Battery SOC prediction method and system based on dynamic electrochemical impedance spectroscopy measurement

Abstract

The invention discloses a battery SOC prediction method and system based on dynamic electrochemical impedance spectroscopy measurement in the technical field of lithium battery state prediction, and the method comprises the steps: superposing DIBS square wave signals as excitation current input on the basis of the main charging and discharging current of a battery, and collecting the voltage and current data of the battery in real time; according to the impedance spectrum, fitting a fractional order equivalent circuit model by adopting a nonlinear least square optimization method to obtain initial parameters of the fractional order equivalent circuit model; the initial parameters and voltage and current data collected in real time are input into a self-adaptive dual augmented extended Kalman filter, the main filter and the secondary filter operate cooperatively, state prediction and parameter prediction are executed alternately, and real-time synchronous prediction of SOC and fractional order equivalent circuit model parameters is achieved. The method is suitable for the SOC estimation requirement of the battery under the dynamic working condition, the working state of the battery does not need to be interrupted, and the method has good linearity, robustness and adaptivity.

Description

Technical Field

[0001] The present invention relates to a battery SOC prediction method and system based on dynamic electrochemical impedance spectroscopy measurement, belonging to the technical field of lithium battery state prediction. Background Art

[0002] With the rapid development of energy storage systems, new energy vehicles and other fields, lithium battery packs, as core components, are becoming more and more widely used.

[0003] As the global energy structure accelerates toward a cleaner, lower-carbon future, lithium-ion batteries, with their high energy density, long cycle life, and rapid response, have become a core energy storage medium for electric vehicles (EVs), smart grid energy storage systems, and consumer electronics. By 2025, global new energy vehicle penetration is projected to exceed 45%, and the scale of renewable energy connected to the grid will nearly triple compared to 2020. As the "power heart" supporting this transformation, lithium-ion batteries are increasingly needed for real-time monitoring and management of their operating status.

[0004] State of Charge (SOC), a core parameter characterizing a battery's remaining available charge, requires accurate prediction, not only for optimizing energy scheduling and improving system energy efficiency but also as a critical line of defense for ensuring safe battery operation. For example, in electric vehicle scenarios, misjudgment of SOC can lead to false range claims, battery overcharge / over-discharge, and even the risk of thermal runaway. In energy storage systems, the dynamic balance of SOC directly impacts the economic efficiency and reliability of grid frequency and peak regulation. However, the strong nonlinear electrochemical properties of lithium-ion batteries, their temperature sensitivity under dynamic operating conditions, and the time-varying parameters caused by electrode material aging throughout their lifecycles pose a challenge to SOC prediction. Therefore, developing high-precision, robust, and computationally cost-effective SOC prediction algorithms is not only a key path to breaking through bottlenecks in battery management technology but also an inevitable choice for driving the energy storage industry's transition from scale to intelligence.

[0005] Existing mainstream methods for lithium-ion battery SOC prediction still face significant limitations. The open-circuit voltage (OCV) method relies on the stable relationship between the battery's voltage and SOC after resting. While it offers high static accuracy, it cannot meet the real-time requirements of dynamic scenarios such as electric vehicle acceleration or energy storage system frequency modulation. The real-time integration method suffers from current sensor noise accumulation and uncorrectable initial errors, resulting in deteriorating long-term accuracy as operating conditions become more complex. While the equivalent circuit model combined with the Kalman filter can dynamically track SOC changes, the model parameters require offline calibration, making it difficult to adapt to parameter drift caused by battery aging and temperature fluctuations in real time. Furthermore, the computational overhead of high-order models is prohibitive, making them difficult to integrate into the limited computing power of an onboard BMS. Data-driven methods (such as LSTM neural networks) circumvent the bottleneck of mechanistic modeling through big data learning, but their generalization ability is limited by the coverage of the training data and lacks physical interpretability. Therefore, developing a highly accurate, versatile, and computationally fast battery SOC prediction method has become a critical task to address battery management challenges and support the stable development of smart grids. Summary of the Invention

[0006] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a battery SOC prediction method and system based on dynamic electrochemical impedance spectroscopy measurement.

[0007] To achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0008] In a first aspect, the present invention provides a battery SOC prediction method based on dynamic electrochemical impedance spectroscopy measurement, comprising:

[0009] On the basis of the main charge and discharge current of the battery, the DIBS square wave signal is superimposed as the excitation current input to collect the voltage and current data of the battery in real time;

[0010] The collected voltage and current data are processed to obtain an impedance spectrum of the battery; a fractional-order equivalent circuit model is fitted using a nonlinear least squares optimization method based on the impedance spectrum to obtain initial parameters of the fractional-order equivalent circuit model;

[0011] Inputting the initial parameters and the real-time collected voltage and current data into an adaptive dual augmented extended Kalman filter, wherein the adaptive dual augmented extended Kalman filter has a dual filter structure, wherein the primary filter is used to predict the SOC, and the secondary filter is used to predict the parameters of the fractional-order equivalent circuit model;

[0012] The main filter and the secondary filter operate in coordination, alternately performing state prediction and parameter prediction, and realizing real-time synchronous prediction of SOC and fractional-order equivalent circuit model parameters through a cross-feedback mechanism.

