Method and system for comprehensively sorting and clustering retired lithium ion batteries

Abstract

The invention discloses a comprehensive sorting and clustering method and system for retired lithium ion batteries, and the method comprises the steps: obtaining the combination weight of battery evaluation indexes through a game theory method, combining a VIKOR algorithm of comprehensive sorting with a KSOM algorithm of clustering, achieving the two-stage sorting and clustering, and improving the sorting and clustering precision. According to the algorithm, subjective and objective weights are combined by using the thought of the game theory, weight distortion caused by human experience and data extreme values is avoided, comprehensive sorting is performed by using VIKOR, compromise coefficients are introduced on the basis of positive and negative ideal solutions, preferences can be manually controlled, and finally the Euclidean distance in a traditional SOM algorithm is replaced by using a kernel function, so that the algorithm has high robustness. And the method has higher clustering precision and capability of processing high-dimensional nonlinear data. The method is suitable for the field of echelon utilization of the retired lithium ion battery.

Description

Technical Field

[0001] This invention belongs to the field of technology for the cascade utilization of retired lithium-ion batteries, and relates to a comprehensive sorting and clustering method and system for retired lithium-ion batteries. Background Technology

[0002] To ensure the safety and reliability of electric vehicles, the industry currently requires batteries to be replaced when their capacity drops to 80% of their rated capacity. Directly disposing of these retired batteries through shredding and recycling would result in significant resource waste. Currently, these retired batteries can be used in applications with lower battery performance requirements, such as energy storage systems and backup power supplies, thus achieving the secondary use of retired batteries. Due to the inherent inhomogeneity of lithium-ion batteries and significant differences in operating conditions, retired batteries exhibit considerable inconsistency. Directly reusing retired batteries would create a "weakest link" effect, shortening their lifespan. Therefore, batteries need to be sorted for consistency before being reassembled into groups for reuse.

[0003] Currently, commonly used sorting and clustering methods can be mainly divided into three types: dynamic parameter sorting, static parameter sorting, and hybrid parameter sorting. ① Dynamic parameter sorting uses dynamic information from the battery's dynamic curve for sorting and clustering. Battery dynamic parameters can effectively reflect the internal aging characteristics of the battery, ensuring that the sorted battery packs maintain good consistency under operating conditions. ② Static parameter sorting can be divided into single-parameter sorting and multi-parameter sorting. This method sorts by measuring parameters such as open-circuit voltage, capacity, and internal resistance of retired lithium-ion batteries. It is simple to operate and has a short processing time. ③ Hybrid parameter sorting combines the battery's static and dynamic parameters, which can effectively reflect the battery's internal characteristics and improve the reliability and scalability of retired battery sorting and clustering. However, these algorithms do have some limitations in practical applications and need to be selected according to different application scenarios. For example, dynamic parameter sorting requires too much data, and dynamic parameters are difficult to obtain; static parameter sorting cannot guarantee the long-term consistency of the reconstituted battery packs; hybrid parameter sorting often requires parameters with different dimensions, making data processing complex.

[0004] In recent years, numerous scholars have systematically reviewed the research progress and development trends of the cascade utilization of retired lithium-ion batteries. These studies have played a significant role in promoting this field and are of great importance. Traditional sorting methods are mostly based on threshold classification using single static parameters such as battery capacity, internal resistance, or cycle life. Although these methods are simple to operate and easy to implement industrially, they ignore the nonlinear decay characteristics of multi-parameter coupling during battery aging, resulting in insufficient matching between sorting results and actual performance, and potential risks to the lifespan and safety of reassembled battery packs. To improve sorting accuracy, some studies have introduced multi-parameter weighted scoring methods, constructing a comprehensive evaluation model by integrating dynamic indicators such as voltage, capacity decay rate, and impedance spectrum characteristics. However, the weighting of these methods relies on experience or fixed rules, making it difficult to adapt to the differences between different batches of batteries, and they are prone to misjudgment under complex noise interference. In recent years, machine learning algorithms (such as K-means clustering and support vector machines) have been introduced into the sorting field, achieving multi-dimensional data classification through unsupervised or semi-supervised learning. For example, K-means-based clustering methods can achieve rapid grouping based on the similarity of battery parameters, but they are sensitive to the initial cluster centers and cannot effectively handle nonlinear relationships in high-dimensional data; hierarchical clustering can optimize the classification hierarchy through a tree structure, but the computational complexity increases exponentially with the sample size, making it difficult to meet the real-time sorting requirements of large-scale retired batteries. Summary of the Invention

[0005] The purpose of this invention is to provide a comprehensive sorting and clustering method and system for retired lithium-ion batteries, so as to overcome the problems of insufficient sorting accuracy, unsatisfactory results, inconsistent data dimensions, and complex processing in the existing technology for retired lithium-ion batteries.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A comprehensive sorting and clustering method for retired lithium-ion batteries includes the following steps: S1. Obtain the characteristic parameters of the battery from different datasets. Based on the obtained characteristic parameters of the battery, determine the subjective and objective weights of the battery evaluation index using BWM and EWM. Then, use the game theory-based combination weighting method to combine the subjective and objective weights to obtain the combined weights. Use VIKOR to comprehensively rank the combined weights. S2, based on the combined weights after comprehensive ranking, uses a kernel function-improved self-organizing map neural network clustering method to perform consistent clustering of retired batteries, thereby completing the sorting and clustering of batteries.

