Data-driven battery temperature field prediction method based on Hilbert curve order reduction

Abstract

The invention relates to a data-driven battery temperature field prediction method based on Hilbert curve order reduction, and belongs to the technical field of battery thermal management and machine learning crossing. The problems that in a traditional method, due to the fact that sensor distribution points are limited, temperature field sensing is incomplete, errors are introduced through physical model simplification, and electrochemical parameter dependence universality is poor are solved. According to the technical scheme, the method comprises the steps of establishing a three-dimensional thermal network model to generate temperature data, performing dimensionality reduction mapping to a two-dimensional plane through a three-dimensional Hilbert curve to generate a temperature map sequence, performing time sequence temperature field prediction by adopting a convolutional long-short-term memory network, and performing inverse operation on an output temperature map to reconstruct a temperature value. The method has the advantages that global temperature field dynamic sensing is achieved, complex physical modeling is omitted, real-time thermal management decision is supported, computing resource consumption is reduced, and safety and reliability of a battery system are enhanced.

Description

Technical Field

[0001] The present invention belongs to the interdisciplinary technical field of battery thermal management and machine learning, and relates to a data-driven battery temperature field prediction method based on Hilbert curve order reduction. Background Art

[0002] As a core energy storage component in new energy vehicles, the performance and lifespan of power batteries directly impact vehicle safety and reliability. With advantages such as long cycle life, high energy density, and zero pollution, these batteries have become a representative of the next generation of green energy sources and are widely used in transportation and energy storage. However, power batteries generate significant amounts of heat during the charging and discharging process, primarily from internal electrochemical reaction heat and material internal heat resistance. If the battery's heat generation consistently exceeds its heat dissipation, heat will accumulate in and around the battery, causing a sharp rise in temperature.

[0003] Battery temperature significantly impacts its performance: low temperatures cause severe capacity degradation, while high temperatures accelerate aging and may even lead to thermal runaway or explosion. Therefore, power battery temperature monitoring is a core technology for ensuring safe operation. By monitoring and controlling temperature in real time, the battery management system can effectively reduce the frequency of use under extreme operating conditions, extending battery life and improving overall performance. Furthermore, maintaining the battery within an optimal temperature range ensures that voltage and current remain within safe thresholds, thereby enhancing the reliability and market competitiveness of electric vehicles.

[0004] Accurately predicting battery temperature plays a key role in optimizing thermal management strategies. First, temperature prediction models can predict temperature trends in advance, providing a theoretical basis for thermal management strategies. Second, active cooling or heating can prevent battery overheating or overcooling, improving battery performance and reliability. Third, predicting abnormal temperatures can trigger safety protection mechanisms in advance, preventing major accidents such as thermal runaway. Therefore, developing high-precision battery temperature field prediction technology is of great value in promoting the development of the electric vehicle industry and ensuring public safety.

[0005] However, existing prediction methods have significant flaws:

[0006] Direct measurement method: Although simple to operate, the number of deployable temperature sensors is limited, and there is thermal delay, making it difficult to capture transient temperature field distribution.

[0007] Thermal modeling: Physical models based on thermodynamic differential equations require simplification of complex boundary conditions, resulting in insufficient model accuracy. Solving three-dimensional heat transfer equations is computationally expensive, and the model's generalizability is limited.

[0008] Electrochemical impedance spectroscopy: Although it can alleviate the thermal delay problem, its parameter identification depends on the battery's chemical characteristics. Parameters need to be recalibrated for different battery models. It lacks universality and the prediction results fluctuate significantly.

[0009] In summary, there is an urgent need to develop a battery time-series temperature field prediction method that takes into account both computational efficiency and prediction accuracy to provide a scientific basis for the thermal management system of electric vehicles. Summary of the Invention

[0010] In view of this, an object of the present invention is to provide a data-driven battery temperature field prediction method based on Hilbert curve order reduction.

