Soft dynamic time warping based method for grouping retired batteries
By grouping retired batteries using a soft dynamic time warping method, the problems of poor battery pack performance consistency and low grouping efficiency in existing technologies are solved, achieving efficient and reliable battery pack grouping and improving battery pack performance and safety.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHONGQING UNIV
- Filing Date
- 2024-05-14
- Publication Date
- 2026-06-05
AI Technical Summary
Existing methods for grouping retired batteries cannot fully reflect the aging process and dynamic changes of batteries, resulting in reduced performance, lifespan and safety of the reassembled battery packs. Furthermore, the grouping efficiency is low and cannot meet the grouping needs of large-scale retired batteries.
A soft dynamic time warping method is adopted. After measuring the capacity increment sequence of individual cells in the battery pack and performing filtering and noise reduction, the cells are grouped using a segmented aggregation approximation algorithm and a k-medoids clustering algorithm. The optimal grouping scenario is determined by combining the contour coefficient, thereby improving the performance consistency of the battery pack.
It improves the reliability and accuracy of retired battery grouping, enhances the performance consistency and safety of battery packs, increases grouping efficiency, and is suitable for large-scale retired battery grouping.
Smart Images
Figure CN118312834B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of battery testing, and specifically to a method for grouping retired batteries based on soft dynamic time warping. Background Technology
[0002] As the power source in electric vehicles, the battery pack has a crucial impact on vehicle performance, safety, and driving range. To improve resource utilization, once a battery pack reaches its retirement standard, it needs to be disassembled into individual battery cells. These cells are then retested, screened, and reassembled as retired batteries to achieve tiered utilization. They can be reused in scenarios with lower battery performance requirements, such as energy storage power stations, low-speed electric vehicles, and home energy storage. By recycling retired batteries, the overall life-cycle value of the battery pack is increased, and the procurement cost of the battery pack is reduced.
[0003] As battery packs age, the dispersion of parameters such as internal resistance, capacity, and self-discharge rate increases over time, inevitably leading to some degree of inconsistency among individual cells. During the reassembly process, due to the "weakest link" effect, the rapid performance degradation of some retired cells can cause a sharp decline in the overall performance of the reassembled battery pack. Connecting excessively inconsistent retired cells in series can lead to overcharging and over-discharging of some cells, while connecting them in parallel can cause circulating currents. The inconsistency among individual cells after reassembly primarily results in reduced battery pack performance, lifespan, and safety. Therefore, it is crucial to ensure the performance consistency of each individual cell in the power battery pack meets requirements during the initial screening and grouping stages to improve the performance, lifespan, and safety of the reassembled battery pack.
[0004] Existing methods for grouping retired batteries, such as the "A Clustering and Sorting Method for Retired Power Batteries" disclosed in CN112651431A, mainly use a set of discrete features to group the disassembled battery cells. For example, one-dimensional features such as maximum voltage change rate, maximum voltage value, battery impedance, and IC curve peak value are used as static characteristic data. This method only considers the static characteristics of retired batteries and cannot fully reflect the aging process and dynamic changes of the batteries. It cannot fully reflect the aging state and aging mode of the batteries. Therefore, the selected batteries only have short-term consistency and not long-term consistency.
[0005] Moreover, most existing methods for grouping retired batteries require a complete charge and discharge cycle, resulting in relatively low grouping efficiency. Given the rapid development of electric vehicles leading to a much larger scale of retired batteries, existing grouping methods are no longer suitable for such large-scale grouping. Summary of the Invention
[0006] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for grouping retired batteries based on soft dynamic time warping. This method involves disassembling all individual cells from a battery pack, measuring the constant current charging data of each cell, and calculating the capacity increment sequence (i.e., the capacity increment curve) as the characteristic data of each cell. These characteristic data are then filtered and denoised, and a segmented aggregation approximation algorithm is used to unify the sequence length of the characteristic data for each cell. Finally, a k-medoids clustering algorithm combined with a soft dynamic time warping algorithm is used to re-sort and group the individual cells. The optimal grouping scenario is determined using a contour coefficient, and the individual cells of the battery pack are then grouped accordingly.
[0007] The objective of this invention is achieved through the following scheme: a method for grouping retired batteries based on soft dynamic time warping, comprising the following steps:
[0008] 1) By measuring and calculating the capacity increment sequence vector of each individual cell in the battery pack, the capacity increment sequence vector is smoothed and denoised to form a set of filtered feature sequence vectors;
[0009] 2) The lengths of the capacity increment sequence vectors of each individual battery cell are unified into a set of feature sequence vectors with unified lengths.
[0010] 3) Combine all the individual cells of the battery pack in pairs to form different battery combinations. Calculate the soft dynamic time-normalized distance of each battery combination using the feature sequence vector set with uniform length, and form the battery pack distance matrix.
[0011] 4) Calculate all grouping scenarios of retired batteries using the soft dynamic time warping distance of each battery combination in the battery pack distance matrix;
[0012] 5) The cohesion and separation of each individual cell in different grouping scenarios are calculated using soft dynamic time warping distance;
[0013] 6) Calculate the profile coefficients of each individual cell in the battery pack in different grouping scenarios using the cohesion and separation of each individual cell.
[0014] 7) Calculate the average profile coefficient for each group scenario, take the group scenario with the largest average profile coefficient as the best group scenario, and group each individual cell of the battery pack according to the best group scenario.
[0015] Preferably, the capacity increment sequence vector of each individual cell in the battery pack is obtained in the following manner:
[0016] 1-1) Charge the single cell using a constant current source, measure and record the voltage between the positive and negative terminals of the single cell and the corresponding cell charge value multiple times at timed intervals until the voltage between the positive and negative terminals of the single cell reaches the charging cutoff voltage.
[0017] 1-2) Calculate the capacity increment of the single cell at each time step using the following formula:
[0018]
[0019] In the formula, ic i Let Q be the capacity increment of the single cell at time i. i Let Q be the capacity value of the single cell at time i. i-1 Let V be the capacity value of the single cell at time (i-1). i Let V be the voltage value of the single cell at time i. i-1 Let be the voltage value of the single cell at time (i-1);
[0020] 1-3) Use the capacity increment values of the single cell at each time point to form the capacity increment sequence vector of the single cell.
