Method for generating a three-dimensional nodal model, associated computer program and electronic device
The method optimizes nodal model construction by adjusting node placement based on prediction errors, enhancing simulation speed and accuracy for battery behavior prediction.
Patent Information
- Authority / Receiving Office
- FR · FR
- Patent Type
- Applications
- Current Assignee / Owner
- AUTOMOTIVE CELLS CO SE
- Filing Date
- 2024-12-13
- Publication Date
- 2026-06-19
AI Technical Summary
Existing three-dimensional nodal models for simulating battery behavior are faster but less accurate than finite element simulations, and their construction methods lack optimization, leading to difficulty in interpreting simulation results and achieving sufficient accuracy.
A method for generating a three-dimensional nodal model that optimizes node placement by calculating accuracy indicators based on prediction errors, allowing for node deletion, merging, or separation to balance accuracy and speed, using a spatially informed nodal structure.
The optimized nodal model provides faster simulation with improved accuracy in predicting battery behavior, balancing speed and precision through a physically interpretable model.
Smart Images
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Abstract
Description
Title of the invention: Method for generating a three-dimensional nodal model, associated computer program and electronic device
[0001] The present invention relates to a method for generating a three-dimensional nodal model to simulate a physical quantity related to a battery. It also relates to a computer program comprising software instructions which, when implemented by a computer, implement such a method. Finally, it relates to an electronic device for generating a three-dimensional nodal model.
[0002] During the development or diagnostics of automotive batteries, it is useful to be able to predict battery behavior, for example, thermal behavior, based on their use. Such predictions make it possible, for example, to control battery behavior in many use cases without performing experimental tests, or to predict battery aging. Numerous multiphysics simulation software programs are available that allow the prediction of physical quantities, for example, thermal or electrical properties, in a battery of known geometry, particularly through finite element simulation.
[0003] In order to reduce computation time compared to the finite element method, it is also known to use a three-dimensional nodal model.
[0004] One limitation of using a nodal model is the accuracy of the simulation. Indeed, while such models are faster than finite element simulations, they are also less accurate. However, most publications describing nodal models do not describe how the nodal structure is constructed, or simply use a standard selection of nodes without optimization. The accuracy performance of such models is therefore significantly lower than that of finite element simulations.
[0005] Other publications describe a mathematical reduction of the model, or general principles of physical optimization. For example, the article “Reduction and optimization of thermal models using Kirchhoff network theory” by Marc Broussely, Yves Bertin, and Patrick Lagonotte, published in the International Journal of Thermal Sciences, Volume 42, Issue 8, 2003, Pages 795–804, describes a method for optimizing a nodal thermal model. However, this method requires defining a number of nodes a priori. Furthermore, the final position of the nodes in the model obtained by this method has no physical meaning and therefore does not allow for easy interpretation of simulation results.
[0006] The aim of the invention is then to propose a method for generating a three-dimensional nodal model that allows for faster simulation of a physical quantity relating to a battery, while having sufficient accuracy.
[0007] To this end, the invention relates to a method for generating a three-dimensional nodal model to simulate a physical quantity related to a battery, the three-dimensional nodal model comprising a set of nodes, each node being characterized by a spatial position, the method comprising a step of acquiring an initial nodal model, the initial nodal model having been previously generated from a known geometry of the battery, the initial nodal model comprising fixed and non-fixed nodes, the method further comprising a step of optimizing the initial nodal model comprising: - a sub-step of calculating at least one accuracy indicator for each non-fixed node of the initial nodal model, each accuracy indicator of a respective node depending on a first prediction error of a value of the physical quantity from said node relative to a reference simulation and a second prediction error of a time evolution of the physical quantity from said node relative to the reference simulation; - a sub-step for determining an optimized model, comprising: • for each non-fixed node of the initial nodal model where each accuracy indicator belongs to a first range of values, the implementation of one action among deleting said node and merging said node with another non-fixed node of the initial nodal model, and • for each non-fixed node of the initial nodal model where at least one precision indicator belongs to a second range of values, a separation of said node into several nodes;
[0008] the initial model optimization step providing an optimized nodal model, to predict battery behavior relative to the physical quantity.