[0011] In order to achieve the above object, the present invention provides the following technical solutions:

[0012] A data-driven battery temperature field prediction method based on Hilbert curve order reduction includes the following steps:

[0013] S1. Establish a battery thermal model based on a three-dimensional thermal network to generate temperature data at each moment of the battery discharge process;

[0014] S2. Using a three-dimensional Hilbert curve, the three-dimensional temperature field corresponding to the temperature data is reduced in dimension and mapped to a two-dimensional plane to generate a two-dimensional temperature map sequence;

[0015] S3. Using a Convolutional Long Short-Term Memory (ConvLSTM) model to perform time series prediction on the two-dimensional temperature map sequence, and output a predicted temperature map at a future moment;

[0016] S4. Perform image processing and temperature inverse calculation on the predicted temperature map to obtain predicted temperature values ​​of each point in the battery temperature field.

[0017] A battery temperature field prediction system for implementing the method, comprising:

[0018] Thermal network modeling module: configured to execute S1 and generate three-dimensional temperature field data;

[0019] Dimensionality reduction processing module: configured to execute S2 and output a two-dimensional temperature map sequence;

[0020] Time Series Forecasting Module: This module is configured to execute S3 and contains a trained ConvLSTM model.

[0021] Temperature Inversion Module: Configured to execute S4, extracting temperature values ​​from the predicted temperature map.

[0022] Furthermore, the time series prediction module integrates a batch normalization layer to accelerate the training convergence of the ConvLSTM model.

[0023] The beneficial effects of the present invention are:

[0024] (1) The battery temperature field is spatially encoded using a three-dimensional Hilbert curve and then dimensionality-reduced and mapped onto a two-dimensional plane to generate a temperature map sequence, fully preserving the spatial distribution characteristics and temporal evolution of the temperature field. Compared to traditional single-point temperature measurement or local area monitoring, this method can simultaneously perceive the temperature dynamics of all key locations inside and on the surface of the battery, providing global temperature field information for the thermal management system.

[0025] (2) A purely data-driven prediction framework is adopted to eliminate reliance on complex physical relationships such as battery thermodynamic equations and electrochemical models. The convolutional long short-term memory network is used to autonomously mine the spatiotemporal evolution of the temperature field, avoiding errors introduced by simplified model assumptions. This significantly improves prediction accuracy and model generalization capabilities, adapting to different battery models and operating conditions.

[0026] (3) The prediction model can output the complete temperature field distribution at future moments online, allowing the battery management system to perceive the hotspot location and temperature rise trend in advance. Based on the prediction results, the cooling strategy can be dynamically adjusted, such as starting the liquid cooling system in advance or reducing the charge and discharge rate, effectively preventing the risk of thermal runaway and extending battery life.

[0027] (4) Hilbert curve dimensionality reduction compresses the three-dimensional temperature field into two-dimensional image data, reducing the computational complexity by several orders of magnitude. Combined with the lightweight convolutional long short-term memory network design, millisecond-level temperature field prediction can be achieved on embedded devices, meeting the real-time requirements of the vehicle battery management system.

[0028] (5) The system's full temperature field prediction capability enables it to identify areas of abnormal temperature rise that are not covered by traditional sensors, such as hot spots inside the battery cell or heat dissipation dead zones at the edges. By integrating predicted data with real-time monitoring values, a dual safety protection mechanism is established, significantly improving the safety level under extreme operating conditions.

[0029] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0031] Figure 1 It is the overall framework flow chart of the present invention;

[0032] Figure 2 This is a schematic diagram of the battery three-dimensional thermal network nodes;

[0033] Figure 3 It is a schematic diagram of the internal temperature network nodes;

[0034] Figure 4 is the external temperature network node diagram;

[0035] Figure 5 Construct a schematic diagram for a two-dimensional Hilbert curve;

[0036] Figure 6 is the first six-order two-dimensional Hilbert curve graph;

[0037] Figure 7 Construct a schematic diagram for a two-dimensional Hilbert curve;

[0038] Figure 8 is a three-dimensional Hilbert curve graph;

[0039] Figure 9 The corresponding diagram of the temperature nodes of the three-dimensional thermal network and the three-dimensional Hilbert curve;

