Battery SOH estimation method based on fractional order equivalence and memristor degradation modeling

Abstract

The invention belongs to the technical field of battery SOH estimation, and particularly discloses a battery SOH estimation method based on fractional order equivalence and memristor degradation modeling, and the method comprises the steps: building a joint state space model based on the operation data of a battery according to a fractional order equivalent circuit model and a memristor degradation model; combining the fractional order equivalent circuit model with the memristor degradation model to establish a joint state space model, and solving the joint state space model by adopting an unscented Kalman filtering algorithm so as to synchronously estimate the health state of the battery and the parameters of the fractional order equivalent circuit model on line; correcting and adjusting the estimation process based on double time scales, wherein the double time scales comprise short-time scale online correction based on model internal consistency and long-time scale offline correction based on historical data review; and outputting the corrected and adjusted battery health state estimation result. According to the invention, high-precision, strong-mechanism and full-life-cycle adaptive estimation of the SOH of the battery can be realized.

Description

Technical Field

[0001] This application belongs to the field of battery SOH estimation technology, and more specifically, relates to a battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling. Background Technology

[0002] With the rapid development of industries such as electric vehicles and energy storage power stations, lithium-ion batteries, as a core energy carrier, have received unprecedented attention regarding their safety, reliability, and economic efficiency throughout their entire lifecycle. The Battery Management System (BMS) is the brain that ensures the efficient and safe operation of the battery pack, and the accurate estimation of the battery's State of Health (SOH) is the fundamental basis for the BMS to make critical decisions such as energy management, thermal management, equalization control, and lifespan prediction. Inaccurate SOH estimations can lead to overcharging and over-discharging of the battery, a precipitous drop in driving range, and even serious safety accidents such as thermal runaway.

[0003] Currently, mainstream SOH estimation techniques primarily rely on the battery's equivalent circuit model (ECM). Traditional integer-order ECMs, such as the widely used second-order RC model, while simple in structure and easy to implement, have limited physical interpretation capabilities. The capacitors and resistors in these models cannot accurately correspond to the complex electrochemical processes inside the battery, such as the electric double-layer effect during charge transfer and the diffusion process of lithium ions in electrode materials (i.e., Warburg impedance). This model-level approximation makes it difficult to maintain high accuracy over a wide range of operating temperatures and dynamic conditions, especially as the model mismatch problem becomes increasingly severe in the later stages of battery aging.

[0004] To improve model accuracy, researchers have begun to introduce fractional-order calculus theory. Fractional-order models, with their inherent "memory properties," can more naturally and accurately describe the impedance spectrum characteristics of electrochemical systems using constant phase elements (CPEs). However, most existing research focuses on using fractional-order models to "better fit" experimental data, failing to delve into the physical implications of the core parameter, the fractional-order "order." In these studies, the order is often treated as a fixed mathematical fitting constant, ignoring a crucial fact: as batteries age, their internal microstructure (such as electrode surface morphology and the integrity of active particles) undergoes irreversible changes. These changes inevitably lead to variations in their electrochemical kinetics, ultimately reflected in the dynamic evolution of the fractional-order order. Therefore, establishing a model that directly correlates the order parameter with the internal physical state of the battery is key to achieving the leap from "mathematical fitting" to "physical characterization."

[0005] On the other hand, the essence of SOH (State of Health) is the degradation of a battery's maximum usable capacity relative to its initial capacity. This degradation is the result of the accumulation of irreversible internal chemical side reactions (such as SEI film thickening and active lithium loss) under the combined effects of various external stresses, including cyclic charging and discharging, temperature changes, and high-rate operating conditions. Existing degradation models describing this process are mostly empirical formulas or data-driven black-box models. While they can fit capacity degradation curves under specific conditions, their generalization ability is poor, and they cannot reveal the dependence of the aging path on different stress histories. How to construct a mechanistic model that can "memorize" and "quantify" historical accumulated damage and directly correlate it with capacity degradation is a bottleneck that urgently needs to be overcome in the current field of SOH estimation. Memristors, as nonlinear elements with memory function, provide a highly promising mathematical tool for describing this cumulative and nonlinear degradation process, but their application in battery health modeling is still in its early stages.

[0006] In summary, existing methods have significant shortcomings in terms of model mechanistic aspects, parametric physical properties, and adaptive characterization of the aging process. Therefore, achieving high-precision, mechanism-driven, and life-cycle adaptive estimation of battery state of harmonic aging (SOH) is a pressing issue that needs to be addressed. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the purpose of this application is to provide a battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling, which can achieve high-precision, mechanism-driven, and full-lifecycle adaptive estimation of battery SOH.

