A method for predicting the capacity of a sodium-ion battery

Abstract

The present application relates to the technical field of battery management and electrochemical modeling, in particular to a sodium-ion battery capacity prediction method, comprising: dividing the particle swarm into multiple subgroups and initializing them according to the differences in battery working characteristics, and searching cooperatively through sharing the global optimal solution among the subgroups; constructing a weighted fitness function that fuses temperature and electrolyte concentration exponential attenuation factors, so that the optimization process is consistent with the physical mechanism of the battery; adopting dynamic inertia weight and adaptive learning factor to balance the global exploration and local search capabilities; and introducing Pareto front multi-objective optimization to handle the trade-off between multiple indexes such as capacity and service life. The present application can accurately fit the parameters of the capacity attenuation model, effectively overcome the defects of traditional methods such as being easily trapped in local optimum and low prediction accuracy, significantly improve the prediction accuracy, stability and engineering practical value under complex working conditions, and provide a reliable basis for battery state evaluation and service life management.

Description

Technical Field

[0001] This invention relates to the field of battery management and electrochemical modeling technology, specifically a method for predicting the capacity of sodium-ion batteries. Background Technology

[0002] Sodium-ion batteries, as a novel electrochemical energy storage device with abundant resources and low cost, have shown broad application prospects in large-scale energy storage, electric vehicles, and other fields. Accurately predicting the capacity decay trend and remaining lifespan of sodium-ion batteries is crucial for optimizing battery design, ensuring safe and reliable system operation, and achieving precise state management. However, the performance decay of sodium-ion batteries is a complex nonlinear process involving multiple physics fields and multiple scales. The battery's capacity retention and lifespan are affected by the coupling of various factors such as operating temperature, electrolyte concentration, electrode material system, and charge / discharge rate. The interaction between these factors makes battery capacity prediction a typical multi-parameter, nonlinear optimization problem.

[0003] Currently, this technology field mainly suffers from the following limitations:

[0004] Traditional empirical models lack accuracy: Existing battery empirical models (such as simple exponential decay and polynomial models) often fail to fully consider the complex electrochemical mechanisms inside the battery. In particular, these models generally lack a quantitative description of the dynamic effects of key operating parameters (such as temperature and electrolyte concentration), resulting in a sharp drop in prediction accuracy under changing operating conditions, making it difficult to accurately reflect the actual decay behavior of the battery.

[0005] Limitations of general-purpose optimization algorithms: While intelligent optimization algorithms such as Particle Swarm Optimization (PSO) have been attempted for parameter identification, standard PSO algorithms tend to converge prematurely to local optima rather than global optima when dealing with complex optimization problems characterized by high dimensionality, nonlinearity, and multimodality. This is mainly due to its single search strategy and fixed parameter settings, which make it difficult to achieve an effective balance between global exploration and refined local search, resulting in unstable prediction results and low reliability.

[0006] Lack of multi-objective optimization capability: In practical applications, battery performance is often a trade-off between multiple objectives such as capacity, lifespan, and rate performance. Existing prediction methods mostly focus on optimizing a single performance indicator (such as capacity), lacking the ability to coordinate optimization of multiple conflicting objectives. They cannot provide a comprehensive Pareto optimal solution set for battery design and usage strategies, making it difficult to meet the needs of comprehensive performance optimization in engineering applications.

[0007] The algorithm is disconnected from the physical mechanism: Most current optimization prediction methods treat the battery system as a black box, resulting in a serious disconnect between the optimization algorithm and the physicochemical characteristics of the battery itself. The design of algorithm parameters and fitness functions lacks specific consideration for the working mechanism unique to sodium-ion batteries (such as the degradation path under different material systems), causing deviations between the optimization process and the actual physical process of the battery, thus limiting the practicality and generalization ability of the prediction model.

[0008] Therefore, there is an urgent need in this field for a high-precision capacity prediction method that can closely integrate the working mechanism of sodium-ion batteries, possess strong global optimization capabilities, and effectively handle multi-objective trade-offs, in order to overcome the above-mentioned deficiencies of existing technologies. Summary of the Invention

[0009] The purpose of this invention is to provide a method for predicting the capacity of sodium-ion batteries, so as to solve the problems of traditional methods mentioned in the background art being prone to getting trapped in local optima and having low prediction accuracy.

[0010] To achieve the above objectives, the present invention provides the following technical solution:

[0011] A method for predicting the capacity of a sodium-ion battery includes the following steps:

[0012] S1 divides the particle swarm into multiple subgroups, each of which is initialized according to the different characteristics of the sodium-ion battery, and the subgroups share the global optimal solution.

[0013] S2 incorporates the historical optimal solution within the subgroup and the global optimal solution into the velocity update formula for each particle to update the particle position.

[0014] S3 employs a weighted fitness function based on the characteristics of sodium-ion batteries, which includes a weighted decay factor for temperature and electrolyte concentration to dynamically adjust the battery performance target.

[0015] S4 employs a particle update mechanism based on dynamic inertia weights and adaptive learning factors. As the number of iterations increases, the inertia weights are gradually reduced and the learning factors are increased.

[0016] S5 determines the Pareto optimal solution through non-dominated sorting and updates the particle positions based on the Pareto front, performing multi-objective optimization that combines battery capacity, battery life, and charging speed performance indicators.

[0017] Preferably, in the particle swarm division step, it is assumed that the particle swarm has a total of N particles, which are divided into M subgroups, and the number of particles in each subgroup is... ,satisfy Each subgroup of particles is initialized within the battery's working space according to the battery's characteristics;

[0018] In the particle position initialization step, the position and velocity of each particle are initialized according to the working characteristics of the battery, and the specific initialization function is set according to the battery's working temperature and electrolyte concentration.

