PIKAN-lstm-based soc estimation method for low-temperature lithium battery

Abstract

The present application relates to the technical field of lithium ion battery state estimation, in particular to a low-temperature lithium battery SOC estimation method based on PIKAN-LSTM, which firstly carries out low-rate discharge test under multiple temperature environments, constructs the relationship curve of open-circuit voltage, state of charge and temperature, and completes the training and verification of the first KAN model; then builds a PIKAN model containing a circuit equation solving unit and a second KAN network unit, identifies the battery equivalent resistance and two-stage polarization voltage in combination with the second-order RC equivalent circuit equation; then obtains the estimated open-circuit voltage through voltage compensation operation, inputs the first KAN model to output the preliminary state of charge; finally, the time series error correction is carried out by using the bidirectional LSTM network to obtain the final estimation result, which effectively solves the problems of battery model parameter drift and estimation error accumulation under low-temperature working conditions, and significantly improves the estimation accuracy and robustness.

Description

Technical Field

[0001] This invention relates to the field of lithium-ion battery state estimation technology, specifically to a low-temperature lithium battery SOC estimation method based on PIKAN-LSTM. Background Technology

[0002] The state of charge (SOC) of lithium-ion batteries is a core parameter for battery management systems to perform energy management, lifespan prediction, and safety warnings. Accurate SOC estimation is crucial for range assessment and system reliability in fields such as new energy vehicles and aerospace. However, in low-temperature environments, the internal electrochemical reaction kinetics of lithium-ion batteries decrease, internal resistance increases significantly, and polarization intensifies, posing a severe challenge to traditional SOC estimation methods.

[0003] Currently, mainstream SOC estimation methods mainly include model-based open-loop methods and data-driven closed-loop methods. Model-based methods, such as the extended Kalman filter combining the ampere-hour integral method with the equivalent circuit model, heavily rely on the accuracy of the equivalent circuit model. Under low-temperature conditions, the battery's internal resistance, polarization resistance, capacitance, and other model parameters will drift drastically and nonlinearly with temperature, leading to severe mismatch in the fixed-parameter equivalent circuit model and thus generating significant SOC estimation errors. The ampere-hour integral method itself has accumulated errors, which are further amplified at low temperatures due to the influence of current measurement accuracy and changes in battery usable capacity.

[0004] On the other hand, purely end-to-end data-driven methods, such as SOC estimation models based on long short-term memory networks or convolutional neural networks, can capture complex nonlinear relationships by learning from historical data. However, their "black box" nature leads to a lack of physical interpretability. When extrapolating to extreme conditions not covered by the training data (such as extremely low temperatures and high rates), their generalization ability and reliability are insufficient, and they are highly dependent on the quality and quantity of training data. Although there are existing technologies that attempt to integrate models with data-driven approaches, such as combining convolutional neural networks with unscented Kalman filters, they still fail to fundamentally solve how to deeply couple the physical dynamic equations of the battery into the neural network to achieve accurate modeling of time-varying parameters (especially the dynamic characteristics of polarization voltage) at low temperatures, and how to effectively model the complex multidimensional coupling relationship between OCV, SOC, and temperature.

[0005] Therefore, there is an urgent need for a new method for estimating the SOC of lithium-ion batteries that can achieve physical consistency, high accuracy, and strong robustness over a wide temperature range, especially in low-temperature environments, in order to overcome the shortcomings of existing technologies such as model mismatch, error accumulation, and poor extrapolation when dealing with extreme temperatures. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a low-temperature lithium battery SOC estimation method based on PIKAN-LSTM, which solves the defects of the prior art in dealing with model mismatch, error accumulation and poor extrapolation when dealing with extreme temperatures.

[0007] To address the above problems, the technical solution of this invention is as follows: A low-temperature lithium battery SOC estimation method based on PIKAN-LSTM, comprising the following steps: S1. Conduct low-rate discharge tests on lithium batteries in different temperature environments. Construct a relationship curve between open-circuit voltage, state of charge, and temperature based on the test data. Use some of the relationship curve data and corresponding temperature data to train the first KAN model. Use the remaining data for verification to obtain the trained first KAN model. S2. Construct a PIKAN model. The PIKAN model includes a circuit equation solving unit and a second KAN network unit. Collect voltage, current, temperature and state of charge data during the operation of the lithium battery. Combine the relationship curve obtained in S1 to train the PIKAN model to identify the equivalent resistance and two polarization voltages corresponding to the second-order RC equivalent circuit model of the lithium battery. S3. Based on the current terminal voltage and current of the lithium battery and the equivalent resistance and polarization voltage identified in S2, perform compensation calculations to obtain the estimated open-circuit voltage of the lithium battery at the current moment. S4. Input the estimated open-circuit voltage and current temperature obtained in S3 into the first KAN model trained in S1 to obtain the preliminary state of charge estimate of the lithium battery. S5. Input the preliminary state of charge estimate obtained in S4 into the LSTM network, output the state of charge error compensation amount through the LSTM network, add the state of charge error compensation amount to the preliminary state of charge estimate, and obtain the final state of charge estimate.

