A method for identifying parameters of a retired battery

Abstract

The application discloses a kind of retired battery parameter identification method, it is related to lithium ion battery management technical field, including: to retired lithium ion battery is carried out pulse charging-discharging test and obtains relaxation voltage sequence, relaxation voltage sequence is smoothed pretreatment, candidate cut-off termination time set is constructed in relaxation time interval, corresponding relaxation data is cut off for each cut-off termination time and parameter fitting is carried out based on second-order equivalent circuit model, the root mean square error under each cut-off termination time is calculated and the parameter group of minimum error is selected as target equivalent circuit parameter.The data fitting interval is selected to be modeled as the minimum root mean square error minimization problem, the automation adaptive identification of retired battery equivalent circuit parameters is realized, the E point selection dilemma under fixed window is solved, the robustness and physical consistency of parameter identification result are improved, the model prediction error is significantly reduced and the generalization ability under multiple working conditions is improved.

Description

Technical Field

[0001] This invention relates to the field of lithium-ion battery management technology, specifically a method for identifying parameters of retired batteries. Background Technology

[0002] With the booming development of the new energy vehicle industry, a large number of power batteries are gradually entering the retirement stage. Utilizing these retired batteries, which still retain a high level of remaining capacity, not only greatly enhances their economic value throughout their entire life cycle but is also a key measure to achieve resource recycling and sustainable development. To ensure the safe and reliable operation of retired batteries in scenarios such as energy storage power stations and low-speed electric vehicles, a high-precision Battery Management System (BMS) is essential. The core of a BMS lies in a mathematical model that can accurately characterize the dynamic and static properties of the battery.

[0003] Among numerous battery models, the second-order RC equivalent circuit model has become the mainstream choice in academic research and industrial applications due to its relatively simple structure, ability to simulate the electrochemical and concentration polarization processes inside the battery well, and moderate computational complexity. This model typically consists of a series connection of an ohmic internal resistance (R0), an RC network representing electrochemical polarization (R1, C1), and an RC network representing concentration polarization (R2, C2). The model's prediction accuracy depends entirely on the accuracy of identifying these key parameters.

[0004] Currently, the mainstream method for obtaining these model parameters is identification based on experimental data. Among them, the hybrid pulse power characteristic (HPPC) test is one of the most commonly used experimental methods. This test applies a series of charge and discharge current pulses to the battery at different states of charge (SOC) and records its voltage response. The focus of parameter identification is usually on the voltage relaxation (resting) phase after the current pulse ends, because the voltage recovery curve in this phase contains rich information about the internal polarization process.

[0005] In existing technologies, such as the "Joint Estimation Method of SOC and SOH for Retired Batteries" disclosed in Chinese Patent CN112649736A, data is typically obtained through HPPC testing. Then, intelligent optimization algorithms such as least squares method, particle swarm optimization, and genetic algorithm are used to fit the relaxation stage data to identify model parameters. A common practice in these methods is to extract a fixed-time window of relaxation stage data (e.g., allowing it to rest for 30 minutes or 1 hour) as input to the algorithm.

[0006] However, this "one-size-fits-all" fixed window method has serious technical flaws, especially when applied to retired batteries with large performance dispersion and complex aging mechanisms. These flaws are mainly manifested in the "E-point selection dilemma" when analyzing HPPC experimental data, namely the difficulty in selecting the data cutoff endpoint, which is analyzed in detail below:

[0007] This ignores the individual differences among batteries: retired batteries have undergone different service histories, resulting in significant variations in their aging levels, internal resistance increases, and capacity decay characteristics. This means that their internal electrochemical relaxation rates also differ. A fixed data window cannot accommodate the unique characteristics of all batteries; it may be too long for batteries with fast relaxation and too short for batteries with slow relaxation.

[0008] An excessively short data window leads to underfitting: If the selected relaxation time window is too short, the slower relaxation process inside the battery (mainly dominated by concentration polarization, corresponding to the large time constant τ2=R2*C2 in the second-order RC model) is not fully represented. The fitting algorithm, lacking key information describing this slow dynamic process, cannot accurately identify parameters such as R2 and C2, resulting in the model's inability to accurately predict the battery's long-term voltage response, causing underfitting and severely insufficient model accuracy.

[0009] Excessively long data windows can lead to overfitting and noise interference: If the selected relaxation time window is too long, the battery voltage change becomes extremely weak and tends to stabilize at the end of the relaxation process. At this point, the voltage change "signal" is very weak, while the inherent measurement "noise" amplitude of the test equipment sensor remains essentially unchanged, resulting in an extremely low signal-to-noise ratio for this data segment. Introducing this noisy data into the fitting algorithm makes the algorithm abnormally sensitive to noise, and the identification results may fluctuate drastically or even produce parameter values ​​that do not conform to physical laws, causing "overfitting" to the noise and severely affecting the robustness and reliability of the parameter identification results.

