Silver electrolysis process parameter design method and system based on multi-objective optimization

Abstract

The invention relates to the technical field of process parameter design, and discloses a silver electrolysis process parameter design method and system based on multi-objective optimization. The method comprises the following steps: performing differential time sequence parameter decomposition on operation data of the silver electrolysis process to obtain a sensitive parameter set and a reference parameter set; performing reweighted periodic feature extraction on the sensitive parameter set and the reference parameter set, and establishing a dynamic mathematical model of the silver electrolysis process parameters; based on the dynamic mathematical model of the silver electrolysis process parameters, physical and chemical process numerical simulation is conducted through COMSOLMultiphysics software, and a response curved surface model is obtained; and according to the response curved surface model, a process parameter combination evaluation value sequence is generated, silver electrolysis process parameter multi-objective optimization is carried out based on the process parameter combination evaluation value sequence, and a silver electrolysis process parameter optimization scheme is output. According to the application, multi-physical-field collaborative simulation of electrode reaction, ion transmission, heat conduction and the like is realized, and performance index responses under different process parameters are accurately predicted.

Description

Technical Field

[0001] The present application relates to the technical field of process parameter design, and in particular to a silver electrolysis process parameter design method and system based on multi-objective optimization. Background Art

[0002] With the development of high-tech industries, the requirements for silver recovery and purity are becoming increasingly stringent. Electrolytic refining is a key method for purifying silver, effectively removing impurities and producing high-purity silver products. However, the process efficiency and product quality of this technology are highly dependent on the precise control of multiple process parameters, including current density, electrolyte concentration, temperature, pH, and voltage.

[0003] Currently, the optimization of silver electrolysis process parameters relies primarily on engineers' experience and trial-and-error methods, lacking a systematic, quantitative optimization approach. Traditional parameter design methods typically employ single-factor analysis or orthogonal experimental methods, which fail to fully account for the complex interactions and dynamic changes between parameters. Furthermore, these methods often optimize only for a single objective, making it difficult to achieve a comprehensive balance among multiple performance indicators such as recovery rate, purity, energy consumption, and cost. This results in irrational process parameter settings and low resource utilization. Summary of the Invention

[0004] The present application provides a method and system for designing silver electrolysis process parameters based on multi-objective optimization. The present application fully considers the periodic characteristics of electrochemical reactions, enhances the ability to express parameter timing characteristics and periodic characteristics, realizes the collaborative simulation of multiple physical fields such as electrode reactions, ion transport and heat conduction, and accurately predicts the performance indicator responses under different process parameters.

[0005] In a first aspect, the present application provides a method for designing silver electrolysis process parameters based on multi-objective optimization, the method comprising:

[0006] Perform differential time series parameter decomposition on the silver electrolysis process operation data to obtain a sensitive parameter set and a baseline parameter set;

[0007] Performing reweighted periodic feature extraction on the sensitive parameter set and the reference parameter set to establish a dynamic mathematical model of silver electrolysis process parameters;

[0008] Based on the dynamic mathematical model of the silver electrolysis process parameters, the physical and chemical process numerical simulation was performed using COMSOL Multiphysics software to obtain a response surface model;

[0009] According to the response surface model, a process parameter combination evaluation value sequence is generated, and based on the process parameter combination evaluation value sequence, multi-objective optimization of silver electrolysis process parameters is performed, and a silver electrolysis process parameter optimization plan is output.

[0010] In a second aspect, the present application provides a silver electrolysis process parameter design system based on multi-objective optimization, the silver electrolysis process parameter design system based on multi-objective optimization comprising:

[0011] A decomposition module is used to perform differential time series parameter decomposition on the silver electrolysis process operation data to obtain a sensitive parameter set and a baseline parameter set;

[0012] A feature extraction module, configured to perform reweighted periodic feature extraction on the sensitive parameter set and the reference parameter set, and establish a dynamic mathematical model of silver electrolysis process parameters;

[0013] A numerical simulation module is used to perform a numerical simulation of the physical and chemical process based on the dynamic mathematical model of the silver electrolysis process parameters using COMSOL Multiphysics software to obtain a response surface model;

[0014] The multi-objective optimization module is used to generate a process parameter combination evaluation value sequence according to the response surface model, and perform multi-objective optimization of silver electrolysis process parameters based on the process parameter combination evaluation value sequence, and output a silver electrolysis process parameter optimization plan.

[0015] In the technical solution provided by this application, a systematic analysis of the silver electrolysis process operation data is carried out through the differential time series parameter decomposition technology, which realizes the objective identification of sensitive parameters and benchmark parameters, avoids the subjectivity of traditional empirical judgment, and adopts the reweighted periodic feature extraction technology to construct a dynamic mathematical model, fully considers the periodic characteristics of the electrochemical reaction, enhances the expression ability of the parameter time series characteristics and periodic characteristics, and accurately describes the dynamic relationship between parameters. In combination with COMSOL Multiphysics software, a multi-physics field coupling model is established to realize the collaborative simulation of multiple physical fields such as electrode reaction, ion transport and heat conduction, and accurately predict the performance index response under different process parameters. A comprehensive evaluation model is established by an improved approximate ideal solution sorting method, and the entropy weight method and indicator correlation matrix are introduced to realize the objective and comprehensive evaluation of the process parameter combination, overcoming the subjectivity and one-sidedness of the traditional evaluation method. Multi-objective optimization is realized based on the non-dominated sorting genetic algorithm, while considering multiple objectives such as silver recovery rate, purity, energy consumption and cost, and a series of balanced Pareto optimal solutions are obtained, providing diversified choices for decision-making. Through cluster analysis, sensitivity analysis and multiple regression analysis, the interaction patterns among process parameters were deeply revealed, the influence mechanism of key parameters was verified, and theoretical support was provided for process parameter optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0017] Figure 1 Schematic diagram of an embodiment of a method for designing silver electrolysis process parameters based on multi-objective optimization in an embodiment of the present application;

[0018] Figure 2 This is a schematic diagram of an embodiment of a silver electrolysis process parameter design system based on multi-objective optimization in an embodiment of the present application. DETAILED DESCRIPTION

[0019] The embodiments of the present application provide a method and system for designing silver electrolysis process parameters based on multi-objective optimization. The terms "first", "second", "third", "fourth", etc. (if any) in the specification and claims of this application and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments described herein can be implemented in an order other than that illustrated or described herein. In addition, the terms "including" or "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0020] For ease of understanding, the specific process of the embodiment of the present application is described below. Figure 1 In the embodiments of the present application, an embodiment of the method for designing silver electrolysis process parameters based on multi-objective optimization includes:

[0021] Step S101: performing differential time series parameter decomposition on the silver electrolysis process operation data to obtain a sensitive parameter set and a reference parameter set;

[0022] It is understandable that the execution subject of this application can be a silver electrolysis process parameter design system based on multi-objective optimization, or a terminal or a server, which is not limited here. The embodiment of this application is described by taking the server as the execution subject as an example.

[0023] Specifically, the operating data of the silver electrolysis process is arranged in time series. This data includes key parameters such as current density, electrolyte concentration, temperature, pH, and voltage. All data are arranged chronologically to form a parameter matrix. Based on this data matrix, a reference characteristic spectrum under normal operating conditions and comparative characteristic spectra under different operating conditions are established. The reference characteristic spectrum is a set of feature vectors generated by extracting features from the normal operating condition data, reflecting the variation characteristics of the process parameters under normal conditions. The comparative characteristic spectrum is a set of feature vectors obtained by applying the same feature extraction to data collected under different operating conditions, reflecting the variation of process parameters under different operating conditions. By calculating the difference between the reference and comparative characteristic spectra, a difference matrix is ​​obtained, reflecting the degree of parameter variation between different operating conditions and the normal condition, reflecting the variation characteristics of each parameter under different operating conditions. The difference matrix is ​​Fourier transformed to convert the original time domain data into frequency domain data. The spectral characteristics of the parameter variations are extracted, effectively revealing the periodicity and frequency characteristics of the parameter variations. Based on the parameter variation spectrum and the process indicator difference vector, a convex optimization mathematical model is constructed to minimize the residual error. The goal of this model is to minimize the impact of parameter variations on process indicators under different operating conditions by optimizing the parameter influence weight vector. By solving the optimization problem, the influence weight of each parameter is obtained, and the size of the weight reflects the contribution of each parameter to the performance of the silver electrolysis process. According to the size of the parameter influence weight, the parameters are divided into different categories. When the weight value of a parameter is greater than the first threshold, the parameter is considered to be a sensitive parameter and enters the sensitive parameter set. These parameters have a significant impact on key indicators such as recovery rate, purity, energy consumption and cost of the silver electrolysis process, and need to be paid special attention to when optimizing the process. When the weight value of the parameter is between the first threshold and the second threshold, these parameters are classified into the baseline parameter set. These parameters have a certain impact on the process indicators, but their changes are relatively stable. They are monitored and maintained as baseline parameters for process operation. When the weight value of the parameter is lower than the second threshold, it is regarded as an interference factor because it has little impact on the process performance.