[0013] Furthermore, the fractional-order equivalent circuit model is used to simulate a battery, and the fractional-order equivalent circuit model includes an ohmic resistance, a polarization resistance, a constant phase element CPE, and a Warburg impedance;

[0014] The initial parameters include the resistance value of the ohmic resistor , resistance value of polarization resistor , capacitance of constant phase element CPE , fractional order The resistive component of Warburg impedance , according to the resistance component Calculate the impedance value of Warburg impedance , as shown below:

[0015] ;

[0016] ;

[0017] Where: represents the angular frequency; represents the sampling interval after the continuous time is discretized; Indicates the sampling interval Number.

[0018] Furthermore, the process of the primary filter and the secondary filter operating in coordination includes:

[0019] The main filter performs state prediction based on the current current, the fractional-order equivalent circuit model parameters and the state estimation of the last filtering iteration;

[0020] The secondary filter performs parameter prediction based on the parameter estimate of the previous filtering iteration;

[0021] After obtaining the actual measurement value, the primary filter and the secondary filter perform state update and parameter update respectively;

[0022] The updated parameters of the secondary filter in the current filtering iteration are used as the input of the state prediction of the next filtering iteration of the main filter. At the same time, the covariance of the main filter state estimate is fed back to the secondary filter to dynamically adjust the parameter process noise covariance, realizing cross feedback and adaptive adjustment.

[0023] Furthermore, the main filter performs state prediction based on the current current, the fractional-order equivalent circuit model parameters and the state estimation of the previous filtering iteration, as shown in the following formula:

[0024] ;

[0025] ;

[0026] Where: k represents the number of the filter time step; represents the state prior prediction value of the kth filtering iteration based on the state prediction value of the k−1th filtering iteration; represents the state transition function; represents the state prediction value of the k-1th filtering iteration; represents the parameter prediction value of the kth filtering iteration; represents the state prediction error covariance matrix of the kth filtering iteration obtained based on the state prediction error covariance matrix of the k−1th filtering iteration; The Jacobian matrix representing the state transfer function; represents the state prediction error covariance matrix of the k-1th filtering iteration; Represents matrix transpose; represents the state process noise covariance matrix of the k-th filtering iteration;

[0027] The secondary filter performs parameter prediction based on the parameter estimate of the previous filtering iteration, as shown in the following equation:

[0028] ;

[0029] ;

[0030] Where: represents the prior prediction value of the parameter of the kth filtering iteration based on the parameter prediction value of the k−1th filtering iteration; represents the parameter prediction value of the k-1th filtering iteration; represents the parameter prediction error covariance matrix of the kth filtering iteration obtained based on the parameter prediction error covariance matrix of the k-1th filtering iteration; represents the parameter prediction error covariance matrix of the k-1th filtering iteration; represents the parameter process noise covariance matrix of the kth filtering iteration.

[0031] Furthermore, after obtaining the actual measurement value, the primary filter and the secondary filter perform state update and parameter update respectively, including:

[0032] Calculate the Kalman gain of the main filter as shown below:

[0033] ;

[0034] Where: represents the Kalman gain of the main filter; Predict the Jacobian matrix for the state; is the prediction noise covariance matrix, which indicates the size of the prediction error;

[0035] Then the state update and covariance update are performed. The state update is shown as follows:

[0036] ;

[0037] ;

[0038] Where: Indicates that after obtaining the actual measurement value of the kth filtering iteration, the fusion state prior prediction value The state posterior prediction value of the kth filtering iteration obtained by correcting the main filter with the actual measurement value; represents the voltage value actually measured at the kth filtering iteration; Represents the operating current at the kth filtering iteration; represents the voltage value predicted by the kth filtering iteration; represents the prediction function; represents the prediction noise of the kth filtering iteration;

[0039] The covariance update is shown below:

[0040] ;

[0041] Where: represents the updated state prediction error covariance matrix of the kth filtering iteration;

[0042] Calculate the Kalman gain of the secondary filter as shown below:

[0043] ;

[0044] Where: represents the Kalman gain of the secondary filter; Jacobian matrix for parameter prediction;

[0045] Then the parameters are updated and the covariance is updated. The parameter update is shown as follows:

[0046] ;

[0047] Where: Indicates the prior prediction value of the fusion parameter after obtaining the actual measurement value of the kth filtering iteration Compared with the actual measured value, the posterior predicted value of the parameter of the kth filtering iteration is obtained by the filter correction;

[0048] The covariance update is shown below:

[0049] ;

[0050] Where: represents the updated parameter prediction error covariance matrix of the kth filtering iteration.

