IPOA optimization-based improved unscented Kalman lithium battery state joint estimation method

Abstract

The invention provides an improved unscented Kalman lithium battery state joint estimation method based on IPOA optimization. The improved unscented Kalman lithium battery state joint estimation method comprises the following steps: S1, firstly, constructing a fractional-order second-order RC equivalent circuit model number; according to the method, a battery fractional-order second-order equivalent circuit model is constructed, model parameters are identified by adopting an adaptive genetic algorithm (AGA), the influence of historical data is considered on the basis of UKF, a multi-information theory is combined, an adaptive attenuation factor is introduced to overcome the influence of historical measured values on an estimation result, initial value deviation is inhibited, and the estimation accuracy is improved. A noise adaptive link is introduced to carry out adaptive updating on system noise covariance, an improved pelican algorithm (IPOA) is adopted to optimize distribution adjustment parameters of a UKF during UT transformation, the improved pelican algorithm is adopted to optimize a fractional order multi-innovation adaptive unscented Kalman algorithm (IPOA-FOMIAUKF) to estimate SOC, and finally, a multi-time scale theory is combined, so that the system noise covariance is optimized. The SOC of the battery is estimated by adopting the IPOA-FOMIAUKF under the micro-scale, the SOH is estimated through the UKF under the macro-scale, and the state joint estimation based on the IPOA-FOMIAUKF-UKF is realized through iterative updating.

Description

Technical Field

[0001] This invention relates to the field of battery management technology, and in particular to an improved unscented Kalman lithium battery state joint estimation method based on IPOA optimization. Background Technology

[0002] Against the backdrop of global sustainable development, electric vehicles have broad prospects. As the most important energy storage unit and power source for electric vehicles, the development of power batteries is particularly crucial. Lithium batteries have been widely used due to their advantages such as low pollution and long lifespan. At present, battery management systems (BMS) can be used to monitor and manage battery packs, which can effectively improve the lifespan of battery packs, ensure battery pack safety, and avoid driving hazards. Among them, the estimation of state of charge (SOC) and state of health (SOH) is the core of BMS. Accurate estimation of battery SOC and SOH can ensure the safety and reliability of battery system. Establishing an accurate battery model is an important prerequisite for accurately estimating the battery state. The equivalent circuit model represents the external characteristics of the battery through circuit elements. It has a simple structure and is easy to implement, and is the most widely used in practical applications. According to the order of the state equation, it can be divided into two categories: integer order model (IOM) and fractional order model (FOM). Most existing studies are based on the equivalent circuit model of the battery with integer order. However, the integer order model often produces certain errors because it does not take into account the fractional order characteristics of the circuit elements. In terms of state estimation, current SOC estimation methods mainly fall into three categories: traditional experimental methods, data-driven methods, and model-based methods. Traditional experimental methods are easy to implement and relatively stable, but long-term static use can accumulate errors, leading to a decrease in accuracy. Data-driven SOC estimation methods have also received widespread attention in recent years. These methods offer high model accuracy but require a large amount of data for training. Model-based methods are based on battery models and incorporate filters, and are currently the mainstream of estimation algorithm research. They mainly include Kalman filter algorithms and particle filter algorithms. Compared to particle filtering, Kalman filtering converges faster and is more stable. Among them, the unscented Kalman filter (UKF) algorithm is more suitable for solving strongly nonlinear system problems, and scholars at home and abroad have conducted extensive research based on it. Traditional UKF does not consider the correction of historical data. Aung H, based on an integer-order equivalent circuit model, extended the single innovation in the algorithm to multiple innovations, proposing the multi-innovation unscented Kalman filter (MIUKF) algorithm, but the accuracy of the integer-order model is limited. Patent CN202410317286.X builds the algorithm on a fractional-order battery model and proposes a multi-scale fractional-order multi-novel unscented Kalman filter (DFOMIUKF) to estimate the SOC, which further improves the accuracy. However, it does not take into account the influence of initial value deviation and noise that may exist during battery charging and discharging. In addition, the selection of parameters in UKF will also affect the algorithm performance. The algorithm still has a lot of room for improvement.

[0003] Accurate estimation of battery state is essential for ensuring the safety and reliability of battery systems. Battery charging and discharging behaviors (such as deep discharge or overcharge) affect changes in SOC and further accelerate battery aging, leading to a decrease in SOH. As SOH decreases, the actual capacity of the battery decreases, which in turn causes deviations in the calculation of SOC. Therefore, SOC and SOH are often independent but closely coupled. Current state estimation research mostly focuses on SOC and often does not consider the influence and role of SOH on SOC. To address this, we propose an improved unscented Kalman lithium battery state joint estimation method based on IPOA optimization. Summary of the Invention

[0004] In view of this, embodiments of the present invention provide an improved unscented Kalman lithium battery state joint estimation method based on IPOA optimization to solve or alleviate the technical problems existing in the prior art, and at least provide a beneficial option.