[0009] Thanks to the invention, the optimized nodal model makes it possible to perform a simulation of the physical quantity related to the battery that is faster than a finite element simulation, due to the nodal structure, while being optimized in terms of accuracy. In particular, by taking into account the first and second prediction errors, the prediction of the physical quantity as well as the prediction of its temporal evolution are improved. Implementing one action among node deletion and node merging makes it possible to locally reduce the number of nodes, and therefore the simulation time, when the accuracy indicator shows that the accuracy is excessive, i.e., when the speed can be optimized. Conversely, node separation makes it possible to locally increase the number of nodes. Therefore, accuracy is affected when the accuracy indicator shows that the precision is insufficient. The choice of the first and second value ranges allows for adjusting the trade-off between accuracy and speed according to the specific need. The method according to the invention thus optimizes the ratio between accuracy and execution speed of a simulation of a physical quantity related to a battery. Furthermore, since the generation method is based on physical reasoning, the physical interpretation of the simulation is facilitated.
[0010] According to other advantageous aspects of the invention, the method comprises one or more of the following features, taken individually or in all technically possible combinations:
[0011] - each precision indicator of a respective node is the product of a first a first accuracy sub-indicator, dependent on the first prediction error, and a second accuracy sub-indicator, dependent on the second prediction error, the first accuracy sub-indicator preferably being larger the larger the first prediction error, and the second accuracy sub-indicator preferably being larger the larger the second prediction error;
[0012] - the first range of values includes any value below a minimum threshold of predetermined error and the second range of values includes any value above a predetermined maximum error threshold;
[0013] - the physical quantity is a temperature;
[0014] - the process is such that: • the initial nodal model further includes at least one primary thermal conduction axis for each node, said primary axis being an axis along which heat transmission within the node is predominant or exceeds a predetermined minimum heat transmission threshold; and • the calculation substep includes the calculation of an accuracy indicator for each primary thermal conduction axis of each non-fixed node;
[0015] - for each non-fixed node of the initial nodal model and for each primary axis of thermal conduction of said node, the corresponding accuracy indicator depends on: • a temperature gradient between the hottest and coldest cross-sections among cross-sections of the node perpendicular to said primary thermal conduction axis, the hottest and coldest cross-sections being obtained via the reference simulation; and • a distance along said primary axis of thermal conduction between the hottest cross-section and the coldest cross-section, called the characteristic length of thermal conduction;
[0016] the accuracy indicator being preferably greater the greater the temperature gradient and the greater the characteristic length of thermal conduction;
[0017] - for each node of the initial nodal model and for each primary axis of conduction of said node: • the first corresponding accuracy sub-indicator is proportional to the temperature gradient; and • the corresponding second precision sub-indicator is greater the larger the characteristic length of thermal conduction and the larger the volume of the node;
[0018] - the optimization step is repeated, taking as the initial nodal model the model optimized from the previous iteration of the optimization step, until, for each non-fixed node of the optimized nodal model, at least one precision indicator of said node does not belong to the first range of values and each precision indicator of said node does not belong to the second range of values.
[0019] The invention also relates to a computer program comprising software instructions which, when executed by a computer, implement a method for generating a three-dimensional nodal model, as defined above.
[0020] The invention also relates to an electronic device for generating a three-dimensional nodal model to simulate a physical quantity related to a battery, the three-dimensional nodal model comprising a set of nodes, each node being characterized by a spatial position, the device comprising a module for acquiring an initial nodal model, the initial nodal model having been previously generated from a known geometry of the battery, the initial nodal model comprising fixed and non-fixed nodes, the device further comprising an optimization module for the initial nodal model comprising: - a submodule for calculating at least one accuracy indicator for each non-fixed node of the initial nodal model, each accuracy indicator of a respective node depending on a first prediction error of a value of the physical quantity from said node relative to a reference simulation and a second prediction error of a time evolution of the physical quantity from said node relative to the reference simulation; - a sub-module for determining the optimized model, configured to perform: • for each non-fixed node of the initial nodal model, where each accuracy indicator belongs to a first range of values, the implementation of an action including deleting said node and merging said node with another node of the initial model, and • for each non-fixed node of the initial nodal model where at least one precision indicator belongs to a second range of values, a separation of said node into several nodes;
[0021] the initial model optimization module providing an optimized model, to predict battery behavior relative to the physical quantity.
[0022] The invention will become clearer upon reading the following description, given solely by way of non-limiting example, and made with reference to the drawings in which:
[0023] [Fig-1] [Fig.1] is a schematic of a device for generating a nodal model three-dimensional according to the invention;
[0024] [Fig.2] [Fig.2] is a flowchart of a method for generating a three-dimensional nodal model according to the invention; and
[0025] [Fig.3] [Fig.3] is a diagram representing different ranges of values used in the process of [Fig.2].
