A real-time estimation method and system for internal temperature field of cylindrical lithium battery

Abstract

The application discloses a cylindrical lithium battery internal temperature field real-time estimation method and system, first, a temperature space distribution model is established based on a heat conduction equation, normalized space-time volume is obtained through scaling transformation, and a non-homogeneous boundary condition is converted into a homogeneous one through variable replacement; a double decomposition technique is used to decouple the space-time relationship between the temperature distribution volume and the heat production volume, and the heat production time variable is regarded as a virtual source; a finite-dimensional ordinary differential equation model is established by using a Galerkin method. An adaptive observer is designed, a low-order state variable and a virtual source time sequence are estimated online in combination with an adaptive learning algorithm, a temperature error is measured and estimated, and an update rate is driven; through space-time synthesis of an estimated sequence and a preset space base function, a temperature distribution volume and a virtual source estimated value are reconstructed. Only temperature measurement data are required, voltage and current sensors are not required, and real-time estimation of the cylindrical lithium battery internal temperature field and the heat production can be effectively realized with the aid of a small amount of thermocouples.

Description

Technical Field

[0001] This invention belongs to the field of new energy vehicles, and in particular relates to a method and system for real-time estimation of the internal temperature field of a cylindrical lithium battery. Background Technology

[0002] Lithium-ion batteries play a dominant role in electric and hybrid vehicle technologies due to their high theoretical energy density and durability. The increasing demand for lithium-ion batteries has drawn widespread attention from academia and industry regarding their safe operation. It is well known that thermal effects are a major factor limiting the usability of lithium-ion batteries. Under abuse, the most common reaction of batteries is the generation of gas and heat, which affects performance indicators such as capacity, lifespan, and safety. Therefore, real-time estimation of the battery's temperature field is essential, which also facilitates battery management systems' monitoring and control of the battery. The thermal process of a battery can be described by a distributed parameter system, mathematically based on partial differential equations. The spatiotemporal dynamic complexity caused by partial differential equations makes modeling the thermal process a very challenging task. Fine-grained temperature field estimation covering the entire space typically employs spatiotemporal models. Spatiotemporal modeling methods include model-based methods and data-driven methods. Model-based methods rely on a known system model. Data-driven methods, on the other hand, use collected sensor data and emerging artificial intelligence technologies for modeling. Data-driven methods require a large number of various sensors, and due to the large amount of data processed, real-time estimation of the temperature field cannot be guaranteed. Therefore, current methods for estimating the temperature field of lithium batteries are greatly limited in industrial applications. Summary of the Invention

[0003] To address the above technical problems, this invention provides a method for real-time estimation of the internal temperature field of a cylindrical lithium battery.

[0004] The technical solution adopted by this invention to solve its technical problem is:

[0005] A method for real-time estimation of the internal temperature field of a cylindrical lithium battery, the method comprising the following steps:

[0006] S100: Establishing a spatial temperature distribution model inside a cylindrical battery based on the heat conduction equation;

[0007] S200: By normalizing the spatial location and time quantities through scaling transformation, a normalized spatiotemporal distribution model of internal temperature is established;

[0008] S300: By substituting variables, the non-homogeneous boundary conditions of the normalized internal temperature spatiotemporal distribution model are transformed into homogeneous boundary conditions, resulting in a homogeneous temperature spatiotemporal distribution model.

[0009] S400: Employs a dual decomposition technique to decouple the temperature distribution and heat generation terms of the homogeneous temperature spatiotemporal distribution model in time and space, and treats the time variable of heat generation as a virtual source variable;

[0010] S500: The Galerkin method is used to project the decoupled system and establish a finite-dimensional ordinary differential equation model.

[0011] S600: An adaptive observer is designed for finite-dimensional ordinary differential equation models to estimate the time series of low-order state variables and virtual source variables online. The estimation of virtual sources adopts an adaptive learning algorithm, and the update rate of the adaptive observer is driven by the error between the measured temperature data and the estimated temperature data.

[0012] S700: By estimating the time series of low-order state variables and virtual source variables, and combining them with a preset spatial basis function, the estimated values ​​of the internal temperature distribution of the battery and the virtual source are reconstructed.

[0013] Preferably, S100 specifically comprises:

[0014] ;

[0015] in, This indicates the temperature distribution inside a cylindrical battery. Let be the first derivative of the temperature at a point in space along the radius of the cylindrical battery. Let be the second derivative of the temperature at a point in space along the radius of the cylindrical battery. For heat generated per unit volume, Let be the first derivative of the cylindrical battery at the first boundary along the radial direction. Let be the first radial derivative at the second boundary of the cylindrical battery. For the radius length, The radial spatial coordinates of the cylindrical battery are... For time quantity, Density quantity Specific heat capacity, Thermal conductivity, For convection coefficient, For ambient temperature, Indicates the surface temperature of the battery. Indicates a time quantity.

