Lithium battery modeling and temperature estimation method based on starfish optimization and adaptive filtering

Abstract

The application provides a lithium battery modeling and temperature estimation method based on starfish optimization and adaptive filtering, belongs to the technical field of lithium battery modeling, and solves the technical problem that accurate estimation of the temperature of a lithium battery cannot be realized in the case that noise covariance is unknown or inaccurate, thereby causing modeling difficulty, and the technical scheme is as follows: including the following steps: step 1) constructing a lithium battery variable parameter lumped thermal model based on the thermoelectric similarity principle to obtain model description of an identification system; step 2) constructing a starfish optimization iterative identification algorithm SFOA to accurately estimate unknown parameters of the lithium battery variable parameter lumped thermal model; and step 3) constructing a fading factor adaptive filter FFAKF to accurately estimate the temperature of the lithium battery thermal model. The application realizes lithium battery temperature estimation in the case that noise covariance is unknown or difficult to obtain.

Description

Technical Field

[0001] This invention belongs to the field of lithium battery modeling and temperature estimation technology, and particularly relates to the research and application of lithium battery temperature estimation method based on filtering under unknown noise covariance. Background Technology

[0002] In the field of lithium battery temperature modeling, lumped parameter technology is a simplified thermal modeling method that obtains information from measured operational data while allowing for physical interpretation of components and processes. This model, based on the thermoelectric similarity principle, treats the battery as a whole, using lumped and constant parameters to characterize its temperature characteristics such as heat generation and heat transfer. Resistance simulates heat transfer, and capacitance and power characterize the battery temperature field. However, in practical applications, the thermal parameters of lithium batteries change significantly with battery usage time, ambient temperature, and other factors. Traditional lumped parameter thermal models fix the parameters, failing to track these changes in real time, leading to significant deviations in the estimation of the battery's internal temperature under complex operating conditions, making it difficult to meet the requirements of high-precision battery management systems. To overcome the limitations of traditional lumped parameter thermal models, this invention introduces a variable parameter lumped thermal model. This model can dynamically adjust thermal parameters based on the battery's real-time state and environmental conditions, thus more accurately describing the thermal behavior of lithium batteries under different operating conditions. However, the performance of the variable parameter lumped thermal model is highly dependent on the accuracy of the model parameters; therefore, accurate parameter identification is crucial.

[0003] In optimization algorithms, swarm optimization algorithms are widely used for identifying model parameters. For example, the paper "Review and empirical analysis of sparrow search algorithm" proposes an improved sparrow search algorithm, demonstrating faster convergence speed and higher convergence accuracy. The paper "Sand cat swarm optimization: a nature-inspired algorithm to solve global optimization problems" proposes a sand cat swarm optimization algorithm and verifies its good performance in terms of convergence rate and localization. However, for models with multiple parameters, most swarm optimization algorithms cannot achieve high-precision parameter identification, and low-precision parameter identification results can lead to large model errors.

[0004] Furthermore, state estimation is also an important aspect of lumped parameter modeling. The Kalman filter, also known as a linear quadratic estimation filter, recursively estimates the current state of the system over time using input measurements from the model. The Kalman filter has wide applications and is still used in many fields. For example, the paper "A combined state-of-charge estimation method for lithium-ion battery using an improved BGRU network and UKF" proposes an improved Kalman filter algorithm and demonstrates its good performance under various special conditions. The paper "Kalman filtering techniques for the online model parameters and state of charge estimation of the Li-ion batteries: A comparative analysis" uses the Kalman filter algorithm to achieve simultaneous estimation of online model parameters and the state of charge of the lithium battery. However, in practical applications, the Kalman filter requires obtaining the process noise covariance and measurement noise covariance, which are often difficult or impossible to obtain accurately. How to solve these technical problems is the challenge faced by this invention. Summary of the Invention

[0005] The purpose of this invention is to provide a lithium battery modeling and temperature estimation method based on starfish optimization and adaptive filtering. First, a lumped thermal model of the lithium battery with variable parameters based on the thermoelectric similarity principle is established. Then, a starfish optimization iterative identification algorithm is proposed to accurately estimate the unknown parameters of the lumped thermal model of the lithium battery with variable parameters. Finally, an adaptive filtering algorithm with a fading factor is proposed to estimate the temperature of the lithium battery thermal model. This invention takes lithium batteries with unknown noise covariance as the research object and provides a new solution for temperature estimation of lithium batteries with unknown noise covariance. By combining the adaptive filtering algorithm with a fading factor with the starfish optimization iterative identification algorithm, accurate temperature estimation of the lumped thermal model of the lithium battery with variable parameters under unknown noise covariance is achieved.