[0008] Furthermore, S1 includes: S11. In a constant temperature environment, conduct a constant current discharge experiment on the lithium battery at a discharge rate not exceeding 0.1C, and record the change data of the battery terminal voltage over time at different temperatures. S12. Record the terminal voltage and discharge time of the lithium battery during the discharge process, and approximate the terminal voltage as the open circuit voltage of the corresponding state of charge at that temperature. S13. Calculate the state of charge at each sampling time based on the ampere-hour integration method. The calculation formula for the ampere-hour integration method is as follows: , in, Let be the battery state of charge at time t. This represents the initial state of charge of the battery. For the battery's rated capacity, for The charging and discharging current at any given time, Let be the integral variable, taking the value 0-t. It is an integral infinitesimal element; S14. The obtained open-circuit voltage, state of charge, and temperature relationship curves are processed by optimizing the weights of the B-spline function to make the discrete data continuous, resulting in a continuous three-dimensional correspondence.

[0009] Furthermore, in S2, the state equation of the second-order RC equivalent circuit model is: , , in, , These are the first polarization voltage and the second polarization voltage, respectively. , These are the time constants of the two RC circuits, , Polarization resistor, , Polarized capacitor, This is the charging and discharging current. For time differentiation; The output equation of the second-order RC equivalent circuit model is: , in, Terminal voltage, This is the mapping function between open-circuit voltage and state of charge. This is the equivalent resistance.

[0010] Furthermore, in S2, the second KAN network unit uses temperature as input and fits the temperature dependence of the equivalent resistance and time constant using B-spline basis functions. The PIKAN model training employs a joint loss function: , in, For the total loss, For data fitting loss, For physical constraint loss, , These are the weighting coefficients.

[0011] Furthermore, in S2, the data fitting loss for: , in, For the sample size, For the first The measured terminal voltage at each sampling time. Let be the model predicted terminal voltage at the i-th sampling time.

[0012] Furthermore, in S2, the physical constraint loss for: , in, This is the first derivative of the first polarization voltage with respect to time. This is the first derivative of the second polarization voltage with respect to time. , Let be the time constant of the two RC circuits.

[0013] Furthermore, in S3, the compensation calculation formula is: , in, To estimate the open-circuit voltage.

[0014] Furthermore, in S4, the first KAN model internally optimizes the B-spline weights to make the discrete open-circuit voltage, state of charge, and temperature data continuous. Its basis function expression is: , in, It is a mapping function of open-circuit voltage, state of charge, and temperature. The number of B-spline basis functions for the temperature dimension. The number of B-spline basis functions in the charged state dimension. For the first i The basis functions of the charge state dimension and the first j The weighting coefficients corresponding to the basis functions of each temperature dimension. Let be the B-spline basis function for the i-th charged state dimension. Let be the B-spline basis function for the j-th temperature dimension.

[0015] Furthermore, in S5, the LSTM network is a bidirectional LSTM network, and the input is a feature sequence with a time window length of L: , Among them, feature vector ,Include t Preliminary state of charge estimates, battery temperature, and battery current at time t; The bidirectional LSTM network is trained using the feature sequence as input and the difference between the reference state of charge and the preliminary state of charge estimate as the target label. In online application, the final state of charge estimate is: , in, This is the final estimated state of charge. For preliminary state of charge estimation, This is for compensating for the state of charge error output by the LSTM network.

[0016] Compared with the prior art, the present invention has the following beneficial effects: The PIKAN model of the present invention embeds the state equation of the second-order RC equivalent circuit model into the KAN network structure. The circuit equation solving unit provides the initial value of the polarization voltage under physical constraints. At the same time, the second KAN network unit uses temperature as input and fits the temperature dependence of the equivalent resistance and time constant through B-spline basis functions. During the training process, a joint loss function including data fitting loss and physical constraint loss is adopted. The circuit model parameters and network weights are updated synchronously through the adaptive momentum gradient descent algorithm, so that the model has both physical consistency and data-driven flexibility. It effectively overcomes the problem of easy drift of pure equivalent circuit model parameters and realizes real-time and adaptive identification of circuit parameters in low temperature environment.

[0017] Based on the equivalent resistance and two polarization voltages identified by the PIKAN model, the current terminal voltage is compensated by subtracting the voltage drop caused by the ohmic internal resistance and the voltage drop caused by the polarization internal resistance from the terminal voltage, thus obtaining the predicted open-circuit voltage that is not affected by the internal resistance. This compensation mechanism effectively isolates voltage disturbances under dynamic operating conditions, provides accurate input for subsequent state of charge estimation based on open-circuit voltage, and significantly improves the reliability of state estimation.

