Lithium battery parameter online identification method based on dynamic weight particle swarm optimization

Abstract

The invention provides a lithium battery parameter online identification method based on dynamic weight particle swarm optimization, and relates to the field of power lithium battery model parameter identification. According to the method, a lithium battery equivalent circuit model based on a second-order RC network is established, and a state-space equation is derived according to the Kirchhoff's current law and the voltage law; a discrete output model is obtained through Laplace transformation and discretization processing; constructing a recursive least square parameter updater with a forgetting factor, and jointly optimizing an initial parameter vector of the forgetting factor recursive least square and the forgetting factor by adopting a dynamic weight particle swarm optimization algorithm; and based on the optimized initial parameter vector and the forgetting factor, performing recursive least square updating with the forgetting factor, performing online identification on model parameters, and reversely deducing an equivalent parameter value in an original circuit. According to the method, the parameter identification precision can be remarkably improved, and the problem that data saturation parameter convergence is slow in a traditional recursive least square method is solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power lithium battery model parameter identification, in particular to a lithium battery parameter online identification method based on dynamic weight particle swarm optimization. BACKGROUND

[0002] In recent years, with the rapid development of the electric vehicle industry, battery energy storage technology has attracted widespread attention and has shown significant value in practical applications. Lithium-ion batteries have become the most widely used power battery type due to their high energy density, long cycle life, high output voltage, and fast charging and discharging capabilities. In the battery management system (BMS), the estimation of the battery state of charge (SOC) is one of the core functions, and its estimation accuracy is directly related to the safety, service life, and overall efficiency of the vehicle. Therefore, constructing a high-precision battery model and achieving accurate parameter identification are key foundations for improving SOC estimation accuracy and thus improving the overall performance of the BMS.

[0003] Currently, the parameter identification methods for lithium-ion batteries mainly include offline parameter identification and online parameter identification. Offline parameter identification usually starts from physical modeling, focusing on deeply mining the physical meaning of battery model parameters, which is helpful to understand the model structure and the coupling relationship between parameters, and is suitable for model development and theoretical analysis. However, this method has poor adaptability to working conditions and is difficult to meet the dynamic needs in actual operation. In contrast, online parameter identification methods focus on mathematical modeling and numerical calculation, which can update model parameters in real time to adapt to the dynamic characteristics of battery state changes with working conditions, and have stronger robustness and higher estimation accuracy. Although online identification methods have significant advantages in practical applications, they have relatively weak physical interpretability and require higher algorithm design and computational efficiency.

[0004] Among the many online parameter identification methods, recursive least squares (RLS) and its extended forms are widely used. This type of method has the advantages of high computational efficiency and simple implementation, but also has certain limitations: on the one hand, the convergence speed of the algorithm is highly dependent on the setting of the initial value of the parameters, and unreasonable initial values may lead to large identification errors; on the other hand, the traditional least squares method is prone to data saturation in long-term identification, which leads to the influence of old data on parameter estimation being too strong, thereby reducing the response ability to changes in new working conditions. At the same time, this type of method also has certain deficiencies in data utilization efficiency. Therefore, optimizing the parameter adjustment mechanism of traditional RLS to improve its adaptability and identification accuracy in dynamic environments has become one of the important directions in the current research on lithium battery modeling and SOC estimation. SUMMARY

[0005] Therefore, in order to accurately identify the lithium battery model parameters, the purpose of the present application is to construct an online parameter identification method (DFFRLS) based on dynamic weight particle swarm optimization and forgetting factor recursive least square combined with the second-order RC equivalent circuit model of the power lithium battery, and the initial value of the model parameter and the forgetting factor in the recursive process are jointly optimized by introducing the dynamic weight particle swarm optimization algorithm to obtain the optimal identification initial value and dynamic adjustment weight.

[0006] The present application optimizes the initialization weight and the forgetting factor setting by using the particle swarm algorithm, realizes the dynamic weighting of the historical data and the current data in the online parameter updating process, enhances the adaptive ability of the algorithm, and effectively solves the problem of reduced identification accuracy caused by improper initial value setting in the traditional RLS.

