Lithium battery cross-working-condition multi-state joint estimation method only needing single identification and not needing offline OCV data
By combining a fractional-order physical model and an adaptive forgetting factor recursive least squares method with the quasi-static OCV assumption, an adaptive fractional-order model is constructed. This solves the problems of strong coupling and high cost in lithium battery state estimation, achieves high-precision joint estimation of SOC and capacity, reduces development costs, and improves the model's generalization ability and robustness.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- KUNMING UNIV OF SCI & TECH
- Filing Date
- 2026-01-29
- Publication Date
- 2026-05-12
AI Technical Summary
Existing lithium battery state estimation technologies suffer from problems such as strong coupling between SOC and capacity, long development cycles, high calibration costs, and difficulty in achieving both model generalization ability and accuracy. In particular, it is difficult to achieve high-precision estimation under dynamic operating conditions and wide temperature ranges.
An adaptive fractional-order model is constructed by combining a fractional-order physical model with an adaptive forgetting factor recursive least squares method and a quasi-static OCV assumption. The joint estimation of lithium battery SOC and capacity is achieved through a linear migration mechanism and a sparse information injection mechanism, and real-time correction is performed using a particle filter algorithm.
It achieves the elimination of repeated parameter identification and offline OCV experiments, significantly reducing development costs, improving the estimation accuracy and stability of the model under dynamic conditions, isolating the erosion of slowly changing parameters by high-frequency noise, and realizing high-precision decoupling of multiple states.
Smart Images
Figure CN122017582A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of lithium-ion battery technology, and specifically to a method for joint estimation of lithium batteries across multiple operating conditions and states that requires only a single identification and does not require offline OCV data. Background Technology With the escalating global energy crisis and increasing environmental awareness, electric vehicles (EVs) and hybrid electric vehicles (HEVs) have become the main development direction of the automotive industry. Lithium-ion batteries, with their advantages of high energy density, long cycle life, and low self-discharge rate, have become the preferred power source for electric vehicles. The Battery Management System (BMS), as a core component ensuring the safe and efficient operation of batteries, has one of its key tasks: real-time and accurate monitoring of the battery's state, especially its state of charge (SOC), state of health (SOH), and capacity. These parameters are not only the foundation of energy management but also crucial for extending battery life.
[0002] However, existing battery state estimation techniques still face several bottlenecks in practical applications: First, there is a complex and strong coupling relationship between SOC (state of charge) and capacity (slow-changing parameter), which traditional methods struggle to decouple effectively, leading to rapid error accumulation through ampere-hour integration. Second, high-precision modeling typically relies on cumbersome Hybrid Pulse Power Characterization (HPPC) testing and parameter identification, resulting in long development cycles, high calibration costs, and a lack of flexibility. Furthermore, existing fixed-order fractional-order models struggle to accurately capture the nonlinear dispersion characteristics of batteries under dynamic operating conditions and wide temperature ranges, making it difficult to simultaneously achieve model generalization ability and estimation accuracy. Therefore, developing a joint estimation method that eliminates the need for repeated parameter identification and offline open circuit voltage (OCV) testing and enables high-precision decoupling across multiple states is particularly important. Summary of the Invention
[0003] To address the aforementioned technical problems, this invention provides a method for joint estimation of lithium batteries across multiple operating conditions and states that requires only a single identification and does not require offline OCV data.
[0004] To achieve the above technology, the steps include: S1. Experimental data acquisition of lithium batteries under baseline conditions; S2. Construct the fractional-order physical model to be identified: Establish an equivalent circuit model that includes fractional-order impedance characteristics; S3. Parameter and OCV synchronous identification based on quasi-static assumption: The quasi-static OCV assumption is introduced to reconstruct the nonlinear voltage response into a linear regression form. The impedance parameters and OCV curves are identified online using the Adaptive Forgetting Factor Recursive Least Squares (AFFRLS) method, and then the analytical mapping relationship between the model parameters and SOC under the reference state is established. S4. Construct an adaptive fractional-order model that integrates linear migration mechanism and internal resistance anchoring characteristics: Based on the benchmark analytical mapping relationship, a linear migration factor is introduced to perform first-order approximate compensation for the nonlinear drift of model parameters under the coupling effects of multiple stresses such as temperature, aging, and pressure. A dynamic mapping mechanism from the benchmark parameter library to the current multi-stress condition is constructed to obtain adaptive parameters that implicitly contain multi-physics coupling information. Within this architecture, a reference SOH characterization based on physical characteristics is established, and an adaptive fractional-order model containing capacity evolution is established in combination with an adaptive correction factor to achieve an integrated description of model parameter adaptation and capacity state observation. S5. A joint estimation framework for lithium battery SOC and capacity based on a unified augmented state space and sparse information injection mechanism: Addressing the strong rigid coupling characteristics of lithium batteries, a unified augmented state vector containing SOC, polarization voltage, and capacity correction factors is constructed. A time-varying noise covariance matrix is designed to inject sparse information, achieving decoupled evolution of fast-changing states and slow-changing parameters. Based on this, a particle filter algorithm with a risk-sensitive criterion is introduced to estimate the capacity state in the long time domain. The SOC is then corrected in real time using the voltage residual in the short time domain and the updated capacity in the long time domain, ultimately achieving a joint estimation of lithium battery SOC and capacity under the influence of multiple stress couplings.