[0018] The estimated open-circuit voltage obtained in step S3 and the current temperature are input into the first KAN model pre-trained in step S1. The model directly outputs the preliminary state of charge estimate using its internally optimized B-spline weights. The first KAN model can quickly and accurately query the corresponding state of charge based on the open-circuit voltage at any temperature through a continuous three-dimensional mapping relationship, without the need for complex iterative calculations, thus balancing estimation accuracy and real-time performance.

[0019] The initial state of charge (SOC) estimate, battery temperature, and battery current are combined into a feature sequence and input into a bidirectional LSTM network. The forward LSTM subnetwork captures the trend of SOC change over time, while the backward LSTM subnetwork captures the lag effect of temperature change on SOC. By utilizing bidirectional contextual information to learn the error evolution law, the SOC error compensation is output. This time-series error correction mechanism is equivalent to adding a self-learning feedback loop to SOC estimation, which can adaptively compensate for model errors. As the running data accumulates, the correction capability is continuously optimized, significantly improving the accuracy and robustness of SOC estimation under complex operating conditions. Attached Figure Description

[0020] Figure 1 This is a flowchart of the estimation method of the present invention; Figure 2The result is shown in the estimation method of this invention. Detailed Implementation

[0021] This invention provides a method for estimating the state of charge (SOC) of lithium batteries at low temperatures based on PIKAN-LSTM. It employs a hierarchical modeling strategy. First, a relationship curve between open-circuit voltage, SOC, and temperature is constructed through low-rate discharge experiments, and a first KAN model is trained. Then, a PIKAN model containing circuit equation solving units and a second KAN network unit is constructed to identify the parameters of the second-order RC equivalent circuit model. Next, a compensation operation is performed to obtain the estimated open-circuit voltage. Subsequently, the first KAN model is used to obtain a preliminary SOC estimate. Finally, an LSTM network is used to correct timing errors, yielding the final SOC estimate. Through the multi-dimensional collaboration of physical information neural networks and deep learning, the problem of model parameter drift and error accumulation in low-temperature environments is effectively solved. The specific technical solution is as follows: This invention provides a low-temperature lithium battery state of charge estimation system, which includes: a battery data acquisition module, a PIKAN modeling module, a SOC estimation module, an error correction module, and an output module.

[0022] The battery data acquisition module is used to acquire real-time operating data such as terminal voltage, current, and temperature of lithium-ion batteries through multi-channel sensors, and provide this data to subsequent modules for processing. This module uses a semi-solid-state single-cell battery with a rated capacity of 16Ah and a nominal voltage of 3.7V as the test object. It is equipped with a voltage sensor with an accuracy of ±0.5mV, a current sensor with an accuracy of ±0.1A, and a PT100 temperature sensor with an accuracy of ±0.1℃. The sampling frequency is set to 10Hz, covering six typical test temperature points: 0℃, 10℃, 25℃, and 40℃, to meet the data acquisition and model identification requirements under low-temperature dynamic operating conditions.

[0023] The PIKAN modeling module receives the battery data and performs training and calculation of the PIKAN model, outputting the first polarization voltage, second polarization voltage, and equivalent resistance of the lithium battery, as well as the estimated open-circuit voltage of the battery calculated based on the battery terminal voltage and the parameters. The PIKAN modeling module is further divided into two functional units: a circuit equation solving unit and a second PIKAN network unit. The circuit equation solving unit performs physical quantity calculations on the sensor-acquired data based on an embedded second-order RC equivalent circuit model, using a method that... The pre-Eulerian method is used for time-domain discretization with a step size of 0.1s to solve for the initial polarization voltage, ohmic voltage drop, and other physical states of the battery in real time. The model has built-in physical constraints on the following parameters: internal ohmic resistance R0 ∈ [1.2mΩ, 8.5mΩ], first polarization resistance R1 ∈ [5mΩ, 30mΩ], polarization capacitance C1 ∈ [1000F, 8000F], second polarization resistance R2 ∈ [20mΩ, 120mΩ], polarization capacitance C2 ∈ [5000F, 30000F], ensuring that the solution results conform to the boundaries of the battery's electrochemical characteristics. The second KAN network unit uses the physical state provided by the circuit equation solving unit as input, and takes current, temperature, and the two polarization voltages from the previous time step as input features. It obtains precise polarization voltage values ​​and temperature-related parameter adjustments through neural network fitting. This KAN network employs a single hidden layer structure with 8 hidden layer nodes, a B-spline basis function order of 3, and a single-dimensional grid size of 8. It is trained using the Adam optimizer with an initial learning rate of 1×10⁻⁶. - ³, During training, a physical consistency loss term is introduced with a weight coefficient set to 0.3, constraining the network output to satisfy circuit equation constraints. The PIKAN modeling module internally combines physical model calculations with neural network calculations. This ensures the physical rationality of the battery behavior modeling while improving the model's accuracy and adaptability at low temperatures through neural network corrections.