[0024] Step S102: performing reweighted periodic feature extraction on the sensitive parameter set and the reference parameter set to establish a dynamic mathematical model of silver electrolysis process parameters;

[0025] Specifically, the sensitive parameter set and the baseline parameter set are standardized to eliminate the influence of different parameter dimensions and map the parameters to the same scale range for subsequent timing feature analysis. Through standardization, a sensitive normalized parameter set and a baseline normalized parameter set are obtained. Based on the sensitive and baseline normalized parameter sets, the inter-parameter temporal correlations are calculated to quantify the parameter relationships and the dynamic associations between different parameters. By calculating the inter-parameter temporal correlations, a parameter timing characteristic analysis matrix is ​​formed. The elements in this matrix represent the correlation strength of different parameters under different time delays, capturing the correlation characteristics and temporal evolution patterns between the parameters. To extract the periodic characteristics of the process parameters, the parameter timing characteristic analysis matrix is ​​periodically decomposed into periodic and non-periodic components. The periodic components reflect the periodic patterns of parameter changes over time, while the non-periodic components describe random fluctuations or interference signals. To enhance the characteristic information of the periodic components, an exponential non-convex function is applied to the periodic components. The significant features of the parameter periodic characteristics are amplified through a nonlinear enhancement mechanism, resulting in an enhanced periodic characteristic matrix that effectively highlights the periodic patterns of parameter changes. Based on a set of sensitive and baseline normalized parameters, a multivariate autoregressive model is established to describe the dynamic evolution of silver electrolysis process parameters. This model can capture the dynamic relationships between multiple parameters and simulate their temporal trends. The core of the model is to obtain an autoregressive coefficient matrix through training with parameter time series data, thereby reflecting the inherent patterns of parameter variation. Because the correlations between parameters exhibit complex periodic characteristics, the coefficient matrix of the multivariate autoregressive model is reweighted to fully account for the influence of these periodic characteristics. Based on the enhanced periodic matrix, a reweighting mechanism is introduced to adjust the weights of the autoregressive coefficient matrix, thereby improving the model's prediction accuracy and making it more consistent with the dynamic patterns of silver electrolysis process changes. A dynamic mathematical model of silver electrolysis process parameters is established to describe the dynamic relationships between sensitive and baseline parameters and accurately predict changes in process indicators under different operating conditions.

[0026] Step S103: Based on the dynamic mathematical model of silver electrolysis process parameters, numerical simulation of the physical and chemical process is performed using COMSOL Multiphysics software to obtain a response surface model;

[0027] Specifically, a 3D electrolytic cell model was created based on the geometry of an actual silver electrolytic cell. The model includes the geometric parameters of the anode, cathode, electrolyte region, electrode conductive device, and cell structure. The anode is constructed from crude silver, the cathode is a pure silver plate or stainless steel plate as a deposition substrate, and the electrolyte region primarily consists of silver nitrate and nitric acid solution. By specifying the anode and cathode dimensions, interelectrode distance, cell depth, cell boundary conditions, and the geometric parameters of the conductive device, the 3D model accurately reflects the physical properties of the actual electrolytic cell. Material physical parameters were set for the 3D electrolytic cell model. The anode material was set to crude silver containing impurities, which contains approximately 97.5% silver, with major impurities including copper, lead, and gold; the cathode material was set to pure silver plate or stainless steel; and the electrolyte was set to a mixture of silver nitrate and nitric acid solution. These material parameters were precisely adjusted based on experimental data and process requirements to ensure the model accurately simulated the physical and chemical reactions under real-world conditions. Based on a dynamic mathematical model of silver electrolysis process parameters, the key parameters of the electrolysis process are coupled with the physical field model. The electrochemical module and transport phenomenon module in COMSOL Multiphysics software are used to construct a coupled physical field model of electrode reactions and ion transport. During this process, the electrode reaction includes the dissolution of crude silver at the anode into silver ions and the release of electrons, and the deposition of silver ions at the cathode onto the pure silver substrate to form a silver layer. The kinetics and reaction rate of the electrode reactions are affected by factors such as current density, voltage, pH, and temperature. The model incorporates relevant electrode reaction equations and ion transport equations, and combines electrochemical reaction mechanisms to simulate electrode surface reactions and ion migration, diffusion, and convection in the electrolyte, thereby accurately capturing the complex characteristics of ion transport and reaction kinetics during the electrolysis process. To improve the accuracy of the model, a heat conduction module is added to the coupled physical field model to simulate the generation and transfer of Joule heat during the electrolysis process. During the electrolysis process, Joule heating generated by current flowing through the electrolyte causes the electrolyte temperature to rise. This temperature change, in turn, affects ion migration rates, electrode reaction rates, and silver deposition rates. Therefore, a heat conduction module was introduced to accurately simulate the evolution of the temperature field and evaluate the impact of temperature variations on the electrolysis process under different operating conditions. This model, which integrates the interplay of the three physical fields of electrode reaction, ion transport, and heat conduction, was developed. This model was then adaptively meshed and solved using a finite element method. The adaptive meshing focused on mesh refinement at the electrode surface, areas with large silver ion concentration gradients, and the boundary between the electrolyte and the tank to improve computational accuracy and ensure reliable simulation results. Through the finite element method, key performance data, including current distribution, silver ion concentration distribution, potential distribution, temperature distribution, silver deposition rate, and energy consumption, were obtained under different process parameters, reflecting the changes in various physicochemical properties during the electrolysis process.Based on the acquired data on current distribution, silver ion concentration, potential, temperature, silver deposition rate, and energy consumption, a mapping relationship between process parameters and silver recovery rate, silver purity, energy consumption, and cost was established, forming a response surface model. This response surface model can quantify the impact of different process parameter combinations on silver electrolysis performance and provide a precise mathematical description for multi-objective optimization. This allows key indicators such as recovery rate, purity, energy consumption, and cost to be weighed against different objectives during the optimization process, achieving precise optimization of silver electrolysis process parameters.

[0028] Step S104: Generate a process parameter combination evaluation value sequence according to the response surface model, perform multi-objective optimization of silver electrolysis process parameters based on the process parameter combination evaluation value sequence, and output a silver electrolysis process parameter optimization solution.

[0029] Specifically, a response surface model was used to evaluate multiple different combinations of silver electrolysis process parameters. The response surface model had established a mapping relationship between process parameters and key indicators through previous numerical simulations. Different parameter combinations were input into the response surface model, generating response data for each silver electrolysis process parameter combination in terms of silver recovery, silver purity, energy consumption, and production cost, forming a parameter combination performance dataset. This response data was organized into an original decision matrix containing all first-order silver electrolysis process parameter combinations. Each row of this matrix represents a specific silver electrolysis process parameter combination, and each column corresponds to a key evaluation indicator, such as silver recovery, silver purity, energy consumption, and cost. The original decision matrix was normalized to map the evaluation data for different parameter combinations to the same scale, forming a standardized decision matrix. Based on the standardized decision matrix, the entropy value of each indicator was calculated to determine its weight. The entropy calculation is based on the distribution characteristics of the indicator. A larger entropy value indicates a more dispersed information distribution for the indicator, resulting in a lower weight. A smaller entropy value indicates a greater impact on the final evaluation, resulting in a higher weight. By calculating the entropy of each indicator and generating a weight vector, we can avoid subjective bias caused by human weighting. The objective weight vector is weighted with the standardized decision matrix to obtain a weighted standardized decision matrix. From this weighted standardized decision matrix, we determine the ideal and negative ideal solutions. The ideal solution is the optimal parameter combination for each indicator, while the negative ideal solution is the worst parameter combination for each indicator. These two solutions serve as evaluation benchmarks for calculating the distances of each parameter combination to the ideal and negative ideal solutions. Because the indicators are correlated, an indicator correlation matrix is ​​constructed to quantify the degree of correlation between different indicators and to correct the distances of each parameter combination to the ideal and negative ideal solutions. By incorporating indicator correlation information into the corrected distances, we more accurately measure the overall performance of each parameter combination and obtain a corrected target distance. Based on the target distances, we calculate a comprehensive evaluation value for each silver electrolysis process parameter combination. This comprehensive evaluation value reflects the overall performance of each parameter combination under multi-objective conditions. The comprehensive evaluation values ​​of all parameter combinations are ranked to form a process parameter combination evaluation value sequence. Multi-objective optimization of silver electrolysis process parameters is performed based on the process parameter combination evaluation value sequence. The optimal parameter combination is screened out through a non-dominated sorting genetic algorithm or other multi-objective optimization algorithm, and finally an optimization solution for the silver electrolysis process parameters is output.