[0021] Preferably, the method for smoothing and denoising each capacity increment sequence vector in step 1) includes Gaussian filtering, low-pass filtering, and wavelet transform.
[0022] Preferably, the specific steps for smoothing and denoising each capacity increment sequence vector using Gaussian filtering are as follows:
[0023] ① Based on the number of capacity increment values in the single cell capacity increment sequence vector, a Gaussian weight is constructed, and the Gaussian weight vector is shown below:
[0024] w = [w1, w2, ..., w s ,…,w 2s+1 ]
[0025]
[0026] In the formula, w i Let be the i-th Gaussian weight in the Gaussian weight vector, π be pi, e be the natural constant, s be the window size, i be the number of capacity increment values in the single-cell capacity increment sequence vector, σ be the standard deviation of the Gaussian distribution, and w be the weight of the Gaussian weight vector. s Let w be the center weight of the Gaussian weight vector;
[0027] ② Normalize the Gaussian weight vector as follows:
[0028] (1) Remove the center weights of the Gaussian weight vector;
[0029] (2) Reassign each remaining Gaussian weight in the Gaussian weight vector according to the following formula:
[0030]
[0031] In the formula, w i w represents the i-th Gaussian weight in the Gaussian weight vector before reassignment. i ' represents the i-th Gaussian weight in the reassigned Gaussian weight vector, s is the window size, and w j This refers to the j-th Gaussian weight in the Gaussian weight vector before reassignment;
[0032] (3) The normalized Gaussian weight vector is constructed using the reassigned Gaussian weights as shown below:
[0033] w′=[w1′,w2′,…,w2′ s ]
[0034] In the formula, w′ is the normalized Gaussian weight vector, w1′ is the first Gaussian weight in the normalized Gaussian weight vector, w2′ is the second Gaussian weight in the normalized Gaussian weight vector, and w2′ is the third Gaussian weight in the normalized Gaussian weight vector. s The second-s Gaussian weight in the normalized Gaussian weight vector;
[0035] ③ Calculate the filtered capacity increment value of the single cell at each time step according to the following formula, and construct the filtered capacity increment sequence vector of the single cell:
[0036]
[0037] IC j ′=[ic1′,ic2′,…,ic i ′,…,ic q-1 ′]
[0038] In the formula, ic i ic1′ represents the filtered capacity increment of the single cell at time i, ic2′ represents the filtered capacity increment of the single cell at time 1, and ic2′ represents the filtered capacity increment of the single cell at time 2. q-1 ′ represents the filtered capacity increment of the single cell at time (q-1), w j-i+s For the (j-i+s)th Gaussian weight in the Gaussian weight vector before reassignment, ic j Let IC be the capacity increment of the single cell at time j. j ′ represents the set of filtered feature sequence vectors of the j-th individual cell in the battery pack;
[0039] ④ Repeat steps ① to ③ to obtain the filtered capacity increment sequence vector of each individual cell in the battery pack. The set of filtered feature sequence vectors of the battery pack is constructed as shown below:
[0040] IC′=[IC1′,IC2′,…,IC j ′,…,IC n ′]
[0041] In the formula, IC′ is the set of filtered feature sequence vectors of the battery pack, IC1′ is the set of filtered feature sequence vectors of the first individual cell of the battery pack, IC2′ is the set of filtered feature sequence vectors of the second individual cell of the battery pack, and IC... j Let ' be the set of filtered feature sequence vectors of the j-th individual cell in the battery pack, and IC n ′ represents the set of filtered feature sequence vectors of the nth individual cell in the battery pack.
[0042] Preferably, the specific method for determining the length of the capacity increment sequence vector of each individual battery in the unified filtered feature sequence vector set in step 2) is as follows:
[0043] 2-1) Perform data segmentation and aggregation approximation on the capacity increment sequence vectors of each individual cell in the filtered feature sequence vector set. Calculate the capacity increment value of each individual cell at each time step after aggregation using the following formula, and construct the capacity increment sequence vector of each individual cell in the battery pack after aggregation:
[0044]
[0045]
[0046] In the formula, Let be the sequence vector of the capacity increment of the j-th individual cell in the battery pack. This represents the capacity increment of the single cell after aggregation at time i. This represents the capacity increment of the single cell after polymerization at the first time step. This represents the capacity increment of the single cell after polymerization at the second time step. Let be the aggregated capacity increment value of the individual cell at time N, where N is the number of data segments in the capacity increment sequence vector of each individual cell, L is the length of each data segment in the capacity increment sequence vector of each individual cell, and ic j ′ represents the filtered capacity increment of the single cell at time j;
[0047] 2-2) Using the capacity increment sequence vector of each individual cell after the battery pack is aggregated, construct a set of feature sequence vectors for the aggregated battery pack as a set of feature sequence vectors with uniform length:
[0048]
[0049] In the formula, This is the set of feature sequence vectors aggregated from the battery pack. This is the capacity increment sequence vector of the first individual cell in the battery pack. This is the capacity increment sequence vector of the second individual cell in the battery pack. Let be the sequence vector of the capacity increment of the j-th individual cell in the battery pack. This is the capacity increment sequence vector of the nth individual cell in the battery pack.
