Lithium battery SOC estimation method based on multi-scale physical information neural network

Abstract

The invention relates to a lithium battery SOC estimation method based on a multi-scale physical information neural network, and belongs to the technical field of battery SOC estimation. The method comprises the steps that S1, a first-order RC equivalent circuit model is adopted to describe the dynamic characteristics of a battery, and electrical parameters in the first-order RC equivalent circuit model serve as Mama model output and serve as physical knowledge; s2, performing multi-scale fusion on the voltage features, the current features, the time features and the edge features to obtain new features, and taking the new features as input of a Mama model; s3, constructing a Mama model, wherein the Mama model comprises SSM, a convolutional layer, a linear layer and an element operator; the SSM represents a selective state space model and is formed by combining a structured state space sequence model with a selection mechanism and a scanning module; and S4, estimating the SOC of the lithium battery by using a Mamba model, and improving the model training efficiency by adopting an SPKF adaptive weight. According to the invention, the accuracy and reliability of SOC prediction are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of battery state of charge estimation, and relates to a lithium battery SOC estimation method based on a multi-scale physical information neural network. Background Art

[0002] In the industry chain of new energy vehicles, lithium batteries are widely used in electric vehicles (EV) and hybrid electric vehicles (HEV). However, lithium-ion batteries face many challenges in practical applications, such as aging, increased internal resistance, and temperature changes. These problems not only affect the performance and safety of the battery, but may also cause premature battery failure, thereby affecting the reliability and economy of the overall vehicle.

[0003] To solve these problems, the battery management system (BMS) is particularly important as a key technology. An efficient BMS can monitor various battery parameters in real time, accurately estimate the battery state of charge (SOC), and ensure that the battery operates within a safe range. In order to ensure that the BMS can accurately monitor the working state of the lithium battery, it is particularly important to design an efficient, fast-converging and adaptable lithium-ion battery model. At present, a variety of mainstream battery models have been established, including electrochemical models, data-driven models, and equivalent circuit models (ECMs). Electrochemical models use a series of complex partial differential equations to describe the physical and electrochemical processes inside the battery. Although they can provide a relatively accurate description, their calculation process is complex and time-consuming, and they are difficult to apply to real-time applications that require fast response. In contrast, data-driven models rely on large-scale data sets and use machine learning techniques to construct nonlinear mapping relationships between battery characteristics and SOC and remaining useful life (RUL). Although this method can achieve good results in some cases, it still has limitations in physical interpretability and sensitivity to input noise. To solve this problem, the equivalent circuit model has become an ideal choice for real-time monitoring due to its simple structure based on circuit theory and high computational efficiency.

[0004] With the in-depth study of lithium battery mechanism models, many researchers have begun to combine these mechanism models with deep learning technology. For example, physical information neural networks introduce physical information to uniformly explain the behavior of batteries, improving the interpretability and accuracy of the model. In addition, some new models, such as neural networks based on differential equations, embed the physical laws of batteries into the training process of the network, so that the model can better learn the dynamic characteristics of batteries. The above methods have improved the performance and interpretability of the model to a certain extent, but there are still three problems: First, traditional neural network models are always a huge challenge in nonlinear mode, and they are prone to forgetting the information of early time steps when processing long time series data of battery systems. Secondly, the generalization ability of training at a single scale is not strong, it cannot adapt well to different data distributions, and lacks flexibility to deal with different complex tasks. Finally, fixed weights cannot guarantee that the training reaches the optimal value, and cannot effectively change dynamically to enhance robustness. Summary of the invention

[0005] In view of this, an object of the present invention is to provide a lithium battery SOC estimation method based on a multi-scale physical information neural network, so as to improve the accuracy and reliability of SOC prediction.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A lithium battery SOC estimation method based on a multi-scale physical information neural network specifically includes the following steps:

[0008] S1: A first-order RC equivalent circuit model is used to describe the dynamic characteristics of the battery, and its internal electrical parameters serve as physical knowledge as the output of the Mamba model;

[0009] S2: Multi-scale fusion of voltage features, current features, time features and edge features to obtain new features as input of the Mamba model;

[0010] S3: Construct the Mamba model, including SSM, convolutional layers, linear layers and element operators; SSM stands for Selective State Space Model, which is formed by combining the structured state space sequence model with the selection mechanism and scanning module;

[0011] S4: Use the Mamba model to estimate the SOC of lithium batteries, and use SPKF (nonlinear Sigma point Kalman filter algorithm) adaptive weights to improve model training efficiency.