[0030] A multi-objective optimization function is defined based on a sequence of process parameter combination evaluation values. This multi-objective optimization function includes four objectives: maximizing silver recovery, maximizing silver purity, minimizing energy consumption, and minimizing production cost. These four objectives are mutually constrained, so the optimization goal is to find the optimal balance between recovery, purity, energy consumption, and cost while satisfying different constraints, forming an effective multi-objective optimization problem. When constructing the optimization model, the value ranges of current density, electrolyte concentration, temperature, pH, and voltage are set as constraints. These constraints are derived from actual production data and process safety limits of the silver electrolysis process. By setting these value ranges, the parameter search is bounded, ensuring that the parameter combinations during the optimization process are within a reasonable process space. A process parameter value space is constructed based on these constraints. Within this parameter value space, a population of initial parameter combinations that meet the constraints is randomly generated. These parameter combinations serve as individuals in the population. The diversity of the initial population has a significant impact on the convergence speed of the optimization algorithm and the quality of the solution. Therefore, the population should cover as wide a range of parameter combinations as possible to improve the comprehensiveness of the optimization process. After the initial population is generated, a non-dominated sorting is performed on the second silver electrolysis process parameter combinations within the initial parameter combination population, dividing the population into non-dominated hierarchies. The core of this non-dominated sorting is to compare the strengths and weaknesses of individuals in the population according to a multi-objective optimization function and divide the population into different non-dominated strata. Individuals in the first non-dominated stratum represent the optimal solution in the current population, while individuals in higher non-dominated strata gradually approach the optimal solution. Furthermore, within each non-dominated stratum, the crowding distance is calculated. This is an important metric for measuring the density of individuals in the solution space. This calculation ensures that the multi-objective optimization algorithm maintains solution diversity on the Pareto front, thus preventing the optimization process from becoming trapped in local optima. After the non-dominated sorting and crowding distance calculation are completed, the population evolution phase begins. Based on the non-dominated stratum and crowding distance, a binary tournament selection operation is used to select parent individuals. This binary tournament selection operation is a selection mechanism that randomly selects two individuals and compares their non-dominated hierarchies and crowding distances to select the more superior individual for inclusion in the parent population, thereby maintaining diversity in the parent population. Simulated binary crossover and polynomial mutation are performed on the selected parent individuals. Simulated binary crossover generates offspring individuals with diverse and excellent properties, while polynomial mutation introduces a certain amount of random perturbation to prevent the population from falling into a local optimum. The crossover and mutation operations further enhance the diversity of the population, providing a more optimal search space for subsequent population evolution. After the offspring population is generated, the parent and offspring populations are merged and sorted by non-dominated levels. The merged population is then sorted again by non-dominated layer, and a new generation of populations is selected based on the crowding distance. This new population replaces the previous generation, and iterative optimization continues. This process is repeated until the maximum number of iterations is reached or the population converges.The convergence of the population is marked by the stability of the Pareto frontier solution. The resulting Pareto optimal solution set contains a set of silver electrolysis process parameter combinations that balance silver recovery rate, silver purity, energy consumption, and production cost, thus forming the optimal solution for multi-objective optimization. After optimization and iteration, the optimized solution for the silver electrolysis process parameters is finally output.

[0031] Two individuals with different second silver electrolysis process parameter combinations are randomly selected from the current population as candidate individuals. These two candidates are compared based on their non-dominated rank and crowding distance. The criterion for judging superiority is to prioritize individuals with higher non-dominated rank. This is because, in a non-dominated sorting, individuals in lower tiers exhibit better Pareto properties—that is, they outperform individuals in higher tiers on multiple objectives. When two candidates are in the same non-dominated tier, the crowding distance is compared to determine which individual to select as the parent. The crowding distance reflects the density of the solution distribution. Individuals with larger crowding distances tend to be located at the boundary of the solution space, helping to maintain the diversity of solutions on the Pareto front. Therefore, when the two candidates are in the same tier, the individual with the larger crowding distance is selected to join the parent set. This binary tournament selection operation is repeated multiple times until a predetermined number of parents are selected to form the parent set. The parents are then randomly grouped into mating pairs, and each mating pair serves as a candidate for the crossover operation. During the crossover phase, a preset crossover probability determines whether to perform a crossover on a mating pair. If a crossover is performed, a simulated binary crossover method is used to generate offspring pairs. This simulated binary crossover method is a highly efficient crossover method based on a genetic algorithm. It uses information from the parent individuals to restructure parameters, thereby producing offspring pairs with diverse and superior characteristics. If the crossover probability indicates that a crossover is not performed, the parent individuals in the mating pair are retained as offspring pairs, ensuring that the diversity of the population is not excessively compromised. After the offspring pairs are generated, an initial offspring population is generated, and each silver electrolysis process parameter combination in this initial offspring population is mutated. The core of the mutation operation lies in determining whether to perform a polynomial mutation on an individual based on the mutation probability. If a mutation is performed, a polynomial mutation is performed on each element of the parameter vector corresponding to that individual. Polynomial mutation is an efficient parameter perturbation mechanism that makes small adjustments to the parameters based on the preset mutation probability and distribution index, allowing individuals to explore new solution regions in the solution space, thereby preventing the population from becoming trapped in local optima. During the polynomial mutation process, each parameter value undergoes a slight change based on a probability distribution, forming a new mutated parameter vector. This new parameter vector is used to replace the original second silver electrolysis process parameter combination individuals, enhancing the diversity of the population. After all individuals have been mutated, the response surface model is used to evaluate the objective function values ​​of all mutated silver electrolysis process parameter combinations. The response surface model has established a mapping relationship between process parameters and key performance indicators through previous numerical simulations. The mutated parameter combinations are input into the response surface model to obtain performance evaluation results for each individual on multiple objectives, such as silver recovery rate, silver purity, energy consumption, and production cost.Finally, a descendant population is formed after crossover and mutation optimization. The descendant population will enter the next round of non-dominated sorting and evolution process together with the parent population, and will continue to iterate until the optimization algorithm converges, thereby obtaining the optimal solution set of the Pareto frontier and providing the optimal parameter combination scheme for the optimization of silver electrolysis process parameters.

[0032] In the embodiment of the present application, the silver electrolysis process operation data is systematically analyzed by differential time series parameter decomposition technology, and the objective identification of sensitive parameters and reference parameters is achieved, avoiding the subjectivity of traditional empirical judgment. The dynamic mathematical model is constructed by using the reweighted periodic feature extraction technology, which fully considers the periodic characteristics of the electrochemical reaction, enhances the expression ability of the parameter time series characteristics and periodic characteristics, and accurately describes the dynamic relationship between the parameters. A multi-physics field coupling model is established in combination with COMSOL Multiphysics software, which realizes the collaborative simulation of multiple physical fields such as electrode reaction, ion transport and heat conduction, and accurately predicts the performance index response under different process parameters. A comprehensive evaluation model is established by an improved approximate ideal solution sorting method, and the entropy weight method and indicator correlation matrix are introduced to achieve an objective and comprehensive evaluation of the process parameter combination, overcoming the subjectivity and one-sidedness of the traditional evaluation method. Multi-objective optimization is achieved based on the non-dominated sorting genetic algorithm, while considering multiple objectives such as silver recovery rate, purity, energy consumption and cost, and a series of balanced Pareto optimal solutions are obtained, providing diversified choices for decision-making. Through cluster analysis, sensitivity analysis and multiple regression analysis, the interaction patterns among process parameters were deeply revealed, the influence mechanism of key parameters was verified, and theoretical support was provided for process parameter optimization.

