Lithium battery system charge state estimation method based on Hammerstein model

Abstract

The invention discloses a lithium battery system state-of-charge estimation method based on a Hammerstein model, and the method comprises the steps: constructing a second-order RC circuit equation of a lithium battery, describing a dynamic linear module of the Hammerstein model through a noise transfer function model, and constructing a lithium battery system through a static nonlinear module of an adaptive neural fuzzy network; designing a Gaussian signal, inputting the Gaussian signal into the agent model of the lithium battery system to obtain corresponding Gaussian signal output, and decoupling the static nonlinear module and the dynamic linear block by using the covariance function characteristic of the Gaussian signal; identifying parameters of the noise transfer function model by using a least square method based on a covariance function, solving parameters of the adaptive neural fuzzy network by using a crown porcupine optimization algorithm, and updating the weight of the adaptive neural fuzzy network by using a stochastic gradient algorithm with a forgetting factor; and constructing an OCV-SOC curve of the open-circuit voltage and the state of charge by adopting polynomial fitting, and taking output obtained by the Hammerstein model as input of the polynomial fitting to obtain an estimated value of the state of charge SOC.

Description

Technical Field

[0001] The present invention relates to a method for estimating the state of charge of a lithium battery system based on a Hammerstein model. Background Art

[0002] Accurate state-of-charge (SOC) estimation is a major research topic in lithium-ion batteries. SOC reflects the remaining charge in a battery, and its accurate estimation is crucial for extending battery life and improving energy efficiency. However, the SOC value of lithium-ion batteries cannot be directly measured using sensors. Therefore, accurate SOC estimation is necessary to ensure the reliable operation of battery management systems. Lithium-ion batteries are dynamic, time-varying electrochemical systems with nonlinear behavior and complex internal reaction mechanisms, which pose challenges for system modeling. The internal state of lithium-ion batteries cannot be directly measured using sensors and is highly susceptible to ambient temperature and noise, making accurate SOC estimation difficult. Common SOC estimation methods include open-circuit voltage, equivalent circuit models, and data-driven approaches. The open-circuit voltage method requires the battery to be stationary for an extended period of time, making it difficult to directly apply to engineering applications. While high-precision equivalent circuit models can yield more accurate SOC estimates, increasing model complexity with increasing accuracy increases the complexity of the model, making the computational complexity of the SOC estimate more difficult. Furthermore, numerous factors influence the battery's state during use, making it difficult for models to fully capture these factors. Data-driven approaches break free from the constraints of physical models and build predictive models simply by learning input and output data, directly estimating the battery's SOC.

[0003] The Hammerstein model is a typical nonlinear system with a specific structure. It combines static nonlinear modules and dynamic linear modules. It can effectively describe the static nonlinear and linear dynamic characteristics of lithium battery systems and has important theoretical and practical significance for the accurate estimation of the SOC value of lithium batteries. At present, the data-driven Hammerstein model has been applied to lithium battery modeling, and the OCV-SOC relationship is established using a polynomial model. However, the finite-order polynomial model has difficulty in revealing the characteristics of load current and terminal voltage data. In general, the existing lithium battery SOC estimation still has the following two problems:

[0004] 1. Lithium-ion batteries are dynamic, nonlinear systems with complex internal reaction mechanisms. Using a single neural network or fuzzy clustering method makes it difficult to obtain an accurate mathematical model. Establishing a mathematical model that meets the process characteristics of lithium-ion battery systems is fundamental to solving optimization problems and implementing effective predictions.

[0005] 2. Regarding lithium battery SOC estimation, existing Hammerstein model parameter estimation methods often contain product terms of system parameters, requiring the use of decomposition techniques to separate the parameters, which increases computational complexity and reduces identification accuracy. The challenge is to utilize effective parameter estimation methods to reduce computational complexity and improve system parameter estimation accuracy and robustness. To address these challenges, the present invention designs a lithium battery system SOC estimation method based on the Hammerstein model. Summary of the Invention

[0006] The present invention aims to solve the above problems in the prior art and provides a method for estimating the state of charge of a lithium battery system based on the Hammerstein model.

