Battery state of charge estimation method based on fuzzy mathematics and genetic algorithm

Abstract

The present invention aims to provide a battery state of charge (SOC) estimation method based on fuzzy mathematics and genetic algorithm. The present invention comprises the following steps: step a, establishing a fuzzy model, using the fuzzy model to capture the fuzzy boundaries and uncertainties of parameters, and then constructing and fuzzy optimizing the fitness function through the fuzzy boundaries and uncertainties; step b, integrating the fuzzy optimized fitness function into the actual calculation process of the genetic algorithm, and making decisions based on the fuzzy optimized fitness function; step c, through multiple generations of genetic iterations, the population gradually converges to individuals with high fitness, and obtains the optimal estimation model of the target SOC value, then, compares the estimation result of the model with the actual observed value, and modifies the model parameters or structure according to the comparison result, and enters the next cycle, and repeats this process to dynamically adjust and optimize the model to adapt to the nonlinear changes in the state of the power battery. The present invention can be applied to the field of battery state monitoring and estimation technology.

Description

Technical Field

[0001] The present invention relates to the technical field of battery state monitoring and estimation, and in particular to a battery state of charge (SOC) estimation method based on fuzzy mathematics and genetic algorithm. Background Art

[0002] In electric vehicles, the battery state of charge (SOC) is like the dipstick in a fuel car, which has a decisive impact on energy management decisions, mileage estimation, battery working status, safety and life. However, SOC is not obtained through direct measurement, and its accurate estimation is affected by many factors such as ambient temperature, load curve, aging degree, self-discharge rate, etc., which has become a key issue to be solved in power battery research.

[0003] At present, researchers have proposed a variety of single-cell battery SOC estimation methods, which are mainly divided into two categories: direct estimation methods based on battery measurement data and indirect estimation methods based on battery models. These methods are committed to improving estimation accuracy and reliability, laying a solid foundation for the design and application of power battery management systems.

[0004] In the estimation problem, according to the different processing methods, it can be divided into static estimation and state estimation (optimal estimation). Static estimation focuses on using measurement equations and measurement data to directly infer system parameters or states; while optimal estimation emphasizes using the system's dynamic state equations and measurement equations, combined with observations to estimate the system's state values. The goal of optimal estimation is to process observations using some optimal criteria based on system process noise, measurement noise, and initial conditions to obtain the most reliable estimate of system variables in the current state.

[0005] In battery management technology and vehicle control decisions for electric vehicles, power battery SOC estimation is a crucial and highly concerned core issue. In response to this challenge, scholars have proposed a variety of unique solutions. Among them, the single-cell SOC estimation method based on the Kalman filter algorithm system is highly respected by the academic community for its extremely high estimation accuracy and excellent online error correction capabilities, and has become one of the hot spots in the current research field.

[0006] However, in practical applications, due to the nonlinear characteristics of power batteries and the complex and changeable vehicle application environment, there are many difficulties in estimating and calculating SOC. The SOC estimation using fuzzy mathematics for optimal estimation has the following three technical disadvantages:

[0007] 1. Limitations of existing SOC estimation methods:

[0008] Strong dependence: Direct estimation methods based on battery measurement data often rely on high-precision sensors and a stable measurement environment. In actual applications, sensor accuracy may have errors, and changes in environmental conditions (such as temperature and humidity) may affect the reliability of measurement data.

[0009] Model complexity and parameter uncertainty: Indirect estimation methods based on battery models usually require the establishment of complex electrochemical models. Accurate calibration of model parameters is often difficult, and parameters change with battery aging and operating conditions, resulting in reduced model prediction accuracy.

[0010] Limited nonlinear processing capabilities: Existing methods may be insufficient in processing the complex nonlinear dynamic behavior inside the battery, especially under battery aging and extreme operating conditions, where nonlinear effects may lead to increased estimation errors;

[0011] Lack of adaptability: Most existing methods lack effective online learning and adaptive adjustment mechanisms when faced with dynamic changes in battery status and the complexity of environmental conditions, making it difficult for the estimation results to respond to changes in actual operating conditions in real time.

[0012] 2. Universality of optimal estimation methods:

[0013] Noise sensitivity: When dealing with system process noise and measurement noise, the optimal estimation method strives to minimize their impact, but large errors may still occur in high-noise environments;

[0014] Dependence on initial conditions: The convergence speed and final accuracy of the optimal estimate often depend on the accurate setting of the initial state, but in practical applications the initial state may be difficult to accurately know.

[0015] 3. Challenges of fuzzy mathematics application:

[0016] Difficulty in designing membership functions: In battery state prediction, constructing a realistic fuzzy membership function is a complex task that requires a deep understanding of battery characteristics and a large amount of experimental data support. Otherwise, the fuzzy model may not be able to generalize well enough.

[0017] Uncertainty of fuzzy reasoning: In the process of fuzzy logic reasoning, the operations of intersection, union, complement, etc. of fuzzy sets and the synthesis of fuzzy rules may increase the uncertainty of the results, which may affect the accuracy of the final estimation results.

[0018] In summary, the main technical disadvantages of existing battery state of charge (SOC) estimation methods include strong dependence, model complexity and parameter uncertainty, limited nonlinear processing capabilities, lack of adaptability, and noise sensitivity and initial condition dependence of the optimal estimation method. When applying fuzzy mathematics, there are challenges such as difficulty in designing membership functions and uncertainty in fuzzy reasoning. Summary of the invention

[0019] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a battery state of charge (SOC) estimation method based on fuzzy mathematics and genetic algorithm. The method of the present invention can more flexibly adapt to the nonlinear characteristics and complex environmental conditions of the battery, thereby improving the accuracy and reliability of SOC estimation.

[0020] The technical solution adopted by the present invention is a battery state of charge (SOC) estimation method based on fuzzy mathematics and genetic algorithm, which includes the following steps:

[0021] Step a: According to the physical and chemical parameters involved in battery SOC estimation, fuzzy sets and membership functions that conform to actual characteristics are established, fuzzy models are established through fuzzy sets and membership functions, fuzzy boundaries and uncertainties of parameters are captured by fuzzy models, and fitness functions are constructed and fuzzily optimized through fuzzy boundaries and uncertainties;

[0022] Step b, integrating the fuzzy optimized fitness function into the actual calculation process of the genetic algorithm, generating an initial population with diversity and covering the solution space in the initialization stage; making decisions based on the fuzzy optimized fitness function in the genetic operations of selection, crossover and mutation;

[0023] Step c: Through multiple generations of genetic iterations, the population gradually converges to individuals with high fitness, that is, the optimal estimation model of the target SOC value. Then, the estimated results of this model are compared with the actual observed values, and the model parameters or structure are corrected according to the comparison results to enter the next round of "estimation-observation-correction" cycle. This cycle is repeated to dynamically adjust and optimize the model to adapt to the nonlinear changes in the power battery state and improve the accuracy and robustness of SOC estimation.