[0040] Figure 10 Illustration of the 3D Hilbert Curve of the battery temperature field;

[0041] Figure 11 It is a 3D-2D temperature field dimensionality reduction mapping diagram;

[0042] Figure 12 Generate a plot for the 2D temperature field;

[0043] Figure 13 This is the ConvLSTM model architecture diagram;

[0044] Figure 14 Schematic diagram of the encoding module and prediction module of the ConvLSTM model;

[0045] Figure 15 This is a schematic diagram of the time series prediction of the two-dimensional temperature field image;

[0046] Figure 16 Schematic diagram of the pixel values ​​of the two-dimensional temperature map and its cropping area. DETAILED DESCRIPTION

[0047] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0048] like Figure 1 The figure shows a data-driven battery temperature field prediction strategy algorithm, the specific contents of which are as follows:

[0049] S1: Establish a battery thermal model based on a three-dimensional thermal network;

[0050] (1) Establish a battery heat generation model. During the discharge process, a series of physical and chemical reactions will occur in the battery, which will generate a large amount of heat (reaction heat, Joule heat, side reaction heat, polarization heat). Bernardi et al. proposed a battery theoretical heat generation model based on the law of conservation of energy. However, the model is too complex, has too many parameters and is extremely difficult to measure. Therefore, Thomas et al. optimized the model based on it. The optimized model is widely used. The calculation formula is as follows:

[0051]

[0052] Among them, Q T represents the battery heat generation rate, I represents the battery operating current, U represents the battery electromotive force, U OCV represents the battery open circuit voltage, T represents the battery temperature, dU OCV / dT represents the battery entropy thermal coefficient. The reversible heat of the battery can be measured by ITdU OCV / dT, the irreversible heat can be obtained by I(UU OCV ) is obtained. Since irreversible heat is divided into Joule heat (ohmic internal resistance R O heat generated) and polarization heat (polarization internal resistance R P heat production).

[0053] (2) Establish a battery heat transfer model. During operation, the battery generates heat and exchanges heat with the outside world. In terms of heat exchange forms, there are three main types: heat conduction, heat convection, and heat radiation. For a single battery, heat exchange occurs in the form of heat conduction. According to Fourier's law, the heat transfer is:

[0054]

[0055] Among them, φ is the heat transfer, λ is the thermal conductivity, A is the heat exchange area, The temperature change rate along the x-direction is shown. For the outside of the battery, heat convection is dominant, which describes the heat transfer between the battery and the external fluid. It is converted from Newton's cooling formula and the mathematical expression is as follows:

[0056] φ=-αAΔT (3)

[0057] Where α is the convection heat transfer coefficient. Thermal radiation can be explained by Boltzmann's law in thermodynamics:

[0058] φ=AσT4 (4)

[0059] Where σ refers to the radiation heat transfer coefficient. Generally speaking, the impact on battery thermal radiation is very small and can be almost ignored.

[0060] Considering only heat conduction inside the battery, and combining Fourier's law and the law of conservation of energy, the thermal model of the single battery involved in the present invention can be described by formula (5):

[0061]

[0062] Substituting the above battery unit volume heat generation rate q into formula (5), we can obtain

[0063]

[0064] Where ρ represents the battery density. Assuming that the material inside the battery is uniform, the result calculated above is 2311.89 kg / m 3 ; C p represents specific heat capacity, k x 、k y 、k z They represent the thermal conductivity of the battery in the x, y, and z directions respectively.

[0065] (3) Heat transfer model based on three-dimensional thermal network. Three-dimensional thermal network model (such as Figure 2 As shown in Figure 2, the three-dimensional temperature field distribution of the battery can be obtained, which mainly includes the calculation of heat generation and internal heat transfer. (1) The heat generation has been calculated, and (2) the heat transfer has been introduced. This section mainly describes the construction of the internal heat transfer model based on the three-dimensional thermal network. For a certain node in the three-dimensional thermal network, the temperature point conducts heat with the surrounding points in different directions (such as Figure 3 As shown), thermal interactions occur between them, resulting in temperature changes.