[0010] In summary, existing technologies essentially involve a blind or experience-based subjective trade-off between "insufficient information" and "excessive noise." This approach lacks objective, quantifiable evidence, leading to a high dependence on operator experience and compromising repeatability and reliability. More importantly, the industry suffers from a technological bias that "more data is better," or reliance on a fixed "golden time" (e.g., one hour). This bias results in research focusing on optimizing the "fitting algorithm" itself (e.g., improving particle swarm optimization and genetic algorithms), while systematically neglecting the more fundamental issue of "input data quality." Therefore, the "E-point selection dilemma," a bottleneck in front-end data processing, has long remained unresolved effectively and systematically. Establishing an adaptive data range determination mechanism that can overcome subjective experience dependence and automatically reveal the personalized relaxation characteristics of batteries is a critical technical challenge that urgently needs to be addressed to improve the accuracy of retired battery models and BMS management. Summary of the Invention

[0011] Based on the shortcomings of the prior art described above, the purpose of this invention is to provide a method for identifying parameters of retired batteries to solve the aforementioned technical problems.

[0012] To achieve the above objectives, the present invention provides the following technical solution: a method for identifying parameters of retired batteries, comprising:

[0013] For the identified retired lithium-ion batteries, pulse charge-discharge tests are performed. Under the set pulse current conditions, the terminal voltage change data over time after the current switches from the pulse phase to the rest phase is collected to generate a relaxation voltage sequence.

[0014] The relaxation voltage sequence is smoothed and preprocessed to obtain the preprocessed relaxation voltage sequence.

[0015] Within the time interval from the current interruption time to the preset relaxation end time, multiple cutoff termination time points are constructed according to the preset time step. Each cutoff termination time point is calculated from the current interruption time to generate a candidate cutoff termination time set.

[0016] For each cutoff termination time in the candidate cutoff termination time set, the preprocessed relaxation voltage data between the current interruption time and the current cutoff termination time is used as the fitting object. The relaxation process of the retired lithium-ion battery is modeled by a preset second-order equivalent circuit model, and the set of parameters to be identified corresponding to the current cutoff termination time is solved. The root mean square error is calculated based on the difference between the preprocessed relaxation voltage data and the model simulation voltage. The root mean square error is set as the error index corresponding to the current cutoff termination time.

[0017] After traversing the candidate truncation termination time set, the error indices corresponding to all truncation termination times are compared, the target truncation termination time with the smallest error index is determined, and the set of parameters to be identified corresponding to the target truncation termination time is determined as the target equivalent circuit parameter set.

[0018] The present invention is further configured such that performing a pulse charge-discharge test on the retired lithium-ion battery to be identified includes: applying a mixed pulse sequence containing charging pulses and discharging pulses to retired lithium-ion batteries in different states of charge under constant ambient temperature conditions; collecting data on the change of terminal voltage over time after the current switches from the pulse phase to the resting phase in each state of charge; and generating a corresponding relaxation voltage sequence.

[0019] The present invention is further configured to perform smoothing preprocessing on the relaxation voltage sequence, including: using a polynomial fitting smoothing method based on a sliding window, approximating the relaxation voltage change curve with a low-order polynomial in each sliding window, and removing or interpolating abnormal sampling points that deviate from the fitting curve by more than a preset threshold, so as to obtain a preprocessed relaxation voltage sequence with noise suppression and continuous curve shape.

[0020] The present invention is further configured such that, when generating a set of candidate cutoff termination times, a first preset time after the current interruption moment is used as the starting cutoff termination time point, and a second preset time before the preset relaxation end moment is used as the ending cutoff termination time point. Multiple cutoff termination time points are generated sequentially between the starting cutoff termination time point and the ending cutoff termination time point in a manner that is not less than the first time step and not greater than the second time step. The first preset time is used to avoid the voltage jump section at the moment of current switching, and the second preset time is used to avoid the noise-dominated section at the end of relaxation.

[0021] The present invention is further configured such that the preset second-order equivalent circuit model includes an ohmic internal resistance connected in series with the terminal voltage of the retired lithium-ion battery and two sets of different parallel resistor-capacitor branches. The first parallel resistor-capacitor branch is used to characterize the rapid polarization process, and the second parallel resistor-capacitor branch is used to characterize the slow polarization or concentration transport process.

[0022] The present invention is further configured such that the parameter group to be identified includes at least the ohmic internal resistance, the resistance and capacitance in the first parallel resistor-capacitor branch, and the resistance and capacitance in the second parallel resistor-capacitor branch.