[0005] As a preferred technical solution of the present invention, in step S1, the environmental conditions are set as follows: the ambient temperature is 25°C and the battery is not subjected to external pressure; the data collected includes the changes in the battery's current and voltage over time.
[0006] As a preferred embodiment of the present invention, in step S2, the fractional-order physical model to be identified is a first-order RC fractional-order equivalent circuit model, and in order to ensure the convergence of the initial identification process, the fractional-order is first defined. The value is fixed at 0.9, and the expression is as follows: In the formula, for The current lithium battery terminal voltage For fractional differential operators, The open-circuit voltage associated with the current state of charge (SOC). Polarization voltage, For ohmic internal resistance, For polarization internal resistance, For current, is the generalized capacitive coefficient of the constant-phase element CPE.
[0007] As a preferred embodiment of the present invention, the step of parameter synchronization identification with OCV based on the quasi-static assumption in S3 includes: S3.1. Use GL to define the discretized fractional derivative, and assume that within the preset sampling interval... The nonlinear model is reconstructed into a linear regression equation: In the formula, These are terminal voltage observations. For the data regression vector, Let be the parameter vector to be identified. This represents the prediction error; S3.2. Use the AFFRLS algorithm to identify the model parameters and OCV under the baseline state online, based on the prediction error. The forgetting factor is adjusted in real time to balance parameter tracking speed and noise suppression capability; S3.3. A baseline analytical mapping relationship between model parameters and SOC is constructed using 5th-order polynomial fitting: In the formula, Let be the ohmic internal resistance as a function of SOC. Let be the polarization resistance as a function of SOC. Let be the generalized capacitive coefficient as a function of SOC. The open-circuit voltage associated with the current state of charge (SOC). , , and These represent the fitting coefficients for each item, obtained through AFFRLS identification and fitting.
[0008] As a preferred embodiment of the present invention, the forgetting factor in S3.2 The update formula is as follows: In the formula, The preset minimum forgetting factor, For prediction error, As the baseline error threshold, It is a non-linear activation function used to map the standardized error to the adjustment range of the forgetting factor.
[0009] As a preferred embodiment of the present invention, the linear migration mechanism in S4 is expressed as follows: In the formula, To adapt the model parameters to the current specific working conditions, The first and second impedance migration factors are, These are the model parameters under the baseline condition; It is the SOC after migration correction. For a rough SOC under the influence of multiple stress coupling, The scaling and translation factors for SOC; the model parameters in the reference state. Including: Ohmic internal resistance Polarization internal resistance Generalized capacitive coefficient of constant phase element Open circuit voltage and fractional order .
[0010] As a preferred technical solution of the present invention, in step S4, the capacity observation equation is constructed based on the internal resistance anchoring characteristic, and the steps include: S4.1 Constructing a reference system based on the physical characteristics of internal resistance. : In the formula, This is a reference health status estimate based on internal resistance; This is the internal resistance threshold at the end of the battery's lifespan. The internal resistance is ohmic; This is the nominal internal resistance of the battery at the time of manufacture. S4.2 Introduce an adaptive correction layer to establish the final SOH and capacity observation equations: In the formula, This is the final corrected estimate of SOH. and These are the scaling correction factor and offset correction factor based on terminal voltage residual correction, respectively; This represents the actual usable capacity. This refers to the standard rated capacity of the battery.