[0019] In the particle update formula, the particle velocity update formula is:

[0020] ;

[0021] in, It is a particle In subgroup The speed in the middle, It is a particle In subgroup The best historical position in China It is a subgroup The globally optimal position.

[0022] Preferably, in the weighted fitness function, the battery performance objective function includes the battery capacity retention rate and service life, and the fitness function is corrected by the decay factor of weighted temperature and electrolyte concentration, and the specific decay function adopts the exponential decay form;

[0023] The performance of sodium-ion batteries is typically comprised of multiple objectives, the most common being capacity retention and battery life. The objective function is set as a combination function of battery performance, and usually includes the following components:

[0024] ;

[0025] in: This represents the retention rate of battery capacity. This indicates the battery's lifespan;

[0026] The battery's operating environment has a significant impact on its performance; therefore, it is necessary to weight the fitness function and set weighting factors. and To represent the effects of temperature and electrolyte concentration on battery performance, then:

[0027] ;

[0028] in: and It is the degradation factor of battery performance as temperature and electrolyte concentration change; It refers to the battery operating temperature; It refers to the electrolyte concentration.

[0029] Preferably, the weighting factors for the battery capacity and lifespan targets adopt an exponential decay form, which is adjusted according to the battery's operating temperature and electrolyte concentration, as follows:

[0030] (1) Increased temperature and electrolyte concentration usually lead to a decrease in battery capacity and lifespan. This relationship is described using an exponential decay function. As the operating temperature and electrolyte concentration increase, battery performance will decrease exponentially. The specific decay function is as follows: This decay function can dynamically adjust the battery's performance under different environments.

[0031] (2) During the optimization process, the battery is evaluated according to different working environments. Therefore, for each particle, its fitness value is: ;in, It is a small perturbation term that ensures that the fitness value of each particle is not too sensitive to changes in the environment.

[0032] Preferably, the particle update mechanism for the dynamic inertia weight and adaptive learning factor includes the following steps:

[0033] Inertia weights in particle swarm optimization Controlling the inertia of a particle directly affects its exploration range; therefore, dynamic inertia weights must be designed.

[0034] ;in, It is the current iteration number. It is the maximum number of iterations. and These are the maximum and minimum values ​​of the inertia weight, respectively.

[0035] During velocity updates, the particle's velocity is guided by the historical optimal solution and the global optimal solution, and is also adjusted according to dynamic weights:

[0036] ,in, and These are random numbers, used to control the randomness of the particle search.

[0037] In addition to inertial weights, the learning factors of particles also need to be adaptively adjusted:

[0038] ;

[0039] By dynamically adjusting the inertia weight and learning factor, the particles can extensively explore the solution space in the early stages.

[0040] Preferably, the multi-objective optimization determines the Pareto optimal solution through non-dominated sorting and updates the particle positions based on the Pareto front to optimize multiple performance objectives, specifically including the following steps:

[0041] For sodium-ion batteries, performance targets typically include capacity, battery life, and charging speed. The objective function is set as a combination function of battery performance, and usually includes the following parts:

[0042] ,in, This represents the battery capacity retention rate; Indicates battery life; Indicates charging time;

[0043] In multi-objective optimization, a solution is considered Pareto optimal if no solution exists such that:

[0044] ,

[0045] Solution It is not dominated by other solutions on any objective, and is superior to at least one objective. ;

[0046] The Pareto front is determined by non-dominated sorting, the optimal solution set is selected, and the particle updates its position based on the solutions of the Pareto front. By using the Pareto front, the algorithm can find the optimal balance between multiple objectives, thereby improving the overall performance of the battery and avoiding the limitations of single-objective optimization.

[0047] Preferably, the sodium-ion battery uses nickel cobalt aluminum oxide (NCA) and sodium iron phosphate (NaFePO4) as the positive electrode material, sodium titanium oxide (Na4Ti4O12) as the negative electrode material, and lithium difluorophosphate (LiPF6) and lithium hexafluorophosphate (LiBF4) as the electrolyte base to optimize battery performance. The preparation steps of the sodium-ion battery positive electrode material include the following steps:

[0048] T1: Prepare equipment and materials including an adjustable temperature high-temperature furnace, weighing equipment, nickel nitrate Ni(NO3)2, cobalt nitrate Co(NO3)2, aluminum chloride AlCl3, iron phosphate FePO4, and a sintering furnace under an oxygen atmosphere;

[0049] T2: Dissolve each chemical precursor separately in an appropriate amount of deionized water to form a homogeneous solution, and then mix all the solutions to ensure that the components are homogeneous;

[0050] T3 Drying treatment: Place the mixed solution in an oven and dry at 80°C for 24 hours to remove excess moisture;

[0051] T4 sintering process: The dried powder is placed in a high-temperature furnace, and the furnace temperature is controlled between 900℃ and 1100℃ for high-temperature sintering. The sintering time is 6 hours to promote the crystallization of the material and ensure the stability of the structure.

[0052] T5 Cooling and Sieving: After sintering, the product is naturally cooled to room temperature, and then sieved to remove unqualified particles, ensuring the uniformity of the material particles, and obtaining a nickel cobalt aluminum oxide (NCA) and sodium iron phosphate (NaFePO4) composite material with high specific energy density.