[0005] The technical solution of this invention is implemented as follows: an improved unscented Kalman lithium battery state joint estimation method based on IPOA optimization, comprising the following steps: S1. First, construct a fractional second-order RC equivalent circuit model. Obtain the state space model of the model according to Kirchhoff's laws. Discretize it using the GL definition of fractional calculus. Reduce the subsequent computation by defining fractional calculus in direct discrete time form. Use AGA to identify model parameters in the discrete model. The discrete state-space equations of the fractional-order model of the nonlinear system of a lithium battery are as follows: (1) in, for The state variables of the system at any given time, ; , for The input variable of the system at any given time is the load current; for The output variable of the system at any given time is the terminal voltage; The state equations are nonlinear. The equation is a nonlinear observation equation; and For random variables With observed variables Gaussian white noise, and These are the variance matrices; We obtained current-voltage related data under constant current pulse charge and discharge conditions through experiments, obtained the relationship between SOC and OCV through polynomial fitting, and used AGA to identify the parameters to be identified in the battery fractional-order model. S2. In terms of the state estimation algorithm, it is improved based on UKF, initializes the state and system state covariance matrix, performs UT transformation to collect Sigma points and calculates the corresponding weights; S3. When calculating the Sigma sampling points, the matrix may be non-positive definite. Singular value decomposition is used to decompose the system state covariance matrix P. S4. When performing UT transformation on UKF, the distribution adjustment parameters are optimized. Based on POA, three optimization strategies are introduced: Sine chaotic mapping, Lévy flight strategy and adaptive nonlinear decay factor. IPOA is proposed, and the UT transformation distribution adjustment parameters are optimized based on IPOA. S5. Perform prior state estimation at the microscale, update the state vector and covariance, design an adaptive decay factor multiplied with the prior error covariance, update the prior error covariance matrix and perform weighted processing. S6. Define a single-innovation sequence for , representing the difference between the current measurement value and the previous measurement value of the system, expands the single innovation by introducing multiple innovations, iteratively updates the innovation sequence, and updates the posterior state and the posterior state error covariance; S7. Since the noise cannot be kept at a fixed value due to changes in the actual environment, a noise adaptive step is introduced to adaptively update the system noise covariance. S8. The battery's State of Harmony (SOH) is represented by the degradation of battery capacity. During charging and discharging, the maximum usable capacity of the battery gradually decreases. Introducing multi-timescale theory, a joint estimation algorithm of IPOA-FOMIAUKF-UKF is constructed. IPOA-FOMIAUKF estimates the State of Charge (SOC) at the microscale, while UKF estimates the SOH at the macroscale. The time step at the macroscale is set to... The time step at the microscale is set to ,and When the time step achieve At that time, a transformation from micro to macro scale is performed, using battery capacity as the parameter and state quantity of the SOH estimation algorithm. The health state is calculated by estimating the maximum actual capacity of the battery at the current moment, and the input of the SOC estimation is updated with the SOH estimation output, thus realizing the joint estimation of SOC and SOH.

[0006] In some embodiments, the steps in S4 of introducing three optimization strategies based on POA—Sine chaotic mapping, Lévy flight strategy, and adaptive nonlinear decay factor—are as follows: S41. Set population initialization parameters and use Sine chaotic mapping to initialize the population to improve the diversity of the initial population; S42. The algorithm performs the first stage of global search, and performs a global search based on minimizing the fitness function. S43. The algorithm proceeds to the second stage, the local search stage. In this stage, the algorithm simulates a pelican diving into the water to catch prey and conducts a local search near the current optimal solution. The Levy flight is introduced to solve the problem that traditional wandering search lacks long-distance jumping ability and is prone to premature convergence and getting trapped in local optima. S44. In the local search phase, design an adaptive nonlinear decreasing factor to replace the traditional linear weight factor in the original algorithm, establish the algorithm behavior formula for the second-stage local search, and select a new position and update the position by judging the fitness function.

[0007] In some embodiments, in S4, the optimization of the UT transformation distribution adjustment parameters based on IPOA uses the root mean square error of the SOC estimation as the fitness function of the algorithm, defining the distribution adjustment parameters... Fitness function for optimization As shown in the following formula: (2) in, Population size; The first SOC estimate One actual value; For the first Output estimate obtained from one measurement; The algorithm performs global exploration and local fine-grained search based on the fitness function. Iteratively searches for the parameter with the minimum mean square error until the maximum number of iterations. At this point, the sampling point distribution state control parameter found by the optimization algorithm is the optimal value, and the optimal value is returned to the estimation algorithm.

[0008] In some embodiments, in S6, the multiple innovation matrix As shown in the following formula: (3) Since the multi-news unscented Kalman filter algorithm cannot distinguish between new and old data during the calculation process, and the influence of new and old measurements on the calculation is the same, in order to solve the problem of data saturation caused by the cumulative interference of historical data, a weight factor is introduced into the state vector to weaken the correction weight of historical data and update the posterior state and the posterior state error covariance.