[0016] Preferably, S200 includes:

[0017] S210: The normalized spatial position and time quantities in the radial direction are obtained through scaling transformation, specifically:

[0018] ;

[0019] ;

[0020] in, These are the normalized spatial coordinates in the radial direction. For time;

[0021] S220: Establish a normalized spatiotemporal temperature distribution model based on the normalized spatial location and time parameters, specifically:

[0022] ;

[0023] The normalized temperature spatiotemporal distribution model includes the following boundary conditions:

[0024] ;

[0025] in, This represents the normalized temperature distribution of the cylindrical battery. Normalized and , To normalize the heat production per unit volume, for A vector composed of thermocouples, with superscript... This represents the transpose of a vector. This is the output vector of the thermocouple sensor. Let be the Dirac function; where, Each thermocouple is located along the radial direction. place, Indicates the position along the radial direction. These represent the first internal thermocouple to the second internal thermocouple. The position of the thermocouple along the radial direction Represents the set of real number vectors. This represents the first derivative of the normalized temperature distribution model at the first boundary along the radial direction. This represents the first derivative of the normalized temperature distribution model at the second boundary along the radial direction;

[0026] Normalized heat production per unit volume It is in the following form:

[0027] ;

[0028] in, These represent the current, open-circuit voltage, and terminal voltage of the cylindrical battery, respectively. Remaining charge capacity Temperature distribution of cylindrical battery abbreviation of This indicates the volume of a cylindrical battery.

[0029] Preferably, S300 includes:

[0030] make The homogeneous temperature spatiotemporal distribution model is as follows:

[0031] ;

[0032] The homogeneous temperature spatiotemporal distribution model includes the following boundary conditions:

[0033] ;

[0034] in, This represents the temperature distribution of the cylindrical cell after homogenization. Homogeneous and , For heat generated per unit volume, Defined as a heat production term. After homogenization A vector composed of thermocouples, with superscript... This represents the transpose of a vector. This is the output vector of the thermocouple sensor.

[0035] Preferably, S400 includes:

[0036] S410: Decompose the simplified temperature distribution using the method of separation of variables.

[0037] First, define the space operator. for:

[0038] ;

[0039] in, Let be a spatial function of the temperature distribution of the homogenized cylindrical battery. for domain, Let be a space of square-integrable functions. This represents the value at the second boundary along the radial direction of the temperature distribution model;

[0040] For the above spatial operators Its corresponding eigenvalue problem is defined as:

[0041] ;

[0042] in, For the first One eigenfunction, For the corresponding eigenvalues;

[0043] Then, the homogenized temperature distribution is written in a spatiotemporally decoupled form:

[0044] ;

[0045] ;

[0046] in, For spatial basis functions, eigenfunctions are directly used. For the corresponding time variable;

[0047] S420: By separating variables, the heat production term is... Decompose:

[0048] A new variable is defined as:

[0049] ;

[0050] Then, the above variables are written in a spatiotemporally decoupled form:

[0051] ;

[0052] in, The time variable is defined as a virtual source. For the corresponding space basis functions, .

[0053] Preferably, S500 includes:

[0054] S510: The homogenized temperature spatiotemporal distribution model is transformed into a finite-dimensional ordinary differential equation using the Galerkin method.

[0055] ;

[0056] The finite-dimensional ordinary differential equation contains the following initial conditions:

[0057] ;

[0058] in,

[0059] ;

[0060] The ordinary differential equation representing the temperature distribution model is divided into slow subsystems and fast subsystems, using subscripts. and They represent respectively, among which For the slow subsystem Each eigenvalue It is a finite value; For an infinite number of eigenvalues ​​in the fast subsystem; and These are the state variables of the slow subsystem and the fast subsystem, respectively. and The system matrices for the slow subsystem and the fast subsystem are respectively. and Virtual sources for the slow subsystem and the fast subsystem, respectively. This is the output vector of the ordinary differential equation. and These are the output vectors of the slow subsystem and the fast subsystem, respectively. and The output matrices of the slow subsystem and the fast subsystem are respectively. and These are the operators for the slow subsystem and the fast subsystem, respectively. This represents the value of the temperature distribution model at t=0. and These are the space basis functions for the slow subsystem and the fast subsystem, respectively. express and The inner product of.