[0006] The core idea of ​​this invention is as follows: Most filtering algorithms for lithium battery temperature estimation require accurate noise covariance, but in most practical situations, the noise covariance is unknown or difficult to obtain, leading to low accuracy or unreasonable estimation results. Therefore, this invention uses an adaptive filtering algorithm with a fading factor to estimate the temperature of a lithium battery's variable parameter lumped thermal model. The fading factor adaptively adjusts the noise covariance based on the system's real-time state, enabling the filter to better track changes in the system state. Thus, an estimation method based on starfish optimization and adaptive filtering is constructed to accurately estimate the temperature of a lithium battery's variable parameter lumped thermal model under unknown noise covariance.

[0007] To achieve the aforementioned objectives, the present invention employs the following technical solution: a lithium battery modeling and temperature estimation method based on starfish optimization and adaptive filtering, comprising the following steps:

[0008] Step 1) Construct a variable parameter lumped thermal model of a lithium battery based on the principle of thermoelectric similarity to obtain a model description of the identification system.

[0009] Step 2) Construct the starfish optimization iterative identification algorithm to accurately estimate the unknown parameters of the lumped thermal model of the variable parameters of the lithium battery.

[0010] Step 2-1) Initialize parameters and set appropriate parameters for the lithium battery modeling and temperature estimation method based on starfish optimization and adaptive filtering;

[0011] Step 2-2) Collect measurable data including lithium battery surface temperature, ambient temperature, and internal heat generation rate of the battery. ;

[0012] Steps 2-3) Set the initial value for the number of iterations. Set the initial position matrix to 1, and calculate the initial position fitness value of the population.

[0013] Steps 2-4) Calculate dynamic parameters Then calculate the updated i-th The position values ​​of all dimensions of an individual;

[0014] Steps 2-5) Calculate the difference between the current optimal position and the position of the selected individual, and then calculate the result after the next update. The position values ​​of all dimensions of an individual;

[0015] Steps 2-6) Let the number of iterations be... Add one more time and return to step (2-4);

[0016] Steps 2-7) When the number of iterations... Reaching the maximum number of iterations At that time, finally obtained The optimal parameter vector identified by the starfish optimization algorithm.

[0017] Step 3) Construct an adaptive filter with a fading factor to accurately estimate the temperature of the lithium battery variable parameter lumped thermal model.

[0018] Step 3-1) Set the initial value for the number of samples. Set to 1, Substituting the temperature characteristic equations of the variable parameter lumped heat model, we calculate the estimate of the system matrix. and estimation of the control matrix ;

[0019] Step 3-2) Calculate the prior estimates of the system state variables;

[0020] Step 3-3) Calculate the updated covariance matrix Then calculate the fading factor. And construct the fading factor matrix ;

[0021] Steps 3-4) Calculate the error covariance of the prior estimates of the system state variables;

[0022] Steps 3-5) Calculate the filter gain matrix Then update the posterior estimates of the system state variables;

[0023] Steps 3-6) Update the error covariance of the posterior estimates of the system state variables;

[0024] Steps 3-7) Let the number of samples be... Add one more time, then return to step (3-2);

[0025] Steps 3-8) When the number of samples Reaching its maximum number of sampling points Finally, an estimate of the battery's internal temperature is obtained. And estimation of battery surface temperature .

[0026] This invention studies a lithium battery modeling and temperature estimation method based on starfish optimization and adaptive filtering, including the following steps:

[0027] (1-1) The structure of a variable parameter lumped heat model for lithium batteries based on the principle of thermoelectric similarity is constructed;

[0028] (1-2) Based on this model, the temperature characteristic equation of the variable parameter lumped thermal model of the lithium battery is expressed as follows:

[0029]

[0030]

[0031] Where t is time, Represents the derivative with respect to time. This refers to the uniform and equivalent heat capacity inside the battery. The equivalent heat capacity of the battery surface is uniform. The internal uniform equivalent thermal resistance represents the internal heat transfer rate of the battery. The externally uniform equivalent thermal resistance represents the rate of heat transfer between the battery surface and the environment. time, For battery internal temperature, For surface temperature, For ambient temperature, The rate of heat generation inside the battery. and It is a measurable quantity.

[0032] (1-3) Define the intermediate variable as the difference between the battery surface temperature and the ambient temperature. The difference between the internal temperature of the battery and the ambient temperature The expression is as follows:

[0033]

[0034]

[0035] Therefore, the temperature characteristic equation becomes:

[0036]

[0037]

[0038] (1-4) In order to handle continuous-time models in practical applications, the lithium battery temperature characteristic equation needs to be discretized and simplified to obtain:

[0039]

[0040] (8)

[0041] in, and For sampling points, The sampling time interval, and The first Second and third The difference between the internal temperature of the battery and the ambient temperature at each sampling point. and The first Second and third The difference between the battery surface temperature and the ambient temperature at each sampling point.

[0042] (1-5) Define the system state, input, and output variables as follows:

[0043]

[0044] Where the superscript T is the transpose of the vector or matrix, in the th... Secondary sampling point, For system state variables, For system output variables, Input variables into the system.