[0007] The technical solutions adopted in the present invention are:

[0008] A method for estimating the state of charge of a lithium battery system based on the Hammerstein model includes the following steps:

[0009] S1: Analyze the mechanism characteristics of the lithium battery system and construct the second-order RC circuit equation of the lithium battery. Based on this, use the noise transfer function model in the Hammerstein model to describe the dynamic linear module of the Hammerstein model. At the same time, use the adaptive neuro-fuzzy network to describe the static nonlinear module of the Hammerstein model to construct a lithium battery system based on the Hammerstein model.

[0010] S2: Designing a Gaussian signal and inputting the Gaussian signal into the proxy model of the lithium battery system constructed by the adaptive neuro-fuzzy network to obtain a corresponding Gaussian signal output. Based on the input and output data of the Gaussian signal, the covariance function characteristics of the Gaussian signal are utilized to decouple the static nonlinear module and the dynamic linear block of the Hammerstein model;

[0011] S3: The parameters of the noise transfer function model are identified using the least squares method based on the covariance function. The parameters of the adaptive neuro-fuzzy network are solved using the crested porcupine optimization algorithm, and the weights of the adaptive neuro-fuzzy network are updated using the stochastic gradient algorithm with forgetting factor.

[0012] S4: constructing an open circuit voltage and state of charge (OCV-SOC) curve using polynomial fitting, using the output of the Hammerstein model as input to the polynomial fitting, and then obtaining an estimated value of the state of charge (SOC) of the lithium battery system.

[0013] Furthermore, S1 specifically includes the following steps:

[0014] (11) Based on the second-order RC circuit model of lithium batteries and combining its linear and nonlinear characteristics, a lithium battery system based on the Hammerstein model is established;

[0015] (12) In the lithium battery system, the polarization voltages are defined as U1 and U2, and the open circuit voltage is defined as U oc , the terminal voltage is U a , the charging current is I, the polarization resistance is R1, R2, and the polarization capacitance is C1, C2; at the same time, the lithium battery system is regarded as a nonlinear time-varying system;

[0016] (13) Based on the second-order RC circuit model of the lithium battery and Kirchhoff's theorem, a model state equation is established. The model state equation is a mechanism model for describing the mechanism characteristics of the lithium battery system. The mechanism model expression is:

[0017]

[0018] in: They are polarization voltage U1 and U2 and open circuit voltage U oc The rate of change of; R0 is the internal resistance of the battery;

[0019] (14) The expression of the mechanism model is transformed into a frequency domain transfer function through Laplace transform, and U(s) = U a (s)-U oc (s), we get:

[0020]

[0021] Where G(q) is the frequency domain transfer function, s is the complex frequency variable, τ1 = R1C1, τ2 = R2C2, represents the polarization time constant;

[0022] The impulse response invariance method is used to discretize the frequency domain transfer function into a difference equation and convert the continuous time transfer function into a discrete time transfer function:

[0023]

[0024] Where a is a constant, Ts is the sampling time period of the lithium battery system, and q is the backshift operator;

[0025] Finally, the differential equation form of the mechanism model is obtained:

[0026]

[0027] Among them, n1, n2, n3, m1, and m2 are parameters to be identified, respectively representing the numerator and denominator polynomial coefficients of the mechanism model.

[0028] Furthermore, the Hammerstein model is:

[0029] v(t)=f(u(t))

[0030]

[0031] Among them: u(t)=[u1(t),u2(t),…,u m (t)] T The input vector for the Hammerstein model. In a lithium battery system, u(t) represents variables related to the lithium battery input, such as the charging current.

[0032] v(t)=[v1(t),v2(t),…,v m (t)] T It is the intermediate variable vector after passing through the static nonlinear module, which is used to characterize the static nonlinear characteristics of the lithium battery system;

[0033] y(t)=[y1(t),y2(t),…,y n (t)] T is the output vector of the Hammerstein model; in the lithium battery system, y(t) represents the variables related to the lithium battery output, such as the terminal voltage.

[0034] is the denominator polynomial of the dynamic linear module, which is used to describe the dynamic characteristics of the lithium battery system.

[0035] is the numerator polynomial of the dynamic linear module; it works together with the denominator polynomial to describe the dynamic characteristics of the system.

[0036] z -1 represents the unit backshift operator, which is used to formulate the dynamic equations of discrete-time systems.

[0037] n m and n n are the orders of the denominator and numerator polynomials respectively; are predetermined model parameters.