[0024] The specific steps of step a above are:

[0025] Step a1, defining fuzzy sets and membership functions: according to the characteristics of the optimization problem, define a set of fuzzy sets related to the target parameters, corresponding to different fuzzy levels or categories of battery capacity and polarization voltage; design a corresponding membership function for each fuzzy set;

[0026] Step a2: Construct a multi-objective fuzzy fitness function: Use weighted sum or product operation to combine the membership values ​​of each single objective:

[0027] or

[0028] ,

[0029] Among them, (C, Capacity) and (V, Voltage) represent fuzzy sets, which are expressed in order-even notation. w1 and w2 are weight coefficients used to balance the importance of different target parameters. Membership represents the membership function of the corresponding parameter in the corresponding fuzzy set. The fuzzy distribution adopts the intermediate Cauchy type, which is expressed as follows:

[0030] , ( ,β is a positive even number),

[0031] (χ, variable) is the fuzzy set of the membership function, which indicates the membership of the input value χ to the fuzzy set variable, where variable is the fuzzy set, χ is the input variable, which indicates the value of its membership to be evaluated; α is a parameter for adjusting the shape of the membership function, which determines the steepness of the function. The larger the α, the steeper the function and the faster the membership changes; β is another parameter for adjusting the shape of the membership function, which determines the tail behavior of the function. When β increases, the tail of the function becomes smoother and the membership changes more slowly;

[0032] Step a3, combining fuzzy decision rules and fuzzy logic operations to construct a fitness function: According to fuzzy rules and fuzzy logic operations, the performance of the solution vector on multiple fuzzy attributes is comprehensively judged, and finally an overall fitness value is obtained, and then a fitness function is constructed.

[0033] The specific steps of step b are:

[0034] Step b1, initializing the global solution set population space: creating a set number of solution vectors, which represent the battery state estimation;

[0035] Step b2: Construct a two-dimensional initial solution global solution set population space :The system equation of the battery model is defined as two-dimensional, and the solution vector obtained in step a directly constitutes the two-dimensional initial solution space ;

[0036] Step b3, designing a fuzzy optimized fitness function according to the power battery model: using fuzzy mathematical methods, defining a membership function to quantify the degree of match between each solution vector and the ideal battery state, the membership function takes into account the physical and chemical parameters of the battery model and its performance under different working conditions, and transforms the original continuous and uncertain evaluation into a definite membership value as the fitness function fitness through fuzzy sets and fuzzy logic operations;

[0037] Step b4, calculate the fitness of the solution vector: for each solution vector in the population space of the initial solution global solution set, apply the fuzzy optimized fitness function fitness to calculate its fitness value; construct a multi-objective fuzzy fitness function, and comprehensively consider the influence of multiple objectives by assigning variable weights to each single objective membership;

[0038] Step b5, select elite community: sort according to the fuzzy fitness value of the solution vector, select a set number of individuals with the highest fitness to form an elite community, and these individuals will be retained in subsequent iterations;

[0039] Step b6, eliminate low fitness solution vectors: low fitness solution vectors except the elite population are eliminated to make room for the new generation of population;

[0040] Step b7, pairing selection: using an appropriate mate selection strategy operator, select the paired paternal solution vector and maternal solution vector from the elite population for gene crossover operation;

[0041] Step b8, gene crossover and recombination: perform a crossover operation on the selected paternal and maternal solution vectors to generate a new offspring solution vector;

[0042] Step b9, mutation: According to the preset mutation probability, randomly select the solution vector in the offspring population for mutation operation, and use the mutation operator to change some genes of the solution vector in unpredictable directions;

[0043] Step b10, obtaining the offspring population: after crossover and mutation, a new offspring global solution set population space is formed;

[0044] Step b11, judging convergence and termination conditions: judging whether the algorithm has reached convergence according to a preset maximum number of generations or a convergence criterion based on the fuzzy fitness value;

[0045] Step b12, outputting the optimal solution vector: when the algorithm converges or reaches the maximum number of generations, the solution vector with the highest fuzzy fitness in the current global solution set population space is selected as the optimal solution, and this solution vector includes the predicted battery capacity and the predicted polarization voltage;

[0046] Step b13, end the algorithm: after the algorithm is executed, the optimal solution vector is output as the solution of the system equation of the predicted battery model.

[0047] In step c, error estimation is performed using an indicator function of the minimum model error criterion, wherein the indicator function of the minimum model error criterion is defined as:

[0048] J [ d ( t )] = 0 . 5 [ y ( t + D t ) − y ^ ( t + D t )] T R v − 1 [ y ( t + D t ) − y ^ ( t + D t )] + 0 . 5 d ( t ) T Wd ( t ) ,

[0049] in, is the system sampling interval, is the observation function output of the battery model, is the observation function output of the power battery. The indicator function consists of two penalty functions:

[0050] 1) Measurement residuals The weighted sum of squares,

[0051] 2) Model Error The weighted sum of squares,

[0052] in, is the error weighting matrix of the semi-positive definite model, and its parameter selection method adopts the NPF algorithm;

[0053] It is the inversion of the measurement noise covariance matrix. This parameter refers to the modeling process of the system measurement noise. Assuming that the system measurement noise is a stationary random process, the noise covariance matrix R v is modeled as:

[0054] R v ≈ 1 M ∑ k = 1 M { y ( t k ) − h [ x ^ ( t k ), t k ] } { y ( t k ) − h [ x ^ ( t k ), t k ] } T ,

[0055] in, is the time at time k, is the model observation value at time k, M is an integer representing the number of samples used to calculate the covariance matrix, T is the transposed symbol, represents the estimated state value at time k, h [ x ^ ( t k ), t k ] represents a functional function representing the estimated relationship of the model;

[0056] Under the nonlinear system model, the observation function output of the battery model is expressed as:

[0057] y ( t k ) = h [ x ˙ ( t k ), t k , i ( t k )] + n ( t k ) ,

[0058] in, is the time at time k, is the model observation value at time k, is the state equation output at time k, is a time-varying parameter, h [ x ˙ ( t k ), t k , i ( t k )] is a functional function representing the model-observation relationship, is a zero-mean Gaussian white noise;

[0059] Under the nonlinear system model, the observation function output of the power battery is expressed as:

[0060] y ^ ( t k ) = q [ x ˙ ( t k ), t k , i ( t k )] + w ( t k )

[0061] in, is the time at time k, is the power battery observation value at time k, is the state equation output at time k, is a time-varying parameter, q [ x ˙ ( t k ), t k , i ( t k )] is a functional function representing the observation relationship of the power battery, is a zero-mean Gaussian white noise;

[0062] The Taylor series expansion of the index function of the minimum model error criterion is performed, and the calculation expression of the model error term d(t) is expressed as:

[0063] d ( t ) =− { [ L ( D t ) S ( x ^ ( t )) ] T R − 1 L ( D t ) S ( x ^ ( t )) + W } − 1 × [ L ( D t ) S ( x ^ ( t )) ] T R − 1 [ Z ( x ^ ( t ), D t ) + y ^ ( t ) − y ( t + D t )]

[0064] in, , and They are all intermediate parameter matrices. The specific calculation methods are as follows:

[0065] S ( x ^ ( t )) = [ L g 1 L f r 1 − 1 h 1 ( x ^ ( t )) ⋯ L gn L f r 1 − 1 h 1 ( x ^ ( t )) ⋮ ⋱ ⋮ L g 1 L f rm − 1 h m ( x ^ ( t )) ⋯ L gn L f rm − 1 h m ( x ^ ( t )) ]

[0066]

[0067] L ( D t ) = [ l 11 ⋯ 0 ⋮ l ii ⋮ 0 ⋯ l mm ] , l ii = D t r i r i ! , i = 1 , 2 ,..., m

[0068] is the Lie derivative, where the parameters are defined as follows:

[0069] It is a Jacobi matrix that describes the sensitivity of the system state to the output, and is defined as the intermediate parameter matrix composed of the Jacobi matrices of the Lie derivative operator on the two vector fields g1 and f;

[0070] is the Lie derivative operator, which represents the directional derivative along the vector field g1,

[0071] represents the r1-1 iteration of the Lie derivative operator Lf,

[0072] is a scalar function, which represents the output state of the system and is the initial function of Lie derivative operation.