[0066] According to the differential equation of heat transfer inside the battery (5), the heat transfer relationship for point P can be expressed as:

[0067]

[0068] Where k x 、k y 、k z are the thermal conductivity of the node along the X, Y, and Z heat flow directions, Q x,y,z,t is the heat generated at the node, T x,y,z,t Represents the temperature of the node at time t, T x-1,y,z,t 、T x+1,y,z,t represents the temperature of the node adjacent to the node along the X direction at time t, T x,y-1,z,t 、T x,y+1,z,tIndicates the temperature of the node adjacent to the node along the Y direction at time t, T x,y,z-1,t 、T x,y,z+1,t represents the temperature of the node's adjacent nodes along the Z direction at time t; x1, x2, y1, y2, z1, z2 represent the distance between the node and the adjacent nodes, which are battery geometric parameters. Therefore, the temperature of the internal node at time t+1 can be expressed as:

[0069]

[0070] Simplifying and sorting can be obtained:

[0071]

[0072] For the external nodes of the battery in the three-dimensional thermal network, there is both heat conduction with the adjacent nodes and heat exchange with the ambient temperature in the form of heat convection (such as Figure 4 shown).

[0073] Therefore, it can be calculated according to the following expression:

[0074]

[0075] Where x h 、y h 、z h Represents the surface fluid temperature boundary layer thickness, T A Represents the ambient temperature. Arranging the above formula can obtain the temperature calculation formula of the surface point:

[0076]

[0077] Simplifying and sorting can be obtained:

[0078]

[0079] The above is the heat transfer expression of the surface point of the thermal network. In order to unify the temperature point form inside and outside the battery, define the function F, let C = Δt / ρC p , then

[0080]

[0081]

[0082] Similarly, we can get F(P y-1 )、F(P y+1 )、F(P z-1 )、F(P z+1 ) adjacent points define a function. This allows us to obtain the temperature expression for any temperature node in the three-dimensional thermal network model:

[0083]

[0084] Where, T P,t+1 represents the temperature of node P at time t+1, N represents the number of heat-generating nodes in the thermal network, Q P Indicates the heat generated by the node, Q' P is the heat generated per unit volume. If the node is a surface point, then P P =Q' P =0.

[0085] S2: Research on dimensionality reduction of battery three-dimensional temperature field;

[0086] (1) Fractals and space-filling curves

[0087] 1) Fractal. Fractal belongs to the category of geometry, which refers to the self-similarity between the whole and the parts of a graphic. It reflects that the local enlargement of the whole graphic is consistent with the original shape, and thus forms fractal geometry. The basic idea of ​​fractal geometry is self-similarity. This self-similar structure can be enlarged or reduced according to a certain proportion, and the overall structure will not change. Next, the construction principle of fractals will be studied. (This invention is explained by taking the L-system binary fractal tree as an example).

[0088] The L-system fractal construction method was proposed by Aristid Lindenmayer, among which the binary tree fractal structure is the most classic. In L-system, its generation method is generally expressed as

[0089]

[0090] The meanings of the symbols in formula (18) are as follows:

[0091] ω: Initial state. f: Advance a distance. P: Iteration process. [: Push, i.e. record the current position. ]: Pop, i.e. return to the last pushed position. +: Indicates a clockwise rotation of the specified angle θ. -: Indicates a counterclockwise rotation of the specified angle θ.

[0092] The generation process of the binary tree structure can be described as follows: for n=1, move f upward from the origin to construct a curve, walk a unit length, then push it into the stack for storage, then rotate θ clockwise, continue to construct the curve, move f, and the distance walked at this time is r, then pop the stack (the curve has been constructed and saved), then return to the original stack state, this time the direction is upward, then rotate θ counterclockwise, continue to construct the curve, move f, and the distance walked at this time is also r, and finally pop the stack, then the first-order bifurcation tree curve construction is completed; for n=2, the construction principle is similar. First, move f upward from the origin to construct a curve, walk a unit length, then push it into the stack for storage, then rotate θ clockwise, and now perform first-order curve construction, repeat the above behavior for n=1, denoted as P1. (In P1, the length of the curve walked in the first step is no longer 1, but r, and the length walked in the second step is r 2 ) Then pop the stack and return to the original stack state (note that the stack at this time refers to the stack state when the second-order curve is constructed in the first step, the direction is upward, which is different from the stack state in P1, the direction is clockwise rotation θ). At this time, the direction is upward, then rotate counterclockwise θ, continue to construct the curve in P1, and finally pop the stack. The second-order bifurcation tree curve is constructed, and its mathematical expression is f[+P1][-P1]. When extended to order n, the curve construction is f[+P n-1 ][-P n-1 ], the first step forward length is unit 1, the nth fork forward length is r n length.

