An Electrolytic Copper Current Optimization Method Based on Non-Dominated Sorting Genetic Algorithm

Abstract

This invention discloses a current optimization method for electrolytic copper based on a non-dominated sorting genetic algorithm. The method includes establishing a sub-model of a multi-objective optimization problem in the electrolytic copper production process; establishing a prediction model for the concentration of key ions in the electrolytic cell based on the principle of mass conservation; setting production process constraints, including at least the maximum rectifier current constraint and daily output target constraint, and transforming the constrained multi-objective optimization problem into an unconstrained optimization problem through a penalty function; and solving the unconstrained optimization problem using a non-dominated sorting genetic algorithm, outputting a sequence of optimal current values ​​for each time period within the next 24 hours, in units of a set time interval. This invention, by constructing a multi-objective model that integrates ion concentration prediction and employing an efficient algorithm for solving it, can achieve refined and collaborative optimization of the current in the electrolytic copper production process, thereby effectively reducing electricity costs while ensuring both output and quality.

Description

Technical Field

[0001] This invention relates to the field of electrolytic copper current optimization technology, and in particular to an electrolytic copper current optimization method based on a non-dominated sorting genetic algorithm. Background Technology

[0002] Electrolytic copper processing is a key technology used to purify crude copper into high-purity cathode copper, widely applied in the modern copper smelting industry. Its basic principle is to utilize the electrochemical reaction between the copper anode and the pure copper cathode during electrolysis to convert the higher copper content in crude copper into high-purity cathode copper. In this process, impurities such as iron and nickel adhere to the anode or remain in the electrolyte. Electrolytic copper not only meets the stringent requirements of the electronics and electrical industries but also recovers precious metals from the anode sludge, demonstrating significant economic and environmental value.

[0003] Currently, the current in copper electrolysis is typically calculated as a fixed value based on production targets, and then set according to this value without real-time adjustments. However, this approach has several problems. First, since electricity prices usually fluctuate, especially with peak and off-peak pricing, setting the current to a fixed value increases production costs. Second, the current setting only considers production output and ignores changes in electrolyte ion concentration at different times, which can affect the quality of the finished product. Therefore, the existing current setting method cannot simultaneously meet the requirements of reducing costs and improving product quality.

[0004] This invention aims to overcome the shortcomings of existing technologies by optimizing current settings through a non-dominated genetic algorithm. The method establishes a multi-objective optimization model that comprehensively considers the relationship between current and key indicators such as output, quality, and electricity costs. A non-dominated genetic algorithm is then used to solve the problem, thereby obtaining the optimal current setting. This real-time dynamic current optimization strategy can effectively reduce costs and improve product quality, especially demonstrating significant advantages under conditions of fluctuating electricity prices and changes in electrolyte composition. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology. To achieve the above objective, an electrolytic copper current optimization method based on a non-dominated sorting genetic algorithm is adopted to solve the problems mentioned in the background technology.

[0006] An electrolytic copper current optimization method based on a non-dominated sorting genetic algorithm includes the following steps:

[0007] Step S1: Establish a multi-objective optimization problem sub-model for the electrolytic copper production process. The model includes at least: a production model for predicting future copper production based on current value and electrolysis parameters; an electricity cost model for predicting production electricity cost based on current value and time-of-use electricity price; and a quality scoring model for evaluating production quality based on current value, current change and key ion concentration deviation. Step S2: Based on the principle of conservation of mass, establish a predictive model for the concentration of key ions in the electrolytic cell. The model is used to predict the ion concentration in future time periods based on historical concentrations, the influence of the purification process, and current values. Step S3: Set production process constraints, including at least the rectifier maximum current constraint and daily output target constraint, and transform the constrained multi-objective optimization problem into an unconstrained optimization problem through a penalty function; Step S4: Use a non-dominated sorting genetic algorithm to solve the unconstrained optimization problem, and output the optimal current value sequence for each time period in the next 24 hours in a set time interval.