[0007] Preferably, the different datasets include experimentally obtained datasets and publicly available battery datasets. Specifically, the experimentally obtained datasets are obtained by conducting maximum usable capacity tests, hybrid power pulse characteristic tests, and cycle aging experiments on lithium iron phosphate batteries, yielding data on battery capacity, ohmic internal resistance, constant current charging ratio, two polarization capacitors, and two polarization internal resistances when the battery health drops to 80%. The publicly available battery datasets are selected from battery data published by the MIT-Stanford-Toyota Research Center, with a total of 140 batteries selected from this dataset. The data of these batteries when the SOH drops to 80% are analyzed to obtain data on battery capacity, ohmic internal resistance, and open circuit voltage.

[0008] Preferably, the subjective and objective weights of battery evaluation indicators are determined using BWM and EWM, specifically including: The objective weights obtained using EWM are The subjective weights obtained using BWM are: The combination weights are obtained by performing a linear combination according to the following formula. .

[0009] (1) In the formula, and These are the optimal combination coefficients of objective weights and subjective weights, respectively.

[0010] Preferably, the Nash equilibrium point is obtained using game theory, that is, the equilibrium point satisfies... , and The minimum deviation is shown in the following formula: (2) According to the differential properties of a matrix, equation (2) must be satisfied, and its first derivative must satisfy the following system of linear equations: (3) The final portfolio weights are determined as follows: (4).

[0011] Preferred, a comprehensive sorting method based on the multi-criteria compromise sorting algorithm (VIKOR): Determine the positive and negative ideal solutions: Let the standardized matrix of the input index be... The set of maximum and minimum values ​​corresponding to each index is calculated, that is, the positive and negative ideal solutions; (5) In the formula, For the positive ideal solution, It is a negative ideal solution; Calculate the group benefit value and individual regret value , It is the distance between the indicator and the positive ideal solution. It is the distance between the index and the negative ideal solution, calculated as follows: (6) (7) In the formula, Weights for different indicators; Calculate the comprehensive metric value This is used to measure the overall performance of each alternative; a trade-off factor is set. Weights used to control whether decision outcomes favor group benefits or individual regret values. The larger the value, the more the result leans towards group benefits; conversely, the smaller the value, the more it leans towards individual regret. The specific calculation is as follows: (8) In the formula, , , , , Indicates the compromise factor; Determine the order of the options: according to , and The decision options are sorted from smallest to largest.

[0012] Preferred, recorded The first and second ranked values ​​correspond to the evaluation objects. and , and These are the compromise values ​​for these two evaluation objects; define the following two conditions: Condition 1: Acceptable advantages: (9) Condition 2: Acceptable stability: (10) If both condition 1 and condition 2 are satisfied, then This is the final compromise solution; if condition 1 is satisfied, but condition 2 cannot be satisfied, then the compromise solution is... and If condition 2 is satisfied and condition 1 is not satisfied, then All are compromise solutions, among which The value satisfies The maximum value.

[0013] Preferably, the self-organizing map neural network clustering method specifically includes: (1) Normalize and reduce the dimensionality of the input data; (2) Initialize network model parameters: Set the initial weight values ​​between the input layer and the competition layer. Initial value of the winning neighborhood radius Initial learning rate and maximum number of iterations ; (3) Finding the BMU: Calculate the Euclidean distance between each neuron as shown in equation (11); select the neuron with the smallest Euclidean distance. As shown in equation (12): (11) (12) In the formula, Let be the Euclidean distance between vectors. For preprocessed input data, For the weight vector, The minimum neuron distance; (4) Update the neighborhood function, neighborhood radius and learning rate: Set the neighborhood function of BMU to 1, and the values ​​of other neurons decay with distance. The neighborhood function corresponding to this iteration is shown in Equation (13); update the neighborhood radius as shown in Equation (14), and update the learning rate as shown in Equation (15). (13) In the formula, These are the coordinates of the neuron in the output layer grid. Here are the coordinates of the BMU in the output layer mesh, and the neighborhood radius. The effect decreases as the number of iterations increases, thus reducing the degree of influence with increasing iteration count. The specific calculation is as follows: (14) (15) (5) Update the weight matrix: Update the weights of neurons in the winning neighborhood. The specific calculation is as follows: (16) (6) Repeat steps (3) to (5) until the iteration termination condition is met, and then complete the training.

[0014] A comprehensive sorting and clustering system for retired lithium-ion batteries includes a comprehensive sorting module and a sorting and clustering module; Comprehensive ranking module: Obtains battery feature parameters from different datasets, determines subjective and objective weights of battery evaluation indicators based on the obtained battery feature parameters, uses BWM and EWM to determine the subjective and objective weights, then uses a game theory-based combination weighting method to combine the subjective and objective weights to obtain the combined weights, and uses VIKOR to comprehensively rank the combined weights. Sorting and Clustering Module: Based on the combined weights after comprehensive ranking, a kernel function-improved self-organizing map neural network clustering method is used to perform consistent clustering of retired batteries, thereby completing the sorting and clustering of batteries.