[0073] r is the relative order,

[0074] yes The order of

[0075] It is the Taylor series expansion form of the output function of a nonlinear system. It represents the approximate value of the system output Z at time t and time interval Δt. Each term in the formula is a Taylor series expansion term based on the Lie derivative.

[0076] in, is the time interval;

[0077] is the time interval raised to the power of a,

[0078] is the factorial of a,

[0079] is the index of the Taylor series expansion term,

[0080] is the order of the Taylor series expansion;

[0081] represents a Lie derivative L f For the output function h i a iterations of ;

[0082] is a matrix that describes the dynamic characteristics of a nonlinear system in time intervals. It is an m×m diagonal matrix, where the elements on the diagonal are λ ii , i=1,2,…,mi=1,2,…,m; it is positioned as an intermediate parameter matrix constructed in the form of a diagonal matrix with respect to the dynamic characteristics of the time interval;

[0083] in, is the time interval,

[0084] is the diagonal element of this matrix, which is defined as ,

[0085] is the factorial of the order of the Taylor series expansion,

[0086] is the order of the Taylor series expansion of the time interval Power,

[0087] yes The order of The order m is consistent,

[0088] is the index into this matrix;

[0089] According to the ergodic theorem, the covariance calculation expression of the model error term d(t) is as follows:

[0090] D =Cov[d(t)]=E[(d(t)-E[d(t)])(d(t)-E[d(t)]) T ] ,

[0091] Where D is the covariance of the model error term d(t) calculated by the time series, Cov[d(t)] is the covariance matrix of the model error term d(t), and the covariance matrix reflects the linear dependence between random variables. E[d(t)] is the expected mean of the model error term d(t), which represents the average value of the model error in all possible cases. (d(t)-E[d(t)]) represents the difference between the model error term d(t) and its expected value E[d(t)], which represents the deviation of the model error from its mean. (d(t)-E[d(t)]) T represents the transpose of the above bias vector;

[0092] The model error weighted matrix W is taken as the inverse of D, and then the current power battery state is updated according to this error:

[0093] x ˙ ( t ) = f [ x ˙ ( t ), t ] + g ( t ) d ( t ) ,

[0094] in, is the state variable of the system, which is the rate of change of the power battery state within this calculation cycle. f [ x ˙ ( t ), t ] It is used to describe the natural dynamic behavior of a system when there is no external disturbance, and reflects how the internal dynamics of the system affect the change of state. represents the model error correction term, d(t) is the model error amount, and g(t) is the model error allocation matrix;

[0095] Then record it as the power battery status of the next calculation cycle, which is ;

[0096] Enter the next round of "estimation-observation-correction" cycle, and repeat this process to dynamically adjust and optimize the model to adapt to the nonlinear changes in the power battery state.

[0097] The beneficial effects of the present invention are as follows: in the present invention, fuzzy mathematics and fitness function are deeply integrated, not only the model prediction accuracy is considered, but also multiple evaluations such as fuzzy attributes and environmental adaptability are included, thereby enhancing the comprehensiveness and accuracy of the fitness function; the fuzzy optimization fitness function is applied to the selection, crossover, mutation and other links of the genetic algorithm, thereby realizing the reasonable transmission and evolution of the fuzzy attributes, and improving the search efficiency and the generalization ability of the model; through the algorithm structure of the "inference-observation-correction" cycle, the model is adjusted and optimized in real time, effectively responding to the nonlinear changes in the state of the power battery, and ensuring the stability and accuracy of the estimation method under various working conditions; D is calculated, and then the error between the result of the nonlinear prediction based on the genetic algorithm and the actual measurement result is judged, thereby correcting the inference method, so the method of the present invention can more flexibly adapt to the nonlinear characteristics and complex environmental conditions of the battery, thereby improving the accuracy and reliability of SOC estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 It is a nonlinear prediction and estimation flow chart of power battery status using genetic algorithm optimized by fuzzy mathematics;

[0099] Figure 2 It is a simplified schematic diagram of the algorithm structure in the method of the present invention;

[0100] Figure 3 This is a graph showing the state of charge estimation results of the LCO battery at an operating temperature of 25°C. DETAILED DESCRIPTION

[0101] State of charge (SOC) is mainly used to describe the remaining power of the battery. It is the ratio of the remaining available power of the battery to the rated capacity. It can be expressed by the following formula:

[0102]

[0103] in, is the battery state of charge at time t, is the remaining battery power at time t, is the rated capacity of the battery, is the initial state of charge of the battery, is the coulombic efficiency of the battery, is the battery load current.

[0104] In engineering, the main parameters of the battery model can be regarded as functions of the operating temperature, thereby redefining the system equation of the battery model into the following form:

[0105]

[0106] U t ( t k ) = U OC [ SOC ( t k )] + U p ( t k ) + I L ( t k ) R s ( T ) + v ( t k )

[0107] Among them, the capacity of the battery , the DC internal resistance of the battery , the polarization resistance of the battery , the polarization capacitance of the battery All are functions of the operating temperature T. is the battery terminal voltage at a certain moment, is the polarization voltage. The model error term Contains the relevant errors of SOC(t) and Up (t), respectively expressed as model error and express.

[0108] Fuzzy mathematics was founded in 1965 by Professor LAZadeh, an American computer and control expert, to deal with uncertainty, ambiguity and imprecision. When the fitness evaluation of the optimization problem involves subjective factors, difficult-to-quantify attributes or uncertain boundaries, fuzzy mathematics can provide an effective method to quantify these fuzzy attributes. For example, a design may have multiple conflicting goals, and the importance of each goal or the satisfaction with the ideal solution can be described in fuzzy language (such as "very good", "good", "average", "poor"). Fuzzy mathematics can convert these fuzzy evaluations into numerical forms and incorporate them into the fitness function calculation. In some complex environments, data may contain noise, observation errors or incomplete information, resulting in uncertainty in the calculation of fitness values. Fuzzy mathematics can describe this uncertainty through fuzzy sets or fuzzy logic models and take it into account in the fitness calculation, so that the fitness function can better reflect the complexity of the real world. Fuzzy mathematics methods can introduce a certain degree of robustness to the fitness function, making it less sensitive to parameter changes or environmental disturbances. Through fuzzification, the fitness function may be able to tolerate a certain degree of data variation or model deviation, thereby maintaining stability and reliability during the optimization process.

[0109] like Figure 1 to Figure 3 As shown, in the method of the present invention, fuzzy mathematics is used to optimize the fitness function in the genetic algorithm. Specifically, firstly, a fuzzy set and a membership function that conform to the actual characteristics are established according to the physical and chemical parameters involved in the battery SOC estimation (such as Faraday voltage, working current, theoretical energy density and impedance spectrum, etc.), a fuzzy model is established through the fuzzy set and membership function, and the fuzzy model is used to capture the fuzzy boundaries and uncertainties of the parameters, and then the fitness function is constructed and fuzzily optimized through the fuzzy boundaries and uncertainties.