[0050] Preferably, the battery pack distance matrix in step 3) is obtained as follows:
[0051] 3-1) Combine all the individual cells of the battery pack in pairs to form different battery combinations. Then, combine the capacity increment values at each time step in the capacity increment sequence vector of different individual cells in each battery combination in pairs to form several capacity increment value combinations. Calculate the soft dynamic time warping distance corresponding to each capacity increment value combination according to the following formula to form the soft dynamic time warping distance matrix of each battery combination:
[0052]
[0053]
[0054] In the formula, r i , j Let D be the soft dynamic time warping distance corresponding to the combination of the capacity increment value at time i in the capacity sequence vector of the a-th individual cell of the battery pack and the capacity increment value at time j in the capacity increment sequence vector of the b-th individual cell. i , j Let r be the square of the Euclidean distance between the capacity increment sequence vector of the a-th individual cell in the battery pack at time i and the capacity increment sequence vector of the b-th individual cell at time j. i-1，j Let r be the soft dynamic time warping distance corresponding to the combination of the capacity increment value at time (i-1) in the capacity sequence vector of the a-th individual cell of the battery pack and the capacity increment value at time j in the capacity increment sequence vector of the b-th individual cell. i，j-1 Let r be the soft dynamic time warping distance corresponding to the combination of the capacity increment value at time i in the capacity sequence vector of the a-th individual cell of the battery pack and the capacity increment value at time (j-1) in the capacity increment sequence vector of the b-th individual cell. i-1，j-1Let γ be the soft dynamic time warping distance corresponding to the combination of the capacity increment value at time (i-1) in the capacity sequence vector of the a-th individual cell of the battery pack and the capacity increment value at time (j-1) in the capacity increment sequence vector of the b-th individual cell, where γ is the regularization parameter. Let be the capacity increment value at time i in the capacity increment sequence vector of the a-th individual cell in the battery pack. Let be the capacity increment value at time j in the capacity increment sequence vector of the b-th individual cell of the battery pack, where e is the natural constant and S(i,j) is the state transition matrix;
[0055] 3-2) Take the element in the lower right corner of the soft dynamic time warp distance matrix of each battery pack as the final distance between two different batteries in the battery pack, and use the final distances corresponding to each battery pack to form the battery pack distance matrix.
[0056] Preferably, the specific steps in step 4) for iteratively calculating all grouping scenarios of retired batteries using the soft dynamic time warping distance of each battery combination in the battery pack distance matrix are as follows:
[0057] 4-1) Within the range of values [k] min k max Take a value k from the data as the number of groups corresponding to the current grouping scenario, and establish a many-to-one partitioning function to divide the set of feature sequence vectors with uniform length into k disjoint clusters;
[0058] 4-2) Randomly select k individual battery capacity increment sequence vectors from the feature sequence vector set after unification of length as the initial cluster center of each cluster;
[0059] 4-3) Use the K-nearest neighbor algorithm to allocate the capacity increment sequence vectors of the remaining individual cells in the feature sequence vector set after the length is unified, so that the sum of the soft dynamic time warping distances between the capacity increment sequence vectors of each individual cell and the cluster center of the cluster is minimized.
[0060] 4-4) Adjust the number of groups k in the current group, repeating steps 4-1) to 4-4) until the value range [k] is reached. min k max All grouping scenarios corresponding to the values within the bracket have been recorded.
[0061] Preferably, the degree of cohesion for each individual cell is calculated according to the following formula:
[0062]
[0063] In the formula, α(a) is the cohesion corresponding to the a-th single cell capacity increment sequence sample, and R n[a, b] represents the soft dynamic time warping distance between the capacity increment sequence vectors of the a-th and b-th individual cells in the battery pack, where n is the distance between the two cells. l For cluster label G l The corresponding number of capacity increment sequence vectors, G l This refers to the cluster labels corresponding to the capacity increment sequence vectors of the a-th and b-th individual cells in the battery pack.
[0064] Preferably, the degree of cohesion for each individual cell is calculated according to the following formula:
[0065]
[0066] β(a)=min{d1,d2,…,d nk}
[0067] k∈[k min k max ], k min ∈[1, n], k max ∈[1, n], where n is a positive integer;
[0068] In the formula, β(a) is the separation degree corresponding to the sequence of capacity increments of the a-th individual cell in the battery pack, and Ra is the resolution degree. n [a, b] represents the soft dynamic time warping distance between the capacity increment sequence vectors of the a-th and b-th individual cells in the battery pack, and d1 is... The first capacity increment sequence vector in its own cluster and The average soft dynamic time warp distance, d2 is The second capacity increment sequence vector in its own cluster and The average distance, d nk for The nth in its own cluster k Each capacity increment sequence vector and average distance, Let n be the sequence vector of the capacity increment of the a-th individual cell in the battery pack. k This represents the number of capacity increment sequence vectors in the k-th cluster of the set of feature sequence vectors after the length is unified.
[0069] Preferably, the profile coefficients of each individual cell in the battery pack in different grouping scenarios are calculated according to the following formula:
[0070]
[0071] In the formula, s(a) is The silhouette coefficients are given, where α(a) represents the cohesion of the a-th battery capacity increment sequence sample, and β(a) represents the separation of the a-th single-cell capacity increment sequence sample. Let be the capacity increment sequence vector of the a-th individual cell in the battery pack.
[0072] The advantages of this invention are as follows:
[0073] ① This invention fully utilizes the dynamic time-series information of the current cycle of retired batteries, employing a capacity increment curve sequence as the characteristic data for each individual cell. This reduces reliance on feature engineering, using the entire capacity increment sequence as characteristic data instead of selecting only a portion or certain points. This continuous time-series feature (i.e., the capacity increment curve sequence) not only includes all capacity increment data but also preserves the sequential relationships and time dependencies between these data. This feature reveals the dynamic process of electrochemical reactions within the battery, thus providing more comprehensive and in-depth battery aging information, enabling this invention to fully guarantee the consistency of retired batteries after regrouping.
[0074] ② This invention uses Soft Time Warping (SoftDTW) instead of Euclidean distance in KMedoids to achieve classification between time series.
[0075] ③ This invention only considers the continuous time series of capacity increments of retired batteries during the constant current charging period, which is highly correlated with the internal electrochemical reactions and aging of the battery. For large-scale grouping of retired batteries, this invention can greatly improve the reliability, accuracy, and efficiency of retired battery grouping.
[0076] Glossary
[0077] Battery cell: Commonly known as a single cell, it is the smallest unit in a power battery pack and is the basic unit used to realize the interconversion of chemical energy and electrical energy. It consists of a positive electrode, a negative electrode, a separator, an electrolyte, a battery case, a battery cover, and terminals (see the Baidu Encyclopedia entry "Battery Cell").