[0009] In some embodiments, in S8, SOH can be obtained by solving the following formula: (4) in, This represents the battery's maximum actual capacity at the current moment. This refers to the battery's rated capacity.

[0010] In some embodiments, in S1, the fractional-order second-order equivalent circuit model structure can be used to obtain the state-space expression of the above model according to Kirchhoff's laws: (5) For ohmic internal resistance, and For resistance, and A fractional capacitor, abbreviated as and , This refers to the open circuit voltage (OCV) of a lithium battery. and They are respectively and The voltage across the two ends, and These are the terminal voltage and the load current, respectively. and fractional-order element and The order; The battery SOC value is obtained using the ampere-hour integration method, which is the sampling period. The rated capacity of the battery. For Coulomb efficiency.

[0011] In some embodiments, in S1, the GL definition of fractional calculus discretizes the state-space expression. By defining fractional calculus in direct discrete-time form, the resulting discretized fractional state-space model reduces subsequent computational complexity. The discretized form of the GL fractional derivative is defined as follows: (6) In the formula, For order, The sampling time interval is... For memory length, The range of values ​​is integers, It is a time-domain function. The binomial coefficients in fractional calculus are defined as: (7) In the formula, For gamma function, It is a natural constant; Discretization yields: (8) The above formula and They are respectively denoted as and Define the state vector The SOC value of the battery is obtained using the ampere-hour integration method, and its discrete expression is obtained by integrating the current over time: (9) In the formula, The rated capacity of the battery. Coulomb efficiency, which is the efficiency of the battery during cyclic charging and discharging, can be set to 1; Discretizing the state-space equations and writing them in matrix form yields: (10) Define measurement value , The discretized model can be obtained by rearranging the equations as follows: (11) In the formula, for System state variables at any given time, for Output variables at all times; and These are observation noise and measurement noise, respectively. , , , .

[0012] In some embodiments, in S1, the AGA algorithm dynamically adjusts its parameters by introducing an adaptive mechanism, thereby improving the search optimization speed and identification accuracy of the algorithm. This is achieved by adopting the AGA identification model parameters. , , , , and ; The fitness function is used to evaluate the quality of an individual, and the optimal fitness function can be expressed as: (12) in, Represents the fitness of each individual. Indicates the current population, This represents the maximum value of the sum of squared errors; In the AGA algorithm, crossover and mutation can dynamically adjust the population state based on fitness, and the crossover probability... and mutation probability The adaptive adjustment function is: (13) (14) in, The maximum fitness in the population, For average fitness, , , and A constant used to adjust the probability; When the battery charging / discharging starts or stops, the capacitor... and voltage and It is constant, but the terminal voltage will change due to internal resistance. The value changes with the current, decreasing or increasing; therefore, among the parameters to be identified... It can be calculated using the characteristics of the terminal voltage change, except... All other parameters are identified using AGA.

[0013] The embodiments of the present invention have the following advantages due to the adoption of the above technical solutions: I. This invention constructs a fractional-order second-order equivalent circuit model of a battery and uses an adaptive genetic algorithm (AGA) to identify model parameters. For state estimation, it considers the influence of historical data on the UKF model and incorporates multiple innovation theory, introducing an adaptive decay factor to overcome the influence of historical measurements on the estimation results and suppress initial value bias. A noise adaptive stage is introduced to adaptively update the system noise covariance. Simultaneously, an improved pelican algorithm (IPOA) is used to optimize the distribution adjustment parameters of the UKF during UT transformation, and the pelican algorithm is further improved to optimize the fractional-order multiple-innovation adaptive unscented Kalman algorithm (IPOA-FOMIAUKF) for SOC estimation. Finally, combining multi-timescale theory, the IPOA-FOMIAUKF is used to estimate the battery SOC at the microscale, and the UKF is used to estimate the SOH at the macroscale. Iterative updates achieve joint state estimation based on IPOA-FOMIAUKF-UKF.

[0014] Second, this invention establishes a fractional-order equivalent circuit model of a battery by utilizing the fractional-order characteristics of circuit elements, thereby reducing the error caused by the integer-order model neglecting this fractional-order characteristic. The AGA is used to identify model parameters to further improve model accuracy.

[0015] Third, this invention optimizes the distribution adjustment parameters in the unscented transformation of UKF by proposing an IPOA that integrates the Sine chaotic mapping strategy, the Lévy flight strategy, and the adaptive nonlinear decay factor for optimizing the distribution adjustment parameters.

[0016] Fourth, this invention introduces multiple innovation theory into the UKF-based estimation algorithm, taking into account the influence of historical data, and uses innovations at multiple times to correct the state of the system.

[0017] Fifth, this invention overcomes the influence of historical measurements on the estimation results by introducing an adaptive attenuation factor, increases the weight of the current measurement's influence, limits the filter's memory length, and suppresses initial value bias. Furthermore, it introduces a noise adaptive mechanism to adaptively update the system noise covariance, improving the algorithm's robustness and accuracy. This enhances the accuracy and stability of state estimation.