[0008] To achieve the above objectives, in a first aspect, this application provides a battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling, comprising the following steps: S10, acquire the battery's operating data during the current charge-discharge cycle, the operating data including operating current, port voltage, temperature and state of charge; S20, Based on the aforementioned operating data, a joint state-space model is constructed according to the fractional-order equivalent circuit model and the memristor degradation model; Among them, the memristor degradation model is used to calculate the comprehensive stress factor based on multiple stress factors during the battery charge-discharge cycle, and update the memristor state value according to the nonlinear update rule. The state value is used to characterize the cumulative damage of the battery. The order of the fractional-order components in the fractional-order equivalent circuit model is dynamically modeled as a function of the battery's internal operating state and the memristor state value. S30, the fractional-order equivalent circuit model and the memristor degradation model are combined to establish a joint state-space model, and the unscented Kalman filter algorithm is used to solve the joint state-space model so as to simultaneously estimate the battery health state and the parameters of the fractional-order equivalent circuit model online. S40, The estimation process is corrected and adjusted based on dual time scales, which include short-timescale online correction based on the inherent consistency of the model and long-timescale offline correction based on historical data review; S50 outputs the corrected and adjusted battery health status estimate.

[0009] As a further preferred embodiment, in step S20, the order of the fractional-order element includes the order characterizing the charge transfer process. and the order characterizing solid-phase diffusion processes ; The order of the charge transfer process Modeled as:

[0010] The order characterizing the solid-phase diffusion process Modeled as:

[0011] In the formula, Indicates the new battery at the reference temperature The initial order below; It is the decay coefficient of memristor impairment with respect to order; It is the temperature influence coefficient; T Indicates battery temperature; M This indicates the state value of the memristor. As a further preferred embodiment, in step S20, the comprehensive stress factor Calculate using the following formula:

[0012] in, and These are the current ratio influence coefficient and the average absolute ratio, respectively. and These are the depth of discharge and its power-law exponent, respectively. Equivalent activation energy; It is the gas constant; Average temperature; Indicates the reference temperature.

[0013] As a further preferred embodiment, in step S20, the calculation formula for updating the memristor state value according to the nonlinear update rule is as follows:

[0014] In the formula, This indicates the memristor state value after the current cycle; This represents the memristor state value after the previous cycle, initial value. ; It is the base aging rate related to the average SOC; This represents the overall stress factor for the current cycle; It has a power exponent The saturation inhibition term, It is the theoretical maximum charge loss.

[0015] As a further preferred embodiment, in step S20, the state vector of the joint state-space model includes the battery's state of charge, overpotential characterizing the charge transfer process, overpotential characterizing the solid-phase diffusion process, charge transfer resistance, solid-phase diffusion resistance, and memristor state value.

[0016] As a further preferred embodiment, in step S40, the short timescale online correction includes: dynamically adjusting the process noise covariance matrix of the unscented Kalman filter based on the consistency residual between the charge transfer resistance estimated by the unscented Kalman filter and the theoretical internal resistance calculated according to the memristor degradation model.

[0017] As a further preferred embodiment, in step S40, the long-timescale offline correction includes: periodically using historical charge-discharge cycle data and the corresponding true values ​​of health status to construct a global optimization problem with the goal of minimizing the health status estimation error, and using an optimization algorithm to solve the problem to update the hyperparameters in the fractional-order equivalent circuit model and the memristor degradation model.

[0018] As a further preferred option, the optimization algorithm is the particle swarm optimization algorithm.

[0019] As a further preferred embodiment, in step S50, the output battery health status estimation result includes a real-time updated health status value and multi-dimensional diagnostic indicators derived from the fractional-order equivalent circuit model parameters and memristor state values.

[0020] Secondly, this application provides a battery management system, including a processor and a memory, wherein the memory stores a computer program that, when executed by the processor, implements the steps of the battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling as described above.

[0021] The battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling provided in this application has the following advantages: 1. Based on the traditional equivalent circuit model, a novel fractional-order model is constructed that deeply couples fractional-order parameters with the internal electrochemical mechanism. The core of this model lies in integrating fractional-order parameters (such as...) with the internal electrochemical mechanism. Instead of being regarded as a fixed fitting constant, it is modeled as a dynamic function related to the internal state of the battery (temperature, SOC) and the degree of aging (memristor state), so that the model parameters can directly reflect the electrode / electrolyte interface characteristics and the health status of the lithium-ion diffusion path.

[0022] 2. To accurately characterize the nonlinear, cumulative capacity decay of batteries, a novel degradation modeling method based on memristor theory is proposed. This method extends the memristor concept from a circuit element to a mathematical paradigm describing "damage accumulation," constructing a memristor state equation capable of "memorizing" historical operating conditions (current, temperature, DOD) and quantifying its cumulative damage. This innovatively transforms the estimation problem of SOH into a problem of tracking an internal state variable (memristor value) with a clear physical meaning.