[0007] To achieve the above purpose, the present application provides the following technical solutions: Based on the above purpose, in the first aspect, the present application provides a lithium battery parameter online identification method based on dynamic weight particle swarm optimization, comprising the following steps: Establishing a lithium battery equivalent circuit model based on a second-order RC network, deriving a state space equation according to Kirchhoff's current law and voltage law, and obtaining a discrete output model through Laplace transform and discretization processing; Based on the discrete output model, a recursive least square parameter updater with a forgetting factor is constructed, and the initial parameter vector and the forgetting factor of the forgetting factor recursive least square (FFRLS) are jointly optimized by using the dynamic weight particle swarm optimization algorithm (DFWPSO); Based on the optimized initial parameter vector and the forgetting factor, the recursive least square update with the forgetting factor is performed, the model parameters are identified online, and the equivalent parameter values in the original circuit are back calculated.

[0008] As a further scheme of the present application, the lithium battery equivalent circuit model based on the second-order RC network includes the open-circuit voltage of the lithium battery , the output voltage , the ohmic internal resistance , and the polarization resistance polarization resistance polarization capacitance polarization resistance and polarization capacitance .

[0009] As a further scheme of the present application, the state space equation is derived according to the Kirchhoff current law and the voltage law as follows: wherein, and are the polarization voltages of the circuit and the circuit, respectively, is the load current of the lithium battery, is the time variable.

[0010] As a further scheme of the present application, the state space equation is converted into the least square form in the Laplace domain by Laplace transform and discretization processing, and the following equation is obtained: wherein, is the Laplace transform of the battery terminal voltage, which is the expression form of the output voltage signal in the frequency domain; is the Laplace transform of the open circuit voltage of the battery; is the Laplace variable in the complex frequency domain; is the Laplace transform of the battery input current , which is the input signal of the system.

[0011] As a further scheme of the present application, the time constant is defined, and the Laplace transform of the battery terminal voltage is arranged as follows: wherein, let: then, the Laplace transform of the battery terminal voltage is simplified as: to obtain the simplified Laplace transform result.

[0012] As a further scheme of the present application, the difference operator is introduced for discretization processing when the Laplace transform and the discretization processing are performed, and let , ; wherein, is the sampling time; is the Laplace variable in the complex frequency domain; is the variable in the discrete time. ​​the value of the sampling point; general representation of a certain physical variable; is the first sampling time, ; adopt to represent the error term; to represent the battery terminal voltage of the first sampling; to represent the battery open-circuit voltage of the first sampling; to represent the current at the first sampling time, then the discrete expression of the error term after the discretization processing is: In the formula, , , , , respectively represent the coefficient of the system feedback term , the coefficient of the feedback term , the coefficient of the current , the coefficient of , the reference coefficient of , and the parameter coefficient is: The parameter vector is defined as , and the data vector is , wherein: The discrete output model of the system output is represented as: In the formula, represents the output value of the system at the first time; represents the parameter vector at the first time; represents the transpose of the parameter vector at the first time; represents the data vector at the first time.

[0013] As a further scheme of the present application, when the Laplace transform and the discretization processing are performed, the response time constant corresponding to the battery ohmic internal resistance is , the time constant corresponding to the polarization resistance , the polarization resistance and the polarization capacitance , and the polarization capacitance is , then the response time constant response time constant according to the time scale parameter , the dimension of the particle swarm search space is divided; wherein the time scale parameter is associated with the lithium battery equivalent circuit model based on the second-order RC network, and the time constant mapping relationship is: In the formula, corresponding to the electrochemical polarization process, corresponding to the concentration polarization process, through the discrete parameter coefficient - establishes a mathematical equivalence relationship, and the time scale parameter According to , is set, and the sampling interval is set in the range of 0.1-10s, specifically, for the slowly varying characteristics of the internal electrochemical process of the battery, the sampling interval of the slow variation process resolution is 1s; the time scale parameter According to the response time of the ohmic internal resistance is set, and the sampling interval is set in the range of 0.1-10ms, specifically, when the instantaneous voltage drop and recovery characteristics in the charging and discharging process are caught, the sampling interval of the fast variation process resolution is 1ms.

[0014] As a further scheme of the present application, based on the discrete output model, a recursive least square parameter updater with a forgetting factor is constructed, and when the recursive least square algorithm with a forgetting factor is used to estimate the parameters online, the update formula is: In the formula, is a forgetting factor; is a gain matrix; is a covariance matrix; is an identity matrix; is a prediction error; represents the output value of the system at the time; represents the parameter vector at the time; represents the transpose of the parameter vector at the time; represents the data vector at the time; represents the transpose of the data vector at the time.