[0024] The SOC estimation module is used to calculate the preliminary SOC estimate of the lithium battery based on the predicted open-circuit voltage and the pre-established open-circuit voltage, state of charge, and temperature mapping model (first KAN model). The first KAN model is constructed through a 0.05C low-rate discharge test, with discrete sampling across the entire range of 0% to 100% at 5% SOC intervals. It sets 12 grid nodes along the SOC dimension and 6 grid nodes along the temperature dimension, employs a third-order B-spline basis function to construct a two-dimensional continuous mapping, and introduces a second-order derivative smoothing regularization term (regularization coefficient 1×10⁻⁶). -4 By optimizing the spline weights, a globally interpolable OCV-SOC-T three-dimensional continuous surface is finally obtained, with a model fitting mean square error of less than 0.2mV.

[0025] The error correction module is used to perform time-series error correction on the preliminary state of charge (SOC) estimate. It employs an LSTM network to calculate the SOC estimation error compensation and correct the preliminary SOC estimate to obtain the final SOC estimate. This LSTM network has an input time window length of 20 steps, contains two hidden layers with 64 hidden units per layer, and uses Tanh as the recurrent activation function. The input features include four types of time-series data: preliminary SOC estimate, real-time terminal voltage, operating current, and battery temperature. The network uses a batch size of 32 and an initial learning rate of 5×10⁻⁶. -4 The Adam optimizer was trained for 200 epochs, and the error mapping relationship was fitted using the DST dynamic operating condition dataset. Validation showed that, under 0℃ low-temperature dynamic operating conditions, the mean absolute error of the corrected SOC estimation was less than 0.8%, and the root mean square error was less than 1.2%.

[0026] The output module is used to output the final state of charge estimate to the battery management system at an update frequency of 1Hz for display and further battery management decisions, and supports both CAN bus and serial port communication output modes.

[0027] The aforementioned system modules can be implemented through hardware circuits or software programs. In one implementation, the functions of each module can be accomplished by the microcontroller or processor in the battery management system by executing corresponding software instructions. For example, the microcontroller can periodically read sensor data, run the stored software program to perform the aforementioned PIKAN model calculation and LSTM error correction algorithm, and store the results in memory or send them to the host computer through a communication interface. In another implementation, some modules (such as the data acquisition module and the output module) are implemented in hardware, while the modeling calculation and error correction are implemented in software by the vehicle computing platform. This invention does not limit this aspect.

[0028] like Figure 1 As shown in the figure, the low-temperature lithium battery state-of-charge estimation method based on PIKAN-LSTM provided in this embodiment of the invention includes the following steps: Step S1: Construct the relationship curves between open-circuit voltage, state of charge, and temperature, and train the first KAN model. The lithium battery was placed in different temperature environments to carry out low-rate discharge tests. Based on the test data, the relationship curves of open circuit voltage, state of charge and temperature were constructed. Part of the relationship curve data and the corresponding temperature data were used to train the first KAN model, and the remaining data were used for verification to obtain the trained first KAN model.

[0029] This step specifically includes the following sub-steps: S11. In a constant temperature environment, conduct a constant current discharge experiment on the lithium battery at a discharge rate not exceeding 0.1C, and record the change data of the battery terminal voltage over time at different temperatures.

[0030] Specifically, in a constant temperature chamber, the lithium battery is discharged at multiple temperature points with a constant current rate not exceeding 0.1C, with the temperature points spaced no more than 5°C apart, and the temperature range covering -40°C to 40°C. During low-rate discharge, the internal resistance voltage drop of the lithium battery is extremely small and can be ignored, so the battery's terminal voltage can be equivalent to the open-circuit voltage of the lithium battery.

[0031] S12. Record the terminal voltage and discharge time of the lithium battery during the discharge process, and approximate the terminal voltage as the open circuit voltage of the corresponding state of charge at that temperature.

[0032] Because the internal current density of the battery is small during low-rate discharge, the voltage drop caused by the ohmic internal resistance and polarization internal resistance approaches zero. At this time, the terminal voltage of the battery is approximately equal to the open-circuit voltage of the battery. This design avoids the complicated parameter identification process and directly obtains accurate open-circuit voltage data, providing a reliable physical calibration basis for subsequent steps.

[0033] S13. Calculate the state of charge at each sampling time based on the ampere-hour integration method.

[0034] The calculation formula for the ampere-hour integration method is as follows: , in, for The state of charge of the battery at any given time. This represents the initial state of charge of the battery. For the battery's rated capacity, for The charging and discharging current at any given time, The variable is the integral variable, and its value is 0- , It is an integral infinitesimal element.

[0035] S14. Obtain the relationship curves of open-circuit voltage, state of charge, and temperature. Optimize the weights of the B-spline function to make the discrete data continuous, thus obtaining a continuous three-dimensional correspondence.