[0053] Preferably, the preparation steps of the sodium-ion battery anode material include the following steps:

[0054] Equipment and materials required for R1: solution stirrer; high-temperature furnace; tetrasodium titanate; sodium chloride; furnace under hydrogen atmosphere;

[0055] R2 Dissolution and Mixing: First, add tetrasodium titanate and sodium chloride to deionized water and stir until homogeneous to ensure optimal solubility of the titanium and sodium sources.

[0056] R3 Precipitation reaction: The titanium source and sodium source in the mixed solution are chemically reacted to obtain sodium titanium oxide precipitate; this step requires pH adjustment to ensure complete chemical reaction;

[0057] R4 Filtration and Washing: The precipitate is extracted by filtration and repeatedly washed with deionized water to remove residual impurities;

[0058] R5 Drying: Place the filtered precipitate in an oven, set the temperature to 80℃, and dry for 24 hours until a dry powder is obtained;

[0059] R6 High-Temperature Heat Treatment: The dried powder is placed in a high-temperature furnace and heat-treated under a hydrogen atmosphere at a temperature of 700℃ for 6 hours to ensure the complete formation of sodium titanium oxide Na4Ti5O12, resulting in high-purity sodium titanium oxide Na4Ti5O12 powder with high electrochemical stability.

[0060] Preferably, the preparation steps of the sodium-ion battery electrolyte include the following steps:

[0061] Q1 Required equipment and materials: electrolyte stirrer, deionized water, sodium salt NaPF6, lithium hexafluorophosphate LiPF6, electrolyte solvents including ethylene carbonate EC and dimethyl carbonate DMC;

[0062] Q2 Dissolving Sodium Salt: Dissolve sodium salt NaPF6 in deionized water, ensuring complete dissolution to form the basis of sodium ion electrolyte;

[0063] Q3 Add lithium salt: Add lithium hexafluorophosphate (LiPF6) to the sodium salt solution and mix thoroughly;

[0064] Q4 Electrolyte Solvent: Add ethylene carbonate EC and dimethyl carbonate DMC, and stir with a stirrer until completely mixed;

[0065] Q5 Settling and Filtration: Let the prepared electrolyte stand for several hours to remove any air bubbles that may be generated; finally, filter it through a 0.45μm filter membrane to remove insoluble impurities and obtain the sodium-ion battery electrolyte.

[0066] Preferably, the sodium-ion battery uses a porous polymer separator to improve the safety and stability of the battery. The preparation of the porous polymer separator includes the following steps:

[0067] Equipment and materials required for P1: Polypropylene (PP) or polyethylene (PE), polypropylene film mold, high-temperature oven

[0068] P2 Polymer Dissolution: Dissolve polypropylene (PP) or polyethylene (PE) in a suitable solvent to form a homogeneous solution;

[0069] P3 Coating and Film Formation: The solution is uniformly coated onto the mold to ensure the uniformity and thickness of the film;

[0070] P4 heat treatment: The coated film is heated at 120°C for 24 hours in an oven to promote complete curing of the film and form a membrane with high porosity.

[0071] P5 Cutting and Inspection: The membrane after film formation is cut into appropriate sizes, and its porosity and thermal stability are tested to ensure that it meets the standard requirements, thus obtaining a porous polymer membrane.

[0072] Compared with the prior art, the beneficial effects of the present invention are:

[0073] This invention provides a sodium-ion battery capacity prediction method that deeply integrates the physicochemical mechanisms of batteries with advanced optimization algorithms, creatively solving the problems of insufficient accuracy and premature convergence that traditional methods encounter when dealing with highly nonlinear, multi-factor coupled battery systems. Specifically, this is reflected in:

[0074] 1. Significantly improved prediction accuracy: By directly embedding key physical parameters of battery operation, such as temperature and electrolyte concentration, into the fitness function of the optimization algorithm in the form of exponential decay factors, the prediction model closely matches the actual electrochemical mechanism of the battery, greatly overcoming the shortcomings of traditional black box models in terms of insufficient accuracy under complex working conditions.

[0075] 2. Effectively avoids local optima and has strong global search capabilities: Employing a cluster optimization strategy, different subgroups can explore different regions of the solution space in parallel, and then collaborate in the search through a global information sharing mechanism. Combined with dynamically adjusted inertia weights, the algorithm can explore extensively in the early stages of iteration and converge precisely in the later stages, thus efficiently finding the global optimum and solving the problem of premature convergence in traditional optimization algorithms.

[0076] 3. More practical multi-objective balance optimization: Adopting a multi-objective optimization method based on the Pareto frontier, it can simultaneously handle multiple mutually constraining performance indicators such as battery capacity, lifespan, and charging speed, and output a set of optimal balance solutions. This provides a scientific and comprehensive basis for battery design and performance evaluation, rather than a single or potentially one-sided optimization result.

[0077] 4. Highly practical and directly serves the research and development of high-performance batteries: This method is deeply integrated with specific high-performance electrode materials and electrolyte systems. Its optimization process and prediction results are directly targeted at the application scenarios of high-performance sodium-ion batteries, enabling researchers to quickly and accurately evaluate and screen battery formulations and operating parameters, shorten the research and development cycle, and reduce development costs. Attached Figure Description

[0078] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are explained in detail together with the embodiments of the invention, but do not constitute a limitation thereof.

[0079] Figure 1 The convergence curve of the improved particle swarm optimization algorithm in the process of finding the optimal battery model parameters is shown in the figure.