[0012] Further, in step S2, the voltage feature, current feature, time feature and edge feature are multi-scale fused and expressed by the formula:

[0013]

[0014]

[0015]

[0016] Among them, T1 represents voltage features, T2 represents current features, T3 represents time features, T1′, T2′, T3′ are new voltage, current, and time features after layer-by-layer fusion of features; Cat is a connection operation that combines features of the same dimension; Conv is a convolution operation; BN is a batch normalization operation, which is used to improve the stability of training and accelerate convergence, and reduce internal covariate shift; It is an addition operation of the same dimension.

[0017] Further, in step S3, the structure of the SSM is: the input sequence of the structured state space sequence model Through the implicit potential state Map to The superscripts b, L, D, and N represent the batch size, input length, number of features, and number of hidden channels, respectively, describing The discrete state equation can be written as:

[0018]

[0019] y t =Ch t

[0020] The discretization formula of continuous parameters is as follows:

[0021] Δ t =τ Δ (Parameter)

[0022]

[0023]

[0024] Among them, x t ,h t ,y t represents the input, hidden state and output of t=1,2,...,L, where t represents the discrete time length; represents the state transfer matrix, and Represent the mapping matrices from input to state and from state to output respectively; is the discretization parameter of (Δ, A, B), using zero-order hold (ZOH); τ Δis the softplus activation function; I represents the identity matrix; Parameter represents the learnable folding parameter; the structured state space sequence model follows the convolution calculation, and its convolution process can be defined as K=(k0,...,k t ) is the convolution kernel, where The equivalence of convolution and recurrence enables sequences to be trained in parallel with quadratic complexity, facilitating regression mapping by efficiently decoupling computational steps.

[0025] Further, in step S3, the selection mechanism is as follows:

[0026]

[0027] y t =C t h t

[0028] Δ t =τ Δ (Parameter+s Δ (x t ))=softplus(Linear(x t ))

[0029]

[0030] Among them, τ Δ is the softplus activation function; s Δ is a linear function; given an input x t =[T1′ T2′ T3′] T In this case, each layer can selectively capture important features based on the dependencies between the sequences.

[0031] Furthermore, in step S3, the information transmission of each layer of the Mamba model is defined as:

[0032] x′ t =SilU(Conv1D(Linear(x t ))),z t =SilU(Linear(x t ))

[0033]

[0034] y′ t =LayerNorm(y t +x)

[0035]

[0036] in, is element-wise multiplication.

[0037] Further, in step S4, the Mamba model is used to estimate the SOC of the lithium battery, specifically including: assuming that the ohmic internal resistance R0, the polarization resistance R1 and the polarization capacitance C1 at the specified temperature remain unchanged, the first-order RC equivalent circuit equation of the lithium battery EMC model is discretized, and the following equation can be obtained:

[0038]

[0039] U L [k]=h(SOC[k])-R1·I1[k]-R0·I[k]

[0040] Where I1 is the current through R1; η is the charging conversion efficiency; Q is the rated capacity of the battery; Δt is the sampling interval; h(SOC[k]) is the open circuit voltage; U L [k] represents the output voltage at time k; I[k] represents the input current at time k; k represents time discretization; τ1=R1C1 represents the RC time constant; the Mamba model establishes a dynamic model by identifying a specific PDE (partial differential equation) error. The PDE error ζ of the SOC PDE It can be expressed by the following formula:

[0041]

[0042] In order to reflect the impact on SOC according to circuit parameters, the weight value is used to change the voltage loss function to affect the updated network. The resistance and capacitance are brought into SPKF to obtain the weights, and the state equation and observation equation are established:

[0043] x k+1 =A k x k +B k (u k +w k )

[0044] Among them, x k =[SOC k U k ] is the state vector, SOC k represents the SOC value at time k, U k represents the output voltage value at time k; u k =I k is the input, I k represents the current at time k; w k is the state noise; is the state transfer matrix, and the elements on the diagonal represent the linear evolution of SOC and OCV (open circuit voltage) over time; is the input matrix used to transform the input u k and noise w k Mapped to the state x at the next moment k+1 ;

[0045] y k =C k x k +D k u k +v k

[0046] Among them, y k =U k is the observed value; v k is the observation noise; is the observation matrix, which reflects the state variables SOC and OCV on the observation y k The degree of influence; D k =-R0 is the input matrix;