[0023] The present invention is further configured such that, when solving for the set of parameters to be identified corresponding to the current cutoff termination time, the preprocessed relaxation voltage data corresponding to the current cutoff termination time is used as a constraint, and a nonlinear least squares iterative solution strategy is adopted based on the initial parameter estimation to jointly update the parameters of the ohmic internal resistance and each parallel resistor and capacitor. During the iteration process, parameter value range constraints and convergence judgment conditions are applied to ensure that the obtained set of parameters to be identified is numerically stable and meets the electrochemical rationality.

[0024] The present invention is further configured to calculate the root mean square error, including: for all sampling times corresponding to the current cutoff termination time, squaring the difference between the preprocessed relaxation voltage and the model simulation voltage at each sampling time and averaging it within the sampling time range, then taking the square root of the average value, and setting the result as the root mean square error.

[0025] The present invention is further configured to include: after determining the target equivalent circuit parameter set, using the target equivalent circuit parameter set for constant current discharge condition simulation and open circuit voltage relaxation condition simulation respectively; based on the voltage error between the simulated voltage and the measured voltage under the corresponding condition, verifying the fitting accuracy and cross-condition applicability of the target equivalent circuit parameter set under different conditions; when the voltage error under each condition meets the preset accuracy requirements, using the target equivalent circuit parameter set for state estimation and tiered utilization classification of retired lithium-ion batteries.

[0026] This invention provides a method for identifying parameters of retired batteries. The method involves performing a pulse charge-discharge test on the retired lithium-ion battery to be identified. Under a set pulse current condition, the method collects data on the change in terminal voltage over time after the current switches from the pulse phase to the resting phase, generating a relaxation voltage sequence. The relaxation voltage sequence is then smoothed to obtain a preprocessed relaxation voltage sequence. Within the time interval from the current interruption time to the preset relaxation end time, multiple cutoff termination time points are constructed according to a preset time step, each calculated from the current interruption time, generating a candidate cutoff termination time set. For each cutoff termination time in the candidate cutoff termination time set, the method considers the current interruption time and the current cutoff time. Using preprocessed relaxation voltage data between termination times as the fitting object, the relaxation process of retired lithium-ion batteries is modeled using a pre-defined second-order equivalent circuit model, and the parameter set to be identified corresponding to the current cutoff termination time is solved. The root mean square error (RMSE) is calculated based on the difference between the preprocessed relaxation voltage data and the simulated voltage, and this RMS error is set as the error index corresponding to the current cutoff termination time. After traversing the candidate cutoff termination time set, the error indices corresponding to all cutoff termination times are compared, and the target cutoff termination time with the smallest error index is determined. The parameter set to be identified corresponding to the target cutoff termination time is then determined as the target equivalent circuit parameter set. The beneficial effects include:

[0027] 1. This invention automates and objectifies the parameter identification process, resolving the "E-point selection dilemma": By establishing an iterative optimization mechanism centered on minimizing the root mean square error (RMSE), the selection of the data fitting interval is transformed from a subjective judgment relying on human experience into an automated process with a clear mathematical optimization objective. The system can objectively find the trough of the RMSE "U-shaped curve" (approximately 3720 seconds in this embodiment) representing the optimal balance between information content and noise interference, based on the battery's voltage response characteristics, thus completely solving the E-point selection dilemma commonly found in existing technologies.

[0028] 2. Enhanced robustness and physical consistency of parameter identification results: One of the technical effects of this invention is the improved robustness and physical consistency of the identification results. Once the candidate cutoff endpoint enters the optimal equilibrium region of the "U-shaped valley" sought by the method of this invention, the two time constants τ1 and τ2 converge rapidly and remain highly stable. This phenomenon strongly proves that the DRIS strategy of this invention can automatically guide the identification algorithm to converge to a stable and physically meaningful solution space. This is also evidenced by the parameter results in Table 1, where the identified fast and slow process time constants (τ1 and τ2) show a clear order-of-magnitude separation, which is highly consistent with the battery electrochemical theory, proving the correctness of the physical meaning of the parameters.

[0029] 3. Improved Model Prediction Accuracy and Reliability: This invention achieves significant technical advantages over existing technologies, a fact clearly verified through direct comparative experiments. The model constructed using the traditional fixed-window method exhibits a root mean square error (RMSE) as high as 22.21 mV under HPPC conditions. In stark contrast, the model constructed using the DRIS strategy of this invention achieves an RMS error of only 3.39 mV under the same conditions, representing an accuracy improvement of approximately 85% compared to the traditional method. This reduction in error from tens of millivolts to a few millivolts demonstrates that this invention achieves a qualitative leap in model prediction accuracy and reliability.

[0030] 4. Superior Model Generalization Ability and Multi-Condition Adaptability: Another unexpected and significant advantage of this invention lies in the superior generalization ability of the constructed model. Applying the model built based on parameters identified by HPPC operating conditions to two verification conditions—continuous constant current (CC) discharge and open-circuit voltage (OCV) relaxation—the model still exhibits extremely high voltage prediction accuracy (RMSE as low as 22.21mV and 4.15mV, respectively). This demonstrates the high fidelity of the parameters obtained by the method of this invention, enabling the model to avoid "overfitting" to specific test data and accurately predict battery behavior under various real-world operating scenarios, demonstrating significant industrial practical value.