[0015] As a further aspect of the present invention, the equivalent parameter values ​​in the original circuit are derived as follows:

[0016] As a further aspect of the present invention, when using the dynamic weighted particle swarm optimization algorithm to jointly optimize the initial parameter vector and the forgetting factor in the recursive least squares method, the velocity and position of the particles are updated according to the following formula: In the formula, Indicates the first The middle generation The velocity of each particle; Its current location; For the first The optimal position of each particle to date; This represents the globally optimal position within the current population. and These are individual cognitive factors and social cognitive factors, used to regulate the degree to which particles depend on their own experience and group experience; The inertial weight determines the particle's ability to retain its previous velocity; These are uniformly distributed random numbers; Let be the current iteration algebra.

[0017] As a further aspect of the present invention, the online identification method for lithium battery parameters based on dynamic weighted particle swarm optimization also includes the introduction of a compression factor. Used to limit the particle velocity range, improve search stability and convergence performance, among which, the compression factor Defined as: In the formula, The compressibility factor is used to stabilize the search process and suppress particle velocity divergence; and , This represents the sum of cognitive and social factors, and Based on compression factor The particle velocity update formula is: The dynamic inertia weight model is expressed as: In the formula, and These are the minimum and maximum values ​​of the inertia weight, respectively, which determine the gradual change in search capability from global to local. This represents the current iteration number; This represents the maximum number of iterations. Disturbance intensity coefficient is a random disturbance term for Beta distribution, and parameters and control its skewness and kurtosis. is the inertia weight; e is the base of natural logarithm.

[0018] As a further scheme of the present application, in the dynamic weight particle swarm optimization lithium battery parameter online identification method, the particle swarm optimization algorithm (PSO) is used to construct a fitness function by minimizing the error function between the predicted value and the measured value, which is expressed as: In the formula, represents the measured voltage, represents the estimated voltage, represents the number of sampling points. represents the loss function.

[0019] As a further scheme of the present application, the dynamic weight particle swarm optimization lithium battery parameter online identification method further includes parameter prediction correction, wherein the parameter prediction correction based on deep learning includes the following steps: establishing a parameter change prediction model based on an LSTM network; training the prediction network using historical data; fusing the prediction result and the identification result: through the formula is realized, wherein is an adaptive fusion coefficient, ranging from 0 to 1, and is dynamically adjusted; is a parameter vector obtained by online identification of the FFRLS algorithm; is a parameter vector predicted by the LSTM network; wherein the adaptive fusion coefficient is adaptively adjusted according to the following strategy: In the formula, is a basic fusion coefficient, and the default is 0.3; is an adjustment factor, and the default is 1.0; is the standard deviation of the recent prediction error; is the maximum allowed error standard deviation.

[0020] Compared with the prior art, the dynamic weight particle swarm optimization lithium battery parameter online identification method has the following beneficial effects: The application solves the slow convergence problem of the traditional RLS algorithm caused by improper initial value setting by jointly optimizing the initial parameters and the forgetting factor of the forgetting factor recursive least square method (FFRLS) through a dynamic weight particle swarm optimization algorithm (DFWPSO), the dynamic inertia weight model has exponential decay and Beta random disturbance, improves the convergence stability, enhances the ability to jump out of local extreme value, and avoids premature convergence. The influence of historical data is reduced by the optimal forgetting factor dynamic attenuation, and the proportion of current measurement data in parameter updating is improved, which significantly relieves the data saturation problem of the traditional RLS. Through the dynamic weight mechanism, the particle swarm convergence is accelerated, and combined with the recursive update of the FFRLS, the millisecond-level online parameter identification is realized.

[0021] Therefore, by fusing the dynamic weight PSO and the FFRLS, the application overcomes the three bottlenecks of data saturation, initial value sensitivity and local convergence of the traditional online identification method, realizes the accuracy improvement, strong working condition adaptability and engineering easy deployment in the parameter identification of the power lithium battery, and provides key technical support for the high-reliability BMS system.