[0036] Data on open-circuit voltage, state of charge, and temperature from all sampling points at different temperatures are collected to form a three-dimensional correspondence. This relationship curve can be regarded as the static characteristic calibration result of the battery. Since the open-circuit voltage and state of charge curves change with temperature as a set of discrete curves, this invention solves the problem that traditional methods are difficult to construct a temperature-dimensional state of charge model by introducing temperature parameters into the first KAN model and using B-spline functions to interpolate and fit the discrete data.

[0037] Part of the aforementioned relationship curve data and corresponding temperature data were used to train the first KAN model, and the remaining data were used for validation, resulting in a well-trained first KAN model. Internally, the first KAN model optimizes the B-spline weights to make the discrete open-circuit voltage, state of charge, and temperature data continuous. Its basis function expression is as follows: , in, It is a mapping function of open-circuit voltage, state of charge, and temperature. The number of B-spline basis functions for the temperature dimension. The number of B-spline basis functions in the charged state dimension. For the first The basis functions of the charge state dimension and the first The weighting coefficients corresponding to the basis functions of each temperature dimension. For the first B-spline basis functions for each charged state dimension For the first B-spline basis functions for each temperature dimension.

[0038] This step involves conducting low-rate discharge experiments over a wide temperature range to obtain open-circuit voltage and state-of-charge calibration data that include the temperature dimension. The B-spline basis functions of the first KAN model are used to realize the continuous processing of discrete data, constructing an accurate three-dimensional mapping relationship. This provides a reliable physical calibration basis and temperature-adaptive query capability for subsequent steps.

[0039] Step S2: Construct the PIKAN model and identify the parameters of the second-order RC equivalent circuit model. A PIKAN model is constructed, which includes a circuit equation solving unit and a second KAN network unit. Voltage, current, temperature and state of charge data during the operation of the lithium battery are collected. The PIKAN model is trained by combining the relationship curve obtained by S1 to identify the equivalent resistance and two polarization voltages corresponding to the second-order RC equivalent circuit model of the lithium battery.

[0040] The second-order RC equivalent circuit model includes an equivalent resistance, a first RC element consisting of a first polarization resistor and a first polarization capacitor connected in parallel, and a second RC element consisting of a second polarization resistor and a second polarization capacitor connected in parallel.

[0041] The state equation of the second-order RC equivalent circuit model is: , , in, , These are the first polarization voltage and the second polarization voltage, respectively. For time, , These are the time constants of the two RC circuits, , Polarization resistor, , Polarized capacitor, This is the charging and discharging current. For time derivative.

[0042] The output equation of the second-order RC equivalent circuit model is: , in, Terminal voltage, This is the mapping function between open-circuit voltage and state of charge. This is the equivalent resistance.

[0043] The PIKAN model includes a circuit equation solving unit and a second KAN network unit.

[0044] Circuit equation solving unit: Based on a second-order RC equivalent circuit structure, this unit calculates the initial values ​​of polarization voltage and equivalent resistance in real time. By embedding the physical circuit equations of the lithium battery, this unit utilizes Kirchhoff's laws and Ohm's law, combined with real-time input current and voltage data, to construct differential equations containing polarization resistance and capacitance. It then preliminarily solves for the initial values ​​of the first and second polarization voltages, providing a physically constrained initial parameter space for subsequent network training.

[0045] The second KAN network unit: Taking temperature as input, it fits the nonlinear changes of temperature-related parameters through interpretable basis functions. Considering the complex nonlinear characteristics of lithium battery parameters with temperature, this unit adopts the Kolmogorov-Arnold network structure. It models the temperature dependence of equivalent resistance and RC link time constant through preset orthogonal basis functions, and achieves high-precision fitting of temperature-parameter mapping relationship.

[0046] The PIKAN model uses a joint loss function during training: , in, For the total loss, For data fitting loss, For physical constraint loss, , These are the weighting coefficients.

[0047] The data fitting loss for: , in, For the sample size, For the first The measured terminal voltage at each sampling time. For the first The model-predicted terminal voltage at each sampling time.

[0048] The physical constraint loss for: , in, This is the first derivative of the first polarization voltage with respect to time. This is the first derivative of the second polarization voltage with respect to time. , Let be the time constant of the two RC circuits.

[0049] During training, the adaptive momentum gradient descent algorithm is used to synchronously update the circuit model parameters and network weights, enabling the model to accurately characterize the impact of low temperature on the dynamic characteristics of the battery. Through multiple rounds of iterative training, the model parameters gradually converge.