[0051] Furthermore, the updated parameters of the secondary filter in the current filtering iteration are used as the input of the state prediction of the next filtering iteration of the primary filter. At the same time, the covariance of the primary filter state estimate is fed back to the secondary filter to dynamically adjust the parameter process noise covariance, realizing cross-feedback and adaptive adjustment, including:

[0052] The posterior prediction value of the parameter of the kth filtering iteration obtained by modifying the filter , as the input of the main filter, used to predict the state value of the k+1th filtering iteration;

[0053] The state prediction error covariance matrix of the kth filtering iteration after the main filter is updated is , dynamically adjust the parameter process noise covariance matrix of the secondary filter when performing parameter prediction , as shown below:

[0054] ;

[0055] Where: represents the prediction noise covariance matrix of the k-1th filtering iteration; Represents the smoothing factor, which is used to suppress noise mutations; Represents the new information sequence of the kth filtering iteration, which is used to represent the error between the predicted value output by the main filter and the actual measured value;

[0056] ;

[0057] Where: represents the parameter process noise covariance matrix of the k-1th filtering iteration; Represents the forgetting factor.

[0058] Furthermore, the method further comprises:

[0059] If the prediction error of the fractional-order equivalent circuit model parameters exceeds a preset threshold in several consecutive filtering iterations, or the time since the last electrochemical impedance spectroscopy measurement exceeds a preset time, a new round of electrochemical impedance spectroscopy measurement is triggered and the fractional-order equivalent circuit model parameters are updated to cover the accumulated filter error.

[0060] Furthermore, the prediction error is determined by the statistical test method of the innovation sequence.

[0061] ;

[0062] Where: represents the new information sequence of the kth filtering iteration; represents the voltage value actually measured at the kth filtering iteration; represents the prediction function;

[0063] Construct the innovation covariance matrix , as shown below:

[0064] ;

[0065] Where: Jacobian matrix for parameter prediction; Represents matrix transpose; represents the parameter prediction error covariance matrix of the kth filtering iteration obtained based on the parameter prediction error covariance matrix of the k-1th filtering iteration; is the prediction noise covariance matrix, which indicates the size of the prediction error;

[0066] Then construct the chi-square test statistic in the form of Mahalanobis distance :

[0067] ;

[0068] Where: represents the number of filter iterations; k represents the number of filter time steps; represents the chi-square distribution threshold; represents the significance level;

[0069] If continuous Chi-square test statistic in filtering iterations Greater than the preset threshold , a new round of electrochemical impedance spectroscopy measurement is triggered to fit the parameters of the fractional-order equivalent circuit model.

[0070] In a second aspect, the present invention provides a system for an online SOC estimation method based on dynamic electrochemical impedance spectroscopy measurement, comprising:

[0071] The electrochemical impedance spectroscopy measurement test module is used to superimpose the DIBS square wave signal as the excitation current input on the basis of the main charge and discharge current of the battery, and collect the battery voltage and current data in real time; the collected voltage and current data are processed to obtain the battery impedance spectrum;

[0072] An equivalent circuit model fitting module is used to fit the fractional-order equivalent circuit model according to the impedance spectrum using a nonlinear least squares optimization method to obtain initial parameters of the fractional-order equivalent circuit model;

[0073] An adaptive dual augmented extended Kalman filter algorithm calculation module is used to input the initial parameters and the real-time collected voltage and current data into the adaptive dual augmented extended Kalman filter. The adaptive dual augmented extended Kalman filter has a dual-filter structure, in which the main filter is used to estimate the SOC and the secondary filter is used to estimate the parameters of the fractional-order equivalent circuit model; the main filter and the secondary filter operate in coordination, alternately performing state prediction and parameter prediction, and realize real-time synchronous prediction of the SOC and the fractional-order equivalent circuit model parameters through a cross-feedback mechanism.

[0074] Compared with the prior art, the present invention has the following beneficial effects:

[0075] The battery SOC estimation method provided by the present invention is based on online electrochemical impedance spectroscopy measurement and adaptive dual augmented extended Kalman filter. It can obtain the dynamic impedance information of the battery in real time during operation and accurately model its internal characteristics using a fractional-order equivalent circuit model. The model parameters are fitted by a nonlinear least squares optimization method to provide high-precision initial values for the filter, effectively improving the stability and convergence speed of subsequent SOC estimation. A dual-filter structure is introduced to achieve synchronous prediction and update of battery status and model parameters, in which the main filter is used to track the state of charge, and the secondary filter is used to dynamically identify battery model parameters. The two are mutually optimized through a cross-feedback mechanism, which significantly enhances the system's adaptability to battery status changes and model drift.

[0076] The method of the present invention has good linearity, robustness and adaptability, and is particularly suitable for battery SOC estimation needs under dynamic working conditions. It can maintain high estimation accuracy under complex working conditions without interrupting the battery working state, providing reliable power prediction support for battery management systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 This is a flow chart of a battery SOC prediction method based on dynamic electrochemical impedance spectroscopy measurement provided in Example 1 of the present invention;

[0078] Figure 2 is a circuit diagram of the fractional-order equivalent circuit model provided in the first embodiment of the present invention;

[0079] Figure 3 This is a current diagram after the DIBS square wave is superimposed in the time domain, as provided in the first embodiment of the present invention. DETAILED DESCRIPTION

[0080] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present application and the specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations on the technical solution of the present application. Unless there is a conflict, the embodiments of the present application and the technical features in the embodiments can be combined with each other.