[0078] Capacity increment curve: The peaks in the capacity increment (IC) curve have unique shapes, heights, and positions. They reflect the electrochemical reactions during the charging and discharging process of lithium batteries. Changes in the peak values may be related to the loss of active materials in lithium batteries. They are commonly used in capacity increment analysis to study the electrochemical reactions inside the battery.
[0079] Capacitance increment analysis: Capacitance increment analysis is a non-destructive electrochemical analysis method that uses capacity increment sequences to study the internal electrochemical reactions of a battery without damaging its physical structure.
[0080] Soft Dynamic Time Warping (SoftDTW) is a method in the field of time series analysis, primarily used to compare and align two time series, taking into account their similarity rather than an exact match. SoftDTW is an extension of Dynamic Time Warping (DTW) that allows for more flexible time alignment by introducing "soft constraints."
[0081] The goal of soft dynamic time warping is to find the optimal time alignment path that minimizes the overall distance between two time series. Unlike standard DTW, SoftDTW introduces a smooth path rather than forcing a strict match between time points.
[0082] Charging cutoff voltage: Also known as the charging termination voltage or finite charge voltage, it is the voltage at which a battery reaches a fully charged state during a specified constant current charging period. This voltage is a key parameter in the battery charging process, defining when the charging process ends.
[0083] K-Nearest Neighbor Algorithm: Also known as the K-Nearest Neighbor (kNN) classification algorithm, it finds the k nearest neighbors (samples) and selects the class with the highest frequency among the first k samples as the predicted class.
[0084] Piecewise Aggregate Approximation (PAA) is an algorithm that generates a short sequence of data based on a long sequence of data, such that the short sequence of data has a similar trend to the long sequence of data. Attached Figure Description
[0085] Figure 1 This is a flowchart of the present invention;
[0086] Figure 2 This is a schematic diagram of the classification results in an embodiment of the present invention. Detailed Implementation
[0087] like Figure 1 As shown, a method for grouping decommissioned batteries based on soft dynamic time warping includes the following steps:
[0088] 1) Calculate the capacity increment sequence vector of each individual cell in the battery pack as follows, and smooth and denoise each capacity increment sequence vector to form a set of filtered feature sequence vectors:
[0089] 1-1) Charge the single cell using a constant current source, measure and record the voltage between the positive and negative terminals of the single cell and the corresponding cell charge value multiple times at timed intervals until the voltage between the positive and negative terminals of the single cell reaches the charging cutoff voltage.
[0090] 1-2) Calculate the capacity increment of the single cell at each time step using the following formula:
[0091]
[0092] In the formula, ic i Let Q be the capacity increment of the single cell at time i. i Let Q be the capacity value of the single cell at time i. i-1 Let V be the capacity value of the single cell at time (i-1). i Let V be the voltage value of the single cell at time i. i-1 Let be the voltage value of the single cell at time (i-1);
[0093] 1-3) Use the capacity increment values of the single cell at each time point to form the capacity increment sequence vector of the single cell.
[0094] Typically, methods for smoothing and denoising the capacity increment sequence vectors include Gaussian filtering, low-pass filtering, and wavelet transform. This embodiment uses Gaussian filtering to smooth and denoise the obtained capacity increment sequence vectors. The specific steps include:
[0095] ① Based on the number of capacity increment values in the single cell capacity increment sequence vector, a Gaussian weight is constructed, and the Gaussian weight vector is shown below:
[0096] w = [w1, w2, ..., w s ,…,w 2s+1 ]
[0097]
[0098] In the formula, w i Let be the i-th Gaussian weight in the Gaussian weight vector, π be pi, e be the natural constant, s be the window size, i be the number of capacity increment values in the single-cell capacity increment sequence vector, σ be the standard deviation of the Gaussian distribution, and w be the weight of the Gaussian weight vector. s Let w be the center weight of the Gaussian weight vector;
[0099] ② Normalize the Gaussian weight vector as follows:
[0100] (1) Remove the center weights from the Gaussian weight vector;
[0101] (2) Reassign each remaining Gaussian weight in the Gaussian weight vector according to the following formula:
[0102]
[0103] In the formula, w i w represents the i-th Gaussian weight in the Gaussian weight vector before reassignment. i ' represents the i-th Gaussian weight in the reassigned Gaussian weight vector, s is the window size, and w j This refers to the j-th Gaussian weight in the Gaussian weight vector before reassignment;
[0104] (3) The normalized Gaussian weight vector is constructed using the reassigned Gaussian weights as shown below:
[0105] w′=[w1′,w2′,…,w2′ s ]
[0106] In the formula, w′ is the normalized Gaussian weight vector, w1′ is the first Gaussian weight in the normalized Gaussian weight vector, w2′ is the second Gaussian weight in the normalized Gaussian weight vector, and w2′ is the third Gaussian weight in the normalized Gaussian weight vector. s The second-s Gaussian weight in the normalized Gaussian weight vector;
[0107] ③ Calculate the filtered capacity increment value of the single cell at each time step according to the following formula, and construct the filtered capacity increment sequence vector of the single cell:
[0108]
[0109] IC j ′=[ic1′,ic2′,…,ic i ′,…,ic q-1 ′]
[0110] In the formula, ic i ic1′ represents the filtered capacity increment of the single cell at time i, ic2′ represents the filtered capacity increment of the single cell at time 1, and ic2′ represents the filtered capacity increment of the single cell at time 2. q-1 ′ represents the filtered capacity increment of the single cell at time (q-1), w j-i+s For the (j-i+s)th Gaussian weight in the Gaussian weight vector before reassignment, ic j Let IC be the capacity increment of the single cell at time j. j ′ represents the set of filtered feature sequence vectors of the j-th individual cell in the battery pack;
[0111] ④ Repeat steps ① to ③ to obtain the filtered capacity increment sequence vector of each individual cell in the battery pack. The set of filtered feature sequence vectors of the battery pack is shown below:
[0112] IC′=[IC1′,IC2′,…,IC j ′,…,IC n ′]
[0113] In the formula, IC′ is the set of filtered feature sequence vectors of the battery pack, IC1′ is the set of filtered feature sequence vectors of the first individual cell of the battery pack, IC2′ is the set of filtered feature sequence vectors of the second individual cell of the battery pack, and IC... j Let ' be the set of filtered feature sequence vectors of the j-th individual cell in the battery pack, and IC n ′ represents the set of feature sequence vectors after filtering the nth individual cell of the battery pack.
