Lithium ion battery temperature field online reconstruction method and device

Abstract

The present application belongs to the technical field of lithium ion batteries, and particularly relates to a lithium ion battery temperature field online reconstruction method and device. The method comprises the following steps: obtaining battery surface temperature boundary data and heat generation rate data under variable working conditions of the lithium ion battery; constructing a physical information-Kolmogorov-Arnold network, converting the initial thermal equilibrium condition, central axis symmetry boundary and battery surface temperature boundary of the lithium ion battery into forced hard constraints for forward propagation of the network, mapping the input features and output forms of the network through a mathematical analysis construction rule, and analyzing and constructing a temperature field; taking the heat conduction partial differential equation residual of the analyzed and constructed temperature field with respect to the space-time coordinates as the only loss function, training the physical information-Kolmogorov-Arnold network, and then online reconstructing the space-time temperature field distribution data of the target battery interior. The present application realizes high-fidelity and extremely fast reconstruction of the non-uniform dynamic temperature field in the battery interior.

Description

Technical Field

[0001] This invention belongs to the field of lithium-ion battery technology, and particularly relates to a method and apparatus for online reconstruction of the temperature field of lithium-ion batteries. Background Technology

[0002] Real-time and accurate online acquisition of the internal temperature field distribution of batteries is of great significance for battery thermal safety early warning and thermal management optimization. With the intersection of artificial intelligence and physics, Physical Information Neural Networks (PINNs) have been introduced into this field, attempting to balance computational speed with physical laws.

[0003] However, existing PINN methods typically employ a "soft constraint" mechanism when solving heat conduction PDEs. This involves treating physical boundary conditions (such as measured surface temperature boundaries and internal axisymmetric zero heat flux boundaries) as additional penalty terms, manually assigning weights and directly adding them to the total loss function. This soft constraint approach leads the network into a "multi-objective optimization" dilemma during training, easily causing gradient conflicts and convergence oscillations. More critically, soft constraints cannot mathematically guarantee that the final prediction results will strictly and absolutely satisfy the physical laws and boundary conditions of real heat transfer, severely limiting its accuracy in industrial-grade safety monitoring. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, this invention provides an online reconstruction method and device for the temperature field of lithium-ion batteries. It innovatively uses mathematical analytical construction rules to directly transform the measured temperature boundary of the battery surface and the internal axisymmetric physical conditions into "hard constraints" at the input and output of a deep neural network. This simplifies the loss to the pure heat transfer PDE (partial differential equation of heat conduction) residual. Thus, without completely eliminating the dependence on internal temperature sensors and without the need for complex multi-objective weight parameter tuning, it achieves high-fidelity and rapid reconstruction of the non-uniform dynamic temperature field inside the battery. This provides highly reliable underlying information support for the refined thermal management and non-destructive condition assessment of the battery management system (BMS).

[0005] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions: The first aspect of this invention provides a method for online reconstruction of the temperature field of a lithium-ion battery.

[0006] A method for online reconstruction of the temperature field of a lithium-ion battery includes the following steps: Acquire boundary data of battery surface temperature and heat generation rate data of lithium-ion battery under varying operating conditions; A physical information-Kolmogorov-Arnold network is constructed to transform the initial thermal equilibrium conditions, central axisymmetric boundary, and battery surface temperature boundary of the lithium-ion battery into mandatory hard constraints for the forward propagation of the network. The input characteristics and output form of the network are mapped through mathematical analytical construction rules to analytically construct the temperature field. The physical information-Kolmogorov-Arnold network was trained using the residual of the partial differential equation of heat conduction with respect to the spatiotemporal coordinates of the temperature field constructed analytically as the unique loss function. Using a trained physical information-Kolmogorov-Arnold network, the spatiotemporal temperature field distribution data inside the target battery is reconstructed online.

[0007] A second aspect of the present invention provides an online temperature field reconstruction device for lithium-ion batteries.

[0008] An online temperature field reconstruction device for lithium-ion batteries includes: The data acquisition module is configured to acquire boundary data of battery surface temperature and heat generation rate data under varying operating conditions of lithium-ion batteries. The temperature field estimation module is configured to: construct a physical information-Kolmogorov-Arnold network, transform the initial thermal equilibrium conditions, central axisymmetric boundary, and battery surface temperature boundary of the lithium-ion battery into mandatory hard constraints for network forward propagation, and map the input features and output form of the network through mathematical analytical construction rules to analytically construct the temperature field. The model training module is configured to train the physical information-Kolmogorov-Arnold network using the residuals of the heat conduction partial differential equation of the temperature field with respect to the spatiotemporal coordinates, which are analytically constructed, as the only loss function. The online reconstruction module is configured to reconstruct the spatiotemporal temperature field distribution data inside the target battery online using a trained physical information-Kolmogorov-Arnold network.