[0031] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0033] Figure 1 A flowchart illustrating a method for identifying parameters of a decommissioned battery, as shown in an exemplary embodiment of the present invention;

[0034] Figure 2 This is a schematic diagram of the equivalent circuit model of a second-order RC circuit.

[0035] Figure 3 This is a trend chart of the root mean square error (RMSE) as the data truncation endpoint changes;

[0036] Figure 4 The model fitting effect is shown at the optimal truncation endpoint.

[0037] Figure 5 The residual distribution of the fit at the optimal cutoff endpoint;

[0038] Figure 6 This is a convergence analysis plot showing the change of the model time constant as a function of the data truncation endpoint.

[0039] Figure 7 The HPPC condition prediction effect of the model constructed by the method of this invention is shown in the figure.

[0040] Figure 8 HPPC prediction results of the model built using the traditional fixed window method;

[0041] Figure 9 The diagram shows the prediction effect and error analysis of the model of this invention under constant current (CC) discharge conditions;

[0042] Figure 10 The diagram shows the prediction performance and error analysis of the model of this invention under the open-circuit voltage (OCV) relaxation condition.

[0043] Figure 11 This is a schematic diagram of the experimental platform used to implement the present invention;

[0044] Figure 12This is a Simulink simulation system architecture diagram used to verify the model of this invention. Detailed Implementation

[0045] The embodiments of the present invention will be described below with reference to the accompanying drawings and preferred embodiments. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred embodiments are only for illustrating the present invention and not for limiting the scope of protection of the present invention.

[0046] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0047] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0048] A method for identifying parameters of retired batteries, such as Figure 1 As shown, it includes:

[0049] For the identified retired lithium-ion batteries, pulse charge-discharge tests are performed. Under the set pulse current conditions, the terminal voltage change data over time after the current switches from the pulse phase to the rest phase is collected to generate a relaxation voltage sequence.

[0050] The relaxation voltage sequence is smoothed and preprocessed to obtain the preprocessed relaxation voltage sequence.

[0051] Within the time interval from the current interruption time to the preset relaxation end time, multiple cutoff termination time points are constructed according to the preset time step. Each cutoff termination time point is calculated from the current interruption time to generate a candidate cutoff termination time set.

[0052] For each cutoff termination time in the candidate cutoff termination time set, the preprocessed relaxation voltage data between the current interruption time and the current cutoff termination time is used as the fitting object. The relaxation process of the retired lithium-ion battery is modeled by a preset second-order equivalent circuit model, and the set of parameters to be identified corresponding to the current cutoff termination time is solved. The root mean square error is calculated based on the difference between the preprocessed relaxation voltage data and the model simulation voltage. The root mean square error is set as the error index corresponding to the current cutoff termination time.

[0053] After traversing the candidate truncation termination time set, the error indices corresponding to all truncation termination times are compared, the target truncation termination time with the smallest error index is determined, and the set of parameters to be identified corresponding to the target truncation termination time is determined as the target equivalent circuit parameter set.

[0054] Specifically, voltage relaxation data acquisition and preprocessing: Following standard experimental testing procedures, the response data of the terminal voltage of the decommissioned battery under test as a function of time after a single current pulse (charging or discharging) ends and it enters an open-circuit resting state is acquired, forming a voltage relaxation curve. The experimental testing procedure can be a hybrid pulse power characteristic (HPPC) test. To suppress the interference of measurement noise on the subsequent identification process, the acquired raw voltage data can be selectively filtered and preprocessed, for example, using a Savitzky-Golay filter for smoothing.

[0055] Construction of the candidate fitting endpoint set: Within the acquired complete voltage relaxation time interval, a candidate truncation endpoint set containing multiple discrete time nodes is defined. The construction of this set should cover the period from the early stage of the relaxation process to the late stage where it tends to stabilize. For example, starting from a certain moment after the relaxation begins, a series of time points can be generated at fixed time steps (such as tens or hundreds of seconds) until the relaxation ends, thus forming a systematic library of candidate endpoints for the fitting window to be evaluated.

[0056] Iterative optimization based on the root mean square error minimization criterion: This step is the core of this invention. By traversing the set of candidate endpoints, the merits of each candidate endpoint as a data fitting interval are evaluated. The specific operation is as follows:

[0057] (a) Iterative initialization: Set a variable RMSE_min to record the minimum root mean square error (RMSE) (initial value is set to the maximum value), and set a variable Optimal_Params to store the optimal model parameters (initial value is empty).