[0018] VI. The multi-timescale theory used in this invention for state estimation takes into account the influence of SOH on SOC. It proposes to estimate SOC at the microscale using IPOA-FOMIAUKF and estimate SOH at the macroscale using UKF. The joint estimation of SOC and SOH is achieved through alternating iterative updates.

[0019] The above overview is for illustrative purposes only and is not intended to be limiting in any way. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features of the invention will become readily apparent from the accompanying drawings and the following detailed description. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a diagram illustrating the overall technical framework of the present invention; Figure 2 This is a diagram of the fractional-order second-order RC equivalent circuit of the present invention; Figure 3 This is a flowchart of the AGA parameter identification process of the present invention; Figure 4 The flowchart of the IPOA-FOMIAUKF-UKF joint estimation algorithm of the present invention is shown below; Figure 5 The SOC estimation results and error curves of this invention are shown below; Figure 6 The above is a graph showing the SOH estimation results and error curves of this invention. Detailed Implementation

[0022] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0023] It is important to note that terms such as "first," "second," "symmetric," "array," "set in," and "set with" are used only to distinguish between descriptive and positional descriptions and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, features specified with terms such as "first" or "symmetric" may explicitly or implicitly include one or more of that feature; similarly, when the quantity of certain features is not limited by words such as "two" or "three," it should be noted that such features also explicitly or implicitly include one or more features.

[0024] In this invention, unless otherwise explicitly specified and limited, terms such as "installation," "connection," and "fixation" should be interpreted broadly; for example, they can refer to a fixed connection, a detachable connection, or an integral molding; they can refer to a mechanical connection, a direct connection, a welding connection, or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the accompanying drawings and specific circumstances.

[0025] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0026] like Figures 1-6 As shown, this embodiment of the invention provides an improved unscented Kalman lithium battery state joint estimation method based on IPOA optimization, including the following steps: S1. First, a fractional second-order RC equivalent circuit model is constructed. The state space model of the model is obtained according to Kirchhoff's laws. The model is discretized using the GL definition of fractional calculus. The fractional calculus is defined in direct discrete time form to reduce the subsequent computation. The model parameters are identified using AGA. Current and voltage related data under constant current pulse charging and discharging conditions are obtained through experiments. The relationship between SOC and OCV is obtained through polynomial fitting. AGA is used to identify the parameters to be identified in the fractional-order battery model. S2. In terms of the state estimation algorithm, it is improved based on UKF, initializes the state and system state covariance matrix, performs UT transformation to collect Sigma points and calculates the corresponding weights; S3. When calculating the Sigma sampling points, the matrix may be non-positive definite. Singular value decomposition is used to decompose the system state covariance matrix P. S4. When performing UT transformation on UKF, the distribution adjustment parameters are optimized. Based on POA, three optimization strategies are introduced: Sine chaotic mapping, Lévy flight strategy and adaptive nonlinear decay factor. IPOA is proposed, and the UT transformation distribution adjustment parameters are optimized based on IPOA. S5. Perform prior state estimation at the microscale, update the state vector and covariance, design an adaptive decay factor multiplied with the prior error covariance, update the prior error covariance matrix and perform weighted processing. S6. Define a single-innovation sequence for , representing the difference between the current measurement value and the previous measurement value of the system, expands the single innovation by introducing multiple innovations, iteratively updates the innovation sequence, and updates the posterior state and the posterior state error covariance; S7. Since the noise cannot be kept at a fixed value due to changes in the actual environment, a noise adaptive step is introduced to adaptively update the system noise covariance. S8. The battery's State of Harmony (SOH) is represented by the degradation of battery capacity. During charging and discharging, the maximum usable capacity of the battery gradually decreases. Introducing multi-timescale theory, a joint estimation algorithm of IPOA-FOMIAUKF-UKF is constructed. IPOA-FOMIAUKF estimates the State of Charge (SOC) at the microscale, while UKF estimates the SOH at the macroscale. The time step at the macroscale is set to... The time step at the microscale is set to ,and When the time step achieve At that time, a transformation from micro to macro scale is performed, using battery capacity as the parameter and state quantity of the SOH estimation algorithm. The health state is calculated by estimating the maximum actual capacity of the battery at the current moment, and the input of the SOC estimation is updated with the SOH estimation output, thus realizing the joint estimation of SOC and SOH.

[0027] In this embodiment, specifically in S1, the fractional-order second-order equivalent circuit model structure is as follows: Figure 2 As shown, according to Kirchhoff's laws, the state-space expression of the above model can be obtained: (5) For ohmic internal resistance, and For resistance, and A fractional capacitor, abbreviated as and , This refers to the open circuit voltage (OCV) of a lithium battery. and They are respectively and The voltage across the two ends, and These are the terminal voltage and the load current, respectively. and fractional-order element and The order; The battery SOC value is obtained using the ampere-hour integration method, which is the sampling period. The rated capacity of the battery. For Coulomb efficiency.