[0022] These aspects or other aspects of the application will be more apparent in the following description of the embodiments. It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the application. BRIEF DESCRIPTION OF DRAWINGS

[0023] In order to more clearly illustrate the technical solutions in the embodiments of the application or the related art, the following will briefly introduce the drawings needed to be used in the exemplary embodiments or the related art description. The drawings are used to provide further understanding of the application, and constitute a part of the specification. The drawings are used together with the embodiments of the application to explain the application, and do not constitute a limitation on the application. In the drawings: Figure 1 A flow chart of a lithium battery parameter online identification method of a dynamic weight particle swarm optimization according to an embodiment of the application.

[0024] Figure 2 A circuit diagram of a second-order RC equivalent circuit model in a lithium battery parameter online identification method of a dynamic weight particle swarm optimization according to an embodiment of the application.

[0025] Figure 3 A model parameter identification result diagram under BBDST working condition in a lithium battery parameter online identification method of a dynamic weight particle swarm optimization according to an embodiment of the application.

[0026] Figure 4 A model parameter identification error result diagram under BBDST working condition in a lithium battery parameter online identification method of a dynamic weight particle swarm optimization according to an embodiment of the application. DETAILED DESCRIPTION

[0027] The application will be further described below with reference to the accompanying drawings. The following examples are intended to illustrate the application in more detail and to give a detailed implementation. However, the scope of protection of the application is not limited to the following examples.

[0028] In order to accurately identify the lithium battery model parameters, the application is based on a second-order RC equivalent circuit model of a power lithium battery. The application proposes a dynamic weight particle swarm optimization lithium battery parameter online identification method. By introducing a dynamic weight particle swarm optimization algorithm, the initial value of the model parameters and the forgetting factor in the recursive process are jointly optimized to obtain the optimal initial identification value and dynamic adjustment weight. In the parameter updating process, the optimal forgetting factor can adaptively attenuate the influence of historical data and improve the proportion of current measurement data in the parameter updating process, thereby enhancing the response capability of the algorithm to the battery state change, significantly improving the accuracy of parameter identification, and solving the problem of slow parameter convergence due to data saturation in the traditional recursive least squares method.

[0029] The application uses a particle swarm algorithm to optimize the initialization weight and forgetting factor setting, realizes dynamic weighting of historical data and current data in the parameter online updating process. This method enhances the adaptive ability of the algorithm while effectively reducing the identification accuracy decline problem caused by improper initial value setting in the traditional RLS. The application has the advantages of simple structure, fast convergence speed and high identification accuracy, and is especially suitable for real-time parameter identification of power lithium batteries under variable working conditions. The simulation results show that this method has significant advantages in dealing with battery dynamic working condition changes, improving modeling accuracy and parameter stability, and is an efficient parameter identification technology scheme with good engineering practicability.

[0030] Referring to Figure 1 The embodiments of the application provide a dynamic weight particle swarm optimization lithium battery parameter online identification method, which comprises the following steps: A lithium battery equivalent circuit model based on a second-order RC network is established, state space equations are derived according to Kirchhoff's current law and voltage law, and a discrete output model is obtained through Laplace transform and discretization processing; Based on the discrete output model, a recursive least squares parameter updater with a forgetting factor is constructed, and a dynamic weight particle swarm optimization algorithm (DFWPSO) is used to jointly optimize the initial parameter vector and the forgetting factor of the recursive least squares (FFRLS); Based on the optimized initial parameter vector and the forgetting factor, the recursive least squares update with a forgetting factor is performed, the model parameters are identified online, and the equivalent parameter values in the original circuit are back calculated.

[0031] In this embodiment, the ternary lithium-ion battery with rated capacity of 72 Ah is taken as the research object, and the lithium battery equivalent circuit model based on the second-order RC network is established. According to Kirchhoff's voltage and current law, the corresponding state space equation is derived. The DFFRLS algorithm is used to identify the model parameters, and the simulation experiment is carried out to verify the accuracy and effectiveness of the proposed DFFRLS algorithm in the parameter identification process. Referring to Figure 2 , the lithium battery equivalent circuit model based on the second-order RC network includes the open-circuit voltage , output voltage , ohmic resistance , polarization resistance , polarization resistance , polarization capacitance and polarization capacitance . According to Kirchhoff's current law and voltage law, the state space equation is derived as follows: In the formula, and are the polarization voltages of the loop and loop respectively, is the load current of the lithium battery, is the time variable.