[0033] In a specific embodiment, the process of executing step S101 may specifically include the following steps:

[0034] Arrange the silver electrolysis process operation data in time series and construct a parameter matrix including current density, electrolyte concentration, temperature, pH value, and voltage;

[0035] A reference characteristic spectrum of normal operating parameters and a comparative characteristic spectrum of parameters under different operating conditions are established based on the parameter matrix;

[0036] Calculate the difference between the reference characteristic spectrum and the comparison characteristic spectrum to obtain a difference matrix, and convert the difference matrix into a parameter change spectrum through Fourier transform;

[0037] According to the parameter variation spectrum and process index difference vector, a convex optimization mathematical model for minimizing residual error is constructed, and the parameter influence weight vector is obtained by solving the model.

[0038] Parameters whose weight values ​​in the parameter influence weight vector are greater than a first threshold are classified into a sensitive parameter set, and parameters whose weight values ​​in the parameter influence weight vector are between the first threshold and the second threshold are classified into a benchmark parameter set.

[0039] Specifically, the operating data of the silver electrolysis process is systematically arranged in a time series. The collected data includes key process parameters such as current density, electrolyte concentration, temperature, pH value, and voltage. This data is obtained through an online monitoring system or regular manual sampling. After data collection is completed, the data is arranged in chronological order to form a parameter matrix containing all key process parameters. Each column of the parameter matrix represents a process parameter, and each row corresponds to the parameter measurement value at a certain point in time, thus forming a time series data matrix. Based on the parameter matrix, a reference characteristic spectrum of the normal operating parameters and a comparative characteristic spectrum of the parameters under different operating conditions are established. The reference characteristic spectrum is a set of feature vectors extracted from data collected over a long period of time under normal operating conditions. These feature vectors reflect the parameter variation patterns of the silver electrolysis process under stable operating conditions. Feature extraction is performed on the parameter matrix under normal operating conditions. For example, principal component analysis, singular value decomposition, or other feature extraction algorithms are used to condense the large amount of parameter data into a set of feature vectors that can represent the key variation characteristics. Simultaneously, the same feature extraction is performed on the data under different operating conditions to form comparative characteristic spectra under different operating conditions. This reflects the variation characteristics of silver electrolysis process parameters under various abnormal operating conditions or different parameter combinations. The difference between the reference and comparative characteristic spectra is calculated to quantify the magnitude of parameter variation between different operating conditions and normal conditions. A difference matrix is ​​constructed by subtracting the comparative characteristic spectrum from the reference characteristic spectrum. Each element of the matrix represents the degree of change of a characteristic under different operating conditions compared to normal conditions. A Fourier transform is performed on the difference matrix to convert the time-domain difference information into the frequency domain, forming a parameter variation spectrum. The original time series data is decomposed into different frequency components, revealing the periodicity and spectral characteristics of process parameter variations. By analyzing the parameter variation spectrum, the dominant variation frequency and variation pattern of each parameter are identified. Based on the parameter variation spectrum and the process indicator difference vector, a convex optimization mathematical model is constructed to minimize the residual error. The goal of the model is to determine the influence of each parameter on the silver electrolysis process performance by minimizing the residual error between the parameter influence weight vector and the process indicator difference vector. When establishing the optimization model, a parameter influence weight vector is introduced. Each element of this vector represents the contribution of a process parameter to the difference in process indicators such as silver recovery rate, silver purity, energy consumption and cost. The goal is to solve this weight vector so that the residual between the parameter change spectrum and the process indicator difference is minimized, thereby accurately quantifying the impact of each parameter on the process performance. By solving this convex optimization problem, a parameter influence weight vector is obtained. The size of the weight value in this vector reflects the relative importance of each parameter to the performance of the silver electrolysis process. The parameters are classified according to the size of the weight value, and the parameters with weight values ​​greater than the first threshold are classified into the sensitive parameter set. These sensitive parameters have a significant impact on the key performance indicators of the silver electrolysis process and are therefore the focus of attention in process optimization.Parameters with weights between the first and second thresholds are classified as baseline parameters. These parameters have a certain impact on process indicators but are relatively stable, and are maintained and monitored as process benchmarks. Parameters with weights below the second threshold are considered interference factors due to their minimal impact on process indicators and do not need to be considered in the subsequent optimization process.

[0040] In a specific embodiment, the process of executing step S102 may specifically include the following steps:

[0041] Standardizing the sensitive parameter set and the benchmark parameter set respectively to obtain a sensitive normalized parameter set and a benchmark normalized parameter set;

[0042] Based on the sensitive normalized parameter set and the reference normalized parameter set, the time series correlation between the parameters is calculated to quantify the parameter relationship, and the parameter time series characteristic analysis matrix is ​​obtained;

[0043] Decompose the parameter time series characteristic analysis matrix into periodic components and non-periodic components, and apply the exponential non-convex function to the periodic components to obtain the periodic characteristic matrix after feature enhancement;

[0044] A multivariate autoregressive model is established based on the sensitive normalized parameter set and the benchmark normalized parameter set. The coefficient matrix of the multivariate autoregressive model is reweighted and adjusted according to the periodic characteristic matrix after feature enhancement to establish a dynamic mathematical model of silver electrolysis process parameters.

[0045] Specifically, the sensitive parameter set and the benchmark parameter set are standardized to eliminate the influence of different parameter dimensions and value ranges, so that subsequent analyses can be compared on the same scale. The sensitive parameter set includes key parameters that have a significant impact on the recovery rate, purity, energy consumption and cost of the silver electrolysis process, while the benchmark parameter set includes parameters that have a certain impact on process performance but are relatively stable. During standardization, the raw data of each parameter is mean normalized or minimum-maximum normalized, and the parameter values ​​are converted to the same scale range to form a sensitive normalized parameter set and a benchmark normalized parameter set. A time series correlation analysis is performed on the sensitive normalized parameter set and the benchmark normalized parameter set to quantify the dynamic correlation between different parameters. By calculating the time series correlation between each parameter, a parameter time series characteristic analysis matrix is ​​obtained, and each element of the matrix represents the correlation strength between two parameters at different time points. The time series correlation is calculated using a cross-correlation function or time series delay correlation analysis, and the parameter data at different time points are correlated through a sliding window to quantify the dynamic relationship between each parameter over time. The parameter time series characteristic analysis matrix reflects the degree of correlation between parameters and reveals the potential dynamic influence between sensitive parameters and baseline parameters. The parameter time series characteristic analysis matrix is ​​decomposed into periodic and non-periodic components to extract the periodic characteristics of parameter variations. The periodic components reflect the dominant frequency and periodic characteristics of parameter variations in the silver electrolysis process, while the non-periodic components contain random fluctuations or noise signals during the process. To enhance the characteristic information of the periodic components, an exponential non-convex function is applied to the periodic components to enhance the periodic characteristics. The exponential non-convex function is an enhancement mechanism with nonlinear amplification properties. By applying nonlinear transformations to the periodic components, it effectively highlights the significant characteristics of periodic variations, making the periodic patterns of the parameters clearer and more recognizable. The enhanced periodic characteristic matrix is ​​obtained. A multivariate autoregressive model is established based on the sensitive normalized parameter set and the baseline normalized parameter set. This model can capture the dynamic correlations between parameters and simulate the trends of parameter changes over time. By introducing a time lag term, the multivariate autoregressive model links the parameter state at the current moment with the parameter state at historical moments, establishing a mathematical relationship between the parameter evolution over time. The core of the autoregressive model lies in obtaining an autoregressive coefficient matrix through historical data training. This coefficient matrix reflects the dynamic relationships between parameters and their impact on future states. Because the dynamic relationships between parameters exhibit complex cyclical characteristics, the coefficient matrix of the multivariate autoregressive model is reweighted and adjusted based on the feature-enhanced cyclical characteristic matrix. Incorporating cyclical information into the coefficient matrix of the autoregressive model fully accounts for the impact of cyclical changes in the model's dynamic relationships, significantly improving the model's predictive capabilities.To achieve reweighted adjustment of the autoregressive coefficient matrix, the enhanced periodic characteristic matrix is ​​diagonalized and used as the basis for weight adjustment. By incorporating the periodic information from the periodic characteristic matrix into the weights of the autoregressive coefficient matrix, the model's sensitivity to periodic variations is effectively enhanced, forming a dynamically adaptive autoregressive coefficient matrix. Using this reweighted autoregressive model, a more accurate dynamic mathematical model of silver electrolysis process parameters is established, describing the dynamic relationship between sensitive and baseline parameters and accurately predicting the changing trends of process parameters under different operating conditions.