[0110] The fuzzy optimized fitness function is used as a tool to evaluate the correlation between the battery electrochemical model and the actual SOC value. This function not only takes into account the deviation between the model prediction value and the actual observation value, but also integrates fuzzy evaluation factors such as the adaptability of the model under different working conditions and the tolerance of parameter uncertainty. In this way, the fitness function can more comprehensively and accurately reflect the estimation performance of the model in a complex environment.

[0111] The fuzzy optimization fitness function is integrated into the actual process of the genetic algorithm. In the initialization phase, an initial population with a certain diversity and covering solution space is generated. In genetic operations such as selection, crossover and mutation, decisions are made based on the fuzzy optimization fitness function.

[0112] Through multiple generations of genetic iterations, the population gradually converges to individuals with high fitness, that is, the optimal estimation model for the target SOC value. Then, the estimated results of this model are compared with the actual observed values, and the model parameters or structure are corrected according to the comparison results, entering the next round of "estimation-observation-correction" cycle. This is repeated to dynamically adjust and optimize the model to adapt to the nonlinear changes in the power battery state and improve the accuracy and robustness of SOC estimation.

[0113] The specific steps are as follows.

[0114] Constructing the fitness function in a genetic algorithm using fuzzy mathematics involves the following steps:

[0115] 1. Define fuzzy sets and membership functions:

[0116] Fuzzy set: According to the characteristics of the optimization problem, a set of fuzzy sets related to the target parameters are defined. For example, for the problem of predicting the state of the power battery, fuzzy sets such as "high capacity", "medium capacity", "low capacity" and "ideal voltage", "close to ideal voltage", "deviate from ideal voltage" can be defined, corresponding to different fuzzy levels or categories of battery capacity and polarization voltage.

[0117] Membership function: Design a corresponding membership function for each fuzzy set. The membership function is a real-valued function whose domain is the actual value range under consideration (such as the actual measurement range of battery capacity or the variation range of polarization voltage) and whose range is [0, 1], indicating the degree to which a specific value belongs to the fuzzy set. Common types of membership functions include triangular membership function, trapezoidal membership function and Gaussian membership function. Choose appropriate shapes and parameters to reflect the transition characteristics of the target parameters at different fuzzy levels.

[0118] 2. Construct multi-objective fuzzy fitness function:

[0119] Generally speaking, for optimization problems that only focus on one target parameter (such as only considering battery capacity), the fitness function can be directly defined as the membership value of the fuzzy set corresponding to the parameter. For example, if the battery capacity corresponding to the current solution vector is C, then its fitness value F(C) is the membership of the "high capacity" fuzzy set to C. In this way, the fitness function converts the continuous and uncertain battery capacity evaluation into a definite membership value, reflecting the effectiveness of the solution vector in battery capacity prediction. In fact, the present invention needs to consider multi-objective situations. If multiple target parameters (such as battery capacity and polarization voltage) are considered at the same time, a multi-objective fuzzy fitness function needs to be constructed. A common method is to combine the membership values ​​of each single target using a weighted sum or product operation:

[0120] or

[0121]

[0122] Among them, (C, Capacity) and (V, Voltage) represent fuzzy sets, w1 and w2 are weight coefficients used to balance the importance of different target parameters. Membership represents the membership function of the corresponding parameter in the corresponding fuzzy set. w1 and w2 are used to balance the importance of different target parameters. The choice of weights can be dynamically adjusted according to the characteristics of the problem and actual needs or determined by optimization methods. There are three common representation methods used for fuzzy sets: (1) Zadeh representation (2) order-pair representation (3) vector representation. The above formula samples the order-pair representation. The above three methods are only a written expression method and have no effect on the implementation process of the present invention.

[0123] Membership represents the membership function of the corresponding parameter in the corresponding fuzzy set. It is determined according to the assignment method. In fact, the assignment method is a subjective method, which is mainly based on people's practical experience to determine a method of membership function of certain fuzzy sets. In practical applications, there are many methods for determining the membership function of fuzzy sets, which are mainly determined according to the practical significance of the problem. For example, in economic management and social management, the existing "objective scale" can be used as the membership of the fuzzy set. The fuzzy distribution assigned by the present invention is an intermediate Cauchy type, which is expressed as follows:

[0124] ( ,β is a positive even number)

[0125] (χ, variable) is a fuzzy set of the membership function, which indicates the membership of the input value χ corresponding to the fuzzy set variable, wherein variable is a fuzzy set, χ is an input variable, which indicates the value of its membership to be evaluated, and in fuzzy logic, χ can be any quantity that needs to be fuzzified, such as temperature, speed, etc. In the present invention, it is the capacity C and the voltage V; α is a parameter for adjusting the shape of the membership function, which determines the steepness of the function. The larger α is, the steeper the function is, which means that the membership changes faster near a certain value; β is another parameter for adjusting the shape of the membership function, which determines the tail behavior of the function. When β increases, the tail of the function becomes smoother, which means that the membership changes more slowly away from the central value.

[0126] 3. Combining fuzzy decision rules with fuzzy logic operations to construct fitness function:

[0127] In more complex scenarios, the fitness function can be constructed by combining fuzzy decision rules (such as IF-THEN rules) and fuzzy logic operations (such as fuzzy logic AND, OR, NOT). For example, a series of fuzzy rules are used to comprehensively judge the performance of the solution vector on multiple fuzzy attributes, and finally an overall fitness value is obtained.

[0128] In some practical applications of fuzzy analysis, it may be necessary to fuzzify the original data (map it to the membership of the fuzzy set), and then convert the fuzzy fitness value into a single value that can be used for comparison and selection through defuzzification methods (such as the centroid method, the maximum membership method, etc.). However, the membership function constructed based on the Cauchy-type fuzzy distribution can already be used as the fitness function in the genetic algorithm.

[0129] Through the above steps, fuzzy mathematics methods can be used to construct a fitness function suitable for genetic algorithms to evaluate the quality of candidate solution vectors (i.e., battery state estimation) in prediction problems. In practical applications, the division of fuzzy sets, the form of membership functions, and multi-objective fusion strategies should be adjusted according to the needs of specific problems and data characteristics to ensure that the fitness function can effectively guide the search process of the genetic algorithm.

[0130] The following is a simple Python code example showing how to construct a fitness function using fuzzy mathematics. It is possible to express fuzzy sets for multi-objective situations of battery capacity and polarization voltage, and obtain the use of fuzzy fitness in genetic algorithms. Assuming that the fuzzy membership function has been implemented, its implementation is as follows:

[0131] "membership_function(x, fuzzy_set):

[0132] import numpy as np

[0133] # Assume that the fuzzy membership function membership_function(x, fuzzy_set) has been implemented

[0134] def fuzzy_fitness(capacity, voltage=None):

[0135] if voltage is None: # Single target case (only considering battery capacity)

[0136] capacity_memberships = {

[0137] 'Low': membership_function(capacity, 'Low'),

[0138] 'Medium': membership_function(capacity, 'Medium'),

[0139] 'High': membership_function(capacity, 'High')

[0140] }

[0141] return max(capacity_memberships.values()) # Use the maximum membership as the fitness value

[0142] else: #Multi-objective situation (considering battery capacity and polarization voltage)

[0143] capacity_memberships = {

[0144] 'Low': membership_function(capacity, 'Low_Capacity'),

[0145] 'Medium': membership_function(capacity, 'Medium_Capacity'),

[0146] 'High': membership_function(capacity, 'High_Capacity')

[0147] }

[0148] voltage_memberships = {

[0149] 'Low': membership_function(voltage, 'Low_Voltage'),

[0150] 'Medium': membership_function(voltage, 'Medium_Voltage'),

[0151] 'High': membership_function(voltage, 'High_Voltage')

[0152] }

[0153] # Example weight, can be adjusted according to actual situation

[0154] weight_capacity = 0.7

[0155] weight_voltage = 0.3

[0156] # Weighted sum method to calculate fuzzy fitness

[0157] fuzzy_fitness_value = (

[0158] weight_capacity * max(capacity_memberships.values()) +

[0159] weight_voltage * max(voltage_memberships.values()) )

[0161] return fuzzy_fitness_value

[0162] # Using fuzzy fitness function in genetic algorithm

[0163] for individual in population:

[0164] if is_single_objective():

[0165] individual.fitness = fuzzy_fitness(individual.capacity)

[0166] else:

[0167] individual.fitness = fuzzy_fitness(individual.capacity,individual.voltage)".