[0032] Through Laplace transform and discretization processing, the state space equation is converted into the least square form in the Laplace domain, and the following equation is obtained: In the formula, is the Laplace transform of the battery terminal voltage, which is the expression form of the output voltage signal in the frequency domain; is the Laplace transform of the battery open-circuit voltage; is the Laplace variable in the complex frequency domain; is the Laplace transform of the battery input current , which is the input signal of the system.

[0033] In this embodiment, the time constant is defined, and the Laplace transform of the battery terminal voltage is arranged as follows: Among them, let: Then, the Laplace transform of the battery terminal voltage is simplified as: The simplified Laplace transform result is obtained.

[0034] In this embodiment, the difference operator is introduced for the discretization process when the Laplace transform and discretization process are performed, and let , ; wherein, is the sampling time; is the Laplace variable in the complex frequency domain; is the variable representing the discrete time The value of the th sampling point; represents the general representation of a certain physical variable; is the th sampling time, ; the error term is represented by ; the battery terminal voltage of the th sampling is represented by ; the battery open-circuit voltage of the th sampling is represented by ; the current at the th sampling time is represented by , then the discrete expression of the error term after the discretization process is: In the formula, , , , , respectively represent the coefficient of the system feedback term , the coefficient of the feedback term , the coefficient of the current , the coefficient of , the reference coefficient of , and the parameter coefficient is: The parameter vector is defined as , and the data vector is , wherein: The discrete output model of the system output is represented as: In the formula, represents the output value of the system at the th time; represents the parameter vector at the th time; represents the transpose of the parameter vector at the th time; represents the data vector at the th time.

[0035] wherein, by Laplace transform and discretization processing, the response time constant corresponding to the ohmic internal resistance of the battery , the time constant of the response time constant corresponding to the polarization resistance , the polarization resistance and the polarization capacitance , the polarization capacitance , the response time constant , the response time constant , according to the time scale parameter , the dimension of the particle swarm search space is divided; wherein, the time scale parameter is associated with the equivalent circuit model of the lithium battery based on the second-order RC network, and the time constant mapping relationship is: In the formula, corresponds to the electrochemical polarization process, corresponds to the concentration polarization process, and the discretization parameter coefficient - a mathematical equivalence relationship is established, and the time scale parameter is set according to , , the sampling interval is set in the range of 0.1-10s, and specifically, for the slow-varying characteristics of the internal electrochemical process of the battery, the sampling interval of the slow-varying process resolution is 1s; the time scale parameter is set according to the response time of the ohmic internal resistance , and the sampling interval is set in the range of 0.1-10ms, and specifically, when the instantaneous voltage drop and recovery characteristics in the charging and discharging process are caught, the sampling interval of the fast-varying process resolution is 1ms.

[0036] Based on the discrete output model, a recursive least square parameter updater with a forgetting factor is constructed, and when the recursive least square algorithm with a forgetting factor is used for online estimation of the parameters, the update formula is: In the formula, is a forgetting factor; is a gain matrix; is a covariance matrix; is an identity matrix; is a prediction error; denotes the output value of the system at the time; denotes the output value of the system at the ​​The parameter vector at each time step; Indicates the first Transpose of the parameter vector at each time step; Indicates the first A data vector at each moment; Indicates the first The transpose of the data vector at each time step.

[0037] Based on the identified model parameters, the equivalent parameter values ​​in the original circuit can be deduced as follows:

[0038] To improve the initial accuracy and recognition stability of the algorithm, a Dynamic Weighted Particle Swarm Optimization (DFWPSO) algorithm is introduced to jointly optimize the initial parameters and forgetting factor settings of FFRLS. Particle Swarm Optimization (PSO) is a global optimization method based on swarm intelligence. Its core idea is to collaboratively search for the optimal solution in the solution space through individual memory and group cooperation. In the algorithm initialization phase, the search space is constructed by randomly generating a swarm of particles (i.e., a set of candidate solutions). Each particle represents a potential solution and has two state variables: position and velocity. During iteration, the particle's motion is guided by two "extreme" values: the particle's own historical best position (i.e., the individual best value, pBest) and the current best position found in the entire population (i.e., the global best value, gBest). Furthermore, some improved algorithms introduce a local optimum strategy, where particles only refer to the best solution within their neighborhood to enhance population diversity and reduce the risk of getting trapped in local optima.