[0050] In this step, the PIKAN model embeds the state equation of the second-order RC equivalent circuit model into the KAN network structure. The circuit equation solving unit provides the initial value of the polarization voltage under physical constraints. At the same time, the second KAN network unit uses temperature as input and fits the temperature dependence of the equivalent resistance and time constant through B-spline basis functions. During training, a joint loss function including data fitting loss and physical constraint loss is used. The circuit model parameters and network weights are updated synchronously through the adaptive momentum gradient descent algorithm, so that the model has both physical consistency and data-driven flexibility. This effectively overcomes the problem of easy drift of pure equivalent circuit model parameters and realizes real-time and adaptive identification of circuit parameters in low-temperature environments.

[0051] Step S3: Compensation calculation to obtain the estimated open-circuit voltage Based on the current terminal voltage and current of the lithium battery, as well as the equivalent resistance and polarization voltage identified by S2, a compensation calculation is performed to obtain the estimated open-circuit voltage of the lithium battery at the current moment.

[0052] The compensation calculation formula is: , in, To estimate the open-circuit voltage, This is the measured terminal voltage of the lithium battery at the current moment. The charging and discharging current at the current moment. Equivalent resistance , These are two polarization voltages.

[0053] This step uses the equivalent resistance and two polarization voltages identified by the PIKAN model to perform compensation calculations on the terminal voltage at the current moment. The voltage drop caused by the ohmic internal resistance and the voltage drop caused by the polarization internal resistance are subtracted from the terminal voltage to obtain the estimated open-circuit voltage that is not affected by the internal resistance. This compensation mechanism effectively isolates voltage disturbances under dynamic operating conditions, provides accurate input for subsequent state of charge estimation based on open-circuit voltage, and significantly improves the reliability of state estimation.

[0054] Step S4: First KAN model estimates the initial state of charge. The estimated open-circuit voltage and current temperature obtained in S3 are input into the first KAN model trained in S1 to obtain the preliminary state-of-charge estimate of the lithium battery.

[0055] Specifically, the first KAN model optimizes the B-spline weights to quickly query the corresponding state of charge based on the open-circuit voltage at any temperature, without the need for complex iterative calculations.

[0056] This step inputs the estimated open-circuit voltage obtained in step S3 and the current temperature into the first KAN model pre-trained in step S1. It uses the optimized B-spline weights to directly output the preliminary state of charge estimate. The first KAN model, through a continuous three-dimensional correspondence, can quickly and accurately query the corresponding state of charge based on the open-circuit voltage at any temperature, thus balancing estimation accuracy and real-time performance.

[0057] Step S5: LSTM Network Error Correction The preliminary state of charge estimate obtained in S4 is input into the LSTM network, and the state of charge error compensation is output through the LSTM network. The state of charge error compensation is added to the preliminary state of charge estimate to obtain the final state of charge estimate.

[0058] The LSTM network is a bidirectional LSTM network, and the input is a time window with a length of [value missing]. Feature sequences: , Among them, feature vector ,Include Preliminary state of charge estimates, battery temperature, and battery current at time t.

[0059] The bidirectional LSTM network is trained using the feature sequence as input and the difference between the reference state of charge and the preliminary state of charge estimate as the target label. In online application, the final state of charge estimate is: , in, This is the final estimated state of charge. These are preliminary estimates of the state of charge. This is the charge state error compensation amount output by the LSTM network.

[0060] In an LSTM network, the input sequence is processed by two LSTM sub-networks, forward and backward, respectively, to extract the change pattern of the state of charge over time and the correlation features with temperature changes from both past and future directions. Bidirectional LSTM can utilize the bidirectional contextual information of the time series to capture a more complete dynamic relationship than unidirectional LSTM. When the temperature changes, the evolution of the state of charge estimation error can be learned by the LSTM network. For example, a sudden drop in temperature may cause the model to temporarily underestimate the state of charge. The features extracted by the LSTM hidden layer are processed by the fully connected layer to calculate the compensation value of the state of charge error. This compensation value represents the amount of correction to the initial state of charge estimation value.

[0061] This step takes the preliminary state of charge (SOC) estimate, battery temperature, and battery current as a feature sequence and inputs it into a bidirectional LSTM network. The forward LSTM subnetwork captures the trend of SOC change over time, and the backward LSTM subnetwork captures the lag effect of temperature change on SOC. By using bidirectional contextual information to learn the error evolution law, the SOC error compensation is output. This time-series error correction mechanism is equivalent to adding a self-learning feedback loop to SOC estimation, which can adaptively compensate for model errors. As the running data accumulates, the correction capability is continuously optimized, which significantly improves the accuracy and robustness of SOC estimation under complex operating conditions.

[0062] This invention achieves an organic integration of physical interpretability and data-driven capability through multi-dimensional collaboration between the PIKAN model and the LSTM network. It adopts a hierarchical modeling strategy. The first layer integrates physical equations and the KAN network through the PIKAN model, ensuring the physical consistency and extrapolation capability of the model under extreme low-temperature conditions. The second layer uses historical time-series data to correct errors through the LSTM network, compensating for the bias caused by the simplification assumptions of the physical model. The two layers work together to avoid the "black box" characteristics and poor extrapolation of pure data-driven models, and overcome the defects of parameter drift and insufficient adaptability of pure physical models. This forms a multi-dimensional collaborative state of charge estimation framework that combines interpretability, adaptability and high accuracy.