[0047] Adaptive weights are calculated using nonlinear mapping based on the observed values, and the Sigmoid function is used for nonlinear mapping:

[0048]

[0049] Among them, k is a parameter that controls the steepness of the function, and y mid is an observed median value; once the weight w(y) is calculated, the weighted MSE can be calculated as follows:

[0050]

[0051] in, is the voltage loss function, y i is the observed predicted value, y true is the true value of voltage; the gradient optimization differential equation, the SOC loss function can be expressed as:

[0052]

[0053] Among them, SOC k and SOC k+1 They are the estimated values ​​of SOC at the upper and lower moments respectively; the final total loss function is obtained after weighting the values ​​of the above two loss functions

[0054]

[0055] Where N is the number of samples; M is the differential; α is the voltage constraint factor; the Adam optimizer is used to calculate the gradient of the loss function relative to θ, which can be obtained by the following formula:

[0056]

[0057] Loss function g t The first-order and second-order moment estimates of Adam are passed in for deviation correction, and the weight W between the output layer and the hidden layer is updated with reverse gradient. t and deviation b t ; For the propagation gradient, W t 、b t The update formula is as follows:

[0058]

[0059]

[0060]

[0061]

[0062] Among them, β1 and β2 are the first-order moment and second-order moment estimates m respectively. t 、v t The decay rate of Indicates m t 、v t is the bias correction; ξ is the network learning rate; ∈ is a small constant to prevent the algorithm from dividing by zero.

[0063] The beneficial effects of the present invention are as follows: first, the present invention combines the laws of physics with deep learning, fully utilizes the mechanism model of lithium batteries, and effectively improves the accuracy of state estimation. By introducing the electrochemical characteristics and physical behavior of the battery, the model can more accurately reflect the true state of the battery under different working conditions, thereby improving the reliability of the prediction. Secondly, the Mamba model uses multi-scale combined features to improve the accuracy of the estimation. In addition, Mamba significantly enhances the ability to explain the internal state of the lithium battery by embedding physical constraints. At the same time, the network output adapts the weight of the voltage loss according to the SPKF algorithm to achieve the best training effect. Mamba can effectively handle the time-varying characteristics of the lithium battery system and the mutual influence between multiple variables, thereby providing more accurate state estimation in practical applications. Finally, the present invention has good practicality and operability, and can be easily integrated into the existing battery management system to provide strong support for real-time monitoring and prediction.

[0064] In summary, the method of the present invention shows significant advantages in the task of lithium battery state estimation, has good application prospects, and provides important technical support for improving the safety and reliability of lithium batteries.

[0065] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0067] Figure 1 It is a schematic diagram of the first-order RC equivalent circuit model;

[0068] Figure 2 This is a schematic diagram of the Mamba model structure framework;

[0069] Figure 3 This is a flow chart of the lithium battery SOC estimation method based on the Mamba model. DETAILED DESCRIPTION

[0070] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0071] See also Figure 1 to Figure 3 The present invention provides a lithium battery SOC estimation method based on a multi-scale physical information neural network. First, a lithium-ion battery modeling method is proposed. The first-order RC equivalent circuit model describes the dynamic characteristics of the battery through a simple circuit structure, and its internal electrical parameters serve as physical knowledge as the output of the neural network. Secondly, it is proposed to combine the model features using multiple scales, and analyze the application of state space equations in deep learning, especially the Mamba model derived from the state space. In addition, SPKF adaptive weights are proposed to improve the network training efficiency. Finally, based on the selective attention mechanism and characteristics of the Mamba model plus the battery mechanism model, a method for estimating the internal state of the lithium battery is proposed. The data input current, voltage and time, through the dynamic state space and mechanism constraints to more accurately capture the changes in the SOC of the lithium battery.

[0072] 1) First-order RC electrochemical equivalent circuit model

[0073] The first-order RC equivalent circuit model is mainly composed of a voltage source, an ohmic internal resistance and a first-order RC network. The output of the voltage source can be approximated as an open-circuit voltage, and there is nonlinearity between it and the SOC. The ohmic internal resistance reflects the transient response capability of the battery and characterizes the voltage fluctuation of the battery under different loads. The first-order RC network is used to capture the dynamic characteristics of the battery and help analyze the performance of the battery under different working conditions. The simplified partial differential equation of the EMC of lithium batteries can be defined as the following formula:

[0074]

[0075] Where, η is the charge conversion efficiency; I(t) is the applied current of the battery, discharge current is positive and charge current is negative; Q is the rated capacity of the battery; R0 is the ohmic internal resistance; R1 is the polarization resistance; C1 is the polarization capacitance; I1(t), U1(t) are the applied current and voltage of R1; h(*) is the OCV-SOC curve function.