[0093] 2) Space filling curve. The present invention uses the Hilbert Curve (HilbertCurve) to reduce the dimensionality of the battery temperature field. The curve is a space filling curve (SFC). Simply put, SFC is a curve that can fill the entire space. It first fills the space around itself, and then extends it through continuous fractals to fill a "smaller" space. SFC can effectively reduce the spatial dimension. When the data space is divided into small grids, SFC will pass through each grid and number each grid in a certain linear order; the numbered grids passed through in sequence will change from disorder to order, and the scattered spatial data will be converted into one-dimensional ordered data. This filling can be regarded as a continuous line passing through every point in the space.

[0094] The first space-filling curve was proposed by Italian mathematician Peano in 1890. He discovered a curve that can fill a square, known as the Peano curve. The Peano curve is constructed by dividing a plane square into nine smaller squares and then connecting the centers of the nine smaller squares in sequence, forming a first-order Peano curve. Continuing the iterations of the first-order curve, each smaller square is further divided into nine smaller squares, resulting in a total of 81 smaller square centers. Connecting each of these points in sequence forms a second-order Peano curve. Further divisions and connecting the centers of the smaller squares create a third-order Peano curve, and so on. As the order increases, the plane is divided into smaller and smaller sections. When the order approaches infinity, the curve can fill the entire plane.

[0095] The mathematical explanation for the ability of these curves to fill space involves the concept of dimension. Traditionally, dimensions are integers, and here we are referring to Euclidean dimensions. As we all know, points form lines, lines form planes, and planes form solids. The Euclidean dimensions of these lines, planes, and solids are 1, 2, and 3, respectively, all integers. For example, the Koch snowflake cannot fill space because its dimension is not an integer. The dimension referred to here is the Hausdorff dimension. Generally speaking, when measuring a geometric object, the basic units of measurement are usually a line segment of unit length, a square of unit area, or a cube of unit volume. When measuring a Koch curve using a unit line segment (a one-dimensional scale), the curve length is infinite, indicating that the measurement scale is too small. However, when measuring a Koch curve using a unit square (a two-dimensional scale), the result is zero, indicating that the measurement scale is too large. Regardless of the measurement method used, it is impossible to obtain an exact measurement result for a Koch curve, indicating that the measurement result is dependent on the selected measurement scale. Therefore, the Koch curve can be imagined as a geometric object between 1 dimension and 2 dimension, so we must consider measuring it with a scale between 1 dimension and 2 dimension. Therefore, we have to use the Hausdorff dimension. HausdorffDimension is mainly used to describe the "dimension" of unconventional geometric objects, especially those "fragmented" or "irregular" geometric objects, such as fractals and some irregular sets. It can be used to measure the "complexity" of complex graphics, and unlike the Euclidean dimension, it is not limited to integers, which is very convenient for measuring fractal graphics such as Koch curves and (Sierpinski) triangles. According to the properties of Hausdorff measure:

[0096] For 0≤s<t<∞, have

[0097]

[0098] Where, R: a set in a general metric space;

[0099] E: a subset of the general metric space;

[0100] s, t: non-negative real numbers, representing the dimension;

[0101] H s (E): s-dimensional Hausdorff measure of E;

[0102] H t (E): The t-dimensional Hausdorff measure of E.