[0045] (1-6) During the data measurement process, there is process noise that cannot be ignored. With observation noise Therefore, the temperature characteristic equation can be rewritten as:

[0046]

[0047]

[0048] Define the system matrix Control matrix and output matrix They are respectively

[0049]

[0050]

[0051]

[0052] (1-7) Therefore, the final state equation and output equation of the lithium battery variable parameter lumped thermal model can be written as follows:

[0053]

[0054]

[0055] in, and In order to be in The system state variables and system output variables at the sampling points.

[0056] (2-1) In order to determine the unknown parameters in the system state equation and system output equation To achieve accurate estimation, the following optimized iterative starfish identification algorithm is constructed:

[0057] The set population size is The maximum number of iterations is The minimum value vector of the identification range is The maximum value vector is The population can be explored in the following dimensions: Initial population location for

[0058]

[0059] in, for OK Column matrix , The matrix stores the position of each individual in each dimension of the population, which is a random position within the identification range. Composed of random numbers between 0 and 1 from a normal distribution OK Column matrix.

[0060] (2-2) Calculate the initial fitness and find the initial optimal solution. Within the population... Substituting the parameters of each individual into the system state equation (12) and the system output equation (13), we obtain the estimated values ​​of the output variables of the parameters of each i-th individual. The fitness is defined as the root mean square error between the estimated battery surface temperature and the actual battery surface temperature. A smaller fitness indicates a more accurate parameter estimation. The fitness function is:

[0061]

[0062] Where N is the number of sampling points, The current iteration number identified for the parameters ( ), The maximum number of iterations, It is the first The parameters of each individual in the first... The fitness value for each iteration. In each iteration, the obtained... The fitness values ​​of the groups are compared, and the group with the lowest fitness is selected as the group. Its fitness value is used as .

[0063] (2-3) Before the exploration phase of the starfish optimization iterative identification algorithm, a dynamic parameter for adjusting random numbers needs to be generated. :

[0064]

[0065] in, For the first Dynamic parameters for each iteration. It is a cosine function.

[0066] (2-4) During the exploration phase, the first [number] of the population is randomly selected. The first individual Dimensions Then randomly select another individual from the population. ( and the same dimension For the first The first individual The following updates will be made to each dimension:

[0067]

[0068] Among them, in the first iteration For the first The first individual The position of the dimension update; in the first dimension iteration For the first The first individual The location of each dimension update. For the first The first individual Position values ​​in each dimension and for A random number between [variable values]. If the updated position value... If an element is not within the parameter identification range, then the position value of that dimension for that individual will retain the position value before the update.

[0069] (2-5) Before the development phase, the population size should be determined. Five individuals are randomly selected from the individuals, and in the second... In the next iteration, the current optimal position is calculated. The position of the selected individual The difference is denoted as Used for position updates during the development phase, the formula is:

[0070]

[0071] in, In the first In the next iteration, the positions of all dimensions of 5 randomly selected individuals are determined.

[0072] (2-6) During the development phase, for the first in the population The iteration of the ... For each individual, a dynamic difference is randomly selected. The two values ​​in and The following updates will be made:

[0073]

[0074] in, and for Random numbers between, in the 1st iteration For the previous version The position of an individual across all dimensions For the updated version The position values ​​of all dimensions for each individual. If the updated position values... If an element is outside the parameter identification range, then the position value of that dimension for that individual retains the position value before the update, ensuring that the updated position lies within the upper and lower parameter identification boundaries. and Within the range.

[0075] (2-7) After the exploration and development phases, calculate the fitness of each individual in the population after this iteration. (The sentence fragment "within the population..." appears to be incomplete and requires further context.) Substituting the parameters of each individual into the system state equation (12) and the system output equation (13), the fitness of each individual's parameters is calculated. The minimum fitness value is then compared with the minimum fitness value before the update, and the smaller fitness value is selected as the new fitness value. And update the optimal parameter vector. Then the next iteration update process begins. After all iterations are completed, the set of parameters with the minimum fitness value, that is, the set with the smallest error between the output estimate and the true value, is finally obtained. Parameter identification results optimized for starfish.

[0076] (3-1) To filter out process noise and measurement noise, an adaptive filter with a fading factor is introduced to estimate the lithium battery temperature when the noise covariance is unknown. The identified parameter vector... Substitute into the system matrix Control matrix From the expression, the estimate of the system matrix is ​​obtained. and estimation of the control matrix :

[0077]

[0078]

[0079] in, Estimation of the uniform equivalent heat capacity inside the battery. To estimate the equivalent heat capacity of a uniform battery surface, For estimating the internal uniform equivalent thermal resistance, This is an estimate of the externally uniform equivalent thermal resistance.

[0080] (3-2) Based on the system state prediction equation (20), calculate the prior estimates of the system state variables. for

[0081]

[0082] in, This is an estimate of the system state variables for the previous sampling point.

[0083] (3-3) Based on the error covariance prediction equation (21), the error covariance of the prior estimate of the system state variables is obtained. for

[0084]

[0085] in, Let be the covariance matrix of the system process noise. The error covariance is the posterior estimate of the state variable at the previous sampling point. This is the fading factor matrix.