[0076] 2) Multi-scale feature fusion

[0077] The voltage, circuit and time information extracted from the database are often separated from each other. In the initial data processing, the underlying data features are not interconnected and contain more detailed information such as timing. In order to ensure that each layer has sufficient feature information and the accuracy of the target main features, multi-scale feature fusion can be used to achieve the combination of the first layer feature, the second and third layer features and the edge features, so as to improve the clarity of the significant SOC target.

[0078] There are three main characteristics at the input, namely voltage, current and time, which are represented by T i {i=1,2,3}, where T1 represents voltage feature, T2 represents current feature, and T3 represents time feature. The edge random feature E is fused with other features to obtain a new feature, and its formula flow is expressed as follows:

[0079]

[0080]

[0081]

[0082] Among them, T1′, T2′, T3′ are the new voltage, current, and time features after layer-by-layer fusion of features; Cat is a connection operation that combines features of the same dimension; Conv is a convolution operation; BN improves the stability of training and accelerates convergence, reducing internal covariate shift. Its BN formula can be expressed as follows:

[0083]

[0084]

[0085] Normalize the input using the calculated mean and variance:

[0086]

[0087] The normalized output is linearly transformed to obtain the output:

[0088]

[0089] Where m is the batch size, x i is the i-th sample in the current batch. μ and σ are the mean and variance, respectively. ∈ is a small constant used to prevent division by zero. γ and β are learnable parameters for scaling and translation, respectively.

[0090] 3) Selective State Space Model (SSM)

[0091] The input sequence of the structured state-space sequence model (S4) is Through the implicit potential state Map to describe The discrete state equation can be written as:

[0092]

[0093] y t =Ch t (10)

[0094] The discretization formula of continuous parameters is as follows:

[0095] Δ t =τ Δ (Parameter) (11)

[0096]

[0097]

[0098] Among them, x t ,h t ,y t represents the input, hidden state and output of t=1,2,...,L; represents the state transfer matrix, and Represent the mapping matrices from input to state and from state to output respectively; is the discretization parameter of (Δ, A, B), using zero-order hold (ZOH); is the step size; Parameter represents the learnable folding parameter. The structured state space sequence model follows the convolution calculation, and its convolution process can be defined as K=(k0,...,k t ) is the convolution kernel, where The equivalence of convolution and recurrence enables sequences to be trained in parallel with quadratic complexity, facilitating regression mapping by efficiently decoupling computational steps.

[0099] However, the state matrix of the structured state space sequence model does not change with the input, and it is impossible to selectively focus on different features (tokens) according to their importance. The Mamba model combines the structured state space sequence model with the selection mechanism and scanning module to form a selective state space model (SSM), which realizes the selection of time series input data by the state space. The selection mechanism is as follows:

[0100]

[0101] y t =C t h t (15)

[0102] Δ t =τ Δ (Parameter+s Δ (x t ))=softplus(Linear(x t )) (16)

[0103]

[0104] Among them, τ Δ is the softplus activation function; s Δ is a linear function. The state equation of the Mamba model has the same structure as equations (9) and (10), except that the matrix dimension has changed. Given an input x t =[T1′ T2′ T3′] T In this case, each layer can selectively capture important features based on the dependencies between the sequences. The entire neural network (Mamba model) contains SSM blocks, convolutional layers, linear layers, and element operators. The information transfer between each layer can be defined as:

[0105] x′ t =SilU(Conv1D(Linear(x t ))),z t =SilU(Linear(x t )) (18)

[0106]

[0107] y′ t =LayerNorm(y t +x) (20)

[0108] in, is element multiplication. At the same time, since the state matrix becomes dynamic, the space cannot be calculated using the assumed solid core and can only be represented recursively. Therefore, Mamba abandons the convolution operation and uses the new operation process of formula (21), which satisfies the commutative law and associative law.

