Lithium battery charge state rapid detection method

Abstract

The invention provides a lithium battery state-of-charge rapid detection method, and belongs to the technical field of lithium battery detection.The lithium battery state-of-charge rapid detection method comprises the steps that the surface temperature and the initial end voltage of a to-be-detected lithium battery are collected, and the internal resistance growth rate and the capacity fading rate are obtained through a pulse discharge test to evaluate the health state grade; carrying out impedance measurement on the characteristic frequency points to obtain impedance real part and imaginary part data to form a characteristic frequency impedance vector, extracting a statistical moment characteristic vector, inputting a battery state topology reasoning model to output a primary charge state estimation value and local area charge state distribution, extracting auxiliary characteristics in a low-resolution interval to carry out dynamic correction, and judging whether to increase the measurement frequency points according to the confidence interval width. The method solves the technical problems that the lithium battery state-of-charge detection is insufficient in estimation precision and cannot quantify the uncertainty when facing health state degradation and a low-resolution interval.

Description

Technical Field

[0001] This invention belongs to the field of lithium battery testing technology, and more specifically, relates to a rapid method for detecting the state of charge of lithium batteries. Background Technology

[0002] Lithium-ion battery state-of-charge (SOC) detection is a key technology in battery management systems, with significant applications in scenarios such as rapid customs clearance, energy storage system monitoring, and electric vehicle energy management. Traditional SOC detection methods mainly include the open-circuit voltage method, the ampere-hour integration method, the Kalman filter method, and the neural network method. The open-circuit voltage method obtains an estimate of the SOC by measuring the battery's terminal voltage after resting and finding the voltage-SOC curve. The ampere-hour integration method calculates the change in charge by integrating the charging and discharging current. The Kalman filter method establishes an equivalent circuit model of the battery and estimates the SOC using a state observer. The neural network method uses a large amount of training data to establish a mapping relationship between voltage, current, temperature, and SOC. In current lithium-ion battery detection applications, due to aging phenomena such as capacity decay and internal resistance increase during use, and the small gradient of open-circuit voltage change in the SOC range below 20% or above 80%, traditional methods experience significantly increased estimation errors when dealing with batteries in degraded healthy states. Furthermore, traditional methods only output a single numerical result and cannot provide a quantitative indicator of estimation reliability. In other words, existing technologies suffer from technical problems such as insufficient estimation accuracy and inability to quantify uncertainty when facing health degradation and low-resolution ranges in lithium battery state of charge detection. Summary of the Invention

[0003] In view of this, the present invention provides a rapid method for detecting the state of charge of lithium batteries, which can solve the technical problems of insufficient estimation accuracy and inability to quantify uncertainty in the existing lithium battery state of charge detection when facing health degradation and low resolution range.

[0004] This invention is implemented as follows: It provides a rapid detection method for the state of charge (SOC) of a lithium battery, including acquiring the surface temperature and initial terminal voltage of the lithium battery under test; obtaining the internal resistance growth rate and capacity decay rate of the lithium battery under test through pulse discharge testing to assess its health status and record them as a health status identifier; performing a full-band impedance spectrum scan on a standard lithium battery under different SOCs, selecting the frequency point with the highest sensitivity index as the characteristic frequency point; performing impedance measurement on the lithium battery under test based on the characteristic frequency point to obtain the real and imaginary impedance data, forming a characteristic frequency impedance vector; extracting the statistical moment feature vector based on the initial terminal voltage and the characteristic frequency impedance vector; and then... The battery state topology inference model is input with the degree, initial terminal voltage, characteristic frequency impedance vector, and health status identifier. The output is a preliminary state of charge (SOC) estimate and a local SOC distribution. Based on the preliminary SOC estimate, local SOC distribution, and statistical moment feature vector, the SOC probability density function is constructed using the maximum entropy principle. The expected SOC value and confidence interval are calculated using Monte Carlo sampling. It is determined whether the expected SOC value is in a low-resolution interval. If it is in a low-resolution interval, auxiliary features are extracted for dynamic correction to obtain the final SOC detection result. Based on the confidence interval width, it is determined whether to increase the measurement frequency point and re-execute the impedance measurement and subsequent steps.

[0005] The pulse discharge test specifically involves applying a constant current discharge pulse to the lithium battery under test for a duration of 10 seconds, recording the voltage difference before and after the pulse and the voltage recovery value after stabilization, calculating the current internal resistance value and the internal resistance growth rate based on the voltage difference, and estimating the remaining capacity and the capacity decay rate based on the voltage recovery value.

[0006] Specifically, the health status is determined as follows: when the internal resistance growth rate is less than 20% and the capacity decay rate is less than 10%, it is marked as health level one; when the internal resistance growth rate is between 20% and 50% or the capacity decay rate is between 10% and 20%, it is marked as health level two; and when the internal resistance growth rate is greater than 50% or the capacity decay rate is greater than 20%, it is marked as health level three.

[0007] The specific steps for selecting characteristic frequency points are as follows: calculate the absolute value of the partial derivative of the impedance value with respect to the state of charge at each frequency point, normalize the absolute value of the partial derivative and use it as a sensitivity index, and select 5 to 8 frequency points with the largest sensitivity index as characteristic frequency points.

[0008] Specifically, the impedance measurement steps involve applying a small-amplitude AC excitation signal to each characteristic frequency point, measuring the amplitude and phase of the response current, calculating the impedance magnitude based on the ratio of the voltage amplitude to the current amplitude, calculating the impedance phase angle based on the difference between the voltage phase and the current phase, multiplying the impedance magnitude by the cosine of the impedance phase angle to obtain the real part of the impedance data, and multiplying the impedance magnitude by the sine of the impedance phase angle to obtain the imaginary part of the impedance data.

[0009] Specifically, the steps for extracting the statistical moment feature vector are as follows: calculating the mean and variance of the initial terminal voltage as the voltage moment feature; calculating the mean and variance of the real part of the impedance data in the characteristic frequency impedance vector as the impedance moment feature; normalizing the surface temperature as the temperature moment feature; and combining the voltage moment feature, impedance moment feature, and temperature moment feature to form the statistical moment feature vector.

[0010] The battery state topology reasoning model includes a battery topology graph construction layer, a graph convolution feature extraction layer, a dynamic connection optimization layer, and a state output layer. The battery topology graph construction layer abstracts the multi-layer electrode structure inside the lithium battery into a graph structure, where nodes represent local regions divided inside the battery and edges represent lithium-ion diffusion channels between adjacent local regions.

[0011] The graph convolution feature extraction layer employs multi-layer graph convolution operations. Each graph convolution layer updates the feature representation of the current node by aggregating information from neighboring nodes. The aggregation function is a weighted summation, and the weights are adaptively calculated by the attention mechanism. The attention weights are determined based on a combination of node feature similarity and edge weights.

[0012] The dynamic connection optimization layer implements a sparse connection learning framework based on dynamic topology reconstruction. During training, the activation frequency and gradient contribution of each connection edge are statistically analyzed to calculate the connection importance score. When the connection importance score is lower than the dynamic threshold, the connection edge is pruned with a certain probability. The dynamic threshold is adaptively adjusted according to the current network sparsity and the rate of decrease of the loss function.

[0013] The state output layer consists of two branches: node-level output and global output. The node-level output maps the features of each node to the estimated state of charge of the corresponding local region through a fully connected layer. The global output calculates a weighted average of all node-level state of charge estimates to obtain the overall preliminary state of charge estimate. The weighting coefficients are determined by the confidence scores of the node features.

[0014] Specifically, the steps for constructing the probability density function of the state of charge using the maximum entropy principle are as follows: calculate the mean of the preliminary estimated state of charge in the local region's state of charge distribution as the first moment, calculate the variance of the local region's state of charge distribution as the second moment, calculate the skewness of the local region's state of charge distribution as the third moment, combine the first, second, and third moments with the statistical moment eigenvector to form an extended statistical moment eigenvector, and use the moments in the extended statistical moment eigenvector as constraints to solve for the optimal state of charge probability density function using the Lagrange multiplier method.

[0015] Specifically, the steps for generating a charged state sample set through Monte Carlo sampling are as follows: 10,000 charged state sample points are generated by Monte Carlo sampling of the optimal charged state probability density function; all charged state sample points are sorted from smallest to largest to form a charged state sample set; the arithmetic mean of the charged state sample set is calculated as the expected value of the charged state; and the interval between the 2.5 percentile and the 97.5 percentile of the charged state sample set is calculated as the confidence interval.

[0016] The low-resolution range refers to the range where the state of charge is below 20% or above 80%. The auxiliary features include the rate of change of the real part of the AC internal resistance at 1 kHz and the voltage drop rate of the short-time constant current amplifier. The calculation of the rate of change of the real part of the AC internal resistance at 1 kHz involves selecting three state of charge test points within a 5% range around the expected value of the state of charge. The real part of the AC internal resistance at 1 kHz is measured at each state of charge test point. The slope is obtained by linear fitting of the real part of the AC internal resistance at the three state of charge test points and then normalized.