[0086] (3-4) Gradually diminishing factor matrix Defined as follows

[0087]

[0088] The fading factor matrix is ​​composed of Composed of a gradually diminishing factor, , and For the first The first, second, and third sampling points were calculated. There are several fading factors. The expression for the fading factor is as follows:

[0089]

[0090] in, express The matrix calculated at each sampling point No. Line number Column elements, express The matrix calculated at each sampling point No. Line number The elements of the column, when When less than 1, take =1. Matrix and The definition is as follows:

[0091]

[0092]

[0093] in, Introducing a fixed adjustment factor can make the state estimation results more consistent with the true system value. This is the covariance matrix of the system measurement noise. To ensure that the fading factor can adjust for the noise covariance, this invention sets... . The updated covariance matrix is ​​obtained through equation (26).

[0094]

[0095] in, As a weakening factor, The covariance matrix updated for the previous sampling point. When hour, Output error The expression is as follows:

[0096]

[0097] in, This provides a posterior estimate of the system state variables from the previous sampling point. When system parameters change, the updated covariance matrix becomes distorted. Adaptive filters with fading factors utilize this characteristic, calculating the fading factor through the updated covariance matrix to achieve feedback adjustment of the noise covariance, thereby adjusting the filter gain and ultimately making the estimated result closer to the true value.

[0098] (3-5) Next, based on the filter gain equation (28), the filter gain matrix is... The calculation formula is

[0099]

[0100] Let be the covariance matrix of the system's observation noise.

[0101] (3-6) Then, according to the system state update equation (29), update the posterior estimate of the system state variable at the current sampling point. for

[0102]

[0103] (3-7) Finally, based on the error covariance update equation (30), the error covariance matrix of the posterior estimate of the system state variables at the current sampling point is updated. for

[0104]

[0105] in, It is an identity matrix.

[0106] (3-8) After filtering and estimating the system state variables, the difference between the estimated battery surface temperature and the ambient temperature can be directly obtained. The difference between the estimated internal temperature of the battery and the ambient temperature. Based on this, add the ambient temperature This allows us to obtain estimates of the battery surface temperature and the battery internal temperature. and Right now

[0107]

[0108]

[0109] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0110] 1. This invention establishes a lithium battery modeling and temperature estimation method based on starfish optimization and adaptive filtering. It introduces a variable parameter lumped thermal model system to address the problems of lithium battery modeling and the inability of parameters to adapt to changing environmental temperatures. The key technology of this invention is the establishment of a lithium battery temperature estimation method based on starfish optimization and adaptive filtering, which enables temperature estimation even when the noise covariance is unknown or difficult to obtain.

[0111] 2. To address the issue of the inability to dynamically adjust the parameters of lithium battery thermal models, this invention establishes a variable-parameter lumped thermal model for lithium batteries. This model can dynamically adjust the thermal parameters based on the real-time state of the battery and the ambient temperature, thereby more accurately describing the thermal behavior of lithium batteries under different operating conditions. Therefore, the technology of this invention enables the dynamic adjustment of lithium battery thermal model parameters and provides a more accurate description of the lithium battery thermal model.

[0112] 3. To address the difficulty of obtaining accurate noise covariance in practical applications of filtering algorithms, this invention establishes a starfish-based optimization and adaptive filtering algorithm. By introducing a fading factor, the noise covariance can be adaptively adjusted according to the real-time state of the system, enabling the filter to better track changes in the system state. When system parameters undergo abrupt changes or significant interference occurs, the fading factor can promptly adjust the filter gain, enhancing the filter's noise suppression capability and improving the accuracy of the estimation results when the noise covariance is unknown. Attached Figure Description

[0113] The accompanying drawings are provided to further illustrate the invention and form part of the specification. Simulations of the invention are used to explain the invention and do not constitute a limitation thereof.

[0114] Figure 1 This is a structural diagram of the variable lumped parameter thermal model of the lithium-ion battery in this invention.

[0115] Figure 2 This is a flowchart of the lithium battery temperature estimation method based on starfish optimization and adaptive filtering in this invention.

[0116] Figure 3 This is a convergence curve of the fitness value of the starfish optimization iterative identification algorithm in Embodiment 1 of the present invention.

[0117] Figure 4 This is a graph showing the lithium battery temperature estimation results and error based on starfish optimization and adaptive filtering in Embodiment 1 of the present invention.

[0118] Figure 5 This is a convergence curve of the fitness value of the starfish optimization iterative identification algorithm in Embodiment 2 of the present invention.

[0119] Figure 6 This is a graph showing the lithium battery temperature estimation results and error based on starfish optimization and adaptive filtering in Embodiment 2 of the present invention. Detailed Implementation

[0120] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0121] The system environment was set as follows: Panasonic 18650PF lithium-ion battery; measurement data were obtained from the University of Wisconsin public dataset; the input variable was the internal heat generation rate of the battery; the output variable was the surface temperature of the lithium-ion battery; process noise and measurement noise were used as system disturbances; the data collection length was 35,000 bytes as the sample size; and the data sampling interval was 0.1 s. Simulations were performed using Matlab software to implement a lithium-ion battery modeling and temperature estimation method based on starfish optimization and adaptive filtering.