[0046] In a specific embodiment, the process of executing step S103 may specifically include the following steps:

[0047] Create a three-dimensional electrolytic cell model based on the electrolytic cell geometry, and set the geometric parameters of the anode, cathode, electrolyte area, electrode conductive device, and cell structure;

[0048] Set the material physical parameters for the 3D electrolytic cell model, setting the anode material to coarse silver, the cathode material to pure silver plate, and the electrolyte to silver nitrate and nitric acid solution;

[0049] Based on the dynamic mathematical model of silver electrolysis process parameters, the electrochemical module and the transport phenomenon module were applied, and the coupled physical field model of electrode reaction and ion transport was established using COMSOL Multiphysics software.

[0050] Add a heat conduction module to the coupled physical field model to form a comprehensive numerical simulation model that includes Joule heat generation and transfer;

[0051] Adaptive meshing and finite element solution were performed on the comprehensive numerical simulation model to obtain current distribution, silver ion concentration distribution, potential distribution, temperature distribution, silver deposition rate and energy consumption data;

[0052] Based on the current distribution, silver ion concentration distribution, potential distribution, temperature distribution, silver deposition rate and energy consumption data, a mapping relationship between process parameters and silver recovery rate, silver purity, energy consumption and cost was established to form a response surface model.

[0053] Specifically, a 3D electrolytic cell model is created based on the actual cell geometry. The cell geometry includes the anode, cathode, electrolyte region, electrode conductor, and complete details of the cell structure. The anode is composed of a coarse silver plate with microscopic surface inhomogeneities. This coarse silver plate releases silver ions into the electrolyte when it dissolves as an anode. The cathode, a substrate made of pure silver or stainless steel, is used for silver ion deposition. This material must ensure good adhesion and conductivity during the deposition process. The electrolyte region is filled with a mixture of silver nitrate and nitric acid solution to ensure efficient migration and diffusion of silver ions during the electrolysis process. The electrode conductor connects the anode and cathode and provides a stable current supply. The cell structure supports and encapsulates the entire electrolytic cell. By precisely defining the geometric parameters of each component, including the distance between the anode and cathode, the depth of the cell, and the thickness of the cell wall, a geometric foundation is provided for subsequent numerical simulations. After the 3D electrolytic cell model is established, physical parameters are set for the material properties of each component. The anode material is set to crude silver, of which the silver content is generally about 97.5%, and the rest are impurities, including copper, lead, gold and other elements. These impurities have a certain impact on the electrolysis process during the anode dissolution process. The cathode material is set to pure silver plate or stainless steel plate. These materials have high conductivity and good silver deposition performance. The electrolyte is composed of silver nitrate and nitric acid solution. Its concentration has an important influence on the migration speed, deposition rate and electrode reaction kinetics of silver ions. Therefore, the initial concentration, pH value and temperature of the electrolyte are accurately set according to the process requirements. After completing the geometric modeling and material parameter setting, based on the dynamic mathematical model of the silver electrolysis process parameters, the electrochemical module and transport phenomenon module in the COMSOL Multiphysics software are used to establish a coupled physical field model of electrode reaction and ion transport. The electrode reaction is the core process of the silver electrolysis process. The crude silver on the anode dissolves into silver ions and releases electrons. The reaction equation is Ag→Ag + +e - , while the silver ions on the cathode accept electrons on the pure silver substrate and deposit to form a silver layer. The reaction equation is Ag + +e -→Ag. This process is influenced by multiple factors, including current density, voltage, temperature, and ion concentration. Therefore, the electrochemical reaction kinetics are coupled with ion transport phenomena in the electrolyte for modeling. The transport phenomenon module simulates the diffusion, migration, and convection of ions in the electrolyte, simulating the ion concentration distribution, migration rate, and electric field distribution within the electrolytic cell, providing the necessary data support for the subsequent simulation of the silver deposition rate. After establishing the coupled physical field model of the electrode reaction and ion transport, the heat conduction module is added to form a comprehensive numerical simulation model that includes the generation and transfer of Joule heat. During the electrolysis process, Joule heat is generated when current passes through the electrolyte. The heat conduction module simulates the heat transfer process within the electrolyte and electrolytic cell structure. The generation of Joule heat affects the temperature distribution of the electrolyte and changes the ion migration rate and electrode reaction kinetics. Therefore, the coupling between the thermal field, flow field, and electric field is considered in the simulation process. By comprehensively considering the interactive effects of the three physical fields of electrode reaction, ion transport, and heat conduction, a more complete numerical simulation model of the silver electrolysis process is formed. After completing the comprehensive physical field model, the model is adaptively meshed and solved using the finite element method. Adaptive meshing is an important guarantee for the accuracy of numerical simulations, especially on the electrode surface, in areas with large silver ion concentration gradients, and in the electrolyte interface region, where mesh encryption is performed to improve solution accuracy and computational stability. Finite element solution is achieved by dividing the solution domain into a finite number of small units and solving each unit to obtain the numerical solution of the entire model. The finite element method is used to obtain key physical data under different process parameters, including current distribution, silver ion concentration distribution, potential distribution, temperature distribution, silver deposition rate, and energy consumption. Based on the acquired data, a mapping relationship is established between process parameters and silver recovery rate, silver purity, energy consumption, and cost to form a response surface model. The response surface model is a multi-objective mapping relationship model established based on simulation data. By associating process parameters with key indicators, a continuous functional relationship is formed to quantify the impact of different process parameter combinations on silver electrolysis performance. The response surface model is constructed using machine learning methods such as polynomial regression, support vector regression or neural networks for fitting. Through training with a large amount of simulation data, a response surface model is obtained. This model can predict performance indicators such as silver recovery rate, purity, energy consumption and cost under different parameter combinations, and provide a clear evaluation function for subsequent multi-objective optimization.

[0054] In a specific embodiment, the process of executing step S104 may specifically include the following steps:

[0055] Based on the response surface model, multiple groups of different first silver electrolysis process parameter combinations were evaluated to obtain the response value data of each group of silver electrolysis process parameters in terms of silver recovery rate, silver purity, energy consumption and cost;

[0056] The response value data are organized into an original decision matrix containing all combinations of the first silver electrolysis process parameters, and the original decision matrix is ​​normalized to obtain a standardized decision matrix;

[0057] Calculate the entropy value of each indicator based on the standardized decision matrix, generate an objective weight vector, and calculate the weighted standardized decision matrix using the objective weight vector and the standardized decision matrix;

[0058] Determining the ideal solution and the negative ideal solution from the weighted standardized decision matrix, and constructing an indicator correlation matrix, and using the indicator correlation matrix to correct the distances of each first silver electrolysis process parameter combination to the ideal solution and the negative ideal solution to obtain a target distance;

[0059] Calculating the comprehensive evaluation value of each first silver electrolysis process parameter combination using the target distance to form a process parameter combination evaluation value sequence;

[0060] Multi-objective optimization of silver electrolysis process parameters is performed based on the process parameter combination evaluation value sequence, and the silver electrolysis process parameter optimization plan is output.