[0026] Figure 1 represents an electronic device 1 for generating a three-dimensional nodal model. The electronic device 1 is configured to implement a method 100 for generating a three-dimensional nodal model, described below. The method 100 provides an optimized three-dimensional nodal model Mo for simulating a physical quantity related to a battery, for example, a thermal or electrical quantity. In the example developed in this description, and without limitation, the physical quantity is the temperature of a material constituting the battery in different areas of the battery. Alternatively, the physical quantity is an electrical potential or a force.
[0027] A three-dimensional nodal model is a model comprising a set of nodes, each node being characterized by a spatial position. The three-dimensional nodal model of the battery is intended to predict the battery's behavior with respect to the physical quantity. More specifically, in the example, the prediction consists of predicting the battery temperature at each node of the three-dimensional nodal model and the evolution of the temperature over time, as a function of battery operating conditions, in particular as a function of the current applied to the battery terminals.
[0028] To do this, the electronic device of generation 1 includes an acquisition module 3 and an optimization module 5. The optimization module 5 includes a calculation sub-module 7 and a determination sub-module 9. The role of these different modules and sub-modules is described in the rest of the description.
[0029] In the example of [Fig.1], the electronic device 1 includes an information processing unit 11 formed for example of a memory 13 and a processor 15 associated with the memory 13.
[0030] In the example of [Fig. 1], the acquisition module 3 and the optimization module 5, as well as the calculation sub-module 7 and the determination sub-module 9, are each implemented as a software program, or a software component, executable by the processor 15. The memory 13 of the electronic device 1 is then capable of storing an acquisition program and an optimization program, the optimization program comprising a calculation software component and a determination software component. The processor is then capable of executing each of the programs, including the acquisition program and the optimization program.
[0031] In an alternative not shown, the acquisition module 3 and the optimization module 5, as well as the calculation sub-module 7 and the determination sub-module 9, are each implemented as a programmable logic component, such as an FPGA (Field Programmable Gate Array), or as an integrated circuit, such as an ASIC (Application-Specific Integrated Circuit).
[0032] When the electronic device 1 is implemented in the form of one or more software programs, that is, in the form of a computer program, also called a computer program product, it is further capable of being stored on a computer-readable medium (not shown). The computer-readable medium is, for example, a medium capable of storing electronic instructions and being connected to a bus of a computer system. By way of example, the readable medium is an optical disc, a magneto-optical disc, a ROM, a RAM, any type of non-volatile memory (for example, FLASH or NVRAM), or a magnetic card. A computer program comprising software instructions is then stored on the readable medium.
[0033] The method of generating a three-dimensional nodal model 100, implemented by the electronic generation device 1, is described in the following description with reference to [Fig.2].
[0034] Method 100 is performed for a battery, not shown, whose geometry and constituent materials are known. The objective of method 100 is to determine the optimized three-dimensional nodal model Mo, allowing the thermal behavior of the battery to be simulated more quickly than a reference finite element simulation S and optimizing the accuracy of the prediction.
[0035] To do this, the process 100 includes an acquisition step 102 and an optimization step 104.
[0036] Acquisition step 102 is implemented by acquisition module 3 and consists of acquiring an initial nodal model Mi, the initial nodal model Mi having been previously generated from the known geometry of the battery.
[0037] More precisely, the initial nodal model Mi is advantageously generated by positioning one node per element of the known battery geometry. An element of the battery geometry is, for example, a face of an external battery casing or a stack of anodes and cathodes within the battery. For a battery with a substantially rectangular shape, the nodes are advantageously positioned according to a Cartesian coordinate system. Alternatively, for a cylindrical battery, the nodes are preferably positioned in a cylindrical coordinate system. Generally, the initial nodal model Mi comprises between 10 and 40 nodes, preferably between 20 and 30 nodes. It is understood that such a model is significantly faster to simulate, but also less accurate, than a conventional finite element battery model.Because of this distribution of nodes by battery elements, the initial nodal model Mi retains a physical meaning, which facilitates the interpretation of simulation results.
[0038] The initial nodal model Mi comprises fixed and non-fixed nodes. Fixed nodes generally correspond to nodes to which a boundary condition is applied on the physical quantity during the simulation of the physical quantity using the nodal model. Fixed nodes are intended to remain unchanged during process 100. Conversely, non-fixed nodes are modified during process 100, as described below, and remain unchanged at the end of process 100.