[0038] e(t) is a noise term that represents the unmodeled dynamic or measurement noise in the lithium battery system.

[0039] is the noise transfer function;

[0040] t represents time.

[0041] Furthermore, the adaptive neuro-fuzzy network includes five layers, each of which is represented as:

[0042] (1) First layer: Calculate the Gaussian membership function of the input variable, expressed as:

[0043]

[0044] Among them, c l As the center, σ l is the width, μ l represents the Gaussian membership function, l=1,2,…,L represents the number of fuzzy rules, and u(t) is the input vector of the Hammerstein model;

[0045] (2) The second layer: Calculate the triggering strength of the fuzzy rule, expressed as:

[0046] o2=φ l =μ l (u(1))×μ l (u(2))…×μ l (u(n))

[0047] (3) The third layer: normalize the triggering strength of the fuzzy rules, expressed as:

[0048]

[0049] (4) The fourth layer: Calculate the product of the normalized fuzzy rule strength and weight, expressed as:

[0050]

[0051] Among them, q l is the weight function, w l and s l is the weight;

[0052] (5) The fifth layer: sum the outputs of all fuzzy rules, expressed as:

[0053]

[0054] The final output is:

[0055]

[0056] Among them, v(t) is the intermediate variable vector after passing through the static nonlinear module, which is used to characterize the static nonlinear characteristics of the lithium battery system.

[0057] Furthermore, S2 specifically includes the following steps:

[0058] (1) Designing a zero-mean Gaussian signal u(t) and inputting it into the proxy model to obtain the corresponding output;

[0059] (2) For the static nonlinear module, assuming that the input is a zero-mean Gaussian signal, the product of the autocovariance function of the Gaussian input signal u(t) and the constant matrix is ​​equal to the covariance function of the intermediate variable v(t) and the input u(t), that is:

[0060] R vu (τ) = αR u (τ),

[0061] Among them: α is the constant matrix, τ is the time constant;

[0062] The cross-covariance function matrix Rvu(τ) is defined as:

[0063]

[0064] Autocovariance function matrix R u (τ) is defined as:

[0065]

[0066] Utilizing αR u (τ) instead of R vu (τ), realizing the decoupling of the static nonlinear module and the linear module of the Hammerstein model.

[0067] Furthermore, in S3, the stochastic gradient algorithm with forgetting factor is used to update the weights of the adaptive neuro-fuzzy network. The expression for weight update is:

[0068]

[0069] Where: θ NL (t) represents the adaptive neuro-fuzzy network weight vector after updating at time t;

[0070] θ NL (t-1) represents the adaptive neuro-fuzzy network weight vector at time t-1;

[0071] Φ(t) is the regression vector, specifically defined as:

[0072] Φ(t)=[-y(t-1),…,-y(tn a ),φ1(u(t-1)),…,φ N (u(t-1)),…,φ N (u(tn b ))];

[0073] Among them, y(t) is the output vector of the Hammerstein model, u(t) is the input vector of the Hammerstein model, and n a and n bis the order of the model, φ is the Gaussian membership function, and N is the number of fuzzy rules;

[0074] y(t) represents the output vector of the Hammerstein model, i.e., the variable related to the lithium battery output, such as the terminal voltage;

[0075] r(t) is the variance of the recursive prediction error, and the update formula is:

[0076] r(t)=r(t-1)γ+||Φ(t)|| 2

[0077] Among them, γ is the forgetting factor, which is used to adjust the weight ratio of old data and new data in weight update.

[0078] is the recursive prediction error, defined as:

[0079]

[0080] θ NL is the parameter vector to be estimated, specifically defined as:

[0081]

[0082] Among them, a i and b j is the model parameter, w l and s l is the weight parameter of the adaptive neuro-fuzzy network.

[0083] Furthermore, in S4, the open circuit voltage method is used to fit the OCV-SOC curve by a polynomial, and the predicted output of the Hammerstein model is used as the input of the polynomial fitting to obtain the SOC estimation.

[0084] The present invention has the following beneficial effects:

[0085] 1) The method of the present invention integrates the mechanism characteristics of the lithium battery system and constructs a lithium battery system based on the Hammerstein model, thereby improving the accuracy and generalization ability of the model.

