loading and decreasing the feed rate when the ore is coarser to ensure sufficient grinding time. Based on the new expert opinions and new time-series data, recurrent neural network and convolutional neural network models are retrained to obtain the updated enterprise perspective matrix.

[0085] Fifth, re-execute S106 and S107. Using the updated market equilibrium payoff vector, firm view matrix, risk estimation covariance matrix, and original error covariance matrix, or updating the error covariance matrix as needed, recalculate the posterior payoff and posterior covariance matrix, run the multi-objective genetic algorithm again to obtain a new Pareto front solution set, and select the new optimal solution.

[0086] The sixth step is to apply the new optimal solution. Apply the new optimal solution to production and continuously monitor its operational status.

[0087] After the model is updated, the new optimal solution may include: The ball mill feed rate is 178 tons per hour, a decrease of 7 tons per hour compared to before. The ball loading rate is 165 kg / hour, an increase of 20 kg / hour compared to before; The overflow particle size target remains unchanged at 68%. Other parameters were also adjusted accordingly.

[0088] After applying the new optimal solution for 24 hours, a second verification showed that all parameter deviations were within 5%. Actual overflow particle size: 67.5%, deviation 0.74%; Actual energy consumption: 120.8 kilowatts, deviation 1.2%.

[0089] The optimization effect has returned to normal, and product quality and energy consumption control have returned to the expected level.

[0090] This embodiment illustrates that when changes in production conditions cause model prediction deviations to exceed a threshold, timely updates to model parameters can maintain the adaptability and effectiveness of the optimization method, enabling the optimization system to cope with dynamically changing production environments.

[0091] Furthermore, another specific embodiment is provided.

[0092] The difference in this embodiment is that it uses different combinations of deep learning models and variants of multi-objective genetic algorithms to further improve optimization performance.

[0093] Improvement of step S103: Use long short-term memory networks and attention mechanisms In step S1033.2, a Long Short-Term Memory (LSTM) network is used to replace the Recurrent Neural Network (RNN) model to extract time-series data features. The LSM network is an improved version of the RNN, capable of better capturing long-term dependencies and avoiding the gradient vanishing problem, making it particularly suitable for processing longer time series.

[0094] Long Short-Term Memory (LSTM) network model parameter settings: input dimension is 6, corresponding to 6 process parameters; number of LSM units is 256; a 2-layer stacked structure is adopted to enhance the model's expressive power; output dimension is 6; dropout rate is set to 0.2 to prevent overfitting; learning rate is set to 0.0005; training batch is 150 epochs.

[0095] Long Short-Term Memory (LSTM) networks, through gating mechanisms, can selectively remember or forget information, thus better capturing long-term trends and cyclical changes in the grinding and classification process.

[0096] In step S1033.3, in addition to using a convolutional neural network model, an attention mechanism is introduced to enable the model to automatically learn the importance weights of different parameters in the expert's opinion and highlight key information.

[0097] The implementation process of the attention mechanism can include: First, mapping the fused features to attention scores through a fully connected layer, with each parameter having a corresponding score; then, normalizing the scores to weights through a softmax function, with the sum of all weights being 1; finally, multiplying the attention weights by the fused features to obtain a weighted enterprise opinion matrix.

[0098] By combining long short-term memory networks and attention mechanisms, the resulting corporate opinion matrix is ​​more accurate, better reflects the complex relationships between different parameters, and can adaptively adjust the importance of each parameter.

[0099] This embodiment illustrates that the method of the present invention has good scalability and flexibility. Different technical implementation schemes can be selected according to actual needs. By adopting more advanced algorithms and models, better optimization results can be obtained.

[0100] Furthermore, another specific embodiment is provided.

[0101] In this embodiment, the multi-objective optimization method may include: S401 incorporates data from multiple sources throughout the grinding and classification process into the data modeling and analysis, including real-time process data collected by sensors and manually recorded data. Key process variables include ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, ball mill current, and ball feed rate.

[0102] S402, Data Processing and Normalization: The collected data is normalized using the Min-Max normalization method, with a mapping range of [-1, 1]. The formula is as follows: S403.1, Market Equilibrium Return is based on historical data of grinding and classification, calculating the average performance of mill feed rate, overflow flow rate, overflow particle size, grinding noise, ball mill current, and ball addition rate, reflecting the expected performance of each optimization objective without additional perspectives.