[0061] Preferably, S600 includes:

[0062] S610: Establish an adaptive observer for the low-order slow subsystem obtained after order reduction:

[0063] ;

[0064] in, , , They are respectively , , The estimated value; It is the observer gain matrix to be determined;

[0065] S620: Define low-order state estimation error Output estimation error and virtual source estimation error They are respectively:

[0066] ;

[0067] Ignoring the fast dynamics, setting up an adaptive observer ;

[0068] S630: The estimation of the virtual source uses an adaptive learning algorithm as follows:

[0069] ;

[0070] in, It is a symmetric positive definite matrix used to define the learning rate. It is a constant auxiliary matrix to be determined.

[0071] Preferably, S700 specifically refers to:

[0072] ;

[0073] in, and These are the estimated values ​​for the internal temperature distribution of the battery and the virtual source, respectively. is the transpose of the spatial basis functions of the slow subsystem.

[0074] A real-time temperature field estimation system for the internal temperature field of a cylindrical lithium battery includes:

[0075] The model building module is used to build a model of the internal temperature spatial distribution of a cylindrical battery based on the heat conduction equation.

[0076] The normalization module is used to normalize spatial location and time quantities through scaling transformation, and to establish a normalized spatiotemporal distribution model of internal temperature.

[0077] The transformation module is used to transform the non-homogeneous boundary conditions of the normalized internal temperature spatiotemporal distribution model into homogeneous boundary conditions through variable substitution, thereby obtaining a homogeneous temperature spatiotemporal distribution model.

[0078] The spatiotemporal decoupling module is used to decouple the temperature distribution and heat generation terms of the homogeneous temperature spatiotemporal distribution model in spatiotemporal using a dual decomposition technique, and to treat the time variable of heat generation as a virtual source variable.

[0079] The module for establishing finite-dimensional ordinary differential equation models is used to project the decoupled system using the Galerkin method to establish a finite-dimensional ordinary differential equation model.

[0080] The online estimation module is used to design adaptive observers for finite-dimensional ordinary differential equation models and to estimate the time series of low-order state variables and virtual source variables online. The estimation of virtual sources adopts an adaptive learning algorithm, and the update rate of the adaptive observer is driven by the error between the measured temperature data and the estimated temperature data.

[0081] The estimated value reconstruction module is used to reconstruct the estimated values ​​of the battery's internal temperature distribution and virtual source by combining the estimated time series of low-order state variables and virtual source variables with a preset spatial basis function.

[0082] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of a method for real-time estimation of the internal temperature field of a cylindrical lithium battery.

[0083] The aforementioned sensorless real-time estimation method for the internal temperature field of a cylindrical lithium battery based on dual decomposition requires only temperature measurement data and does not need data from other sensors such as voltage and current sensors. Utilizing a small number of thermocouple sensors, the internal temperature field and heat generation of a one-dimensional cylindrical lithium-ion battery can be estimated simply and effectively in real time. Attached Figure Description

[0084] Figure 1 A flowchart illustrating a method for real-time estimation of the internal temperature field of a cylindrical lithium battery, as provided in an embodiment of the present invention;

[0085] Figure 2 A theoretical framework diagram of a real-time estimation method for the internal temperature field of a cylindrical lithium battery provided in an embodiment of the present invention;

[0086] Figure 3 The tracking performance diagram of the adaptive observer provided in the embodiments of the present invention;

[0087] Figure 4 Performance graph of the adaptive learning algorithm provided in the embodiments of the present invention;

[0088] Figure 5 A graph showing the variation of the estimation error of the original state provided in an embodiment of the present invention;

[0089] Figure 6 A graph showing the variation of the estimation error of the virtual source provided in this embodiment of the invention. Detailed Implementation

[0090] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0091] In one embodiment, such as Figure 1 and 2 As shown, this invention provides a method for real-time estimation of the internal temperature field of a cylindrical lithium battery, the method comprising the following steps:

[0092] S100: Establishing a spatial temperature distribution model inside a cylindrical battery based on the heat conduction equation;

[0093] S200: By normalizing the spatial location and time quantities through scaling transformation, a normalized spatiotemporal distribution model of internal temperature is established;

[0094] S300: By substituting variables, the non-homogeneous boundary conditions of the normalized internal temperature spatiotemporal distribution model are transformed into homogeneous boundary conditions, resulting in a homogeneous temperature spatiotemporal distribution model.

[0095] S400: Employs a dual decomposition technique to decouple the temperature distribution and heat generation terms of the homogeneous temperature spatiotemporal distribution model in time and space, and treats the time variable of heat generation as a virtual source variable;

[0096] S500: The Galerkin method is used to project the decoupled system and establish a finite-dimensional ordinary differential equation model.