[0114] 2) Unify the length of the capacity increment sequence vector of each individual battery in the filtered feature sequence vector set as follows, to form a feature sequence vector set with unified length:
[0115] 2-1) Perform data segmentation and aggregation approximation on the capacity increment sequence vectors of each individual cell in the filtered feature sequence vector set. Calculate the capacity increment value of each individual cell at each time step after aggregation using the following formula, and construct the capacity increment sequence vector of each individual cell in the battery pack after aggregation:
[0116]
[0117]
[0118] In the formula, Let be the sequence vector of the capacity increment of the j-th individual cell in the battery pack. This represents the capacity increment of the single cell after aggregation at time i. This represents the capacity increment of the single cell after polymerization at the first time step. This represents the capacity increment of the single cell after polymerization at the second time step. Let be the aggregated capacity increment value of the individual cell at time N, where N is the number of data segments in the capacity increment sequence vector of each individual cell, L is the length of each data segment in the capacity increment sequence vector of each individual cell, and ic j ′ represents the filtered capacity increment of the single cell at time j;
[0119] 2-2) Using the capacity increment sequence vector of each individual cell after the battery pack is aggregated, construct a set of feature sequence vectors for the aggregated battery pack as a set of feature sequence vectors with uniform length:
[0120]
[0121] In the formula, This is the set of feature sequence vectors aggregated from the battery pack. This is the capacity increment sequence vector of the first individual cell in the battery pack. This is the capacity increment sequence vector of the second individual cell in the battery pack. Let be the sequence vector of the capacity increment of the j-th individual cell in the battery pack. This is the capacity increment sequence vector of the nth individual cell in the battery pack.
[0122] Therefore, the segmented aggregation approximation algorithm used in this embodiment can be applied to unify the length of the capacity increment sequence vector of each individual battery, as long as it is possible to use time series dimensionality reduction to map long sequences to short sequences and unify the length of all sequences. For example, particle swarm optimization algorithm.
[0123] 3) Combine all individual cells in the battery pack into pairs to form different battery combinations. Calculate the soft dynamic time-warped distance of each battery combination using a set of feature sequence vectors of uniform length, forming the battery pack distance matrix:
[0124] 3-1) Combine all the individual cells of the battery pack in pairs to form different battery combinations. Then, combine the capacity increment values at each time step in the capacity increment sequence vector of different individual cells in each battery combination in pairs to form several capacity increment value combinations. Calculate the soft dynamic time warping distance corresponding to each capacity increment value combination according to the following formula to form the soft dynamic time warping distance matrix of each battery combination:
[0125]
[0126]
[0127] In the formula, r i , j Let D be the soft dynamic time warping distance corresponding to the combination of the capacity increment value at time i in the capacity sequence vector of the a-th individual cell of the battery pack and the capacity increment value at time j in the capacity increment sequence vector of the b-th individual cell. This is the shortest path from the element (1, 1) in the matrix to a point (i, j). i，j Let r be the square of the Euclidean distance between the capacity increment sequence vector of the a-th individual cell in the battery pack at time i and the capacity increment sequence vector of the b-th individual cell at time j. i-1，jLet r be the soft dynamic time warping distance corresponding to the combination of the capacity increment value at time (i-1) in the capacity sequence vector of the a-th individual cell of the battery pack and the capacity increment value at time j in the capacity increment sequence vector of the b-th individual cell. i，j-1 Let r be the soft dynamic time warping distance corresponding to the combination of the capacity increment value at time i in the capacity sequence vector of the a-th individual cell of the battery pack and the capacity increment value at time (j-1) in the capacity increment sequence vector of the b-th individual cell. i-1，j-1 Let γ be the soft dynamic time warping distance corresponding to the combination of the capacity increment value at time (i-1) in the capacity sequence vector of the a-th individual cell of the battery pack and the capacity increment value at time (j-1) in the capacity increment sequence vector of the b-th individual cell, where γ is the regularization parameter. Let be the capacity increment value at time i in the capacity increment sequence vector of the a-th individual cell in the battery pack. Let be the capacity increment value at time j in the capacity increment sequence vector of the b-th individual cell of the battery pack, where e is the natural constant and S(i,j) is the state transition matrix;
[0128] In this embodiment, S(i,j)={(i-1,j),(i,j-1),(i-1,j-1)}, and the soft dynamic time warp distance matrix corresponding to the battery combination formed by the a-th single cell and the b-th single cell of the battery pack is shown below:
[0129]
[0130] Similarly, based on the calculation formula in step 3-1), the soft dynamic time warping distance matrix corresponding to all battery combinations can be obtained.
[0131] 3-2) Take the element in the lower right corner of the soft dynamic time warp distance matrix of each battery pack as the final distance between two different batteries in the battery pack, and use the final distances corresponding to each battery pack to form the battery pack distance matrix.
[0132] For example, the soft dynamic time-warped distance matrix corresponding to the battery combination formed by the a-th cell and the b-th cell of the battery pack is shown below:
[0133]
[0134] In this embodiment, the element r of the above matrix is... m , m R represents the final distance R between the a-th and b-th individual cells of the battery pack. a , b Similarly, the final distances corresponding to each battery combination are integrated into an n×n distance matrix R. n, the battery pack distance matrix is obtained as follows:
[0135]
[0136] In the battery pack distance matrix of this embodiment, R1,2 represents the final distance between the first single battery and the second single battery of the battery pack, and this distance is also the soft dynamic time warping distance.