[0008] As a further aspect of the present invention: in step S1, the specific steps for obtaining the objective function vector of the multi-objective optimization problem are as follows: Establish an individual fitness scoring model in the genetic algorithm, where the individual fitness is represented by a vector:

[0009] The specific calculation formulas are as follows:

[0010]

[0011]

[0012] in, For electricity cost adaptability, For yield adaptability, For quality adaptability; and The results are obtained by subtracting the corresponding constraint penalties from the calculation results of the electricity cost model and the production model, respectively. and As a penalty amount, It is obtained from the average of the quality scores for each time period.

[0013] As a further aspect of the present invention: the formula for calculating the daily output of the production model is as follows:

[0014] in, To predict daily output, Let be the current in the i-th time period. , , , , These are the concentrations of copper ions and hydrogen ions in the electrolyte, temperature, additive flow rate, and electrolyte circulation rate, respectively. - These are the parameters obtained by fitting historical data. This represents the total number of time periods.

[0015] As a further aspect of the present invention: the electricity fee model is as follows:

[0016] in, To predict electricity bills, Let be the current in the i-th time period. Let be the electricity price corresponding to the i-th time period. This is the equivalent resistance of the electrolyte.

[0017] As a further aspect of the present invention: in the quality scoring model, the quality score Q(i) for the i-th time period is:

[0018] in, , , The concentrations of copper, nickel, and iron ions predicted for the i-th time period are: , , This corresponds to the optimal concentration of the historically high-quality batches. Let be the current in the i-th time period. - The negative weighting coefficient is preset.

[0019] As a further aspect of the present invention: in step S2, the relationship between the ion concentration and the charge flux in the i-th time period is established, and the concentration prediction model is as follows:

[0020] in, Let be the predicted copper ion concentration for the i-th time period. This is the initial concentration. Let be the decrease in copper ion concentration caused by the purified solution during the t-th time period. The rate of increase in copper ion concentration per unit current. Let t be the current in the t-th time period; the prediction models for nickel and iron ion concentrations are the same.

[0021] As a further aspect of the present invention: in step S3, the penalty function includes: The formula for the current penalty term is:

[0022] The formula for the production penalty term is:

[0023] in, The maximum allowable current for the rectifier. This is the target daily output value. These are production model predictions. , This is the penalty coefficient.

[0024] As a further aspect of the present invention: in step S4, a non-dominated sorting genetic algorithm is used to solve the problem, including: S41. Initialize the population and base it on vector fitness. Stratify individuals in a population by non-dominated ranking; S42. Calculate the crowding degree of individuals in the same non-dominated layer across each objective dimension; S43. Based on the non-dominant layer priority and individual crowding, select a specified number of individuals from the merged parent and offspring populations as the new generation of parents. S44. Perform selection, crossover, and mutation operations on the new generation of parents to generate the offspring population; S45. Repeat steps S41 to S44 until the termination condition is met, and output the current value sequence corresponding to the Pareto optimal solution set in the final population.

[0025] As a further aspect of the present invention: in step S43, the specific method for selecting the new generation parent is as follows: according to the non-dominated layer from high to low, the entire layer of individuals is added to the new parent set in sequence until a certain layer is added. If the total number exceeds the preset size q, then for this layer... Individuals are sorted from most crowded to least crowded, and the top (q - number of already selected) individuals are added.

[0026] As a further aspect of the present invention: in step S44, the method for generating offspring includes: The top M individuals with the highest fitness in the new generation of parents are directly retained as offspring. The remaining parent individuals are randomly paired up, and the current values ​​over each time period are averaged to generate new individuals; then, the generated new individuals are mutated according to probability.

[0027] Compared with the prior art, the present invention has the following technical advantages: Using the above technical solution, a multi-objective optimization model covering output, electricity costs, and quality is established. A mass conservation-based ion concentration prediction model is specifically introduced to more accurately correlate current with product quality. This method handles production constraints through a penalty function and ultimately employs a non-dominated sorting genetic algorithm for efficient solution, thereby outputting a refined current setting sequence for the next 24 hours at 15-minute intervals. Attached Figure Description

[0028] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings: Figure 1 This is a schematic diagram illustrating the steps of the electrolytic copper current optimization method according to an embodiment of this application. Detailed Implementation