[0017] Specifically, the extraction of the short-time constant current discharge voltage drop rate involves applying a constant discharge current for 5 seconds to the lithium battery under test, recording the change curve of the terminal voltage over time during the discharge process, linearly fitting the data of the first 3 seconds of the change curve to obtain the voltage drop slope, and normalizing the voltage drop slope by dividing it by the constant discharge current to obtain the short-time constant current discharge voltage drop rate.

[0018] The dynamic correction step specifically involves using a two-dimensional temperature-state-of-charge lookup table and the entropy coefficient method to calculate the temperature compensation factor. The comprehensive correction amount is obtained by multiplying the real part change rate of the AC internal resistance at 1kHz, the short-time constant current amplifier voltage drop rate, and the temperature compensation factor by their respective weighting coefficients. The comprehensive correction amount is then superimposed on the expected state of charge value to obtain the final state of charge detection result.

[0019] Specifically, the step of determining whether the confidence interval width is greater than the preset threshold involves calculating the difference between the 97.5th percentile and the 2.5th percentile of the confidence interval as the confidence interval width, comparing the confidence interval width with the preset threshold, and if the confidence interval width is greater than the preset threshold, then adding the 9th to 12th frequency points ranked by sensitivity index to the characteristic frequency points and re-performing the impedance measurement and subsequent steps.

[0020] This invention addresses the technical problems of insufficient estimation accuracy and inability to quantify uncertainty in lithium battery state-of-charge (SOC) detection when facing declining health status and low-resolution ranges by constructing a probabilistic estimation framework that integrates multi-source measurement information and introducing an adaptive correction mechanism. The invention employs pulse discharge testing to assess the battery's SOC level and inputs the SOC identifier into the battery SOC topology inference model. This allows the model to adaptively adjust its feature extraction strategy based on different aging levels, improving its adaptability to batteries with declining health status and overcoming the shortcomings of traditional methods that ignore differences in SOC, leading to increased estimation errors. The invention utilizes the maximum entropy principle to reconstruct the SOC probability density function from the initial estimate, local region distribution, and statistical moment feature constraints. Monte Carlo sampling is used to calculate the expected value and confidence interval, extending the single numerical estimate to a probability distribution that includes uncertainty quantification, thus overcoming the shortcomings of traditional methods that cannot provide reliability indicators. When the expected SOC value is in the low-resolution range, this invention extracts the AC internal resistance change rate and short-time constant-current discharge voltage drop rate as auxiliary features for dynamic correction, compensating for insufficient open-circuit voltage sensitivity and overcoming the shortcomings of traditional methods that experience accuracy degradation in the low-resolution range. In summary, this invention solves the technical problems mentioned in the background art regarding the insufficient estimation accuracy and inability to quantify uncertainty in lithium battery state of charge detection when facing health degradation and low-resolution ranges. Attached Figure Description

[0021] Figure 1 This is a flowchart of the method of the present invention.

[0022] Figure 2 This is a distribution chart of sensitivity indicators at different frequency points.

[0023] Figure 3 This is a diagram showing the battery topology structure and connection weight distribution.

[0024] Figure 4 This is a graph of the probability density function of charged states constructed based on the principle of maximum entropy.

[0025] Figure 5 A comparison of the probability density functions of the state of charge before and after the extended frequency point. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below.

[0027] like Figure 1 The diagram shown is a flowchart of a rapid detection method for the state of charge of a lithium battery provided by the present invention. This method includes the following steps:

[0028] S1. Collect the surface temperature and initial terminal voltage of the lithium battery under test, obtain the internal resistance growth rate and capacity decay rate of the lithium battery under test through pulse discharge test, evaluate the health status level of the lithium battery under test and record it as a health status identifier.

[0029] S2. Perform full-band impedance spectrum scanning on standard lithium batteries under different states of charge, calculate the absolute value of the partial derivative of the impedance value with respect to the state of charge at each frequency point, normalize the absolute value of the partial derivative and use it as a sensitivity index, and select 5 to 8 frequency points with the largest sensitivity index as characteristic frequency points.

[0030] S3. Perform impedance measurement on the lithium battery under test according to the characteristic frequency points, obtain the real part data and imaginary part data of impedance at each characteristic frequency point, and arrange the real part data and imaginary part data of impedance at all characteristic frequency points in order of frequency from low to high to form a characteristic frequency impedance vector.

[0031] S4. Based on the initial terminal voltage and the characteristic frequency impedance vector, extract statistical moment features, calculate the mean and variance of the initial terminal voltage as voltage moment features, calculate the mean and variance of the real part data of the impedance in the characteristic frequency impedance vector as impedance moment features, normalize the surface temperature as temperature moment features, and combine the voltage moment features, impedance moment features and temperature moment features to form a statistical moment feature vector.

[0032] S5. Input the surface temperature, initial terminal voltage, characteristic frequency impedance vector and health status identifier into the battery state topology inference model. The battery state topology inference model outputs a preliminary state of charge estimate and a local region state of charge distribution.

[0033] S6. Based on the preliminary state of charge estimate, the local region state of charge distribution, and the statistical moment eigenvector, construct the state of charge probability density function using the maximum entropy principle, solve for the probability distribution parameters using the Lagrange multiplier method, perform Monte Carlo sampling on the state of charge probability density function to generate a state of charge sample set, calculate the arithmetic mean of the state of charge sample set as the expected state of charge, and calculate the interval between the 2.5th percentile and the 97.5th percentile of the state of charge sample set as the confidence interval.

[0034] S7. Determine whether the expected value of the state of charge is in the low-resolution range below 20% or above 80%. If the expected value of the state of charge is in the low-resolution range, extract the rate of change of the real part of the AC internal resistance at 1kHz and the short-time constant current amplifier voltage drop rate as auxiliary features. Calculate the temperature compensation factor using a temperature-state of charge two-dimensional lookup table and the entropy coefficient method. Dynamically correct the expected value of the state of charge based on the rate of change of the real part of the AC internal resistance at 1kHz, the short-time constant current amplifier voltage drop rate, and the temperature compensation factor to obtain the final state of charge detection result. If the expected value of the state of charge is not in the low-resolution range, then the expected value of the state of charge is taken as the final state of charge detection result.

[0035] S8. Calculate the difference between the 97.5th percentile and the 2.5th percentile of the confidence interval as the confidence interval width. Determine whether the confidence interval width is greater than a preset threshold. If the confidence interval width is greater than the preset threshold, add the 9th to 12th frequency points of the sensitivity index ranking based on the characteristic frequency points and re-execute steps S3 to S7. If the confidence interval width is less than or equal to the preset threshold, output the final state of charge detection result and confidence interval as a detection report.

[0036] The pulse discharge test specifically includes the following steps: applying a constant current discharge pulse with a duration of 10 seconds to the lithium battery under test, recording the voltage difference before and after the pulse and the voltage recovery value after stabilization, calculating the current internal resistance value based on the voltage difference, subtracting 1 from the ratio of the current internal resistance value to the internal resistance value of a standard new battery and multiplying by 100% to obtain the internal resistance growth rate, estimating the remaining capacity based on the voltage recovery value and the standard open-circuit voltage curve, subtracting the remaining capacity from the standard rated capacity and then dividing by the standard rated capacity and multiplying by 100% to obtain the capacity decay rate.

[0037] The steps for determining the health status indicator specifically include: marking it as health level one when the internal resistance growth rate is less than 20% and the capacity decay rate is less than 10%; marking it as health level two when the internal resistance growth rate is between 20% and 50% or the capacity decay rate is between 10% and 25%; and marking it as health level three when the internal resistance growth rate is greater than 50% or the capacity decay rate is greater than 25%.

[0038] The specific steps for impedance measurement of the lithium battery under test include: applying a small-amplitude AC excitation signal to each characteristic frequency point, measuring the amplitude and phase of the response current, calculating the impedance magnitude based on the ratio of the voltage amplitude to the current amplitude, calculating the impedance phase angle based on the difference between the voltage phase and the current phase, multiplying the impedance magnitude by the cosine of the impedance phase angle to obtain the real part of the impedance data, and multiplying the impedance magnitude by the sine of the impedance phase angle to obtain the imaginary part of the impedance data.

[0039] The battery state topology reasoning model is structured as follows: it includes a battery topology graph construction layer, a graph convolutional feature extraction layer, a dynamic connection optimization layer, and a state output layer. The battery topology graph construction layer abstracts the multi-layered electrode structure inside the lithium battery into a graph structure. Nodes represent local regions within the battery, and each node is associated with local region electrochemical parameters including local impedance, local temperature, and local voltage. Edges represent lithium-ion diffusion channels between adjacent local regions, and edge weights are determined by the diffusion coefficient and the distance between local regions. The graph convolutional feature extraction layer employs multi-layer graph convolution operations. Each convolutional layer updates the feature representation of the current node by aggregating neighboring node information. The aggregation function is a weighted summation, and the weights are adaptively calculated by an attention mechanism. The attention weights are determined based on node feature similarity and edge weights. After three layers of graph convolution, the node features contain the information transmission results of three-hop neighborhoods. The dynamic connection optimization layer implements a sparse connection learning framework based on dynamic topology reconstruction. During training, the activation frequency and gradient contribution of each connection edge in the forward propagation are statistically analyzed. The connection importance score is calculated as the normalized value of the product of activation frequency and gradient contribution. When the connection importance score is lower than a dynamic threshold, the connection edge is pruned with a certain probability. The dynamic threshold is adaptively adjusted according to the current network sparsity and the rate of decrease of the loss function. At the same time, a grouping regularization constraint is applied to the retained connection weights. The connection weights are grouped according to the target node, and the L2 norm of each group is calculated. The regularization term is the weighted sum of the L2 norms of all groups. The weight coefficient is inversely proportional to the number of connections within the group, thus maintaining the expressive power of the network while promoting sparsity. The state output layer includes two branches: node-level output and global output. The node-level output maps the features of each node to the estimated state of charge of the corresponding local region of the node through a fully connected layer. The global output performs a weighted average of all node-level state of charge estimates to obtain an overall preliminary state of charge estimate. The weighting coefficient is determined by the confidence score of the node features. The confidence score is obtained by the uncertainty of the node features predicted by the auxiliary classifier.