[0058] (b) Traverse candidate endpoints: For each candidate endpoint E_i in the candidate endpoint set, perform the following sub-steps:

[0059] (b1) Dynamic data truncation: Starting from the starting point of the relaxation process and ending at the current candidate end point E_i, a data subset Data_Subset_i is intercepted from the voltage relaxation data obtained in step one.

[0060] (b2) Model parameter fitting: Based on a preset battery equivalent circuit model (for example, a second-order RC equivalent circuit model), a parameter fitting algorithm is used to fit the data subset Data_Subset_i. The parameter fitting algorithm can be a non-linear least squares method, such as the Levenberg-Marquardt algorithm or the trust region reflection algorithm. Through fitting, a set of temporary model parameters Temp_Params_i corresponding to the current candidate end point E_i is obtained.

[0061] (b3) Fitting error evaluation: Using the obtained temporary model parameters Temp_Params_i, the predicted voltage value of the model on this data subset Data_Subset_i is calculated, and it is compared with the true measured voltage value, and the root mean square error RMSE_i between the two is calculated.

[0062] (b4) Optimal solution update: Compare the currently calculated RMSE_i with the recorded minimum root mean square error RMSE_min. If RMSE_i < RMSE_min, then update RMSE_min = RMSE_i, and store the current temporary model parameters Temp_Params_i in the optimal model parameter variable Optimal_Params.

[0063] (c) Iteration end: After traversing all candidate end points, the iterative optimization process ends.

[0064] Determination and output of the best fitting end point: After the iterative optimization process ends, the model parameters finally stored in the variable Optimal_Params are the set of parameters with the best fitting effect among all candidate data intervals. The corresponding candidate end point is determined as the best fitting end point. These parameters are output as the final identification result of the equivalent circuit model of the retired battery.

[0065] A method for identifying parameters of a retired battery provided in this embodiment is illustrated by taking the parameter identification of an 18650-type lithium-ion battery with a rated capacity of 3000 mAh retired from a new energy vehicle as an example. The rated capacity of this battery has decayed to about 2503.55 mAh.

[0066] Refer to Figure 2This embodiment uses a second-order RC equivalent circuit model to describe the dynamic characteristics of the battery. The model includes: an ideal voltage source Uoc, representing the battery's open-circuit voltage (OCV); an ohmic internal resistance R0, used to simulate the instantaneous voltage drop caused by electronic and ionic conductivity within the battery; and two parallel RC networks (R1-C1 network and R2-C2 network) connected in series. The R1-C1 network simulates rapidly changing electrochemical polarization processes, while the R2-C2 network simulates slowly changing concentration polarization processes. The terminal voltage representing the model, The current flowing through the model is denoted as .

[0067] According to Kirchhoff's Voltage Law (KVL), the electrical behavior of this model can be described by the following set of equations:

[0068]

[0069]

[0070]

[0071] in, Battery current, Terminal voltage, Open circuit voltage, and These are the voltages on the two RC networks, respectively. This set of equations forms the mathematical basis for subsequent parameter identification.

[0072] All experimental data in this embodiment were obtained by referring to... Figure 11 The professional experimental platform shown was obtained. This platform includes a LANHE CT6002A high-precision battery testing system for applying current and acquiring voltage and current data; and a GDBellBTH-1000CT high and low temperature humidity alternating test chamber for providing a precise constant temperature environment of 25℃±1℃. This experimental platform ensures the accuracy and reliability of the raw data required for the method of this invention.

[0073] First, the retired lithium-ion battery was calibrated for capacity and SOC-OCV relationship. Then, in a constant temperature environment of 25℃±1℃, the battery underwent hybrid pulse power characteristic (HPPC) testing. This embodiment focuses on the voltage recovery process, i.e., the voltage relaxation phase, after the battery experiences a single 1C discharge pulse at a specific SOC point (e.g., SOC=80%) and enters an open-circuit resting state. Using a high-precision battery testing system (e.g., LANHE CT6002A), the terminal voltage data during this relaxation phase was continuously recorded for up to 2 hours (7200 seconds) at a sampling frequency of 50Hz, forming the original voltage-time series.

[0074] To eliminate the impact of high-frequency measurement noise on the subsequent fitting accuracy, a Savitzky-Golay (SG) filter is used to smooth the raw voltage data during preprocessing. The SG filter is a filtering method based on local polynomial least squares fitting, which can effectively smooth noise while preserving the macroscopic morphological characteristics of the voltage recovery curve to the greatest extent and avoiding signal distortion.

[0075] Within the preprocessed 7200-second relaxation data interval, a set of candidate endpoints (E-points) for iterative optimization is constructed. In this embodiment, to systematically evaluate the impact of different data window lengths, starting from the 3000th second after the start of relaxation, a series of candidate endpoints are generated with a time step of 100 seconds until the 7000th second. This set is represented as E={3000s,3100s,3200s,...,7000s}.