[0011] As a preferred embodiment of the present invention, in step S4, the specific set of parameter evolution equations for constructing the adaptive fractional-order model that integrates the linear migration mechanism and the internal resistance anchoring characteristic is as follows: In the formula, , indicates the coefficient term, superscript This represents the adaptive model parameters after correction via the transfer mechanism. Used to describe the impact of multiple stress coupling conditions on model parameters. For the baseline parameter mapping function; To obtain a rough SOC value under the influence of multiple stress coupling, a linear transformation is performed. Mapping to the domain of the benchmark model, thereby achieving cross-condition parameter adaptation without additional offline calibration; To adapt the fractional order, As the baseline fractional order, and These are the ohmic resistance and polarization resistance after migration, respectively. The generalized tolerance coefficient after migration. The open-circuit voltage after migration. To migrate the output of the back-end voltage model, The polarization voltage after migration, This represents the current.
[0012] As a preferred embodiment of the present invention, step S5 includes: S5.1 Initial Particle Generation: In the formula, Let be the prior probability density. For the particles at the initial moment, The total number of particles, Index of the total number of particles; It is the Dirac function; For the first An initial particle, For fast-variant subvectors, For slow-varying subvectors, It follows a Gaussian distribution. This is the initial SOC estimate. and These are the initial error covariance matrices for the fast-changing and slow-changing parameter subvectors, respectively; S5.2 Augmented Particle Initialization: Based on a unified framework, this method captures the cross-scale coupling characteristics between different states of a lithium battery and constructs a unified augmented state vector. : In the formula, Discrete time SOC at that time Discrete time Fractional polarization voltage at time Used to represent fast time scales. Used to describe slow time scales; S5.3 Sparse Information Injection and State Evolution: Based on the unified augmented state space equation, a sparse information injection mechanism is introduced to construct a state evolution equation containing a time-varying control matrix: In the formula, For the first The prior predicted state of each particle It is a nonlinear state transition function. For system input, To accommodate the process noise of the sparse injection mechanism, the noise should have a mean of 0 and a covariance of 0. Gaussian distribution; The noise covariance matrix for the dynamic process is used to control the evolution bandwidth of states in different dimensions, and is defined as follows: In the formula, and The process noise variances for SOC and polarization voltage are respectively; and To correct the process noise variance of the parameters; It is a very small positive number. For macro-level update cycles; S5.4, Perform risk-sensitive weight update: Calculate the particle prediction terminal voltage and introduce an exponential cost function to calculate the particle weights, amplifying the differences between superior and inferior particles: In the formula, For the first The non-normalized weights of each particle As a risk-sensitive factor, This is the measured terminal voltage. For the first Predicted terminal voltage of each particle; S5.5, Weight Normalization: In the formula, The normalized weights, Non-normalized weights; S5.6 Perform particle resampling and state estimation: Resample the prior set according to the particle weights to suppress particle degradation, and use weighted summation to calculate the posterior estimate of the augmented state: In the formula, This is the optimal estimation vector that includes SOC and capacity correction factor.
[0013] As a preferred embodiment of the present invention, the joint estimation framework of S5 corrects the current actual available capacity through the correction factor of the filtered output, and injects it as a feedback variable into the ampere-hour integral equation to perform closed-loop correction of the coarse SOC. Its mathematical expression is as follows: In the formula, For the estimated current available capacity, This refers to the battery's nominal rated capacity. The mean of the scaling correction factor. As a reference SOH based on physical characteristics, This represents the mean of the offset correction factor. for Rough SOC at that time For Coulomb efficiency, for Load current at that time The sampling time interval; The coarse SOC is adaptively scaled and translated using the linear migration parameters estimated by particle filtering, and a posteriori weighted calculation is performed based on the particle weights to obtain the final SOC estimate, which is mathematically expressed as follows: In the formula, This represents the true SOC value based on capacity correction under the influence of multiple stress coupling. for The state of the first particle. for The state of the second particle at that time.
[0014] Beneficial effects of the present invention 1. No need for repeated parameter identification and offline OCV experiments, significantly reducing development costs: The single parameter identification method based on the quasi-static OCV assumption proposed in this invention only requires experimental data from one lithium battery baseline state (i.e., a brand new lithium battery at a temperature of 25°C and without external pressure) to establish a parameter model for the entire life cycle. This completely eliminates the tedious process of repeatedly conducting parameter identification and offline OCV experiments under different conditions, and greatly shortens the development cycle of BMS.
[0015] 2. Strong model generalization ability and excellent robustness: The adaptive fractional-order model, which integrates a linear transfer mechanism, can dynamically adjust the fractional-order order and parameters according to actual working conditions, significantly improving the voltage tracking accuracy and state estimation stability of the model under dynamic current impact, drastic changes in ambient temperature, and the later stage of battery aging.
