A method for estimating the state of health of sodium-ion batteries in energy storage scenarios

Abstract

The present invention provides a sodium-ion battery state of health (SOH) estimation method in an energy storage scenario, comprising the following steps: establishing a complete attenuation dataset of sodium-ion batteries under two operating conditions and extracting a plurality of battery degradation features; using three correlation analysis methods to respectively measure the correlation between the battery degradation features and the state of health (SOH), and performing preliminary screening of the battery degradation features and the SOH to obtain the battery degradation features after preliminary screening; then using an integral gradient algorithm to perform secondary feature screening, and simultaneously using a KAN network as a proxy model to perform interpretability analysis, thereby obtaining a feature combination that contributes strongly to battery life prediction; feeding the battery degradation features in the feature combination into a Temporal Residual KAN-LSTM network model for training, and estimating the state of health of the sodium-ion battery, thereby achieving high-precision SOH estimation of the sodium-ion battery and its interpretability.

Description

Technical Field

[0001] The present invention relates to the technical field of sodium ion battery health state estimation, and in particular to a method for estimating the health state of a sodium ion battery in an energy storage scenario. Background Art

[0002] Sodium-ion batteries (Na-ion batteries) are showing promise as a potential replacement for lithium-ion batteries due to their abundant resources, low cost, and environmental advantages. Furthermore, their high material stability, excellent cycling performance, and low operating voltage make them safer and more reliable in large-scale energy storage applications. However, their long-term stability and reliability in energy storage applications remain challenging due to their unique aging mechanisms and limited available state-of-health (SOH) estimation data. With advances in sensor technology and data storage capabilities, data-driven battery SOH estimation methods are becoming mainstream. Leveraging deep learning models, these methods can automatically learn complex patterns of battery aging and achieve accurate predictions by leveraging extensive historical and real-time monitoring data. However, the current development of Na-ion batteries faces numerous challenges. Compared to Li-ion batteries, Na-ion batteries are still in the early stages of development and lack long-term operational and experimental data. Existing research primarily focuses on Li-ion vehicle battery management systems, whereas energy storage systems place even higher demands on SOH estimation accuracy, particularly in capacity management and energy scheduling. Summary of the Invention

[0003] In response to the needs in the prior art, the present invention provides a method for estimating the state of health of a sodium ion battery in an energy storage scenario, aiming to achieve high-precision SOH estimation of a sodium ion battery and its interpretability.

[0004] A method for estimating the state of health of a sodium ion battery in an energy storage scenario comprises the following steps:

[0005] Step 1: Create a complete degradation dataset of sodium-ion batteries at two operating conditions: standard charge rate and lower charge rate;

[0006] Step 2: Extract several battery degradation features based on the complete sodium-ion battery attenuation dataset;

[0007] Step 3: Use the Spearman, Kendall, and Pearson correlation analysis methods to measure the linear correlation, nonlinear monotonicity, and rank order consistency between the battery degradation characteristics and SOH, and perform a preliminary screening of the battery degradation characteristics and SOH to obtain the battery degradation characteristics after preliminary screening;

[0008] Step 4: The battery degradation features after the initial screening are subjected to secondary feature screening using the integral gradient algorithm, and the KAN network is used as a proxy model for interpretability analysis to obtain a feature combination that contributes strongly to battery life prediction;

[0009] Step 5: The battery degradation features in the feature combination are fed into the Temporal Residual KAN-LSTM network model for training. The output of the Temporal Residual KAN-LSTM network model is the estimated health status of the sodium-ion battery.

[0010] Furthermore, the Temporal Residual KAN-LSTM network model includes a first-layer LSTMCell, a second-layer LSTMCell, and a third-layer KAN network. The first-layer LSTMCell and the second-layer LSTMCell are both the smallest units of LSTM. The data passes through the first-layer LSTMCell and the second-layer LSTMCell in sequence and is then sent to the third-layer KAN network. Dynamic residual connection is performed on the output results of the third-layer KAN network to obtain the final SOH result.