[0086] 2) The method of the present invention utilizes the covariance function characteristics of Gaussian signals in static nonlinear systems to achieve decoupling of the series modules of the Hammerstein model, thereby solving the problem that the intermediate variable information of the Hammerstein model is unmeasurable.

[0087] 3) The method of the present invention utilizes the crown porcupine optimization algorithm to optimize and solve the parameters in the adaptive neural fuzzy network, thereby improving the efficiency, solution accuracy and convergence speed, thereby achieving better performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 This is the second-order RC circuit model diagram of the lithium battery of the present invention

[0089] Figure 2 This is a lithium battery system model diagram based on the Hammerstein model.

[0090] Figure 3 This is the structural diagram of the adaptive neuro-fuzzy network of the present invention.

[0091] Figure 4 This is a flow chart of the identification process of the present invention.

[0092] Figure 5 This is the OCV diagram of the present invention.

[0093] Figure 6 This is the OCV-SOC diagram of the present invention. DETAILED DESCRIPTION

[0094] The present invention will be further described below with reference to the accompanying drawings.

[0095] like Figures 1 to 4 The present invention provides a method for estimating the state of charge of a lithium battery system based on the Hammerstein model, comprising the following steps:

[0096] S1: Analyze the mechanism characteristics of the lithium battery system and construct the second-order RC circuit equation of the lithium battery. Based on this, use the noise transfer function model in the Hammerstein model to describe the dynamic linear module of the Hammerstein model. At the same time, use the adaptive neuro-fuzzy network to describe the static nonlinear module of the Hammerstein model to construct a lithium battery system based on the Hammerstein model.

[0097] S2: Designing a Gaussian signal and inputting the Gaussian signal into the proxy model of the lithium battery system constructed by the adaptive neuro-fuzzy network to obtain a corresponding Gaussian signal output. Based on the input and output data of the Gaussian signal, the covariance function characteristics of the Gaussian signal are utilized to decouple the static nonlinear module and the dynamic linear block of the Hammerstein model;

[0098] S3: The parameters of the noise transfer function model are identified using the least squares method based on the covariance function. The parameters of the adaptive neuro-fuzzy network are solved using the crested porcupine optimization algorithm, and the weights of the adaptive neuro-fuzzy network are updated using the stochastic gradient algorithm with forgetting factor.

[0099] S4: constructing an open circuit voltage and state of charge (OCV-SOC) curve using polynomial fitting, using the output of the Hammerstein model as input to the polynomial fitting, and then obtaining an estimated value of the state of charge (SOC) of the lithium battery system.

[0100] Each step is described in detail below.

[0101] (11) Based on the second-order RC circuit model of lithium batteries and combining its linear and nonlinear characteristics, a lithium battery system based on the Hammerstein model is established;

[0102] (12) In the lithium battery system, the polarization voltages are defined as U1 and U2, and the open circuit voltage is defined as U oc , the terminal voltage is U a , the charging current is I, the polarization resistance is R1, R2, and the polarization capacitance is C1, C2; at the same time, the lithium battery system is regarded as a nonlinear time-varying system;

[0103] (13) Based on the second-order RC circuit model of the lithium battery and Kirchhoff's theorem, a model state equation is established. The model state equation is a mechanism model for describing the mechanism characteristics of the lithium battery system. The mechanism model expression is:

[0104]

[0105] in: They are polarization voltage U1 and U2 and open circuit voltage U oc The rate of change of; R0 is the internal resistance of the battery;

[0106] (14) The expression of the mechanism model is transformed into a frequency domain transfer function through Laplace transform, and U(s) = U a (s)-U oc (s), we get:

[0107]

[0108] Where G(q) is the frequency domain transfer function, s is the complex frequency variable, τ1 = R1C1, τ2 = R2C2, represents the polarization time constant;

[0109] The impulse response invariance method is used to discretize the frequency domain transfer function into a difference equation and convert the continuous time transfer function into a discrete time transfer function:

[0110]

[0111] Where a is a constant, Ts is the sampling time period of the lithium battery system, and q is the backshift operator;

[0112] Finally, the differential equation form of the mechanism model is obtained:

[0113]

[0114] Among them, n1, n2, n3, m1, and m2 are parameters to be identified, respectively representing the numerator and denominator polynomial coefficients of the mechanism model.