[0080] Figure 2 This is a prediction diagram of the sodium-ion battery capacity of the present invention;

[0081] Figure 3 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0082] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0083] Predicting the performance of sodium-ion batteries is a complex multidimensional optimization problem, with multiple factors influencing battery performance. These include factors such as temperature, electrolyte concentration, and electrode material structure. The impact of these factors on battery performance is highly nonlinear, and their weights vary under different conditions. Therefore, traditional particle swarm optimization (PSO) methods may lead to local optima, especially when dealing with complex systems.

[0084] The particle swarm optimization algorithm based on cluster optimization divides the particle swarm into multiple subgroups, and each subgroup is initialized according to the different characteristics of sodium-ion batteries. The subgroups share the global optimal solution.

[0085] In the optimization problem of sodium-ion batteries, considering that the search directions of different particle swarms may differ significantly, the particle swarms are divided into multiple sub-swarms. Each sub-swarm is optimized independently for a specific battery characteristic.

[0086] 1.1 Particle swarming:

[0087] Assuming the total number of particles is Each particle is divided into Each subgroup. The number of particles is ,satisfy:

[0088] ;

[0089] The particles in each subgroup are initialized within the battery's working space, and the optimization objective for each subgroup can vary depending on the characteristics of the sodium-ion battery (such as battery type, discharge rate, temperature, etc.).

[0090] 1.2 Particle position initialization:

[0091] The position and velocity of each particle are initialized based on the battery's operating characteristics. For example, assuming the battery's operating temperature is... The electrolyte concentration is ,particle The initialization position can be initialized using the following function:

[0092]

[0093] in, and It is a subgroup Neutron The battery operating temperature and electrolyte concentration.

[0094] Second, the velocity update formula for each particle incorporates the historical optimal solution within the subgroup and the global optimal solution.

[0095] 2.1 Particle Update Formula:

[0096] The position of each particle is updated by introducing the standard update formula for particle swarm optimization. For subswarms... particles The particle velocity update formula is as follows:

[0097]

[0098] in, It is a particle In subgroup The speed in the middle, It is a particle In subgroup The best historical position in China It is a subgroup The globally optimal position.

[0099] 2.2 Particle Position Update

[0100] After the velocity update, the particle's position The update is as follows:

[0101]

[0102] 2.3 Optimized sharing among subgroups:

[0103] Each subgroup influences the others by sharing its optimal solution, thus ensuring the capability of global search:

[0104]

[0105] in The objective function for predicting battery performance is denoted as .

[0106] 2.4 Global Information Sharing:

[0107] Optimal solutions among subgroups It will affect the search process of other subgroups, ensuring the collaborative optimization of the global optimal solution.

[0108] By dividing the particle swarm into multiple subgroups, each subgroup independently searches for its optimal solution while sharing the global optimal solution, the drawback of all particles concentrating in a single solution space is avoided. This strategy improves the efficiency of global optimization, especially in battery performance prediction. Considering the diversity of battery operating conditions, subgroup optimization significantly enhances the stability and accuracy of the search.

[0109] III. A weighted fitness function based on the characteristics of sodium-ion batteries, which includes a weighted decay factor for temperature and electrolyte concentration to dynamically adjust the battery performance target.

[0110] The performance of sodium-ion batteries is affected by multiple factors, such as battery temperature, charge / discharge rate, and electrolyte concentration. Traditional PSO algorithms do not consider these physical characteristics, resulting in an inability to accurately simulate the battery's actual performance under different operating conditions during optimization. Therefore, a weighted fitness function needs to be designed to account for the impact of these characteristics on battery performance.

[0111] 3.1 Battery performance objective function:

[0112] The performance of sodium-ion batteries is typically determined by multiple objectives, the most common being capacity retention and battery life. Setting the objective function... A combination function of battery performance typically includes the following parts:

[0113]

[0114] in: This represents the retention rate of battery capacity. This indicates the battery's lifespan.

[0115] 3.2 Introduction to Battery Characteristics:

[0116] The battery's operating environment (such as temperature and electrolyte concentration) has a significant impact on battery performance, therefore, the fitness function needs to be weighted. Weighting factors need to be set. and To illustrate the effects of temperature and electrolyte concentration on battery performance:

[0117]

[0118] in: and It is the degradation factor of battery performance as temperature and electrolyte concentration change; It refers to the battery operating temperature; It refers to the electrolyte concentration.

[0119] IV. The weighting factors for battery capacity and lifespan targets adopt an exponential decay form and are adjusted according to the battery's operating temperature and electrolyte concentration.

[0120] 4.1 Decrease function of temperature and electrolyte concentration:

[0121] Increased temperature and electrolyte concentration typically lead to a decline in battery capacity and lifespan. This relationship is described using an exponential decay function. As operating temperature increases... and electrolyte concentration As the amount of [something] increases, battery performance will decline exponentially, with the specific decline function being:

[0122]

[0123] This decay function can dynamically adjust the battery's performance under different environments.

[0124] 4.2 Correction of the fitness function:

[0125] During the optimization process, the battery is evaluated based on different operating environments. Therefore, for each particle... Its fitness value is:

[0126]

[0127] in, It is a small perturbation term that ensures that the fitness value of each particle is not too sensitive to changes in the environment.

[0128] By introducing weighted decay factors based on temperature and electrolyte concentration, the algorithm can more accurately reflect the performance of sodium-ion batteries under different operating conditions during the optimization process. This provides an effective adaptation mechanism for the diversity and complexity of batteries in practical applications, thereby improving prediction accuracy.

[0129] V. A particle update mechanism based on dynamic inertia weights and adaptive learning factors: as the number of iterations increases, the inertia weights are gradually reduced and the learning factor is increased.