[0168] In the code example, the fuzzy fitness function fuzzy_fitness() is first defined, and the number of input parameters is used to determine whether it is a single-objective or multi-objective situation. In the case of a single objective, the membership of each fuzzy set corresponding to the battery capacity is directly calculated, and the maximum value is taken as the fitness value. In the case of multiple objectives, the membership of each fuzzy set corresponding to the battery capacity and polarization voltage is calculated respectively, and then the weighted sum is performed according to the given weights to obtain the overall fuzzy fitness value. Finally, in the loop of the genetic algorithm, the fuzzy fitness is calculated for each individual and assigned to its fitness attribute.

[0169] The entire process of nonlinear prediction and estimation of power battery status based on genetic algorithm optimized by fuzzy mathematics is as follows: Figure 1 As shown, the process is described as follows.

[0170] Step b1, initializing the global solution set population space: creating a set number of solution vectors, which represent the battery state estimation. The specific generation method of the solution vectors is not restricted (such as completely random generation, interpolation regression method based on existing parameters, and distribution sampling method, etc.);

[0171] Step b2: Construct a two-dimensional initial solution global solution set population space :The system equation of the battery model is defined as two-dimensional, and the solution vector obtained in step a directly constitutes the two-dimensional initial solution space ;

[0172] Step b3, designing a fuzzy optimized fitness function according to the power battery model: using fuzzy mathematical methods, defining a membership function to quantify the degree of match between each solution vector and the ideal battery state. The membership function takes into account the physical and chemical parameters of the battery model (such as battery capacity, polarization voltage, etc.) and its performance under different working conditions. Through fuzzy sets and fuzzy logic operations, the original continuous and uncertain evaluation is converted into a definite membership value as the fitness function fitness;

[0173] Step b4, calculate the fitness of the solution vector: for each solution vector in the population space of the initial solution global solution set, apply the fuzzy optimized fitness function fitness to calculate its fitness value; construct a multi-objective fuzzy fitness function, and comprehensively consider the influence of multiple objectives by assigning variable weights to each single objective membership;

[0174] Step b5, select elite community: sort according to the fuzzy fitness value of the solution vector, select a set number of individuals with the highest fitness to form an elite community, and these individuals will be retained in subsequent iterations;

[0175] Step b6, eliminate low fitness solution vectors: low fitness solution vectors except the elite population are eliminated to make room for the new generation of population;

[0176] Step b7, pairing selection: using an appropriate mate selection strategy operator (such as roulette selection, tournament selection, etc., without limitation), select a paired paternal solution vector and a maternal solution vector from the elite population for a gene crossover operation;

[0177] Step b8, gene crossover and recombination: perform a crossover operation (such as single-point crossover, uniform crossover, etc.) on the selected paternal and maternal solution vectors to generate a new offspring solution vector;

[0178] Step b9, mutation: According to the preset mutation probability, randomly select the solution vector in the offspring population for mutation operation, and use the mutation operator to change some genes (elements) of the solution vector in an unpredictable direction;

[0179] Step b10, obtaining the offspring population: after crossover and mutation, a new offspring global solution set population space is formed;

[0180] Step b11, judging convergence and termination conditions: judging whether the algorithm has reached convergence according to the preset maximum number of generations or the convergence criteria based on the fuzzy fitness value (such as fitness mean, variance change trend, fuzzy clustering analysis, etc.);

[0181] Step b12, output the optimal solution vector: when the algorithm converges or reaches the maximum number of generations, select the solution vector with the highest fuzzy fitness in the current global solution set population space as the optimal solution. This solution vector contains key parameters such as predicted battery capacity and predicted polarization voltage;

[0182] Step b13, end the algorithm: after the algorithm is executed, the optimal solution vector is output as the solution of the system equation of the predicted battery model.

[0183] In addition, the error estimation is performed using the indicator function of the minimum model error criterion, where the indicator function of the minimum model error criterion is defined as:

[0184] J [ d ( t )] = 0 . 5 [ y ( t + D t ) − y ^ ( t + D t )] T R v − 1 [ y ( t + D t ) − y ^ ( t + D t )] + 0 . 5 d ( t ) T Wd ( t ) ,

[0185] in, is the system sampling interval, is the observation function output of the battery model, is the observation function output of the power battery; the indicator function consists of two penalty functions:

[0186] 1) Measurement residuals The weighted sum of squares,

[0187] 2) Model Error The weighted sum of squares,

[0188] in, is the error weighting matrix of the semi-positive definite model, and its parameter selection method adopts the NPF algorithm;

[0189] It is the inversion of the measurement noise covariance matrix. This parameter refers to the modeling process of the system measurement noise. Assuming that the system measurement noise is a stationary random process, the noise covariance matrix is ​​modeled as:

[0190] R v ≈ 1 M ∑ k = 1 M { y ( t k ) − h [ x ^ ( t k ), t k ] } { y ( t k ) − h [ x ^ ( t k ), t k ] } T ,

[0191] in, is the time at time k, is the model observation value at time k, M is an integer representing the number of samples used to calculate the covariance matrix, T is the transposed symbol, represents the estimated state value at time k, h [ x ^ ( t k ), t k ] represents a functional function representing the estimated relationship of the model;

[0192] Under the nonlinear system model, the observation function output of the battery model is expressed as:

[0193] y ( t k ) = h [ x ˙ ( t k ), t k , i ( t k )] + n ( t k ) ,

[0194] in, is the time at time k, is the model observation value at time k, is the state equation output at time k, is a time-varying parameter, h [ x ˙ ( t k ), t k , i ( t k )] is a functional function representing the model-observation relationship, is a zero-mean Gaussian white noise;

[0195] Under the nonlinear system model, the observation function output of the power battery is expressed as:

[0196] y ^ ( t k ) = q [ x ˙ ( t k ), t k , i ( t k )] + w ( t k )

[0197] in, is the time at time k, is the power battery observation value at time k, is the state equation output at time k, is a time-varying parameter, q [ x ˙ ( t k ), t k , i ( t k )] is a functional function representing the observation relationship of the power battery, is a zero-mean Gaussian white noise;

[0198] The Taylor series expansion of the index function of the minimum model error criterion is performed, and the calculation expression of the model error term d(t) is expressed as:

[0199] d ( t ) =− { [ L ( D t ) S ( x ^ ( t )) ] T R − 1 L ( D t ) S ( x ^ ( t )) + W } − 1 × [ L ( D t ) S ( x ^ ( t )) ] T R − 1 [ Z ( x ^ ( t ), D t ) + y ^ ( t ) − y ( t + D t )]