[0115] The lithium battery system model is established using the Hammerstein model, which is:

[0116] v(t)=f(u(t))

[0117]

[0118] Among them: u(t)=[u1(t),u2(t),…,u m (t)] T The input vector for the Hammerstein model. In a lithium battery system, u(t) represents variables related to the lithium battery input, such as the charging current.

[0119] v(t)=[v1(t),v2(t),…,v m (t)] T It is the intermediate variable vector after passing through the static nonlinear module, which is used to characterize the static nonlinear characteristics of the lithium battery system;

[0120] y(t)=[y1(t),y2(t),…,y n (t)] T is the output vector of the Hammerstein model; in the lithium battery system, y(t) represents the variables related to the lithium battery output, such as the terminal voltage.

[0121] is the denominator polynomial of the dynamic linear module, which is used to describe the dynamic characteristics of the lithium battery system.

[0122] is the numerator polynomial of the dynamic linear module; it works together with the denominator polynomial to describe the dynamic characteristics of the system.

[0123] z -1 represents the unit backshift operator, which is used to formulate the dynamic equations of discrete-time systems.

[0124] n m and n n are the orders of the denominator and numerator polynomials respectively; are predetermined model parameters.

[0125] e(t) is a noise term that represents the unmodeled dynamic or measurement noise in the lithium battery system.

[0126] is the noise transfer function;

[0127] t represents time.

[0128] In S2, the covariance function characteristics of the Gaussian signal are used to decouple the static nonlinear module and the dynamic linear module of the Hammerstein model, which is specifically expressed as:

[0129] A Gaussian signal is designed, and the corresponding output is obtained by passing the Gaussian signal through an agent model constructed by an adaptive neural fuzzy network, thereby obtaining Gaussian signal input and output data.

[0130] For a static nonlinear module, if the input is a zero-mean Gaussian signal, then the Gaussian input signal u G The product of the autocovariance function of (t) and the constant matrix is ​​equal to the intermediate variable v(t) and the input u G The covariance function of (t) is:

[0131]

[0132] Where: α is the constant matrix, τ is the time constant,

[0133] The cross-covariance function matrix Rvu(τ) is defined as:

[0134]

[0135] Autocovariance function matrix R u (τ) is defined as:

[0136]

[0137] Utilizing αR u (τ) instead of R vu (τ), realizing the decoupling of the static nonlinear module and the linear module of the Hammerstein model.

[0138] In the present invention, u G (t) consists of a set of zero-mean Gaussian signals, namely u G (t)=[u G1 (t),u G2 (t)] T , after the Hammerstein model, the output is y G (t). According to the covariance function characteristics It can be seen that the problem of the unmeasurable intermediate variable information v(t) of the Hammerstein model is solved, that is, using Instead of the unknown covariance matrix This achieves the decoupling of the static nonlinear module and the linear module.

[0139] The adaptive neuro-fuzzy network consists of five layers, each of which is represented as:

[0140] (1) First layer: Calculate the Gaussian membership function of the input variable, expressed as:

[0141]

[0142] Among them, c l As the center, σ l is the width, μ l represents the Gaussian membership function, l=1,2,…,L represents the number of fuzzy rules, and u(t) is the input vector of the Hammerstein model;

[0143] (2) The second layer: Calculate the triggering strength of the fuzzy rule, expressed as:

[0144] o2=φ l =μ l (u(1))×μ l (u(2))…×μ l (u(n))

[0145] (3) The third layer: normalize the triggering strength of the fuzzy rules, expressed as:

[0146]

[0147] (4) The fourth layer: Calculate the product of the normalized fuzzy rule strength and weight, expressed as:

[0148]

[0149] Among them, q l is the weight function, w l and s l is the weight;

[0150] (5) The fifth layer: sum the outputs of all fuzzy rules, expressed as:

[0151]

[0152] The final output is:

[0153]

[0154] Among them, v(t) is the intermediate variable vector after passing through the static nonlinear module, which is used to characterize the static nonlinear characteristics of the lithium battery system.

[0155] In S3: The least squares method based on the covariance function is used to identify the parameters of the autoregressive moving average model, that is, to identify the unknown parameters in M(z) and N(z). The specific calculation is as follows:

[0156] θ1=Rψ1 T(ψ1ψ1 T ) -1

[0157] Where: τ(τ≥n M +n N ) is a constant, where θ1 is the linear block parameter to be identified and R represents the information vector.