[0015] Preferably, the different datasets include experimentally obtained datasets and publicly available battery datasets. Specifically, the experimentally obtained datasets are obtained by conducting maximum usable capacity tests, hybrid power pulse characteristic tests, and cycle aging experiments on lithium iron phosphate batteries, yielding data on battery capacity, ohmic internal resistance, constant current charging ratio, two polarization capacitors, and two polarization internal resistances when the battery health drops to 80%. The publicly available battery datasets are selected from battery data published by the MIT-Stanford-Toyota Research Center, with a total of 140 batteries selected from this dataset. The data of these batteries when the SOH drops to 80% are analyzed to obtain data on battery capacity, ohmic internal resistance, and open circuit voltage.

[0016] Preferably, the subjective and objective weights of battery evaluation indicators are determined using BWM and EWM, specifically including: The objective weights obtained using EWM are The subjective weights obtained using BWM are: The combination weights are obtained by performing a linear combination according to the following formula. .

[0017] (1) In the formula, and These are the optimal combination coefficients of objective weights and subjective weights, respectively.

[0018] Compared with the prior art, the present invention has the following beneficial technical effects: This invention discloses a comprehensive sorting and clustering method for retired lithium-ion batteries. By introducing game theory principles, it combines subjective and objective weights and utilizes this combined weight with VIKOR to comprehensively sort retired lithium-ion batteries. The traditional SOM algorithm is improved by using a Gaussian kernel function, overcoming the shortcomings of traditional methods in processing high-dimensional nonlinear data and significantly improving clustering accuracy. Compared to existing technologies, this method can better sort and cluster retired lithium-ion batteries. Research results show that the proposed sorting and clustering algorithm has high accuracy under different datasets and battery evaluation metrics. Furthermore, the proposed KSOM algorithm does not exhibit clustering errors. These findings demonstrate that the new algorithm provides a more advanced and reliable solution for the cascade utilization of retired lithium-ion batteries.

[0019] Preferably, based on the obtained combined weights, the comprehensive sorting of batteries is realized, laying the foundation for subsequent high-precision battery clustering. By using a Gaussian kernel function to replace the Euclidean distance in the traditional self-organizing map neural network, accurate clustering of retired batteries is achieved. Attached Figure Description

[0020] Figure 1 This is a structural diagram of the present invention.

[0021] Figure 2 This is a diagram of the traditional SOM network structure of the present invention.

[0022] Figure 3 In the table, (a) represents the KSOM clustering result of battery dataset 1, (b) represents the KSOM clustering profile coefficient of battery dataset 1, (c) represents the SOM clustering result of battery dataset 1, and (d) represents the SOM clustering profile coefficient of battery dataset 1.

[0023] Figure 4 In the table, (a) represents the KSOM clustering result of the battery dataset 2, (b) represents the KSOM clustering profile coefficient of the battery dataset 2, (c) represents the SOM clustering result of the battery dataset 2, and (d) represents the SOM clustering profile coefficient of the battery dataset 2.

[0024] Figure 5 In the table, (a) represents the KSOM clustering result of the superior batteries in dataset 2, (b) represents the SOM clustering result of the superior batteries in dataset 2, (c) represents the KSOM clustering result of the medium batteries in dataset 2, (d) represents the SOM clustering result of the medium batteries in dataset 2, (e) represents the KSOM clustering result of the poor batteries in dataset 2, and (f) represents the SOM clustering result of the poor batteries in dataset 2.

[0025] Figure 6In the table, (a) represents the KSOM cluster profile coefficient of the superior batteries in dataset 2, (b) represents the KSOM cluster profile coefficient of the superior batteries in dataset 2, (c) represents the KSOM cluster profile coefficient of the average batteries in dataset 2, (d) represents the KSOM cluster profile coefficient of the average batteries in dataset 2, (e) represents the KSOM cluster profile coefficient of the poor batteries in dataset 2, and (f) represents the KSOM cluster profile coefficient of the poor batteries in dataset 2. Detailed Implementation

[0026] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of 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 skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0027] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0028] like Figure 1 As shown, this invention provides a comprehensive sorting and clustering method for retired lithium-ion batteries, specifically including the following steps: S1. Obtain the characteristic parameters of the battery from different datasets. Based on the obtained characteristic parameters of the battery, determine the subjective and objective weights of the battery evaluation indicators using BWM and EWM. Then, use the game theory-based combined weighting method (CWMGT) to combine the subjective and objective weights to obtain the combined weights. Use VIKOR to comprehensively rank the combined weights. S2, based on the combined weights after comprehensive ranking, uses the kernel function-improved self-organizing map neural network (KSOM) clustering method to perform consistent clustering of retired batteries, thereby completing the battery sorting and clustering.