[0039] Advantageously, in addition to the spatial position of each node, the initial nodal model Mi includes at least one primary thermal conduction axis for each node. A primary thermal conduction axis is an axis, or direction, along which heat transfer within the node is predominant or greater than a predetermined minimum heat transfer threshold. The primary thermal conduction axis(es) are thus axes to be considered as a priority when studying the thermal behavior of the battery at the node in question. Determining one or more primary thermal conduction axes for each node makes it possible to limit the amount of computation required by avoiding calculations for directions in which heat transfer is negligible compared to the primary thermal conduction axes, and which therefore have little impact on the model's accuracy.
[0040] The primary axes of thermal conduction are determined, prior to acquisition step 102, based on battery elements likely to generate heat, such as anode and cathode stacks and electrical connections internal or interconnections (busbar in English), as well as external boundary conditions to the battery, usually cooling.
[0041] Advantageously, the initial nodal model Mi further includes a set of property(ies) for each node. The property set(s) includes, for example, a density P of the battery at said node, i.e., of the constituent component of the battery at said node; a thermal conductivity 2 of the battery at said node for each primary thermal conduction axis of said node; a volume V of the node; a specific heat capacity Cp of the battery at said node; and an average area Sq of cross-sections perpendicular to each primary thermal conduction axis of said node. These properties are derived from prior knowledge of the battery and a materials database.
[0042] The optimization step 104 is implemented by the optimization module 5 and consists of optimizing the initial nodal model Mi. The optimization step 104 comprises a calculation substep 106, implemented by the calculation submodule 7, and a determination substep 108, implemented by the determination submodule 9.
[0043] Calculation substep 106 consists of calculating at least one accuracy indicator No for each non-fixed node of the initial nodal model Mi. In particular, calculation substep 106 has the function of characterizing the accuracy of a simulation performed from the initial model Mi with respect to the reference simulation S, at each non-fixed node of the initial nodal model Mi.
[0044] The reference simulation S is advantageously a simulation of the temperature in the battery and the evolution of the temperature over time using physical laws governing the thermal behavior of materials (for example, the unsteady 3D heat equation, which notably includes Fourier's and Newton's laws) and a finite element model of the battery. This reference simulation S is, for example, executed by multiphysics simulation software.
[0045] The reference simulation S makes it possible, in particular, to determine, for each non-fixed node of the initial nodal model Mi and for each primary thermal conduction axis of said node, a hottest cross-section and a coldest cross-section among cross-sections of the node perpendicular to said primary thermal conduction axis. A temperature gradient AT is then defined between the hottest cross-section and the coldest cross-section, and a distance along said primary thermal conduction axis between the hottest cross-section and the coldest cross-section, called the characteristic thermal conduction length Lc. The reference simulation S thus provides, for each non-fixed node of the initial nodal model Mi and for each primary thermal conduction axis thermal of said node, the temperature gradient AT and the corresponding characteristic length of thermal conduction Lc.
[0046] Each accuracy indicator No of a respective node is dependent on a first prediction error of a temperature value from said node relative to the reference simulation S and a second prediction error of a time evolution of the temperature from said node relative to the reference simulation S.
[0047] In particular, each accuracy indicator No is a product of a first accuracy sub-indicator Te, dependent on the first prediction error, and a second accuracy sub-indicator Ti, dependent on the second prediction error.
[0048] The first accuracy sub-indicator Te is preferably larger the larger the first prediction error. The second accuracy sub-indicator Ti is preferably larger the larger the second prediction error.
[0049] In other words, the first accuracy sub-indicator Te is greater the larger the difference between a temperature value at the node considered in the simulation performed from the initial nodal model Mi and the reference simulation S. Similarly, the second accuracy sub-indicator Ti is greater the larger the difference between a temporal temperature evolution at the node considered along the primary conduction axis considered in the simulation performed from the initial nodal model Mi and the reference simulation S. The accuracy indicator No, for its part, reflects the overall accuracy of the initial nodal model Mi at the node considered, taking into account the two accuracy sub-indicators Te and Ti.