[0016] 3. High accuracy of multi-state decoupling and strong anti-interference capability: By constructing a unified augmented state space and introducing a sparse information injection mechanism, this invention physically isolates the erosion of slowly changing capacity parameters by high-frequency voltage noise, effectively blocks the bidirectional transmission of SOC and capacity estimation errors, and realizes high-precision multi-state joint estimation. Attached Figure Description
[0017] Figure 1 This is a flowchart of the process framework of the present invention; Figure 2 This is a schematic diagram of the first-order fractional-order equivalent circuit model of the present invention; Figure 3 This is a schematic diagram of the adaptive fractional-order model that incorporates the linear transfer mechanism of this invention. Detailed Implementation The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0018] Please see Figure 1-3 A joint estimation method for lithium batteries across multiple operating conditions and states that requires only a single identification and does not require offline OCV data includes the following steps: S1. Collect experimental data of the lithium battery under baseline conditions, including: A brand-new lithium battery was selected as the test subject for charge-discharge testing. Environmental conditions: ambient temperature 25℃ and no external pressure; Data collected: Changes in battery current and voltage over time; The specific experimental procedure is as follows: A brand new ternary lithium-ion battery with model number 21700 was selected as the test object and placed in a constant temperature environment chamber at 25°C. A constant current and constant voltage charging program was executed under the condition of no external mechanical constraints. After the charging was terminated, the battery was left to stand for 10 minutes to eliminate the polarization effect. Then, a full discharge test was carried out using the DST-UDDS-FUDS mixed dynamic working condition, and the current and voltage response data were collected simultaneously.
[0019] S2. Construct the fractional-order physical model to be identified; Specifically, based on the data collected by S1, a first-order RC fractional equivalent circuit model is established. To ensure the convergence of the initial identification process, the fractional order is first defined. For a fixed value, the time-domain discretization equation of this model is: In the formula, for The current lithium battery terminal voltage For fractional differential operators, The open-circuit voltage associated with the current state of charge (SOC). Polarization voltage, For ohmic internal resistance, For polarization internal resistance, For current, The generalized capacitive coefficient of the constant-phase element CPE; Considering that simultaneously identifying model parameters and fractional order is prone to getting trapped in local optima and is computationally time-consuming, in order to ensure rapid convergence and global stability in the initial identification process, the fractional order is... The value is locked at an empirical constant of 0.9 (which is close to the typical frequency domain characteristics of the diffusion process in lithium-ion batteries).
[0020] S3. Parameter and OCV Synchronous Identification Based on Quasi-Static Assumption: Introducing the quasi-static OCV assumption, offline OCV experimental data is not required. The DST-UDDS-FUDS hybrid discharge condition data obtained in step S1 are directly used to identify the impedance parameters and OCV online through the AFFRLS algorithm. Then, the analytical mapping relationship between the model parameters and SOC under the reference state is established. The specific steps are as follows: S3.1 Based on the DST-UDDS-FUDS hybrid discharge condition data obtained in step S1, firstly, for the fractional derivative term describing the dynamic characteristics of polarization voltage in the fractional physical model, numerical discretization approximation is performed using the GL definition, that is, during the sampling period... fractional derivative The numerical approximation is expressed as: In the formula, For discrete time points The fractional difference approximation when the fractional order is 0.9; To truncate the length of memory, An index for truncating the memory length; For a historic moment The polarization voltage value; These are the binomial recursive weighting coefficients, and their calculation follows... ; After discretization, in order to transform the nonlinear model into a linear form suitable for online identification, the battery SOC change is extremely small within a micro-sampling interval (e.g., 1 second), thus leading to... Given the physical property that the rate of numerical change is much lower than the rate of dynamic response, a quasi-static OCV assumption is introduced, which determines that the open-circuit voltage at adjacent sampling times satisfies... as well as Approximate conditions.
[0021] Based on the above GL discretization processing and quasi-static assumptions, the simultaneous model state equations are solved and eliminated through difference operations. The term ultimately reconstructs the nonlinear model into a linear regression equation: In the formula, These are terminal voltage observations. For the data regression vector, Let be the parameter vector to be identified. This represents the prediction error; S3.2. Use the AFFRLS algorithm to identify the model parameters and OCV under the baseline state online, based on the prediction error. Real-time adjustment of forgetting factor To balance parameter tracking speed and noise suppression capability, an adaptive forgetting factor is used. The update formula is as follows: In the formula, The preset minimum forgetting factor, For prediction error, As the baseline error threshold, This is a non-linear activation function used to map the standardized error to the adjustment range of the forgetting factor; when the prediction error... When the current increases (e.g., at the instant of a sudden change in current). Automatically reduce and increase the weight of new data to achieve rapid parameter tracking; when prediction error... When decreasing, Increase the length of the memory to suppress measurement noise; S3.3. A baseline analytical mapping relationship between model parameters and SOC is constructed using 5th-order polynomial fitting: In the formula, Let be the ohmic internal resistance as a function of SOC. Let be the polarization resistance as a function of SOC. Let be the generalized capacitive coefficient as a function of SOC. , , and These represent the fitting coefficients for each item, obtained through AFFRLS identification and fitting.