[0039] In this embodiment, when using the dynamic weighted particle swarm optimization algorithm to jointly optimize the initial parameter vector and forgetting factor of the recursive least squares, the particle velocity and position are updated according to the following formula: In the formula, Indicates the first The middle generation The velocity of each particle; Its current location; For the first The optimal position of each particle to date; This represents the globally optimal position within the current population. and These are individual cognitive factors and social cognitive factors, used to regulate the degree to which particles depend on their own experience and group experience; The inertial weight determines the particle's ability to retain its previous velocity; These are uniformly distributed random numbers; Let be the current iteration algebra.

[0040] In the embodiment, the PSO has good global search ability and fast convergence speed in continuous optimization problems, but still has the following deficiencies in high-dimensional complex problems: weak local search ability, easy to fall into local extreme value; low search accuracy, sensitive to the setting of speed parameter; too large speed leads to enhanced particle jumping and difficulty in convergence, while too small speed may lead to search stagnation. To solve the above problems, the dynamic weight particle swarm optimization lithium battery parameter online identification method further comprises introducing a compression factor for limiting the particle speed range, improving search stability and convergence performance, wherein the compression factor is defined as: In the formula, the compression factor is used to stabilize the search process and suppress the divergence of particle speed; and , represents the sum of the cognitive factor and the social factor, and ; based on the compression factor , the particle speed updating formula is: The introduction of the compression factor enables the dynamic balance of the local and global search ability of the particles, thereby improving the robustness and search accuracy of the algorithm. The introduction of the dynamic weight mechanism further improves the optimization effect. To simulate the gradual attenuation trend of the disturbance parameter in the time evolution process and introduce non-Gaussian random disturbance to enhance the population diversity, the dynamic inertia weight model is represented as: In the formula, and are the minimum value and the maximum value of the inertia weight respectively, which determines the gradual change of the search ability from global to local; is the current iteration number; is the maximum iteration number; is the disturbance intensity coefficient is a random disturbance term of Beta distribution, and parameters and control the skewness and kurtosis thereof; is the inertia weight; e is the base of natural logarithm.

[0041] In the dynamic weight particle swarm optimization lithium battery parameter online identification method of the application, the exponential decay term makes the inertia weight gradually converge with iteration, which is conducive to the smooth transition of the algorithm from early global search to later local fine search; and the introduced Beta random disturbance retains a certain degree of exploration ability on this basis, which helps to jump out of the local extremum and improves the global optimization performance and stability of the algorithm. In specific applications such as lithium battery modeling and parameter identification tasks, the particle swarm optimization algorithm (PSO) constructs a fitness function by minimizing the error function between the predicted value and the measured value, which is expressed as: In the formula, represents the measured voltage, represents the estimated voltage, represents the number of sampling points; represents the loss function.

[0042] In an embodiment of the application, the dynamic weight particle swarm optimization lithium battery parameter online identification method further includes parameter prediction correction, wherein the parameter prediction correction based on deep learning includes the following steps: Establishing a parameter change prediction model based on an LSTM network; Training the prediction network using historical data; Fusing the prediction result and the identification result: through the formula is realized, wherein is an adaptive fusion coefficient, ranging from 0 to 1, which is dynamically adjusted; is the parameter vector obtained by online identification of the FFRLS algorithm; is the parameter vector predicted by the LSTM network; wherein the adaptive fusion coefficient is adaptively adjusted as follows: In the formula, is a basic fusion coefficient, defaulting to 0.3; is an adjustment factor, defaulting to 1.0; is the standard deviation of the recent prediction error; is the maximum allowed error standard deviation.

[0043] In the establishment of the parameter change prediction model based on the LSTM network, the input layer of the LSTM network architecture is: a historical parameter sequence wherein is the size of the time window; the hidden layer: 2 layers of LSTM units, 128 neurons per layer, using a tanh activation function; the output layer: a fully connected layer, outputting the predicted parameter θpredicted; the dropout layer: a Dropout rate of 0.2, preventing overfitting.