[0122] See Figures 1 to 6 In the simulation process, the basic structure of the variable lumped parameter lithium battery thermal model was first established. Then, the parameters of the variable lumped parameter lithium battery thermal model were estimated using the starfish-based iterative identification algorithm. Next, the temperature state of the lithium battery thermal model was estimated using the adaptive filtering estimation algorithm. Finally, the estimated lithium battery surface temperature was compared with the actual results. It was determined that the method of the present invention can effectively estimate the lithium battery temperature under conditions where the noise covariance is unknown or inaccurate, and the error is small.

[0123] Example 1

[0124] The parameters are set as follows: Population size Maximum number of iterations Regulatory factors Weakening factor Sampling time interval Number of sampling points The parameter identification range vector for the lithium battery thermal model is set as follows:

[0125]

[0126]

[0127] Covariance matrix of process noise Covariance matrix with observation noise The settings are as follows:

[0128]

[0129]

[0130] Ambient temperature It is 0 degrees Celsius.

[0131] Example 2

[0132] The parameters are set as follows: Population size Maximum number of iterations Regulatory factors Weakening factor Sampling time interval Number of sampling points The parameter identification range vector for the lithium battery thermal model is set as follows:

[0133]

[0134]

[0135] Covariance matrix of process noise Covariance matrix with observation noise The settings are as follows:

[0136]

[0137]

[0138] Ambient temperature It is 25 degrees Celsius.

[0139] The lithium battery modeling and temperature estimation methods based on starfish optimization and adaptive filtering in Examples 1 and 2 include the following steps:

[0140] (1) Construct a variable parameter lumped thermal model for lithium batteries based on the principle of thermoelectric similarity. The specific steps are as follows:

[0141] Step 1: Construct the structure diagram of the variable parameter lumped thermal model of a lithium battery based on the thermoelectric similarity principle. (See attached diagram) Figure 2 ;

[0142] Step 2: Based on this model, the temperature characteristic equation of the variable parameter lumped thermal model of the lithium battery is expressed as follows:

[0143] (1)

[0144] (2)

[0145] Step 3: This invention defines the intermediate variable as the difference between the battery surface temperature and the ambient temperature. The difference between the internal temperature of the battery and the ambient temperature The expression is as follows:

[0146] (3)

[0147] (4)

[0148] Therefore, the temperature characteristic equation becomes:

[0149] (5)

[0150] (6)

[0151] Step 4: In order to handle continuous-time models in practical applications, the battery temperature characteristic equation needs to be discretized and simplified to obtain:

[0152] (7)

[0153] (8)

[0154] in, and For sampling points, The sampling time interval, and The first Second and third The difference between the internal temperature of the battery and the ambient temperature at each sampling point. and The first Second and third The difference between the battery surface temperature and the ambient temperature at each sampling point.

[0155] Step 5: Define in the... The system state variable at the next sampling point System input variables and system output variables They are respectively

[0156] (9)

[0157] Here, the superscript T represents the transpose of a vector or matrix.

[0158] Step 6: During the data measurement process, there is process noise that cannot be ignored. With observation noise Then the state-space equation can be rewritten as:

[0159] (10)

[0160] (11)

[0161] in, and In order to be in The system state variables and system output variables at the sampling points.

[0162] Define the system matrix Control matrix and output matrix They are respectively

[0163]

[0164]

[0165]

[0166] Step 7: Therefore, the final state equation and output equation of the lithium battery variable parameter lumped thermal model can be written as follows:

[0167] (12)

[0168] (13)

[0169] (2) A process for accurately estimating the unknown parameters of the variable parameter thermal model of lithium battery using the starfish-optimized iterative identification method:

[0170] Step 1: Initialize algorithm parameters and set appropriate parameters for the lithium battery modeling and temperature estimation method based on starfish optimization and adaptive filtering;

[0171] Step 2: Collect measurable data including battery surface temperature, ambient temperature, and the rate of heat generation inside the battery. ;

[0172] Step 3: Set the initial value for the number of iterations. Set to 1 to generate the initial position matrix. And calculate the initial position fitness value of the population;

[0173] Step 4: Calculate dynamic parameters Then calculate the updated i-th The position values ​​of all dimensions of an individual;

[0174] Step 5: Calculate the difference between the current optimal position and the position of the selected individual, and then calculate the value of the position after the next update. The position values ​​of all dimensions of an individual;

[0175] Step 6: Increment the iteration count by 1, then return to step 4;

[0176] Step 7: When the number of iterations... Reaching the maximum number of iterations At that time, finally obtained The optimal parameter vector identified by the starfish optimization algorithm.