[0137] 4) Iteratively calculate all grouping scenarios of the retired batteries by using the soft dynamic time warping distances of each battery combination in the battery pack distance matrix in the following manner:
[0138] 4-1) Take a value k within the value range [k min , k max as the number of groups corresponding to the current grouping scenario. Represent the capacity increment sequence samples of each single battery by a positive integer a, and use L(a)=l to represent a many-to-one partitioning function, where a∈{1, 2,..., n} and l∈{1, 2,..., k}, and k < n. Divide the set of feature sequence vectors with unified length into k non-overlapping clusters G1, G2,..., G l ,..., G k ;
[0139] 4-2) Randomly select k capacity increment sequence vectors of single batteries in the set of feature sequence vectors with unified length as the initial cluster centers of each cluster. Assume that the randomly selected initial cluster centers are
[0140] For example, let be the capacity increment sequence vector of a certain single battery in the battery pack, that is, the initial cluster center of the a-th cluster, and so on.
[0141] 4-3) Use the K-nearest neighbor algorithm to allocate the capacity increment sequence vectors of the remaining single batteries in the set of feature sequence vectors with unified length, so that the sum of the soft dynamic time warping distances between each capacity increment sequence vector of a single battery and the cluster center of the cluster where it is located is the minimum value. For example:
[0142] ⑴ For the given initial cluster centers, find the partition L, that is, given the cluster centers, allocate the capacity increment sequence vectors of each single battery to a cluster, so that the sum of the distances between each capacity increment sequence vector of a single battery and the cluster center of the cluster to which it belongs is the smallest, that is, the total soft dynamic time warping distance is the smallest.
[0143] For example, the total soft dynamic time warping distance is calculated according to the following formula to make the objective function C a minimum value. According to the result, allocate each sequence to the class of the nearest center :
[0144]
[0145] In the formula, C is the total soft dynamic time warping distance between the capacity increment sequence vector of each individual cell in all clusters and its cluster center, L is the partitioning function of each individual cell in the battery pack, and R... n [l, a] is the soft dynamic time warping distance between the cluster center of the current cluster (the capacity increment sequence vector of the l-th cell in the battery pack) and the capacity increment sequence vector of the j-th cell.
[0146] (2) Solve the L obtained from the above equation to obtain the new centers of each cluster. Minimize the objective function:
[0147]
[0148] For each n l A cluster G of sequence vectors l Replace its cluster center To obtain the new cluster center
[0149] (3) Repeat steps (1) to (3) until the cluster division and cluster centers no longer change. Record the sorting result corresponding to the number of groups k in the current group, that is, divide all the individual cells of the battery pack into k groups. This grouping scenario is as follows: Figure 2 As shown in the figure, each group has a colored curve, which represents the final cluster center determined after the capacity increment sequence vector of each individual cell is allocated to each cluster.
[0150] 4-4) Adjust the number of groups k in the current group, repeating steps 4-1) to 4-4) until the value range [k] is reached. min k max All grouping scenarios corresponding to the values within the bracket have been recorded.
[0151] 5) In each group scenario, the cohesion and separation of each individual cell are calculated using soft dynamic time warping distance:
[0152] 5-1) The mathematical expression for cohesion is as follows:
[0153]
[0154] In the formula, α(a) is the cohesion corresponding to the a-th single cell capacity increment sequence sample, and R n [a, b] represents the soft dynamic time warping distance between the capacity increment sequence vectors of the a-th and b-th individual cells in the battery pack, where n is the distance between the two cells. l For cluster label G l The corresponding number of capacity increment sequence vectors, Gl This refers to the cluster labels corresponding to the capacity increment sequence vectors of the a-th and b-th individual cells in the battery pack.
[0155] In this embodiment, the capacity increment sequence vector of the a-th individual cell in the battery pack is defined as follows: The cluster label is an integer L(a), and the number of capacity increment sequence vectors corresponding to the cluster label L(a) is n. l In the mathematical expression for cohesion above, the a-th capacity increment sequence vector in the set of feature sequence vectors after the length is unified belongs to the L(a)-th cluster, and L(b) also represents the initial cluster center of the b-th cluster.
[0156] 5-2) The mathematical expression for the separation degree is as follows:
[0157]
[0158] β(a)=min{d1,d2,…,d nk}
[0159] k∈[k min k max ], k min ∈[1, n], k max ∈[1, n], where n is a positive integer;
[0160] In the formula, β(a) is the separation degree corresponding to the sequence of capacity increments of the a-th individual cell in the battery pack, and Ra is the resolution degree. n [a, b] represents the soft dynamic time warping distance between the capacity increment sequence vectors of the a-th and b-th individual cells in the battery pack, and d1 is... The first capacity increment sequence vector in its own cluster and The average soft dynamic time warp distance, d2 is The second capacity increment sequence vector in its own cluster and average distance, for The nth in its own cluster k Each capacity increment sequence vector and average distance, Let n be the sequence vector of the capacity increment of the a-th individual cell in the battery pack. k This represents the number of capacity increment sequence vectors in the k-th cluster of the set of feature sequence vectors after the length is unified.
[0161] 6) Calculate the profile coefficients of each individual cell in the battery pack under different grouping scenarios using the cohesion and separation of each individual cell. The mathematical expressions are as follows:
[0162]
[0163] In the formula, s(a) is The silhouette coefficients are given, where α(a) represents the cohesion of the a-th battery capacity increment sequence sample, and β(a) represents the separation of the a-th single-cell capacity increment sequence sample. Let be the capacity increment sequence vector of the a-th individual cell in the battery pack.
[0164] 7) Calculate the average contour coefficient for each group of scenarios. That is, calculate the range of values for k [k min k max The average contour coefficient of each group of scenes corresponding to all values within the range.
[0165] For example, when k = k min At that time, all the individual cells in the battery pack are divided into k min The grouping process utilizes the cohesion and separation of each individual cell in the current grouping scenario to calculate the silhouette coefficients s1, s2, ..., s of the capacity increment sequence vector of each individual cell in the battery pack within that grouping scenario. i 、…、s n average profile coefficient Calculate using the following formula:
[0166]
[0167] In the formula, When k = k min The average contour coefficient of the grouped scene at that time, s i Let be the profile coefficient of the i-th individual cell in the battery pack, and n be the number of individual cells in the battery pack.