[0109]

[0110] 4) Lithium battery SOC estimation based on Mamba model

[0111] Assuming that R0, R1 and C1 remain unchanged at a specified temperature, the first-order RC equivalent circuit equation of the lithium battery EMC model is discretized to obtain the following equation:

[0112]

[0113] U L [k]=h(SOC[k])-R1·I1[k]-R0·I[k] (23)

[0114] Where I1 is the current through R1; Δt is the sampling interval; h(SOC[k]) is the open circuit voltage; k represents the time discretization; τ1=R1C1 represents the RC time constant. Mamba establishes a dynamic model by identifying specific PDE errors. The PDE error of SOC can be expressed as follows:

[0115]

[0116] In order to reflect the impact on SOC according to circuit parameters, the weight value is used to change the voltage loss function to affect the updated network. The resistance and capacitance are brought into SPKF to obtain the weights, and the state equation and observation equation are established:

[0117] x k+1 =A k x k +B k (u k +w k ) (25)

[0118] Among them, x k =[SOC k U k ] is the state vector; u k =I kis the input; w k is the state noise; is the state transfer matrix, and the elements on the diagonal represent the linear evolution of SOC and V with time; is the input matrix used to transform the input u k and noise w k Mapped to the state x at the next moment k+1 .

[0119] y k =C k x k +D k u k +v k (26)

[0120] Among them, y k =U k is the observed value; v k is the observation noise; is the observation matrix, which reflects the state variables SOC and V on the observation y k The degree of influence; D k =-R0 is the input matrix.

[0121] Adaptive weights are calculated using nonlinear mapping based on the observed values, and the Sigmoid function is used for nonlinear mapping:

[0122]

[0123] Among them, k is a parameter that controls the steepness of the function, and y mid is the median value of an observation. Once the weight w(y) is calculated, the weighted MSE can be calculated as follows:

[0124]

[0125] where y i is the observed predicted value, y true is the true value of voltage. Gradient optimization differential equation, SOC loss function can be expressed as:

[0126]

[0127] Among them, SOC k and SOC k+1 are the estimated values ​​of SOC at the upper and lower moments respectively. After weighting the values ​​of the above two loss functions, we get the final total loss function, that is:

[0128]

[0129] Where N is the number of samples; M is the differential; α is the voltage constraint factor. The gradient of the loss function relative to θ using the Adam optimizer can be obtained by the following formula:

[0130]

[0131] Loss function g t The first-order and second-order moment estimates of Adam are passed in for deviation correction, and the weight W between the output layer and the hidden layer is updated with reverse gradient. t and deviation b t For the propagation gradient, W t 、b t The update formula is as follows:

[0132]

[0133]

[0134]

[0135]

[0136] Among them, β1 and β2 are the first-order moment and second-order moment estimates m t 、v t The decay rate of Indicates m t 、v t is the bias correction; ξ is the network learning rate; ∈ is a small constant to prevent the algorithm from dividing by zero.

[0137] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A lithium battery SOC estimation method based on a multi-scale physical information neural network, characterized in that: The method specifically comprises the following steps: S1: A first-order RC equivalent circuit model is used to describe the dynamic characteristics of the battery, and its internal electrical parameters serve as physical knowledge as the output of the Mamba model; S2: Multi-scale fusion of voltage features, current features, time features and edge features to obtain new features as input of the Mamba model; S3: Construct the Mamba model, including SSM, convolutional layers, linear layers and element operators; SSM stands for Selective State Space Model, which is formed by combining the structured state space sequence model with the selection mechanism and scanning module; S4: Use the Mamba model to estimate the SOC of lithium batteries, and use SPKF adaptive weights to improve model training efficiency.

2. The lithium battery SOC estimation method according to claim 1, characterized in that: In step S2, the multi-scale fusion of voltage features, current features, time features and edge features is expressed by the formula: Among them, T1 represents voltage features, T2 represents current features, T3 represents time features, T1′, T2′, T3′ are new voltage, current, and time features after layer-by-layer fusion of features; Cat is a connection operation that combines features of the same dimension; Conv is a convolution operation; BN is a batch normalization operation; It is an addition operation of the same dimension.