[0011] Further: the battery characteristic data is recorded as a time series Xt, where each time step t contains the state characteristics of the battery, and the data dimension of Xt is , is the feature dimension, and the time series length is , each time step The final output of the corresponding Temporal Residual KAN-LSTM network model is , that is, the final SOH result, the batch size is defined as , the final output feature dimension is , then the final output of the Temporal Residual KAN-LSTM network model in the time dimension is expressed as:

[0012]

[0013] in, and is a learnable weight parameter used to balance the contributions of different paths, and They are the hidden states of the first and second layers of LSTMCell corresponding to the t-th time step; and is the projection matrix, and is the corresponding bias vector, is the hidden state of LSTMCell, is the output of the KAN layer, and is a one-variable nonlinear function.

[0014] Furthermore, in step 1, the standard charging rate is as follows: the battery is first charged at a constant current of 1C to a set voltage, and then switched to a constant current and constant voltage charging mode of 0.5C until the voltage reaches 3.8V; then, the battery is discharged at a constant current of 1C to a cut-off voltage of 1.5V;

[0015] The lower charge rate is: the battery is charged at a constant current and constant voltage of 0.5C, the maximum charge voltage is also set to 3.8V, and then discharged to 1.5V in a constant current mode of 1C.

[0016] Further, step 2 includes 30 types of battery degradation characteristics, which are shown in Table 1:

[0017] Table 1

[0018]

[0019] in, For time; is the time proportion; For constant current charging; Constant voltage charging for flow; It is a constant current discharge; is the temperature data; is the current; is the voltage; is the slope of the voltage curve; is the slope of the current curve; is the charging current; For capacity.

[0020] Further: Pearson's output for:

[0021]

[0022] in, and These are two battery degradation characteristics; for and The Pearson correlation coefficient of , and the value range is [-1,1], when =1, and is completely positively correlated; when = -1, and is completely negatively correlated; when =0, and It is wireless related; For the observations in the variable The value in For the observations in the variable The value in for The mean of for The mean of is the sample size;

[0023] Spearman output for:

[0024]

[0025] in, is the Spearman rank correlation coefficient, when =1, indicating that there is a completely monotonically increasing relationship between the two variables; when = -1, indicating that there is a completely monotonically decreasing relationship between the two variables; when =0, indicating that there is no monotonic relationship between the two variables; is the sample size of the data; For the data points in the first variable The original value in For the data points in the second variable The original value in For the data points in the variable The ranking value in For the data points in the variable The ranking value in For the two variables The ranking difference of data points is: ;

[0026] Kendall's output for:

[0027]

[0028] in, is the number of consistent pairs, is the number of discordant pairs, is the number of tied pairs; : Kendall's Tau coefficient, which reflects the degree of association between variables, ranges from -1≤ ≤1; =1, positive correlation; =-1 indicates negative correlation; =0 means there is no correlation.

[0029] Further: Step 4 specifically includes the following steps:

[0030] Step 4.1: The integral gradient algorithm calculates the cumulative rate of change of the model output with respect to the input features by comparing the difference between the baseline input and the actual input;

[0031] Step 4.2: The initial structure of the proxy model KAN network is [15, [5, 3], 1], which shrinks to [8, [2, 2], 1] after training; the final expression is:

[0032]

[0033] in, is the SOH value of some samples in the feature selection stage, Indicates the rate of voltage change during the discharge process, is the average voltage level during constant current charging; Represents constant current charging time, is the peak value of the IC curve; and are the energy conversion efficiency and aging degree of the battery respectively; and It is the voltage and current integrals that quantify the total energy output during the discharge process;

[0034] Step 4.3: Combining the surrogate model KAN network with the integral gradient algorithm, 6 features are retained based on the contribution of the remaining features to the model prediction, namely .

[0035] Further: Cumulative rate of change Used to measure the contribution of each input feature to the model prediction, namely:

[0036]

[0037] in, is the baseline input, is the function of the deep learning model, is the number of steps into which the integration path is divided.