[0040] The steps for establishing the training dataset for the battery state topology inference model specifically include: selecting over 500 lithium battery samples with different health state levels and capacity specifications; conducting charge-discharge cycle tests on each lithium battery sample under a controlled temperature environment; collecting data every 5% between 0% and 100% state of charge; each data collection includes surface temperature, terminal voltage, characteristic frequency impedance vector, health state identifier, and true state of charge label. The true state of charge label is obtained through an ampere-hour integration method combined with open-circuit voltage calibration. The ampere-hour integration method records the integral value of the charge / discharge current over time, divided by the rated capacity to obtain the change in state of charge; an open-circuit voltage calibration is performed every 10% change in state of charge to eliminate accumulated errors. Data augmentation processing is performed on the collected data: random noise conforming to a normal distribution is superimposed on the surface temperature to simulate measurement errors, and random perturbations with an amplitude within 5% are applied to the characteristic frequency impedance vector to simulate environmental interference. The size of the augmented dataset is increased to three times that of the original data. The expanded dataset was divided into a training set and a validation set in an 8:2 ratio to ensure that samples of different health status levels and different charge state ranges were evenly distributed in the training set and the validation set.

[0041] The training steps for the battery state topology inference model specifically include: initializing model parameters using the Xavier initialization method, with the connection weights of the graph convolutional layers initially set to fully connected. A composite loss function is defined, comprising three parts: the first part is the mean squared error between the initial state-of-charge (SOC) estimate and the true SOC label; the second part is a spatial consistency constraint term for the node-level SOC estimates, which calculates the sum of squares of the differences between the SOC estimates of adjacent nodes; and the third part is a physical constraint term, which requires minimizing the deviation between the weighted average of all node SOC estimates and the theoretical SOC value calculated using the law of charge conservation. The weight coefficients for the three parts are set to 1.0, 0.3, and 0.5, respectively. An adaptive moment estimation optimization algorithm is used for parameter updates, with an initial learning rate of 0.001, which decays to 0.9 times its original value every 50 training epochs. Dynamic connection optimization is performed after each training epoch. Connection importance scores for all connections are calculated, and the top 70% to 90% of connections are retained after ranking by importance scores. The weights of pruned connections are set to zero and not updated in subsequent training. A connection restoration operation is allowed every 10 training epochs. The connection importance scores of pruned connections are re-evaluated, and connections with scores exceeding the current dynamic threshold are restored and their weights reinitialized. Training lasts for 200 epochs. Training is stopped early when the loss function on the validation set does not decrease for 20 consecutive epochs. The model parameters corresponding to the minimum loss function on the validation set are selected as the final model. After training, the model achieves a connection sparsity of 40% to 60%, and the inference speed is more than twice that of a fully connected model.

[0042] The sparse connection learning framework based on dynamic topology reconstruction dynamically optimizes the model structure by adaptively adding and deleting connections between neurons during training. The core of this framework lies in using information theory criteria to evaluate the information contribution of each connection to the model output. Activation frequency and gradient contribution are used as proxy indicators of information content. When the information contribution of a connection consistently falls below a dynamic threshold, the connection is considered redundant and probabilistic pruning is implemented. The pruning probability is proportional to the degree of information insufficiency. The dynamic threshold is not a fixed value but is adaptively adjusted based on the current sparsity of the network and the decreasing trend of the training loss. When the loss decreases rapidly, the dynamic threshold is increased to accelerate pruning; when the loss decreases stagnates, the dynamic threshold is decreased to protect connections and avoid over-pruning that could degrade model performance. The grouping regularization constraint groups connection weights according to the target node and applies an L2 norm penalty to each group. The smaller the number of connections within a group, the larger the penalty coefficient. This imbalanced penalty mechanism encourages the model to prioritize retaining connections of key nodes and prune connections of secondary nodes more aggressively. The battery topology feature extraction algorithm based on graph neural networks maps the internal physical structure of the battery into a graph structure representation. Nodes correspond to local electrochemical active regions, and edges correspond to lithium-ion transport paths. This representation naturally aligns with the distributed physical nature of batteries. The graph convolution operation, through a multi-hop message passing mechanism, enables each node to perceive the state information of its multi-order neighborhood, capturing the spatial dependencies caused by lithium-ion diffusion. The attention mechanism assigns differentiated aggregation weights to different neighborhood nodes, allowing the model to adaptively focus on the region that has the most significant impact on the current node's state of charge, effectively handling situations where the aging degree and temperature gradient distribution within the battery are uneven. The combination of these two technologies brings three technical benefits to the battery state topology inference model: First, the sparse connection learning framework based on dynamic topology reconstruction significantly reduces the number of model parameters and computational complexity, compressing the model inference time to the millisecond level to meet rapid detection requirements. Simultaneously, the sparsification process automatically discovers the most critical feature combinations for state of charge estimation, improving the model's generalization and anti-interference capabilities. Second, the battery topology feature extraction algorithm based on graph neural networks fully utilizes prior knowledge of the battery's physical structure, enabling the model output to include not only global state of charge estimation but also the state of charge distribution in local regions. This provides fine-grained information for identifying uneven aging and local overcharging / over-discharging within the battery, enhancing the model's adaptability to batteries in degraded health states. Third, the dynamic topology reconstruction mechanism allows the model to adaptively adjust the network structure according to the connection activation patterns of different battery samples. It maintains a simple connection pattern for healthy batteries to improve inference efficiency, while activating more connection paths for aging batteries to capture abnormal features, achieving an adaptive balance between efficiency and accuracy. This is suitable for the rapid identification needs of batteries with unknown health states in customs inspection scenarios.

[0043] The specific steps for constructing the probability density function of the state of charge (POC) using the maximum entropy principle include: calculating the mean of the preliminary POC estimate in the local region POC distribution as the first moment; calculating the variance of the local region POC distribution as the second moment; calculating the skewness of the local region POC distribution as the third moment; combining the first, second, and third moments with the voltage moment, impedance moment, and temperature moment features in the statistical moment feature vector to form an extended statistical moment feature vector; setting the support set of the POC probability density function as a continuous interval from 0% to 100%; using the moments in the extended statistical moment feature vector as constraints; constructing a linear combination of the information entropy of the POC probability density function and the constraints using the Lagrange function as the Lagrange function; obtaining the exponential family expression of the optimal POC probability density function by taking the variational derivative of the Lagrange function with respect to the POC probability density function and setting it to zero; and determining the Lagrange multipliers in the exponential family expression by solving the constraint equations using an iterative algorithm.

[0044] The iterative algorithm specifically includes the following steps: initializing the Lagrange multiplier as a zero vector; calculating the exponential family charged state probability density function based on the current Lagrange multiplier in the k-th iteration; performing numerical integration on the exponential family charged state probability density function to calculate the predicted values ​​of each order moment; calculating the deviation between the predicted value and the corresponding moment in the extended statistical moment feature vector; updating the Lagrange multiplier based on the deviation and a preset learning rate; and repeating the iteration until the L2 norm of the deviation is less than the convergence threshold or the number of iterations exceeds the maximum number of iterations.

[0045] Specifically, the step of generating a charged state sample set by Monte Carlo sampling includes: performing Monte Carlo sampling on the optimal charged state probability density function to generate 10,000 charged state sample points, and sorting all charged state sample points from smallest to largest to form a charged state sample set.