[0009] The above one or more technical solutions have the following beneficial effects: This invention provides an online method and apparatus for reconstructing the temperature field of a lithium-ion battery, pioneering an analytical hard-constraint architecture that completely eliminates the convergence problem inherent in traditional soft-penalty terms. This invention innovatively employs mathematical analytical construction rules to strongly couple the spatiotemporal input-output features of the deep neural network with the underlying physical boundaries. By introducing time decay terms, radial coordinate squared mapping, and the product construction of spatial structures, the initial conditions, the central axisymmetric von Neumann boundary, and the surface Dirichlet boundary are implicitly and absolutely locked during the network's forward computation stage. This architecture completely overturns the traditional practice of directly adding boundaries as soft-constraint penalty terms in Physical Information Neural Networks (PINNs), eliminating gradient conflicts and parameter tuning barriers caused by multi-objective optimization, and ensuring that the reconstructed temperature field strictly and absolutely obeys the true laws of heat transfer physics.

[0010] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0011] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0012] Figure 1 This is a flowchart of the method in Example 1.

[0013] Figure 2 This is a structural diagram of the device in Embodiment 2. Detailed Implementation

[0014] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0015] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0016] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0017] Example 1 Lithium-ion batteries undergo complex electrochemical reactions during charging and discharging, resulting in various thermal effects such as Joule heating, reaction heat, and polarization heat. This leads to a significant temperature gradient within the battery, with the core temperature often much higher than the surface temperature. Existing battery management systems (BMS) typically only deploy temperature sensors on the battery surface, acquiring limited surface temperature information and failing to reflect the true spatial distribution of the internal temperature field. When localized overheating or excessive temperature gradients occur within the battery, it not only accelerates localized aging of battery materials but also easily induces serious safety issues such as thermal runaway. Therefore, the ability to acquire real-time and accurate online information about the internal temperature field distribution of the battery is crucial for battery thermal safety early warning and thermal management optimization.

[0018] The spatiotemporal evolution of the internal temperature field of a battery is dominated by the partial differential equation (PDE) of heat conduction. In existing technologies, numerical methods such as the finite element method or finite difference method are typically used to solve this PDE. While these methods can obtain relatively accurate temperature field distributions, they require high-density mesh generation in both space and time, resulting in extremely high computational complexity and time-consuming solutions. This makes them unsuitable for the stringent real-time response requirements of onboard or energy storage edge battery management systems.

[0019] In recent years, while purely data-driven deep learning methods have achieved rapid predictions, they are essentially black-box models, heavily reliant on supervised training with large amounts of data labeled with the battery's actual internal temperature. However, obtaining the highest core temperature inside a battery typically requires destructive sensor implantation, making large-scale data acquisition impossible in practical engineering. This results in a severe lack of realistic calibration values ​​for model training. Furthermore, the lack of support from underlying heat transfer mechanisms directly leads to these data-driven models being highly susceptible to distortion under unseen complex operating conditions, lacking generalization ability and engineering reliability.

[0020] Therefore, in addition to the problems mentioned in the background section, such as the difficulty in balancing multi-objective loss functions and the inability to strictly satisfy physical boundary conditions, which lead to difficulties in network training and limited real-time reconstruction accuracy, existing methods for obtaining the internal temperature field of batteries also have the following obvious limitations in engineering applications: Numerical heat conduction models are typically computationally complex and require many parameters, making them difficult to implement in real time in resource-constrained battery management systems. Purely data-driven methods are limited by the difficulty in obtaining internal data and the poor generalization ability of the model.

[0021] In summary, there is an urgent need for an online temperature field estimation architecture that can strictly satisfy the physical heat transfer boundary laws while ensuring extremely fast computing efficiency, in order to break through the technical bottleneck of power battery safety monitoring.

[0022] Based on this, this embodiment proposes an online reconstruction method for the temperature field of lithium-ion batteries. First, dynamic time-series heat source data and battery surface temperature boundaries under the target operating conditions are acquired. Second, a Physical Information-Kolmogorov-Arnold Network (PI-KAN) is constructed. Through a spatiotemporal joint analytical construction mechanism, the initial conditions, surface boundaries, and central axis symmetry conditions of the cylindrical battery are transformed into rigid hard constraints for network forward propagation. Finally, the pure residual of the underlying heat transfer partial differential equation (PDE) is used as the unique loss function, and information physical fusion is performed using automatic differentiation technology to achieve high-fidelity reconstruction of the spatiotemporal non-uniform temperature field under the condition of no internal sensors.