[0023] 3. In the memristor degradation model, a comprehensive stress model and update rule were designed that can couple multiple electrochemical stress factors and reflect nonlinearity and saturation effects. This model not only considers the nonlinear effects of current, temperature, and DOD on aging, but also innovatively introduces a basic aging rate related to the average SOC, as well as a saturation suppression term with a power exponent that can describe the "tailing" effect in the later stages of aging, making it more consistent with the actual physical process of battery aging.

[0024] 4. Using the unscented Kalman filter (UKF) technique, joint state estimation was performed on the strongly nonlinear fractional-order model and the memristor degradation model. By constructing an enhanced state vector that includes SOC, overpotential, critical internal resistance, and memristor value, synchronous online identification and estimation of battery SOH and key model parameters were achieved, ensuring the high accuracy and robustness of the algorithm.

[0025] 5. To ensure the long-term effectiveness of the model throughout its entire lifecycle, a self-calibration mechanism based on dual time scales was designed. This mechanism includes short-time-scale online drift suppression based on the model's intrinsic consistency, and long-time-scale global hyperparameter recalibration based on historical data review. The synergistic effect of these two mechanisms enables the entire estimation framework to self-evolve and adaptively track the battery aging process. Attached Figure Description

[0026] Figure 1 This is a flowchart of the battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling provided in this application; Figure 2 This is a flowchart illustrating the complete implementation steps of the battery health state estimation method based on fractional-order equivalent circuit and memristor degradation modeling provided in this application embodiment; Figure 3 This is a schematic diagram of the fractional-order equivalent circuit model structure provided in the embodiments of this application; Figure 4 This is a schematic diagram of the memristor degradation model structure provided in the embodiments of this application; Figure 5 This is a comparison of the evolution curves of the nonlinear and linear update rules for the memristor state provided in the embodiments of this application. Figure 6 This is a flowchart of the iterative process of the unscented Kalman filter (UKF) provided in the embodiments of this application; Figure 7 This is a schematic diagram of a model self-correction mechanism based on dual time scales provided in an embodiment of this application. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0028] like Figure 1 As shown, this application provides a battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling, including steps S10 to S50, which are detailed below: Step S10: Obtain the battery's operating data during the current charge / discharge cycle. The operating data includes operating current, port voltage, temperature, and state of charge.

[0029] This step, by collecting multi-dimensional real-time data of the battery during actual operation, can provide accurate and comprehensive input information for subsequent model building and state estimation, ensuring that the model's computational basis closely matches the actual operating conditions.

[0030] Step S20: Based on the running data, construct a joint state-space model according to the fractional-order equivalent circuit model and the memristor degradation model.

[0031] Among them, the memristor degradation model is used to calculate the comprehensive stress factor based on multiple stress factors during the battery charge-discharge cycle, and update the memristor state value according to the nonlinear update rule. This state value is used to characterize the cumulative damage of the battery. The order of the fractional-order components in the fractional-order equivalent circuit model is dynamically modeled as a function of the battery's internal operating state and the memristor state value.

[0032] This step, by adjusting the order parameters of the fractional-order model from fixed constants to functions dynamically related to (temperature, SOC) and aging degree (memristor state), allows the model parameters to directly reflect the health status of the electrode interface characteristics and ion diffusion paths, achieving a leap from mathematical fitting to physical characterization. At the same time, by quantifying the nonlinear cumulative damage caused by various stress factors during historical operation through the memristor model, an internal state variable with clear physical meaning can be provided for SOH estimation.

[0033] Step S30 involves combining the fractional-order equivalent circuit model with the memristor degradation model to establish a joint state-space model. An unscented Kalman filter algorithm is then used to solve this joint state-space model, allowing for simultaneous online estimation of the battery's state of health and the parameters of the fractional-order equivalent circuit model. This step, utilizing the unscented Kalman filter algorithm to handle strongly nonlinear systems, enables high-precision and robust simultaneous online identification and tracking of the battery's state of health and key model parameters.

[0034] Step S40: Correct and adjust the estimation process based on dual time scales. The dual time scales include online correction with short time scales based on the inherent consistency of the model and offline correction with long time scales based on historical data review.

[0035] To ensure the long-term effectiveness of the model throughout its entire lifecycle, this step designs a self-calibration mechanism based on dual time scales. This mechanism includes short-time-scale online drift suppression based on the model's intrinsic consistency, and long-time-scale global hyperparameter recalibration based on historical data review. The synergistic effect of these two mechanisms enables the entire estimation framework to self-evolve and adaptively track the battery aging process.

[0036] Step S50: Output the corrected and adjusted battery health status estimation result.

[0037] This step provides real-time, reliable health status values ​​and related multi-dimensional diagnostic information.