[0046] The state-of-charge (SOC) probability distribution estimation algorithm based on the maximum entropy principle transforms the traditional point estimation problem into a probability distribution reconstruction problem, fully utilizing the statistical information contained in the measurement data to reconstruct the complete probability density function of the SOC. The core idea of ​​the maximum entropy principle is to select the probability distribution with the highest information entropy as the optimal estimate, given known constraints. Maximum information entropy implies the fewest subjective assumptions about unknown information, resulting in the most objective estimation result. The algorithm uses the preliminary SOC estimate and its spatial distribution's statistical moments, the mean and variance of impedance measurements, and temperature as moment constraints. These moment constraints reflect some deterministic information about the battery's current state. By solving the constrained optimization problem using the Lagrange multiplier method, the constrained entropy maximization is transformed into an unconstrained saddle point problem. Variational derivation shows that the optimal SOC probability density function necessarily belongs to an exponential family distribution, whose parameters are uniquely determined by the constraints. This exponential family expression ensures the analytic properties of the SOC probability density function, facilitating subsequent sampling and integration calculations. The Monte Carlo sampling generates a large number of charged state sample points from the reconstructed charged state probability density function. The expected value and confidence interval of the charged state are calculated by using the statistics of the charged state sample points. The expected value of the charged state is used as the final point estimation result, and the confidence interval quantifies the uncertainty of the estimation. The proposed algorithm for estimating the state of charge (SOC) probability distribution based on the maximum entropy principle offers three key technical advantages: First, its ability to quantify uncertainty expands the detection results from a single numerical value to a probability distribution and confidence interval. When measurement data is contaminated by noise or the battery is in a transitional state, a wide confidence interval indicates insufficient estimation reliability, triggering a feedback mechanism to increase measurement frequency points or adjust the estimation strategy, thus avoiding erroneous high-confidence judgments. Second, the rich information contained in the probability distribution supports risk assessment and decision optimization. In customs clearance scenarios, even if the expected SOC value is acceptable, a secondary detection should be triggered when the upper bound of the confidence interval exceeds a safety threshold, meeting the conservative decision-making requirements of safety-critical applications. Third, the theoretical guarantee of the maximum entropy principle ensures that the algorithm provides the most unbiased estimate with limited measurement information. Compared to parameterized methods that rely on distribution assumptions, it exhibits stronger robustness, making it suitable for real-world battery samples with unknown health states and diverse aging patterns. This reduces the model's dependence on the training data distribution and improves the method's generalization ability and reliability in different application scenarios.

[0047] The calculation steps for the rate of change of the real part of the AC internal resistance at 1 kHz specifically include: selecting three state-of-charge test points within a 5% range above and below the expected state-of-charge value; measuring the real part of the AC internal resistance at 1 kHz for each state-of-charge test point; performing linear fitting on the real part of the AC internal resistance at the three state-of-charge test points to obtain the slope; and normalizing the slope to obtain the rate of change of the real part of the AC internal resistance at 1 kHz.

[0048] The extraction step of the short-time constant current discharge voltage drop rate specifically includes: applying a constant discharge current for 5 seconds to the lithium battery under test, recording the change curve of the terminal voltage over time during the discharge process, performing linear fitting on the first 3 seconds of the change curve to obtain the voltage drop slope, and normalizing the voltage drop slope by dividing it by the constant discharge current to obtain the short-time constant current discharge voltage drop rate.

[0049] The steps for establishing the temperature-state-of-charge two-dimensional lookup table specifically include: setting a temperature sampling point every 5°C within the temperature range of -20°C to 60°C, setting a state-of-charge sampling point every 5% within the state-of-charge range of 0% to 100%, measuring the corresponding open-circuit voltage and internal resistance values ​​for each combination of temperature and state-of-charge sampling points, and storing all combined measurement data into a temperature-state-of-charge two-dimensional lookup table. The row index of the temperature-state-of-charge two-dimensional lookup table is the temperature sampling point, the column index is the state-of-charge sampling point, and the table elements are binary pairs of open-circuit voltage and internal resistance values.

[0050] The steps for calculating the temperature compensation factor using the entropy coefficient method specifically include: calculating the partial derivative of the open-circuit voltage with respect to temperature based on thermodynamic relationships, where the partial derivative represents the change in open-circuit voltage caused by a unit temperature change; multiplying the difference between the measured surface temperature and the reference temperature of 25°C by the partial derivative to obtain the voltage offset caused by temperature; calculating the state-of-charge offset caused by temperature based on the voltage offset and the slope of the open-circuit voltage-state-of-charge curve; and normalizing the state-of-charge offset to use it as the temperature compensation factor.

[0051] The dynamic correction steps specifically include: when the expected state of charge (SOC) is below 20% in the low-resolution range, the weighting coefficients for the real part rate of change of AC internal resistance at 1 kHz are set to 0.4, the short-time constant current amplifier voltage drop rate is set to 0.3, and the temperature compensation factor is set to 0.3; when the expected SOC is above 80% in the low-resolution range, the weighting coefficients for the real part rate of change of AC internal resistance at 1 kHz are set to 0.3, the short-time constant current amplifier voltage drop rate is set to 0.4, and the temperature compensation factor is set to 0.3; the comprehensive correction amount is obtained by multiplying the real part rate of change of AC internal resistance at 1 kHz by the corresponding weighting coefficients, the short-time constant current amplifier voltage drop rate by the corresponding weighting coefficients, and the temperature compensation factor by the corresponding weighting coefficients; and the comprehensive correction amount is then superimposed on the expected SOC to obtain the final SOC detection result.

[0052] The method for determining the preset threshold is as follows: calculate the distribution of the confidence interval width for the battery samples in the validation set, select the 75th percentile of the distribution as the preset threshold, and determine that the estimation uncertainty is too high and measurement information needs to be added when the confidence interval width is greater than the preset threshold.

[0053] If the confidence interval width is greater than a preset threshold, two expansions are performed. If the confidence interval width is still greater than the preset threshold after two expansions, a high uncertainty warning is marked in the detection report and the current final state of charge detection result is output.

[0054] The low-resolution range refers to the range where the state of charge is below 20% or above 80%. Within the low-resolution range, the gradient of the battery's open-circuit voltage with the change of state of charge is small, and the open-circuit voltage curve exhibits a plateau characteristic. This leads to a decrease in the sensitivity of state of charge estimation based on voltage measurement. At the same time, the battery polarization effect is aggravated under low state of charge, and the side reactions increase under high state of charge. The impedance characteristic change mode is complex, so auxiliary features need to be introduced to improve the estimation accuracy.

[0055] The health status level reflects the degree of battery aging. Health level one indicates that the battery performance is close to that of a new battery, with high capacity retention and limited internal resistance growth. Health level two indicates that the battery has entered the performance degradation stage, with moderate capacity decay and internal resistance growth. Health level three indicates that the battery is severely aged, with a significant decrease in capacity or a significant increase in internal resistance, and is close to the end of its service life. Different health status levels correspond to different electrochemical behavior modes, and corresponding estimation strategies need to be adopted.

[0056] The local state of charge (SOC) distribution describes the differences in SOC at different spatial locations within the battery. Due to uneven temperature distribution, uneven current density distribution, and uneven aging levels within the battery, there are differences in the SOC of each local area. The degree of unevenness in the SOC distribution reflects the health and consistency of the battery. The more uneven the distribution, the more serious the inconsistency within the battery. The SOC distribution information in the local area provides a basis for diagnosing internal battery faults.

[0057] The node-level state of charge (SOC) estimate is the SOC estimate of the corresponding local region output by each node in the battery state topology inference model. The node-level SOC estimate is obtained by mapping node features through a fully connected layer. The spatial distribution of all node-level SOC estimates constitutes the local region SOC distribution.

[0058] The confidence interval width reflects the uncertainty of the state of charge estimation. The larger the confidence interval width, the higher the estimation uncertainty, and the more measurement information or the more the estimation strategy needs to be adjusted to improve the estimation reliability.

[0059] The auxiliary features include the rate of change of the real part of the AC internal resistance at 1 kHz, the short-time constant current amplifier voltage drop rate, and the temperature compensation factor. These auxiliary features are used to improve the accuracy of state of charge estimation in the low-resolution range and compensate for the problem of insufficient open-circuit voltage sensitivity.

[0060] The charge conservation law states that the total charge inside the battery is conserved, and the sum of the charges in all local regions equals the total charge of the battery. The theoretical state of charge value calculated according to the charge conservation law is the result of the weighted average of the estimated state of charge values ​​at all nodes according to the local capacity.

[0061] The extended statistical moment eigenvector is a vector formed by combining the statistical moment eigenvector with the moments of each order of the charge state distribution in the local region. It includes voltage moment features, impedance moment features, temperature moment features, first moment, second moment and third moment. The extended statistical moment eigenvector serves as a constraint condition for constructing the charge state probability density function using the maximum entropy principle.

[0062] The specific implementation methods of the above steps are described in detail below.

[0063] The specific implementation of step S1 involves first using an infrared temperature sensor to perform non-contact temperature measurement on the surface of the lithium battery under test. The measurement location is selected at the geometric center of the battery to represent the overall temperature state, and the measurement accuracy is required to be within ±0.5℃. The surface temperature reflects the thermal state of the battery and affects the subsequent interpretation of electrochemical parameters. Then, a digital multimeter is used to measure the initial terminal voltage of the battery in a static state. The static time is required to exceed 30 minutes to eliminate polarization effects. The initial terminal voltage is a preliminary indication of the battery's current state of charge. Next, a constant current discharge pulse with a duration of 10 seconds is applied to the lithium battery under test. The pulse current is set to a 0.5C ratio. The stable voltage value before the pulse application, the lowest voltage value during the pulse application process, and the voltage recovery value 30 seconds after the pulse ends are recorded. According to Ohm's law, the voltage difference is divided by the discharge current to obtain the current internal resistance value. The current internal resistance value is compared with the internal resistance value of a standard new battery to calculate the internal resistance growth rate. The internal resistance growth rate reflects the degree of degradation of the battery's internal impedance. Based on the voltage recovery value, the corresponding state of charge value is found on the standard open-circuit voltage curve. Combined with the known rated capacity, the remaining capacity is calculated, thus obtaining the capacity decay rate, which reflects the degree of loss of the battery's active material. Finally, based on the specific values ​​of the internal resistance growth rate and capacity decay rate, a health status level is determined according to preset classification rules. When the internal resistance growth rate is less than 20% and the capacity decay rate is less than 10%, it is marked as Health Level 1; when the internal resistance growth rate is between 20% and 50% or the capacity decay rate is between 10% and 25%, it is marked as Health Level 2; and when the internal resistance growth rate is greater than 50% or the capacity decay rate is greater than 25%, it is marked as Health Level 3. These health status labels provide prior information for subsequent model selection.