[0050] For each non-fixed node of the initial nodal model Mi and for each primary conduction axis of said node, the first accuracy sub-indicator Te is advantageously proportional to the temperature gradient AT. In particular, the first accuracy sub-indicator Te is expressed, for example, as Te − AT. Thus, the first accuracy sub-indicator Te is all the greater the larger the first prediction error. Indeed, the assumption of a nodal model is precisely that there is no temperature gradient within each node, but only between the nodes. It is therefore understandable that if a node that is assumed to be temperature uniform actually has a strong temperature gradient ZI T, the model will lose accuracy.
[0051] For each non-fixed node of the initial nodal model Mi and for each primary conduction axis of said node, the second precision sub-indicator Ti is advantageously larger the greater the characteristic conduction length The thermal conductivity Lc is large and the specific thermal capacity Cp of the battery at said node is large. Furthermore, the second accuracy sub-indicator Ti advantageously depends on the thermal conductivity 2 and the average area Sq. In particular, the second accuracy sub-indicator Ti is expressed, for example:
[0052] -, 11” hSQ
[0053] where the density P is in kg / m³, the thermal conductivity 2 in W / (m*K), the volume V in m³, the specific heat capacity Cp in J / (kg*K), and the average area Sq in m². Thus, the second accuracy sub-indicator Ti is indeed greater the larger the second prediction error. In fact, it is understandable that a node with a large volume V and characteristic length Lc will take less account of actual temporal dynamics than if it were divided into several nodes with a smaller volume V and characteristic length Lc.
[0054] The accuracy indicators No thus calculated are then used during the determination substep 108 to determine the optimized nodal model Mo.
[0055] The optimized nodal model Mo is constructed from the initial nodal model Mi as a function of the precision indicators No. To do this, the determination substep 108 includes, on the one hand, for each non-fixed node of the initial nodal model Mi whose precision indicator No belongs to a first range of values RI, the implementation of an action among a deletion of said node and a merging of said node with another non-fixed node of the initial nodal model Mi; and on the other hand, for each non-fixed node of the initial nodal model Mi whose precision indicator No belongs to a second range of values R2, a separation of said node into several nodes.
[0056] When two nodes are merged, one or more extensive properties of the two initial nodes—that is, one or more properties proportional to the size of the nodes, such as the volume V—are added together to obtain the extensive properties of the resulting node. For one or more intensive properties—that is, one or more properties independent of the size of the nodes, such as the specific heat capacity Cp, the density P, the thermal conductivity 2, and the average area Sq—the value of the property of the resulting node is a combination of the property values of the initial nodes. For example, the specific thermal conductivity Cp of the resulting node is an average of the specific thermal conductivities Cp of the initial nodes, weighted by the mass of the initial nodes.
[0057] The node resulting from the merging of two non-fixed nodes is also non-fixed. Similarly, the two nodes resulting from the separation of a non-fixed node are also non-fixed.
[0058] Alternatively, the non-fixed nodes include specific non-fixed nodes that cannot be deleted and can only be merged with another specific non-fixed node. Specific non-fixed nodes are, for example, nodes that include heat generation.
[0059] In the example illustrated in Figure 3, which represents the first range of values RI and the second range of values R2 as a function of the accuracy indicator No, the first range of values RI includes any value below a predetermined minimum error threshold Tmin, and the second range of values R2 includes any value above a predetermined maximum error threshold Tmax. In the example described above, the accuracy indicator No is larger the larger the first and second prediction errors are. Therefore, a membership of the accuracy indicator No in the first range of values RI indicates that the simulation is excessively accurate at the node considered, and thus, correspondingly, insufficiently fast, the assessment of the term "excessively" being dependent on the predetermined minimum error threshold Tmin.Conversely, a belonging of the accuracy indicator No to the second range of values R2 indicates that the simulation is insufficiently accurate at the node considered, the assessment of the term "insufficiently" being dependent on the predetermined minimum error threshold Tmax.
[0060] In the first case, when the accuracy indicator No belongs to the first range of RI values, therefore the simulation is excessively accurate, the operation of deleting or merging the node makes it possible to locally reduce the number of nodes, and therefore to locally improve the speed of simulation, with less accuracy.
[0061] In the second case, when the accuracy indicator No belongs to the second range of values R2, therefore the simulation is insufficiently accurate, the separation operation makes it possible to increase locally the number of nodes, and therefore to improve locally the accuracy of the simulation.
[0062] Thus, the determination substep 108 allows for a compromise between the speed and accuracy of the simulation, this compromise being determined by the values of the predetermined minimum error threshold Tmin and the predetermined maximum error threshold Tmax. Indeed, increasing the thresholds Tmin and Tmax prioritizes speed over accuracy, while decreasing the thresholds Tmin and Tmax prioritizes accuracy over speed. The determination substep 108 therefore allows for the optimization of the nodal model according to the need.