[0130] In the performance prediction of sodium-ion batteries, traditional particle optimization (PSO) may get trapped in local optima due to the nonlinearity and multimodal nature of the objective function. To overcome this problem, a dynamic particle update mechanism was designed to ensure that particles can avoid local optima during the optimization process.

[0131] 5.1 Dynamic Inertia Weight:

[0132] Inertia weights in particle swarm optimization Controlling the particle's inertia directly affects its exploration range. To maintain greater exploratory activity in the early stages of the search and enhance local search during convergence, a dynamic inertia weight was designed:

[0133]

[0134] in, It is the current iteration number. It is the maximum number of iterations. and These are the maximum and minimum values ​​of the inertia weight, respectively.

[0135] 5.2 Speed ​​Update Formula:

[0136] During velocity updates, the particle's velocity is influenced by the historical optimal solution. and the global optimal solution Guided by dynamic weights, and adjusted accordingly:

[0137]

[0138] in, and It is a random number, which controls the randomness of the particle search.

[0139] 5.3 Adaptive Learning Factors:

[0140] In addition to inertial weights, the learning factors of particles also need to be adaptively adjusted:

[0141]

[0142] By dynamically adjusting the inertia weight and learning factor, the particle can explore the solution space extensively in the early stage, and then focus on searching for local optimal solutions in the later stage, thus avoiding the local optimality dilemma of traditional PSO in nonlinear problems.

[0143] VI. A multi-objective optimization method based on the Pareto front is proposed. The Pareto optimal solution is determined by non-dominated sorting, and the particle position is updated according to the Pareto front to optimize multiple performance objectives.

[0144] Predicting the performance of sodium-ion batteries involves multiple objectives. These objectives often conflict, and optimizing only one objective may lead to a decline in the performance of others. Therefore, the Pareto front method is used for multi-objective optimization to ensure a balance is found among the objectives.

[0145] 6.1 Multi-objective optimization objective function:

[0146] For sodium-ion batteries, performance targets typically include capacity, battery life, and charging speed. Setting the objective function... A combination function of battery performance typically includes the following parts:

[0147]

[0148] in, This represents the battery capacity retention rate; Indicates battery life; This represents the charging time.

[0149] 6.2 Pareto optimal solution:

[0150] In multi-objective optimization, the solution It is considered Pareto optimal if no solution exists. Make:

[0151]

[0152] This indicates the solution. It is not dominated by other solutions on any objective, and is superior to at least one objective. .

[0153] 6.3 Calculation of the Pareto front:

[0154] The Pareto front is determined by non-dominated sorting, and the optimal solution set is selected. The particle updates its position based on the solution of the Pareto front:

[0155]

[0156] By using the Pareto front, the algorithm can find the optimal balance between multiple objectives, thereby improving the overall performance of the battery and avoiding the limitations of single-objective optimization.

[0157] VII. Applicable to multi-objective optimization in sodium-ion battery performance prediction, combining performance indicators such as battery capacity, battery life, and charging speed.

[0158] 7.1 Particle Swarm Optimization Update Formula:

[0159] For subgroups Particles in The updated formula is:

[0160]

[0161] 7.2 Weighted formula for fitness function:

[0162] Particle fitness function The weighting will be based on the battery's operating environment:

[0163]

[0164] 7.3 Particle Update and Multi-Objective Optimization Formulas:

[0165] In multi-objective optimization, the Pareto front method is used to update particle positions:

[0166]

[0167] in, It is the Pareto optimal solution obtained by non-dominated sorting.

[0168] 8. Sodium-ion battery configuration, using nickel cobalt aluminum oxide (NCA) and sodium iron phosphate (NaFePO4) as positive electrode materials, and sodium titanium oxide (Na4Ti5O) as the negative electrode material. 12 Lithium difluorophosphate (LiPF6) and lithium hexafluorophosphate (LiBF4) are used as negative electrode materials and as electrolyte bases to optimize battery performance.

[0169] Experimental Step 1: Synthesis of Cathode Material

[0170] Objective: To synthesize a composite material of nickel cobalt aluminum oxide (NCA) and sodium iron phosphate (NaFePO4) as a cathode material.

[0171] Required equipment and materials: High-temperature furnace (adjustable temperature, up to 1200℃); weighing apparatus; nickel nitrate (Ni(NO3)2); cobalt nitrate (Co(NO3)2); aluminum chloride (AlCl3); ferric phosphate (FePO4); sintering furnace under oxygen atmosphere

[0172] Dissolution and mixing: Dissolve each chemical precursor separately in an appropriate amount of deionized water to form a homogeneous solution. Then mix all solutions to ensure uniform composition.

[0173] Drying treatment: Place the mixed solution in an oven and dry at 80°C for 24 hours to remove excess moisture.

[0174] Sintering process: The dried powder is placed in a high-temperature furnace, and the furnace temperature is controlled between 900℃ and 1100℃ for high-temperature sintering. The sintering time is 6 hours to promote the crystallization of the material and ensure the stability of the structure.

[0175] Cooling and sieving: After sintering, the product is allowed to cool naturally to room temperature, and then sieved to remove unqualified particles, ensuring the uniformity of the material particles.

[0176] A nickel-cobalt-aluminum oxide (NCA) and sodium iron phosphate (NaFePO4) composite material with high specific energy density was obtained.

[0177] Experimental Step 2: Synthesis of Anode Material

[0178] Objective: To synthesize sodium titanium oxide (Na4Ti5O) 12 Anode material.