[0103] From the above properties, we can see that for a set E in a general metric space, A non-negative real number s such that H s (E) jumps from ∞ to 0, and this critical value s is the Hausdorff dimension, which is expressed as dim H If E is expressed, then

[0104]

[0105] For the fractal curve dim H The calculation of E requires the introduction of the concept of self-similar sets. For a metric space (X, d), let Define a mapping S:D→X if there exists a constant c∈(0,1) such that for y∈D has

[0106] d(S(x),S(y))≤cd(x,y) (22) Then S is called a compression map on D. If S(x)=x, then x is called a fixed point of the mapping S. According to the fixed point theorem of compression mapping:

[0107] Let mapping S i :R n →R n (i=1, 2, ..., m) is R n A compression map with a compression constant c on , then there is a unique non-empty subset A such that

[0108]

[0109] It can be seen that such a set A is a compression mapping S i The self-similar set of m refers to the number of iterations, which can be understood as the latter order set is composed of m previous order sets, and the number is equal to the number of mappings after compression change.

[0110] For R n The compression map {Si} 1≤i≤m ,if Opening satisfy

[0111]

[0112] The compression mapping {S i} 1≤i≤m Satisfies the open set condition. If for the contraction map {S i} 1≤i≤m If the open set condition holds, then the Hausdorff dimension of the self-similar set A is dim H A=s, s satisfies formula (25)

[0113]

[0114] And s also satisfies

[0115] s∈{s|0≤H s (A)≤∞} (26)

[0116] From this we can find the dimension of the fractal curve, where H s (A) represents the Hausdorff measure, which is the same as the H mentioned above. s The meaning is the same, and the quantity satisfies the following relationship

[0117]

[0118] For the Koch curve, since the second-order fractal graph is compressed and transformed from four first-order graphs, m is 4. Substituting the compression ratio c and m into formula (25) we can get

[0119]

[0120] The Hausdorff dimension of the Koch curve is calculated to be 1.26, which means that the Koch curve is a curve between one dimension and two dimensions. Therefore, this curve cannot be used to calculate R 2 (dim H A=2) The plane is filled. For the Peano curves mentioned above, their dimensions are as shown in the table:

[0121] Table 1 Dimensions of several fractal curves

[0122]

[0123] The Hilbert curve studied in this invention has a dimension of 2D Hilbert Curve of 2, which can be used for space filling, as will be introduced in the next section.

[0124] The true space-filling curve belongs to the category of finding limits, such as formula (29). It has no length. When a finite number of points is taken, the length of the curve can be calculated. In this case, it is called a pseudo-space-filling curve.

[0125]

[0126] Where S is the curve length and n is the curve order. The second-order three-dimensional Hilbert curve and the third-order two-dimensional Hilbert curve constructed by the present invention are both pseudo-Hilbert curves. The mathematical definition of a two-dimensional plane space-filling curve is:

[0127] f:R→R 2 (30)

[0128] Here, f is a continuous surjective function. From a geometric perspective, as long as the curve is complete and uninterrupted, the mapping from line to space will also be continuous. This has been mathematically proven and will not be repeated here.

[0129] The same principle applies to filling three-dimensional space. For example, in three-dimensional space, a cube is divided into n smaller cubes, and then a continuous curve connects each smaller cube in sequence according to a certain pattern (note that each smaller cube is traversed by the curve only once). As the cube is divided into more and more parts, the curve becomes longer and longer. When n → infinity, the curve is considered to fill the large cube, that is, the three-dimensional space is filled by the curve. This is also the case with the three-dimensional Hilbert curve constructed later.

[0130] (2) Hilbert curve. This invention mainly converts the three-dimensional temperature field into a two-dimensional image to create a data set for the machine learning model. This section mainly introduces the construction principle and properties of the Hilbert curve. The three-dimensional Hilbert curve is used to fill the three-dimensional battery temperature field and establish a corresponding relationship between it and the two-dimensional curve, thereby converting the three-dimensional temperature field into a two-dimensional image to create a data set for the machine learning model.