[0097] S600: An adaptive observer is designed for finite-dimensional ordinary differential equation models to estimate the time series of low-order state variables and virtual source variables online. The estimation of virtual sources adopts an adaptive learning algorithm, and the update rate of the adaptive observer is driven by the error between the measured temperature data and the estimated temperature data.

[0098] S700: By estimating the time series of low-order state variables and virtual source variables, and combining them with a preset spatial basis function, the estimated values ​​of the internal temperature distribution of the battery and the virtual source are reconstructed.

[0099] The aforementioned method achieves high-precision, real-time, full-distribution reconstruction of the internal temperature field of a battery. Based on a rigorous physical model of heat conduction, it effectively simplifies model complexity through scaling normalization and variable substitution homogenization. Employing a dual spatiotemporal decoupling technique, it decomposes the temperature distribution and heat generation term into a combination of spatial basis functions and temporal variables, and innovatively treats the temporal variable of heat generation as a virtual source, avoiding direct modeling of its complex spatial dependencies.

[0100] Furthermore, the infinite-dimensional distributed parameter system is reduced to a finite-dimensional system of ordinary differential equations using the Galerkin method, significantly reducing the computational burden. An adaptive observer designed for this reduced-order model, driven by the error between measured and estimated temperatures, can synchronously estimate low-order state variables and time-varying virtual sources online without requiring precise prior knowledge of the internal heat generation model. It exhibits strong adaptability and robustness to operating condition variations and parameter uncertainties. Finally, the complete internal temperature field and heat generation distribution are reconstructed in real time through spatiotemporal synthesis. The entire method forms an efficient closed-loop estimation system that combines physical rigor with engineering practicality, providing crucial and reliable internal state information for battery thermal safety management.

[0101] In one embodiment, S100 specifically includes:

[0102] ;

[0103] in, This indicates the temperature distribution inside a cylindrical battery. Let be the first derivative of the temperature at a point in space along the radius of the cylindrical battery. Let be the second derivative of the temperature at a point in space along the radius of the cylindrical battery. For heat generated per unit volume, Let be the first derivative of the cylindrical battery at the first boundary along the radial direction. Let be the first radial derivative at the second boundary of the cylindrical battery. For the radius length, The radial spatial coordinates of the cylindrical battery are... For time quantity, Density quantity Specific heat capacity, Thermal conductivity, For convection coefficient, For ambient temperature, Indicates the surface temperature of the battery. Indicates a time quantity.

[0104] Specifically, the establishment of the temperature spatial distribution model inside the cylindrical battery comprehensively considers various physical effects such as internal heat generation, radial heat conduction, and surface-to-environment convective heat transfer, laying a solid physical and mathematical foundation for subsequent high-precision temperature estimation and ensuring the inherent scientificity and accuracy of the estimation method.

[0105] In one embodiment, S200 includes:

[0106] S210: The normalized spatial position and time quantities in the radial direction are obtained through scaling transformation, specifically:

[0107] ;

[0108] ;

[0109] in, These are the normalized spatial coordinates in the radial direction. For time;

[0110] S220: Establish a normalized spatiotemporal temperature distribution model based on the normalized spatial location and time parameters, specifically:

[0111] ;

[0112] The normalized temperature spatiotemporal distribution model includes the following boundary conditions:

[0113] ;

[0114] in, This represents the normalized temperature distribution of the cylindrical battery. Normalized and , To normalize the heat production per unit volume, for A vector composed of thermocouples, with superscript... This represents the transpose of a vector. This is the output vector of the thermocouple sensor. Let be the Dirac function; where, Each thermocouple is located along the radial direction. place, Indicates the position along the radial direction. These represent the first internal thermocouple to the second internal thermocouple. The position of the thermocouple along the radial direction Represents the set of real number vectors. This represents the first derivative of the normalized temperature distribution model at the first boundary along the radial direction. This represents the first derivative of the normalized temperature distribution model at the second boundary along the radial direction;

[0115] Normalized heat production per unit volume It is in the following form:

[0116] ;

[0117] in, These represent the current, open-circuit voltage, and terminal voltage of the cylindrical battery, respectively. Remaining charge capacity Temperature distribution of cylindrical battery abbreviation of This indicates the volume of a cylindrical battery.

[0118] Specifically, by introducing dimensionless coordinate and time variables, the model parameters were normalized. This effectively eliminated the dimensional and numerical differences caused by different battery models, sizes, and material properties (such as thermal conductivity and specific heat capacity), unifying the model into a standard form. This not only greatly simplifies the complexity of subsequent analysis and calculation but also enhances the versatility and robustness of the proposed algorithm, making it easier to apply to different types of cylindrical batteries.