[0177] (3) The process of constructing an adaptive filter with a fading factor to accurately estimate the temperature of the lumped thermal model of the variable parameters of the lithium battery:

[0178] Step 1: Set the initial value for the number of samples Set to 1, Substituting the temperature characteristic equations of the variable parameter lumped heat model, we calculate the estimate of the system matrix. and estimation of the control matrix ;

[0179] Step 2: Calculate the prior estimates of the system state variables;

[0180] Step 3: Calculate the updated covariance matrix Then calculate the fading factor. And construct the fading factor matrix ;

[0181] Step 4: Calculate the error covariance of the prior estimates of the system state variables;

[0182] Step 5: Calculate the filter gain matrix Then, the posterior estimates of the system state variables are updated.

[0183] Step 6: Update the error covariance of the posterior estimates of the system state variables;

[0184] Step 7: Set the number of samples Add one more time, then return to step two.

[0185] Step 8: When the number of samples... Reaching the maximum number of iterations Finally, the estimated internal temperature of the battery is obtained. Battery surface temperature estimation .

[0186] (4) Based on the process of the lithium battery temperature estimation method based on starfish optimization iterative identification and adaptive filtering with fading factor in (2) and (3), the lithium battery temperature estimation method based on starfish optimization and adaptive filtering under the condition of unknown or inaccurate noise covariance is constructed as follows:

[0187] (14)

[0188] (15)

[0189] (16)

[0190] (17)

[0191] (18)

[0192] (19)

[0193] (20)

[0194] (twenty one)

[0195] (twenty two)

[0196] (twenty three)

[0197] (twenty four)

[0198] (25)

[0199] (26)

[0200] (27)

[0201] (28)

[0202] (29)

[0203] (30)

[0204] (31)

[0205] (32)

[0206] See Figure 2 The specific steps of the above method are as follows:

[0207] (1) Parameter initialization: Select an appropriate population size Maximum number of iterations Regulatory factors Weakening factors Minimum value vector of the identification range Maximum value vector Sampling time interval Covariance of process noise Covariance of observation noise .

[0208] (2) Collect measurable data including surface temperature and ambient temperature and the rate of heat generation inside the battery .

[0209] (3) Set the initial value of the number of iterations The initial position matrix is ​​generated according to equation (14) with a value of 1. .

[0210] (4) Calculate the fitness value of each individual in the population according to equation (15). .

[0211] (5) Calculate the dynamic parameters using equation (16) Then, the updated i-th is calculated according to equation (17). Location values ​​of all dimensions of an individual .

[0212] (6) Calculate the difference between the current optimal position and the position of the selected individual using equation (18). Then, according to equation (19), the updated number of th ... Location values ​​of all dimensions of an individual .

[0213] (7) Let the number of iterations be... Add one more time and return to step (4).

[0214] (8) When the number of iterations Reaching the maximum number of iterations At that time, finally obtained The optimal parameter vector identified by the starfish optimization algorithm.

[0215] (9) Set the initial value of the number of samples Set to 1, Substituting the temperature characteristic equations of the variable parameter lumped heat model, we calculate the estimate of the system matrix. and estimation of the control matrix .

[0216] (10) Calculate the prior estimates of the system state variables using equation (20). .

[0217] (11) Calculate the updated covariance matrix using equations (21) and (22). Then, the fading factor is calculated according to equations (23), (24) and (25). And construct the fading factor matrix according to equation (26). .

[0218] (12) The error covariance of the prior estimate of the system state variables is calculated by equation (27). .

[0219] (13) The gain matrix is ​​obtained by calculating equation (28). Then, the posterior estimate of the system state variables is updated according to equation (29). .

[0220] (14) Update the error covariance of the posterior estimate of the system state variables using equation (30). .

[0221] (15) Let the number of samples be Add one more time and return to step (10).

[0222] (16) When the number of samples Reaching the maximum number of iterations Finally, the internal temperature of the battery is estimated according to equations (31) and (32). Battery surface temperature estimation .

[0223] The definitions of each variable are as follows:

[0224] Define t as time. Represents the derivative with respect to time. This refers to the uniform and equivalent heat capacity inside the battery. The equivalent heat capacity of the battery surface is uniform. The internal uniform equivalent thermal resistance represents the internal heat transfer rate of the battery. The externally uniform equivalent thermal resistance represents the rate of heat transfer between the battery surface and the environment. time, For battery internal temperature, For surface temperature, For ambient temperature, This refers to the rate of heat generation inside the battery.

[0225] definition and For sampling points, and The first Second and third The difference between the internal temperature of the battery and the ambient temperature at each sampling point. and The first Second and third The difference between the battery surface temperature and the ambient temperature at each sampling point. The sampling time interval. In the... Secondary sampling point, For system state variables, For system output variables, Input variables to the system, For the system matrix, For the control matrix, For the output matrix, and For the first The system state variables and system output variables of each sampling point.