[0029] In a specific embodiment of the present invention, the different datasets include experimentally obtained datasets and publicly available battery datasets. Specifically, the experimentally obtained datasets were obtained by conducting maximum usable capacity tests, hybrid power pulse characteristic tests, and cycle aging experiments on lithium iron phosphate batteries. Data on battery capacity, ohmic internal resistance, constant current charging ratio, two polarization capacitors, and two polarization internal resistances when the State of Health (SOH) drops to 80% were obtained, and this dataset is designated as Data Set 1. The publicly available battery dataset uses battery data published by the MIT-Stanford-Toyota Research Center. A total of 140 batteries from this dataset were selected, and the data on these batteries with an SOH drop to 80% were analyzed to obtain the battery capacity, ohmic internal resistance, and open-circuit voltage, which is designated as Data Set 2.

[0030] Before sorting and clustering the batteries, it is necessary to extract their characteristic parameters to achieve consistent sorting and clustering based on these parameters. Data from 12 lithium iron phosphate batteries obtained through laboratory experiments (Dataset 1) and battery data from the MIT-Stanford-Toyota Research Center (Dataset 2) were selected.

[0031] Dataset 1 uses 18650 lithium iron phosphate batteries as the research object. This type of battery has a high qualification rate, good consistency, low internal resistance, and a certain degree of safety and performance assurance. The nominal capacity of this battery is 1100mAh, the nominal voltage is 3.2V, and the upper and lower cutoff voltages are 3.65V and 2.5V, respectively.

[0032] Dataset 1 Acquisition: This application selected 12 18650 lithium iron phosphate batteries as research objects, named L1, L2, L3, L4, L5, L6, L7, L8, L9, L10, L11, and L12 in sequence. These batteries were subjected to maximum usable capacity testing, hybrid power pulse characteristic (HPPC) testing, and cycle aging experiments.

[0033] Through the above experiments, we obtained data on the capacity, ohmic internal resistance, constant current charging ratio, two polarization capacitors, and two polarization internal resistances of the battery in Dataset 1 when the State of Health (SOH) dropped to 80%, providing data support for subsequent comprehensive battery sorting and clustering.

[0034] Dataset 2 Acquisition: Dataset 2 in this application uses battery data published by the MIT-Stanford-Toyota Research Center.

[0035] This public dataset consists of 140 commercially available lithium iron phosphate batteries that were cycled to failure under fast-charging conditions. These batteries, manufactured by A123 Systems (model APR18650M1A), were tested using Arbin's 30-channel charge / discharge tester. The batteries have a nominal capacity of 1100 mAh, a nominal voltage of 3.3V, and upper and lower cutoff voltage limits of 3.6V and 2.0V, respectively.

[0036] This application selects 140 batteries from the dataset and analyzes the data of these batteries with a state of harmlessness (SOH) of 80%, obtaining the capacity, internal resistance (ohmic resistance), and open-circuit voltage of the batteries in dataset 2.

[0037] In a specific embodiment of this application, the objective weight obtained using EWM is denoted as... The subjective weights obtained using BWM are: The combination weights are obtained by performing a linear combination according to the following formula. .

[0038] (1) In the formula, and These are the optimal combination coefficients of objective weights and subjective weights, respectively.

[0039] Using game theory, we can find the Nash equilibrium point, which satisfies... , and The minimum deviation is shown in the following formula.

[0040] (2) According to the differential properties of a matrix, equation (2) must be satisfied, and its first derivative must satisfy the following system of linear equations: (3) The final combination weights are determined as follows: (4) Comprehensive sorting based on the multi-criteria compromise sorting method (VIKOR): Determine the positive and negative ideal solutions: Let the standardized matrix of the input index be... The set of maximum and minimum values ​​corresponding to each index is calculated, which are the positive and negative ideal solutions.

[0041] (5) In the formula, For the positive ideal solution, It is a negative ideal solution.

[0042] Calculate the group benefit value and individual regret value , It is the distance between the indicator and the positive ideal solution. It is the distance between the index and the negative ideal solution, calculated as follows: (6) (7) In the formula, The weights for different indicators.

[0043] Calculate the comprehensive metric value This is used to measure the overall performance of each alternative; a trade-off coefficient is set. Weights used to control whether decision outcomes favor group benefits or individual regret values. The larger the value, the more the result leans towards group benefits, and vice versa; the specific calculation is as follows: (8) In the formula, , , , , This represents the compromise factor, which is set according to the decision-maker's personal preference and is generally selected as 0.5.

[0044] Determine the order of the options: according to , and The decision options are sorted from smallest to largest.

[0045] Determine a compromise solution: Note The first and second ranked values ​​correspond to the evaluation objects. and , and These are the compromise values ​​for these two evaluation objects, respectively. Define the following two conditions: Condition 1: Acceptable advantages: (9) Condition 2: Acceptable stability: (10) If both condition 1 and condition 2 are satisfied, then This is the final compromise solution; if condition 1 is satisfied, but condition 2 cannot be satisfied, then the compromise solution is... and If condition 2 is satisfied and condition 1 is not satisfied, then All are compromise solutions, among which The value satisfies The maximum value.