[0023] The core technology of this embodiment lies in: (1) A deep neural network model for solving the temperature field was constructed. The input features and output form of the network were mapped by mathematical analytical construction rules, and the heat transfer boundary conditions were transformed into rigid hard constraints of the network architecture. Thus, the central axisymmetric condition and the physical boundary of the external surface temperature of the cylindrical battery were forced and precisely satisfied in the forward calculation of the model. (2) During the model training optimization process, the internal heat conduction PDE residual is used as the only loss function of the deep neural network; without internal temperature measurement point labels, the information and heat transfer law are deeply integrated through pure physical mechanism, and then the spatiotemporal temperature field distribution inside the battery is reconstructed and output online.

[0024] The online temperature field reconstruction method for lithium-ion batteries provided in this embodiment includes the following steps: Acquire boundary data of battery surface temperature and heat generation rate data of lithium-ion battery under varying operating conditions; A physical information-Kolmogorov-Arnold network is constructed to transform the initial thermal equilibrium conditions, central axisymmetric boundary, and battery surface temperature boundary of the lithium-ion battery into mandatory hard constraints for the forward propagation of the network. The input characteristics and output form of the network are mapped through mathematical analytical construction rules to analytically construct the temperature field. The physical information-Kolmogorov-Arnold network was trained using the residual of the partial differential equation of heat conduction with respect to the spatiotemporal coordinates of the temperature field constructed analytically as the unique loss function. Using a trained physical information-Kolmogorov-Arnold network, the spatiotemporal temperature field distribution data inside the target battery is reconstructed online.

[0025] The method described in this embodiment will now be explained in detail. The method of this embodiment includes the following detailed steps: Step 1: Acquisition of dynamic temporal boundary data and heat source driving terms.

[0026] (1) Construction of high-fidelity electrothermal model and generation of heat source data.

[0027] In this step, such as Figure 1 As shown, electrothermal coupling models at different magnifications and temperatures were built in COMSOL Multiphysics software to obtain the heat generation rate of the driving source and high-fidelity temperature field verification data. The heat generation rate data was used as the physical driving term of the heat conduction partial differential equation.

[0028] Furthermore, in COMSOL Multiphysics software, an electrothermal coupling simulation model is built based on battery parameters (including polarization capacitance / internal resistance in the first-order equivalent circuit model, thermal conductivity, specific heat capacity, etc. in the thermal model) to obtain the heat source. The heat generation rate is calculated and directly input into the subsequent heat transfer partial differential equation as a front-end driving source; and spatiotemporal data of the internal temperature field of the battery are extracted from the simulation results to form a high-fidelity verification dataset.

[0029] It is understood that COMSOL Multiphysics software is a finite element analysis software used for multiphysics simulation and is widely used in engineering and scientific research fields.

[0030] (2) Dynamic boundary acquisition.

[0031] In this step, such as Figure 1 As shown, battery tests under different operating conditions are conducted in the testing equipment to obtain current, voltage, and surface temperature boundary data. In specific implementation, the charging and discharging current, terminal voltage, and surface temperature data of the lithium-ion battery under varying operating conditions are collected in real time through a BMS or external hardware sensing layer.

[0032] In this embodiment, acquiring the battery surface temperature boundary data under varying operating conditions includes: Discrete temperature sensors are arranged on the outer surface of the lithium-ion battery to collect discrete surface temperature data. The discrete surface temperature data is transformed into a continuous surface temperature boundary function along the axial direction using a spatial interpolation algorithm.

[0033] During actual operation or bench testing, macroscopic observation variables of the cylindrical battery are collected in real time using external sensors, with a focus on acquiring data with a time resolution of [missing information]. Battery surface time-series temperature , serving as the reference value for the spatial Dirichlet boundary conditions in subsequent PDE solutions. Where z represents the axial coordinate and t represents time. This indicates the surface boundary temperature obtained in real time through an external sensor.

[0034] Step 2: Spatiotemporal joint hard constraint embedding based on analytical construction mechanism.

[0035] In this step, such as Figure 1 As shown, a Physical Information-Kolmogorov-Arnold Network (PI-KAN) neural network structure is first constructed to approximate the temperature field space, which includes basis functions and activation functions from KAN.

[0036] The Physical Information-Kolmogorov-Arnold Network (PI-KAN) constructed in this embodiment differs from the traditional Multilayer Perceptron (MLP) in that its architecture deploys nonlinear activation functions on network connection edges rather than on neuron nodes. This network uses a time-coordinated approach. Spatial coordinates The real-time operating characteristics (current, voltage, heat source) are used as inputs, and the temperature regulation term is used as the output. For radial coordinates.

[0037] The Physical Information-Kolmogorov-Arnold Network (PI-KAN) is an existing network, and its specific structure will not be elaborated here.