[0063] Alternatively, the merging of two nodes is performed only if all the precision indicators No of the resulting node do not belong to the second range of values R2. According to another embodiment, the splitting of a node into two nodes is performed only if at least one precision indicator No of each of the two resulting nodes does not belong to the first range of values RL. These additional conditions allow us to avoid an infinite optimization loop, by respectively prioritizing accuracy or speed.
[0064] When the accuracy indicator No does not belong to the first range of values RI or to the second range of values R2, which in the example corresponds to an accuracy indicator No between the predetermined minimum error threshold Tmin and the predetermined maximum error threshold Tmax, the compromise set by the thresholds Tmin and Tmax is reached and no local modification of the model is necessary.
[0065] In an unillustrated variant, the accuracy indicator No is greater when the first and second prediction errors are small and the ranges of values RI and R2 are reversed, that is to say that the first range of values RI includes any value above the predetermined maximum error threshold Tmax and the second range of values R2 includes any value below the predetermined minimum error threshold Tmin.
[0066] Advantageously, the optimization step 104 is repeated, taking as the initial model the optimized model Mo from the previous iteration of the optimization step 104, until, for each node of the optimized nodal model Mo, at least one accuracy indicator No of said node does not belong to the first range of values RI and each accuracy indicator No of said node does not belong to the second range of values R2. In other words, the optimization step 104 is repeated until each node of the nodal model is optimized.
[0067] In Figure 2, this recurrence is illustrated by a test step 110, during which it is determined whether the nodal model is optimizable or already optimized. The nodal model is already optimized if at least one accuracy indicator No of each node does not belong to the first range of values RI and if each accuracy indicator No of each node does not belong to the second range of values R2. In this case, process 100 is completed; this corresponds to termination step 120. Otherwise, the nodal model is optimizable, which involves executing the determination step 108, then again the calculation step 106 and test 110, taking as the initial nodal model Mi the optimized nodal model Mo from determination step 108.
[0068] Thus, the initial nodal model Mi is modified as many times as necessary so that each of its nodes is optimized at the end of the process 100.
[0069] The optimized nodal model Mo thus obtained is advantageously calibrated, by a calibration process not shown, before being used to simulate the temperature in the battery by optimizing the compromise between speed and accuracy of simulation.
[0070] Any feature described above for one example or variant can also be implemented in the other examples and variants described above. Nomenclature:
[0071] 1: electronic generation device; 3: acquisition module; 5: module optimization; 7: calculation sub-module; 9: determination sub-module; 11: information processing unit; 13: memory; 15: processor; 100: generation process; 102: acquisition step; 104: optimization step; 106: calculation sub-step; 108: determination sub-step; 110: test step; 120: termination step; Mi: initial nodal model; Mo: optimized nodal model; P: density; A: thermal conductivity; V: volume; Cp: specific heat capacity; So: average area of cross sections; AT: temperature gradient; Lc: characteristic length of thermal conduction; No: accuracy indicator; Te: first sub-accuracy indicator; Ti: second sub-accuracy indicator; S: reference simulation; RI: first value range; R2: second value range; Tmin: predetermined minimum error threshold; Tmax: predetermined maximum error threshold.
Claims
1. Demands A method for generating a three-dimensional nodal model (100) to simulate a physical quantity related to a battery, the three-dimensional nodal model comprising a set of nodes, each node being characterized by a spatial position, the method being implemented by an electronic generation device, the method (100) comprising an acquisition step (102) of an initial nodal model (Mi), the initial nodal model (Mi) having been previously generated from a known geometry of the battery, the initial nodal model (Mi) comprising fixed and non-fixed nodes, characterized in that the method (100) further comprises an optimization step (104) of the initial nodal model (Mi) comprising: - a calculation substep (106) of at least one accuracy indicator (A' O) for each non-fixed node of the initial nodal model (Mi), each accuracy indicator (NO) of a respective node depending on a first prediction error of a value of the physical quantity from said node relative to a reference simulation (S) and a second prediction error of a time evolution of the physical quantity from said node relative to the reference simulation (S); - a substep (108) for determining an optimized model (Mo), comprising: • for each non-fixed node of the initial nodal model (Mi) where each precision indicator (No) belongs to a first range of values (RI), the implementation of one action among deleting said node and merging said node with another non-fixed node of the initial nodal model (Mi), and • for each non-fixed node of the initial nodal model (Mi) of which at least one precision indicator (No) belongs to a second range of values (R2), a separation of said node into several nodes; the optimization step (104) of the initial model (Mi) providing an optimized nodal model (Mo), to predict a behavior of the battery relative to physical quantity, in order to control battery behavior or predict battery aging.