[0061] Specifically, based on the response surface model, multiple different combinations of first silver electrolysis process parameters were evaluated. The response surface model has established a mapping relationship between process parameters and key performance indicators through multi-physics field simulation and data training. Therefore, different parameter combinations are input into the response surface model to obtain the response value data of each parameter combination on key indicators such as silver recovery rate, silver purity, energy consumption and production cost. These parameter combinations are composed of current density, electrolyte concentration, temperature, pH value and voltage. Different parameter combinations correspond to different process conditions and production environments. By evaluating these combinations, the impact of each process parameter combination on silver electrolysis performance is reflected and a data set is formed. The response value data is organized into an original decision matrix containing all first silver electrolysis process parameter combinations. Each row of the original decision matrix represents a different parameter combination, and each column corresponds to a key performance indicator. The dimension of the matrix is ​​m×n, where m is the number of process parameter combinations and n is the number of evaluation indicators. Because different indicators have different dimensions and value ranges, the original decision matrix is ​​normalized to eliminate the impact of different dimensions on the calculation results and ensure that all indicator data fall within the same numerical range. Normalization methods include min-max normalization and mean normalization. This process results in a standardized decision matrix. The entropy value of each indicator is calculated based on the standardized decision matrix to generate an objective weight vector. Entropy calculation is based on the principles of information theory. By calculating the information entropy of each indicator under different parameter combinations, the importance of the indicator is quantified. Indicators with lower entropy values ​​have greater variability and, therefore, greater impact on the overall evaluation, thus receiving higher weights. This entropy calculation generates an objective weight vector encompassing all indicators. The standardized decision matrix is ​​weighted using the objective weight vector to generate a weighted standardized decision matrix. Each element of the weighted standardized matrix is ​​the product of the standardized data and the corresponding indicator weight, forming a weighted matrix that comprehensively considers the importance of each indicator. The ideal solution and the negative ideal solution are determined from the weighted standardized decision matrix. The ideal solution is the optimal parameter combination for each indicator, while the negative ideal solution is the worst parameter combination for each indicator, used to measure the worst-case scenario. These two solutions serve as the evaluation benchmark for multi-objective optimization, calculating the distances of each parameter combination to the ideal and negative ideal solutions. Because different indicators are correlated, an indicator correlation matrix is ​​constructed to quantify the degree of association between the indicators. This matrix is ​​then used to correct the distances of each first silver electrolysis process parameter combination to the ideal and negative ideal solutions. This correction aims to avoid duplicate calculations of highly correlated indicators when calculating distances, thereby more accurately reflecting the overall performance of different parameter combinations.Using the corrected target distance, a comprehensive evaluation value is calculated for each first silver electrolysis process parameter combination. This evaluation value is calculated using a modified TOPSIS (Top-Order by Approximate Ideal Solutions) method. This method determines the relative proximity of each parameter combination to the ideal solution and the negative ideal solution to determine the merits of different combinations. Combinations with higher proximity indicate better performance across multiple objectives, thus forming a sequence of process parameter combination evaluation values. Based on this sequence of process parameter combination evaluation values, a multi-objective optimization of the silver electrolysis process parameters is performed. This evaluation value sequence is screened and optimized using a non-dominated sorting genetic algorithm or other multi-objective optimization algorithm. During the optimization process, the parameter combinations are iteratively updated, and the Pareto frontier is gradually approached based on the optimization direction of the objective function. This results in a set of optimal solutions that balance objectives such as silver recovery rate, silver purity, energy consumption, and cost. This outputs a set of optimized solutions for the silver electrolysis process parameters.

[0062] In a specific embodiment, the execution step performs multi-objective optimization of silver electrolysis process parameters based on the process parameter combination evaluation value sequence, and the process of outputting the silver electrolysis process parameter optimization solution may specifically include the following steps:

[0063] defining a multi-objective optimization function based on a sequence of process parameter combination evaluation values, wherein the multi-objective optimization function includes maximizing silver recovery rate, maximizing silver purity, minimizing energy consumption, and minimizing production cost;

[0064] Set the value range constraints of current density, electrolyte concentration, temperature, pH value and voltage, and construct the process parameter value space based on the value range constraints;

[0065] A population of initial parameter combinations that meet the constraints is randomly generated in the process parameter value space. The second silver electrolysis process parameter combinations in the initial parameter combination population are non-dominated sorted, and the initial parameter combination population is divided into different non-dominated layers. The crowding distance is calculated in each non-dominated layer.

[0066] A binary tournament selection operation is used to select parent individuals based on the non-dominated layer and crowding distance, and simulated binary crossover and polynomial mutation operations are performed to generate the offspring population;

[0067] The parent population composed of parent individuals is merged with the child population, non-dominated sorting is performed, and the new generation population is selected according to the crowding distance. The cycle is iterated until convergence, and the optimization plan for the silver electrolysis process parameters is output.

[0068] Specifically, a multi-objective optimization function is defined based on a sequence of combined process parameter evaluation values. This function aims to simultaneously optimize multiple key indicators in the silver electrolysis process, including maximizing silver recovery, maximizing silver purity, minimizing energy consumption, and minimizing production costs. Silver recovery and purity are important technical indicators for measuring electrolysis effectiveness. A higher recovery indicates better silver extraction efficiency, while a higher purity indicates higher-quality silver products. Energy consumption and production costs are key indicators for process economics; reducing energy consumption can save production costs and improve the overall economic benefits of the process. The multi-objective optimization function jointly optimizes these four objectives and searches for Pareto optimal solutions. This ensures that conflicts between different objectives are balanced during the optimization process, resulting in an optimal solution that balances both technical and economic considerations. Constraints are set for the range of current density, electrolyte concentration, temperature, pH, and voltage, and the value space of the process parameters is constructed based on these constraints. Key parameters in the silver electrolysis process include current density, electrolyte concentration, temperature, pH, and voltage. Each parameter has a reasonable range of values. For example, current density must vary within a certain range to ensure process stability while avoiding negative effects of excessively high or low current densities on silver recovery and purity. Electrolyte concentration influences the migration and deposition rates of silver ions and must be controlled within an appropriate range to maintain a balanced ion concentration. Temperature and pH directly influence the kinetics of the electrode reaction; excessively high or low pH values ​​can alter the reaction rate. The choice of voltage affects the electric field strength within the electrolytic cell and must be adjusted within a safe range. By setting the ranges for these parameters, a process parameter value space is constructed. This space provides a search area for the optimization algorithm, ensuring that unreasonable parameter combinations are avoided during the solution process. Once the process parameter value space is constructed, a population of initial parameter combinations that meet the constraints is randomly generated. These parameter combinations serve as initial individuals in the optimization algorithm. Each individual represents a set of silver electrolysis process parameter combinations and corresponds to a process state. To ensure the diversity of the initial population, random generation or Latin hypercube sampling is used to ensure that parameter combinations cover the entire parameter space, thereby enhancing the global search capability of the optimization algorithm. After generating the initial population of parameter combinations, a non-dominated sorting is performed on each individual in the population, dividing the population into different non-dominated layers. The core of the non-dominated sorting method is to compare individuals based on the objective value of the multi-objective optimization function to determine whether there are other individuals that outperform the current individual in all objectives. If no such individual exists, it is assigned to the first non-dominated layer. Otherwise, it is assigned to the corresponding non-dominated layer based on the Pareto dominance relationship.After completing the non-dominated sorting, the crowding distance is calculated within each non-dominated layer. The crowding distance is an important indicator of the sparse distribution of individuals in the solution space. A larger crowding distance indicates that individuals are located at the boundary of the solution space, which helps maintain the diversity of solutions on the Pareto front. During the optimization process, individuals with larger crowding distances are preferentially retained to prevent the optimization process from falling into local optimal solutions. Based on the non-dominated layer and crowding distance, a binary tournament selection operation is used to select parent individuals for crossover and mutation. The binary tournament selection operation randomly selects two individuals and compares them based on their non-dominated layer and crowding distance to select the superior individual as the parent. This selection mechanism ensures the retention of high-quality individuals while introducing a certain degree of randomness, thereby improving the algorithm's global search capability. After the parent individuals are selected, simulated binary crossover and polynomial mutation operations are performed to generate the offspring population. Simulated binary crossover is a genetic algorithm crossover operation that recombines the genes of parent individuals to generate offspring individuals with diverse and excellent characteristics. After the crossover operation, polynomial mutation is performed on the offspring individuals. The mutation operation introduces small disturbances to prevent the population from falling into the local optimal solution and improve the search ability of the solution space. After the offspring population is generated, the parent population composed of the parent individuals is merged with the offspring population, and non-dominated sorting is performed again. The merged population is redistributed to different non-dominated layers, and the new generation population is selected based on the crowding distance. This process requires multiple loop iterations. Each iteration selects a better solution through non-dominated sorting and crowding distance, and continuously updates the Pareto frontier solution until the maximum number of iterations is met or the population converges. When the population converges, the Pareto optimal solution set obtained is the final silver electrolysis process parameter optimization solution. These solution sets represent the process parameter combination that achieves the best balance between silver recovery rate, silver purity, energy consumption and cost.

[0069] In a specific embodiment, the step of selecting parent individuals using a binary tournament selection operation based on the non-dominated layer and the crowding distance, and performing simulated binary crossover and polynomial mutation operations to generate a child population may specifically include the following steps:

[0070] Randomly select two individuals with the second silver electrolysis process parameter combination from the current population as candidate individuals, compare the candidate individuals according to the non-dominated layer level and crowding distance, and select the second silver electrolysis process parameter combination individual with a higher non-dominated level or a larger crowding distance in the same non-dominated level as the parent individual;

[0071] Repeat the binary tournament selection operation until a preset number of parent individuals are selected to form a parent individual set, and randomly pair the parent individual set to form mating pairs;

[0072] For each mating pair, whether to perform a crossover operation is determined based on the crossover probability. If a crossover operation is determined, a simulated binary crossover method is used to generate a pair of offspring individuals. If no crossover is performed, the mating pair is directly retained as the offspring individual pair.