[0038] The battery health state estimation method based on fractional-order equivalent circuit and memristor degradation modeling provided in this application has the following advantages: 1. Based on the traditional equivalent circuit model, a novel fractional-order model is constructed that deeply couples fractional-order parameters with the internal electrochemical mechanism. The core of this model lies in integrating fractional-order parameters (such as...) with the internal electrochemical mechanism. Instead of being regarded as a fixed fitting constant, it is modeled as a dynamic function related to the internal state of the battery (temperature, SOC) and the degree of aging (memristor state), so that the model parameters can directly reflect the electrode / electrolyte interface characteristics and the health status of the lithium-ion diffusion path.

[0039] 2. To accurately characterize the nonlinear, cumulative capacity decay of batteries, a novel degradation modeling method based on memristor theory is proposed. This method extends the memristor concept from a circuit element to a mathematical paradigm describing "damage accumulation," constructing a memristor state equation capable of "memorizing" historical operating conditions (current, temperature, DOD) and quantifying its cumulative damage. This innovatively transforms the estimation problem of SOH into a problem of tracking an internal state variable (memristor value) with a clear physical meaning.

[0040] 3. In the memristor degradation model, a comprehensive stress model and update rule were designed that can couple multiple electrochemical stress factors and reflect nonlinearity and saturation effects. This model not only considers the nonlinear effects of current, temperature, and DOD on aging, but also innovatively introduces a basic aging rate related to the average SOC, as well as a saturation suppression term with a power exponent that can describe the "tailing" effect in the later stages of aging, making it more consistent with the actual physical process of battery aging.

[0041] 4. Using the unscented Kalman filter (UKF) technique, joint state estimation was performed on the strongly nonlinear fractional-order model and the memristor degradation model. By constructing an enhanced state vector that includes SOC, overpotential, critical internal resistance, and memristor value, synchronous online identification and estimation of battery SOH and key model parameters were achieved, ensuring the high accuracy and robustness of the algorithm.

[0042] 5. To ensure the long-term effectiveness of the model throughout its entire lifecycle, a self-calibration mechanism based on dual time scales was designed. This mechanism includes short-time-scale online drift suppression based on the model's intrinsic consistency, and long-time-scale global hyperparameter recalibration based on historical data review. The synergistic effect of these two mechanisms enables the entire estimation framework to self-evolve and adaptively track the battery aging process.

[0043] In one embodiment, the technical solution to achieve the above objective can be as follows: This application proposes a battery state of health (SOH) estimation method based on fractional-order equivalent circuit and memristor degradation modeling. This method aims to fundamentally address two major challenges faced by existing battery SOH estimation techniques: first, the traditional integer-order equivalent circuit (ECM) model lacks sufficient accuracy in characterizing the complex electrochemical dynamics of batteries at the physical mechanism level; second, existing empirical or semi-empirical degradation models struggle to effectively and accurately characterize the cumulative aging mechanism of batteries under actual nonlinear and time-varying operating conditions. The essential innovation of this solution lies in constructing a complete physical mapping pathway from microscopic electrochemical mechanisms to macroscopic model parameters, and from accumulated stress to capacity decay, achieving high-precision, mechanism-driven, and life-cycle adaptive estimation of battery SOH. Figure 2 As shown in the complete implementation flowchart of this embodiment, the technical process of this solution is precisely divided into the following interrelated and progressive steps: Step 1: Construction of a fractional-order equivalent circuit model based on decoupling and mapping of electrochemical processes The core innovation of this step lies in not simply replacing integer-order components with fractional-order components, but rather establishing a modeling method that deeply physical decouples and maps the key electrochemical processes inside the battery (charge transfer, solid / liquid diffusion) with the "order" of fractional-order circuit components. This makes the model parameters no longer just fitted numbers, but rather "probes" that can directly reflect the health status of specific physical processes inside the battery.

[0044] 1.1. Excitation and Acquisition of Wideband Dynamic Response Characteristics of Battery To comprehensively excite and decouple the electrochemical dynamic response of the battery across different timescales, a designed broadband excitation current signal is first applied to the lithium-ion battery under test. This signal is composed of a pseudo-random binary sequence (PRBS) superimposed with a low-frequency sine wave signal. The PRBS signal is used to detect rapid processes such as charge transfer in the high-frequency range, while the sine wave signal is used to excite slow processes such as diffusion in the low-frequency range. Throughout the excitation process, the battery's port voltage is synchronously recorded at a high-frequency sampling rate (1000Hz in this scheme). and operating current The sequence forms a high-information-density dataset for subsequent parameter identification.