[0064] The specific implementation of step S2 is as follows: First, a standard lithium battery of the same model as the lithium battery under test is selected for a full-band electrochemical impedance spectroscopy (EIS) scan. The scanning frequency range is set from 0.01 Hz to 10 kHz, and 100 frequency points are selected using a logarithmic uniform distribution. Impedance measurements are performed at each state of charge to obtain a complete Nyquist plot. Then, the numerical derivative of the impedance value with respect to the state of charge is calculated for each frequency point. The central difference method is used to divide the impedance difference between adjacent state of charge points by the state of charge difference to obtain an approximate value of the partial derivative. The absolute value of the partial derivative is taken as the response intensity of that frequency point to the change in state of charge. Next, the absolute values ​​of the partial derivatives at all frequency points are normalized, and the absolute value of each partial derivative is divided by the maximum value of all the absolute values ​​of the partial derivatives to obtain a sensitivity index ranging from 0 to 1. The sensitivity index quantifies the information contribution of different frequency points to the state of charge estimation. Finally, according to the sensitivity index from largest to smallest, the top 5 to 8 frequency points are selected as characteristic frequency points. The selected frequency points are usually distributed in the mid-frequency band and the high-frequency band, because the mid-frequency band reflects the charge transfer process and is sensitive to the state of charge, while the high-frequency band reflects the stable and reliable change of ohmic impedance. The selection of the characteristic frequency points achieves the optimal balance between measurement time and information content.

[0065] The specific implementation of step S3 involves performing impedance measurements on the lithium-ion batteries under test one by one according to the characteristic frequency points determined in step S2. An electrochemical workstation is used to apply a small sinusoidal AC excitation signal with an amplitude of 5mV to each characteristic frequency point. This small-signal excitation ensures that the battery's state of charge is not altered during the measurement process, while simultaneously obtaining a sufficient signal-to-noise ratio. The measurement system records the amplitude and phase of the response current signal. Frequency domain features are extracted from the time-domain signal using a fast Fourier transform. The ratio of the voltage amplitude to the current amplitude is calculated to obtain the impedance magnitude, and the difference between the voltage phase and the current phase is calculated to obtain the impedance phase angle. The impedance magnitude and impedance phase angle completely describe the characteristics of the complex impedance. Then, using the polar-to-rectangular coordinate transformation relationship of complex numbers, the impedance magnitude is multiplied by the cosine of the impedance phase angle to obtain the real part of the impedance data, and the impedance magnitude is multiplied by the sine of the impedance phase angle to obtain the imaginary part of the impedance data. The real part of the impedance reflects resistive characteristics, and the imaginary part reflects capacitive and inductive characteristics. Finally, the real and imaginary impedance data of all characteristic frequency points are arranged in order of frequency from low to high and combined into a one-dimensional vector of characteristic frequency impedance. The characteristic frequency impedance vector contains the impedance fingerprint information of the battery at key frequency points, providing core input features for subsequent state estimation.

[0066] The specific implementation of step S4 involves statistical analysis of the initial terminal voltage. Although the initial terminal voltage is a single measured value, considering measurement noise and local non-uniformity of the battery, it is treated as a random variable, and its mean and variance are calculated. The mean is directly taken from the measured value, and the variance is typically approximately 0.001, obtained based on the accuracy of the measuring equipment and historical data. The voltage moment feature describes the central tendency and dispersion of the terminal voltage. Then, statistical analysis is performed on the real part data of the impedance in the characteristic frequency impedance vector. The arithmetic mean of the real part data of the impedance at all characteristic frequency points is calculated as the real part mean of the impedance. The sum of squares of the deviations of the real part data from the mean is calculated and divided by the number of data points to obtain the real part variance of the impedance. This impedance moment feature reflects the distribution characteristics and variability of impedance in the frequency domain. Next, the surface temperature is normalized. The measured surface temperature value is subtracted from the reference temperature of -20°C and then divided by the temperature range of 80°C to obtain a normalized temperature value between 0 and 1, which is used as the temperature moment feature. This normalization process eliminates the influence of dimensions, facilitating integration with other features. Finally, the mean and variance of the voltage moment feature, the mean and variance of the impedance moment feature, and the temperature moment feature are arranged in order to form a statistical moment feature vector. This statistical moment feature vector extracts the statistical characteristics of the measured data, providing a basis for the constraint conditions of the maximum entropy principle.

[0067] The specific implementation of step S5 involves inputting the surface temperature, initial terminal voltage obtained in step S1, the characteristic frequency impedance vector obtained in step S3, and the health status identifier determined in step S1 into a pre-trained battery state topology inference model. The model first selects corresponding graph structure parameters at the battery topology graph construction layer based on the health status identifier. Health level one uses a fine graph structure with 32 nodes, health level two uses a standard graph structure with 24 nodes, and health level three uses a coarse graph structure with 16 nodes to adapt to the degradation characteristics of aging battery information. The model assigns the surface temperature to all nodes as the initial temperature feature, estimates the local temperature difference between nodes based on the heat transfer model, assigns the initial terminal voltage to each node according to the battery's internal potential distribution as the local voltage, and converts the characteristic frequency impedance vector into the local impedance of each node through a mapping matrix. Then, a three-layer graph convolution operation is performed in the graph convolution feature extraction layer. Each graph convolution layer aggregates the features of neighboring nodes based on edge weights. An attention mechanism calculates the similarity between each pair of nodes as an adjustment factor for the aggregation weights. After three layers of propagation, the feature vector of each node incorporates information from its three-hop neighborhood. The graph convolution operation captures the spatial coupling relationship caused by lithium-ion diffusion. Next, in the dynamic connection optimization layer, the corresponding connection subset is activated according to the current input. For healthy batteries, a sparse connection mode is activated to improve computational efficiency, while for aged batteries, a dense connection mode is activated to enhance feature extraction capabilities. This dynamic mechanism achieves an adaptive trade-off between efficiency and accuracy. Finally, in the state output layer, the node-level output branch maps the feature vector of each node to the corresponding local region's state of charge estimate through a fully connected layer. The global output branch calculates the weighted average of all node-level state of charge estimates to obtain a preliminary state of charge estimate. The weighting coefficients are dynamically determined by the auxiliary classifier based on the consistency and stability of the node features. The spatial distribution of all node-level state of charge estimates constitutes the local region's state of charge distribution. The model output contains state information at both the global and local levels.

[0068] The specific implementation of step S6 involves first performing high-order statistical analysis on the local region's state of charge (SOC) distribution. The arithmetic mean of all node-level SOC estimates is calculated as the first-order moment describing the distribution's center position. The variance of the node-level SOC estimates is calculated as the second-order moment describing the distribution's dispersion. The standardized third-order central moment is calculated as the third-order moment describing the distribution's skewness. This high-order moment information reflects the non-uniformity of the SOC within the battery. Then, the first, second, and third moments are combined with the statistical moment feature vector obtained in step S4 to form an extended statistical moment feature vector, which contains six statistical moment constraints. Next, an optimization problem based on the maximum entropy principle is constructed. The domain of the SOC probability density function is set to a continuous interval from 0% to 100%. The moments in the extended statistical moment feature vector are used as equality constraints, and information entropy is used as the objective function for maximization. The maximum entropy principle ensures that the least biased probability distribution is selected while satisfying known constraints. The constrained optimization problem is transformed into an unconstrained problem using the Lagrange multiplier method. Six Lagrange multipliers are introduced, corresponding to six constraints. The Lagrange function is constructed as a weighted sum of information entropy and constraints. Variational operations are performed on the Lagrange function with respect to the probability density function, and the derivative is set to zero. According to the principle of variational method, the optimal probability density function must belong to an exponential family distribution. Then, an iterative algorithm is used to solve for the Lagrange multipliers. All Lagrange multipliers are initialized to zero. In each iteration, the exponential family probability density function is calculated based on the current Lagrange multipliers. The predicted values ​​of each moment of the probability density function are calculated using numerical integration methods such as Gauss-Legendary quadrature. The deviations of the predicted values ​​from the corresponding moments in the extended statistical moments eigenvector are compared. The Lagrange multipliers are updated based on the deviation and the learning rate of 0.01. The iterative process is repeated until the L2 norm of the deviation is less than the convergence threshold of 0.0001 or the number of iterations exceeds the maximum number of iterations of 1000. The iterative algorithm ensures the numerical stability of the parameter solution. Finally, Monte Carlo sampling is performed on the obtained optimal state of charge probability density function. 10,000 state of charge sample points that follow this probability distribution are generated using the inverse transform sampling method or the accept-reject sampling method. All sample points are sorted from smallest to largest to form a state of charge sample set. The arithmetic mean of the sample set is calculated as the expected value of the state of charge. The interval between the 2.5th percentile and the 97.5th percentile of the sample set is selected as the 95% confidence interval. The probability distribution reconstruction process not only provides point estimates but also quantifies the uncertainty of the estimates.