[0073] An initial offspring population is generated based on the offspring individual pairs, and for each silver electrolysis process parameter combination individual in the initial offspring population, whether to perform a polynomial mutation operation is determined according to the mutation probability;

[0074] For the silver electrolysis process parameter combination individual determined to undergo polynomial mutation, polynomial mutation is performed on each element in the corresponding parameter vector according to the mutation probability and the distribution index to obtain a mutated parameter vector, and the mutated parameter vector is used to replace the original second silver electrolysis process parameter combination individual;

[0075] The response surface model was used to evaluate the objective function values ​​of all individual combinations of mutated silver electrolysis process parameters, and finally a progeny population was formed.

[0076] Specifically, two individuals with different second silver electrolysis process parameter combinations are randomly selected from the current population as candidate individuals. These two candidates are compared based on their non-dominated rank and crowding distance. The non-dominated rank is a measure of the performance of individuals in the Pareto frontier solution. Individuals in lower rank have greater advantages in multi-objective optimization. Therefore, individuals with higher non-dominated rank are preferred as parents. If two candidates are in the same non-dominated rank, they are further compared based on their crowding distance. The crowding distance measures the sparse distribution of individuals in the solution space. Individuals with larger crowding distances are typically located at the boundary of the solution space and have greater diversity advantages. Therefore, within the same non-dominated rank, individuals with larger crowding distances are preferred for inclusion in the parent population. This binary tournament selection process is repeated until a preset number of parent individuals are selected, forming a parent set. The parent individuals are randomly grouped into mating pairs, with each mating pair serving as a candidate for a crossover operation. During the crossover phase, whether to perform a crossover operation is determined based on a preset crossover probability. The crossover probability is a value between 0 and 1 that determines the probability of gene exchange within the mating pair. If a crossover is determined, simulated binary crossover is used to generate offspring pairs. This method is an efficient crossover based on a genetic algorithm. It uses information from parent individuals to restructure parameters, resulting in offspring pairs with diverse and superior characteristics. Simulated binary crossover generates offspring parameter combinations by weightedly combining the parameters of the parent individuals, thereby forming new parameter solutions in the solution space and ensuring diversity and superiority in the offspring. If the crossover probability indicates that a crossover is not required, the parent individuals in the mating pair are retained as the offspring pair without any parameter changes. This strategy avoids the loss of diversity in the solution space caused by excessive crossover. After generating offspring pairs, an initial offspring population is generated based on these offspring pairs, and a mutation operation is performed on each silver electrolysis process parameter combination in this initial offspring population. Mutation is designed to introduce perturbations to the solution space, preventing the optimization process from falling into a local optimum. The key to mutation is determining whether to mutate an individual based on a preset mutation probability. If a mutation is determined, a polynomial mutation is performed on each element of the parameter vector corresponding to that individual. Polynomial mutation is a commonly used mutation mechanism that makes small adjustments to parameters based on the mutation probability and distribution index, thereby increasing population diversity and improving the ability to explore solutions. During polynomial mutation, the intensity of the mutation is controlled by the distribution index. A larger distribution index results in a smaller mutation amplitude, while a smaller distribution index results in a larger mutation amplitude, ensuring that the mutated parameters do not deviate from a reasonable range of values. By mutating each element in the parameter vector, a new mutated parameter vector is generated. This vector will be used to replace the original second silver electrolysis process parameter combination individual, forming an updated offspring individual.After the mutation operation is completed, the response surface model is used to evaluate the objective function values ​​of all individual combinations of mutated silver electrolysis process parameters. The response surface model is based on the mapping relationship between parameters and process performance indicators established in the previous multi-physics field simulation. The mutated parameter combination can be input into the response surface model to obtain the performance evaluation results of each individual on multiple targets such as silver recovery rate, silver purity, energy consumption and production cost. The response surface model quickly calculates the corresponding objective function value based on different process parameter combinations, and uses the evaluation results as the objective function value of the individual, providing data support for subsequent non-dominated sorting and crowding distance calculations. After the above steps, a descendant population optimized by crossover and mutation is finally formed. These descendant individuals continue to participate in the evolution process in the next generation population. Through continuous iteration and optimization, a set of Pareto optimal solutions is finally obtained.

[0077] The above describes the silver electrolysis process parameter design method based on multi-objective optimization in the embodiment of the present application. The following describes the silver electrolysis process parameter design system based on multi-objective optimization in the embodiment of the present application. Figure 2 In the embodiment of the present application, an embodiment of a silver electrolysis process parameter design system based on multi-objective optimization includes:

[0078] Decomposition module 201, for performing differential time series parameter decomposition on the silver electrolysis process operation data to obtain a sensitive parameter set and a reference parameter set;

[0079] Feature extraction module 202, for performing reweighted periodic feature extraction on the sensitive parameter set and the reference parameter set, and establishing a dynamic mathematical model of silver electrolysis process parameters;

[0080] Numerical simulation module 203, used to perform numerical simulation of physical and chemical processes based on the dynamic mathematical model of silver electrolysis process parameters using COMSOL Multiphysics software to obtain a response surface model;

[0081] The multi-objective optimization module 204 is used to generate a process parameter combination evaluation value sequence according to the response surface model, and perform multi-objective optimization of the silver electrolysis process parameters based on the process parameter combination evaluation value sequence, and output a silver electrolysis process parameter optimization solution.

[0082] Through the collaborative efforts of these components, a systematic analysis of silver electrolysis process operating data was conducted using differential time-series parameter decomposition technology. This enabled objective identification of sensitive and baseline parameters, avoiding the subjectivity of traditional empirical judgment. A dynamic mathematical model was constructed using reweighted periodic feature extraction technology, fully accounting for the periodic nature of the electrochemical reaction, enhancing the expressive power of parameter time-series and periodic characteristics, and accurately describing the dynamic relationships between parameters. A multiphysics coupling model was established using COMSOL Multiphysics software, enabling collaborative simulation of multiple physics fields, including electrode reactions, ion transport, and heat conduction, and accurately predicting performance indicator responses under varying process parameters. A comprehensive evaluation model was established using an improved approach to ideal solution sorting method, incorporating an entropy weighting method and an indicator correlation matrix, enabling objective and comprehensive evaluation of process parameter combinations, overcoming the subjectivity and bias of traditional evaluation methods. A multi-objective optimization approach, based on a non-dominated sorting genetic algorithm, simultaneously considered multiple objectives, including silver recovery rate, purity, energy consumption, and cost, resulting in a series of balanced Pareto optimal solutions, providing diverse options for decision-making. Through cluster analysis, sensitivity analysis and multiple regression analysis, the interaction patterns among process parameters were deeply revealed, the influence mechanism of key parameters was verified, and theoretical support was provided for process parameter optimization.

[0083] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described systems, systems and units can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0084] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention is essentially or partly contributed to the prior art or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a silver electrolysis process parameter design device based on multi-objective optimization (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0085] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments can still be modified, or some of the technical features thereof can be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for designing silver electrolysis process parameters based on multi-objective optimization, characterized in that: include: Perform differential time series parameter decomposition on the silver electrolysis process operation data to obtain a sensitive parameter set and a baseline parameter set; Performing reweighted periodic feature extraction on the sensitive parameter set and the reference parameter set to establish a dynamic mathematical model of silver electrolysis process parameters; Based on the dynamic mathematical model of the silver electrolysis process parameters, the physical and chemical process numerical simulation was performed using COMSOL Multiphysics software to obtain a response surface model; According to the response surface model, a process parameter combination evaluation value sequence is generated, and based on the process parameter combination evaluation value sequence, multi-objective optimization of silver electrolysis process parameters is performed, and a silver electrolysis process parameter optimization plan is output.