[0038] Beneficial effects of the present invention: The Temporal Residual KAN-LSTM network model combines the time series processing capability of LSTMCell and the nonlinear feature extraction capability of the KAN network, and improves the adaptability to complex time series data by introducing the Temporal Residual mechanism. In energy storage applications, high-precision SOH estimation of sodium-ion batteries and its interpretability are achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flow chart of the present invention;

[0040] Figure 2 It is the process of secondary feature screening and interpretable analysis;

[0041] Figure 3 This is the Temporal Residual KAN-LSTM model diagram in the present invention;

[0042] Figure 4 This is a graph showing the estimation results of different models for sodium-ion battery SOH;

[0043] Figure 5 Error diagram of the estimation results of different models for sodium-ion battery SOH. DETAILED DESCRIPTION

[0044] The present invention will be described in detail below with reference to the accompanying drawings. The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and are not to be construed as limiting the present invention. The directional terms such as left, center, right, top, and bottom in the embodiments of the present invention are merely relative concepts or are based on the normal use state of the product, and should not be considered as restrictive.

[0045] A method for estimating the health status of sodium-ion batteries in energy storage scenarios, such as Figure 1 As shown, the following steps are included:

[0046] Step 1: Create a complete sodium-ion battery degradation dataset under two operating conditions: a standard charge rate and a lower charge rate. For the standard charge rate, the battery is first charged at a constant current of 1C to a set voltage, then switched to a constant current and constant voltage charge mode of 0.5C until the voltage reaches 3.8V. The battery is then discharged at a constant current of 1C to a cutoff voltage of 1.5V. This operating condition simulates the battery performance under standard charging conditions and aims to study the aging characteristics of sodium-ion batteries at standard rates.

[0047] At the lower charge rate, the battery was charged at a constant current and constant voltage (CCCV) rate of 0.5C, with the maximum charge voltage also set at 3.8V, followed by discharge at a constant current of 1C to 1.5V. This simulates milder charging conditions to evaluate the performance degradation of sodium-ion batteries at lower charge rates.

[0048] Step 2: Based on the complete sodium-ion battery degradation dataset, these complex data are converted into indicators with physical meaning and statistical relevance from multiple change dimensions such as voltage, current, and temperature. 30 battery degradation features are extracted, providing a rich and reasonable basis for interpretability. The 30 battery degradation features are shown in Table 1:

[0049] Table 1

[0050]

[0051] in, For time; is the time proportion; For constant current charging; Constant voltage charging for flow; It is a constant current discharge; is the temperature data; is the current; is the voltage; is the slope of the voltage curve; is the slope of the current curve; is the charging current; is capacity;

[0052] Step 3: Use Spearman, Kendall and Pearson correlation analysis methods to measure the linear correlation, nonlinear monotonicity and rank order consistency between battery degradation characteristics and SOH respectively, and preliminarily screen the battery degradation characteristics and SOH to obtain the battery degradation characteristics after preliminary screening; among them, the output of Pearson for:

[0053]

[0054] in, and These are two battery degradation characteristics; for and The Pearson correlation coefficient of , and the value range is [-1,1], when =1, and is completely positively correlated; when = -1, and is completely negatively correlated; when =0, and It is wireless related; For the observations in the variable The value in For the observations in the variable The value in for The mean of for The mean of is the sample size (i.e. and The Pearson correlation coefficient assumes that the relationship between variables is linear and the data follows a normal distribution or approximate normality. It is only suitable for capturing linear relationships between variables.

[0055] The Spearman correlation coefficient is used to measure the monotonic relationship between two variables. Even if the relationship between the variables is not linear, as long as they show a monotonically increasing or decreasing trend, the Spearman correlation coefficient can still capture the correlation. First, for each variable and Rank the observations and get and , that is, the variable and rank; Spearman's output for:

[0056]

[0057] in, is the Spearman rank correlation coefficient, when =1, indicating that there is a completely monotonically increasing relationship between the two variables; when = -1, indicating that there is a completely monotonically decreasing relationship between the two variables; when =0, indicating that there is no monotonic relationship between the two variables; is the sample size of the data; For the data points in the first variable The original value in For the data points in the second variable The original value in For the data points in the variable The ranking value in For the data points in the variable The ranking value in For the two variables The ranking difference of data points is: It does not require the data to follow a specific distribution type and is less sensitive to outliers. It is especially suitable when features and SOH show different increase and decrease trends in different states.