[0044] To verify the accuracy and effectiveness of the proposed DFFRLS algorithm, the present application based on BBDST experimental data, the parameters of the constructed second-order RC equivalent circuit model are identified, and the results are compared with different algorithms. Specifically, the simulated voltage curve estimated by the DFFRLS algorithm is compared with the experimental measured voltage curve, the simulated voltage curve obtained by the DWPSO algorithm and the traditional FFRLS algorithm, and the relevant results are shown in Figure 3 and Figure 4 As can be seen from the figure, the simulated voltage curve generated by the DFFRLS algorithm has the highest fitting degree with the measured voltage curve, which is significantly better than the DWPSO and FFRLS algorithms, and its estimation accuracy shows stronger consistency and stability throughout the test period. In contrast, the simulation results corresponding to DWPSO and FFRLS have obvious deviations from the actual measured values in multiple time periods. In addition, from the trend of the voltage curve, the DFFRLS algorithm shows good convergence characteristics and robustness.

[0045] In order to further quantify the performance of the algorithm, the present application calculates the specific error indicators of each algorithm in the simulation process, and the relevant values are listed in Table 1. Through the comparison of the indicators, the comprehensive advantages of the DFFRLS algorithm in parameter estimation accuracy and stability are further verified.

[0046] Table 1 Performance indicators of several algorithms Algorithm MAE RMSE ME DFFRLS 0.0080 0.0099 0.0323 DWPSO 0.0310 0.0333 0.0666 FFRLS 0.0474 0.0501 0.0972 The performance indicators of a variety of parameter identification algorithms are specifically calculated, and the results are summarized in Table 1. Mean absolute error (MAE) and root mean square error (RMSE) are the two most commonly used indicators to measure prediction accuracy, where MAE reflects the average absolute deviation of predicted values from measured values, and RMSE is more sensitive to outliers, which can reflect the square average level of prediction error. In addition, the maximum error (ME) represents the maximum deviation value of each algorithm. As can be clearly seen from Table 1, all performance indicators of the proposed algorithm achieve the optimal level, showing the lowest error level. This indicates that the algorithm has higher precision and stability in the parameter identification process, fully embodying its superior estimation performance and application potential.

[0047] The above is an exemplary embodiment disclosed by the present application, but it should be noted that various changes and modifications can be made without departing from the scope of the embodiments disclosed by the present application as defined in the claims. The functions, steps and / or actions of the method claims described herein need not be performed in any particular order. In addition, although the elements of the embodiments disclosed by the present application can be described or claimed in singular form, they can also be understood as plural unless explicitly limited to singular.

[0048] Those skilled in the art should understand that the above discussion of any embodiment is only intended to be illustrative and is not intended to be limiting on the scope of the present embodiments, including the claims, which are intended to be limited only by the literal and equivalent language of the claims. The above embodiments, or technical features among different embodiments, can also be combined, and there are many other variations of different aspects of the present embodiments as described above. In order to be brief, they are not provided in details. Therefore, any omission, modification, equivalent replacement, improvement, etc. made in the spirit and principle of the present embodiments should be included in the protection scope of the present embodiments.

Claims

1. A method for online identification of lithium battery parameters using dynamic weighted particle swarm optimization, characterized in that, The method includes the following steps: An equivalent circuit model of a lithium battery based on a second-order RC network is established. The state-space equations are derived according to Kirchhoff's current law and voltage law. The discrete output model is obtained through Laplace transform and discretization. Based on the discrete output model, a recursive least squares parameter updater with a forgetting factor is constructed, and the initial parameter vector and forgetting factor of the recursive least squares with forgetting factor are jointly optimized by the dynamic weighted particle swarm optimization algorithm. Based on the optimized initial parameter vector and forgetting factor, a recursive least squares update with forgetting factor is performed to identify the model parameters online and back-infer the equivalent parameter values ​​in the original circuit.

2. The online identification method for lithium battery parameters using dynamic weighted particle swarm optimization as described in claim 1, characterized in that, Establish an equivalent circuit model of a lithium battery based on a second-order RC network, including the open-circuit voltage of the lithium battery. Output voltage Ohmic internal resistance Polarization resistance Polarization resistance Polarized capacitors and polarization capacitor .

3. The online identification method for lithium battery parameters using dynamic weighted particle swarm optimization as described in claim 2, characterized in that, Based on Kirchhoff's current law and voltage law, the state-space equations are derived as follows: In the formula, and They are circuit and The polarization voltage of the circuit, This is the load current of the lithium battery. It is a time variable.