[0022] S4. Construct an adaptive fractional-order model integrating linear migration mechanism and internal resistance anchoring characteristics: Based on the cross-condition scenarios encountered during actual battery operation, this step no longer repeats the tedious full-condition offline calibration. Instead, using the benchmark parameter library established in step S3.3 as the source domain prior knowledge, a linear migration factor is introduced to perform first-order approximate compensation for the nonlinear drift of model parameters under the coupling effects of multiple stresses such as temperature, aging, and pressure. A dynamic mapping mechanism from benchmark conditions to multi-stress conditions is constructed, the mathematical expression of which is: In the formula, To adapt the model parameters to the current specific working conditions, The first and second impedance migration factors are, These are the model parameters under baseline conditions (including) ); It is the SOC after migration correction. For a rough SOC under the influence of multiple stress coupling, Scaling and translation factors for SOC; By utilizing the online adaptive iteration mechanism of the above factors, the system can correct the SOC range shift and time-varying model parameters caused by the coupling of multiple thermal and mechanical fields in real time, realize the accurate generalization of battery model parameters from the "offline reference domain" to the "online target domain", and complete the adaptive tracking of the current complex working conditions.
[0023] Based on this high-fidelity adaptive parameter system, we further explore the characterization ability of the ohmic internal resistance term in the parameters on battery degradation characteristics, and construct a capacity observation equation based on the internal resistance anchoring characteristic. The specific steps are as follows: S4.1 Constructing a reference system based on the physical characteristics of internal resistance. : In the formula, This is a reference health status estimate based on internal resistance; This is the internal resistance threshold at the end of the battery's lifespan. The internal resistance is ohmic; This is the nominal internal resistance of the battery at the time of manufacture. S4.2 Introduce an adaptive correction layer to establish the final SOH and capacity observation equations: In the formula, This is the final corrected estimate of SOH. and These are the scaling correction factor and offset correction factor based on terminal voltage residual correction, respectively; This represents the actual usable capacity. This represents the standard rated capacity of the battery; the core of this observation equation lies in its use of a "physical benchmark + dynamic correction" strategy. Among these, the internal resistance-based... This provides a reliable physical benchmark range for capacity estimation. Furthermore, considering the inherent nonlinear bias and model mismatch issues of a single internal resistance mapping relationship under different individual batteries and operating conditions, a correction factor identified online by the algorithm is introduced. and By performing a second correction, this strategy not only uses internal resistance to lock in the main aging trend, but also compensates for model errors through dynamic correction, thereby ensuring the accuracy and universality of capacity estimation.
[0024] Based on the independent derivation and correction of model parameters, SOC state, and capacity described above, this step further deeply mathematically couples the linear migration evolution law at the parameter level with the capacity observation equation at the state level, thereby constructing an adaptive fractional-order model (LMM-AFECM) that integrates the linear migration mechanism. The overall analytical form is as follows: In the formula, , indicates the coefficient term, superscript This represents the adaptive model parameters after correction via the transfer mechanism. Used to describe the impact of multiple stress coupling conditions on model parameters. For the baseline parameter mapping function; To obtain a rough SOC value under the influence of multiple stress coupling, a linear transformation is performed. Mapping to the domain of the benchmark model, thereby achieving cross-condition parameter adaptation without additional offline calibration; To adapt the fractional order, As the baseline fractional order, and These are the ohmic resistance and polarization resistance after migration, respectively. The generalized tolerance coefficient after migration. The open-circuit voltage after migration. To migrate the output of the back-end voltage model, The polarization voltage after migration, This is the current. It is worth noting that the new model constructed in this step removes the fixed-order constraint set in the previous steps to ensure identification convergence, and extends the fractional-order to an adaptive fractional-order variable that evolves with the multi-stress conditions. This enables the accurate capture of the frequency domain response differences of battery dynamic characteristics under different physical fields.