[0058] The Kendall correlation coefficient measures the consistency of the rank order between two variables, mainly capturing the rank correlation between variables. It is calculated based on the rank order consistency and inconsistency between pairs of observations. The output of Kendall is for:

[0059]

[0060] in, is the number of consistent pairs, is the number of discordant pairs, is the number of tied pairs; : Kendall's Tau coefficient, which reflects the degree of association between variables, ranges from -1≤ ≤1; =1, positive correlation; =-1 indicates negative correlation; =0 means there is no correlation; it measures the stability of the order relationship when the data may contain noise or irregularities;

[0061] Step 4: Combine the battery degradation characteristics after preliminary screening with Figure 2 As shown in the figure, the integral gradient algorithm is used for secondary feature screening, and the KAN network is used as a proxy model for interpretability analysis; thereby obtaining a feature combination that contributes strongly to battery life prediction; specifically, the following steps are included:

[0062] Step 4.1: The integral gradient algorithm calculates the cumulative rate of change of the model output with respect to the input features by comparing the difference between the baseline input and the actual input; the cumulative rate of change Used to measure the contribution of each input feature to the model prediction, namely:

[0063]

[0064] in, is the baseline input, is the function of the deep learning model, is the number of steps into which the integration path is divided;

[0065] A deep learning model can be viewed as a complex function , for any input , can be calculated by the model to get an output , when the input parameters has changed Finally, if you want to know which input parameter has a greater impact on the result, you only need to look at the output changes. Relative to the input change The ratio of , that is, the corresponding partial differential gradient:

[0066]

[0067] Assuming a deep learning model Accepting Input and produces the output , the baseline input is , then for the input No. The attribution value of the integral gradient algorithm is calculated by the following formula:

[0068]

[0069] Since it is impractical to calculate the integral directly, a numerical approximation method is used to estimate the integral, dividing the integral path into equally spaced points and calculate the gradient at these points, and then take their weighted average:

[0070]

[0071] After obtaining the importance scores of the features, the number of features is selected based on the difference in score ratios and prior knowledge from past work. The sum of the attribution values of all input features equals the total change in the model output, which ensures the consistency of the interpretation results of the integral gradient method.

[0072] Step 4.2: The initial structure of the proxy model KAN network is [15, [5, 3], 1], which shrinks to [8, [2, 2], 1] after training; the final expression is:

[0073]

[0074] in, is the SOH value of some samples in the feature selection stage, Indicates the rate of voltage change during discharge, which is often related to the internal resistance of the battery. An increase in internal resistance will lead to an increase in the rate of voltage change, reflecting battery aging; is the average voltage level during constant current charging. A high voltage means a higher charging efficiency. As the battery ages, the voltage decreases. This trend is reflected in the formula through a negative exponential relationship, indicating that voltage significantly suppresses SOH. Represents the constant current charging time. The extension of constant current charging time means the increase of battery internal resistance and the decrease of charge receiving efficiency, indicating the aging process. The negative exponential term in the denominator further amplifies the negative impact of constant current charging time on SOH. If If the value is large, the denominator will approach zero, thereby amplifying the negative impact of the term and causing a significant decrease in SOH; is the peak value of the IC curve. The decrease of this feature means that the internal reaction rate slows down and the active material decreases. The complex exponential form in the formula reflects the high sensitivity of the IC peak to SOH; and are the energy conversion efficiency and aging degree of the battery respectively. The exponential form of this item reflects the overall impact of the combined changes of different slopes on the battery state; and The voltage and current integrals quantify the total energy output during discharge. The exponential form and denominator structure of this term indicate that changes in the discharge voltage and current integrals can have a significant nonlinear effect on SOH, especially at high depths of discharge, which can negatively impact battery life.

[0075] Combining the symbolic formula with the integral gradient algorithm to further understand the contribution of the remaining features, the first 6 features are retained and the features with contributions of -0.0185 and -0.0127 are removed. and At the same time, from the formula, when multiple variables are combined into the denominator through multiplication and addition, the influence of a single variable will be weakened by the value of other variables. Specifically, the denominator contains and A combination of As the coefficient of another exponential term, it has a greater impact on the value of the denominator. In addition, the constant term (-1.06) in the denominator further suppresses The sensitivity of the denominator to changes in or Even if there is a large change in the value of the product, the change in the overall denominator is relatively limited, which may result in a smaller contribution of this term in the formula;

[0076] Step 4.3: Combining the surrogate model KAN network with the integral gradient algorithm, six battery degradation features are retained based on the contribution of the remaining features to the model prediction, namely ;

[0077] Step 5: The battery degradation features obtained in step 4.3 are fed into the Temporal Residual KAN-LSTM network model for training. The output of the Temporal Residual KAN-LSTM network model is the estimated health state of the sodium-ion battery.