[0063] like Figure 2As shown, the SOC estimation algorithm of this invention can achieve high-precision SOC estimation under three typical operating conditions (WLTC, NEDC, CLTC) and four temperatures. In the figure, the upper part is a scatter plot comparison, and the lower part is a violin plot of error distribution. Among them, (a) is the WLTC operating condition, (b) is the NEDC operating condition, and (c) is the CLTC operating condition. The black solid line is the actual SOC, which serves as a benchmark reference. The orange dotted line represents the output of the basic physical-data hybrid model (i.e., PIKAN + first KAN mapping model) of this application. The blue solid line is the final complete scheme of this application (i.e., PIKAN + LSTM). The red box magnified area is used to more clearly observe the estimation deviation in the low SOC range.

[0064] The experimental results are analyzed as follows: Upper part: Scatter plot comparison, validating the effectiveness of the core architecture. Preliminary solution capability of the physics model (orange dotted line): At a high temperature of 40℃, the orange dotted line closely follows the black solid line, indicating that the PIKAN model constructed in steps S101-S104 of this application has extremely high preliminary estimation accuracy at high temperatures. However, at a low temperature of 0℃ (especially under WLTC and NEDC conditions), the orange dotted line shows obvious deviation (as shown in the red box). This confirms the problem mentioned in the prior art of "battery model parameter drift at low temperatures" causing errors in pure physical / static mapping.

[0065] The decisive role of timing correction (solid blue line): Comparing the orange and blue lines in the same subplot reveals that the blue solid line (PIKAN-LSTM) almost coincides with the black solid line across the entire temperature range (0℃~40℃) and all operating conditions (WLTC / NEDC / CLTC). Especially in the low SOC red box area at 0℃, the blue solid line perfectly eliminates the deviation of the orange dotted line. This proves that the network introduced in step S105 of this application plays a key role. By learning historical time series information, it successfully compensates for the cumulative error caused by low temperature parameter drift.

[0066] Second half: Violin plot of error distribution, quantification of robustness and stability. Error boundaries of the basic model (orange violin plot): Under 0℃ conditions (WLTC-0℃, NEDC-0℃, CLTC-0℃), the orange violin plots become significantly wider and flatter, and even have long tails extending downwards. This indicates that without LSTM correction, the error distribution of the basic PIKAN model at low temperatures is very discrete, with poor robustness, which can easily lead to SOC jumps in the BMS system.

[0067] Error convergence of the complete scheme (blue violin plot): The blue violin plot maintains an extremely narrow and compact shape at all temperature points, with its center tightly aligned with the 0 mark. Especially under the most demanding CLTC-0℃ condition, the blue violin plot remains slender, indicating that the final solution in this application strictly controls the maximum error of SOC estimation to within ±1.5%. This demonstrates the excellent stability brought by the architecture of "physical model providing interpretability + LSTM providing adaptive correction".

[0068] Therefore, the high accuracy and low variance across the entire temperature range (especially 0℃) and under all complex operating conditions (WLTC / NEDC / CLTC) fully demonstrate that this application combines the advantages of physical constraints and data-driven approaches, possessing high accuracy, strong robustness, physical consistency, and good extrapolation.

[0069] Through a systematic design covering a wide temperature range, the method of this invention covers a wide temperature range from 0℃ to 40℃. It establishes a full-temperature-range calibration database through low-rate discharge tests, achieves adaptive identification of circuit parameters at low temperatures through the PIKAN model, realizes full-temperature-range open-circuit voltage-state-of-charge mapping through the first KAN model, and achieves dynamic error correction through the LSTM network. This systematic design enables the battery management system to maintain accurate monitoring of the remaining battery capacity even in extreme low-temperature environments, providing reliable technical support for applications such as the operation of new energy vehicles in cold regions, high-altitude space missions in aerospace, and polar scientific research.

[0070] The above specific embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for estimating the state of charge (SOC) of a low-temperature lithium battery based on PIKAN-LSTM, characterized by: Includes the following steps: S1. Conduct low-rate discharge tests on lithium batteries in different temperature environments. Construct a relationship curve between open-circuit voltage, state of charge, and temperature based on the test data. Use some of the relationship curve data and corresponding temperature data to train the first KAN model. Use the remaining data for verification to obtain the trained first KAN model. S2. Construct a PIKAN model. The PIKAN model includes a circuit equation solving unit and a second KAN network unit. Collect voltage, current, temperature and state of charge data during the operation of the lithium battery. Combine the relationship curve obtained in S1 to train the PIKAN model to identify the equivalent resistance and two polarization voltages corresponding to the second-order RC equivalent circuit model of the lithium battery. S3. Based on the current terminal voltage and current of the lithium battery and the equivalent resistance and polarization voltage identified in S2, perform compensation calculations to obtain the estimated open-circuit voltage of the lithium battery at the current moment. S4. Input the estimated open-circuit voltage and current temperature obtained in S3 into the first KAN model trained in S1 to obtain the preliminary state of charge estimate of the lithium battery. S5. Input the preliminary state of charge estimate obtained in S4 into the LSTM network, output the state of charge error compensation amount through the LSTM network, add the state of charge error compensation amount to the preliminary state of charge estimate, and obtain the final state of charge estimate.