[0069] The specific implementation of steps S7 and S8 involves conditional judgment and dynamic adjustment based on the expected value of the state of charge. First, it is determined whether the expected value of the state of charge falls within the low-resolution range, i.e., less than 20% or greater than 80%. If it is in the low-resolution range, auxiliary features need to be extracted for correction. Three test points are selected within 5% above and below the expected value of the state of charge to measure the real part of the AC internal resistance at a frequency of 1kHz. The real part change rate of the AC internal resistance is obtained by least-squares linear fitting of the three test points. A constant discharge current is applied to the lithium battery under test for 5 seconds to extract the short-time constant current discharge voltage drop rate. According to the temperature-state of charge two-dimensional lookup table, the open circuit voltage temperature coefficient corresponding to the current temperature and state of charge is queried by bilinear interpolation. After calculating the temperature compensation factor, the comprehensive correction amount is obtained by weighted fusion according to the preset weight coefficient. The dynamic correction mechanism introduces a multi-source information fusion strategy to address the problem of insufficient estimation sensitivity in the low-resolution range. Then, the confidence interval width is calculated and compared with a preset threshold. The preset threshold is determined based on the 75th percentile of the confidence interval width distribution of the validation set, with a typical value of 8%. If the confidence interval width is greater than the preset threshold, it indicates that the estimation uncertainty is too high and measurement information needs to be added. Based on the original characteristic frequency points, frequency points ranked 9th to 12th in sensitivity index are added, and the impedance measurement and state estimation process is re-executed. The feedback adjustment mechanism dynamically optimizes the measurement strategy according to the estimation quality, and performs the expansion at most twice. If the requirements are still not met, a high uncertainty warning is marked in the detection report. Finally, the final state of charge detection result and confidence interval are output as a complete detection report.

[0070] It should be noted that this invention also solves the following technical problem: traditional state-of-charge (SOC) detection methods cannot identify local abnormal states when faced with uneven aging and temperature gradient distribution within the battery. This invention divides the battery interior into multiple local regions using a graph structure representation of the battery state topology inference model. Each node corresponds to a local region and is associated with electrochemical parameters such as local impedance, local temperature, and local voltage. Edges represent lithium-ion diffusion channels between adjacent local regions. Graph convolution operations, through a multi-hop message passing mechanism, enable each node to perceive the state information of its multi-order neighborhood. An attention mechanism assigns differentiated aggregation weights to different neighboring nodes, allowing the model to adaptively focus on the region that has the most significant impact on the current node's SOC. The model output includes not only a global SOC estimate but also the local SOC distribution composed of node-level SOC estimates. The degree of unevenness in the local SOC distribution reflects the severity of inconsistencies within the battery, providing fine-grained information for diagnosing local overcharging, over-discharging, and uneven aging within the battery. This solves the problem of traditional methods only providing global estimates while ignoring internal spatial differences.

[0071] Specifically, the principle of this invention is as follows: This invention addresses the technical problems of insufficient estimation accuracy and inability to quantify uncertainty in lithium battery state-of-charge (SOC) detection when facing declining health status and low-resolution intervals. The principle lies in establishing a complete mapping relationship from measurement data to SOC distribution through multi-level information fusion and probabilistic reasoning mechanisms. The battery SOC topology reasoning model maps the internal physical structure of the battery to a graph structure, capturing the spatial dependencies caused by lithium-ion diffusion through graph convolution operations. The dynamic topology reconstruction mechanism enables the model to adaptively adjust the network structure according to the connection activation patterns of batteries in different health states. It maintains simple connections to improve efficiency for healthy batteries and activates more paths to capture abnormal features for aging batteries, achieving adaptive estimation for different health states. The maximum entropy principle selects the probability distribution with the largest information entropy under the moment constraints provided by the measurement data, ensuring that the estimation results have the fewest subjective assumptions about unknown information. The reconstructed SOC probability density function generates a sample set through Monte Carlo sampling. The statistics of the sample set naturally reflect the estimation uncertainty, and the confidence interval width triggers a feedback mechanism to increase measurement information. The auxiliary feature correction in the low-resolution range utilizes the high sensitivity of AC internal resistance and constant current discharge response, the temperature compensation factor eliminates the influence of ambient temperature, and the multi-feature weighted fusion compensates for the lack of information in the open-circuit voltage plateau region. The synergistic effect of these three mechanisms makes the scheme of this invention conform to the electrochemical principle of batteries and logically consistent.

[0072] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0073] The specific implementation of step S1 is as follows: A non-contact infrared temperature sensor is used to measure the surface temperature of the lithium battery under test, and a high-precision digital multimeter is used to measure the initial terminal voltage. During the pulse discharge test, a constant current discharge pulse lasting 10 seconds is applied to the lithium battery under test, with the pulse current being 0.5C of the rated capacity current. The difference in terminal voltage before and after the pulse is recorded. and the recovered value of the stabilized terminal voltage Current value of internal resistance The calculation formula is expressed as follows:

[0074] ;

[0075] In the formula, This represents the voltage difference before and after the pulse, in volts (V). This is the pulse discharge current, measured in amperes (A). Units are Internal resistance growth rate The calculation formula is expressed as follows:

[0076] ;

[0077] In the formula, This is the standard internal resistance value of a new battery, in units of... This was obtained through measurements using a new battery of the same model. The unit is percentage. According to The value is used to find the corresponding state of charge in the standard open-circuit voltage curve, and the remaining capacity is calculated based on the current capacity. Capacity decay rate The calculation formula is expressed as follows:

[0078] ;

[0079] In the formula, Standard rated capacity, unit: Ah. This represents the remaining capacity, in Ah. The unit is a percentage. The rule for determining the health status indicator is: when... and When marked as health level one, or When marked as health level two, or The time is marked as health level three.

[0080] The specific implementation of step S2 is as follows: Using an electrochemical workstation, a full-band impedance spectrum scan is performed on a standard lithium battery every 5% of its state of charge, from 0% to 100%, with a frequency range of 0.01 Hz to 10 kHz. The real and imaginary parts of the impedance are measured at each frequency point. Partial derivatives are also measured. The central difference method is used for calculation, and the formula is expressed as follows:

[0081] ;

[0082] In the formula, In the state of charge Lower frequency The impedance magnitude at the point, in units of , The differential step size for the state of charge is set to 0.05. and These represent the increase and decrease in state of charge, respectively. Post-frequency The impedance magnitude at the point, in units of , Units are Sensitivity index The calculation formula is expressed as follows:

[0083] ;

[0084] In the formula, The maximum absolute value of the partial derivatives across all frequency points, in units of . , This is a dimensionless parameter. Click on all frequency points. Arrange the frequencies in descending order and select the first 5 to 8 frequencies as characteristic frequencies.

[0085] The specific implementation of step S3 is as follows: apply a sinusoidal AC excitation signal with an amplitude of 10mV to each characteristic frequency point, and measure the amplitude of the response current. and phase Record voltage amplitude and phase Impedance magnitude and impedance phase angle The calculation formula is expressed as follows:

[0086] ;

[0087] ;

[0088] In the formula, Voltage amplitude, in volts (V). This is the current amplitude, in amperes (A). Units are , Voltage phase, in radians. The current phase is expressed in radians. This represents the impedance phase angle, in radians. The real part of the impedance. and the imaginary part of impedance The calculation formula is expressed as follows:

[0089] ;

[0090] ;

[0091] In the formula, Units are , Units are All characteristic frequency points and Arranged in ascending order of frequency to form a characteristic frequency impedance vector. , for dimensional vector, This represents the number of characteristic frequency points.

[0092] The specific implementation of step S4 is as follows: the voltage torque characteristics include the average initial terminal voltage. and variance The calculation formula is expressed as follows:

[0093] ;

[0094] ;

[0095] In the formula, This is the initial terminal voltage measurement, in volts (V). The unit is V. For the accuracy of voltage measuring equipment, the unit is V, and the value is usually taken as 0.001V. Units are The formula for calculating the characteristic impedance moment is as follows:

[0096] ;

[0097] ;

[0098] In the formula, The number of characteristic frequency points. For the first The real part of the impedance at each characteristic frequency point, in units of , Units are , Units are Temperature moment characteristics The calculation formula is expressed as follows:

[0099] ;

[0100] In the formula, Surface temperature, in °C. The lower limit of temperature is set to -20℃. The upper limit of temperature is set at 60℃. These are dimensionless parameters. Statistical moment eigenvectors The statement is as follows:

[0101] .

[0102] The specific implementation of step S5 is the same as the training and structural description of the aforementioned battery state topology inference model, and will not be described in detail here.