[0046] The structure of the self-organizing map neural network clustering method is as follows: Figure 2 As shown: (1) Normalize and reduce the dimensionality of the input data; (2) Initialize network model parameters: Set the initial weight values ​​between the input layer and the competition layer. Initial value of the winning neighborhood radius Initial learning rate and maximum number of iterations ; (3) Finding the BMU: Calculate the Euclidean distance between each neuron as shown in equation (11); select the neuron with the smallest Euclidean distance. As shown in equation (12): (11) (12) In the formula, Let be the Euclidean distance between vectors. For the preprocessed input data, For the weight vector, The minimum neuron distance; (4) Update the neighborhood function, neighborhood radius and learning rate: Set the neighborhood function of BMU to 1, and the values ​​of other neurons decay with distance. The neighborhood function corresponding to this iteration is shown in Equation (13); update the neighborhood radius as shown in Equation (14), and update the learning rate as shown in Equation (15).

[0047] (13) In the formula, These are the coordinates of the neuron in the output layer grid. Here are the coordinates of the BMU in the output layer mesh, and the neighborhood radius. The effect decreases as the number of iterations increases, thus reducing the degree of influence with increasing iteration count. The specific calculation is as follows: (14) (15) (5) Update the weight matrix: Update the weights of neurons in the winning neighborhood. The specific calculation is as follows: (16) (6) Repeat steps (3) to (5) until the iteration termination condition is met, and then complete the training.

[0048] A self-organizing map neural network clustering method based on kernel function improvement: If the samples are linearly inseparable in the input space, a nonlinear mapping from the kernel method can be used. This transforms the nonlinear problem into a high-dimensional space. Linearly solvable problems in [the context of the problem].

[0049] In high-dimensional space, define a nonlinear mapping function. ,in , . It is the input sample set. If it is a feature space, then the Euclidean distance in the above method can be calculated using the following objective function: (17) Finally, based on the Mercer condition, the distance in the high-dimensional space is converted into a kernel function form. The kernel function of the Mercer condition is defined as follows: (18) As can be seen from formula (17), each term can be regarded as a feature space. If the inner product of the kernel function satisfies formula (18), then the high-dimensional distance formula expressed by the kernel function is as shown in formula (19).

[0050] (19) In summary, the KSOM algorithm was proposed. Due to the flexibility of kernel mapping, different kernel functions can produce different distance measures. Several commonly used kernel functions will then be introduced.

[0051] Polynomial kernel: (20) In the formula, It represents the power of the polynomial.

[0052] Gaussian kernel: (twenty one) In the formula, This is the bandwidth parameter, which controls the width of the Gaussian distribution.

[0053] Cauchy nucleus: (twenty two) In the formula, The bandwidth parameter controls the width of the Cauchy distribution.

[0054] Because the Gaussian kernel function has better adaptability than other kernel functions and is suitable for handling different types of data, it is often widely used in both unsupervised and supervised learning problems. Therefore, this application uses the Gaussian kernel function to improve the SOM algorithm. Observation and comparison show that the basic framework of the KSOM algorithm remains unchanged. When, through Taylor expansion, we can see that the Gaussian kernel function degenerates into a state that is linearly negatively correlated with the square of the Euclidean distance.

[0055] This application uses the silhouette coefficient (SC) to evaluate the clustering effect. SC is an indicator used to evaluate the accuracy of clustering, measuring the density of sample points within the same cluster and their separation from other clusters. The specific calculation is as follows: (twenty three) In the formula, The total number of sample points. For the sample The average distance to other samples within the same cluster (cluster compactness). For the sample The average distance to all samples from the nearest other cluster (inter-cluster separation). Ensure that the values ​​are normalized so that SC is between -1 and 1.

[0056] As can be seen from the definition of the profile coefficient, when When a sample is close to its own cluster and far from other clusters, the clustering effect is good; when... When the clustering effect is poor, it indicates that the sample may be located at the boundary of two clusters; when... If the clustering error occurs, it means that the sample has been incorrectly assigned to a cluster. In this case, a clustering error has occurred, and it is necessary to reselect the clustering method or adjust the features.

[0057] (1) Verification of the comprehensive sorting results based on CWMGT-VIKOR For the batteries in Dataset 1, this application uses seven evaluation metrics for sorting: capacity, ohmic internal resistance, constant current charging ratio, two polarization capacitors, and two polarization internal resistances. For the batteries in Dataset 2, this application uses three evaluation metrics: capacity, ohmic internal resistance, and open-circuit voltage.

[0058] Based on the specific parameters of the batteries in the dataset, objective weights for each battery metric were obtained using EWM (Enhanced Weighing Method). Simultaneously, based on the opinions of multiple experts, the most important and least important metrics were determined, and these metrics were compared. Subjective weights were then obtained using BWM (Browser-Walter-Mean-Through-Weighing Method), and finally, CWMGT (Combined Weights and Weights) was used to combine the weights. The objective weights, subjective weights, and combined weights for batteries in Dataset 1 are shown in Table 1, and the objective weights, subjective weights, and combined weights for batteries in Dataset 2 are shown in Table 2.