[0028] The GL definition of fractional calculus discretizes the state-space expression. By defining fractional calculus in direct discrete-time form, the resulting discretized fractional state-space model reduces subsequent computational costs. The discretized form of the GL fractional derivative is defined as follows: (6) In the formula, For order, The sampling time interval is... For memory length, The range of values ​​is integers, It is a time-domain function. The binomial coefficients in fractional calculus are defined as: (7) In the formula, For gamma function, It is a natural constant; Discretization yields: (8) The above formula and They are respectively denoted as and Define the state vector. The SOC value of the battery is obtained using the ampere-hour integration method, and its discrete expression is obtained by integrating the current over time:

[0029] (9) In the formula, The rated capacity of the battery. Coulomb efficiency, which is the efficiency of the battery during cyclic charging and discharging, can be set to 1; Discretizing the state-space equations and writing them in matrix form yields: (10) Define measurement value , The discretized model can be obtained by rearranging the equations as follows: (11) In the formula, for System state variables at any given time, for Output variables at all times; and These are observation noise and measurement noise, respectively. , , , .

[0030] In this embodiment, specifically in S1, the AGA algorithm dynamically adjusts its parameters by introducing an adaptive mechanism, thereby improving the search optimization speed and identification accuracy of the algorithm. This is achieved by adopting the AGA identification model parameters. , , , , and ; The fitness function is used to evaluate the quality of an individual, and the optimal fitness function can be expressed as: (12) in, Represents the fitness of each individual. Indicates the current population, This represents the maximum value of the sum of squared errors; In the AGA algorithm, crossover and mutation can dynamically adjust the population state based on fitness, and the crossover probability... and mutation probability The adaptive adjustment function is: (13) (14) in, The maximum fitness in the population, For average fitness, , , and A constant used to adjust the probability; When the battery charging / discharging starts or stops, the capacitor... and voltage and It is constant, but the terminal voltage will change due to internal resistance. The value changes with the current, decreasing or increasing; therefore, among the parameters to be identified... It can be calculated using the characteristics of the terminal voltage change, except... All other parameters are identified using AGA.

[0031] In this embodiment, specifically in S1 to S3, the discrete state-space equations of the fractional-order model of the lithium battery nonlinear system are as follows: (1) in, for The state variables of the system at any given time, ; , for The input variable of the system at any given time is the load current; for The output variable of the system at any given time is the terminal voltage; The state equations are nonlinear. The equation is a nonlinear observation equation; and For random variables With observed variables Gaussian white noise, and These are the variance matrices.

[0032] Initialize state vector Initial value of covariance Initial value of process noise covariance Measure the initial value of noise covariance The initial state and system state covariance matrix are as follows: (15) UKF acquires Sigma points through UT transformation, and the system covariance matrix is ​​obtained after performing a nonlinear transformation on the Sigma points. However, due to the influence of noise and errors, non-positive definite problems may arise in the matrix when calculating the Sigma sampling points. Therefore, the singular value decomposition method is used to calculate the system state covariance matrix. The decomposition is as follows: (16) In the formula, It is a diagonal matrix; and These are the left and right singular vector matrices, respectively. If it is a symmetric matrix, then The Sigma generated in the UT transformation using the decomposed covariance matrix is ​​as follows (17): (17) in, The length of the state vector; It is an adjustable parameter. Used to improve the accuracy of nonlinear approximation. As a scale adjustment factor, This is a distribution adjustment parameter for sampling points, used to set the distance from the point set to the mean point. It is usually set to 0 ≤ ≤1.

[0033] The formula for calculating the weights of Sigma points is as follows: (18) in, As a candidate parameter, These are non-negative weight coefficients.

[0034] In this embodiment, specifically in S4, the IPOA algorithm is proposed by integrating multiple strategies based on POA, and the distribution parameters of the sampling points are adjusted based on IPOA. To find the best option.