4. The online identification method for lithium battery parameters using dynamic weighted particle swarm optimization as described in claim 3, characterized in that, Through Laplace transform and discretization, the state-space equations are transformed into least-squares forms in the Laplace domain, resulting in: In the formula, It is the Laplace transform of the battery terminal voltage, which is the frequency domain expression of the output voltage signal; It is the Laplace transform of the battery open-circuit voltage; It is a Laplace variable in the complex frequency domain; It is the battery input current. The Laplace transform of is the input signal of the system.

5. The online identification method for lithium battery parameters using dynamic weighted particle swarm optimization as described in claim 4, characterized in that, Define time constant Then the Laplace transform of the battery terminal voltage Sorted as: Among them, let: Then, the Laplace transform of the battery terminal voltage Simplified to: The simplified Laplace transform result is obtained.

6. The online identification method for lithium battery parameters using dynamic weighted particle swarm optimization as described in claim 5, characterized in that, During the Laplace transform and discretization process, a difference operator is introduced for discretization, allowing... , ;in, Sampling time; For the Laplace variable in the complex frequency domain; To represent variables in discrete time In the The value of each sampling point; A general representation of a physical variable; For the first Sampling time, ;use Indicates the error term; Indicates the first The battery terminal voltage sampled next; Indicates the first The battery open-circuit voltage sampled next; Indicates the first The current at the next sampling time is then discretized, and the discrete expression for the error term is: In the formula, , , , , These represent system feedback items. coefficients, feedback terms coefficient, current coefficients, coefficients, The reference coefficients are as follows, and the parameter coefficients are: Define the parameter vector as The data vector is ,in: The discrete output model of the system is then expressed as: In the formula, Indicates the system at the 1st Output value at each time point; Indicates the first The parameter vector at each time step; Indicates the first Transpose of the parameter vector at each time step; Indicates the first The data vector at each time point.

7. The online identification method for lithium battery parameters using dynamic weighted particle swarm optimization as described in claim 6, characterized in that, Based on the discrete output model, a recursive least squares parameter updater with a forgetting factor is constructed. When using the recursive least squares algorithm with a forgetting factor to estimate the parameters online, the update formula is: In the formula, Forgetting factor; This is the gain matrix; It is the covariance matrix; It is the identity matrix; This represents the prediction error; Indicates the system at the 1st Output value at each time point; Indicates the first The parameter vector at each time step; Indicates the first Transpose of the parameter vector at each time step; Indicates the first A data vector at each moment; Indicates the first The transpose of the data vector at each time step.

8. The online identification method for lithium battery parameters using dynamic weighted particle swarm optimization as described in claim 7, characterized in that, The equivalent parameter values ​​in the original circuit are derived as follows: 。 9. The online identification method for lithium battery parameters using dynamic weighted particle swarm optimization as described in claim 8, characterized in that, When using the dynamic weighted particle swarm optimization algorithm to jointly optimize the initial parameter vector and forgetting factor of the recursive least squares algorithm, the particle velocity and position are updated according to the following formula: In the formula, Indicates the first The middle generation The velocity of each particle; Its current location; For the first The optimal position of each individual particle to date; This represents the globally optimal position within the current population. and These are individual cognitive factors and social cognitive factors, used to regulate the degree to which particles depend on their own experience and group experience; The inertial weight determines the particle's ability to retain its previous velocity; These are uniformly distributed random numbers; Let be the current iteration algebra.

10. The online identification method for lithium battery parameters using dynamic weighted particle swarm optimization as described in claim 9, characterized in that, The online parameter identification method for lithium batteries using dynamic weighted particle swarm optimization also includes the introduction of a compression factor. Used to limit the particle velocity range, improve search stability and convergence performance, among which, the compression factor Defined as: In the formula, The compressibility factor is used to stabilize the search process and suppress particle velocity divergence; and , This represents the sum of cognitive and social factors, and Based on compression factor The particle velocity update formula is: The dynamic inertia weight model is expressed as: In the formula, and These are the minimum and maximum values ​​of the inertia weight, respectively, which determine the gradual change in search capability from global to local. This represents the current iteration number; This represents the maximum number of iterations. Disturbance intensity coefficient Let be a random perturbation term of a Beta distribution, with parameters and Control its skewness and kurtosis; is the inertial weight; e is the base of the natural logarithm.

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