[0029] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] Please refer to Figure 1 In this embodiment of the invention, a method for optimizing the electrolytic copper current based on a non-dominated sorting genetic algorithm includes the following steps: Step S1: Establish a multi-objective optimization problem sub-model for the electrolytic copper production process. The model includes at least: a production model for predicting future copper production based on current value and electrolysis parameters; an electricity cost model for predicting production electricity cost based on current value and time-of-use electricity price; and a quality scoring model for evaluating production quality based on current value, current change and key ion concentration deviation. In step S1, the specific steps for obtaining the objective function vector of the multi-objective optimization problem are as follows: Establish an individual fitness scoring model in the genetic algorithm, where the individual fitness is represented by a vector:

[0031] The specific calculation formulas are as follows:

[0032]

[0033]

[0034] in, For electricity cost adaptability, For yield adaptability, For quality adaptability; and The results are obtained by subtracting the corresponding constraint penalties from the calculation results of the electricity cost model and the production model, respectively. and As a penalty amount, It is obtained from the average of the quality scores for each time period.

[0035] In this embodiment, an electrolytic copper production model is established to predict future copper production by inputting relevant data. The input data includes the electrolytic cell current (I), cell voltage (U), electrolyte copper ion concentration (Cu), electrolyte hydrogen ion concentration (H), electrolyte temperature (T), and additive flow rate (…). ) and electrolyte circulation rate ( The output data is the copper production yield for the next 24 hours.

[0036] The formula for calculating daily output in the production model is:

[0037] in, To predict daily output, Let be the current in the i-th time period. , , , , These are the concentrations of copper ions and hydrogen ions in the electrolyte, temperature, additive flow rate, and electrolyte circulation rate, respectively. - These are the parameters obtained by fitting historical data. This represents the total number of time periods.

[0038] In this specific implementation, starting from 0:00 each day, every 15 minutes is divided into a time period, resulting in a total of 96 time periods throughout the 24 hours. - To obtain the final production prediction formula, the parameters a1-a5 in the formula are fitted by collecting actual operating data of the electrolytic copper system.

[0039] In this embodiment, local electricity prices for different time periods are obtained, an electricity cost model is established, and the electricity cost required to complete production is predicted. The electricity cost model is as follows:

[0040] in, To predict electricity bills, Let be the current in the i-th time period. Let be the electricity price corresponding to the i-th time period. This represents the equivalent resistance of the electrolyte. Specifically, electricity prices are typically divided into three tiers: peak, off-peak, and flat, or four tiers: peak, off-peak, and flat. The price can be determined based on the price range corresponding to the time period i. R is the resistance of the electrolyte, which can be considered a constant. The specific value can be calculated based on the production data using the cell voltage and resistance, and the average value is taken as the resistance.

[0041] In this embodiment, a quality score prediction model is established. Here, Cu, Fe, and Ni ions are considered to have the greatest impact on quality, while other ions are ignored. A penalty is designed based on the magnitude of the deviation of each ion concentration from its optimal value, and this penalty, along with the current variation amplitude, is used to establish the quality score model. For the i-th time period, the quality score Q(i) in the quality score model for the i-th time period is:

[0042] in, , , The concentrations of copper, nickel, and iron ions predicted for the i-th time period are: , , This corresponds to the optimal concentration of the historically high-quality batches. Let be the current in the i-th time period. - The negative weighting coefficient is preset.

[0043] Specifically, high-quality batches are selected by screening historical data. Production process data for these batches is used to calculate the average concentration of each of the aforementioned ions, which is then taken as the optimal concentration. The screening method is as follows: based on the finished product testing results, the top 10% of batches with the lowest Fe and Ni impurity content are selected as high-quality batches.

[0044] , The concentrations of Cu, Fe, and Ni ions in the i-th time period are... Let be the current value in the i-th time period. For quality scoring, it is assumed that the greater the deviation from the optimal ion concentration or the larger the current variation, the worse the quality. Furthermore, the effect of ion concentration is related to the current magnitude; the higher the current, the greater the impact of ion concentration on quality.

[0045] b1-b4 are manually set parameters, usually negative numbers, making... A higher value indicates higher quality.