3. The lithium battery SOC estimation method according to claim 1, characterized in that: In step S3, the structure of SSM is: the input sequence of the structured state space sequence model Through the implicit potential state Map to The superscripts b, L, D, and N represent the batch size, input length, number of features, and number of hidden channels, respectively, describing The discrete state equation is written as: the t =Ch t The discretization formula of continuous parameters is as follows: D t =t Δ (Parameter) Among them, x t ,h t ,y t represents the input, hidden state and output of t=1,2,...,L, where t represents the discrete time length; represents the state transfer matrix, and Represent the mapping matrices from input to state and from state to output respectively; is the discretization parameter of (Δ, A, B); is the step length; τ Δ is the softplus activation function; I represents the identity matrix; Parameter represents the learnable folding parameter; the structured state space sequence model follows the convolution calculation, and its convolution process is defined as K=(k0,...,k t ) is the convolution kernel, where The equivalence of convolution and recurrence enables sequences to be trained in parallel with quadratic complexity, facilitating regression mapping by efficiently decoupling computational steps.

4. The lithium battery SOC estimation method according to claim 3, characterized in that: In step S3, the selection mechanism is as follows: y t =C t h t Δ t =τ Δ (Parameters+s Δ (x t ))=softplus(Linear(x t )) Among them, τ Δ is the softplus activation function; s Δ is a linear function; given an input x t =[T1′ T2′ T3′] T In this case, each layer selectively captures important features based on the dependencies between the sequences.

5. The lithium battery SOC estimation method according to claim 4, characterized in that: In step S3, the information transmission of each layer of the Mamba model is defined as: x′ t =SilU(Conv1D(Linear(x t ))),from t =SilU(Linear(x t )) y′ t =LayerNorm(y t +x) in, is element-wise multiplication.

6. The lithium battery SOC estimation method according to claim 5, characterized in that: In step S4, the Mamba model is used to estimate the SOC of the lithium battery, specifically including: assuming that the ohmic internal resistance R0, the polarization resistance R1 and the polarization capacitance C1 at the specified temperature remain unchanged, the first-order RC equivalent circuit equation of the lithium battery EMC model is discretized to obtain the following equation: U L [k]=h(SOC[k])-R1·I1[k]-R0·I[k] Where I1 is the current through R1; η is the charging conversion efficiency; Q is the rated capacity of the battery; Δt is the sampling interval; h(SOC[k]) is the open circuit voltage; U L [k] represents the output voltage at time k; I[k] represents the input current at time k; k represents time discretization; τ1=R1C1 represents the RC time constant; the Mamba model establishes a dynamic model by identifying a specific PDE error, and the PDE error ζ of the SOC PDE It is expressed by the following formula: Substitute resistance and capacitance into SPKF to obtain weights and establish the state equation and observation equation: x k+1 =A k x k +B k (u k +w k ) Among them, x k =[SOC k U k ] is the state vector, SOC k represents the SOC value at time k, U k represents the output voltage value at time k; u k =I k is the input, I k represents the current at time k; w k is the state noise; is the state transfer matrix, and the elements on the diagonal represent the linear evolution of SOC and OCV with time; is the input matrix used to transform the input u k and noise w k Mapped to the state x at the next moment k+1 ; y k =C k x k +D k u k +v k Among them, y k =U k is the observed value; v k is the observation noise; is the observation matrix, which reflects the state variables SOC and OCV on the observation y k The degree of influence; D k =-R0 is the input matrix; Adaptive weights are calculated using nonlinear mapping based on the observed values, and the Sigmoid function is used for nonlinear mapping: Among them, k is a parameter that controls the steepness of the function, and y mid is an observed median value; once the weight w(y) is calculated, the weighted MSE can be calculated as follows: in, is the voltage loss function, y i is the observed predicted value, y true is the true value of voltage; the gradient optimization differential equation, the SOC loss function can be expressed as: Among them, SOC k and SOC k+1 They are the estimated values ​​of SOC at the upper and lower moments respectively; the final total loss function is obtained after weighting the values ​​of the above two loss functions Where N is the number of samples; M is the differential; α is the voltage constraint factor; the Adam optimizer is used to calculate the gradient of the loss function relative to θ, which is obtained by the following formula: Loss function g t The first-order and second-order moment estimates of Adam are passed in for deviation correction, and the weight W between the output layer and the hidden layer is updated with reverse gradient. t and deviation b t ; For the propagation gradient, W t , b t The update formula is as follows: Among them, β1 and β2 are the first-order moment and second-order moment estimates m respectively. t 、v t The decay rate of Indicates m t 、v t is the bias correction; ξ is the network learning rate; ∈ is a small constant.

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