[0168] And so on, calculate respectively
[0169] Then through comparison The optimal grouping scenario is determined by the size of the contour coefficient, and the individual cells of the battery pack are grouped according to the optimal grouping scenario.
[0170] Experiments have verified that this invention can greatly improve the reliability, accuracy, and efficiency of retired battery grouping. It is applicable not only to retired battery grouping of a single battery pack, but also to retired battery grouping of multiple battery packs of the same model. Moreover, the larger the number of retired batteries involved in the grouping, the better the grouping effect (for example, the consistency of capacity, charge efficiency, and internal resistance can all be greatly improved).
[0171] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications made to the present invention by those skilled in the art without departing from the spirit of the present invention shall fall within the protection scope of the present invention.
Claims
1. A method for grouping decommissioned batteries based on soft dynamic time warping, characterized in that, Includes the following steps: 1) By measuring and calculating the capacity increment sequence vector of each individual cell in the battery pack, the capacity increment sequence vector is smoothed and denoised to form a set of filtered feature sequence vectors; 2) The lengths of the capacity increment sequence vectors of each individual battery cell are unified into a set of feature sequence vectors with unified lengths. 3) Combine all individual cells of the battery pack in pairs to form different battery combinations. Calculate the soft dynamic time-warped distance of each battery combination using a set of feature sequence vectors of uniform length, forming a battery pack distance matrix. The battery pack distance matrix is obtained as follows: 3-1) Combine all the individual cells of the battery pack in pairs to form different battery combinations. Then, combine the capacity increment values at each time step in the capacity increment sequence vector of different individual cells in each battery combination in pairs to form several capacity increment value combinations. Calculate the soft dynamic time warping distance corresponding to each capacity increment value combination according to the following formula to form the soft dynamic time warping distance matrix of each battery combination: ； ； In the formula, For this battery pack In the capacity sequence vector of the nth single cell The capacity increment value at time t and the first In the capacity increment sequence vector of the nth single cell The soft dynamic time warping distance corresponding to the combination of capacity increment values at any given time. For this battery pack The capacity increment sequence vector of the first individual cell The capacity increment value at time t and the first In the capacity increment sequence vector of the nth single cell The square of the Euclidean distance between the capacity increments at time points. For this battery pack In the capacity sequence vector of the nth single cell The capacity increment value at time t and the first In the capacity increment sequence vector of the nth single cell The soft dynamic time warping distance corresponding to the combination of capacity increment values at any given time. For this battery pack In the capacity sequence vector of the nth single cell The capacity increment value at time t and the first In the capacity increment sequence vector of the nth single cell The soft dynamic time warping distance corresponding to the combination of capacity increment values at any given time. For this battery pack In the capacity sequence vector of the nth single cell The capacity increment value at time t and the first In the capacity increment sequence vector of the nth single cell The soft dynamic time warping distance corresponding to the combination of capacity increment values at any given time. For regularization parameters, For this battery pack In the capacity increment sequence vector of the nth single cell The capacity increment value at time t. For this battery pack In the capacity increment sequence vector of the nth single cell The capacity increment value at time t. It is a natural constant. This is the state transition matrix; 3-2) Take the element in the lower right corner of the soft dynamic time warp distance matrix of each battery pack as the final distance between two different batteries in the battery pack, and use the final distances corresponding to each battery pack to form the battery pack distance matrix. 4) Calculate all grouping scenarios of retired batteries using the soft dynamic time warping distance of each battery combination in the battery pack distance matrix; 5) The cohesion and separation of each individual cell in different grouping scenarios are calculated using soft dynamic time warping distance; 6) Calculate the profile coefficients of each individual cell in the battery pack in different grouping scenarios using the cohesion and separation of each individual cell. 7) Calculate the average profile coefficient for each group scenario, take the group scenario with the largest average profile coefficient as the best group scenario, and group each individual cell of the battery pack according to the best group scenario.
2. The method for grouping decommissioned batteries based on soft dynamic time warping according to claim 1, characterized in that, The capacity increment sequence vector of each individual cell in the battery pack is obtained in the following manner: 1-1) Charge the single cell using a constant current source, measure and record the voltage between the positive and negative terminals of the single cell and the corresponding cell charge value multiple times at timed intervals until the voltage between the positive and negative terminals of the single cell reaches the charging cutoff voltage. 1-2) Calculate the capacity increment of the single cell at each time step using the following formula: ； In the formula, For this single cell in the first The capacity increment value at each moment. For this single cell in the first The capacity value at each moment. For this single cell in the first The capacity value at each moment. For this single cell in the first The voltage value at each moment. For this single cell in the first The voltage value at each moment; 1-3) Use the capacity increment values of the single cell at each time point to form the capacity increment sequence vector of the single cell.
3. The method for grouping decommissioned batteries based on soft dynamic time warping according to claim 1, characterized in that, Step 1) involves smoothing and denoising each capacity increment sequence vector using methods such as Gaussian filtering, low-pass filtering, and wavelet transform.