[0078] Among them, combined Figure 3 As shown in Figure 1, the TemporalResidual KAN-LSTM network model includes the first layer of LSTMCell, the second layer of LSTMCell and the third layer of KAN network. The first layer of LSTMCell and the second layer of LSTMCell are the smallest units of LSTM. The data passes through the first layer of LSTMCell and the second layer of LSTMCell in turn and is sent to the third layer of KAN network. The output result of the third layer of KAN network is dynamically residual connected to obtain the final SOH result. Specifically, the battery feature data is recorded as a time series Xt, where each time step t contains the state characteristics of the battery. The data dimension of Xt is , is the feature dimension, and the time series length is , each time step The final output of the corresponding Temporal Residual KAN-LSTM network model is , that is, the final SOH result, the batch size is defined as , the final output feature dimension is , then the final output of the Temporal Residual KAN-LSTM network model in the time dimension is expressed as:

[0079]

[0080] in, and is a learnable weight parameter used to balance the contributions of different paths, and They are the hidden states of the first and second layers of LSTMCell corresponding to the t-th time step; and is the projection matrix, which maps the hidden state to the same dimension as the KAN output space. and is the corresponding bias vector, is the hidden state of LSTMCell, is the output of the KAN layer, and is a one-variable nonlinear function.

[0081] In response to the higher accuracy requirements for SOH estimation in energy storage applications, the designed Temporal ResidualKAN-LSTM (TRKL) model was verified and compared with the Kolmogorov-ArnoldNetwork (KAN) network, CNN-LSTM-MLP and the Bagging Temporal Attention Network (BTANet) previously used for fast-charging battery SOH estimation on different working condition data sets. The method of the present invention was comprehensively evaluated using six evaluation indicators: mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), coefficient of determination (R2) and maximum error (MAXE).

[0082] Table 2 Estimation results of different models for sodium-ion battery SOH

[0083]

[0084] As shown in Table 2, Figure 4 and Figure 5 As shown in the figure, B101-B104 and B201-B204 represent different sodium batteries. The TRKL model demonstrates significant advantages over other models in multiple error metrics, particularly in accuracy and robustness. The TRKL model combines the time series processing capabilities of LSTM with the nonlinear feature extraction capabilities of the KAN network, and introduces a Temporal Residual mechanism to improve its adaptability to complex time series data. TRKL significantly outperforms the KAN, CNN-LSTM-MLP, and BATNet models in terms of the Mean Separation Estimation (MSE). This has practical implications for energy storage applications, which require stable SOH estimation results. Furthermore, the evaluation metrics of the other models all converged within a reasonable range, demonstrating the effectiveness and importance of feature engineering.