[0038] To enforce the physical laws of cylindrical batteries, the mapping between the network input domain and output domain is mathematically constructed as follows: ① Nonlinear mapping of input feature space: The input feature vector of the PI-KAN deep neural network is set as .

[0039] The core lies in transforming the traditional radial coordinate system. Replace with its squared term Using the chain rule for finding the derivative of a composite function (i.e.) , (indicating temperature), and forcibly ensure that... The spatial derivative at that point is always zero.

[0040] In this embodiment, the physical boundary conditions of the cylindrical battery are forcibly satisfied through analytical construction. The radial spatial coordinates of the PI-KAN deep neural network are input by radial distance. Replace with the square of the radial distance By utilizing the chain rule for the chain of derivatives of composite functions, it is forcibly guaranteed that the axis of the cylinder is aligned with the central axis. The radial temperature spatial derivative at a given point is always zero, thus implicitly and absolutely satisfying the axisymmetric von Neumann boundary conditions for internal heat conduction without additional boundary loss penalties.

[0041] ② Spatiotemporal joint hard constraint analytical construction: Assume the original output of the PI-KAN network is a dimensionless temperature bias adjustment term. ,in These are the network weight parameters. The final reconstructed 3D spatiotemporal temperature field will be output. The analytical construction is as follows:

[0042] In the formula, Let be the absolute outer radius of the cylindrical battery. This is the time transition coefficient. The surface boundary temperature is obtained in real time through an external sensor. This represents the temperature field constructed analytically.

[0043] This construction implicitly and absolutely locks down the three major physical boundaries in the forward computation graph: when At that time, the time decay term Reset to zero, forcibly satisfying the initial thermal equilibrium condition; when At that time, spatial deviation term Zeroing out the surface temperature, forcibly satisfying the measured boundary of the surface temperature; exist At the same time, in coordination The input must satisfy the central axis symmetric Neumann boundary.

[0044] Further: pass The product construction of the medium spatial structure, when the network computation domain extends to the outer surface of the battery (i.e. When ), the deviation term Forced reset to zero, thus This achieves hard constraint embedding of Dirichlet boundary conditions at the network structure level; furthermore, when time... At that time, the time decay term Forced reset to zero, thus , Indicates the initial ( Surface temperature. Since the battery is in thermal equilibrium when it is initially at rest, the initial surface temperature is the overall initial uniform temperature, thus strictly locking the initial physical state in the network structure.

[0045] Step 3: Cyber-physical deep fusion optimization based on pure PDE residuals.

[0046] (1) Construction of pure physical residual loss: Since all boundary conditions have been strictly satisfied in step two, this method completely eliminates the boundary penalty term required by traditional soft constraints. The temperature field is constructed using automatic differentiation (Auto-Diff). By substituting the partial derivatives with respect to spacetime coordinates into the partial differential equation for heat conduction in cylindrical coordinates, a unique objective residual function is constructed:

[0047] The mean squared error of this residual is used as the globally unique loss function. .

[0048] In the formula, This represents the total number of sampling points used to calculate the PDE residuals. This represents the residual of the partial differential equation for heat conduction; Indicates density, Indicates specific heat capacity. Represents the temperature field constructed analytically. Indicates time, Represents radial coordinates, , The radial and axial thermal conductivity are represented by z, where z represents the axial coordinate. Represents heat source data; This represents the absolute value of the residual in the partial differential equation for heat conduction.

[0049] like Figure 1 As shown, this embodiment designs a hard-constraint analytical constructor to force the satisfaction of boundary and initial conditions, and uses the propagated PDE loss as the effective loss function term for the model's unique optimization.

[0050] This embodiment utilizes automatic differentiation technology to accurately calculate the temperature field constructed analytically above. The partial derivatives with respect to time, radial direction, and axial direction are used. These derivatives, along with the obtained heat generation rate, are substituted into the partial differential equation to calculate the pure physical heat transfer residual, which is then used as the sole component of the mean squared error loss function. Since the boundary conditions are strictly satisfied by the pre-construction of the PI-KAN network, the soft penalty weights of the boundary data terms are completely eliminated during the optimization process, thus eliminating gradient conflicts caused by multi-objective optimization and significantly improving the network's convergence speed and robustness in solving the real physical field.

[0051] (2) Network optimization and temperature field output: The PI-KAN network parameters are iteratively updated using an optimization algorithm. During the optimization process, the network focuses entirely on minimizing the residuals of the internal heat transfer physical mechanism, eliminating gradient conflicts caused by multi-objective optimization, and ultimately outputting the parameters at any point inside the battery. At any time High-fidelity true temperature value.