[0035] The main steps for optimizing IPOA distribution adjustment parameters are as follows: S41. Initialize the parameters of the IPOA algorithm, setting the population size, maximum number of iterations, problem dimension, and upper and lower limits of the distribution adjustment parameters. Traditional initialization methods limit population diversity, so a Sine chaotic mapping is introduced. The initialization formula is shown in the following equation: (19) in, is the chaos control parameter, a constant in the interval [0, 1], usually taken as 0.99; S42. Using the root mean square error of the SOC estimate as the fitness function, the fitness function F is defined as follows: (2) In the formula, Population size; The first value of the SOC estimate One predicted output, For the first Each measurement outputs an estimated value, and the fitness of the individual population is calculated based on the fitness function (2). The location of the solution is then randomly generated. In the first phase of global exploration, the algorithm continuously updates its position to approach the vicinity of the optimal solution. The simulation formula for the exploration phase is as follows: (20) In the formula, The first stage Only the Pelicans in the question The position and state of the dimension; Solve the parameters of the battery model. The position of the dimension; and They are random individuals and the first The objective function value for each individual; It is a random number equal to 1 or 2; The pelican's position is calculated according to equation (20), the optimal fitness value is searched globally, and the position is updated according to the following equation. If the new position of the pelican can improve the value of the fitness function, the current result is adopted and the pelican's position is updated. The algorithm can tend to move to the optimal region or position and can avoid the algorithm exploring non-optimal regions: (twenty one) in, For the first The Pelicans' new position status; This represents the objective function value for the first stage. S43. The second stage involves a refined search around the current optimal solution. To address the problem of the algorithm easily getting trapped in local optima during the search process, Lévy flight and an adaptive nonlinear decreasing factor are introduced. The algorithm behavior formula for this stage is: (twenty two) In the formula, For the second phase Only the Pelicans in the question The new positional state of the dimension; As an adaptive nonlinear decreasing factor, the range of local search around the individual is defined. This represents the current iteration number; The maximum number of iterations; This is a parameter that adjusts the step size to affect the effect; Let the random walk step size of the Levi flight be defined as follows: (twenty three) In the formula, For shape parameters; The direction vector follows a normal distribution; The position of the pelican during the local search phase is calculated according to formula (22), and the position is updated by the following formula: (twenty four) in, For the first The Pelicans' new position status; The fitness function value is based on the second stage; S44. When the loop iterates to the maximum number of iterations, output the optimal solution of the current distribution adjustment parameter, return the optimal solution to the estimation algorithm for updating, and re-estimate the SOC.

[0036] In this embodiment, specifically in S5, the prior equation and covariance matrix of the state equation, and the posterior equation and covariance matrix of the observation equation are calculated. During the time update process, the Sigma points are nonlinearly transformed according to the state equation of the nonlinear system, and the prior predictions of the sampling points are transformed. The state prediction is obtained by performing a weighted summation. ; (25) In calculating the covariance matrix To improve the estimation accuracy of the algorithm and reduce the impact of initial SOC values ​​and system noise on the estimation algorithm, an adaptive attenuation factor is introduced into the error covariance matrix. Covariance of prior error Multiplication is performed to update the prior error covariance matrix and weighting is applied to overcome the influence of historical measurements on the estimation results, increase the weight of the current measurement's influence, limit the filter's memory length, suppress initial value bias, prevent excessive divergence, and define an attenuation factor. for: (26) (27) in, Forgetting factor; To adjust the control coefficient, it is usually taken to be much less than 1; To observe the covariance matrix.

[0037] covariance matrix As shown in the following formula: (28) Observation equations of the computational system And update the weighted observations. and the observed covariance matrix ; (29) (30) in, Here is the noise covariance matrix; During the measurement update process, the system covariance matrix is ​​calculated using the following formula. and Kalman gain .

[0038] (31) (32) In this embodiment, specifically in S6, the state observation error covariance matrix and Kalman gain are updated, and the multiple innovation matrix and Kalman gain matrix are calculated. Define a single-innovation sequence for This represents the difference between the current measurement value and the previous measurement value. By introducing multiple innovations to extend the single innovation, and iteratively updating the innovation sequence, the multiple innovation matrix is ​​defined as follows: : (3) The extended Kalman gain is defined as: (33) By introducing multiple innovations, the algorithm considers not only the influence of the previous state information but also the influence of historical states during its operation. However, the multiple innovation unscented Kalman filter algorithm cannot distinguish between new and old data during the calculation process; the influence of new and old measurements on the calculation is the same. To solve the problem of data saturation caused by the cumulative interference of historical data, a weighting factor is introduced into the state vector. This weakens the adjustment weights of historical data. (State vector) Defined as:

[0039] (34) Weighting factors Set as , These are adjustable parameters; The posterior state Kalman gain variance matrix is ​​updated as follows: (35) In this embodiment, specifically in S7, the system noise covariance is adaptively updated. During the measurement update process, the system Kalman gain is calculated using the following formula. : (36) Since changes in the actual environment prevent noise from remaining at a fixed value, a noise adaptation step is introduced into the UKF algorithm to adaptively update the system noise covariance, thereby improving the robustness and accuracy of the algorithm. The formula for adaptively updating the system noise is as follows: (37) in, The window opening factor is set to 5.