[0025] S5. A joint estimation framework for lithium battery SOC and capacity based on a unified augmented state space and sparse information injection mechanism: Addressing the strong rigid coupling characteristics of lithium batteries, a unified augmented state vector containing SOC, polarization voltage, and capacity correction factors is constructed. A time-varying noise covariance matrix is designed to inject sparse information, achieving decoupled evolution of fast-changing states and slowly changing parameters. Based on this, a particle filter algorithm with a risk-sensitive criterion is introduced to estimate the capacity state in the long time domain. The SOC is then corrected in real-time using the voltage residual in the short time domain and the updated capacity in the long time domain. Finally, the joint estimation of lithium battery SOC and capacity under the influence of multi-stress coupling is completed. The steps include: S5.1 Initial Particle Generation: In the formula, Let be the prior probability density. For the particles at the initial moment, The total number of particles, Index of the total number of particles; It is the Dirac function; For the first An initial particle, For fast-variant subvectors, For slow-varying subvectors, It follows a Gaussian distribution. This is the initial SOC estimate. and These are the initial error covariance matrices for the fast-changing and slow-changing parameter subvectors, respectively; through this initialization, the algorithm operates at discrete time points. At that time, a unified description of all parameters was established; S5.2 Augmented Particle Initialization: Based on a unified framework, this method captures the cross-scale coupling characteristics between different states of a lithium battery and constructs a unified augmented state vector. : In the formula, Discrete time SOC at that time Discrete time Fractional polarization voltage at time Used to represent fast time scales. Used to describe slow time scales; S5.3 Sparse Information Injection and State Evolution: Based on the unified augmented state space equation, a sparse information injection mechanism is introduced to construct a state evolution equation containing a time-varying control matrix: In the formula, For the first The prior predicted state of each particle It is a nonlinear state transition function. For system input, To accommodate the process noise of the sparse injection mechanism, the noise should have a mean of 0 and a covariance of 0. Gaussian distribution; The noise covariance matrix for the dynamic process is used to control the evolution bandwidth of states in different dimensions, and is defined as follows: In the formula, and The process noise variances for SOC and polarization voltage are respectively; and To correct the process noise variance of the parameters; It is a very small positive number (such as 10⁻⁶). For macro-level update cycles; During the microscopic preservation stage: The last two terms are extremely small positive numbers. The system suppresses noise injection in slowly varying dimensions, forcing the particle swarm to respond to high-frequency voltage residuals only in the fast-changing subspace, thus ensuring the real-time performance and stability of SOC estimation. In the macro update phase: the system restores noise injection into the slow-varying parameter subspace, allows aging information to flow into the slow-varying parameter subspace, and uses long-period cumulative error to correct the capacity benchmark, thereby achieving decoupled evolution across multiple time scales; S5.4, Perform risk-sensitive weight update: Calculate the particle prediction terminal voltage and introduce an exponential cost function to calculate the particle weights, amplifying the differences between superior and inferior particles: In the formula, For the first The non-normalized weights of each particle As a risk-sensitive factor, This is the measured terminal voltage. For the first Predicted terminal voltage of each particle; S5.5, Weight Normalization: In the formula, The normalized weights, Non-normalized weights; S5.6 Perform particle resampling and state estimation: Resample the prior set according to the particle weights to suppress particle degradation, and use weighted summation to calculate the posterior estimate of the augmented state: In the formula, This is the optimal estimation vector that includes SOC and capacity correction factor; Based on the updated particle set and its weights, a deterministic state estimate is extracted using the Monte Carlo integration approach. First, the current correction capacity is obtained through weighted calculation. Then, this capacity value is used to dynamically correct the SOC integral benchmark, forming a closed-loop feedback path where slowly varying parameters constrain rapidly changing states. The specific equation is as follows: In the formula, For the estimated current available capacity, This refers to the battery's nominal rated capacity. The mean of the scaling correction factor. As a reference SOH based on physical characteristics, This represents the mean of the offset correction factor. for Rough SOC at that time For Coulomb efficiency, for Load current at that time The sampling time interval is defined as follows: Based on this, the linear migration parameters estimated by particle filtering are used to adaptively scale and shift the coarse SOC, and a posterior weighted calculation is performed based on the particle weights to obtain the final SOC estimate, which is mathematically expressed as follows: In the formula, This represents the true SOC value based on capacity correction under the influence of multiple stress coupling. for The state of the first particle. for The state of the second particle at that time.