2. The silver electrolysis process parameter design method based on multi-objective optimization according to claim 1, characterized in that: The differential time series parameter decomposition of the silver electrolysis process operation data is performed to obtain a sensitive parameter set and a reference parameter set, including: Arrange the silver electrolysis process operation data in time series and construct a parameter matrix including current density, electrolyte concentration, temperature, pH value, and voltage; Establishing a reference characteristic spectrum of normal operating condition parameters and a comparative characteristic spectrum of different operating condition parameters based on the parameter matrix; Calculating the difference between the reference characteristic spectrum and the comparison characteristic spectrum to obtain a difference matrix, and converting the difference matrix into a parameter change spectrum through Fourier transform; Constructing a convex optimization mathematical model for minimizing residuals based on the parameter variation spectrum and the process index difference vector, and solving to obtain the parameter influence weight vector; Parameters whose weight values ​​in the parameter influence weight vector are greater than a first threshold are classified into a sensitive parameter set, and parameters whose weight values ​​in the parameter influence weight vector are between the first threshold and the second threshold are classified into a reference parameter set.

3. The silver electrolysis process parameter design method based on multi-objective optimization according to claim 1, characterized in that: The step of performing reweighted periodic feature extraction on the sensitive parameter set and the reference parameter set to establish a dynamic mathematical model of silver electrolysis process parameters includes: Normalizing the sensitive parameter set and the reference parameter set to obtain a sensitive normalized parameter set and a reference normalized parameter set; Calculating the temporal correlation quantification parameter relationship between parameters based on the sensitive normalized parameter set and the reference normalized parameter set to obtain a parameter temporal characteristic analysis matrix; Decomposing the parameter time series characteristic analysis matrix into periodic components and non-periodic components, and applying an exponential non-convex function to the periodic components to obtain a periodic characteristic matrix after feature enhancement; A multivariate autoregressive model is established based on the sensitive normalized parameter set and the benchmark normalized parameter set, and the coefficient matrix of the multivariate autoregressive model is reweighted and adjusted according to the feature-enhanced periodic characteristic matrix to establish a dynamic mathematical model of silver electrolysis process parameters.

4. The silver electrolysis process parameter design method based on multi-objective optimization according to claim 1, characterized in that: The dynamic mathematical model of the silver electrolysis process parameters is used to perform numerical simulation of the physical and chemical process using COMSOL Multiphysics software to obtain a response surface model, including: Create a three-dimensional electrolytic cell model based on the electrolytic cell geometry, and set the geometric parameters of the anode, cathode, electrolyte area, electrode conductive device, and cell structure; Setting material physical parameters for the three-dimensional electrolytic cell model, setting the anode material to coarse silver, the cathode material to a pure silver plate, and the electrolyte to silver nitrate and nitric acid solution; Based on the dynamic mathematical model of the silver electrolysis process parameters, an electrochemical module and a transport phenomenon module are applied, and a coupled physical field model of electrode reaction and ion transport is established using COMSOL Multiphysics software; Adding a heat conduction module to the coupled physical field model to form a comprehensive numerical simulation model including Joule heat generation and transfer; Adaptively meshing and solving the comprehensive numerical simulation model using finite element methods to obtain current distribution, silver ion concentration distribution, potential distribution, temperature distribution, silver deposition rate, and energy consumption data; Based on the current distribution, the silver ion concentration distribution, the potential distribution, the temperature distribution, the silver deposition rate and the energy consumption data, a mapping relationship between process parameters and silver recovery rate, silver purity, energy consumption and cost is established to form a response surface model.

5. The silver electrolysis process parameter design method based on multi-objective optimization according to claim 1, characterized in that: The method comprises generating a process parameter combination evaluation value sequence according to the response surface model, performing multi-objective optimization of silver electrolysis process parameters based on the process parameter combination evaluation value sequence, and outputting a silver electrolysis process parameter optimization scheme, including: Evaluate multiple groups of different first silver electrolysis process parameter combinations based on the response surface model to obtain response value data of each group of silver electrolysis process parameters in terms of silver recovery rate, silver purity, energy consumption and cost; Arranging the response value data into an original decision matrix including all first silver electrolysis process parameter combinations, and normalizing the original decision matrix to obtain a standardized decision matrix; Calculating the entropy value of each indicator based on the standardized decision matrix to generate an objective weight vector, and calculating a weighted standardized decision matrix using the objective weight vector and the standardized decision matrix; Determining an ideal solution and a negative ideal solution from the weighted standardized decision matrix, and constructing an indicator correlation matrix, and using the indicator correlation matrix to correct the distances of each first silver electrolysis process parameter combination to the ideal solution and the negative ideal solution to obtain a target distance; Calculating a comprehensive evaluation value of each first silver electrolysis process parameter combination using the target distance to form a process parameter combination evaluation value sequence; Multi-objective optimization of silver electrolysis process parameters is performed based on the process parameter combination evaluation value sequence, and a silver electrolysis process parameter optimization plan is output.

6. The silver electrolysis process parameter design method based on multi-objective optimization according to claim 5, characterized in that: The multi-objective optimization of silver electrolysis process parameters based on the process parameter combination evaluation value sequence and outputting a silver electrolysis process parameter optimization plan include: defining a multi-objective optimization function based on the process parameter combination evaluation value sequence, wherein the multi-objective optimization function includes maximizing silver recovery rate, maximizing silver purity, minimizing energy consumption, and minimizing production cost; Setting value range constraints for current density, electrolyte concentration, temperature, pH value, and voltage, and constructing a process parameter value space based on the value range constraints; Randomly generating an initial parameter combination population that satisfies the constraint conditions within the process parameter value space, performing non-dominated sorting on the second silver electrolysis process parameter combinations in the initial parameter combination population, dividing the initial parameter combination population into different non-dominated layers, and calculating the crowding distance within each non-dominated layer; Selecting parent individuals using a binary tournament selection operation based on the non-dominated layer and the crowding distance, and performing simulated binary crossover and polynomial mutation operations to generate a child population; The parent population composed of parent individuals is merged with the child population, non-dominated sorting is performed, and the new generation population is selected according to the crowding distance. The cycle is iterated until convergence, and the optimization plan for the silver electrolysis process parameters is output.

7. The silver electrolysis process parameter design method based on multi-objective optimization according to claim 6, characterized in that: The method of selecting parent individuals by using a binary tournament selection operation based on the non-dominated layer and the crowding distance, and performing simulated binary crossover and polynomial mutation operations to generate a child population includes: Randomly selecting two individuals with a second silver electrolysis process parameter combination from the current population as candidate individuals, comparing the candidate individuals according to the non-dominated layer level and the crowding distance, and selecting an individual with a second silver electrolysis process parameter combination having a higher non-dominated level or a larger crowding distance in the same non-dominated level as a parent individual; Repeating the binary tournament selection operation until a preset number of parent individuals are selected to form a parent individual set, and randomly pairing the parent individual set to form mating pairs; For each mating pair, determining whether to perform a crossover operation based on the crossover probability; if it is determined to perform a crossover operation, a simulated binary crossover method is used to generate an offspring individual pair; if not, the mating pair is directly retained as the offspring individual pair; generating an initial offspring population based on the offspring individual pairs, and determining whether to perform a polynomial mutation operation on each silver electrolysis process parameter combination individual in the initial offspring population according to the mutation probability; For the silver electrolysis process parameter combination individual determined to undergo polynomial mutation, polynomial mutation is performed on each element in the corresponding parameter vector according to the mutation probability and the distribution index to obtain a mutated parameter vector, and the mutated parameter vector is used to replace the original second silver electrolysis process parameter combination individual; The response surface model is used to evaluate the objective function values ​​of all individual combinations of silver electrolysis process parameters after variation, and ultimately form a progeny population.

8. A silver electrolysis process parameter design system based on multi-objective optimization, characterized in that: A method for designing silver electrolysis process parameters based on multi-objective optimization according to any one of claims 1 to 7 is provided, wherein the silver electrolysis process parameter design system based on multi-objective optimization comprises: A decomposition module is used to perform differential time series parameter decomposition on the silver electrolysis process operation data to obtain a sensitive parameter set and a baseline parameter set; A feature extraction module, configured to perform reweighted periodic feature extraction on the sensitive parameter set and the reference parameter set, and establish a dynamic mathematical model of silver electrolysis process parameters; A numerical simulation module is used to perform a numerical simulation of the physical and chemical process based on the dynamic mathematical model of the silver electrolysis process parameters using COMSOL Multiphysics software to obtain a response surface model; The multi-objective optimization module is used to generate a process parameter combination evaluation value sequence according to the response surface model, and perform multi-objective optimization of silver electrolysis process parameters based on the process parameter combination evaluation value sequence, and output a silver electrolysis process parameter optimization plan.

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