[0045] 1.2. Structural Design of Fractional-Order ECM Based on Electrochemical Mechanism Mapping This scheme constructs an improved second-order fractional-order ECM, whose physical structure strictly corresponds to the electrochemical processes inside the battery. This model is based on an ohmic internal resistance. (Representing the total resistance of the electrolyte, diaphragm, and current collector), a parallel network characterizing the charge transfer process (resistance) A constant phase angle element is connected in parallel. ), and a parallel network (resistive) characterizing the diffusion process of lithium ions in the electrode solid particles. A constant phase angle element is connected in parallel. ) connected in series, such as Figure 3 As shown. Its voltage response equation in the time domain is expressed as: (1) in, It is the open-circuit voltage of the battery, a nonlinear function of the current state of charge (SOC), and their relationship has been calibrated through previous experiments; and These are overpotentials caused by charge transfer and solid-state diffusion processes, respectively, and they relate to current. The solution to a fractional differential equation. For example, satisfy: (2) in, and They are Generalized capacitance and fractional order; It was defined by Caputo. Fractional differential operators. The equation is similar.

[0046] 1.3. Deep Constraint Modeling of Physical Mechanisms for Fractional Orders This is the most crucial innovation of this step. This scheme abandons the approach of using fractional orders. and The traditional approach to fitting parameters is to analyze the electrochemical mechanism in depth and model it as a function related to the battery's internal state variables (temperature, SOC) and aging state (characterized by the memristor in step two), thereby directly linking the macroscopic order parameters to the health of the microscopic electrochemical process.

[0047] 1) Charge transfer order Modeling: This order reflects the non-ideal capacitance characteristics of the electric double layer at the electrode / electrolyte interface, which is closely related to electrode surface roughness, uniformity of active site distribution, and electrochemical reactivity. These characteristics are affected by temperature. The combined effect of the SEI film thickness and the equivalent thickness of the SEI film. This scheme compares the equivalent thickness of the SEI film with the memristor memristor value defined in step two. (Representing cumulative damage) is directly proportional. Therefore, Modeled as: (3) in, Is the new battery at the reference temperature? The initial order below; It is the decay coefficient of memristor damage to order, characterizing the decrease in interface uniformity caused by the thickening of the SEI film; It is the temperature effect coefficient, which characterizes how increasing the temperature can enhance reaction activity and improve interface uniformity.

[0048] 2) Solid-phase diffusion order Modeling: This order reflects the kinetics of lithium-ion diffusion within the electrode active material particles, with an ideal value of 0.5 (corresponding to pure semi-infinite diffusion). However, as the battery ages, the active particles may break down or become blocked, causing the diffusion path to become tortuous and limited. Furthermore, under extreme SOC conditions, the lithium-ion concentration gradient also affects the diffusion behavior. Therefore, Modeled as: (4) in, It is the coefficient of influence of SOC deviation from the central region on diffusion ideality; It is the attenuation coefficient of aging damage on order, characterizing the change in diffusion path caused by factors such as particle breakage.

[0049] Through this step, this solution constructs a "live" model whose order can adaptively change in response to temperature, SOC, and aging state. This model not only forms the basis for subsequent parameter identification, but its own changing trend also serves as an auxiliary information source for SOH diagnosis.

[0050] Step 2: Memristor Nonlinear Degradation Modeling Based on Multiple Stress Factors The core innovation of this step lies in the first-ever extension of memristor theory from a circuit element concept to a mathematical paradigm describing the "damage accumulation" process. It also involves constructing a battery capacity degradation model that couples multiple electrochemical stress factors (current, temperature, DOD) and reflects nonlinearity and saturation effects. Its structure is as follows: Figure 4 As shown.

[0051] 2.1. Quantification and Decoupling of Cyclic Stress Factor First, the multi-dimensional operational data from each charge-discharge cycle (or an equivalent operational segment) is transformed into a scalar that quantifies the degree of damage in that cycle—the comprehensive stress factor. The contributions of different stress factors to aging are not simply linearly additive, but rather involve a coupling effect. Therefore, Defined as:

[0052] in, and These are the current ratio influence coefficient and the average absolute ratio, respectively. The exponential form better describes the exponentially accelerated aging caused by high current. and These are the depth of discharge and its power-law exponent (usually greater than 1), reflecting the nonlinear exacerbation of mechanical stress caused by deep charge and discharge; the last term is the temperature-accelerated aging term based on the Arrhenius equation. For equivalent activation energy, The gas constant is This represents the average temperature.