[0046] Step S2: Based on the principle of conservation of mass, establish a predictive model for the concentration of key ions in the electrolytic cell. The model is used to predict the ion concentration in future time periods based on historical concentrations, the influence of the purification process, and current values. In step S2, the relationship between the ion concentration and the charge flow rate in the i-th time period is established. The concentration prediction model is as follows: Based on the ion concentration of each tank in the purified liquid area of ​​the purified liquid workshop and the current ion concentration of the electrolytic cell, assuming that the current efficiency remains constant, the relationship between the ion concentration and the charge flow rate in the i-th time period is established according to the principle of conservation of mass. The specific formula is:

[0047] in, Let be the predicted copper ion concentration for the i-th time period. This is the initial concentration. Let be the decrease in copper ion concentration caused by the purified solution during the t-th time period. The rate of increase in copper ion concentration per unit current. Let t be the current in the t-th time period; the prediction models for nickel and iron ion concentrations are the same.

[0048] Specifically, considering that there are multiple different purification devices, each operating for a different time period, this value is related to the time period (t) of each day; if the devices operate in the same way in two time periods, then... The values ​​are also the same. Here, it is assumed that the equipment production schedule for the electrolytic copper workshop remains unchanged, therefore... The value is independent of the day. The specific value can be calculated by substituting the actual copper ion concentration collected from historical data and the equipment schedule of the purification workshop into the above formula.

[0049] The rate of increase of copper ion concentration per unit current is a fixed value, which can be obtained by substituting historical data into the above formula. Let t be the current value during the time interval t.

[0050] Step S3: Set production process constraints, including at least the rectifier maximum current constraint and daily output target constraint, and transform the constrained multi-objective optimization problem into an unconstrained optimization problem through a penalty function; In step S3, the penalty function includes: The formula for the current penalty term is:

[0051] The formula for the production penalty term is:

[0052] in, The maximum allowable current for the rectifier. This is the target daily output value. These are production model predictions. , This is the penalty coefficient. It can be calculated using the formula from the steps above. This indicates the maximum current value of the rectifier. c1 and c2 represent the minimum target output value; c1 and c2 are the corresponding penalty coefficients, which are set according to the actual situation. If it is necessary to strictly ensure that the final solution meets the constraints, c1 and c2 are generally set to around 10000.

[0053] Step S4: Use a non-dominated sorting genetic algorithm to solve the unconstrained optimization problem, and output the optimal current value sequence for each time period in the next 24 hours in a set time interval.

[0054] In this embodiment, step S4 uses a non-dominated sorting genetic algorithm to solve the problem, including: S41. Initialize the population and base it on vector fitness. Stratify individuals in a population by non-dominated ranking; S42. Calculate the crowding degree of individuals in the same non-dominated layer across each objective dimension; S43. Based on the non-dominant layer priority and individual crowding, select a specified number of individuals from the merged parent and offspring populations as the new generation of parents. S44. Perform selection, crossover, and mutation operations on the new generation of parents to generate the offspring population; S45. Repeat steps S41 to S44 until the termination condition is met, and output the current value sequence corresponding to the Pareto optimal solution set in the final population.

[0055] In step S43, the specific method for selecting the new generation parent is as follows: according to the non-dominated layer from high to low, add the entire layer of individuals to the new parent set in turn, until a certain layer is added. If the total number exceeds the preset size q, then for this layer... Individuals are sorted from most crowded to least crowded, and the top (q - number of already selected) individuals are added.

[0056] In step S44, the method for generating offspring includes: The top M individuals with the highest fitness in the new generation of parents are directly retained as offspring. The remaining parent individuals are randomly paired up, and the current values ​​over each time period are averaged to generate new individuals; then, the generated new individuals are mutated according to probability.

[0057] In this embodiment, an individual fitness scoring model is established in the genetic algorithm, and the fitness of an individual is represented by a vector. The values ​​represent the fitness of the three dimensions: electricity cost, output, and quality. The electricity cost and output dimensions are calculated by subtracting the penalty from the daily values; the quality dimension is calculated by averaging the quality scores across all time periods within a day.