[0081] Example 1:

[0082] Figure 1 This is a flow chart of a battery SOC prediction method based on dynamic electrochemical impedance spectroscopy in the first embodiment of the present invention. This flow chart only shows the logical sequence of the method described in this embodiment. In other possible embodiments of the present invention, different methods can be used without conflict. Figure 1 The steps shown or described are performed in the order shown. Figure 1 , the method of this implementation specifically includes the following steps:

[0083] On the basis of the main charge and discharge current of the battery, the DIBS square wave signal is superimposed as the excitation current input to collect the voltage and current data of the battery in real time;

[0084] The collected voltage and current data are processed to obtain an impedance spectrum of the battery; a fractional-order equivalent circuit model is fitted using a nonlinear least squares optimization method based on the impedance spectrum to obtain initial parameters of the fractional-order equivalent circuit model;

[0085] Inputting the initial parameters and the real-time collected voltage and current data into an adaptive dual augmented extended Kalman filter, wherein the adaptive dual augmented extended Kalman filter is a dual-filter structure, wherein the primary filter is used to predict the SOC, and the secondary filter is used to predict the parameters of the fractional-order equivalent circuit model;

[0086] The main filter and the secondary filter operate in coordination, alternately performing state prediction and parameter prediction, and realizing real-time synchronous prediction of SOC and fractional-order equivalent circuit model parameters through a cross-feedback mechanism.

[0087] In actual application scenarios, in order to achieve accurate prediction of battery SOC, the battery SOC prediction method and system based on dynamic electrochemical impedance spectroscopy measurement of the present invention are implemented as follows. Lithium-ion batteries are taken as the research object, and during their charging and discharging process, work is carried out with the help of an electrochemical impedance spectroscopy measurement test module. Unlike traditional electrochemical impedance spectroscopy measurement methods, this implementation performs electrochemical impedance spectroscopy measurement and testing online, and can complete the impedance spectrum measurement during the charging and discharging process of lithium batteries. There is no need to let the battery stand for several hours before measurement as in traditional methods. At the beginning of the measurement, the main charge and discharge current is started first, such as using the CC-CV charging mode or the constant current discharge mode. Then, a set of discrete interval binary sequence DIBS square wave signals containing multiple frequency components is superimposed on the battery output current as the excitation current input. The DIBS sequence set in this embodiment is as follows Figure 3 As shown in the figure, the DIBS square wave signal can provide the battery system with an excitation of a specific frequency and amplitude. Based on the electrochemical characteristics of the battery, it will respond to the excitation. By analyzing this response, the impedance information of the battery at different frequencies can be obtained.

[0088] At the same time, the total current is monitored in real time using the current probe , synchronously collect battery terminal voltage , the sampling frequency must be at least twice the highest frequency of the excitation signal to ensure spectrum integrity.

[0089] The collected signal is then preprocessed, specifically by removing the DC offset from the original voltage and current waveforms and extracting their AC components, as shown in the following equation:

[0090] ;

[0091] Where: Represents the AC voltage component, which is the dynamic part of the original voltage signal after removing the low-frequency or DC components; Indicates the length of the DIBS sequence; express The instantaneous voltage; represents the time-integrated variable;

[0092] ;

[0093] Where: Represents the AC current component, which is the dynamic fluctuation part of the total current after removing the main component; Represents the main current component, the average charge and discharge current of the battery;

[0094] After obtaining the AC signal, a set of well-designed digital bandpass filters are used to filter the multi-frequency components contained in the excitation signal. and Perform frequency band division processing. Each set of bandpass filters corresponds to a target frequency range, which is used to enhance the signal-to-noise ratio of the signal in this frequency band and suppress interference from other frequencies.

[0095] After the filtering operation is completed, the fast Fourier transform (FFT) is applied to the filtered output signal within each frequency band to calculate the spectral response of the voltage and current respectively, and the complex amplitude at each frequency point is obtained. The impedance value at the corresponding frequency is obtained by complex division, as shown in the following formula:

[0096] ;

[0097] Where: Indicates the battery frequency The complex impedance value of represents the Fourier transform.

[0098] Finally, the impedance responses at each frequency point are constructed into an electrochemical impedance spectrum, including the Nyquist plot (the relationship between the real and imaginary parts of the complex impedance) and the Bode plot (the relationship between the impedance amplitude and phase as a function of frequency), providing high-quality frequency domain data support for subsequent fractional-order equivalent circuit model parameter fitting and SOC estimation.

[0099] The resulting impedance spectrum is then transferred to the equivalent circuit model fitting module, which uses a nonlinear least squares optimization method to fit the fractional-order equivalent circuit model and determine its initial parameters.