[0059] Table 1. Weights of different evaluation metrics for batteries in Dataset 1 Objective weighting focuses solely on the degree of data disorder; the greater the difference between different samples of the same indicator, the lower its weight. Table 1 shows that polarization capacitance and polarization resistance have a high weighting ratio in objective weighting, while capacity and ohmic resistance have very low weightings, which does not align with the practical applications of cascaded energy storage. For cascaded energy storage applications, factors such as capacity and constant current charging ratio are often prioritized, while for applications with higher power requirements, such as peak shaving and frequency regulation, the influence of ohmic resistance and polarization parameters is often more important. Objective methods focus on the data structure itself and cannot account for subjective value judgments, potentially assigning excessive weight to indicators with low entropy values ​​that are actually unimportant. Subjective weighting is easily influenced by subjective experience and preferences, such as assigning excessive weight to capacity and ohmic resistance while ignoring battery polarization parameters, leading to distorted weighting results.

[0060] Table 2. Weights of different evaluation metrics for batteries in Dataset 2 As shown in Table 2, EWM assigns an objective weight of 0.0915 to the ohmic internal resistance because the entropy values ​​of the ohmic internal resistance differ significantly between different batteries. However, this deviates significantly from actual engineering requirements. Similarly, BWM sets the open-circuit voltage weight at 0.0909, which also fails to accurately reflect the importance of the parameter.

[0061] In summary, the CWMGT proposed in this application aims to minimize the sum of the differences between subjective and objective weights. Through game theory, it arrives at an optimal position, achieving a combination of subjective and objective weights. This effectively balances the theoretical limitations of the subjective-objective weighting method with the requirements of engineering applicability. It meets the requirements of human-made battery reuse scenarios and can well consider the multifaceted influence of battery performance indicators.

[0062] The comprehensive metric values ​​calculated by VIKOR are between 0 and 1, thus classifying batteries into three categories: Excellent (comprehensive metric value between 0 and 0.3), Medium (comprehensive metric value between 0.3 and 0.6), and Poor (comprehensive metric value between 0.6 and 1).

[0063] Table 3 Battery sorting results for Dataset 1 As shown in Table 3, in Data Set 1, L5, L6, L8, L9, L11, and L12 are excellent batteries, L2, L3, L7, and L10 are medium-grade batteries, and L1 and L4 are poor-grade batteries.

[0064] To better demonstrate the characteristics of VIKOR, this application further categorizes the batteries in Dataset 1 into different batches based on their State of Health (SOH) for sorting and verification. Batteries with an SOH of 100% are defined as batch A, batteries with an SOH of approximately 90% are defined as batch B, and batteries with an SOH of less than 80% are defined as batch C. CWMGT-VIKOR is then used for comprehensive sorting of the batteries.

[0065] Table 4. Sorting results of batteries in different batches of Dataset 1 Table 4 shows that batch A of batteries All values ​​are between 0 and 0.3, for batch B batteries. All were between 0.3 and 0.6, and the C batch of batteries... All values ​​are between 0.6 and 1. In practice, batch A batteries all had a SOH of 100%, in which case all batch A batteries are considered excellent; batch B batteries all had an SOH of approximately 90%, in which case all batch B batteries are considered average; and batch C batteries all had an SOH of less than 80%, in which case all batch C batteries are considered poor. This result is consistent with reality.

[0066] Compared to the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), which only considers the overall merits of indicators to obtain a single objective result, VIKOR can determine the compromise coefficient according to the decision-maker's needs. This application adopts the compromise coefficient. The value is 0.5, which means that the importance of group benefits and individual regrets is considered to be equal.

[0067] This application also uses Dataset 2 batteries for comprehensive sorting, using capacity, internal resistance (ohmic resistance), and open-circuit voltage as evaluation indicators. The final sorting results are shown in Table 5. Table 5. Battery sorting results for Dataset 2 As shown in Table 5, there are 10 superior batteries, 82 medium batteries, and 48 poor batteries in Data Set 2.

[0068] (2) Validation of battery clustering results based on KSOM If the retired batteries differ significantly, the performance of the same type of retired batteries after sorting will still differ significantly

[38] . Considering that the secondary use of batteries is to form modules from individual batteries and then form battery packs, the performance of individual batteries in the same module should be made as similar as possible. This application uses a clustering algorithm to further cluster retired batteries, grouping individual batteries with similar characteristics into a battery cluster, so that they can be connected in series and parallel in a battery module or battery pack in the future.

[0069] This application uses KSOM and SOM-based clustering methods to perform consistent clustering of batteries in dataset 1 and dataset 2.

[0070] 1) Validation of battery clustering results in dataset 1 Based on dataset 1, cluster analysis was performed on the batteries using capacity, ohmic internal resistance, constant current charging ratio, two polarization capacitors, and two polarization internal resistances.

[0071] Depend on Figure 3 It can be seen that both the SOM and KSOM algorithms divided the 12 batteries in dataset 1 into 6 clusters, but the batteries in each cluster had some differences, leading to differences in their silhouette coefficient calculations. The average silhouette coefficient of the KSOM algorithm was 0.7287, while that of the SOM algorithm was 0.6504. Comparatively, the KSOM algorithm improved clustering accuracy by 12%, and the smallest silhouette coefficient in the SOM algorithm was approximately -0.1, indicating that the battery was incorrectly clustered into this cluster. In contrast, all silhouette coefficients in the KSOM algorithm were greater than 0, indicating that no batteries were incorrectly clustered.