[0026] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A method for joint estimation of lithium batteries across multiple operating conditions and states that requires only a single identification and does not require offline OCV data, characterized in that, Includes the following steps: S1. Collect experimental data of lithium batteries under reference conditions; S2. Based on the collected benchmark data, construct the fractional-order physical model to be identified; S3. Based on the fractional-order physical model to be identified and the benchmark data, perform parameter and OCV synchronous identification operations based on the quasi-static assumption, and establish the analytical mapping relationship between the model parameters and SOC under the benchmark state. S4. Based on the analytical mapping relationship between model parameters and SOC under the baseline state, construct an adaptive fractional-order model that integrates linear transfer mechanism and internal resistance anchoring characteristics. S5. By using an adaptive fractional-order model, a joint estimation framework for lithium battery SOC and capacity based on a unified augmented state space and sparse information injection mechanism is constructed, ultimately completing the joint estimation of lithium battery SOC and capacity under the influence of multiple stress coupling.
2. The lithium battery multi-state joint estimation method across operating conditions according to claim 1, which requires only a single identification and does not require offline OCV data, is characterized in that: In S1, the environmental conditions are set as follows: ambient temperature 25°C and no external pressure; the data collected are the changes in battery current and voltage over time.
3. The lithium battery multi-state joint estimation method across operating conditions according to claim 1, which requires only a single identification and does not require offline OCV data, is characterized in that: In step S2, the fractional-order physical model to be identified is a first-order RC fractional-order equivalent circuit model. Furthermore, to ensure the convergence of the initial identification process, the fractional-order is first defined. The value is fixed at 0.9, and the expression is as follows: In the formula, for The current lithium battery terminal voltage, For fractional differential operators, The open-circuit voltage associated with the current state of charge (SOC). Polarization voltage, For ohmic internal resistance, For polarization internal resistance, For current, is the generalized capacitive coefficient of the constant-phase element CPE.
4. The lithium battery multi-state joint estimation method across operating conditions according to claim 1, which requires only a single identification and does not require offline OCV data, is characterized in that: The steps of parameter synchronization identification with OCV based on the quasi-static assumption in S3 include: S3.
1. Use GL to define the discretized fractional derivative, and assume that within the preset sampling interval... The nonlinear model is reconstructed into a linear regression equation: In the formula, These are terminal voltage observations. For the data regression vector, Let be the parameter vector to be identified. This represents the prediction error; S3.
2. Use the AFFRLS algorithm to identify the model parameters and OCV under the baseline state online, based on the prediction error. The forgetting factor is adjusted in real time to balance parameter tracking speed and noise suppression capability; S3.
3. A baseline analytical mapping relationship between model parameters and SOC is constructed using 5th-order polynomial fitting: In the formula, Let be the ohmic internal resistance as a function of SOC. Let be the polarization resistance as a function of SOC. Let be the generalized capacitive coefficient as a function of SOC. The open-circuit voltage associated with the current state of charge (SOC). , , and These represent the fitting coefficients for each item, obtained through AFFRLS identification and fitting.
5. The lithium battery multi-state joint estimation method across operating conditions according to claim 4, which requires only a single identification and does not require offline OCV data, is characterized in that: Forgetting factor in S3.2 The update formula is as follows: In the formula, The preset minimum forgetting factor, For prediction error, As the baseline error threshold, It is a non-linear activation function used to map the standardized error to the adjustment range of the forgetting factor.
6. The lithium battery multi-state joint estimation method across operating conditions according to claim 1, which requires only a single identification and does not require offline OCV data, is characterized in that: The linear migration mechanism in S4 is represented as follows: In the formula, To adapt the model parameters to the current specific working conditions, The first and second impedance migration factors are, These are the model parameters under the baseline condition; It is the SOC after migration correction. For a rough SOC under the influence of multiple stress coupling, Scaling and translation factors for SOC; Model parameters under the baseline state Including: Ohmic internal resistance Polarization internal resistance Generalized capacitive coefficient of constant phase element Open circuit voltage and fractional order .
7. The lithium battery multi-state joint estimation method across operating conditions according to claim 6, which requires only a single identification and does not require offline OCV data, is characterized in that: In step S4, the capacity observation equation is constructed based on the internal resistance anchoring characteristic. The steps include: S4.1 Constructing a reference system based on the physical characteristics of internal resistance. : In the formula, This is a reference health status estimate based on internal resistance; This is the internal resistance threshold at the end of the battery's lifespan. The internal resistance is ohmic; This is the nominal internal resistance of the battery at the time of manufacture. S4.2 Introduce an adaptive correction layer to establish the final SOH and capacity observation equations: In the formula, This is the final corrected estimate of SOH. and These are the scaling correction factor and offset correction factor based on terminal voltage residual correction, respectively; This represents the actual usable capacity. This refers to the standard rated capacity of the battery.