[0076] This step is the core of the method of the present invention: by iteratively traversing the set of candidate endpoints, the best data fitting interval is found.

[0077] For each candidate endpoint E_i in set E, perform the following operations:

[0078] (a) Dynamic data truncation: From the start of relaxation (t=0) to the current candidate endpoint E_i, the preprocessed voltage-time data is truncated to form a data subset.

[0079] (b) Model parameter fitting: The behavior of the battery during the relaxation phase can be obtained from the zero-input response of the second-order RC model.

[0080] Equation description: (1)

[0081] in, It is the terminal voltage at time t. It is the open-circuit voltage after stabilization at that SOC point (which can be considered known). (0) and (0) represents the initial voltage of the two RC networks at the start of relaxation (t=0). (=R1C1) and (=R2C2) are the time constants of the two RC networks. The parameter to be identified is P={ (0), , (0), }

[0082] This embodiment uses the built-in lsqcurvefit function in MATLAB. This function is based on the Trust-Region-Reflective algorithm and performs nonlinear least squares fitting on the truncated subset of data to solve for the parameter set P_i that minimizes the sum of squared residuals between the model's predicted values ​​and the actual measured values.

[0083] (2)

[0084] in, At discrete time points The actual measured voltage, The predicted voltage is calculated from Equation 1. By solving Equation 2, the temporary model parameter vector P_i corresponding to the current candidate cutoff endpoint E_i is obtained.

[0085] (c) Fitting Error Assessment: Substitute the fitted parameter set P_i into the model equation, calculate the predicted voltage sequence on the current data subset, and compare it with the actual measured data. Calculate the root mean square error (RMSE) between the two, denoted as RMSE_i. The formula for calculating RMSE is:

[0086] (3)

[0087] Where N is the number of data points in the data subset.

[0088] After traversing all candidate endpoint sets, a series of RMSE_i values ​​corresponding to each candidate endpoint E_i will be obtained. (See reference...) Figure 3 Plotting these RMSE_i values ​​against their corresponding endpoint E_i reveals a typical U-shaped trend. This curve profoundly reveals the inherent physical laws governing data window selection, which can be analyzed in detail below:

[0089] The descent phase (underfitting zone): In the early stages of relaxation (approximately before 3500 seconds in this embodiment), the RMSE value decreases significantly as the data window lengthens. This data indicates that the amount of data at this stage is insufficient to fully constrain and identify the slow dynamic relaxation process inside the battery (mainly dominated by concentration polarization), causing the model parameters to fail to converge to the true value. The model exhibits an "underfitting" state, resulting in a large prediction error.

[0090] Rising Phase (Noise-Dominated Zone): In the later relaxation phase (approximately after 4500 seconds in this embodiment), as the data window further extends, the RMSE value slowly recovers. This data indicates that the battery terminal voltage has stabilized at this stage, and the amplitude of the actual signal variation is close to or lower than the noise level of the test equipment, resulting in an extremely low signal-to-noise ratio. Introducing this noisy data into the fitting algorithm will cause the algorithm to "overfit" to random noise, leading to a decrease in model prediction accuracy and a deterioration in the reliability of parameter identification results.

[0091] Valley Region (Optimal Balance Zone): Between the two zones mentioned above, there exists a valley region with the lowest RMSE value. This region represents the "optimal balance point" between the amount of information required by the model and noise interference. The core task of this invention is to automatically locate the global optimum within this interval. Figure 4 and Figure 5 As shown, when the model is fitted using point E (3720 seconds in this embodiment) corresponding to the valley bottom, the predicted voltage and the actual voltage highly coincide, and the residuals are randomly distributed near the zero point, proving that the model obtained at this point has the highest accuracy.

[0092] This step compares all RMSE_i values ​​to find the candidate endpoint corresponding to the global minimum RMSE_min, which is the best-fit endpoint E*. This process can be represented by the following formula:

[0093] (4)

[0094] In this embodiment, it was found through calculation that when At 3720 seconds, RMSE reaches its minimum value.

[0095] Will be at the best fit endpoint The corresponding set of model parameters (3720 seconds) is output as the optimal identification result of the battery at that SOC point. By further combining the data from the discharge pulse stage, the complete second-order RC model parameters can be decoupled and obtained, including R0, R1, C1, R2, and C2.

[0096] Verification of technical effectiveness.

[0097] To objectively and quantitatively demonstrate the beneficial effects of this invention, a direct performance comparison is made between the optimal parameter set identified by the DRIS strategy of this invention and the parameter set identified by a traditional fixed-window method (e.g., a fixed 7200-second truncation of relaxation data). Specifically, these two different sets of parameters are respectively placed into a reference... Figure 12 The simulation system model shown is built in MATLAB / Simulink. This simulation model strictly follows... Figure 2 The second-order RC equivalent circuit model shown ensures the fairness and accuracy of the comparison. Subsequently, simulations were performed under the same HPPC input current condition to compare the voltage prediction performance.