[0103] S403.2, the Enterprise Perspective Matrix, combines the experience of process experts with deep learning models to define the impact of different objectives in the grinding and classification process on the entire production process.

[0104] Step 1: Process experts provide their subjective opinions based on production experience. Since there are 6 core parameters, K subjective opinions from the process experts constitute a K*6 matrix. Weights are assigned based on the relationship between the parameters in each opinion. For example, adjusting the mill load can reduce energy consumption and increase overflow particle size. The corresponding matrix rows are: [0, 0, 1, 1, 1, 0]. Step 2: Obtain the time series data from historical data and use an RNN model to extract time series data features.

[0105] Step 3: Combine the two matrices and use a CNN model to convolve the combined matrix to obtain the enterprise opinion matrix.

[0106] S403.5, adjust the posterior returns by combining the equilibrium returns from grinding and classification with the firm's perspective. Also, adjust the posterior covariance matrix by considering market risk and the uncertainty of the firm's perspective.

[0107] S404, after obtaining the posterior benefit and posterior covariance matrix, uses a multi-objective genetic algorithm for optimization to obtain the Pareto front solution set. Decision-makers can then select the optimal solution from the Pareto front solution set based on actual production needs and preferences.

[0108] S405. After applying the selected optimal solution in actual production, the optimization effect needs to be verified. If the deviation exceeds a preset threshold, the model parameters need to be updated.

[0109] As can be seen, this embodiment combines the experience of process experts with a deep learning model to generate an enterprise perspective matrix. The subjective opinions of process experts are incorporated into the model through scientific quantification methods, while time-series data features are extracted using a deep learning model. This makes the enterprise perspective matrix more reflective of production realities and expert experience, resulting in a more scientific and representative perspective matrix.

[0110] The following describes a multi-objective optimization device based on the Black-Litterman model for grinding and classifying processes, provided by an embodiment of this application. The multi-objective optimization device based on the Black-Litterman model for grinding and classifying processes described below and the multi-objective optimization method based on the Black-Litterman model for grinding and classifying processes can be referred to each other.

[0111] Please refer to Figure 2 , Figure 2 This is a schematic diagram of a multi-objective optimization device based on the Black-Litterman model for grinding and classification processes, provided in an embodiment of this application.

[0112] In this embodiment, the device may include: The process data acquisition module 100 is used to collect process data of the grinding and classification process, and to normalize the process data using the Min-Max standardization method to obtain normalized historical data. The process data includes: ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, ball mill current, and ball feed rate. The market equilibrium revenue calculation module 200 is used to calculate the average value of ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, and ball addition amount based on normalized historical data, and obtain the market equilibrium revenue vector. The Enterprise Perspective Matrix Construction Module 300 is used to construct an enterprise perspective matrix by combining the subjective perspective matrix of process experts and a deep learning model. The risk estimation matrix construction module 400 is used to calculate the variance of ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, ball addition amount and corresponding coefficients between each target value based on the volatility of historical data, so as to obtain the risk estimation covariance matrix. The Error Covariance Matrix Construction Module 500 is used to construct the error covariance matrix based on the confidence level of each target in the grinding and classification production process. The error covariance matrix is ​​a diagonal matrix, and the diagonal elements of the diagonal matrix represent the impact levels of the variances of the ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, and ball addition amount on the entire grinding and classification production process. The posterior return calculation module 600 is used to calculate posterior returns and posterior covariance matrices using the Black-Litterman model, combined with the market equilibrium return vector, firm view matrix, risk estimation covariance matrix, and error covariance matrix. The optimization module 700 is used to optimize the posterior gain and posterior covariance matrix using a multi-objective genetic algorithm to obtain the Pareto front solution set, and select the optimal solution from the Pareto front solution set according to actual production needs and preference data. The optimal solution application module 800 is used to apply the optimal solution in actual production, verify the deviation of the optimization effect, and update the model parameters when the deviation exceeds the preset threshold.

[0113] This application also provides a multi-objective optimization apparatus; please refer to [reference needed]. Figure 3 , Figure 3 This is a schematic diagram of the structure of the multi-objective optimization device provided in the embodiments of this application. The multi-objective optimization device may include: Memory, used to store computer programs; The processor, when executing a computer program, can implement the steps of any of the above-described multi-objective optimization methods based on the Black-Litterman model for grinding and classification processes.