[0179] Required equipment and materials: solution stirrer; high-temperature furnace; tetrasodium titanate; sodium chloride; furnace under hydrogen atmosphere.

[0180] Dissolution and mixing: First, add tetrasodium titanate and sodium chloride to deionized water and stir well to ensure that the solubility of the titanium source and sodium source is optimal.

[0181] Precipitation reaction: The titanium source and sodium source in the mixed solution undergo a chemical reaction to obtain a precipitate of sodium titanium oxide. This step requires pH adjustment to ensure the chemical reaction is complete.

[0182] Filtration and washing: The precipitate is extracted by filtration and repeatedly washed with deionized water to remove residual impurities.

[0183] Drying: Place the filtered precipitate in an oven at 80°C and dry for 24 hours until a dry powder is obtained.

[0184] High-temperature heat treatment: The dried powder was placed in a high-temperature furnace and heat-treated under a hydrogen atmosphere at 700℃ for 6 hours to ensure the integrity of the sodium titanium oxide (Na4Ti5O) 12 The complete formation of ).

[0185] High-purity sodium titanium oxide (Na4Ti5O) was obtained. 12The powder has high electrochemical stability.

[0186] Experimental Step 3: Electrolyte Preparation

[0187] Objective: To formulate an electrolyte that exhibits good stability and conductivity under different temperature conditions.

[0188] Required equipment and materials: electrolyte stirrer; deionized water; sodium salt (NaPF6); lithium hexafluorophosphate (LiPF6); electrolyte solvent (ethylene carbonate (EC) and dimethyl carbonate (DMC))

[0189] Dissolving sodium salt: Dissolve sodium salt NaPF6 in deionized water to ensure complete dissolution and form the basis of sodium ion electrolyte.

[0190] Add lithium salt: Add lithium hexafluorophosphate (LiPF6) to the sodium salt solution and mix well.

[0191] Electrolyte solvent: Add ethylene carbonate (EC) and dimethyl carbonate (DMC) and stir until fully mixed.

[0192] Settling and Filtration: Let the prepared electrolyte stand for several hours to remove any air bubbles that may have formed. Finally, filter through a 0.45μm filter membrane to remove insoluble impurities.

[0193] 9. Sodium-ion batteries use porous polymer separators to improve battery safety and stability.

[0194] Experimental Step 4: Diaphragm Preparation

[0195] Objective: To prepare a high-porosity membrane for sodium-ion batteries to ensure efficient battery operation.

[0196] Required equipment and materials: Polypropylene (PP) or polyethylene (PE); Polypropylene film mold; High-temperature drying oven

[0197] Polymer dissolution: Dissolve polypropylene (PP) or polyethylene (PE) in a suitable solvent to form a homogeneous solution.

[0198] Coating and film formation: The solution is evenly coated onto the mold to ensure the uniformity and thickness of the film.

[0199] Heat treatment: The coated membrane is heated at 120°C for 24 hours in an oven to promote complete curing of the membrane and form a membrane with high porosity.

[0200] Cutting and testing: The membrane after film formation is cut into appropriate sizes and its porosity and thermal stability are tested to ensure that it meets the standard requirements.

[0201] 10. The manufacturing method of sodium-ion batteries involves synthesizing positive electrode materials through solid-state synthesis and negative electrode materials through solution synthesis, and using high-purity sodium titanium oxide, sodium iron phosphate and other chemical materials to improve battery performance.

[0202] Experimental Step 5: Battery Assembly

[0203] Objective: To assemble positive and negative electrodes, separator, and electrolyte into a battery.

[0204] Required equipment and materials: battery casing; positive and negative electrode materials; separator; electrolyte

[0205] Positive and negative electrode assembly with separator: The positive electrode material (NCA and NaFePO4 composite material) and the negative electrode material (Na4Ti5O) are assembled. 12 The electrodes are alternately placed with the electrolyte membrane to ensure that the membrane completely covers the positive and negative electrodes.

[0206] Electrolyte injection: In a closed environment, the prepared electrolyte is injected into the assembled battery cell to ensure that the inside of the battery is completely wetted with electrolyte.

[0207] Battery encapsulation: The assembled battery cells are placed into the battery casing and sealed to ensure no leakage inside the battery.

[0208] Activation and Testing: Perform the first charge-discharge cycle and record the battery's initial capacity, discharge plateau, and cycle performance.

[0209] 11. Sodium-ion batteries are suitable for electric vehicles and high-power applications, featuring fast charging and discharging capabilities and long lifespan.

[0210] Sodium-ion battery capacity prediction chart as shown Figure 2 As shown in the table below, the experimental data are as follows:

[0211]

[0212] Choose the experience index model:

[0213]

[0214] in: These are the parameters to be optimized.

[0215] Objective function (minimization):

[0216]

[0217] like Figure 1 As shown, the algorithm settings are as follows:

[0218] Particle swarm size: 50

[0219] Number of groups: 5

[0220] Number of iterations: 200

[0221] Parameter range:

[0222] Algorithm parameters: .

[0223] The core advantage of this invention's sodium-ion battery capacity prediction method lies in its deep integration of the battery's physicochemical mechanisms with advanced optimization algorithms, creatively solving the problems of insufficient accuracy and premature convergence that traditional methods encounter when dealing with highly nonlinear, multi-factor coupled battery systems. Specifically, this is reflected in:

[0224] 1. Significantly improved prediction accuracy: By directly embedding key physical parameters of battery operation, such as temperature and electrolyte concentration, into the fitness function of the optimization algorithm in the form of exponential decay factors, the prediction model closely matches the actual electrochemical mechanism of the battery, greatly overcoming the shortcomings of traditional black box models in terms of insufficient accuracy under complex working conditions.