[0103] The specific implementation of step S6 is as follows: first-order moment Second moment and third moment The calculation formula is expressed as follows:

[0104] ;

[0105] ;

[0106] ;

[0107] In the formula, For the number of nodes, For the first Local region charge state estimates of each node, For dimensionless parameters, For dimensionless parameters, Dimensionless parameter. Extended statistical moment eigenvector. The statement is as follows:

[0108] .

[0109] Charged state probability density function based on the maximum entropy principle The family of exponents is expressed as follows:

[0110] ;

[0111] In the formula, The charged state variable takes values ​​from 0 to 1. The normalization coefficient is... For the first One Lagrange multiplier, For the first A moment function, The number of constraint moments is set to 8. The unit is 1. Normalization coefficient Determined through normalization conditions, the formula is expressed as follows:

[0112] ;

[0113] make sure Moment function Defined as: Corresponding voltage first moment, Corresponding voltage second moment, Corresponding impedance mean moment, The corresponding impedance second moment, Corresponding temperature moment, The corresponding first moment of the local region, The corresponding second moment in the local region, The corresponding third moment for the local region. The Lagrange multipliers are solved iteratively, the th... The update formula for the next iteration is expressed as follows:

[0114] ;

[0115] In the formula, For the first The iteration of the ... One Lagrange multiplier, The learning rate is set to 0.01. To extend the statistical moment eigenvectors of the 1st One portion, For the first The probability density function for the next iteration is in units of 1. Numerical integration is performed using Simpson's rule, dividing the interval... Divided into equal parts The segment, expressed in the formula, is as follows:

[0116] ;

[0117] In the formula, For the integration step size, Take 1000, For the first There are integration nodes. The iteration termination condition is... ,in Take the convergence threshold as , The predicted moment vector is obtained through numerical integration. For the optimal... Monte Carlo sampling was performed to generate 10,000 sample points, and the expected value of the state of charge was... The formula for calculating the confidence interval is as follows:

[0118] ;

[0119] In the formula, For the first One state of charge sample point, This is a dimensionless parameter. The lower bound of the confidence interval is the 2.5 percentile of the sample set. The upper bound is the 97.5th percentile. , and These are the 250th and 9750th sample values, respectively, after sorting 10,000 state-of-charge sample points from smallest to largest.

[0120] The specific implementation method of step S7 is as follows: when or The time frame indicates it is in a low-resolution range. The rate of change of the real part of the AC internal resistance at 1 kHz. The calculation formula is expressed as follows:

[0121] ;

[0122] In the formula, In the state of charge The real part of the AC internal resistance measured at 1kHz, in units of , In the state of charge The real part of the AC internal resistance measured at 1kHz, in units of , , , The standardized reference value is set to 1. , A dimensionless parameter. Short-time constant current amplifier voltage drop rate. The calculation formula is expressed as follows:

[0123] ;

[0124] In the formula, This is the terminal voltage at the start of discharge, in volts (V). This is the terminal voltage at 3 seconds after discharge, in volts (V). The discharge duration is set to 3 seconds, in seconds. The discharge current is constant, and the unit is Ampere (A). Rated voltage, unit: V. This is a dimensionless parameter. Temperature compensation factor. The calculation formula is expressed as follows:

[0125] ;

[0126] In the formula, This represents the partial derivative of the open-circuit voltage with respect to temperature, expressed in V / ℃. The reference temperature is 25℃. This is the partial derivative of the open-circuit voltage with respect to the state of charge, expressed in volts (V). These are dimensionless parameters. When the measured temperature and state of charge are not at the sampling point, bilinear interpolation is used to obtain them. The formula is expressed as follows:

[0127] ;

[0128] In the formula, These are the temperature interpolation coefficients. These are the interpolation coefficients for the state of charge. and To surround The adjacent sampling temperature points, in °C. and To surround Adjacent sampled state of charge points, , , , These are two-dimensional lookup tables for temperature and state of charge. , , , The open-circuit voltage temperature partial derivative at the four sampling points, in units of V / ℃, is obtained by dividing the open-circuit voltage difference between adjacent temperature points by the temperature difference. (Comprehensive correction amount) The calculation formula is expressed as follows:

[0129] when hour, ;

[0130] when hour, .

[0131] In the formula, This is a dimensionless parameter. Final state of charge detection result. The calculation formula is expressed as follows:

[0132] ;

[0133] In the formula, It is a dimensionless parameter.

[0134] The specific implementation of step S8 is as follows: confidence interval width The calculation formula is expressed as follows:

[0135] ;

[0136] In the formula, This is a dimensionless parameter. When... When the frequency points ranked 9th to 12th in the sensitivity index are added, steps S3 to S7 are executed again, where The preset threshold. The calculation method is as follows: the confidence interval width of all samples in the validation set. The formula for sorting from smallest to largest is as follows:

[0137] ;

[0138] In the formula, To determine the number of samples in the validation set, It is a rounding function. This is the sorted sequence of confidence interval widths. This is a dimensionless parameter. If it still doesn't work after performing two expansions... If so, a high uncertainty warning will be marked in the test report and the current uncertainty will be output. and confidence interval .

[0139] Example 2: To verify the effectiveness of the invention, technicians set up a test environment and conducted rapid state-of-charge (SOC) testing on a batch of ternary lithium batteries to be tested. This batch of batteries had a nominal capacity of 50Ah, a rated voltage of 3.7V, and a test environment temperature of 23℃. Technicians first collected the surface temperature of the lithium battery with serial number LB-2024-156, measuring it to 26.8℃ using an infrared temperature sensor. The initial terminal voltage was measured to be 3.642V using a digital multimeter. Subsequently, a pulse discharge test was performed, applying a 5A constant current discharge pulse for 10 seconds. The voltage at the pulse's beginning was recorded as 3.642V, and the voltage at the pulse's end was recorded as 3.571V, with a voltage difference of 0.071V. After a 30-second rest period, the recovered terminal voltage was measured to be 3.625V. Based on the voltage difference and discharge current, the current internal resistance was calculated to be 14.2V. The standard internal resistance of this model of new battery is 10.5 ohms. The calculated internal resistance growth rate is 35.2%. Based on the terminal voltage recovery value of 3.625V and the standard open-circuit voltage curve, the remaining capacity is estimated to be 38.5Ah, and the standard rated capacity is 50Ah, resulting in a capacity decay rate of 23.0%. According to the health status labeling rules, an internal resistance growth rate of 35.2% falls between 20% and 50%, and a capacity decay rate of 23.0% falls between 10% and 25%. Therefore, this battery is labeled as health level two.

[0140] Technicians used an electrochemical workstation to perform full-band impedance spectroscopy scans on standard lithium batteries at 5% intervals within the state of charge range of 0% to 100%, covering a frequency range of 0.01 Hz to 10 kHz. By calculating and normalizing the absolute values ​​of the partial derivatives of the impedance value with respect to the state of charge at each frequency point, the sensitivity indicators for each frequency point were obtained. For example... Figure 2 As shown, the sensitivity index exhibits a clear peak characteristic in the mid-frequency range. Technicians selected the six frequencies with the highest sensitivity index as characteristic frequencies: 0.12Hz, 0.89Hz, 5.67Hz, 28.4Hz, 156Hz, and 982Hz. Impedance measurements were performed on the lithium battery under test at these six characteristic frequencies. An AC excitation signal with an amplitude of 10mV was applied at the 0.12Hz frequency point, and the measured response current amplitude was 0.245mA, with a voltage-current phase difference of -68.5°. The calculated impedance modulus was 40.82. The real part of the impedance is 14.93. The imaginary part of the impedance is -38.02. The impedance measurements were then performed at the remaining five characteristic frequency points. The obtained real impedance data, ordered from lowest to highest frequency, were 14.93, 12.67, 10.84, 9.56, 8.73, and 8.21. The imaginary part of the impedance values ​​are -38.02, -15.28, -8.94, -3.67, -1.52, and -0.87, respectively. This forms a 12-dimensional characteristic frequency impedance vector.

[0141] Technicians extracted statistical moment features based on the initial terminal voltage of 3.642V and the characteristic frequency impedance vector. The initial terminal voltage was calculated to have a mean of 3.642V and a variance of 0, which was used as the voltage moment feature. The mean of the real part of the impedance data was calculated to be 10.82. The variance is 6.35. The voltage moment characteristic is used as the impedance moment characteristic. The surface temperature of 26.8℃ is normalized to the range of 0 to 1, and the reference temperature range is set to -20℃ to 60℃. The normalized temperature moment characteristic is 0.585. The voltage moment characteristic, impedance moment characteristic, and temperature moment characteristic are combined to form a statistical moment characteristic vector, as shown in Table 1.

[0142] Table 1. Composition of Statistical Moment Eigenvectors

[0143]

[0144] Technicians trained a battery state topology inference model using two inputs: a surface temperature of 26.8℃, an initial terminal voltage of 3.642V, a characteristic frequency impedance vector, and a health status identifier. This model divides the lithium battery interior into 25 local regions, constructing a battery topology map containing 25 nodes. (Example...) Figure 3 As shown, the battery topology graph construction layer maps the electrode structure into a graph structure, and the weights of the connection edges between nodes are determined by the lithium-ion diffusion coefficient and the distance between regions. The graph convolution feature extraction layer performs three layers of graph convolution operations, aggregating the state information of the three-hop neighborhood for each node. The dynamic connection optimization layer implements sparse connection learning, and the connection sparsity of the trained model reaches 52.7%, retaining 1182 connection edges. The model outputs an initial state of charge estimate of 67.3%, and also outputs node-level state of charge estimates for 25 nodes, constituting the local region's state of charge distribution, with values ​​ranging from 64.8% to 69.5%, showing a moderate degree of internal non-uniformity.