4. The method for grouping decommissioned batteries based on soft dynamic time warping according to claim 3, characterized in that, The specific steps for smoothing and denoising each capacity increment sequence vector using Gaussian filtering are as follows: ① Based on the number of capacity increment values in the single cell capacity increment sequence vector, a Gaussian weight is constructed, and the Gaussian weight vector is shown below: ； ； In the formula, The first Gaussian weight vector is the... Gaussian weights, Pi It is a natural constant. For window size, This represents the number of capacity increment values in the sequence vector of capacity increments for a single battery cell. The standard deviation is a Gaussian distribution. The center weights of the Gaussian weight vector are... The Gaussian weight vector; ② Normalize the Gaussian weight vector as follows: (1) Remove the center weights from the Gaussian weight vector; (2) Reassign each remaining Gaussian weight in the Gaussian weight vector according to the following formula: ； In the formula, The Gaussian weight vector before reassignment Gaussian weights, For the Gaussian weight vector after reassignment, the first... Gaussian weights, For window size, The Gaussian weight vector before reassignment Gaussian weights; (3) The normalized Gaussian weight vector is constructed using the reassigned Gaussian weights as shown below: ； In the formula, This is the normalized Gaussian weight vector. The first Gaussian weight in the normalized Gaussian weight vector. The second Gaussian weight in the normalized Gaussian weight vector. The second-s Gaussian weight in the normalized Gaussian weight vector; ③ Calculate the filtered capacity increment value of the single cell at each time step according to the following formula, and construct the filtered capacity increment sequence vector of the single cell: ； ； In the formula, For this single cell in the first The filtered capacity increment value at each time point This represents the filtered capacity increment of the single cell at time 1. This represents the filtered capacity increment of the single cell at time step 2. For this single cell in the first The filtered capacity increment value at each time point The Gaussian weight vector before reassignment Gaussian weights, For this single cell in the first The capacity increment value at each moment. For this battery pack A set of feature sequence vectors after filtering of a single battery cell; ④ Repeat steps ① to ③ to obtain the filtered capacity increment sequence vector of each individual cell in the battery pack. The set of filtered feature sequence vectors of the battery pack is constructed as shown below: ； In the formula, This is the set of filtered feature sequence vectors for the battery pack. This is the set of filtered feature sequence vectors for the first individual cell of the battery pack. This is the set of filtered feature sequence vectors for the second individual cell in the battery pack. For this battery pack The set of feature sequence vectors after filtering of individual battery cells For this battery pack A set of feature sequence vectors after filtering each individual battery cell.
5. The method for grouping decommissioned batteries based on soft dynamic time warping according to claim 1, characterized in that, The specific method for determining the length of the capacity increment sequence vector of each individual battery in the unified filtered feature sequence vector set in step 2) is as follows: 2-1) Perform data segmentation and aggregation approximation on the capacity increment sequence vectors of each individual cell in the filtered feature sequence vector set. Calculate the capacity increment value of each individual cell at each time step after aggregation using the following formula, and construct the capacity increment sequence vector of each individual cell in the battery pack after aggregation: ； ； In the formula, The first in this battery pack A sequence vector of capacity increments for each individual battery cell. For this single cell The aggregated capacity increment value at each time point This represents the capacity increment of the single cell after polymerization at the first time step. This represents the capacity increment of the single cell after polymerization at the second time step. For this single cell The aggregated capacity increment value at each time point The number of data segments for each individual battery capacity increment sequence vector. The length of the data segment for each individual battery capacity increment sequence vector. For this single cell in the first The filtered capacity increment value at each time point; 2-2) Using the capacity increment sequence vector of each individual cell after the battery pack is aggregated, construct a set of feature sequence vectors for the aggregated battery pack as a set of feature sequence vectors with uniform length: ； In the formula, This is the set of feature sequence vectors aggregated from the battery pack. This is the capacity increment sequence vector of the first individual cell in the battery pack. This is the capacity increment sequence vector of the second individual cell in the battery pack. The first in this battery pack A sequence vector of capacity increments for each individual battery cell. The first in this battery pack A sequence vector of capacity increments for each individual cell.
6. The method for grouping decommissioned batteries based on soft dynamic time warping according to claim 1, characterized in that, The specific steps for calculating all group scenarios of retired batteries using the soft dynamic time warping distance iteration of each battery combination in the battery pack distance matrix in step 4) are as follows: 4-1) Within the range of values Take a value from Assuming the number of groups corresponding to the current grouping scenario, and establishing a many-to-one partitioning function, the set of feature sequence vectors with uniform length is divided into... A non-overlapping cluster; 4-2) Randomly select from the set of feature sequence vectors of uniform length The capacity increment sequence vector of each individual cell is used as the initial cluster center for each cluster; 4-3) Use the K-nearest neighbor algorithm to allocate the capacity increment sequence vectors of the remaining individual cells in the feature sequence vector set after the length is unified, so that the sum of the soft dynamic time warping distances between the capacity increment sequence vectors of each individual cell and the cluster center of the cluster is minimized. 4-4) Adjust the number of groups in the current group. The size is determined by repeating steps 4-1) to 4-4) until the range of values is reached. All grouping scenarios corresponding to the values within have been recorded.
7. The method for grouping decommissioned batteries based on soft dynamic time warping according to claim 1, characterized in that, The degree of cohesion for each individual cell is calculated using the following formula: ； In the formula, For the first The cohesion corresponding to the sequence of incremental capacity of individual cells For this battery pack The single cell and the first The soft dynamic time warping distance between the capacity increment sequence vectors of individual cells. Cluster label The corresponding number of capacity increment sequence vectors, The first in this battery pack The and the first Cluster labels corresponding to the sequence vectors of individual cell capacity increments.
8. The method for grouping decommissioned batteries based on soft dynamic time warping according to claim 1, characterized in that, The degree of cohesion for each individual cell is calculated using the following formula: ； ； , , It is a positive integer; In the formula, For this battery pack The separation degree corresponding to the sequence of incremental capacity of individual cells For this battery pack The single cell and the first The soft dynamic time warping distance between the capacity increment sequence vectors of individual cells. for The first capacity increment sequence vector in its own cluster and The average soft dynamic time warp distance, for The second capacity increment sequence vector in its own cluster and average distance, for The first in its own cluster Each capacity increment sequence vector and average distance, For this battery pack A sequence vector of capacity increments for each individual battery cell. The first element in the set of feature sequence vectors after unification of length. The number of capacity increment sequence vectors in each cluster.
9. The method for grouping decommissioned batteries based on soft dynamic time warping according to claim 1, characterized in that, The profile coefficients of each individual cell in the battery pack for different grouping scenarios are calculated according to the following formula: ； In the formula, for The profile coefficient, For the first The cohesion corresponding to each battery capacity increment sequence sample For the first The separation degree corresponding to the sequence of incremental capacity of individual cells For this battery pack A sequence vector of capacity increments for each individual cell.