[0158]

[0159] Combined with the structure of the adaptive neuro-fuzzy network, the weight parameters in the five-layer network are multiplied and summed in sequence. The stochastic gradient algorithm with forgetting factor is an optimization technique used in machine learning to process non-stationary data streams or time series data. Its core idea is to give higher weights to new data and "gradually forget" old data to adapt to the dynamic changes of model parameters. Therefore, a stochastic gradient algorithm with forgetting factor is constructed to solve and update the weight parameters in the adaptive neuro-fuzzy network. The specific formula is as follows:

[0160]

[0161] Where: θ NL (t) represents the adaptive neuro-fuzzy network weight vector after updating at time t;

[0162] θ NL (t-1) represents the adaptive neuro-fuzzy network weight vector at time t-1;

[0163] Φ(t) is the regression vector, specifically defined as:

[0164] Φ(t)=[-y(t-1),…,-y(tn a ),φ1(u(t-1)),…,φ N (u(t-1)),…,φ N (u(tn b ))];

[0165] Among them, y(t) is the output vector of the Hammerstein model, u(t) is the input vector of the Hammerstein model, and n a and n b is the order of the model, φ is the Gaussian membership function, and N is the number of fuzzy rules;

[0166] y(t) represents the output vector of the Hammerstein model;

[0167] r(t) is the variance of the recursive prediction error, and the update formula is:

[0168] r(t)=r(t-1)γ+||Φ(t)||2

[0169] Among them, γ is the forgetting factor;

[0170] is the recursive prediction error, defined as:

[0171]

[0172] θ NL is the parameter vector to be estimated, specifically defined as:

[0173]

[0174] Among them, a i and b j is the model parameter, w l and s l is the weight parameter of the adaptive neuro-fuzzy network.

[0175] In S4: Based on the identified Hammerstein model, the current of the lithium battery system is used as the input of the Hammerstein model to obtain the corresponding predicted output; on this basis, the SOC of the lithium battery system is predicted using the identified Hammerstein model, that is, an OCV-SOC fitting method is constructed. A ninth-order polynomial is used to obtain the predicted output of the lithium battery voltage from the Hammerstein model, and the open circuit voltage method is used to estimate the lithium battery SOC. The formula is as follows:

[0176] OCV(SOC)=d0+d1SOC+d2SOC 2 +…+d9SOC 9

[0177] Wherein, OCV represents the open circuit voltage of the lithium battery, SOC represents the state of charge of the lithium battery, and d0…d9 represent polynomial parameters.

[0178] In the aforementioned Hammerstein-based lithium battery system state-of-charge estimation method, a lithium battery mechanism function model is constructed. This model not only retains the advantages of the mechanism's physical characteristics, low data requirements, and good generalization, but also introduces an adaptive neuro-fuzzy network. Through this nested structure, the model can improve prediction accuracy even when data is limited or of insufficient quality, while optimizing computational efficiency and enhancing overall performance.

[0179] In the above identification process, Gaussian signals and lithium battery data are used to realize the separate identification of the static nonlinear module and dynamic linear module parameters of the Hammerstein model, which improves the identification accuracy and has good prediction performance.

[0180] The invention is further described below in conjunction with parameters.

[0181] like Figures 1 to 4 As shown, the Hammerstein model identification of the second-order RC circuit model based on the lithium battery is as follows:

[0182] (1) According to the schematic diagram of the second-order RC equivalent circuit model of lithium batteries, the model state equation, i.e., the mechanism model, can be established by Kirchhoff's theorem:

[0183] (2) A five-layer adaptive neuro-fuzzy network is used to establish an agent model of the lithium battery system, where the network initial values ​​are set to S0=0.999, λ=0.5, ρ=1. The agent model is trained using 2800 sets of lithium battery current and voltage data, with 100 iterations. The mean square error obtained from training is the smallest, with an error of 0.38.

[0184] (3) Gaussian signal u in the present invention G There are 3000 groups with a mean of 0 and a variance of 0.4 2 Gaussian signal, the trained proxy model obtains the corresponding output y G The correlation analysis method is used to identify the unknown parameters of the dynamic linear module of the Hammerstein model, and the circuit parameters of the lithium battery second-order circuit model as the mechanism model are obtained, namely [m1, m2, n1, n2, n3] = [-0.1703, -0.5445, -0.940, -0.0239, -0.0423].