[0098] Performance Comparison Analysis under HPPC Operating Conditions (Reference) Figure 7-8 ):

[0099] Performance limitations of traditional methods (see reference) Figure 8 The model constructed using the traditional fixed-window method exhibits drastic fluctuations in prediction error, with significant spikes at the beginning and end of the current pulse, and the maximum absolute error exceeding 50mV. This indicates that, due to the failure to find the optimal data fitting interval, the fidelity of the identified parameters is low, and the model cannot accurately reproduce the voltage response of the battery under dynamic operating conditions, resulting in insufficient model reliability. The overall calculated root mean square error (RMSE) is as high as 22.21mV.

[0100] Significant advantages of the method of the present invention (see reference) Figure 10 The model constructed using the DRIS strategy of this invention exhibits extremely high stability in its prediction error curve. Throughout the complex HPPC test conditions, the error was consistently and strictly controlled within an extremely narrow ±10mV band, without any significant spikes or fluctuations. This strongly demonstrates that the parameters identified by this invention through automatic location of the optimal data balance point have extremely high fidelity, and the constructed model can accurately and reliably reproduce the internal dynamic characteristics of the battery. The overall root mean square error (RMSE) is only 3.39mV.

[0101] pass Figure 7-8 Direct quantitative comparison demonstrates that the method of this invention achieves a nearly one-order-of-magnitude improvement in model prediction accuracy (approximately 85% improvement) compared to traditional techniques, significantly enhancing the reliability and robustness of the model. The technological advancement is remarkable. The comparative analysis is as follows:

[0102] Further verification of generalization ability and physical meaning

[0103] To further and comprehensively verify the beneficial effects of the method of the present invention, model generalization ability testing and parameter physical meaning analysis were also conducted.

[0104] Generalization capability verification:

[0105] To test the model's predictive ability under non-identification conditions, the constructed model was applied to two validation conditions:

[0106] Constant current discharge condition (refer to) Figure 9 This condition simulates the continuous operating state of the battery. For example... Figure 9 As shown in the upper part, the model's predicted voltage curve almost perfectly matches the actual voltage curve. From Figure 9 The error curve in the lower half shows that, except for the initial stage, the prediction error was stably controlled within a small range of -30mV to +10mV for most of the time, with an overall RMSE of 22.21mV. This proves that the model still has high prediction accuracy and applicability under dynamic, non-pulse conditions.

[0107] OCV relaxation condition (refer to) Figure 10 This operating condition is specifically designed to evaluate the model's ability to characterize the quasi-static properties of the battery. For example... Figure 10 As shown in the upper part, the model accurately reproduces the process of the battery voltage slowly recovering to an equilibrium state during multiple resting phases. From Figure 10 As can be seen from the error curve in the lower half, the prediction error is strictly controlled within an extremely narrow range of -10mV to +5mV, with an overall RMSE of only 4.15mV. This proves that the method of this invention can identify key parameters characterizing the slow dynamic processes inside the battery with extremely high accuracy, fundamentally reflecting a profound characterization of the physical nature of the battery.

[0108] Analysis of the physical meaning of the identification parameters:

[0109] The DRIS strategy yields a series of optimal model parameters under different states of charge (SOC), and the identification results are shown in Table 1. Analysis of the data in Table 1 reveals that the time constant τ1 (calculated from R1 and C1), representing the fast electrochemical polarization process, is consistently significantly smaller in magnitude than the time constant τ2 (calculated from R2 and C2), representing the slow concentration polarization process. This clear separation of time scales is highly consistent with the accepted theoretical models of battery electrochemistry.

[0110]

[0111] like Figure 6As shown, once the candidate interception endpoint enters the optimal equilibrium region of the "U-shaped valley" sought by the method of this invention, the two time constants τ1 and τ2 converge rapidly and remain highly stable. This phenomenon strongly demonstrates that the DRIS strategy of this invention can automatically guide the identification algorithm to converge to a stable and physically meaningful solution space. This is also corroborated by the parameter results in Table 1. The identified fast and slow process time constants (τ1 and τ2) show a clear order-of-magnitude separation, which is highly consistent with the battery electrochemical theory, proving the correctness of the physical meaning of the parameters. This result strongly proves that the method of this invention not only seeks the optimal fit mathematically, but also that the identified parameter set has a clear and correct physical meaning. This further corroborates the high reliability and high fidelity of the model obtained by the method of this invention, which is a significant advancement compared to the prior art.