[0053] 2.2. Nonlinear update rule for memristor states (cumulative damage) Define the memristor value For the first At the end of the cycle, the equivalent charge loss due to irreversible reactions (such as SEI film growth and lithium metal deposition) is considered. The state update equation is designed as a nonlinear difference equation that reflects both path dependence and state saturation. (6) in, This is the memristor value after the previous loop, the initial value. ; It is the intrinsic aging rate related to the average SOC. This is an important innovation because it demonstrates that the intrinsic aging rate of a battery differs when stored or cycled in different SOC ranges (such as high SOC or low SOC). It is the combined stress factor of the current cycle; It has a power exponent saturation inhibition term; It is the theoretical maximum charge loss. The design can more accurately describe the "tailing" phenomenon of the sharp decline in the decay rate in the later stages of aging, which is more realistic than the linear suppression term. The evolution curve comparison diagram is shown below. Figure 5 As shown.

[0054] 2.3. Physical mapping from memristor value to SOH The state of health (SOH) of a battery is defined as its current maximum available capacity. With factory rated capacity The ratio. This solution will use the memristor value A direct mapping relationship, consistent with charge conservation, is established between (equivalent charge loss) and SOH: (7) Here and They are strongly correlated in a physical sense. Through this model, the problem of estimating SOH is transformed into estimating the hidden, indirectly memristor states. The problem of accurate tracking.

[0055] Step 3: Joint estimation of SOH and model parameters based on unscented Kalman filtering Since the models constructed in steps one and two are highly nonlinear, this step adopts the Unscented Kalman Filter (UKF) algorithm because it approximates the probability distribution of the nonlinear function through the Unscented Transform (UT), which has higher accuracy and better robustness than the linearized approximation of EKF.

[0056] 3.1. Establishment of the Joint State-Space Model Construct an enhanced nonlinear discrete state-space model. State vector. It not only includes the core state of the battery but also some parameters in the ECM that slowly drift with aging, enabling online identification. This scheme determines the state vector as follows: (8) This includes the state of charge, two overpotentials, two critical internal resistances, and the memristor's memristor value. and They are also included in the state vector because their growth is another important characteristic of the decrease in SOH.

[0057] Equations of state Based on the fractional-order ECM discretization equation, memristor update rule, and random walk model of resistance (such as... ) Construction.

[0058] Observation equations It is still the voltage response equation from step 1.2.

[0059] 3.2. UKF Iterative Estimation The iterative process of UKF is as follows: Figure 6 As shown, it includes three core components: state prediction, observation prediction, and state update. 1) Sigma point calculation and propagation: estimation based on the current state and its covariance matrix A set of Sigma points is generated. These Sigma points are then substituted into the nonlinear state equation. This yields the predicted Sigma point set.

[0060] 2) State prediction: The predicted state vector is obtained by weighted summation of the predicted Sigma point set. Covariance Matrix .

[0061] 3) Observation, prediction, and update: Substitute the predicted Sigma point set into the observation equation. The predicted observations are obtained. The Kalman gain is calculated, and the current actual voltage observations are used. The predicted state vector and covariance matrix are corrected to obtain the final posterior state estimate. and .

[0062] 3.3. Online Updates and Output of SOH After each iteration of the UKF update, the optimally estimated state vector is used. Extract memristor value Then, using the mapping relationship established in step 2.3, the current state of health (SOH) of the battery can be calculated in real time with high accuracy. The calculation formula is as follows: (9) Step 4: Model self-calibration and result output based on dual time scales This step aims to ensure the long-term accuracy and robustness of the entire estimation framework throughout the battery's lifespan. A dual-timescale self-calibration mechanism is designed, and the final output is a structured, multi-dimensional estimation result. Figure 7 This is a schematic diagram of a model self-correction mechanism based on dual time scales.

[0063] 4.1. Short Timescale Correction: Online Drift Suppression Based on Model Intrinsic Consistency This step operates on the same millisecond to second timescale as UKF, diagnosing and suppressing rapid drift of model parameters in real time. First, a "consistent residual" is established. Used to measure the internal resistance directly estimated by UKF. With the memristor model Consistency between the calculated theoretical internal resistance growth: (10) in, and This is a pre-calibration constant. Then, based on the magnitude of this residual, the process noise covariance matrix in the UKF is dynamically adjusted using the following formula. The middle corresponds to item : (11) in, , , All parameters are preset. This mechanism enables UKF to track more quickly. Actual and unexpected changes.

[0064] 4.2. Long-timescale calibration: Global parameter recalibration based on historical data review This step operates on a long-term timescale of monthly or quarterly, retrospectively optimizing the hyperparameters in the model that describe the intrinsic characteristics of the battery. A recalibration period is set (every 200 equivalent full cycles). The system automatically selects valid segments from historical data and constructs a global optimization objective function aimed at minimizing the root mean square error (RMSE) between the model's predicted SOH and the actual SOH. : (12) in, This is the hyperparameter vector to be optimized. The Particle Swarm Optimization (PSO) algorithm is used to globally optimize the objective function, yielding a set of optimal hyperparameter vectors. And use it to update the existing model, thus completing the model's self-evolution.