[0100] Specifically, the process of using nonlinear least squares optimization to fit the parameters of the fractional-order equivalent circuit model FOMW is as follows:

[0101] The fitting objective function is defined as follows:

[0102] Minimize ∑ m=1 M [ ( Z meas ,m ' - Z model ,m ' ) 2 + ( Z meas ,m '' - Z model ,m '' ) 2 ] ;

[0103] Where: M represents the total number of measurement frequency points; Represents the real part of the impedance actually measured at the mth frequency point; represents the real part of the impedance calculated by the fractional-order equivalent circuit model at the mth frequency point; Represents the imaginary part of the impedance actually measured at the mth frequency point; represents the imaginary part of the impedance calculated by the fractional-order equivalent circuit model at the m-th frequency point.

[0104] This embodiment uses a total of 31 frequency points to form the impedance spectrum, with a frequency range from 0.1 Hz to 3000 Hz. The first few items are linearly spaced (such as 0.1, 0.2, ..., 0.5 Hz), and the middle and latter frequencies are distributed with exponential or logarithmic growth, covering multiple orders of magnitude from low frequency to high frequency. Specific frequency points include 0.1 Hz, 0.2 Hz, 0.3 Hz, 0.4 Hz, 0.5 Hz, 0.7 Hz, 1 Hz, 1.4 Hz, 2 Hz, 2.8 Hz, etc., up to 3000 Hz, ensuring comprehensive acquisition of impedance characteristics over a wide frequency range.

[0105] The following constraints are set during the fitting process:

[0106] , , >0, 0<α≤1, Reasonable range (usually means ∼ F).

[0107] After fitting, to evaluate the matching degree between the model impedance and the measured data, the root mean square error (RMSE) of the impedance amplitude is calculated as shown in the following formula:

[0108] ;

[0109] ;

[0110] ;

[0111] Where: Indicates the impedance amplitude actually measured at the mth frequency point; represents the impedance amplitude calculated by the fractional-order equivalent circuit model at the mth frequency point.

[0112] like Figure 2 As shown, the fractional-order equivalent circuit model used to simulate the battery in this embodiment includes an ohmic resistor , polarization resistance , constant phase element CPE and Warburg impedance; initial parameters include ohmic resistance Resistance value , polarization resistance Resistance value , capacitance of constant phase element CPE , fractional order The resistive component of Warburg impedance .

[0113] Where, the impedance of the constant phase element CPE is The calculation formula is as follows:

[0114] ;

[0115] Where: represents the equivalent capacitance value of the constant phase element, represents the fractional order; represents an imaginary unit; Represents the angular frequency.

[0116] According to the resistance component Calculate the impedance value of Warburg impedance , as shown below:

[0117] ;

[0118] ;

[0119] Where: represents the angular frequency; represents the sampling interval after the continuous time is discretized; Indicates the sampling interval Number.

[0120] Terminal voltage The calculation formula is as follows:

[0121]

[0122] ;

[0123] Where: Indicates the actual measured terminal voltage; represents the prediction function; represents the operating current of the kth filtering iteration; represents the parameters of the kth filtering iteration; represents the prediction noise of the kth filtering iteration; represents the open circuit voltage function; Indicates the current ; The voltage across the ohmic resistance; Represents the voltage of the constant phase element CPE; The voltage representing the Warburg impedance.

[0124] After determining the initial parameters, they are input into an adaptive dual augmented extended Kalman filter along with real-time voltage and current data. The primary and secondary filters operate collaboratively. The primary filter predicts parameters based on the current current, fractional-order equivalent circuit model parameters, and the state estimate from the previous filtering iteration, while the secondary filter performs parameter prediction based on the current observation data and the parameter estimate from the previous filtering iteration. After obtaining the actual measured values, the primary and secondary filters perform state and parameter updates, respectively. The updated parameters of the secondary filter from the current filtering iteration serve as the input for the state prediction of the primary filter for the next filtering iteration. The covariance of the primary filter's state estimate is fed back to the secondary filter to dynamically adjust the parameter process noise covariance, achieving cross-feedback and adaptive adjustment.

[0125] Specifically, the state estimation is as follows:

[0126] ;

[0127] ;

[0128] Where: represents the state prior prediction value of the kth filtering iteration based on the state prediction value of the k−1th filtering iteration; represents the state prediction value of the k-1th filtering iteration; represents the parameter prediction value of the kth filtering iteration; represents the state prediction error covariance matrix of the kth filtering iteration obtained based on the state prediction error covariance matrix of the k−1th filtering iteration; The Jacobian matrix representing the state transfer function; represents the state prediction error covariance matrix of the k-1th filtering iteration; Represents matrix transpose; represents the state process noise covariance matrix of the k-th filtering iteration;

[0129] The parameter estimates are as follows:

[0130] ;

[0131] ;

[0132] Where: represents the prior prediction value of the parameter of the kth filtering iteration based on the parameter prediction value of the k−1th filtering iteration; represents the parameter prediction value of the k-1th filtering iteration; represents the parameter prediction error covariance matrix of the kth filtering iteration based on the k-1th filtering iteration; represents the parameter prediction error covariance matrix of the k-1th filtering iteration; represents the parameter process noise covariance matrix of the kth filtering iteration.