2. The method for estimating the state of charge (SOC) of a low-temperature lithium battery according to claim 1, characterized in that: S1 includes: S11. In a constant temperature environment, conduct a constant current discharge experiment on the lithium battery at a discharge rate not exceeding 0.1C, and record the change data of the battery terminal voltage over time at different temperatures. S12. Record the terminal voltage and discharge time of the lithium battery during the discharge process, and approximate the terminal voltage as the open circuit voltage of the corresponding state of charge at that temperature. S13. Calculate the state of charge at each sampling time based on the ampere-hour integration method. The calculation formula for the ampere-hour integration method is as follows: ， in, Let be the battery state of charge at time t. This represents the initial state of charge of the battery. For the battery's rated capacity, for The charging and discharging current at any given time, Let be the integral variable, taking the value 0-t. It is an integral infinitesimal element; S14. For the open-circuit voltage, state of charge and temperature corresponding data of discrete sampling, a third-order B-spline basis function is used. The weight of the B-spline function is optimized by combining the mean square error loss with the second-order smoothing regularization term to complete the continuous processing of discrete data and obtain a smooth and continuous three-dimensional OCV-SOC-T mapping surface.

3. The method for estimating the state of charge (SOC) of a low-temperature lithium battery according to claim 2, characterized in that: In S2, the state equation of the second-order RC equivalent circuit model is: ， ， in, , These are the first polarization voltage and the second polarization voltage, respectively. , These are the time constants of the two RC circuits, , Polarization resistor, , Polarized capacitor, This is the charging and discharging current. For time differentiation; The output equation of the second-order RC equivalent circuit model is: ， in, Terminal voltage, This is the mapping function between open-circuit voltage and state of charge. This is the equivalent resistance.

4. The method for estimating the state of charge (SOC) of a low-temperature lithium battery according to claim 3, characterized in that: In S2, the second KAN network unit takes temperature as input. It optimizes the B-spline function weights using a third-order B-spline basis function, combining mean squared error loss with a second-order smoothing regularization term to fit the temperature dependence of equivalent resistance and time constant. The PIKAN model training uses a joint loss function: ， in, For the total loss, For data fitting loss, For physical constraint loss, , These are the weighting coefficients.

5. The method for estimating the state of charge (SOC) of a low-temperature lithium battery according to claim 4, characterized in that: In S2, the data fitting loss for: ， in, For the sample size, For the first The measured terminal voltage at each sampling time. Let be the model predicted terminal voltage at the i-th sampling time.

6. The method for estimating the state of charge (SOC) of a low-temperature lithium battery according to claim 5, characterized in that: In S2, the physical constraint loss for: ， in, This is the first derivative of the first polarization voltage with respect to time. This is the first derivative of the second polarization voltage with respect to time. , Let be the time constant of the two RC circuits.

7. The method for estimating the state of charge (SOC) of a low-temperature lithium battery according to claim 6, characterized in that: In S3, the compensation calculation formula is: ， in, To estimate the open-circuit voltage.

8. The method for estimating the state of charge (SOC) of a low-temperature lithium battery according to claim 7, characterized in that: In S4, the first KAN model internally optimizes the B-spline weights to make the discrete open-circuit voltage, state of charge, and temperature data continuous. Its basis function expression is as follows: ， in, It is a mapping function of open-circuit voltage, state of charge, and temperature. The number of B-spline basis functions for the temperature dimension. The number of B-spline basis functions in the charged state dimension. For the first i The basis functions of the charge state dimension and the first j The weighting coefficients corresponding to the basis functions of each temperature dimension. Let be the B-spline basis function for the i-th charged state dimension. Let be the B-spline basis function for the j-th temperature dimension.

9. The method for estimating the state of charge (SOC) of a low-temperature lithium battery according to claim 8, characterized in that: In S5, the LSTM network is a bidirectional LSTM network, and the input is a feature sequence with a time window length of L: ， Among them, feature vector ,Include t Preliminary state of charge estimates, battery temperature, and battery current at time t; The bidirectional LSTM network is trained using the feature sequence as input and the difference between the reference state of charge and the preliminary state of charge estimate as the target label. In online application, the final state of charge estimate is: ， in, This is the final estimated state of charge. For preliminary state of charge estimation, This is for compensating for the state of charge error output by the LSTM network.

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