[0065] 4.3. Generation and Output of Structured Results The ultimate goal of this step is to integrate all the calculation and correction results into specific, actionable data with clearly defined sources for output: 1) Real-time SOH value output: The value estimated online by UKF in step 3.3. The core output is the SOH value, which is updated in real time at the millisecond level.

[0066] 2) Generation and output of diagnostic indicators: This involves estimating the UKF optimal state vector from step 3.3. Extracted internal resistance sequence Perform moving average smoothing to obtain the smoothed internal resistance. The smoothed internal resistance value, and the fractional order calculated in step 1.3 under the current operating condition, are then used. and These data are combined into a diagnostic data structure and output at a low frequency (per minute). This data structure provides multi-dimensional information about the health of the battery's internal electrochemical environment.

[0067] To verify the effectiveness and advancement of the proposed method, a series of experiments were conducted, and a detailed performance comparison was performed with existing mainstream methods. The experimental results fully demonstrate the significant advantages of this scheme in terms of SOH estimation accuracy, full lifecycle robustness, and remaining lifetime prediction.

[0068] The verification experiment of this scheme selected a 50Ah square lithium iron phosphate (LFP) power battery produced by a mainstream brand as the test object. Due to its flat open-circuit voltage (OCV) curve, LFP batteries require extremely high model accuracy and can effectively verify the algorithm's performance. A "dynamic full life cycle test" procedure was designed and executed in the experiment, which cycled the battery from 100% SOH to 70% SOH (end of life). Each large cycle included multiple dynamic stress test (DST) conditions and low-rate (0.5C) charge-discharge conditions performed at different temperatures (10°C, 25°C, 45°C). To obtain the true SOH value, a standard capacity test of 1 / 3C constant current discharge was performed on the battery every 50 cycles under a standard environment of 25°C.

[0069] To comprehensively evaluate the performance of this scheme, two representative comparison methods were established.

[0070] Comparison Method 1 (Traditional Method): This method represents the current widely used technical benchmark. It adopts the second-order RC equivalent circuit model commonly used in industry, combines it with the extended Kalman filter (EKF) for state estimation, and uses the Ah-throughput empirical model for SOH estimation.

[0071] Comparison Method Two (Partially Improved Method): The purpose of this method is to isolate and verify the performance gain brought about by the core innovation of "memristor degradation modeling" in this scheme. It adopts the same fractional equivalent circuit model and unscented Kalman filter (UKF) as this scheme, but the SOH estimation part still adopts the empirical model of ampere-hour throughput.

[0072] 1) Comparison and analysis of SOH estimation accuracy The root mean square error (RMSE) of SOH estimation for the three methods was statistically analyzed in three key stages of the battery life cycle (early stage SOH≈95%, mid-stage SOH≈85%, and late stage SOH≈75%), and the results are shown in Table 1. Table 1. Root mean square error results for SOH estimation using the three methods.

[0073] (1) Superior performance throughout the entire battery life cycle: As can be clearly seen from the table, the SOH estimation error of this method is always the lowest throughout the entire battery life cycle, especially in the later stages of aging, where its accuracy advantage is extremely significant. When the error of the comparison method 1 has increased to more than 5%, the error of this method can still be stably controlled within 1%.

[0074] (2) Contribution of fractional-order model: Compared with method one, method two has significantly improved accuracy (for example, the mid-term error decreased from 2.80% to 1.35%). This proves that the fractional-order ECM coupled with physical mechanism adopted in this scheme can more accurately characterize the dynamic characteristics of the battery than the traditional integer-order model, and provides a more reliable underlying model for SOH estimation.

[0075] (3) The core value of memristor degradation modeling: Compared with the second comparative method, the accuracy of this method has achieved a further and decisive leap (for example, the later error is reduced from 2.10% to 0.85%). This strongly proves the great superiority of the core innovation of this method - "memristor degradation modeling". Traditional ampere-hour throughput models cannot distinguish the differences in damage caused to the battery by different current and temperature stresses, while the memristor model of this method can accurately "memorize" and "quantify" the cumulative damage under dynamic conditions by integrating stress factors and nonlinear update rules. Therefore, its SOH estimation results are highly consistent with the actual physical aging process.

[0076] 2) Remaining useful life (RUL) prediction and results analysis When the battery's state of equilibrium (SOH) decays to 90%, the remaining number of cycles (RUL) required for the battery to reach its end-of-life (defined as SOH=80%) is predicted using the internal state of each model at that time. The experimentally measured true RUL is 1250 cycles, and the results are shown in Table 2.