[0112] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for identifying parameters of retired batteries, characterized in that, include: For the identified retired lithium-ion batteries, pulse charge-discharge tests are performed. Under the set pulse current conditions, the terminal voltage change data over time after the current switches from the pulse phase to the rest phase is collected to generate a relaxation voltage sequence. The relaxation voltage sequence is smoothed and preprocessed to obtain the preprocessed relaxation voltage sequence. Within the time interval from the current interruption time to the preset relaxation end time, multiple cutoff termination time points are constructed according to the preset time step. Each cutoff termination time point is calculated from the current interruption time to generate a candidate cutoff termination time set. For each cutoff termination time in the candidate cutoff termination time set, the preprocessed relaxation voltage data between the current interruption time and the current cutoff termination time is used as the fitting object. The relaxation process of the retired lithium-ion battery is modeled by a preset second-order equivalent circuit model, and the set of parameters to be identified corresponding to the current cutoff termination time is solved. The root mean square error is calculated based on the difference between the preprocessed relaxation voltage data and the model simulation voltage. The root mean square error is set as the error index corresponding to the current cutoff termination time. After traversing the candidate truncation termination time set, the error indices corresponding to all truncation termination times are compared, the target truncation termination time with the smallest error index is determined, and the set of parameters to be identified corresponding to the target truncation termination time is determined as the target equivalent circuit parameter set. When generating a set of candidate cutoff termination times, the first preset time after the current interruption is taken as the start cutoff termination time point, and the second preset time before the preset relaxation end time is taken as the end cutoff termination time point. Multiple cutoff termination time points are generated sequentially between the start cutoff termination time point and the end cutoff termination time point in a manner that is not less than the first time step and not greater than the second time step. The first preset time is used to avoid the voltage jump section at the moment of current switching, and the second preset time is used to avoid the noise-dominated section at the end of relaxation. When solving for the set of parameters to be identified corresponding to the current cutoff termination time, the preprocessed relaxation voltage data corresponding to the current cutoff termination time is used as a constraint. Based on the initial parameter estimation, a nonlinear least squares iterative solution strategy is adopted to jointly update the parameters of the ohmic internal resistance and each parallel resistor and capacitor. During the iteration process, parameter value range constraints and convergence judgment conditions are applied to ensure that the obtained set of parameters to be identified is numerically stable and meets the electrochemical rationality.

2. The method for identifying parameters of decommissioned batteries according to claim 1, characterized in that, The pulse charge-discharge test performed on the retired lithium-ion batteries to be identified includes: applying a mixed pulse sequence containing charging pulses and discharging pulses to retired lithium-ion batteries in different states of charge under constant ambient temperature conditions; collecting data on the change of terminal voltage over time after the current switches from the pulse phase to the resting phase in each state of charge; and generating a corresponding relaxation voltage sequence.

3. The method for identifying parameters of decommissioned batteries according to claim 1, characterized in that, The relaxation voltage sequence is smoothed by preprocessing, including: using a polynomial fitting smoothing method based on a sliding window, approximating the relaxation voltage change curve with a low-order polynomial in each sliding window, and removing or interpolating abnormal sampling points that deviate from the fitting curve by more than a preset threshold, so as to obtain a preprocessed relaxation voltage sequence with noise suppression and continuous curve shape.

4. The method for identifying parameters of a decommissioned battery according to claim 1, characterized in that, The preset second-order equivalent circuit model includes an ohmic internal resistance connected in series with the terminal voltage of the retired lithium-ion battery and two sets of different parallel resistor-capacitor branches. The first parallel resistor-capacitor branch is used to characterize the rapid polarization process, and the second parallel resistor-capacitor branch is used to characterize the slow polarization or concentration transport process.

5. The method for identifying parameters of a decommissioned battery according to claim 4, characterized in that, The parameter group to be identified includes at least the ohmic internal resistance, the resistance and capacitance in the first parallel resistor-capacitor branch, and the resistance and capacitance in the second parallel resistor-capacitor branch.

6. The method for identifying parameters of a decommissioned battery according to claim 1, characterized in that, The calculation of root mean square error includes: for all sampling times corresponding to the current cutoff termination time, squaring the difference between the preprocessed relaxation voltage and the model simulation voltage at each sampling time and averaging it within the sampling time range, then taking the square root of the average value, and setting the result as the root mean square error.

7. The method for identifying parameters of a decommissioned battery according to claim 1, characterized in that, Also includes: After determining the target equivalent circuit parameter set, the target equivalent circuit parameter set is used for constant current discharge condition simulation and open circuit voltage relaxation condition simulation, respectively. Based on the voltage error between the simulated voltage and the measured voltage under the corresponding condition, the fitting accuracy and cross-condition applicability of the target equivalent circuit parameter set under different conditions are checked. When the voltage error under each condition meets the preset accuracy requirements, the target equivalent circuit parameter set is used for state estimation and tiered utilization classification of retired lithium-ion batteries.

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