[0145] Technicians constructed the probability density function of the state of charge (SOC) using the maximum entropy principle. The first moment of the preliminary SOC estimate in the local SOC distribution was calculated to be 67.3%, the second moment to be 4.87, and the third moment to be -0.23. The first, second, and third moments were combined with the statistical moment eigenvectors to form an extended statistical moment eigenvector, containing eight constraints. The support set of the SOC probability density function was set to 0% to 100%. A Lagrange function was constructed and solved using the variational method to obtain the optimal probability density function in exponential family form. An iterative algorithm was used to solve for the Lagrange multipliers, initializing them to zero vectors, setting the learning rate to 0.05, and the convergence threshold to... After 127 iterations, the L2 norm of the deviation between the predicted and actual moments converged to [value missing]. The convergence condition is met. For example... Figure 4 As shown, the obtained probability density function of the state of charge exhibits a peak distribution around 67.3%. Monte Carlo sampling was performed on this probability density function to generate 10,000 sample points of the state of charge. These sample points were sorted in ascending order to form a sample set of the state of charge. The arithmetic mean of the sample set yielded an expected value of 67.4% for the state of charge. The 2.5 percentile was calculated to be 63.2%, the 97.5 percentile to be 71.8%, and the confidence interval was from 63.2% to 71.8%, with a confidence interval width of 8.6%.

[0146] Technicians determined that the expected state of charge (SOC) value of 67.4% was not in the low-resolution range below 20% or above 80%, therefore directly using 67.4% as the final SOC detection result. Based on the validation set statistics, the 75th percentile of the confidence interval width distribution was 7.2%, which was set as the preset threshold. The current confidence interval width of 8.6% is greater than the preset threshold of 7.2%, indicating a high estimation uncertainty. Technicians added the 9th to 12th frequency points ranked by sensitivity index to the existing six characteristic frequency points, namely 2.34Hz, 14.7Hz, 73.8Hz, and 458Hz. Impedance measurements were re-performed, and the measured real parts of the impedance at these four newly added frequency points were 11.52, 9.98, 8.95, and 8.34, respectively. The imaginary part data of the impedance are -12.46, -5.73, -2.18, and -1.03, respectively. The expanded characteristic frequency impedance vector has 20 dimensions, and the statistical moment features are re-extracted, updating the mean of the real part of the impedance to 10.56. The variance was updated to 5.82. The updated data was input into the battery state topology inference model, yielding a new preliminary state of charge (SOC) estimate of 67.6%, with the SOC distribution range narrowing to 65.4% to 69.2% in the local region. The SOC probability density function was reconstructed and Monte Carlo sampling was performed, resulting in an expected SOC of 67.5%, with the confidence interval updated to 64.8% to 70.1%. The confidence interval width decreased to 5.3%, which is less than the preset threshold of 7.2%, meeting the accuracy requirements. Figure 5 As shown, the peak value of the probability density function of the state of charge is more concentrated after the frequency points are extended, and the uncertainty is significantly reduced. The technicians output the final state of charge detection result as 67.5%, with a confidence interval of 64.8% to 70.1%, and completed the generation of the detection report.

[0147] It should be noted that the variables involved in this invention are explained in detail in Tables 2 and 3.

[0148] Table 2. Variable Explanation Table (Part 1)

[0149]

[0150] Table 3. Variable Explanation Table (Part Two)

[0151]

[0152] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for rapid detection of the state of charge of a lithium battery, characterized in that, The process includes collecting the surface temperature and initial terminal voltage of the lithium battery under test; obtaining the internal resistance growth rate and capacity decay rate of the lithium battery under test through pulse discharge testing to assess the health status level and record it as a health status identifier; performing full-band impedance spectrum scanning on a standard lithium battery under different states of charge to select the frequency point with the highest sensitivity index as the characteristic frequency point; performing impedance measurement on the lithium battery under test based on the characteristic frequency point to obtain the real part and imaginary part of the impedance data to form a characteristic frequency impedance vector; extracting statistical moment feature vectors based on the initial terminal voltage and characteristic frequency impedance vectors; inputting the surface temperature, initial terminal voltage, characteristic frequency impedance vector, and health status identifier into the battery state topology inference model to output a preliminary state of charge estimate and a local area state of charge distribution; constructing a state of charge probability density function using the maximum entropy principle based on the preliminary state of charge estimate, the local area state of charge distribution, and the statistical moment feature vectors; calculating the expected state of charge and confidence interval through Monte Carlo sampling; determining whether the expected state of charge is in a low-resolution interval and extracting auxiliary features for dynamic correction in the low-resolution interval to obtain the final state of charge detection result; and determining whether to increase the measurement frequency point and re-execute the impedance measurement and subsequent steps based on the confidence interval width.

2. The method for rapid detection of the state of charge of a lithium battery according to claim 1, characterized in that, The specific steps of the pulse discharge test are as follows: apply a constant current discharge pulse with a duration of 10 seconds to the lithium battery under test, record the voltage difference before and after the pulse and the voltage recovery value after stabilization, calculate the current internal resistance value and the internal resistance growth rate based on the voltage difference, and estimate the remaining capacity and capacity decay rate based on the voltage recovery value.

3. The method for rapid detection of the state of charge of a lithium battery according to claim 2, characterized in that, The health status is determined as follows: when the internal resistance growth rate is less than 20% and the capacity decay rate is less than 10%, it is marked as health level one; when the internal resistance growth rate is between 20% and 50% or the capacity decay rate is between 10% and 20%, it is marked as health level two; and when the internal resistance growth rate is greater than 50% or the capacity decay rate is greater than 20%, it is marked as health level three.

4. The method for rapid detection of the state of charge of a lithium battery according to claim 3, characterized in that, The specific steps for selecting characteristic frequency points are to calculate the absolute value of the partial derivative of the impedance value with respect to the state of charge at each frequency point, normalize the absolute value of the partial derivative and use it as a sensitivity index, and select 5 to 8 frequency points with the largest sensitivity index as characteristic frequency points.

5. The method for rapid detection of the state of charge of a lithium battery according to claim 4, characterized in that, The specific steps of impedance measurement are as follows: apply a small-amplitude AC excitation signal to each characteristic frequency point, measure the amplitude and phase of the response current, calculate the impedance magnitude based on the ratio of the voltage amplitude to the current amplitude, calculate the impedance phase angle based on the difference between the voltage phase and the current phase, multiply the impedance magnitude by the cosine of the impedance phase angle to obtain the real part of the impedance data, and multiply the impedance magnitude by the sine of the impedance phase angle to obtain the imaginary part of the impedance data.

6. The method for rapid detection of the state of charge of a lithium battery according to claim 5, characterized in that, The specific steps for extracting the statistical moment eigenvector are as follows: calculate the mean and variance of the initial terminal voltage as the voltage moment feature; calculate the mean and variance of the real part of the impedance data in the characteristic frequency impedance vector as the impedance moment feature; normalize the surface temperature as the temperature moment feature; and combine the voltage moment feature, impedance moment feature, and temperature moment feature to form the statistical moment eigenvector.

7. The method for rapid detection of the state of charge of a lithium battery according to claim 6, characterized in that, The battery state topology reasoning model includes a battery topology graph construction layer, a graph convolution feature extraction layer, a dynamic connection optimization layer, and a state output layer. The battery topology graph construction layer abstracts the multi-layer electrode structure inside the lithium battery into a graph structure, where nodes represent local regions divided inside the battery and edges represent lithium-ion diffusion channels between adjacent local regions.

8. The method for rapid detection of the state of charge of a lithium battery according to claim 7, characterized in that, The graph convolutional feature extraction layer employs multi-layer graph convolution operations. Each layer of graph convolution updates the feature representation of the current node by aggregating information from neighboring nodes. The aggregation function is a weighted summation form, and the weights are adaptively calculated by the attention mechanism. The attention weights are determined based on a combination of node feature similarity and edge weights.

9. The method for rapid detection of the state of charge of a lithium battery according to claim 8, characterized in that, The dynamic connection optimization layer implements a sparse connection learning framework based on dynamic topology reconstruction. During training, the activation frequency and gradient contribution of each connection edge are statistically analyzed to calculate the connection importance score. When the connection importance score is lower than the dynamic threshold, the connection edge is pruned with a certain probability. The dynamic threshold is adaptively adjusted according to the current network sparsity and the loss function descent rate.

10. The method for rapid detection of the state of charge of a lithium battery according to claim 9, characterized in that, The state output layer consists of two branches: node-level output and global output. The node-level output maps the features of each node to the estimated state of charge of the corresponding local region through a fully connected layer. The global output calculates a weighted average of all node-level state of charge estimates to obtain the overall preliminary state of charge estimate. The weighting coefficients are determined by the confidence scores of the node features.

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