[0052] Ultimately, as Figure 1 As shown, the reconstructed temperature of the center point output by the model is dynamically compared with the true value measured by the FBG fiber optic sensor implanted in the laboratory to verify the accuracy of the method proposed in this embodiment.

[0053] The method proposed in this embodiment will be explained in the following specific application scenarios.

[0054] This application scenario takes the 21700 type LiNCM lithium-ion energy storage battery as the object, and based on the aforementioned spatiotemporal hard-constrained PDE solution framework, provides a specific engineering implementation plan for online estimation of temperature field using physical information neural network.

[0055] LiNCM lithium-ion energy storage batteries refer to lithium-ion batteries that use lithium nickel cobalt manganese oxide as the positive electrode material. It is a type of ternary lithium battery with balanced performance and wide applications.

[0056] Equipment to be implemented: Battery testing system and thermal test bench: Arbin BT-2000, equipped with a multi-point surface thermocouple array to acquire terminal voltage, charge / discharge current, and data at different axial heights. data. That is The abbreviated form of .

[0057] The Arbin BT-2000 is a high-precision, multi-channel battery testing system manufactured by Arbin Instruments, Inc. in the United States. It is mainly used for performance testing and research of various batteries and battery materials.

[0058] Destructive temperature measurement equipment for verification: a built-in fiber optic temperature sensor, precisely implanted in the center of a 21700 battery core, intended solely for laboratory accuracy verification. To obtain the true value of the nuclear temperature.

[0059] Computing platform: The training end uses a high-performance workstation equipped with an NVIDIA RTX 4090 GPU; the online inference end is deployed on BMS.

[0060] Software environment: PyTorch deep learning framework and COMSOL Multiphysics.

[0061] Implementation steps: Step 1: Establishment of electrothermal coupling model and application of operating conditions.

[0062] Physical parameter measurement: For a physical 21700 battery, its geometric and thermal boundary constants were precisely measured and solidified: the outer radius of the battery was set as follows: (mm), effective core height The radial and axial thermal conductivity, density, specific heat capacity, and convection coefficient of this type of battery material were reviewed and verified.

[0063] Electrothermal coupling model construction: The electrical parameters (DC internal resistance, polarization capacitance, and polarization internal resistance) of the first-order equivalent circuit were obtained through offline HPPC testing at different temperatures, currents, and SOC ranges. An electrothermal coupling model was built in Comsol simulation software to obtain high-fidelity heat source data and temperature field calibration values ​​for subsequent training and verification.

[0064] Application of operating conditions and preprocessing of data streams: Under a constant temperature environment of 25℃, the same type of battery was subjected to constant current charge and discharge tests at 0.5C (C represents the current rate), 1C, 2C, and 4C, as well as dynamic discharge tests under UDDS and DST conditions. The system synchronously recorded the external surface temperature at a frequency of 1Hz. Along the axial direction on the outer surface of the target battery ( A limited number of discrete temperature sensors are arranged at characteristic locations (e.g., three patch thermocouples are arranged near the upper part of the positive electrode tab, the middle of the core, and the bottom of the negative electrode, respectively). Then, a spatial interpolation algorithm (such as linear interpolation) is used to analyze the collected discrete temperature points. The shaft extends smoothly, reconstructing a continuous axis. The time coefficient is set to... .

[0065] UDDS (Urban Dynamometer Driving Schedule) simulates the vehicle's driving conditions in urban environments, while DST (Dynamic Stress Test) is a simplified current load test specifically designed for battery dynamic stress testing. Both are commonly used dynamic test methods in battery research.

[0066] Step 2: PI-KAN neural network structure design and hybrid optimization settings.

[0067] Network internal operator architecture (edge ​​activation mechanism): To accurately fit the steep temperature gradient within the two-dimensional space, this embodiment abandons the traditional MLP and adopts a 4-layer (structure [4, 20, 20, 1]) Physical Information-Kolmogorov-Arnold Network (PI-KAN). Its nonlinear activation function is deployed on the network weight edges. For each node... To the node The connection signal, whose internal activation evolution satisfies the following algebraic equation:

[0068] in, Indicates from the first The node is passed to the first node. The learnable activation function of the nth node, x represents the learningable activation function of the nth node in this layer of the network. The input signals of each node; As the base weights, For activation function, The number of control points is (This embodiment sets the grid size) The local B-spline basis functions of ) For learnable spline coefficients, K represents the total number of control points used to construct the B-spline basis function (i.e., the number of B-spline grids), and k represents the index number of the B-spline basis function, used to indicate which B-spline basis function is currently being used.

[0069] Loss function weight setting and training strategy: Substitute the above PI-KAN output into Example 1 Generate in the analytical construction formula In this specific project, the weight configuration of the loss function is very clear: the weight of the internal PDE residual is set to 1.0, while the weight of the surface boundary data penalty and the weight of the initial condition penalty are both forcibly set to 0.