[0133] The status update process is as follows:

[0134] Calculate the Kalman gain of the main filter as shown below:

[0135] ;

[0136] Where: represents the Kalman gain of the main filter; is the state prediction Jacobian matrix, which indicates the sensitivity of the measurement value to the state; is the prediction noise covariance matrix, which indicates the size of the prediction error;

[0137] Then the state update and covariance update are performed. The state update is shown as follows:

[0138] ;

[0139] ;

[0140] Where: Indicates that after obtaining the actual measurement value of the kth filtering iteration, the fusion state prior prediction value The state posterior prediction value of the kth filtering iteration obtained by correcting the main filter with the actual measurement value; represents the actual voltage observed at the kth filtering iteration; represents the voltage value predicted by the kth filtering iteration; represents the prediction function; represents the prediction noise of the kth filtering iteration;

[0141] The covariance update is shown below:

[0142] ;

[0143] Where: represents the updated state prediction error covariance matrix of the kth filtering iteration;

[0144] The parameter update process is as follows:

[0145] ;

[0146] Where: represents the Kalman gain of the secondary filter; The Jacobian matrix is the parameter prediction matrix, which indicates the sensitivity of the measured value to the parameter;

[0147] Then the parameters are updated and the covariance is updated. The parameter update is shown as follows:

[0148] ;

[0149] Where: Indicates the prior prediction value of the fusion parameter after obtaining the actual measurement value of the kth filtering iteration Compared with the actual measured value, the posterior predicted value of the parameter of the kth filtering iteration is obtained by the filter correction;

[0150] The covariance update is shown below:

[0151] ;

[0152] Where: represents the updated parameter prediction error covariance matrix of the kth filtering iteration.

[0153] The process of cross-feedback and adaptive adjustment between the primary filter and the secondary filter includes:

[0154] The posterior prediction value of the parameter of the kth filtering iteration obtained by modifying the filter , as the input of the main filter, used to predict the state value of the k+1th filtering iteration;

[0155] The state prediction error covariance matrix of the kth filtering iteration after the main filter is updated is , dynamically adjust the parameter process noise covariance matrix of the secondary filter when performing parameter prediction , as shown below:

[0156] ;

[0157] Where: represents the prediction noise covariance matrix of the k-1th filtering iteration; Represents the smoothing factor, which is used to suppress noise mutations; Represents the new information sequence of the kth filtering iteration, which is used to represent the error between the predicted value output by the main filter and the actual measured value;

[0158] ;

[0159] Where: represents the parameter process noise covariance matrix of the k-1th filtering iteration; Represents the forgetting factor.

[0160] In order to determine whether the secondary filter (i.e., the extended Kalman filter used to estimate the parameters of the fractional-order equivalent circuit model) produces significant estimation deviations after long-term operation, the present invention further introduces an innovation statistical test mechanism to achieve dynamic monitoring of parameter estimation errors and abnormality judgment.

[0161] Specifically, in each filtering cycle, the innovation vector between the current observation value and the main filter prediction value, that is, the observation error, is calculated as shown in the following formula:

[0162] ;

[0163] Construct the innovation covariance matrix as shown below:

[0164] ;

[0165] Next, the chi-square test statistic is constructed in the form of Mahalanobis distance :

[0166] ;

[0167] And with the chi-square distribution critical value at the set confidence level For comparison, is the significance level. In this example, The value is 0.05. If the value exceeds the critical value, it is determined that the filter output is abnormal.

[0168] To enhance robustness, this embodiment is provided with an exception counter. When the exception is satisfied for several consecutive filtering cycles (e.g. N=10), When , it is considered that the parameters of the fractional-order equivalent circuit model estimated by the current filter have large deviations and there is a significant model mismatch. At this time, a new round of online electrochemical impedance spectroscopy will be triggered.

[0169] To prevent cumulative deviations in the filter model parameters due to long-term operation, this embodiment further incorporates a time threshold strategy for periodic updates to the battery model. When the time since the last electrochemical impedance spectroscopy measurement exceeds a preset time, the system automatically triggers a new round of online EIS measurements and refits the fractional-order equivalent circuit model parameters with the latest measured impedance data, thereby correcting for model drift and maintaining estimation accuracy.

[0170] In this embodiment, the EIS measurement cycle is set to 10 minutes, that is, a dynamic EIS detection is performed every 10 minutes; if the current filter iteration is more than 10 minutes away from the last model parameter update, the online EIS measurement process is started, and the obtained impedance spectrum data is used to perform parameter fitting on the fractional-order equivalent circuit model, and the model parameters in the filter are updated in real time.