[0119] In one embodiment, S300 includes:

[0120] make The homogeneous temperature spatiotemporal distribution model is as follows:

[0121] ;

[0122] The homogeneous temperature spatiotemporal distribution model includes the following boundary conditions:

[0123] ;

[0124] in, This represents the temperature distribution of the cylindrical cell after homogenization. Homogeneous and , For heat generated per unit volume, Defined as a heat production term. After homogenization A vector composed of thermocouples, with superscript... This represents the transpose of a vector. This is the output vector of the thermocouple sensor.

[0125] Specifically, through clever variable substitution, the originally complex non-homogeneous boundary conditions are transformed into homogeneous boundary conditions. This transformation eliminates non-zero terms on the boundaries, making the model easier to solve using the method of separation of variables. This removes mathematical obstacles for subsequent spatiotemporal decoupling and order reduction, and is a key step in simplifying the problem-solving process.

[0126] In one embodiment, S400 includes:

[0127] S410: Decompose the simplified temperature distribution using the method of separation of variables.

[0128] First, define the space operator. for:

[0129] ;

[0130] in, Let be a spatial function of the temperature distribution of the homogenized cylindrical battery. for domain, Let be a space of square-integrable functions. This represents the value at the second boundary along the radial direction of the temperature distribution model;

[0131] For the above spatial operators Its corresponding eigenvalue problem is defined as:

[0132] ;

[0133] in, For the first One eigenfunction, For the corresponding eigenvalues;

[0134] Then, the homogenized temperature distribution is written in a spatiotemporally decoupled form:

[0135] ;

[0136] ;

[0137] in, For spatial basis functions, eigenfunctions are directly used. For the corresponding time variable;

[0138] S420: By separating variables, the heat production term is... Decompose:

[0139] A new variable is defined as:

[0140] ;

[0141] Then, the above variables are written in a spatiotemporally decoupled form:

[0142] ;

[0143] in, The time variable is defined as a virtual source. For the corresponding space basis functions, .

[0144] Specifically, the core innovation of this step lies in the simultaneous spatiotemporal decoupling of the temperature field and the unknown heat generation term. The temperature distribution and heat generation are decomposed into products of spatial basis functions and time coefficients, successfully transforming the complex spatiotemporal coupling problem into a problem of solving for the time coefficients. In particular, defining the time component of the heat generation term as a virtual source avoids the difficulty of directly modeling the complex nonlinear spatial dependencies of the heat generation term, making it possible to reconstruct the complete spatiotemporal heat generation distribution solely through time series estimation.

[0145] In one embodiment, S500 includes:

[0146] S510: The homogenized temperature spatiotemporal distribution model is transformed into a finite-dimensional ordinary differential equation using the Galerkin method.

[0147] ;

[0148] The finite-dimensional ordinary differential equation contains the following initial conditions:

[0149] ;

[0150] in,

[0151] ;

[0152] The ordinary differential equation representing the temperature distribution model is divided into slow subsystems and fast subsystems, using subscripts. and They represent respectively, among which For the slow subsystem Each eigenvalue It is a finite value; For an infinite number of eigenvalues ​​in the fast subsystem; and These are the state variables of the slow subsystem and the fast subsystem, respectively. and The system matrices for the slow subsystem and the fast subsystem are respectively. and Virtual sources for the slow subsystem and the fast subsystem, respectively. This is the output vector of the ordinary differential equation. and These are the output vectors of the slow subsystem and the fast subsystem, respectively. and The output matrices of the slow subsystem and the fast subsystem are respectively. and These are the operators for the slow subsystem and the fast subsystem, respectively. This represents the value of the temperature distribution model at t=0. and These are the space basis functions for the slow subsystem and the fast subsystem, respectively. express and The inner product of.

[0153] Specifically, by utilizing the Galerkin weighted residual method, an infinite-dimensional distributed parameter system is projected onto a low-dimensional subspace spanned by a finite number of eigenfunctions, thus obtaining a finite-dimensional system of ordinary differential equations. This model reduction technique significantly reduces computational complexity and online computational burden, transforming a partial differential equation problem that is difficult to solve directly into an ordinary differential equation problem more suitable for online real-time computation and state estimation, serving as a bridge to real-time applications.