[0058] The specific calculation formulas are as follows:

[0059]

[0060]

[0061] An initial solution is generated using the actual current adjustment strategy used in the field. Based on this initial solution, the current for each time period is randomly increased or decreased by a random value, resulting in 2q-1 remaining solutions. These solutions, along with the initial solution, form the first generation solution set. Here, q is the number of individuals in each generation, a hyperparameter that is adjusted according to the actual situation. To improve the quality of the first generation solution, the maximum range of the random value is set to 20% of the initial solution.

[0062] Determine the dominant and non-dominated solutions in the solution set, and then divide the solution set into layers.

[0063] The specific method is as follows: a. First, calculate the number of dominated individuals j in the solution set. and the set of solutions dominated by that individual. ; The definition of dominance and subordination is as follows: For individuals A and B, if the three values ​​in A's fitness vector ( If all values ​​are greater than or equal to individual B, and there exists a value greater than individual B, then individual A dominates individual B.

[0064] b. Individuals with a value of 0 are placed in set G1; c. For each individual k in G1, find its dominant solution set. Individual d in the data, the number of individuals controlled by these individuals. Subtract 1, and then put the individuals whose number of dominance is 0 into set G2; d. Repeat step 3 until all solutions are layered, resulting in m sets. - express.

[0065] In this embodiment, for - For each individual in each set, calculate their crowding degree in three dimensions, specifically as follows: a. For the electricity cost dimension in set G1, calculate the electricity cost of all individuals in the set. The values ​​are sorted from largest to smallest. The crowding degree of the first and last individuals is set to infinite. The crowding degree of the remaining individuals is calculated using the following formula:

[0066] CD represents the degree of congestion. This represents the fitness value of the (i-1)th individual in the sorted G1 set in terms of electricity cost. , These represent the individuals with the highest and lowest fitness in set G1, respectively.

[0067] b. For the product and quality dimensions in G1, repeat the method in step a, and then... Replace with This yields the crowding level of each individual in G1; c. Repeat steps a and b to obtain the crowding degree of each individual in the remaining G2-Gm set.

[0068] The q parent solutions from the previous iteration are combined with the q child solutions. These solutions are then stratified and their crowding is calculated. Finally, q individuals are selected from these 2q individuals to serve as new parent individuals. The selection method is as follows: if Then All individuals in the layer are incorporated into the new parent generation; otherwise, The front with the highest level of crowding Each individual is incorporated into the new parent individual, and the process ends. express The total number of individuals in the layer; from Start repeating the above steps, one cycle at a time. +1, until the termination condition is triggered. If there are no parent and child generations initially, use the 2q initial solutions from the above steps for filtering.

[0069] A genetic algorithm is used to obtain a new generation of individuals. Specifically, from the q new parent individuals, the M individuals with the highest fitness are directly used as offspring. Then, two individuals are randomly selected to form a group, resulting in (qM) groups. The average current of the two individuals in each group at each time period is taken to obtain a new individual. Finally, the mutation operation of the genetic algorithm is performed on the new individuals to obtain offspring. M is a manually set parameter, typically 5% of the number of offspring individuals.

[0070] Repeat the above steps until the specified number of times to obtain the final optimized current values ​​for each time period.

[0071] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention. The scope of the invention is defined by the appended claims and their equivalents, all of which should be included within the scope of protection of the invention.

Claims

1. A method for optimizing the electrolytic copper current based on a non-dominated sorting genetic algorithm, characterized in that, Includes the following steps: Step S1: Establish a multi-objective optimization problem sub-model for the electrolytic copper production process. The model includes at least: a production model for predicting future copper production based on current value and electrolysis parameters; an electricity cost model for predicting production electricity cost based on current value and time-of-use electricity price; and a quality scoring model for evaluating production quality based on current value, current change and key ion concentration deviation. Step S2: Based on the principle of conservation of mass, establish a predictive model for the concentration of key ions in the electrolytic cell. The model is used to predict the ion concentration in future time periods based on historical concentrations, the influence of the purification process, and current values. Step S3: Set production process constraints, including at least the rectifier maximum current constraint and daily output target constraint, and transform the constrained multi-objective optimization problem into an unconstrained optimization problem through a penalty function; Step S4: Use a non-dominated sorting genetic algorithm to solve the unconstrained optimization problem, and output the optimal current value sequence for each time period in the next 24 hours in a set time interval.