[0072] 2) Validation of battery clustering results in dataset 2 Based on dataset 2, cluster analysis of batteries was performed using capacity, ohmic internal resistance, and open-circuit voltage.

[0073] Depend on Figure 4 It can be seen that both the SOM and KSOM algorithms divided the 140 batteries in the dataset into 12 clusters. The average silhouette coefficient of the KSOM algorithm was 0.6680, while that of the SOM algorithm was 0.5704. Comparatively, the KSOM algorithm improved clustering accuracy by 17.1%. By judging the sign of the silhouette coefficient, it can be seen that the SOM algorithm incorrectly clustered 8 batteries into clusters that did not belong to it, while the silhouette coefficients of the KSOM algorithm were all positive, meaning that every battery was correctly assigned to its appropriate cluster.

[0074] Depend on Figure 5 and Figure 6It can be seen that for 10 high-quality batteries, the clustering results of the KSOM and SOM algorithms are consistent, with silhouette coefficients of 0.8878, and the number of clusters and the number of batteries within each cluster are the same. However, for medium-quality and low-quality batteries, the silhouette coefficients of the KSOM algorithm are 0.5407 and 0.7315, respectively, while those of the SOM algorithm are 0.4738 and 0.7233, respectively. Calculations show that the clustering accuracy is improved by 14.1% and 1.1%, respectively. Furthermore, we can observe that the silhouette coefficients of the KSOM algorithm are all greater than 0, meaning that the KSOM algorithm does not exhibit incorrect battery clustering, while the SOM algorithm incorrectly clustered 7 batteries for medium-quality batteries and incorrectly clustered 1 battery for low-quality batteries.

[0075] By comparing the batteries in Dataset 2 that underwent initial VIKOR sorting followed by secondary clustering with those that were directly clustered, it can be seen that the average silhouette coefficient of the KSOM algorithm (sorting first, then clustering) is 0.72, resulting in 17 clusters. The average silhouette coefficient of the SOM algorithm (sorting first, then clustering) is 0.6883, also resulting in 17 clusters. Conversely, the average silhouette coefficient of the KSOM algorithm (direct clustering) is 0.6680, resulting in 12 clusters, and the average silhouette coefficient of the SOM algorithm (direct clustering) is 0.5846, also resulting in 12 clusters. Calculations show that the silhouette coefficients of the KSOM and SOM algorithms are improved by 7.8% and 17.7%, respectively. This indicates that initial sorting effectively improves the accuracy of battery clustering and reduces inconsistencies between batteries during subsequent tiered utilization. Table 6 shows a comparison of the accuracy of the KSOM and SOM algorithms.

[0076] Table 6. Accuracy Comparison of KSOM Algorithm and SOM Algorithm In summary, the KSOM algorithm significantly improves clustering accuracy compared to the SOM algorithm and avoids incorrect clustering. Furthermore, the secondary clustering after initial sorting further improves the accuracy of both the SOM and KSOM algorithms.

Claims

1. A comprehensive sorting and clustering method for retired lithium-ion batteries, characterized in that, Includes the following steps: S1. Obtain the characteristic parameters of the battery from different datasets. Based on the obtained characteristic parameters of the battery, determine the subjective and objective weights of the battery evaluation index using BWM and EWM. Then, use the game theory-based combination weighting method to combine the subjective and objective weights to obtain the combined weights. Use VIKOR to comprehensively rank the combined weights. S2, based on the combined weights after comprehensive ranking, uses a kernel function-improved self-organizing map neural network clustering method to perform consistent clustering of retired batteries, thereby completing the sorting and clustering of batteries.

2. The comprehensive sorting and clustering method for retired lithium-ion batteries according to claim 1, characterized in that, The different datasets include experimentally obtained datasets and publicly available battery datasets. The experimentally obtained datasets specifically obtained data on the capacity, ohmic internal resistance, constant current charging ratio, two polarization capacitors, and two polarization internal resistances of lithium iron phosphate batteries when their state of health dropped to 80% through maximum usable capacity testing, hybrid power pulse characteristic testing, and cycle aging experiments. The publicly available battery datasets used battery data released by the MIT-Stanford-Toyota Research Center, which included 140 batteries. Data on the state of health (SOH) of these batteries when it dropped to 80% were analyzed to obtain data on battery capacity, ohmic internal resistance, and open circuit voltage.

3. The comprehensive sorting and clustering method for retired lithium-ion batteries according to claim 1, characterized in that, Using BWM and EWM to determine the subjective and objective weights of battery evaluation indicators, specifically including: The objective weights obtained using EWM are The subjective weights obtained using BWM are: The combination weights are obtained by performing a linear combination according to the following formula. ; （1） In the formula, and These are the optimal combination coefficients of objective weights and subjective weights, respectively.