2. A method (100) according to claim 1, wherein each accuracy indicator (No) of a respective node is a product of a first accuracy sub-indicator, dependent on the first prediction error, and a second accuracy sub-indicator, dependent on the second prediction error, the first accuracy sub-indicator preferably being larger the larger the first prediction error, and the second accuracy sub-indicator preferably being larger the larger the second prediction error.
3. A method (100) according to any one of the preceding claims, wherein the first range of values (RI) includes any value below a predetermined minimum error threshold (Tmin) and wherein the second range of values (R2) includes any value above a predetermined maximum error threshold (Tmax).
4. Method (100) according to any one of the preceding claims, wherein the physical quantity is a temperature.
5. Method (100) according to claim 4, wherein: - the initial nodal model (Mi) further comprises at least one primary thermal conduction axis for each node, said primary axis being an axis along which heat transmission within the node is predominant or is greater than a predetermined minimum heat transmission threshold; and - the calculation substep (106) comprises the calculation of an accuracy indicator (No) for each primary thermal conduction axis of each non-fixed node.
6. A method (100) according to claim 5, wherein, for each non-fixed node of the initial nodal model (Mi) and for each primary thermal conduction axis of said node, the corresponding accuracy indicator (No) depends on: - a temperature gradient 0^) between a hottest cross-section and a coldest cross-section among cross-sections of the node perpendicular to said primary thermal conduction axis, the hottest cross-section and the coldest cross-section being obtained via the reference simulation (S); and - a distance along said primary thermal conduction axis between the hottest cross-section and the coldest cross-section, called characteristic thermal conduction length (Lc); the accuracy indicator (No) being preferably greater as the temperature gradient (AT) is greater and the characteristic thermal conduction length (Lc) is greater.
7. Method (100) according to claim 6 taken with claim 2, wherein, for each node of the initial nodal model (Mi) and for each primary conduction axis of said node: - the first corresponding accuracy sub-indicator is proportional to the temperature gradient (AT); and - the second corresponding accuracy sub-indicator is greater the larger the characteristic thermal conduction length (Lc) and the larger the volume (V) of the node.
8. A method (100) according to any one of the preceding claims, wherein the optimization step (104) is repeated, taking as the initial nodal model (Mi) the optimized model (Mo) from the previous iteration of the optimization step (104), until, for each non-fixed node of the optimized nodal model (Mo), at least one accuracy indicator (No) of said node does not belong to the first range of values (RI) and each accuracy indicator (No) of said node does not belong to the second range of values (R2).
9. Computer program, comprising software instructions which, when implemented by computer, implement a method (100) according to any one of the preceding claims.
10. An electronic device for generating a three-dimensional nodal model (1) to simulate a physical quantity related to a battery, the three-dimensional nodal model comprising a set of nodes, each node being characterized by a spatial position, the device (1) comprising an acquisition module (3) for an initial nodal model (Mi), the initial nodal model (Mi) having been previously generated from a known geometry of the battery, the initial nodal model (Mi) comprising fixed and non-fixed nodes, characterized in that the device further comprises an optimization module (5) for the initial nodal model (Mi) comprising: - a calculation submodule (7) of at least one accuracy indicator (No) for each non-fixed node of the initial nodal model (Mi), each accuracy indicator (No) of a respective node depending on a first prediction error of a value of the physical quantity from said node relative to a reference simulation (S) and a second prediction error of a time evolution of the physical quantity from said node relative to the reference simulation (S); - a sub-module for determining (9) the optimized model (Mo), configured to perform: • for each non-fixed node of the initial nodal model (Mi) where each precision indicator (NO) belongs to a first range of values (RI), the implementation of one action among deleting said node and merging said node with another node of the initial model (Mi), and • for each non-fixed node of the initial nodal model (Mi) of which at least one precision indicator (No) belongs to a second range of values (R2), a separation of said node into several nodes; the optimization module (108) of the initial model providing an optimized model (Mo), to predict battery behavior relative to the physical quantity, in order to control battery behavior or predict battery aging.