[0226] Define population size as The maximum number of iterations is The minimum value vector of the identification range is The maximum value vector is The population can be explored in the following dimensions: Initial population location for OK Column matrix ( , The matrix stores the position of each individual in each dimension of the population, which is a random position within the identification range. Composed of random numbers from a normal distribution between 0 and 1 OK Column matrix. It is the number of sampling points. It is the first The true surface temperature value of each sampling point The current iteration number identified for the parameters ( ), The maximum number of iterations, It is the first Group parameters in the first The fitness value of the next iteration. It is the first Substituting the parameters of each individual into the system state equation yields the first... The estimated battery surface temperature is obtained from each sampling point. At each sampling point, the fitness values ​​of each group are compared, and the group with the lowest fitness is selected as the optimal group. Its fitness value is used as .

[0227] definition For the first Dynamic parameters for each iteration. Let be a cosine function, in the th... iteration For the first The first individual The position of the dimension update, at the _th ... iteration For the first The first individual The location of each dimension update. For the first The first individual Position values ​​in each dimension and for Calculate the current optimal position using random numbers between the given values. The position of the selected individual The difference is denoted as , ( ) represents the positions of all dimensions of 5 randomly selected individuals. and for Random numbers between and For dynamic difference Two values ​​are randomly selected from the data. For the previous version The position of an individual across all dimensions For the updated version The positional values ​​of all dimensions for an individual. The set of parameters that minimizes the error between the estimated and true values. Parameter identification results optimized for starfish.

[0228] The estimated value of the system matrix is ​​defined as follows: The estimated value of the control matrix is The output matrix is ​​C. The prior estimates of the state variables are... The error covariance matrix of the prior estimates of the system state variables is: , This is an estimate of the state variables from the previous moment. Input variables into the system. Let be the covariance matrix of the system process noise. Represents the transpose of a matrix. Let be the error covariance matrix of the posterior estimate of the state variables from the previous time step. This is the fading factor matrix. , and For the first The first, second, and third sampling points were calculated. A gradually disappearing factor. express The matrix calculated in this step No. Line number Column elements, express The matrix calculated from the next sampling point. No. Line number Column elements, As a regulating factor, For the updated covariance matrix, As the attenuation factor, the Kalman gain matrix is: , Let be the covariance matrix of the system observation noise, and let be the system posterior state estimate for the current sampling point. The error covariance matrix of the posterior estimate of the system state variables at the current sampling point is: The estimated values ​​for the battery surface temperature and the battery internal temperature are: and .

[0229] The estimation results of the temperature estimation method designed in this embodiment are shown in [reference]. Figure 3 , Figure 4 , Figure 5 and Figure 6 The estimation results show that, in terms of estimation accuracy and convergence speed, the method of this invention has the following advantages: as the number of iterations M increases, the fitness value becomes smaller and smaller, eventually stabilizing. The temperature estimation curve matches the actual temperature curve very well, and the temperature estimation error is consistently less than 0.1 degrees Celsius. Therefore, the proposed lithium battery modeling and temperature estimation method based on starfish optimization and adaptive filtering can effectively estimate the lithium battery temperature, and the final estimation result output is very close to the actual output. Thus, this invention can effectively achieve lithium battery temperature state estimation, solve the problem of unknown or inaccurate noise covariance, and is fully applicable to lithium battery thermal models under unknown noise covariance.