[0185] (4) A five-layer adaptive neuro-fuzzy network was used to establish the static nonlinear module of the Hammerstein model. The network model was trained based on the current and voltage data of 2800 sets of lithium batteries. The parameters of the adaptive neuro-fuzzy network, namely the center and width, were solved using the crested porcupine optimization algorithm. The initial parameters were S0 = 0.999, ρ = 1, and λ = 0.01. When the forgetting factor was set to 0.86, the training achieved the lowest mean square error of 0.0096.

[0186] (5) After the Hammerstein model is identified, the output of the Hammerstein model is used to estimate the SOC using the OCV-SOC method, where a ninth-order polynomial is used for fitting, and the parameters are:

[0187]

[0188] like Figure 5As shown in the figure, the present invention uses lithium battery current and voltage data to train the Hammerstein model. The training result is the open circuit voltage (OCV) of the lithium battery. The training achieves the lowest mean square error, 0.0096. The training results clearly demonstrate that the Hammerstein model designed in this invention can achieve high accuracy, providing support for modeling and prediction of lithium battery systems.

[0189] like Figure 6 As shown, based on the original collected current and open circuit voltage data, a real OCV-SOC curve is constructed, and the lithium battery OCV data predicted and output by the Hammerstein model is used as the input of the polynomial model to predict the OCV of the lithium battery. It can be clearly seen from the prediction results that the lithium battery system state of charge estimation method based on the Hammerstein model designed by the present invention can achieve higher prediction accuracy.

[0190] The above description is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principles of the present invention. These improvements should also be regarded as the scope of protection of the present invention.

Claims

1. A method for estimating the state of charge of a lithium battery system based on the Hammerstein model, characterized by: The following steps are involved: S1: Analyze the mechanism characteristics of the lithium battery system and construct the second-order RC circuit equation of the lithium battery. Based on this, use the noise transfer function model in the Hammerstein model to describe the dynamic linear module of the Hammerstein model. At the same time, use the adaptive neuro-fuzzy network to describe the static nonlinear module of the Hammerstein model to construct a lithium battery system based on the Hammerstein model. S2: Designing a Gaussian signal and inputting the Gaussian signal into the proxy model of the lithium battery system constructed by the adaptive neuro-fuzzy network to obtain a corresponding Gaussian signal output. Based on the input and output data of the Gaussian signal, the covariance function characteristics of the Gaussian signal are utilized to decouple the static nonlinear module and the dynamic linear block of the Hammerstein model; S3: The parameters of the noise transfer function model are identified using the least squares method based on the covariance function. The parameters of the adaptive neuro-fuzzy network are solved using the crested porcupine optimization algorithm, and the weights of the adaptive neuro-fuzzy network are updated using the stochastic gradient algorithm with forgetting factor. S4: constructing an open circuit voltage and state of charge (OCV)-SOC curve using polynomial fitting, using the output obtained by the Hammerstein model as input to the polynomial fitting, and then obtaining an estimated value of the state of charge (SOC) of the lithium battery system.

2. The method for estimating the state of charge of a lithium battery system based on the Hammerstein model according to claim 1, wherein: S1 specifically includes the following steps: (11) Based on the second-order RC circuit model of lithium batteries and combining its linear and nonlinear characteristics, a lithium battery system based on the Hammerstein model is established; (12) In the lithium battery system, the polarization voltages are defined as U1 and U2, and the open circuit voltage is defined as U oc , the terminal voltage is U a , the charging current is I, the polarization resistance is R1, R2, and the polarization capacitance is C1, C2; at the same time, the lithium battery system is regarded as a nonlinear time-varying system; (13) Based on the second-order RC circuit model of the lithium battery, the model state equation is established according to Kirchhoff's theorem. The model state equation is the mechanism model used to describe the mechanism characteristics of the lithium battery system. The mechanism model expression is: ， in: 、 、 They are polarization voltage U1 and U2 and open circuit voltage U oc The rate of change of; R0 is the internal resistance of the battery; (14) The expression of the mechanism model is transformed into a frequency domain transfer function through Laplace transform, and U(s)=U a (s)-U oc (s), we get: ， Where G(q) is the frequency domain transfer function, s is the complex frequency variable, τ1=R1C1 and τ2=R2C2 represent the polarization time constants; The impulse response invariance method is used to discretize the frequency domain transfer function into a difference equation and convert the continuous time transfer function into a discrete time transfer function: ， Where a is a constant, Ts is the sampling time period of the lithium battery system, and q is the backshift operator; Finally, the differential equation form of the mechanism model is obtained: ， Among them, n1, n2, n3, m1, and m2 are parameters to be identified, respectively representing the numerator and denominator polynomial coefficients of the mechanism model.