[0085] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for estimating the state of health of a sodium-ion battery in an energy storage scenario, characterized by: The following steps are involved: Step 1: Create a complete degradation dataset of sodium-ion batteries at two operating conditions: standard charge rate and lower charge rate; The standard charge rate is as follows: the battery is first charged at a constant current of 1C to a set voltage, then switched to a constant current and constant voltage charge mode of 0.5C until the voltage reaches 3.8V; then, the battery is discharged at a constant current of 1C to a cut-off voltage of 1.5V. The lower charge rate is: the battery is charged at a constant current and constant voltage of 0.5C, with the maximum charge voltage also set at 3.8V, and then discharged to 1.5V in a constant current mode of 1C; Step 2: Extract 30 battery degradation features based on the complete sodium-ion battery degradation dataset. The 30 battery degradation features are shown in Table 1: Table 1 ； in, For time; is the proportion of time; For constant current charging; Charging with constant current and constant voltage; It is a constant current discharge; is the temperature data; is the current; is the voltage; is the slope of the voltage curve; is the slope of the current curve; is the charging current; is capacity; Step 3: Use the Spearman, Kendall, and Pearson correlation analysis methods to measure the linear correlation, nonlinear monotonicity, and rank order consistency between the battery degradation characteristics and SOH, and perform a preliminary screening of the battery degradation characteristics and SOH to obtain the battery degradation characteristics after preliminary screening; Among them, Pearson's output for: ； in, and These are two battery degradation characteristics; for and The Pearson correlation coefficient of , and the value range is [-1,1], when =1, and is completely positively correlated; when = -1, and is completely negatively correlated; when =0, and It is wireless related; For the observations in the variable The value in For the observations in the variable The value in for The mean of for The mean of is the sample size; Spearman output for: ； in, is the Spearman rank correlation coefficient, when =1, indicating that there is a completely monotonically increasing relationship between the two variables; when = -1, indicating that there is a completely monotonically decreasing relationship between the two variables; when =0, indicating that there is no monotonic relationship between the two variables; is the sample size of the data; For the data points in the first variable The original value in For the data points in the second variable The original value in For the data points in the variable The ranking value in For the data points in the variable The ranking value in For the two variables The ranking difference of data points is: ; Kendall's output for: ；； in, is the number of consistent pairs, is the number of discordant pairs, is the number of tied pairs; : Kendall's Tau coefficient, which reflects the degree of association between variables, ranges from -1≤ ≤1; =1, positive correlation; =-1 indicates negative correlation; =0 means no correlation; Step 4: The battery degradation features after the initial screening are subjected to secondary feature screening using the integral gradient algorithm, and the KAN network is used as a proxy model for interpretability analysis to obtain a feature combination that contributes strongly to battery life prediction. The specific steps include: Step 4.1: The integral gradient algorithm calculates the cumulative rate of change of the model output with respect to the input features by comparing the difference between the baseline input and the actual input; Step 4.2: The initial structure of the proxy model KAN network is [15, [5, 3], 1], which shrinks to [8, [2, 2], 1] after training; the final expression is: ； in, is the SOH value of some samples in the feature selection stage, Indicates the rate of voltage change during the discharge process, is the average voltage level during constant current charging; Represents constant current charging time, is the peak value of the IC curve; and are the energy conversion efficiency and aging degree of the battery respectively; and It is the voltage and current integrals that quantify the total energy output during the discharge process; Step 4.3: Combining the surrogate model KAN network with the integral gradient algorithm, 6 features are retained based on the contribution of the remaining features to the model prediction, namely ; Step 5: The battery degradation features in the feature combination are fed into the Temporal Residual KAN-LSTM network model for training. The output of the Temporal Residual KAN-LSTM network model is the estimated health status of the sodium-ion battery.

2. The method for estimating the state of health of a sodium-ion battery in an energy storage scenario according to claim 1, wherein: The Temporal Residual KAN-LSTM network model includes the first layer LSTMCell, the second layer LSTMCell, and the third layer KAN network. The first and second layers LSTMCell are both the smallest units of LSTM. The data passes through the first and second layers LSTMCell in sequence and is then sent to the third layer KAN network. Dynamic residual connection is performed on the output results of the third layer KAN network to obtain the final SOH result.

3. The method for estimating the health status of a sodium-ion battery in an energy storage scenario according to claim 2, characterized in that: The battery characteristic data is recorded as a time series Xt, where each time step t contains the state characteristics of the battery. The data dimension of Xt is , is the feature dimension, and the time series length is , each time step The final output of the corresponding Temporal ResidualKAN-LSTM network model is , that is, the final SOH result, the batch size is defined as , the final output feature dimension is , then the final output of the Temporal Residual KAN-LSTM network model in the time dimension is expressed as: ； ； in, and is a learnable weight parameter used to balance the contributions of different paths, and They are the hidden states of the first and second layers of LSTMCell corresponding to the t-th time step; and is the projection matrix, and is the corresponding bias vector, is the hidden state of LSTMCell, is the output of the KAN layer, and is a one-variable nonlinear function.

4. The method for estimating the state of health of a sodium-ion battery in an energy storage scenario according to claim 1, wherein: Cumulative rate of change Used to measure the contribution of each input feature to the model prediction, namely: ； in, is the baseline input, is the function of the deep learning model, is the number of steps into which the integration path is divided.

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