[0070] A composite optimization strategy is used to accelerate convergence: First, a coarse search of 2000 epochs is performed using the Adam optimizer (learning rate 1e-3), and then a second-order L-BFGS optimizer (learning rate 0.1) is seamlessly switched to perform precise convergence of 1000 epochs until the PDE residual is reduced to the order of 1e-5.

[0071] Step 3: Reconstruction and verification of the microscopic temperature field at the edge.

[0072] Edge deployment and online simulation: The KAN spline coefficient matrix and basis weights after training convergence are extracted, compiled into a lightweight C++ operator matrix, and embedded into the BMS chip. During simulation, the system only needs to be fed with the real-time current corresponding to the heat source and the single-point temperature of the outer surface to instantly output the 2D cross-sectional temperature field distribution tensor of the battery with a grid density of 10×20 within 20 milliseconds.

[0073] High-fidelity accuracy verification: The center point output by the model ( The reconstructed temperature is dynamically compared with the "true core temperature" measured by a laboratory-destructively implanted FBG (Bragg grating) fiber optic sensor. Under severe variable load conditions lasting up to 2 hours, the mean absolute error (MAE) of the estimated maximum central temperature is strictly controlled within 0.6℃. This hard constraint mechanism completely eliminates the boundary oscillation problem common in soft-penalty networks, providing impeccable underlying digital twin-level data support for refined thermal management and early warning of thermal runaway of the battery.

[0074] Compared with the prior art, this embodiment has the following technical advantages: (1) A high-fidelity reconstruction of the spatiotemporal temperature field under zero-destructive hardware was achieved.

[0075] This invention proposes an online estimation method for the internal temperature field of lithium-ion batteries based on analytical physical hard-constraint neural networks. This method completely eliminates the dependence on destructive temperature measurement hardware inside the battery. It can deduce the highly hidden evolution law of the internal spatiotemporal temperature field online using only the surface temperature that is easily obtained by the system. This fundamentally removes the application obstacle of traditional data-driven models that cannot be implemented in engineering due to the lack of internal truth labels.

[0076] (2) It pioneered the analytical hard constraint architecture, which completely eradicated the convergence problem of traditional soft penalty terms.

[0077] This invention innovatively employs mathematical analytical construction rules to strongly couple the spatiotemporal input-output features of deep neural networks with the underlying physical boundaries. This is achieved by introducing a time decay term and radial coordinate squaring mapping. and spatial structure product construction This invention implicitly and absolutely locks the initial conditions, the central axisymmetric Neumann boundary, and the surface Dirichlet boundary during the network's forward computation stage. This architecture completely overturns the traditional approach of directly adding the boundaries as soft constraint penalty terms in Physical Information Neural Networks (PINN), eliminating gradient conflicts and parameter tuning barriers caused by multi-objective optimization, and ensuring that the reconstructed temperature field strictly and absolutely obeys the real laws of heat transfer physics.

[0078] (3) It combines extremely high physical consistency with computational efficiency for edge deployment.

[0079] This invention creatively introduces the Physical Information-Kolmogorov-Arnold Network (PI-KAN) architecture into the solution of the thermal conduction partial differential equation (PDE), utilizing its edge weight activation characteristics to accurately fit the extremely steep and complex nonlinear temperature gradient inside a large cylindrical battery. Furthermore, thanks to the complete analytical satisfaction of boundary conditions, the model only needs to calculate the pure PDE thermodynamic residuals as the sole loss function during optimization. This not only endows the model with extremely high data efficiency and cross-condition generalization ability but also significantly reduces unnecessary computational overhead, enabling this high-fidelity model to be perfectly deployed in computationally limited BMS systems. It provides a groundbreaking underlying algorithm engine for refined thermal management and early thermal runaway warning of batteries.

[0080] Example 2 This embodiment discloses an online temperature field reconstruction device for lithium-ion batteries.

[0081] An online temperature field reconstruction device for lithium-ion batteries includes: The data acquisition module is configured to acquire boundary data of battery surface temperature and heat generation rate data under varying operating conditions of lithium-ion batteries. The temperature field estimation module is configured to: construct a physical information-Kolmogorov-Arnold network, transform the initial thermal equilibrium conditions, central axisymmetric boundary, and battery surface temperature boundary of the lithium-ion battery into mandatory hard constraints for network forward propagation, and map the input features and output form of the network through mathematical analytical construction rules to analytically construct the temperature field. The model training module is configured to train the physical information-Kolmogorov-Arnold network using the residuals of the heat conduction partial differential equation of the temperature field with respect to the spatiotemporal coordinates, which are analytically constructed, as the only loss function. The online reconstruction module is configured to reconstruct the spatiotemporal temperature field distribution data inside the target battery online using a trained physical information-Kolmogorov-Arnold network.