8. The lithium battery multi-state joint estimation method across operating conditions according to claim 7, which requires only a single identification and does not require offline OCV data, is characterized in that: In S4, the specific set of parameter evolution equations for constructing the adaptive fractional-order model that integrates the linear migration mechanism and the internal resistance anchoring characteristic is as follows: In the formula, , indicates the coefficient term, superscript This represents the adaptive model parameters after correction via the transfer mechanism. Used to describe the impact of multiple stress coupling conditions on model parameters. For the baseline parameter mapping function; To obtain a rough SOC value under the influence of multiple stress coupling, a linear transformation is performed. Mapping to the domain of the benchmark model, thereby achieving cross-condition parameter adaptation without additional offline calibration; To adapt the fractional order, As the baseline fractional order, and These are the ohmic resistance and polarization resistance after migration, respectively. The generalized tolerance coefficient after migration. The open-circuit voltage after migration. To migrate the output of the back-end voltage model, The polarization voltage after migration, This represents the current.
9. The lithium battery multi-state joint estimation method across operating conditions according to claim 1, which requires only a single identification and does not require offline OCV data, is characterized in that: The steps in S5 include: S5.1 Initial Particle Generation: In the formula, Let be the prior probability density. For the particles at the initial moment, The total number of particles, Index of the total number of particles; It is the Dirac function; For the first An initial particle, For fast-variant subvectors, For slow-varying subvectors, It follows a Gaussian distribution. This is the initial SOC estimate. and These are the initial error covariance matrices for the fast-changing and slow-changing parameter subvectors, respectively; S5.2 Augmented Particle Initialization: Based on a unified framework, this method captures the cross-scale coupling characteristics between different states of a lithium battery and constructs a unified augmented state vector. : In the formula, Discrete time SOC at that time Discrete time Fractional polarization voltage at time Used to represent fast time scales. Used to describe slow time scales; S5.3 Sparse Information Injection and State Evolution: Based on the unified augmented state space equation, a sparse information injection mechanism is introduced to construct a state evolution equation containing a time-varying control matrix: In the formula, For the first The prior predicted state of each particle It is a nonlinear state transition function. For system input, To accommodate the process noise of the sparse injection mechanism, the noise should have a mean of 0 and a covariance of 0. Gaussian distribution; The noise covariance matrix for the dynamic process is used to control the evolution bandwidth of states in different dimensions, and is defined as follows: In the formula, and The process noise variances for SOC and polarization voltage are respectively; and To correct the process noise variance of the parameters; It is a very small positive number. For macro-level update cycles; S5.4, Perform risk-sensitive weight update: Calculate the particle prediction terminal voltage and introduce an exponential cost function to calculate the particle weights, amplifying the differences between superior and inferior particles: In the formula, For the first The non-normalized weights of each particle As a risk-sensitive factor, This is the measured terminal voltage. For the first Predicted terminal voltage of each particle; S5.5, Weight Normalization: In the formula, The normalized weights Non-normalized weights; S5.6 Perform particle resampling and state estimation: Resample the prior set according to the particle weights to suppress particle degradation, and use weighted summation to calculate the posterior estimate of the augmented state: In the formula, This is the optimal estimation vector that includes SOC and capacity correction factor.
10. The lithium battery multi-state joint estimation method across operating conditions according to claim 9, which requires only a single identification and does not require offline OCV data, is characterized in that: The joint estimation framework of S5 corrects the current actual available capacity through the correction factor of the filtered output, and injects it as a feedback variable into the ampere-hour integral equation to perform closed-loop correction of the coarse SOC. Its mathematical expression is as follows: In the formula, For the estimated current available capacity, This refers to the battery's nominal rated capacity. The mean of the scaling correction factor. As a reference SOH based on physical characteristics, This represents the mean of the offset correction factor. for Rough SOC at that time For Coulomb efficiency, for Load current at that time The sampling time interval; The coarse SOC is adaptively scaled and translated using the linear migration parameters estimated by particle filtering, and a posteriori weighted calculation is performed based on the particle weights to obtain the final SOC estimate, which is mathematically expressed as follows: In the formula, This represents the true SOC value based on capacity correction under the influence of multiple stress coupling. for The state of the first particle. for The state of the second particle at that time.