[0154] In one embodiment, S600 includes:

[0155] S610: Establish an adaptive observer for the low-order slow subsystem obtained after order reduction:

[0156] ;

[0157] in, , , They are respectively , , The estimated value; It is the observer gain matrix to be determined;

[0158] S620: Define low-order state estimation error Output estimation error and virtual source estimation error They are respectively:

[0159] ;

[0160] Ignoring the fast dynamics, setting up an adaptive observer ;

[0161] S630: The estimation of the virtual source uses an adaptive learning algorithm as follows:

[0162] ;

[0163] in, It is a symmetric positive definite matrix used to define the learning rate. It is a constant auxiliary matrix to be determined.

[0164] Specifically, an advanced adaptive observer was designed that can simultaneously estimate online the low-order state variables representing the temperature field and the virtual source variables representing changes in heat production power. The observer's gain and the virtual source's update law are driven by the error between the measured and estimated temperatures, giving the system adaptive capabilities and enabling it to automatically adjust the estimates to approximate the real system dynamics. This design does not require prior knowledge of the exact heat production model and exhibits good adaptability and robustness to changes in internal parameters and external operating conditions.

[0165] In one embodiment, S700 specifically refers to:

[0166] ;

[0167] in, and These are the estimated values ​​for the internal temperature distribution of the battery and the virtual source, respectively. is the transpose of the spatial basis functions of the slow subsystem.

[0168] Specifically, the S700 completes the reconstruction process from low-dimensional time series to high-dimensional spatial distribution. Using the spatial basis functions obtained from the previous decomposition, it synthesizes the time coefficients of the online estimated low-order state variables and dummy source variables, ultimately reconstructing in real time the complete temperature field distribution and heat generation rate distribution inside the battery, which cannot be directly measured. This provides crucial input for the precise control of the battery thermal management system.

[0169] In one detailed embodiment, the present invention constructs an experimental platform including a battery testing cabinet, a constant temperature chamber, and a battery management system to identify thermal model parameters. The experimental object is a 32650 cylindrical lithium-ion battery, and three thermocouples are evenly distributed on its surface to collect temperature data (the average value of the three sensors is used as the surface temperature measurement value). First, the characteristic value is calculated as follows: Therefore, the order of the slow subsystem =2. Slow subsystem matrix and They are respectively:

[0170] ;

[0171] Observer gain matrix and constant auxiliary matrix They are respectively:

[0172] ;

[0173] Define the symmetric positive definite matrix of the learning rate as follows: .

[0174] The tracking performance graph of the adaptive observer is shown below. Figure 3 As shown, this includes state variables of reduced order. and its estimated value The trajectory curve; the state quantity of price reduction Quickly track its estimated value It exhibits excellent tracking performance. The performance graph of the adaptive learning algorithm is shown below. Figure 4 As shown, including virtual sources and its estimated value The trajectory curve, virtual source Quickly track its estimated value It has excellent tracking performance.

[0175] Original state estimation error The change graph is as follows Figure 5 As shown, virtual source estimation error The change graph is as follows Figure 6 As shown, and The convergence to near 0 indicates that the state and virtual source estimates can be obtained by spatiotemporal synthesis. The error between the measured temperature data and the estimated temperature data drives the update rate of the adaptive observer, thereby achieving real-time and accurate estimation of the temperature field and heat generation terms.

[0176] The aforementioned method for real-time estimation of the internal temperature field of a cylindrical lithium-ion battery based on dual decomposition uses only a few thermocouple sensors. It employs an adaptive observer and an adaptive algorithm to achieve accurate real-time estimation of the internal temperature field of the battery. In addition, the use of a reduced-order model can significantly reduce the processing of large amounts of data, resulting in high computational efficiency.

[0177] In one embodiment, a real-time temperature field estimation system for the interior of a cylindrical lithium battery is also provided, comprising:

[0178] The model building module is used to build a model of the internal temperature spatial distribution of a cylindrical battery based on the heat conduction equation.

[0179] The normalization module is used to normalize spatial location and time quantities through scaling transformation, and to establish a normalized spatiotemporal distribution model of internal temperature.

[0180] The transformation module is used to transform the non-homogeneous boundary conditions of the normalized internal temperature spatiotemporal distribution model into homogeneous boundary conditions through variable substitution, thereby obtaining a homogeneous temperature spatiotemporal distribution model.

[0181] The spatiotemporal decoupling module is used to decouple the temperature distribution and heat generation terms of the homogeneous temperature spatiotemporal distribution model in spatiotemporal using a dual decomposition technique, and to treat the time variable of heat generation as a virtual source variable.

[0182] The module for establishing finite-dimensional ordinary differential equation models is used to project the decoupled system using the Galerkin method to establish a finite-dimensional ordinary differential equation model.

[0183] The online estimation module is used to design adaptive observers for finite-dimensional ordinary differential equation models and to estimate the time series of low-order state variables and virtual source variables online. The estimation of virtual sources adopts an adaptive learning algorithm, and the update rate of the adaptive observer is driven by the error between the measured temperature data and the estimated temperature data.