[0225] 2. Effectively avoids local optima and has strong global search capabilities: Employing a cluster optimization strategy, different subgroups can explore different regions of the solution space in parallel, and then collaborate in the search through a global information sharing mechanism. Combined with dynamically adjusted inertia weights, the algorithm can explore extensively in the early stages of iteration and converge precisely in the later stages, thus efficiently finding the global optimum and solving the problem of premature convergence in traditional optimization algorithms.

[0226] 3. More practical multi-objective balance optimization: Adopting a multi-objective optimization method based on the Pareto frontier, it can simultaneously handle multiple mutually constraining performance indicators such as battery capacity, lifespan, and charging speed, and output a set of optimal balance solutions. This provides a scientific and comprehensive basis for battery design and performance evaluation, rather than a single or potentially one-sided optimization result.

[0227] 4. Highly practical and directly serves the research and development of high-performance batteries: This method is deeply integrated with specific high-performance electrode materials and electrolyte systems. Its optimization process and prediction results are directly targeted at the application scenarios of high-performance sodium-ion batteries, enabling researchers to quickly and accurately evaluate and screen battery formulations and operating parameters, shorten the research and development cycle, and reduce development costs.

[0228] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for predicting the capacity of a sodium-ion battery, characterized in that, Includes the following steps: S1 divides the particle swarm into multiple subgroups, each of which is initialized according to the different characteristics of the sodium-ion battery, and the subgroups share the global optimal solution. S2 incorporates the historical optimal solution within the subgroup and the global optimal solution into the velocity update formula for each particle to update the particle position. S3 employs a weighted fitness function based on the characteristics of sodium-ion batteries, which includes a weighted decay factor for temperature and electrolyte concentration to dynamically adjust the battery performance target. S4 employs a particle update mechanism based on dynamic inertia weights and adaptive learning factors. As the number of iterations increases, the inertia weights are gradually reduced and the learning factors are increased. S5 determines the Pareto optimal solution through non-dominated sorting and updates the particle position according to the Pareto front, performing multi-objective optimization and combining battery capacity, battery life, and charging speed performance indicators. In the weighted fitness function, the battery performance objective function includes the battery capacity retention rate and service life. The fitness function is corrected by the decay factor of weighted temperature and electrolyte concentration. The specific decay function adopts the exponential decay form. The performance of sodium-ion batteries consists of multiple objectives, the most common being capacity retention and lifespan. The objective function is defined as a combination function of battery performance, including the following components: ； in: This represents the retention rate of battery capacity. This indicates the battery's lifespan; The battery's operating environment has a significant impact on its performance; therefore, it is necessary to weight the fitness function and set weighting factors. and To represent the effects of temperature and electrolyte concentration on battery performance, then: ； in: and It is the degradation factor of battery performance as temperature and electrolyte concentration change; It refers to the battery operating temperature; It refers to the electrolyte concentration.

2. The sodium-ion battery capacity prediction method according to claim 1, characterized in that, In the particle swarm division step, it is assumed that the particle swarm has a total of N particles, which are divided into M subgroups, and the number of particles in each subgroup is... ,satisfy Each subgroup of particles is initialized within the battery's working space according to the battery's characteristics; In the particle position initialization step, the position and velocity of each particle are initialized according to the working characteristics of the battery, and the specific initialization function is set according to the battery's working temperature and electrolyte concentration. In the particle update formula, the particle velocity update formula is: ； in, It is a particle In subgroup The speed in the middle, It is a particle In subgroup The best historical position in China It is a subgroup The globally optimal position.

3. The sodium-ion battery capacity prediction method according to claim 1, characterized in that, The weighting factors for the battery capacity and lifespan targets adopt an exponential decay form and are adjusted according to the battery's operating temperature and electrolyte concentration, as follows: (1) Increased temperature and electrolyte concentration lead to a decrease in battery capacity and lifespan. This relationship is described using an exponential decay function. As the operating temperature and electrolyte concentration increase, battery performance will decrease exponentially. The specific decay function is as follows: This decay function can dynamically adjust the battery's performance under different environments. (2) During the optimization process, the battery is evaluated according to different working environments. Therefore, for each particle, the fitness value is: ; in, It is a small perturbation term that ensures that the fitness value of each particle is not too sensitive to changes in the environment.

4. The sodium-ion battery capacity prediction method according to claim 2, characterized in that, The particle update mechanism for the dynamic inertia weights and adaptive learning factors includes the following steps: Inertia weights in particle swarm optimization Controlling the inertia of a particle directly affects its exploration range; therefore, dynamic inertia weights must be designed. ;in, It is the current iteration number. It is the maximum number of iterations. and These are the maximum and minimum values ​​of the inertia weight, respectively. During velocity updates, the particle's velocity is guided by the historical optimal solution and the global optimal solution, and is also adjusted according to dynamic weights: ,in, and These are random numbers, used to control the randomness of the particle search. In addition to inertial weights, the learning factors of particles also need to be adaptively adjusted: ； By dynamically adjusting the inertia weight and learning factor, the particles can extensively explore the solution space in the early stages.