[0230] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A lithium battery modeling and temperature estimation method based on starfish optimization and adaptive filtering, characterized in that, It comprises the following steps: Step 1) constructing a variable parameter lumped thermal model of lithium battery based on the thermoelectric similarity principle to obtain a model description of the identification system; Step 2) constructing a sea star optimization iterative identification algorithm to accurately estimate unknown parameters of the variable parameter lumped thermal model of the lithium battery; (2-1) Accurate estimation of unknown parameters in the system state equation and the system output equation The sea star optimization iterative identification algorithm is constructed as follows: The set population size is , the maximum iteration number is , the minimum recognition range vector is , the maximum vector is , the population exploratory dimension is , and the initial population position is ​ wherein, is a row matrix, , The matrix saves the position of each dimension of each individual in the population, and is a random position in the recognition range, is a normal distribution of 0 to 1 row matrix; (2-2) Calculate initial fitness and find initial optimal solution, put the parameters of each individual in the system state equation (12) and the system output equation (13) to get the estimated value of the output variable of each ith individual parameter , define the root mean square error of the estimated battery surface temperature and the actual battery surface temperature as fitness, and the fitness function is: ​ ； Wherein, N is the number of sampling points, is the current iteration number of parameter identification, , is the maximum iteration number, is the fitness value of the parameter of the i-th individual in the j-th iteration, is the fitness value of the parameter of the i-th individual in the j-th iteration, is the fitness value of the parameter of the i-th individual in the j-th iteration, is the fitness value of the parameter of the i-th individual in the j-th iteration, is the fitness value of the parameter of the i-th individual in the j-th iteration, is the fitness value of the parameter of the i-th individual in the j-th iteration, (2-3) A dynamic parameter for adjusting random numbers is generated before the exploration phase of the starfish optimization iterative identification algorithm : ； wherein is the dynamic parameter for the th iteration, is the cosine function; (2-4) In the exploration phase, a first dimension of a first individual of the population is randomly selected, a second dimension of a second individual of the population is randomly selected, and the same dimension of the first and second individuals is updated as follows: ​​​​​​ ； wherein, at the first iteration, the position of the first dimension of the first individual is updated to wherein, at the second iteration, the position of the first dimension of the first individual is updated to wherein, at the third iteration, the position of the first dimension of the first individual is updated to wherein, at the fourth iteration, the position of the first dimension of the first individual is updated to wherein, at the fifth iteration, the position value of the first dimension of the first individual is wherein, at the sixth iteration, the position value of the first dimension of the first individual is wherein, at the seventh iteration, the position value of the first dimension of the first individual is wherein, at the eighth iteration, the position value of the first dimension of the first individual is (2-5) Before the development stage, 5 individuals are randomly selected from the population of N = 100 individuals, and in the first iteration, the difference between the current optimal position and the position of the selected individual is calculated, denoted as d, which is used for position updating in the development stage, with the formula: ​​​​​ ； wherein, for the first iteration, the positions of all dimensions of the 5 randomly selected individuals; (2-6) In the development phase, for the i-th individual of the population in the j-th iteration, randomly select 2 values from the dynamic difference values and, and perform the following update: ​​​​ ； wherein, with is a random number between the first iteration, is the position of all dimensions of the first individual before updating, is the position of all dimensions of the first individual after updating, if the value of the position after updating is not within the parameter identification range, the position value of the dimension of the individual is kept the position value before updating, ensuring that the position after updating is within the upper and lower parameter identification boundaries and ranges. (2-7) After the exploration stage and the development stage, the fitness of each individual in the population after this iteration is calculated, and the parameters of each individual in the population are substituted into the system state equation (12) and the system output equation (13) to calculate the fitness of each individual parameter. The minimum fitness value is compared with the minimum fitness value before the above iteration, and the minimum fitness value in the comparison result is selected as the new fitness value, and the parameter vector is updated . Then enter the next iteration update process; after all iterations are completed, a set of parameters is finally obtained, which makes the fitness value, so that the error between the output estimate value and the true value is minimized The parameter identification result of the starfish optimization Step 3) constructing a temperature estimation of the variable parameter lumped thermal model of the lithium battery with a fading factor adaptive filter.

2. The starfish optimization and adaptive filtering based lithium battery modeling and temperature estimation method according to claim 1, wherein, The step 1) comprises the following steps: (1-1) constructing a variable parameter lumped thermal model of lithium battery based on the thermoelectric similarity principle; (1-2) according to the variable parameter lumped thermal model of lithium battery based on the thermoelectric similarity principle, the temperature characteristic equation expression of the constructed variable parameter lumped thermal model of lithium battery is as follows: (1)； (2)； wherein, is time, denotes differentiation with respect to time, is the internal uniform equivalent heat capacity of the battery, is the surface uniform equivalent heat capacity of the battery, is the internal uniform equivalent thermal resistance, is the external uniform equivalent thermal resistance, at time, is the internal temperature of the battery, is the surface temperature, is the ambient temperature, is the internal heat generation rate of the battery; (1-3) discretizing and simplifying the temperature characteristic equation to obtain: (3)； (4)； in, and For sampling points, and The first Second and third The difference between the internal temperature of the battery and the ambient temperature at each sampling point. and The first Second and third The difference between the battery surface temperature and the ambient temperature at each sampling point. The sampling time interval; (1-4) In the data measurement process, there is process noise and observation noise , the temperature characteristic equation is simplified to obtain the state equation and the output equation as (5)； (6)； wherein, at the sampling point, is a system state variable, is a system output variable, is a system input variable, is a system matrix, is a control matrix, is an output matrix, and is a system state matrix and a system output matrix at the sampling point.

3. The starfish optimization and adaptive filtering based lithium battery modeling and temperature estimation method of claim 1, wherein, The step 3) comprises the following steps: (3-1) Setting initial value of sampling number = 1, and Substituting the temperature characteristic equation of the lithium battery variable parameter lumped heat model, the estimation of the system matrix and the estimation of the control matrix ; (3-2) Calculate the prior estimate of the system state variable ; (3-3) Computing the updated covariance matrix Then compute the fading factors and construct the fading factor matrix ; (3-4) Calculate the error covariance of the prior estimate of the system state variable ; (3-5) The filter gain matrix is calculated The posterior estimate of the system state variable is then updated ; (3-6) updating the error covariance of the posterior estimate of the system state variable ; (3-7) Let the number of samples by 1, and return to step (3-2); (3-8) When the number of samplings reaches its maximum number of sampling points , the battery internal temperature estimation and the battery surface temperature estimation are finally obtained.

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