[0184] The estimated value reconstruction module is used to reconstruct the estimated values ​​of the battery's internal temperature distribution and virtual source by combining the estimated time series of low-order state variables and virtual source variables with a preset spatial basis function.

[0185] Specific limitations regarding the real-time estimation system for the internal temperature field of a cylindrical lithium battery can be found in the limitations of the real-time estimation method for the internal temperature field of a cylindrical lithium battery described above, and will not be repeated here. Each module in the aforementioned real-time estimation system for the internal temperature field of a cylindrical lithium battery can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0186] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of a method for real-time estimation of the internal temperature field of a cylindrical lithium battery.

[0187] The present invention provides a detailed description of a method and system for real-time estimation of the internal temperature field of a cylindrical lithium-ion battery using a few sensors. Specific examples have been used to illustrate the principles and implementation methods of the invention. The descriptions of these embodiments are merely for the purpose of helping to understand the core ideas of the invention. It should be noted that those skilled in the art can make various improvements and modifications to the invention without departing from its principles, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A method for real-time estimation of the internal temperature field of a cylindrical lithium battery, characterized in that, The method includes the following steps: S100: Establishing a spatial temperature distribution model inside a cylindrical battery based on the heat conduction equation; S200: Establishes a normalized spatiotemporal distribution model of internal temperature by normalizing spatial location and temporal quantities through scaling transformation; S200 includes: S210: The normalized spatial position and time quantities in the radial direction are obtained through scaling transformation, specifically: ； ； in, These are the normalized spatial coordinates in the radial direction. For time; S220: Establish a normalized spatiotemporal temperature distribution model based on the normalized spatial location and time parameters, specifically: ； The normalized temperature spatiotemporal distribution model includes the following boundary conditions: ； in, This represents the normalized temperature distribution of the cylindrical battery. Normalized and , To normalize the heat production per unit volume, for A vector composed of thermocouples, with superscript... This represents the transpose of a vector. This is the output vector of the thermocouple sensor. Let be the Dirac function; where, Each thermocouple is located along the radial direction. place, Indicates the position along the radial direction. These represent the first internal thermocouple to the second internal thermocouple. The position of the thermocouple along the radial direction Represents the set of real number vectors. This represents the first derivative of the normalized temperature distribution model at the first boundary along the radial direction. This represents the first derivative of the normalized temperature distribution model at the second boundary along the radial direction; Normalized heat production per unit volume It is in the following form: ； in, These represent the current, open-circuit voltage, and terminal voltage of the cylindrical battery, respectively. Remaining charge capacity Temperature distribution of cylindrical battery abbreviation of Indicates the volume of a cylindrical battery; S300: By substituting variables, the non-homogeneous boundary conditions of the normalized internal temperature spatiotemporal distribution model are transformed into homogeneous boundary conditions, resulting in a homogeneous temperature spatiotemporal distribution model; S300 includes: make The homogeneous temperature spatiotemporal distribution model is as follows: ； The homogeneous temperature spatiotemporal distribution model includes the following boundary conditions: ； in, This represents the temperature distribution of the cylindrical cell after homogenization. Homogeneous and , For heat generated per unit volume, Defined as a heat production term. After homogenization A vector composed of thermocouples, with superscript... This represents the transpose of a vector. This is the output vector of the thermocouple sensor. S400: Employs a dual decomposition technique to decouple the temperature distribution and heat generation terms in the homogeneous temperature spatiotemporal distribution model, and treats the time variable of heat generation as a virtual source variable; S400 includes: S410: Decompose the simplified temperature distribution using the method of separation of variables. First, define the space operator. for: ； in, Let be a spatial function of the temperature distribution of the homogenized cylindrical battery. for domain, Let be a space of square-integrable functions. This represents the value at the second boundary along the radial direction of the temperature distribution model; For the above spatial operators Its corresponding eigenvalue problem is defined as: ； in, For the first One eigenfunction, For the corresponding eigenvalues; Then, the homogenized temperature distribution Written as a form of spacetime decoupling: ； ； in, For spatial basis functions, eigenfunctions are directly used. For the corresponding time variable; S420: By separating variables, the heat production term is... Decompose: A new variable is defined as: ； Then, the above variables are written in a spatiotemporally decoupled form: ； in, The time variable is defined as a virtual source. For the corresponding space basis functions, ; S500: The Galerkin method is used to project the decoupled system and establish a finite-dimensional ordinary differential equation model. S600: An adaptive observer is designed for finite-dimensional ordinary differential equation models to estimate the time series of low-order state variables and virtual source variables online. The estimation of virtual sources adopts an adaptive learning algorithm, and the update rate of the adaptive observer is driven by the error between the measured temperature data and the estimated temperature data. S700: By estimating the time series of low-order state variables and virtual source variables, and combining them with a preset spatial basis function, the estimated values ​​of the internal temperature distribution of the battery and the virtual source are reconstructed.