4. The comprehensive sorting and clustering method for retired lithium-ion batteries according to claim 3, characterized in that, Using game theory, we can find the Nash equilibrium point, which satisfies... , and The minimum deviation is shown in the following formula: （2） According to the differential properties of a matrix, equation (2) must be satisfied, and its first derivative must satisfy the following system of linear equations: （3） The final portfolio weights are determined as follows: （4）。 5. The comprehensive sorting and clustering method for retired lithium-ion batteries according to claim 4, characterized in that, Comprehensive sorting based on the multi-criteria compromise sorting method (VIKOR): Determine the positive and negative ideal solutions: Let the standardized matrix of the input index be... The set of maximum and minimum values ​​corresponding to each index is calculated, that is, the positive and negative ideal solutions; （5） In the formula, For the positive ideal solution, It is a negative ideal solution; Calculate the group benefit value and individual regret value , It is the distance between the indicator and the positive ideal solution. It is the distance between the index and the negative ideal solution, calculated as follows: （6） （7） In the formula, Weights for different indicators; Calculate the comprehensive metric value This is used to measure the overall performance of each alternative. Set a compromise factor Weights used to control whether decision outcomes favor group benefits or individual regret values. The larger the value, the more the result leans towards group benefits; conversely, the smaller the value, the more it leans towards individual regret. The specific calculation is as follows: （8） In the formula, , , , , Indicates the compromise factor; Determine the order of the options: according to , and The decision options are sorted from smallest to largest.

6. The comprehensive sorting and clustering method for retired lithium-ion batteries according to claim 5, characterized in that, remember The first and second ranked values ​​correspond to the evaluation objects. and , and These are the compromise values ​​for these two evaluation objects; define the following two conditions: Condition 1: Acceptable advantages: （9） Condition 2: Acceptable stability: （10） If both condition 1 and condition 2 are satisfied, then This is the final compromise solution; if condition 1 is satisfied, but condition 2 cannot be satisfied, then the compromise solution is... and If condition 2 is satisfied and condition 1 is not satisfied, then All are compromise solutions, among which The value satisfies The maximum value.

7. The comprehensive sorting and clustering method for retired lithium-ion batteries according to claim 1, characterized in that, Self-organizing map neural network clustering methods specifically include: (1) Normalize and reduce the dimensionality of the input data; (2) Initialize network model parameters: Set the initial weight values ​​between the input layer and the competition layer. Initial value of the winning neighborhood radius Initial learning rate and maximum number of iterations ; (3) Finding the BMU: Calculate the Euclidean distance between each neuron as shown in equation (11); select the neuron with the smallest Euclidean distance. As shown in equation (12): （11） （12） In the formula, Let be the Euclidean distance between vectors. For the preprocessed input data, For the weight vector, The minimum neuron distance; (4) Update the neighborhood function, neighborhood radius and learning rate: Set the neighborhood function of BMU to 1, and the values ​​of other neurons decay with distance. The neighborhood function corresponding to this iteration is shown in Equation (13); update the neighborhood radius as shown in Equation (14), and update the learning rate as shown in Equation (15). （13） In the formula, These are the coordinates of the neuron in the output layer grid. Here are the coordinates of the BMU in the output layer mesh, and the neighborhood radius. The effect decreases as the number of iterations increases, thus reducing the degree of influence with increasing iteration count. The specific calculation is as follows: （14） （15） (5) Update the weight matrix: Update the weights of neurons in the winning neighborhood. The specific calculation is as follows: （16） (6) Repeat steps (3) to (5) until the iteration termination condition is met, and then complete the training.

8. A comprehensive sorting and clustering system for retired lithium-ion batteries, characterized in that, It includes a comprehensive ranking module and a sorting and clustering module; Comprehensive ranking module: Obtains battery feature parameters from different datasets, determines subjective and objective weights of battery evaluation indicators based on the obtained battery feature parameters, uses BWM and EWM to determine the subjective and objective weights, then uses a game theory-based combination weighting method to combine the subjective and objective weights to obtain the combined weights, and uses VIKOR to comprehensively rank the combined weights. Sorting and Clustering Module: Based on the combined weights after comprehensive ranking, a kernel function-improved self-organizing map neural network clustering method is used to perform consistent clustering of retired batteries, thereby completing the sorting and clustering of batteries.

9. A comprehensive sorting and clustering system for retired lithium-ion batteries according to claim 8, characterized in that, The different datasets include experimentally obtained datasets and publicly available battery datasets. The experimentally obtained datasets specifically obtained data on the capacity, ohmic internal resistance, constant current charging ratio, two polarization capacitors, and two polarization internal resistances of lithium iron phosphate batteries when their state of health dropped to 80% through maximum usable capacity testing, hybrid power pulse characteristic testing, and cycle aging experiments. The publicly available battery datasets used battery data released by the MIT-Stanford-Toyota Research Center, which included 140 batteries. Data on the state of health (SOH) of these batteries when it dropped to 80% were analyzed to obtain data on battery capacity, ohmic internal resistance, and open circuit voltage.

10. A comprehensive sorting and clustering system for retired lithium-ion batteries according to claim 8, characterized in that, Using BWM and EWM to determine the subjective and objective weights of battery evaluation indicators, specifically including: The objective weights obtained using EWM are The subjective weights obtained using BWM are: The combination weights are obtained by performing a linear combination according to the following formula. ; （1） In the formula, and These are the optimal combination coefficients of objective weights and subjective weights, respectively.

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