[0200] in, , and They are all intermediate parameter matrices. The specific calculation methods are as follows:

[0201] S ( x ^ ( t )) = [ L g 1 L f r 1 − 1 h 1 ( x ^ ( t )) ⋯ L gn L f r 1 − 1 h 1 ( x ^ ( t )) ⋮ ⋱ ⋮ L g 1 L f rm − 1 h m ( x ^ ( t )) ⋯ L gn L f rm − 1 h m ( x ^ ( t )) ]

[0202]

[0203] L ( D t ) = [ l 11 ⋯ 0 ⋮ l ii ⋮ 0 ⋯ l mm ] , l ii = D t r i r i ! , i = 1 , 2 ,..., m

[0204] is the Lie derivative, where the parameters are defined as follows:

[0205] It is a Jacobian matrix that describes the sensitivity of the system state to the output. It is defined as the intermediate parameter matrix formed by the Jacobian matrix of the Lie derivative operator on the two vector fields g1 and f. The Jacobian matrix is ​​a matrix in which the first-order partial derivatives are arranged in a certain way. Its determinant is called the Jacobian determinant. The importance of the Jacobian matrix lies in that it embodies the optimal linear approximation of a differentiable equation to a given point. Therefore, the Jacobian matrix is ​​similar to the derivative of a multivariate function.

[0206] is the Lie derivative operator, which represents the directional derivative along the vector field g1,

[0207] represents the r1-1 iteration of the Lie derivative operator Lf,

[0208] is a scalar function, representing the output state of the system, and is the initial function of the Lie derivative operation.

[0209] r is the relative order,

[0210] yes The order of

[0211] It is the Taylor series expansion form of the output function of a nonlinear system. It represents the approximate value of the system output Z at time t and time interval Δt. Each term in the formula is a Taylor series expansion term based on the Lie derivative.

[0212] in, is the time interval;

[0213] is the time interval raised to the power of a,

[0214] is the factorial of a,

[0215] is the index of the Taylor series expansion term,

[0216] is the order of the Taylor series expansion;

[0217] represents a Lie derivative L f For the output function h i a iterations of ;

[0218] is a matrix that describes the dynamic characteristics of a nonlinear system in time intervals. It is an m×m diagonal matrix, where the elements on the diagonal are λ ii , i=1,2,…,mi=1,2,…,m; it is positioned as an intermediate parameter matrix constructed in the form of a diagonal matrix with respect to the dynamic characteristics of the time interval;

[0219] in, is the time interval,

[0220] is the diagonal element of this matrix, which is defined as ,

[0221] is the factorial of the order of the Taylor series expansion,

[0222] is the order of the Taylor series expansion of the time interval Power,

[0223] yes The order of The order m is consistent,

[0224] is the index into this matrix;

[0225] According to the ergodic theorem, the covariance calculation expression of the model error term d(t) is as follows:

[0226] D =Cov[d(t)]=E[(d(t)-E[d(t)])(d(t)-E[d(t)]) T ] ,

[0227] Where D is the covariance of the model error term d(t) calculated by the time series, Cov[d(t)] is the covariance matrix of the model error term d(t), and the covariance matrix reflects the linear dependence between random variables. E[d(t)] is the expected mean of the model error term d(t), which represents the average value of the model error in all possible cases. (d(t)-E[d(t)]) represents the difference between the model error term d(t) and its expected value E[d(t)], which represents the deviation of the model error from its mean. (d(t)-E[d(t)]) T represents the transpose of the above bias vector;

[0228] The model error weighted matrix W is taken as the inverse of D, and then the current power battery state is updated according to this error:

[0229] x ˙ ( t ) = f [ x ˙ ( t ), t ] + g ( t ) d ( t ) ,

[0230] in, is the state variable of the system, which is the rate of change of the power battery state within this calculation cycle. f [ x ˙ ( t ), t ] It is used to describe the natural dynamic behavior of a system when there is no external disturbance, and reflects how the internal dynamics of the system affect the change of state. represents the model error correction term, d(t) is the model error amount, and g(t) is the model error allocation matrix;

[0231] Then record it as the power battery status of the next calculation cycle, which is ;

[0232] Enter the next round of "estimation-observation-correction" cycle, and repeat this process to dynamically adjust and optimize the model to adapt to the nonlinear changes in the power battery state.

[0233] The entire algorithm structure of the present invention will repeatedly repeat the process of "inference"-"observation"-"correction and inference".

[0234] First of all, "inference" is the genetic algorithm mentioned above, which will be imported into the power battery model according to the remaining battery capacity and polarization voltage of the battery, and the solution vector will be calculated through the fitness function fitness optimized by fuzzy mathematics. This is a two-dimensional vector representing the predicted battery capacity and predicted polarization voltage in the system equation of the battery model.

[0235] Then, “observation” is to measure and record the operating temperature, input current and battery terminal voltage of the power battery in real time, and then calculate the corresponding system equation based on the known battery model.

[0236] Finally, the “corrected calculation” is to calculate this D, which will be used to judge the error between the nonlinear prediction result based on the genetic algorithm and the actual measurement result. Then, the system equation of the power battery state calculated at the end is updated.

[0237] The entire algorithm structure of the present invention will cycle through the above three processes, such as Figure 2 shown.

[0238] When implementing the invention, it is necessary to adjust and improve it according to the actual hardware interface, data type and programming environment. The overall embodiment of the invention is as follows:

[0239] “import numpy as np

[0240] from fuzzylogic import FuzzySet, MembershipFunction, FuzzyInferenceSystem# Assume that a library called fuzzylogic is used for fuzzy logic processing

[0241] from genetic_algorithm import GeneticAlgorithm # Assume that a library called genetic_algorithm is used for genetic algorithm processing

[0242] # Define fuzzy sets and membership functions (this is just an example, the actual design should be based on battery characteristics)

[0243] def create_fuzzy_membership_functions():

[0244] voltage_set = FuzzySet('Voltage', MembershipFunction.triangle(-1, 0, 1))

[0245] current_set = FuzzySet('Current',MembershipFunction.trapezoid(-1, -0.5, 0.5, 1))

[0246] density_set = FuzzySet('Density', MembershipFunction.gaussian(0, 0..jpg))

[0247] # ... more definitions of fuzzy sets and membership functions

[0248] return {

[0249] 'voltage':voltage_set,

[0250] 'current':current_set,

[0251] 'density': density_set,

[0252] # ...

[0253] }

[0254] # Define fuzzy inference system (based on battery model and fuzzy rules)

[0255] def create_fuzzy_inference_system(membership_functions):

[0256] fis = FuzzyInferenceSystem()

[0257] # Add fuzzy rules, such as:

[0258] # IF Voltage is High AND Current is Low THEN SOC is High

[0259] # ... more fuzzy rules

[0260] return fis

[0261] # Define the fitness function, combined with the fuzzy reasoning results

[0262] def fitness_function(chromosome, fuzzy_inference_system, actual_soc):

[0263] # Convert chromosome to battery model parameters or other forms of data

[0264] model_params = decode_chromosome(chromosome)

[0265] # Apply the fuzzy inference system to get the fuzzy SOC value

[0266] fuzzy_soc = fuzzy_inference_system.evaluate(model_params)

[0267] # Convert the fuzzy SOC value to a fitness score (e.g., using a sharpening method such as the centroid method)

[0268] fitness = defuzzify(fuzzy_soc)

[0269] # It may be necessary to add a comparison with the actual SOC value and adjust the fitness function

[0270] fitness -= np.abs(fitness - actual_soc)

[0271] return fitness

[0272] # Initialize the genetic algorithm

[0273] ga = GeneticAlgorithm(population_size=..., mutation_rate=...,crossover_rate=...)