[0082] Furthermore, the aforementioned data acquisition module includes an external data acquisition module and an electrothermal coupling model module, such as... Figure 2 As shown, where: External data acquisition module: Communicates with the bottom sensing layer of the battery pack to collect discrete temperature data of the outer surface of the battery in real time during actual operation, and converts it into a continuous surface temperature boundary function along the axial direction through a spatial interpolation algorithm. Electrothermal Coupled Model Module: An electrothermal coupled model is built based on Comsol software to calculate the dynamic volumetric heat generation rate, which serves as the physical driving term for the subsequent internal heat conduction partial differential equation; a high-fidelity temperature field calibration dataset is output for subsequent algorithm verification.

[0083] like Figure 2 As shown, the temperature field estimation module is the core computing unit of the system. This module pre-installs and runs the PI-KAN model, receiving the surface temperature boundary function determined by the external data acquisition module and the dynamic volumetric heat generation rate determined by the electrothermal coupling model module. It then maps the radial spatial input coordinates of the network by squaring. And combined with the spatial structure deviation term ( The analytical construction of the time decay term transforms the battery's initial thermal equilibrium conditions, central axisymmetric boundary, and measured surface temperature boundary into a forced hard constraint for network forward propagation. Without requiring internal temperature measurement data, optimization is performed based on the residuals of the thermal conduction partial differential equation, and the temperature field distribution inside the battery is output in real time.

[0084] It also includes a status monitoring and decision-making module: like Figure 2 As shown, the status monitoring and decision-making module is configured to: receive temperature field distribution data determined by the temperature field estimation module, extract the highest core temperature and spatial temperature gradient inside the battery, and perform a battery thermal safety and health status assessment accordingly. When the assessment determines that the internal core temperature or temperature gradient is close to a preset safety threshold, it generates corresponding battery thermal management control commands, including but not limited to: dynamically adjusting the coolant flow rate of the thermal management system, implementing a charge / discharge power derating strategy, or triggering a system-level thermal runaway warning to ensure the safe operation of the battery.

[0085] The status monitoring and decision-making module visualizes and reconstructs the highest core temperature and spatial temperature gradient inside the battery in the laboratory R&D platform or scientific research testing system; then, based on this, it conducts local heat accumulation analysis inside the battery, realizes battery thermal safety and health status assessment, and provides high-precision data support and theoretical verification benchmark for the operation strategy and safety status assessment of the battery thermal management system.

[0086] It also includes a human-computer interaction and display module: like Figure 2 As shown, the human-computer interaction and display module is configured to: configure system parameters, display microstate estimation results, alarm information and system operating status.

[0087] The system parameters are configured for the temperature field estimation module, external data acquisition module, and electrothermal coupling model module through the human-computer interaction and display module, and commands are input for the status monitoring and decision module. The output results of the status monitoring and decision module and the temperature field distribution output by the temperature field estimation module are displayed synchronously through the human-computer interaction and display module.

[0088] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0089] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for online reconstruction of the temperature field of a lithium-ion battery, characterized in that, Includes the following steps: Acquire boundary data of battery surface temperature and heat generation rate data of lithium-ion battery under varying operating conditions; A physical information-Kolmogorov-Arnold network is constructed to transform the initial thermal equilibrium conditions, central axisymmetric boundary, and battery surface temperature boundary of the lithium-ion battery into mandatory hard constraints for the forward propagation of the network. The input characteristics and output form of the network are mapped through mathematical analytical construction rules to analytically construct the temperature field. The physical information-Kolmogorov-Arnold network was trained using the residual of the partial differential equation of heat conduction with respect to the spatiotemporal coordinates of the temperature field constructed analytically as the unique loss function. Using a trained physical information-Kolmogorov-Arnold network, the spatiotemporal temperature field distribution data inside the target battery is reconstructed online.

2. The online temperature field reconstruction method for lithium-ion batteries as described in claim 1, characterized in that, Obtain the surface temperature boundary data of a lithium-ion battery under varying operating conditions, including: Discrete temperature sensors are arranged on the outer surface of the lithium-ion battery to collect discrete surface temperature data. The discrete surface temperature data is transformed into a continuous surface temperature boundary function along the axial direction using a spatial interpolation algorithm.

3. The online temperature field reconstruction method for lithium-ion batteries as described in claim 1, characterized in that, Obtain heat generation rate data of lithium-ion batteries under varying operating conditions, including: An electrothermal coupling simulation model was established in the simulation software to calculate the heat generation rate data under different operating conditions. The heat production rate data is used as the physical driving term of the partial differential equation of heat conduction.