[0114] like Figure 3 The diagram shows the structural composition of a multi-objective optimization device, which may include a processor 10, a memory 11, a communication interface 12, and a communication bus 13. The processor 10, memory 11, and communication interface 12 communicate with each other through the communication bus 13.

[0115] In this embodiment, the processor 10 may be a central processing unit (CPU), an application-specific integrated circuit, a digital signal processor, a field-programmable gate array, or other programmable logic devices.

[0116] The processor 10 can call the program stored in the memory 11. Specifically, the processor 10 can execute the operations in the embodiment of the abnormal IP identification method.

[0117] The memory 11 is used to store one or more programs. The programs may include program code, which includes computer operation instructions. In this embodiment, the memory 11 stores at least a program for implementing the following functions: Process data of the grinding and classification process were collected and normalized using the Min-Max standardization method to obtain normalized historical data. The process data included: ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, ball mill current, and ball feed rate. Based on the normalized historical data, the average values ​​of ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, and ball addition amount were calculated to obtain the market equilibrium revenue vector. Construct an enterprise opinion matrix by combining the subjective opinion matrix of process experts and a deep learning model; Based on the volatility of historical data, the variances of ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, ball addition rate, and the corresponding coefficients between each target value are calculated to obtain the risk estimation covariance matrix. Based on the confidence level of each target in the grinding and classification production process, an error covariance matrix is ​​constructed. The error covariance matrix is ​​a diagonal matrix, and the diagonal elements of the diagonal matrix represent the influence levels of the variances of ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, and ball addition amount on the entire grinding and classification production process. Using the Black-Litterman model, combined with the market equilibrium payoff vector, firm view matrix, risk estimation covariance matrix, and error covariance matrix, the posterior payoff and posterior covariance matrix are calculated. A multi-objective genetic algorithm is used to optimize the posterior gain and posterior covariance matrix to obtain the Pareto front solution set. The optimal solution is then selected from the Pareto front solution set based on actual production needs and preference data. In actual production, the optimal solution is applied, and the optimization effect is verified by deviation. When the deviation exceeds the preset threshold, the model parameters are updated.

[0118] In one possible implementation, the memory 11 may include a program storage area and a data storage area, wherein the program storage area may store the operating system and applications required for at least one function; and the data storage area may store data created during use.

[0119] In addition, memory 11 may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device or other volatile solid-state storage device.

[0120] Communication interface 12 can be an interface for the communication module, used to connect with other devices or systems.

[0121] Of course, it should be noted that, Figure 3 The structure shown does not constitute a limitation on the multi-objective optimization device in the embodiments of this application. In practical applications, the multi-objective optimization device may include more than Figure 3 More or fewer components as shown, or combinations of certain components.

[0122] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, can implement the steps of any of the above-described multi-objective optimization methods for grinding and classifying processes based on the Black-Litterman model.

[0123] The computer-readable storage medium may include 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.

[0124] For a description of the computer-readable storage medium provided in this application, please refer to the above method embodiments; further details will not be repeated here.

[0125] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0126] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0127] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0128] The foregoing has provided a detailed description of a multi-objective optimization method based on the Black-Litterman model for grinding and classification processes, a multi-objective optimization device based on the Black-Litterman model for grinding and classification processes, a multi-objective optimization apparatus, and a computer-readable storage medium. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and its core ideas. It should be noted that those skilled in the art can make various improvements and modifications to this application without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of this application.