[0274] # Create fuzzy sets and membership functions required for fuzzy logic

[0275] membership_functions = create_fuzzy_membership_functions()

[0276] fis = create_fuzzy_inference_system(membership_functions)

[0277] # Start genetic algorithm iteration

[0278] for generation in range(num_generations):

[0279] # Generate an initial population or perform operations such as selection, crossover, and mutation

[0280] population = ga.generate_population() # or ga.evolve()

[0281] # Calculate the fitness of each individual

[0282] fitness_scores = [fitness_function(individual, fis, actual_soc)for individual in population]

[0283] # Update the genetic algorithm state and prepare for the next iteration

[0284] ga.update(population, fitness_scores)

[0285] # Finally, the optimal individual is obtained, that is, the calculation model of the target SOC value

[0286] best_individual = ga.best_individual()

[0287] # Compare the best individual's estimated result with the actual observed value, make corrections, and enter the next round of estimated SOC value to feed back to the battery management system (BMS) or other related modules;

[0288] # Output the calculation results

[0289] figure(1);

[0290] plot(time, Z_);hold on;

[0291] plot(time, XLog(1, :), 'r.');

[0292] title(' Comparison of SOC estimation and reference value');

[0293] xlabel('Time');ylabel('SOC');

[0294] figure(2);

[0295] plot(time, v_);hold on;

[0296] plot(time, XLog(2, :), 'r.');

[0297] title('SOC estimation error');

[0298] xlabel('time');ylabel('balanced current');

[0299] figure(3);

[0300] plot(time, Z_);hold on;

[0301] plot(time, XLog(1, :), 'r.');

[0302] title('Mean absolute error of SOC estimation');

[0303] xlabel('Time');ylabel('SOC');

[0304] figure(4);

[0305] plot(time, v_);hold on;

[0306] plot(time, XLog(2, :), 'r.');

[0307] title('Root mean square error of SOC estimation');

[0308] xlabel('time');ylabel('balanced current');

[0309] # Output four graphs: (a) SOC estimation and reference value comparison; (b) SOC estimation error; (c) mean absolute error of SOC estimation; (d) root mean square error of SOC estimation".

[0310] As shown in the above code, according to the actual project requirements, choose a suitable fuzzy logic library (such as Scikit-Fuzzy, PyFuzzy, etc.) or implement fuzzy sets, membership functions, fuzzy inference systems and other components yourself. Please note that the above pseudo code only provides a basic framework. The following tasks need to be completed in actual implementation:

[0311] Specific form of fitness function: According to the fuzzy reasoning results, the specific calculation method of the fitness function is clarified, including the clarification method of the fuzzy SOC value and the comparison strategy with the actual SOC value.

[0312] Implementation and parameter adjustment of genetic algorithms: Select or implement a genetic algorithm library, set appropriate parameters (such as population size, crossover probability, mutation probability, etc.), and adjust them according to actual results.

[0313] •Interfacing with hardware: writing code to read actual measurement data (such as current, voltage, temperature, etc.) and push matching parameters of the corresponding microcontroller and ADC;

[0314] •Establishment of battery model and fuzzy rules: Design specific fuzzy sets, membership functions and fuzzy rules based on the battery's physical characteristics, working principles and expert knowledge.

[0315] After completing the above work, the above pseudocode framework can be filled with specific content to form a complete program to implement a method for nonlinear prediction and estimation of power battery status based on fuzzy comprehensive evaluation optimization genetic algorithm.

[0316] Finally, the algorithm runs as follows Figure 3 shown. Figure 3 In the figure, the results of the four small figures are: (a) SOC estimation and reference value comparison, where A is the reference value and B is the estimated value; (b) SOC estimation error; (c) mean absolute error of SOC estimation; (d) root mean square error of SOC estimation. Under the operating temperature of 25°C, the SOC estimation method achieved good estimation accuracy, with the maximum SOC estimation error less than 2%, and MAE and RMSE both less than 1%. Under different operating temperatures, the accuracy of the SOC estimation method does not change much and maintains a small estimation error. Based on the above analysis, it can be seen that by incorporating the functional relationship between battery model parameters and operating temperature into the SOC estimation method based on genetic algorithm, the application of the SOC estimation method can be expanded to a wider battery operating temperature range, and a good estimation effect has been achieved.

[0317] This paper introduces a nonlinear predictive filtering algorithm based on a genetic algorithm optimized by fuzzy mathematics. It is applied to the field of battery state estimation for the first time and aims to solve the SOC estimation problem with unknown form of battery model process noise. This method can more flexibly adapt to the nonlinear characteristics of the battery and complex environmental conditions, thereby improving the accuracy and reliability of SOC estimation. By introducing this algorithm, a more accurate and reliable SOC estimation result is provided for battery management system design and electric vehicle whole vehicle control decision, demonstrating more outstanding research innovation and practical value.

[0318] Finally, it should be emphasized that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various changes and modifications. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A battery state of charge estimation method based on fuzzy mathematics and genetic algorithm, characterized in that: The method comprises the following steps: Step a, establishing fuzzy sets and membership functions that conform to actual characteristics according to the physical and chemical parameters involved in battery SOC estimation, establishing a fuzzy model through the fuzzy sets and membership functions, using the fuzzy model to capture the fuzzy boundaries and uncertainties of the parameters, and then constructing and fuzzily optimizing the fitness function through the fuzzy boundaries and uncertainties; Step b, integrating the fuzzy optimized fitness function into the actual calculation process of the genetic algorithm, generating an initial population with diversity and covering the solution space in the initialization stage; making decisions based on the fuzzy optimized fitness function in the genetic operations of selection, crossover and mutation; Step c: Through multiple generations of genetic iterations, the population gradually converges to individuals with high fitness, that is, the optimal estimation model of the target SOC value. Then, the estimated results of this model are compared with the actual observed values, and the model parameters or structure are corrected according to the comparison results to enter the next round of "estimation-observation-correction" cycle. This cycle is repeated to dynamically adjust and optimize the model to adapt to the nonlinear changes in the power battery state and improve the accuracy and robustness of SOC estimation.

2. The battery state of charge estimation method based on fuzzy mathematics and genetic algorithm according to claim 1, characterized in that: The specific steps of step a are: Step a1, defining fuzzy sets and membership functions: according to the characteristics of the optimization problem, define a set of fuzzy sets related to the target parameters, corresponding to different fuzzy levels or categories of battery capacity and polarization voltage; design a corresponding membership function for each fuzzy set; Step a2: Construct a multi-objective fuzzy fitness function: Use weighted sum or product operation to combine the membership values ​​of each single objective: or ， Among them, (C, Capacity) and (V, Voltage) represent fuzzy sets, which are expressed in order-even notation. w1 and w2 are weight coefficients used to balance the importance of different target parameters. Membership represents the membership function of the corresponding parameter in the corresponding fuzzy set. The fuzzy distribution adopts the intermediate Cauchy type, which is expressed as follows: , ( ,β is a positive even number), (χ, variable) is the fuzzy set of the membership function, which indicates the membership of the input value χ to the fuzzy set variable, where variable is the fuzzy set, χ is the input variable, which indicates the value of its membership to be evaluated; α is a parameter for adjusting the shape of the membership function, which determines the steepness of the function. The larger the α, the steeper the function and the faster the membership changes; β is another parameter for adjusting the shape of the membership function, which determines the tail behavior of the function. When β increases, the tail of the function becomes smoother and the membership changes more slowly; Step a3, combining fuzzy decision rules and fuzzy logic operations to construct a fitness function: According to fuzzy rules and fuzzy logic operations, the performance of the solution vector on multiple fuzzy attributes is comprehensively judged, and finally an overall fitness value is obtained, and then a fitness function is constructed.