[0171] Example 2:

[0172] The embodiment of the present invention further provides a system for an online SOC estimation method based on dynamic electrochemical impedance spectroscopy measurement, comprising:

[0173] The electrochemical impedance spectroscopy measurement test module is used to superimpose the DIBS square wave signal as the excitation current input on the basis of the main charge and discharge current of the battery, and collect the battery voltage and current data in real time; the collected voltage and current data are processed to obtain the battery impedance spectrum;

[0174] An equivalent circuit model fitting module is used to fit the fractional-order equivalent circuit model according to the impedance spectrum using a nonlinear least squares optimization method to obtain initial parameters of the fractional-order equivalent circuit model;

[0175] An adaptive dual augmented extended Kalman filter algorithm calculation module is used to input the initial parameters and real-time collected voltage and current data into the adaptive dual augmented extended Kalman filter, wherein the primary filter is used to estimate the SOC and the secondary filter is used to estimate the parameters of the fractional-order equivalent circuit model; the primary filter and the secondary filter operate in coordination, alternately performing state prediction and parameter prediction, and realize real-time synchronous prediction of the SOC and the parameters of the fractional-order equivalent circuit model through a cross-feedback mechanism.

[0176] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A battery SOC prediction method based on dynamic electrochemical impedance spectroscopy measurement, characterized in that: include: On the basis of the main charge and discharge current of the battery, the DIBS square wave signal is superimposed as the excitation current input to collect the voltage and current data of the battery in real time; The collected voltage and current data are processed to obtain an impedance spectrum of the battery; a fractional-order equivalent circuit model is fitted using a nonlinear least squares optimization method based on the impedance spectrum to obtain initial parameters of the fractional-order equivalent circuit model; Inputting the initial parameters and the real-time collected voltage and current data into an adaptive dual augmented extended Kalman filter, wherein the adaptive dual augmented extended Kalman filter has a dual filter structure, wherein the primary filter is used to predict the SOC, and the secondary filter is used to predict the parameters of the fractional-order equivalent circuit model; The main filter and the secondary filter operate in coordination, alternately performing state prediction and parameter prediction, and realizing real-time synchronous prediction of SOC and fractional-order equivalent circuit model parameters through a cross-feedback mechanism.

2. The battery SOC prediction method based on dynamic electrochemical impedance spectroscopy measurement according to claim 1, characterized in that: The fractional-order equivalent circuit model is used to simulate the battery, and the fractional-order equivalent circuit model includes ohmic resistance, polarization resistance, constant phase element CPE and Warburg impedance; The initial parameters include the resistance value of the ohmic resistor , resistance value of polarization resistor , capacitance of constant phase element CPE , fractional order The resistive component of Warburg impedance , according to the resistance component Calculate the impedance value of Warburg impedance , as shown below: ； ； Where: represents the angular frequency; represents the sampling interval after the continuous time is discretized; Indicates the sampling interval Number.

3. The battery SOC prediction method based on dynamic electrochemical impedance spectroscopy measurement according to claim 1, characterized in that: The process of the primary filter and the secondary filter operating in coordination includes: The main filter performs state prediction based on the current current, the fractional-order equivalent circuit model parameters and the state estimation of the last filtering iteration; The secondary filter performs parameter prediction based on the parameter estimate of the previous filtering iteration; After obtaining the actual measurement value, the primary filter and the secondary filter perform state update and parameter update respectively; The updated parameters of the secondary filter in the current filtering iteration are used as the input of the state prediction of the next filtering iteration of the main filter. At the same time, the covariance of the main filter state estimate is fed back to the secondary filter to dynamically adjust the parameter process noise covariance, realizing cross feedback and adaptive adjustment.

4. The battery SOC prediction method based on dynamic electrochemical impedance spectroscopy measurement according to claim 3, characterized in that: The main filter performs state prediction based on the current current, the fractional-order equivalent circuit model parameters and the state estimation of the previous filtering iteration, as shown in the following equation: ； ； Where: k represents the number of the filter time step; represents the state prior prediction value of the kth filtering iteration based on the state prediction value of the k−1th filtering iteration; represents the state transition function; represents the state prediction value of the k-1th filtering iteration; represents the parameter prediction value of the kth filtering iteration; represents the state prediction error covariance matrix of the kth filtering iteration obtained based on the state prediction error covariance matrix of the k−1th filtering iteration; The Jacobian matrix representing the state transfer function; represents the state prediction error covariance matrix of the k-1th filtering iteration; Represents matrix transpose; represents the state process noise covariance matrix of the k-th filtering iteration; The secondary filter performs parameter prediction based on the parameter estimate of the previous filtering iteration, as shown in the following equation: ； ； Where: represents the prior prediction value of the parameter of the kth filtering iteration based on the parameter prediction value of the k−1th filtering iteration; represents the parameter prediction value of the k-1th filtering iteration; represents the parameter prediction error covariance matrix of the kth filtering iteration obtained based on the parameter prediction error covariance matrix of the k-1th filtering iteration; represents the parameter prediction error covariance matrix of the k-1th filtering iteration; represents the parameter process noise covariance matrix of the kth filtering iteration.