[0040] In this embodiment, specifically in S8, a dual-filter method is used, combined with the multi-timescale principle to construct a discrete-time state-space equation. At the micro-timescale, the IPOA-FOMIAUKF algorithm is used to estimate and update the battery SOC, followed by SOH estimation at the macro-timescale, using the UKF algorithm for iterative updating and calculation of the estimated SOH. The timescale conversion value is set to... When the time step achieve At this time, a transformation from micro to macro time scales is performed to achieve simultaneous estimation of SOC and SOH by the IPOA-FOMIAUKF-UKF joint estimation algorithm. At both micro and macro scales, the two filtering algorithms run independently and iteratively update to achieve accurate estimation of the battery state. The flowchart of the IPOA-FOMIAUKF-UKF joint estimation algorithm at multiple time scales is shown below. Figure 4 The specific steps are as follows:

[0041] S81. Estimating SOC at the microscale and performing time and measurement updates of the state are described in detail in S3. S82. After the SOC estimation stage, compare the microscale step size. and macro scale The size of the step size, if Not achieved If the time series is calculated to the prior estimate, the loop will restart, and the result will be used as the new initial value for estimation. If the loop ends, the time scale is changed, and the prior state estimate and covariance error, and the posterior state estimate and error covariance are entered into the state update of SOH at the macro scale. S83. Perform time updates and measurement updates of SOH on a macroscopic time scale; State estimation was performed under constant current pulse charge-discharge conditions. The SOC results estimated based on the IPOA-FOMIAUKF-UKF and MIUKF, and IPOA-FOMIAUKF proposed in this invention are as follows: Figure 5 As shown in (a) and (b), the SOH estimation and error curves of the battery are as follows: Figure 6 As shown in (a) and (b), the estimated value of SOH has a small error compared with the reference value, indicating high accuracy and the ability to reflect the health status of the battery well.

[0042] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various variations or substitutions within the technical scope disclosed in the present invention, and these should all be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. An improved unscented Kalman lithium battery state joint estimation method based on IPOA optimization, characterized in that, Includes the following steps: S1. First, construct a fractional second-order RC equivalent circuit model. Obtain the state space model of the model according to Kirchhoff's laws. Discretize it using the GL definition of fractional calculus. Reduce the subsequent computation by defining fractional calculus in direct discrete time form. Use AGA to identify model parameters in the discrete model. The discrete state-space equations of the fractional-order model of the nonlinear system of a lithium battery are as follows: （1） in, for The state variables of the system at any given time, ; , for The input variable of the system at any given time is the load current; for The output variable of the system at any given time is the terminal voltage; The state equations are nonlinear. The equation is a nonlinear observation equation; and For random variables With observed variables Gaussian white noise, and These are the variance matrices; We obtained current-voltage related data under constant current pulse charge and discharge conditions through experiments, obtained the relationship between SOC and OCV through polynomial fitting, and used AGA to identify the parameters to be identified in the battery fractional-order model. S2. In terms of the state estimation algorithm, it is improved based on UKF, initializes the state and system state covariance matrix, performs UT transformation to collect Sigma points and calculates the corresponding weights; S3. When calculating the Sigma sampling points, the matrix may be non-positive definite. Singular value decomposition is used to decompose the system state covariance matrix P. S4. When performing UT transformation on UKF, the distribution adjustment parameters are optimized. Based on POA, three optimization strategies are introduced: Sine chaotic mapping, Lévy flight strategy and adaptive nonlinear decay factor. IPOA is proposed, and the UT transformation distribution adjustment parameters are optimized based on IPOA. S5. Perform prior state estimation at the microscale, update the state vector and covariance, design an adaptive decay factor multiplied with the prior error covariance, update the prior error covariance matrix and perform weighted processing. S6. Define a single-innovation sequence for , representing the difference between the current measurement value and the previous measurement value of the system, expands the single innovation by introducing multiple innovations, iteratively updates the innovation sequence, and updates the posterior state and the posterior state error covariance; S7. Since the noise cannot be kept at a fixed value due to changes in the actual environment, a noise adaptive step is introduced to adaptively update the system noise covariance. S8. The battery's State of Harmony (SOH) is represented by the degradation of battery capacity. During charging and discharging, the maximum usable capacity of the battery gradually decreases. Introducing multi-timescale theory, a joint estimation algorithm of IPOA-FOMIAUKF-UKF is constructed. IPOA-FOMIAUKF estimates the State of Charge (SOC) at the microscale, while UKF estimates the SOH at the macroscale. The time step at the macroscale is set to... The time step at the microscale is set to ,and When the time step achieve At that time, a transformation from micro to macro scale is performed, using battery capacity as the parameter and state quantity of the SOH estimation algorithm. The health state is calculated by estimating the maximum actual capacity of the battery at the current moment, and the input of the SOC estimation is updated with the SOH estimation output, thus realizing the joint estimation of SOC and SOH.

2. The improved unscented Kalman lithium battery state joint estimation method based on IPOA optimization according to claim 1, characterized in that: In S4, the steps for introducing three optimization strategies based on POA—Sine chaotic mapping, Lévy flight strategy, and adaptive nonlinear decay factor—are as follows: S41. Set population initialization parameters and use Sine chaotic mapping to initialize the population to improve the diversity of the initial population; S42. The algorithm performs the first stage of global search, and performs a global search based on minimizing the fitness function. S43. The algorithm proceeds to the second stage, the local search stage. In this stage, the algorithm simulates a pelican diving into the water to catch prey and conducts a local search near the current optimal solution. The Levy flight is introduced to solve the problem that traditional wandering search lacks long-distance jumping ability and is prone to premature convergence and getting trapped in local optima. S44. In the local search phase, design an adaptive nonlinear decreasing factor to replace the traditional linear weight factor in the original algorithm, establish the algorithm behavior formula for the second-stage local search, and select a new position and update the position by judging the fitness function.