[0077] Table 2. Remaining Useful Life (RUL) Prediction and Result Analysis

[0078] The prediction error of our proposed method for RUL is only 2.4%, far lower than the more than 16% of the two comparative methods. The fundamental reason is that the ampere-hour throughput model relied upon by the comparative methods is essentially a linear extrapolation, which cannot predict the accelerated aging phenomenon caused by stresses such as high rates and high temperatures under future dynamic operating conditions. In contrast, the memristor model of our proposed method already incorporates the influence of these nonlinear stress factors, and its inference of the future aging rate is more consistent with physical reality, thus resulting in more accurate and reliable predictions.

[0079] Furthermore, the dual-timescale self-calibration mechanism in this scheme ensures that the model can maintain long-term estimation accuracy and robustness when faced with sensor noise, sudden environmental changes, or aging of small, unmodeled anomalies, which is not available in the comparison methods.

[0080] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A battery SOH estimation method based on fractional order equivalent and memristor degeneration modeling, characterized in that, Includes the following steps: S10, acquire the battery's operating data during the current charge-discharge cycle, the operating data including operating current, port voltage, temperature and state of charge; S20, Based on the aforementioned operating data, a joint state-space model is constructed according to the fractional-order equivalent circuit model and the memristor degradation model; Among them, the memristor degradation model is used to calculate the comprehensive stress factor based on multiple stress factors during the battery charge-discharge cycle, and update the memristor state value according to the nonlinear update rule. The state value is used to characterize the cumulative damage of the battery. The order of the fractional-order components in the fractional-order equivalent circuit model is dynamically modeled as a function of the battery's internal operating state and the memristor state value. S30, the fractional-order equivalent circuit model and the memristor degradation model are combined to establish a joint state-space model, and the unscented Kalman filter algorithm is used to solve the joint state-space model so as to simultaneously estimate the battery health state and the parameters of the fractional-order equivalent circuit model online. S40, The estimation process is corrected and adjusted based on dual time scales, which include short-timescale online correction based on the inherent consistency of the model and long-timescale offline correction based on historical data review; S50 outputs the corrected and adjusted battery health status estimate.

2. The battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling as described in claim 1, characterized in that, In step S20, the order of the fractional element includes an order characterizing a charge transfer process and an order characterizing a solid phase diffusion process ; The order of the charge transfer process Modeled as: The order characterizing the solid-phase diffusion process Modeled as: In the formula, Indicates the new battery at the reference temperature The initial order below; It is the decay coefficient of memristor impairment with respect to order; It is the temperature influence coefficient; T Indicates battery temperature; M This indicates the state value of the memristor.

3. The battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling as described in claim 1, characterized in that, In step S20, the comprehensive stress factor Calculate using the following formula: in, and These are the current ratio influence coefficient and the average absolute ratio, respectively. and These are the depth of discharge and its power-law exponent, respectively. Equivalent activation energy; It is the gas constant; Average temperature; Indicates the reference temperature.

4. The battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling as described in claim 1, characterized in that, In step S20, the memristor state value is updated according to the nonlinear update rule, and the calculation formula is as follows: In the formula, This indicates the memristor state value after the current cycle; This represents the memristor state value after the previous cycle, initial value. ; It is the base aging rate related to the average SOC; This represents the overall stress factor for the current cycle; It has a power exponent The saturation inhibition term, It is the theoretical maximum charge loss.

5. The battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling as described in claim 1, characterized in that, In step S20, the state vector of the joint state-space model includes the battery's state of charge, overpotentials characterizing the charge transfer process, overpotentials characterizing the solid-phase diffusion process, charge transfer resistance, solid-phase diffusion resistance, and memristor state values.

6. The battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling as described in claim 1, characterized in that, In step S40, the short timescale online correction includes: dynamically adjusting the process noise covariance matrix of the unscented Kalman filter based on the consistency residual between the charge transfer resistance estimated by the unscented Kalman filter and the theoretical internal resistance calculated according to the memristor degradation model.

7. The battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling as described in claim 1, characterized in that, In step S40, the long-timescale offline correction includes: periodically using historical charge-discharge cycle data and the corresponding true health state values ​​to construct a global optimization problem with the goal of minimizing the health state estimation error, and using an optimization algorithm to solve it to update the hyperparameters in the fractional-order equivalent circuit model and the memristor degradation model.

8. The battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling as described in claim 7, characterized in that, The optimization algorithm is the particle swarm optimization algorithm.

9. The battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling as described in claim 1, characterized in that, In step S50, the output battery health status estimation result includes a real-time updated health status value and multi-dimensional diagnostic indicators derived from the fractional equivalent circuit model parameters and memristor state values.

10. A battery management system, characterized in that, It includes a processor and a memory, the memory storing a computer program that, when executed by the processor, implements the steps of the battery SOH estimation method based on fractional-order equivalent and memristor degradation modeling as described in any one of claims 1 to 9.

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