5. The battery SOC prediction method based on dynamic electrochemical impedance spectroscopy measurement according to claim 3, characterized in that: After obtaining the actual measurement value, the primary filter and the secondary filter perform state update and parameter update respectively, including: Calculate the Kalman gain of the main filter as shown below: ； Where: represents the Kalman gain of the main filter; Predict the Jacobian matrix for the state; is the prediction noise covariance matrix, which indicates the size of the prediction error; Then the state update and covariance update are performed. The state update is shown as follows: ； ； Where: Indicates that after obtaining the actual measurement value of the kth filtering iteration, the fusion state prior prediction value The state posterior prediction value of the kth filtering iteration obtained by correcting the main filter with the actual measurement value; represents the voltage value actually measured at the kth filtering iteration; Represents the operating current at the kth filtering iteration; represents the voltage value predicted by the kth filtering iteration; represents the prediction function; represents the prediction noise of the kth filtering iteration; The covariance update is shown below: ； Where: represents the updated state prediction error covariance matrix of the kth filtering iteration; Calculate the Kalman gain of the secondary filter as shown below: ； Where: represents the Kalman gain of the secondary filter; Jacobian matrix for parameter prediction; Then the parameters are updated and the covariance is updated. The parameter update is shown as follows: ； Where: Indicates the prior prediction value of the fusion parameter after obtaining the actual measurement value of the kth filtering iteration Compared with the actual measured value, the posterior predicted value of the parameter of the kth filtering iteration is obtained by the filter correction; The covariance update is shown below: ； Where: represents the updated parameter prediction error covariance matrix of the kth filtering iteration.

6. The battery SOC prediction method based on dynamic electrochemical impedance spectroscopy measurement according to claim 3, characterized in that: The updated parameters of the secondary filter in the current filtering iteration are used as the input of the state prediction of the next filtering iteration of the primary filter. At the same time, the covariance of the primary filter state estimate is fed back to the secondary filter to dynamically adjust the parameter process noise covariance, realizing cross-feedback and adaptive adjustment, including: The posterior prediction value of the parameter of the kth filtering iteration obtained by modifying the filter , as the input of the main filter, used to predict the state value of the k+1th filtering iteration; The state prediction error covariance matrix of the kth filtering iteration after the main filter is updated is , dynamically adjust the parameter process noise covariance matrix of the secondary filter when performing parameter prediction , as shown below: ； Where: represents the prediction noise covariance matrix of the k-1th filtering iteration; Represents the smoothing factor, which is used to suppress noise mutations; Represents the new information sequence of the kth filtering iteration, which is used to represent the error between the predicted value output by the main filter and the actual measured value; ； Where: represents the parameter process noise covariance matrix of the k-1th filtering iteration; Represents the forgetting factor.

7. The battery SOC prediction method based on dynamic electrochemical impedance spectroscopy measurement according to claim 1, characterized in that: Also includes: If the prediction error of the fractional-order equivalent circuit model parameters exceeds a preset threshold in several consecutive filtering iterations, or the time since the last electrochemical impedance spectroscopy measurement exceeds a preset time, a new round of electrochemical impedance spectroscopy measurement is triggered and the fractional-order equivalent circuit model parameters are updated to cover the accumulated filter error.

8. The battery SOC prediction method based on dynamic electrochemical impedance spectroscopy measurement according to claim 7, characterized in that: The prediction error is determined by the innovation sequence statistical test method, as shown in the following formula: ； Where: represents the new information sequence of the kth filtering iteration; represents the voltage value actually measured at the kth filtering iteration; represents the prediction function; Construct the innovation covariance matrix , as shown below: ； Where: Jacobian matrix for parameter prediction; Represents matrix transpose; represents the parameter prediction error covariance matrix of the kth filtering iteration obtained based on the parameter prediction error covariance matrix of the k-1th filtering iteration; is the prediction noise covariance matrix, which indicates the size of the prediction error; Then construct the chi-square test statistic in the form of Mahalanobis distance : ； Where: represents the number of filter iterations; k represents the number of filter time steps; represents the chi-square distribution threshold; represents the significance level; If continuous Chi-square test statistic in filtering iterations Greater than the preset threshold , a new round of electrochemical impedance spectroscopy measurement is triggered to fit the parameters of the fractional-order equivalent circuit model.

9. A system for online SOC estimation based on dynamic electrochemical impedance spectroscopy, characterized in that: include: The electrochemical impedance spectroscopy measurement test module is used to superimpose the DIBS square wave signal as the excitation current input on the basis of the main charge and discharge current of the battery, and collect the battery voltage and current data in real time; the collected voltage and current data are processed to obtain the battery impedance spectrum; An equivalent circuit model fitting module is used to fit the fractional-order equivalent circuit model according to the impedance spectrum using a nonlinear least squares optimization method to obtain initial parameters of the fractional-order equivalent circuit model; An adaptive dual augmented extended Kalman filter algorithm calculation module is used to input the initial parameters and the real-time collected voltage and current data into the adaptive dual augmented extended Kalman filter. The adaptive dual augmented extended Kalman filter has a dual-filter structure, in which the main filter is used to estimate the SOC and the secondary filter is used to estimate the parameters of the fractional-order equivalent circuit model; the main filter and the secondary filter operate in coordination, alternately performing state prediction and parameter prediction, and realize real-time synchronous prediction of the SOC and the fractional-order equivalent circuit model parameters through a cross-feedback mechanism.

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