5. The sodium-ion battery capacity prediction method according to claim 1, characterized in that, The multi-objective optimization determines the Pareto optimal solution through non-dominated sorting and updates the particle positions based on the Pareto front to optimize multiple performance objectives. Specifically, it includes the following steps: For sodium-ion batteries, performance targets include capacity, battery life, and charging speed. The objective function is set as a combination function of battery performance, including the following parts: ,in, This represents the battery capacity retention rate; Indicates battery life; Indicates charging time; In multi-objective optimization, a solution is considered Pareto optimal if no solution exists such that: ， Solution It is not dominated by other solutions on any objective, and is superior to at least one objective. ; The Pareto front is determined by non-dominated sorting, the optimal solution set is selected, and the particle updates its position based on the solutions of the Pareto front. By using the Pareto front, the algorithm can find the optimal balance between multiple objectives, thereby improving the overall performance of the battery and avoiding the limitations of single-objective optimization.

6. The sodium-ion battery capacity prediction method according to claim 1, characterized in that, The sodium-ion battery uses nickel cobalt aluminum oxide (NCA) and sodium iron phosphate (NaFePO4) as the positive electrode material, sodium titanium oxide (Na4Ti4O12) as the negative electrode material, and lithium difluorophosphate (LiPF6) and lithium hexafluorophosphate (LiBF4) as the electrolyte base to optimize battery performance. The preparation steps of the sodium-ion battery positive electrode material include the following steps: T1: Prepare equipment and materials including an adjustable temperature high-temperature furnace, weighing equipment, nickel nitrate Ni(NO3)2, cobalt nitrate Co(NO3)2, aluminum chloride AlCl3, iron phosphate FePO4, and a sintering furnace under an oxygen atmosphere; T2: Dissolve each chemical precursor separately in an appropriate amount of deionized water to form a homogeneous solution, and then mix all the solutions to ensure that the components are homogeneous; T3 Drying treatment: Place the mixed solution in an oven and dry at 80°C for 24 hours to remove excess moisture; T4 sintering process: The dried powder is placed in a high-temperature furnace, and the furnace temperature is controlled between 900℃ and 1100℃ for high-temperature sintering. The sintering time is 6 hours to promote the crystallization of the material and ensure the stability of the structure. T5 Cooling and Sieving: After sintering, the product is naturally cooled to room temperature, and then sieved to remove unqualified particles, ensuring the uniformity of the material particles, and obtaining a nickel cobalt aluminum oxide (NCA) and sodium iron phosphate (NaFePO4) composite material with high specific energy density.

7. The sodium-ion battery capacity prediction method according to claim 6, characterized in that, The preparation steps of the sodium-ion battery anode material include the following steps: Equipment and materials required for R1: solution stirrer; high-temperature furnace; tetrasodium titanate; sodium chloride; furnace under hydrogen atmosphere; R2 Dissolution and Mixing: First, add tetrasodium titanate and sodium chloride to deionized water and stir until homogeneous to ensure optimal solubility of the titanium and sodium sources. R3 Precipitation reaction: The titanium source and sodium source in the mixed solution are chemically reacted to obtain sodium titanium oxide precipitate; this step requires pH adjustment to ensure complete chemical reaction; R4 Filtration and Washing: The precipitate is extracted by filtration and repeatedly washed with deionized water to remove residual impurities; R5 Drying: Place the filtered precipitate in an oven, set the temperature to 80℃, and dry for 24 hours until a dry powder is obtained; R6 High-Temperature Heat Treatment: The dried powder is placed in a high-temperature furnace and heat-treated under a hydrogen atmosphere at a temperature of 700℃ for 6 hours to ensure the complete formation of sodium titanium oxide Na4Ti5O12, resulting in high-purity sodium titanium oxide Na4Ti5O12 powder with high electrochemical stability.

8. The sodium-ion battery capacity prediction method according to claim 6, characterized in that, The preparation steps of the sodium-ion battery electrolyte include the following steps: Q1 Required equipment and materials: electrolyte stirrer, deionized water, sodium salt NaPF6, lithium hexafluorophosphate LiPF6, electrolyte solvents including ethylene carbonate EC and dimethyl carbonate DMC; Q2 Dissolving Sodium Salt: Dissolve sodium salt NaPF6 in deionized water, ensuring complete dissolution to form the basis of sodium ion electrolyte; Q3 Add lithium salt: Add lithium hexafluorophosphate (LiPF6) to the sodium salt solution and mix thoroughly; Q4 Electrolyte Solvent: Add ethylene carbonate EC and dimethyl carbonate DMC, and stir with a stirrer until completely mixed; Q5 Settling and Filtration: Let the prepared electrolyte stand for several hours to remove any air bubbles that may be generated; finally, filter it through a 0.45μm filter membrane to remove insoluble impurities and obtain the sodium-ion battery electrolyte.

9. The sodium-ion battery capacity prediction method according to claim 6, characterized in that, The sodium-ion battery uses a porous polymer separator to improve the safety and stability of the battery. The preparation of the porous polymer separator includes the following steps: Equipment and materials required for P1: Polypropylene (PP) or polyethylene (PE), polypropylene film mold, high-temperature oven P2 Polymer Dissolution: Dissolve polypropylene (PP) or polyethylene (PE) in a suitable solvent to form a homogeneous solution; P3 Coating and Film Formation: The solution is uniformly coated onto the mold to ensure the uniformity and thickness of the film; P4 heat treatment: The coated film is heated at 120°C for 24 hours in an oven to promote complete curing of the film and form a membrane with high porosity. P5 Cutting and Inspection: The membrane after film formation is cut into appropriate sizes, and its porosity and thermal stability are tested to ensure that it meets the standard requirements, thus obtaining a porous polymer membrane.

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