Claims

1. A multi-objective optimization method based on the Black-Litterman model for grinding and classification processes, characterized in that, include: Process data of the grinding and classification process are collected, and the process data are normalized using the Min-Max standardization method to obtain normalized historical data; wherein, the process data includes: ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, ball mill current and ball addition rate; Based on the normalized historical data, the average values ​​of ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, and ball addition are calculated to obtain the market equilibrium revenue vector. Construct an enterprise opinion matrix by combining the subjective opinion matrix of process experts and a deep learning model; Based on the volatility of the historical data, the variances of the ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, ball addition rate, and the corresponding coefficients between each target value are calculated to obtain the risk estimation covariance matrix. Based on the confidence level of each target in the grinding and classification production process, an error covariance matrix is ​​constructed; wherein, the error covariance matrix is ​​a diagonal matrix, and the diagonal elements of the diagonal matrix represent the influence levels of the variances of ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, and ball addition amount on the entire grinding and classification production process. Using the Black-Litterman model, combined with the market equilibrium payoff vector, the firm view matrix, the risk estimation covariance matrix, and the error covariance matrix, the posterior payoff and the posterior covariance matrix are calculated. A multi-objective genetic algorithm is used to optimize the posterior gain and the posterior covariance matrix to obtain the Pareto front solution set, and the optimal solution is selected from the Pareto front solution set according to actual production needs and preference data. In actual production, the optimal solution is applied to verify the deviation of the optimization effect. When the deviation exceeds the preset threshold, the model parameters are updated.

2. The multi-objective optimization method according to claim 1, characterized in that, A corporate opinion matrix is ​​constructed by combining the subjective opinion matrix of process experts and a deep learning model, including: Based on the production experience data of process experts, a K×6 matrix composed of K subjective viewpoints is determined, and corresponding weights are assigned according to the relationship between the parameters in each viewpoint, thus obtaining the process expert subjective viewpoint matrix. Time-series data is obtained from the historical data, and features are extracted from the time-series data using an RNN model to obtain a time-series data feature matrix; The subjective opinion matrix of the process experts is combined with the time-series data feature matrix, and the combined matrix is ​​convolved using a CNN model to obtain the enterprise opinion matrix.

3. The multi-objective optimization method according to claim 1, characterized in that, The risk estimation covariance matrix is ​​a symmetric matrix, with the diagonal elements representing the variance of each optimization objective and the off-diagonal elements representing the covariance between each optimization objective. It is calculated by multiplying the corresponding coefficients and standard deviations.

4. The multi-objective optimization method according to claim 1, characterized in that, The posterior return is calculated by adding the market equilibrium return vector to an adjustment based on the firm's viewpoint; wherein the adjustment is determined by the firm's viewpoint matrix, the risk estimation covariance matrix, the error covariance matrix, and the viewpoint influence weight; the posterior covariance matrix is ​​calculated by scaling the risk estimation covariance matrix and subtracting the adjustment term based on the firm's viewpoint.

5. A multi-objective optimization device based on the Black-Litterman model for grinding and classification processes, characterized in that, include: The process data acquisition module is used to collect process data of the grinding and classification process, and to normalize the process data using the Min-Max standardization method to obtain normalized historical data; wherein, the process data includes: ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, ball mill current and ball addition rate; The market equilibrium revenue calculation module is used to calculate the average value of ball mill feed rate, average value of overflow flow rate, average value of overflow particle size, average value of grinding noise, average value of energy consumption, and average value of ball addition amount based on the normalized historical data, so as to obtain the market equilibrium revenue vector. The Enterprise Perspective Matrix Construction Module is used to construct an enterprise perspective matrix by combining the subjective perspective matrix of process experts and a deep learning model. The risk estimation matrix construction module is used to calculate the variance of ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, ball addition amount and corresponding coefficients between each target value based on the volatility of the historical data, so as to obtain the risk estimation covariance matrix. The error covariance matrix construction module is used to construct an error covariance matrix based on the confidence level of each target in the grinding and classification production process. The error covariance matrix is ​​a diagonal matrix, and the diagonal elements of the diagonal matrix represent the influence levels of the variances of the ball mill feed rate, overflow flow rate, overflow particle size, grinding noise, energy consumption, and ball addition amount on the entire grinding and classification production process. The posterior return calculation module is used to calculate the posterior return and the posterior covariance matrix using the Black-Litterman model, combined with the market equilibrium return vector, the firm view matrix, the risk estimation covariance matrix, and the error covariance matrix. The optimization solution module is used to optimize the posterior benefit and the posterior covariance matrix using a multi-objective genetic algorithm to obtain the Pareto front solution set, and select the optimal solution from the Pareto front solution set according to actual production needs and preference data. The optimal solution application module is used to apply the optimal solution in actual production, verify the deviation of the optimization effect, and update the model parameters when the deviation exceeds a preset threshold.

6. A multi-objective optimization device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the steps of the multi-objective optimization method as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the multi-objective optimization method as described in any one of claims 1 to 4.

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