2. The method for optimizing electrolytic copper current based on a non-dominated sorting genetic algorithm according to claim 1, characterized in that, In step S1, the specific steps for obtaining the objective function vector of the multi-objective optimization problem are as follows: Establish an individual fitness scoring model in the genetic algorithm, where the individual fitness is represented by a vector: The specific calculation formulas are as follows: in, For electricity cost adaptability, For yield adaptability, For quality adaptability; and The results are obtained by subtracting the corresponding constraint penalties from the calculation results of the electricity cost model and the production model, respectively. and As a penalty amount, It is obtained from the average of the quality scores for each time period.

3. The method for optimizing electrolytic copper current based on a non-dominated sorting genetic algorithm according to claim 2, characterized in that, The formula for calculating the daily output of the production model is as follows: in, To predict daily output, Let be the current in the i-th time period. , , , , These are the copper ion concentration, hydrogen ion concentration, temperature, additive flow rate, and electrolyte circulation rate, respectively. - These are the parameters obtained by fitting historical data. This represents the total number of time periods.

4. The method for optimizing electrolytic copper current based on a non-dominated sorting genetic algorithm according to claim 3, characterized in that, The electricity cost model is as follows: in, To predict electricity bills, Let be the current in the i-th time period. Let be the electricity price corresponding to the i-th time period. This is the equivalent resistance of the electrolyte.

5. The method for optimizing electrolytic copper current based on a non-dominated sorting genetic algorithm according to claim 4, characterized in that, In the quality scoring model, the quality score Q(i) for the i-th time period is: in, , , The concentrations of copper, nickel, and iron ions predicted for the i-th time period are: , , This corresponds to the optimal concentration of the historically high-quality batches. Let be the current in the i-th time period. - The negative weighting coefficient is preset.

6. The method for optimizing electrolytic copper current based on a non-dominated sorting genetic algorithm according to claim 5, characterized in that, In step S2, the relationship between the ion concentration and the charge flux in the i-th time period is established, and the concentration prediction model is as follows: in, Let be the predicted copper ion concentration for the i-th time period. This is the initial concentration. Let be the decrease in copper ion concentration caused by the purified solution during the t-th time period. The rate of increase in copper ion concentration per unit current. Let t be the current in the t-th time period; the prediction models for nickel and iron ion concentrations are the same.

7. The method for optimizing electrolytic copper current based on a non-dominated sorting genetic algorithm according to claim 1, characterized in that, In step S3, the penalty function includes: The formula for the current penalty term is: The formula for the production penalty term is: in, The maximum allowable current for the rectifier. This is the target daily output value. These are production model predictions. , This is the penalty coefficient.

8. The method for optimizing electrolytic copper current based on a non-dominated sorting genetic algorithm according to claim 1, characterized in that, In step S4, a non-dominated sorting genetic algorithm is used to solve the problem, including: S41. Initialize the population and base it on vector fitness. Stratify individuals in a population by non-dominated ranking; S42. Calculate the crowding degree of individuals in the same non-dominated layer across each objective dimension; S43. Based on the non-dominant layer priority and individual crowding, select a specified number of individuals from the merged parent and offspring populations as the new generation of parents. S44. Perform selection, crossover, and mutation operations on the new generation of parents to generate the offspring population; S45. Repeat steps S41 to S44 until the termination condition is met, and output the current value sequence corresponding to the Pareto optimal solution set in the final population.

9. The method for optimizing electrolytic copper current based on a non-dominated sorting genetic algorithm according to claim 8, characterized in that, In step S43, the specific method for selecting the new generation parent is as follows: according to the non-dominated layer from high to low, add the entire layer of individuals to the new parent set in sequence until a certain layer is added. If the total number exceeds the preset size q, then for this layer... Individuals are sorted from most crowded to least crowded, and the top (q - number of already selected) individuals are added.

10. The method for optimizing electrolytic copper current based on a non-dominated sorting genetic algorithm according to claim 8, characterized in that, In step S44, the method for generating offspring includes: The top M individuals with the highest fitness in the new generation of parents are directly retained as offspring. The remaining parent individuals are randomly paired up, and the current values ​​over each time period are averaged to generate new individuals; then, the generated new individuals are mutated according to probability.

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