2. The method according to claim 1, characterized in that, S100 specifically refers to: ； in, This indicates the temperature distribution inside a cylindrical battery. Let be the first derivative of the temperature at a point in space along the radius of the cylindrical battery. Let be the second derivative of the temperature at a point in space along the radius of the cylindrical battery. For heat generated per unit volume, Let be the first derivative of the cylindrical battery at the first boundary along the radial direction. Let be the first radial derivative at the second boundary of the cylindrical battery. For the radius length, The radial spatial coordinates of the cylindrical battery are... For time quantity, Density quantity Specific heat capacity, Thermal conductivity, For convection coefficient, For ambient temperature, Indicates the surface temperature of the battery. Indicates a time quantity.

3. The method according to claim 2, characterized in that, The S500 includes: S510: The homogenized temperature spatiotemporal distribution model is transformed into a finite-dimensional ordinary differential equation using the Galerkin method. ； The finite-dimensional ordinary differential equation contains the following initial conditions: ； in, ； The ordinary differential equation representing the temperature distribution model is divided into slow subsystems and fast subsystems, using subscripts. and They represent respectively, among which For the slow subsystem Each eigenvalue It is a finite value; For an infinite number of eigenvalues ​​in the fast subsystem; and These are the state variables of the slow subsystem and the fast subsystem, respectively. and The system matrices for the slow subsystem and the fast subsystem are respectively. and Virtual sources for the slow subsystem and the fast subsystem, respectively. This is the output vector of the ordinary differential equation. and These are the output vectors of the slow subsystem and the fast subsystem, respectively. and The output matrices of the slow subsystem and the fast subsystem are respectively. and These are the operators for the slow subsystem and the fast subsystem, respectively. This represents the value of the temperature distribution model at t=0. and These are the space basis functions for the slow subsystem and the fast subsystem, respectively. express and The inner product of.

4. The method according to claim 3, characterized in that, The S600 includes: S610: Establish an adaptive observer for the low-order slow subsystem obtained after order reduction: ； in, , , They are respectively , , The estimated value; It is the observer gain matrix to be determined; S620: Define low-order state estimation error Output estimation error and virtual source estimation error They are respectively: ； Ignoring the fast dynamics, setting up an adaptive observer ; S630: The estimation of the virtual source uses an adaptive learning algorithm as follows: ； in, It is a symmetric positive definite matrix used to define the learning rate. It is a constant auxiliary matrix to be determined.

5. The method according to claim 4, characterized in that, The S700 specifically refers to: ； in, and These are the estimated values ​​for the internal temperature distribution of the battery and the virtual source, respectively. is the transpose of the spatial basis functions of the slow subsystem.

6. A real-time estimation system for the internal temperature field of a cylindrical lithium battery performing the method according to any one of claims 1 to 5, characterized in that, include: The model building module is used to build a model of the internal temperature spatial distribution of a cylindrical battery based on the heat conduction equation. The normalization module is used to normalize spatial location and time quantities through scaling transformation, and to establish a normalized spatiotemporal distribution model of internal temperature. The transformation module is used to transform the non-homogeneous boundary conditions of the normalized internal temperature spatiotemporal distribution model into homogeneous boundary conditions through variable substitution, thereby obtaining a homogeneous temperature spatiotemporal distribution model. The spatiotemporal decoupling module is used to decouple the temperature distribution and heat generation terms of the homogeneous temperature spatiotemporal distribution model in spatiotemporal using a dual decomposition technique, and to treat the time variable of heat generation as a virtual source variable. The module for establishing finite-dimensional ordinary differential equation models is used to project the decoupled system using the Galerkin method to establish a finite-dimensional ordinary differential equation model. The online estimation module is used to design adaptive observers for finite-dimensional ordinary differential equation models and to estimate the time series of low-order state variables and virtual source variables online. The estimation of virtual sources adopts an adaptive learning algorithm, and the update rate of the adaptive observer is driven by the error between the measured temperature data and the estimated temperature data. The estimated value reconstruction module is used to reconstruct the estimated values ​​of the battery's internal temperature distribution and virtual source by combining the estimated time series of low-order state variables and virtual source variables with a preset spatial basis function.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 5.

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