4. The online temperature field reconstruction method for lithium-ion batteries as described in claim 1, characterized in that, The input features of the network are mapped using mathematical analytical construction rules, specifically including: The radial spatial coordinate input of the physical information-Kolmogorov-Arnold network is squared and mapped, replacing the radial distance with the square of the radial distance; By using the chain rule for the chain of derivatives of composite functions, the radial temperature spatial derivative at the central axis of the cylinder is kept constant at zero, thus satisfying the axisymmetric von Neumann boundary conditions.

5. The online temperature field reconstruction method for lithium-ion batteries as described in claim 4, characterized in that, The output form of the network is mapped using mathematical analytical construction rules to analytically construct the temperature field, specifically including: Suppose the raw output of the physical information-Kolmogorov-Arnold network is a dimensionless temperature bias adjustment term. ,in These are network weight parameters; Three-dimensional spatiotemporal temperature field The analytical construction is as follows: ； In the formula, Let z represent the radial coordinate, z represent the axial coordinate, and t represent time. This indicates the surface boundary temperature obtained in real time via an external sensor. This represents the absolute outer radius of the cylindrical battery. Indicates the time transition coefficient; The analytically constructed temperature field locks in the three major physical boundaries in the forward computation graph: when At that time, the time decay term Reset to zero, forcibly satisfying the initial thermal equilibrium condition; when At that time, spatial deviation term Zeroing out the surface temperature, forcibly satisfying the measured boundary of the surface temperature; exist At that time, the central axis symmetric Neumann boundary must be satisfied.

6. The online temperature field reconstruction method for lithium-ion batteries as described in claim 1, characterized in that, The unique loss function of the Physical Information-Kolmogorov-Arnold Network is as follows: ； ； In the formula, The unique loss function representing the physical information-Kolmogorov-Arnold network; This represents the total number of sampling points used to calculate the PDE residuals; This represents the absolute value of the residual in the partial differential equation for heat conduction. This represents the residual of the partial differential equation for heat conduction; Indicates density, Indicates specific heat capacity. Represents the temperature field constructed analytically. Indicates time, Represents radial coordinates, , The radial and axial thermal conductivity are represented by z, where z represents the axial coordinate. This represents heat source data.

7. The online temperature field reconstruction method for lithium-ion batteries as described in claim 1, characterized in that, Also includes: The constructed physical information-Kolmogorov-Arnold network deploys nonlinear activation functions on the network connection edges; Physical Information-Kolmogorov-Arnold Network with Time Coordinates Spatial coordinates The real-time operating conditions are taken as input, and the temperature regulation term is taken as output. z represents the radial coordinate, and z represents the axial coordinate.

8. The online temperature field reconstruction method for lithium-ion batteries as described in claim 1, characterized in that, Using a trained physical information-Kolmogorov-Arnold network, the spatiotemporal temperature field distribution data inside the target battery is reconstructed online, including: The heat source corresponding to the real-time current of the target battery and the single-point temperature on the outer surface of the target battery are input into the trained physical information-Kolmogorov-Arnold network to obtain the 2D cross-sectional temperature field distribution tensor inside the target battery.

9. The online temperature field reconstruction method for lithium-ion batteries as described in claim 1, characterized in that, After reconstructing the spatiotemporal temperature field distribution data inside the target battery, the following is also included: Extract the highest core temperature and spatial temperature gradient inside the target battery to assess the battery's thermal safety and health status. When the assessment determines that the core temperature or spatial temperature gradient inside the target battery is greater than the preset safety threshold, a corresponding battery thermal management control command is generated. The battery thermal management control commands include dynamically adjusting the coolant flow rate of the thermal management system, implementing charge / discharge power derating strategies, or triggering system-level thermal runaway warnings to ensure the safe operation of the battery.

10. A lithium-ion battery temperature field online reconstruction device, characterized in that, include: The data acquisition module is configured to acquire boundary data of battery surface temperature and heat generation rate data under varying operating conditions of lithium-ion batteries. The temperature field estimation module is configured to: construct a physical information-Kolmogorov-Arnold network, transform the initial thermal equilibrium conditions, central axisymmetric boundary, and battery surface temperature boundary of the lithium-ion battery into mandatory hard constraints for network forward propagation, and map the input features and output form of the network through mathematical analytical construction rules to analytically construct the temperature field. The model training module is configured to train the physical information-Kolmogorov-Arnold network using the residuals of the heat conduction partial differential equation of the temperature field with respect to the spatiotemporal coordinates, which are analytically constructed, as the only loss function. The online reconstruction module is configured to reconstruct the spatiotemporal temperature field distribution data inside the target battery online using a trained physical information-Kolmogorov-Arnold network.

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