3. The improved unscented Kalman lithium battery state joint estimation method based on IPOA optimization according to claim 1, characterized in that: In S4, the optimization of the UT transformation distribution adjustment parameters based on IPOA uses the root mean square error of the SOC estimation as the fitness function of the algorithm, defining the adjustment parameters for the distribution. Fitness function for optimization As shown in the following formula: （2） in, Population size; The first SOC estimate One actual value; For the first Output estimate obtained from one measurement; The algorithm performs global exploration and local fine-grained search based on the fitness function. Iteratively searches for the parameter with the minimum mean square error until the maximum number of iterations. At this point, the sampling point distribution state control parameter found by the optimization algorithm is the optimal value, and the optimal value is returned to the estimation algorithm.

4. The improved unscented Kalman lithium battery state joint estimation method based on IPOA optimization according to claim 1, characterized in that: In S6, the multiple innovation matrix As shown in the following formula: （3） Since the multi-news unscented Kalman filter algorithm cannot distinguish between new and old data during the calculation process, and the influence of new and old measurements on the calculation is the same, in order to solve the problem of data saturation caused by the cumulative interference of historical data, a weight factor is introduced into the state vector to weaken the correction weight of historical data and update the posterior state and the posterior state error covariance.

5. The improved unscented Kalman lithium battery state joint estimation method based on IPOA optimization according to claim 1, characterized in that: In S8, SOH can be obtained by solving the following formula: （4） in, This represents the battery's maximum actual capacity at the current moment. This refers to the battery's rated capacity.

6. The improved unscented Kalman lithium battery state joint estimation method based on IPOA optimization according to claim 1, characterized in that: In S1, the fractional-order second-order equivalent circuit model structure can be used to obtain the state-space expression of the above model according to Kirchhoff's laws: （5） For ohmic internal resistance, and For resistance, and A fractional capacitor, abbreviated as and , This refers to the open circuit voltage (OCV) of a lithium battery. and They are respectively and The voltage across the two ends, and These are the terminal voltage and the load current, respectively. and fractional-order element and The order; The battery SOC value is obtained using the ampere-hour integration method, which is the sampling period. The rated capacity of the battery. For Coulomb efficiency.

7. The improved unscented Kalman lithium battery state joint estimation method based on IPOA optimization according to claim 1, characterized in that: In S1, the GL definition of fractional calculus discretizes the state-space expression. By defining fractional calculus in direct discrete-time form, the resulting discretized fractional state-space model reduces subsequent computational complexity. The discretized form of the GL fractional derivative is defined as follows: （6） In the formula, For order, The sampling time interval is... For memory length, The range of values ​​is integers, It is a time-domain function. The binomial coefficients in fractional calculus are defined as: （7） In the formula, For gamma function, It is a natural constant; Discretization yields: （8） The above formula and They are respectively denoted as and Define the state vector The SOC value of the battery is obtained using the ampere-hour integration method, and its discrete expression is obtained by integrating the current over time: （9） In the formula, The rated capacity of the battery. Coulomb efficiency, which is the efficiency of the battery during cyclic charging and discharging, can be set to 1; Discretizing the state-space equations and writing them in matrix form yields: （10） Define measurement value , The discretized model can be obtained by rearranging the equations as follows: （11） In the formula, for System state variables at any given time, for Output variables at all times; and These are observation noise and measurement noise, respectively. , , , .

8. The improved unscented Kalman lithium battery state joint estimation method based on IPOA optimization according to claim 1, characterized in that: In S1, the AGA algorithm dynamically adjusts its parameters by introducing an adaptive mechanism, thereby improving the search optimization speed and identification accuracy. The AGA identification model parameters are adopted. , , , , and ; The fitness function is used to evaluate the quality of an individual, and the optimal fitness function can be expressed as: （12） in, Represents the fitness of each individual. Indicates the current population, This represents the maximum value of the sum of squared errors; In the AGA algorithm, crossover and mutation can dynamically adjust the population state based on fitness, and the crossover probability... and mutation probability The adaptive adjustment function is: （13） （14） in, The maximum fitness in the population, For average fitness, , , and A constant used to adjust the probability; When the battery charging / discharging starts or stops, the capacitor... and voltage and It is constant, but the terminal voltage will change due to internal resistance. The value changes with the current, decreasing or increasing; therefore, among the parameters to be identified... It can be calculated using the characteristics of the terminal voltage change, except... All other parameters are identified using AGA.

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