3. The battery state of charge estimation method based on fuzzy mathematics and genetic algorithm according to claim 1, characterized in that: The specific steps of step b are: Step b1, initializing the global solution set population space: creating a set number of solution vectors, which represent the battery state estimation; Step b2: Construct a two-dimensional initial solution global solution set population space :The system equation of the battery model is defined as two-dimensional, and the solution vector obtained in step b1 directly constitutes the two-dimensional initial solution space ; Step b3, designing a fuzzy optimized fitness function according to the power battery model: using fuzzy mathematical methods, defining a membership function to quantify the degree of match between each solution vector and the ideal battery state, the membership function takes into account the physical and chemical parameters of the battery model and its performance under different working conditions, and transforms the original continuous and uncertain evaluation into a definite membership value as the fitness function fitness through fuzzy sets and fuzzy logic operations; Step b4, calculate the solution vector fitness: for each solution vector in the initial solution global solution set population space, apply the fuzzy optimization fitness function fitness to calculate its fitness value; A multi-objective fuzzy fitness function is constructed to comprehensively consider the impact of multiple objectives by assigning variable weights to the membership of each single objective; Step b5, select elite community: sort according to the fuzzy fitness value of the solution vector, select a set number of individuals with the highest fitness to form an elite community, and these individuals will be retained in subsequent iterations; Step b6, eliminate low fitness solution vectors: low fitness solution vectors except the elite population are eliminated to make room for the new generation of population; Step b7, pairing selection: using an appropriate mate selection strategy operator, select the paired paternal solution vector and maternal solution vector from the elite population for gene crossover operation; Step b8, gene crossover and recombination: perform a crossover operation on the selected paternal and maternal solution vectors to generate a new offspring solution vector; Step b9, mutation: According to the preset mutation probability, randomly select the solution vector in the offspring population for mutation operation, and use the mutation operator to change some genes of the solution vector in unpredictable directions; Step b10, obtaining the offspring population: after crossover and mutation, a new offspring global solution set population space is formed; Step b11, judging convergence and termination conditions: judging whether the algorithm has reached convergence according to a preset maximum number of generations or a convergence criterion based on the fuzzy fitness value; Step b12, outputting the optimal solution vector: when the algorithm converges or reaches the maximum number of generations, the solution vector with the highest fuzzy fitness in the current global solution set population space is selected as the optimal solution, and this solution vector includes the predicted battery capacity and the predicted polarization voltage; Step b13, end the algorithm: after the algorithm is executed, the optimal solution vector is output as the solution of the system equation of the predicted battery model.

4. The battery state of charge estimation method based on fuzzy mathematics and genetic algorithm according to claim 1, characterized in that: In step c, error estimation is performed using an indicator function of the minimum model error criterion, wherein the indicator function of the minimum model error criterion is defined as: ， in, is the system sampling interval, is the observation function output of the battery model, is the observation function output of the power battery. The indicator function consists of two penalty functions: 1) Measurement residuals The weighted sum of squares, 2) Model Error The weighted sum of squares, in, is the error weighting matrix of the semi-positive definite model, and its parameter selection method adopts the NPF algorithm; is the inverse of the measurement noise covariance matrix. This parameter refers to the modeling process of the system measurement noise. Assuming that the system measurement noise is a stationary random process, then the noise covariance matrix R v is modeled as: ， in, is the time at time k, is the model observation value at time k, M is an integer indicating the number of samples used to calculate the covariance matrix. T is the transpose symbol, represents the estimated state value at time k, represents a functional function representing the estimated relationship of the model; Under the nonlinear system model, the observation function output of the battery model is expressed as: ， in, is the time at time k, is the model observation value at time k, is the state equation output at time k, is a time-varying parameter, is a functional function representing the model-observation relationship, is a zero-mean Gaussian white noise; Under the nonlinear system model, the observation function output of the power battery is expressed as: ， in, is the time at time k, is the power battery observation value at time k, is the state equation output at time k, is a time-varying parameter, is a functional function representing the observation relationship of the power battery, is a zero-mean Gaussian white noise; The Taylor series expansion of the index function of the minimum model error criterion is performed, and the calculation expression of the model error term d(t) is expressed as: ， in, , and They are all intermediate parameter matrices. The specific calculation methods are as follows: ， ， ， is the Lie derivative, where the parameters are defined as follows: It is a Jacobian matrix describing the sensitivity of the system state to the output, which is defined as the intermediate parameter matrix composed of the Jacobian matrices of the Lie derivative operator on the two vector fields g1 and f; is the Lie derivative operator, which represents the directional derivative along the vector field g1, represents the r1-1 iteration of the Lie derivative operator Lf, is a scalar function, representing the output state of the system, and is the initial function of the Lie derivative operation. r is the relative order, yes The order of It is the Taylor series expansion form of the output function of a nonlinear system. It represents the approximate value of the system output Z at time t and time interval Δt. Each term in the formula is a Taylor series expansion term based on the Lie derivative. in, is the time interval; is the time interval raised to the power of a, is the factorial of a, is the index of the Taylor series expansion term, is the order of the Taylor series expansion; represents a Lie derivative L f For the output function h i a iterations of ; is a matrix that describes the dynamic characteristics of a nonlinear system in time intervals. It is an m×m diagonal matrix, where the elements on the diagonal are λ ii ,i=1,2,…,m; it is positioned as an intermediate parameter matrix formed in the form of a diagonal matrix with respect to the dynamic characteristics of the time interval; in, is the time interval, is the diagonal element of this matrix, which is defined as , is the factorial of the order of the Taylor series expansion, is the order of the Taylor series expansion of the time interval Power, yes The order of The order m is consistent, is the index into this matrix; According to the ergodic theorem, the covariance calculation expression of the model error term d(t) is as follows: ， Where D is the covariance of the model error term d(t) calculated by the time series, Cov[d(t)] is the covariance matrix of the model error term d(t), and the covariance matrix reflects the linear dependence between random variables. E[d(t)] is the expected mean of the model error term d(t), which represents the average value of the model error in all possible cases. (d(t)-E[d(t)]) represents the difference between the model error term d(t) and its expected value E[d(t)], which represents the deviation of the model error from its mean. (d(t)-E[d(t)]) T represents the transpose of the above bias vector; The model error weighted matrix W is taken as the inverse of D, and then the current power battery state is updated according to this error: ， in, is the state variable of the system, which is the rate of change of the power battery state within this calculation cycle. It is used to describe the natural dynamic behavior of a system when there is no external disturbance, and reflects how the internal dynamics of the system affect the change of state. represents the model error correction term, d(t) is the model error amount, and g(t) is the model error allocation matrix; Then record it as the power battery status of the next calculation cycle, which is ; Enter the next round of "estimation-observation-correction" cycle, and repeat this process to dynamically adjust and optimize the model to adapt to the nonlinear changes in the power battery state.

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