3. The method for estimating the state of charge of a lithium battery system based on the Hammerstein model according to claim 1, wherein: The Hammerstein model is: ， in: Input vector for Hammerstein model; is the intermediate variable vector after passing through the static nonlinear module; is the output vector of the Hammerstein model; is the denominator polynomial of the dynamic linear module; is the numerator polynomial of the dynamic linear module; represents the unit shift operator; and are the orders of the denominator and numerator polynomials respectively; e(t) is the noise term; is the noise transfer function; t represents time.

4. The method for estimating the state of charge of a lithium battery system based on the Hammerstein model according to claim 1, wherein: The adaptive neuro-fuzzy network consists of five layers, each of which is represented as: (1) First layer: Calculate the Gaussian membership function of the input variable, expressed as: ， Among them, c l As the center, σ l is the width, μ l represents the Gaussian membership function, l=1,2,…,L represents the number of fuzzy rules, and u(t) is the input vector of the Hammerstein model; (2) The second layer: Calculate the trigger strength of the fuzzy rule, expressed as: ， (3) The third layer: normalize the triggering strength of the fuzzy rules, expressed as: ， (4) The fourth layer: Calculate the product of the normalized fuzzy rule strength and weight, expressed as: ， Among them, q l is the weight function, w l and s l is the weight; (5) The fifth layer: sum the outputs of all fuzzy rules, expressed as: ， The final output is: ， Among them, v(t) is the intermediate variable vector after passing through the static nonlinear module, which is used to characterize the static nonlinear characteristics of the lithium battery system.

5. The method for estimating the state of charge of a lithium battery system based on the Hammerstein model according to claim 1, wherein: S2 specifically includes the following steps: (1) Design a zero-mean Gaussian signal u(t) and input it into the agent model to obtain the corresponding output; (2) For the static nonlinear module, assuming that the input is a zero-mean Gaussian signal, the product of the autocovariance function of the Gaussian input signal u(t) and the constant matrix is ​​equal to the covariance function of the intermediate variable v(t) and the input u(t), that is: ， in: is a constant matrix, is the time constant; The cross-covariance function matrix Rvu(τ) is defined as: ， Autocovariance function matrix R u (τ) is defined as: ； use replace , realizing the decoupling of the static nonlinear module and linear module of the Hammerstein model.

6. The method for estimating the state of charge of a lithium battery system based on the Hammerstein model according to claim 1, wherein: In S3, the stochastic gradient algorithm with forgetting factor is used to update the weights of the adaptive neuro-fuzzy network. The expression for weight update is: ， in: represents the adaptive neuro-fuzzy network weight vector after updating at time t; represents the weight vector of the adaptive neuro-fuzzy network at time t−1; is the regression vector, specifically defined as: ; Among them, y(t) is the output vector of the Hammerstein model, u(t) is the input vector of the Hammerstein model, and n a and n b is the order of the model, is the Gaussian membership function, N is the number of fuzzy rules; y(t) represents the output vector of the Hammerstein model; r(t) is the variance of the recursive prediction error, and the update formula is: ， Among them, γ is the forgetting factor; is the recursive prediction error, defined as: ， is the parameter vector to be estimated, which is defined as: ， Among them, a i and b j is the model parameter, w l and s l is the weight parameter of the adaptive neuro-fuzzy network.

7. The method for estimating the state of charge of a lithium battery system based on the Hammerstein model according to claim 1, wherein: In S4, the open circuit voltage method is used to fit the OCV-SOC curve by a polynomial, and the predicted output of the Hammerstein model is used as the input of the polynomial fitting to obtain the SOC estimation.

Images