[0131] 1) Construction and properties of 2D-HilbertCurve. Although the fractal dimension of Peano curve is 2, it can be R 2 Filling of the plane, but for R 3 The fractal dimension of a three-dimensional space is 2.68, which means it cannot completely fill the three-dimensional space. The present invention involves a three-dimensional temperature field for power batteries, so a new space-filling curve, the Hilbert curve, is required. Unlike the Peano curve, its fractal dimension increases to 3 as the number of series increases. Therefore, if the recursive construction is repeated multiple times, it will completely fill the unit cube. The following will discuss the definition, properties, and construction of two-dimensional and three-dimensional Hilbert curves.

[0132] The Hilbert curve is defined as the n-dimensional space R n The one-to-one mapping between and one-dimensional space is expressed as:

[0133] H: R→R n (31)

[0134] Among them, let R n ={X1, X2, X3, ..., X n}, indicating R n The n dimensions of the space, the corresponding 1-dimensional space coordinate value is the Hilbert code, denoted as H code A Hilbert curve can fill a 2 m ×2 m ×...×2 m (2 mn ) in n-dimensional space, then use Indicates that the curve is called the n-dimensional m-order Hilbert curve.

[0135] Since the Hilbert curve is also a fractal curve, its construction principle conforms to fractal principles and can be used as a reference for fractal construction. To construct an m-order pseudo-Hilbert curve in two-dimensional space, first, divide a plane into four equal parts. Next, place an m-1-order pseudo-Hilbert curve rotated 90° clockwise in the lower-left plane region, and place an m-1-order pseudo-Hilbert curve rotated 90° counterclockwise in the lower-right plane region. Finally, connect the endpoint of the m-1-order pseudo-Hilbert curve in the lower-left plane region to the starting point of the m-1-order pseudo-Hilbert curve in the upper-left plane region, the endpoint of the m-1-order pseudo-Hilbert curve in the upper-left plane region to the starting point of the m-1-order pseudo-Hilbert curve in the upper-right plane region, and the endpoint of the m-1-order pseudo-Hilbert curve in the upper-right plane region to the starting point of the m-1-order pseudo-Hilbert curve in the lower-right plane region. This constructs an m-order pseudo-Hilbert curve. When m approaches infinity, it becomes a true Hilbert curve.

[0136]

[0137] There are four basic building blocks of the Hilbert curve, such as Figure 5 As shown, the construction expressions are:

[0138]

[0139] Among them, the meanings of the four basic expression symbols are:

[0140] The opening curves downward in a clockwise direction. The opening curves counterclockwise to the left. The opening curves counterclockwise to the right. Construct curves clockwise with the opening upward. ↑: Connect curves from bottom to top. →: Connect curves from left to right. ↓: Connect curves from top to bottom. ←: Connect curves from right to left.

[0141] The second order is constructed based on the first order, such as Figure 5 Here we take the downward opening as an example. When m = 1, a plane is divided into four small squares, and then the centers of each small square are connected in sequence. When m = 2, the second-order pseudo-Hilbert curve expression is: The opening direction of the basic unit of the curve in the expression is the opening direction of the first-order curve. The curve construction process is shown in the figure. Similarly, when m = 3, the expression of the third-order pseudo-Hilbert curve is still: However, it is worth noting that the opening direction of the basic unit of the curve is no longer the opening direction of the first order, but the opening direction corresponding to the second order pseudo Hilbert curve.

[0142] It follows that for the m-order pseudo-Hilbert curve (opening downward), the expression is:

[0143]

[0144] The symbols in the expression mean

[0145] A downward-opening m-1 order pseudo-Hilbert curve.

[0146] An m-1 order pseudo-Hilbert curve opening to the left.

[0147] An m-1 order pseudo-Hilbert curve opening to the right.

[0148] An m-1 order pseudo-Hilbert curve that opens upward.

[0149] The meanings of the remaining terms remain unchanged.

[0150] From the above, we can see that the second-order pseudo-Hilbert curve is composed of four first-order curve compression transformations, and its compression ratio is 1 / 2, so the Hausdorff dimension is In4 / In2=2, which means that the Hilbert curve can fill two-dimensional space.

[0151] For the two-dimensional space R 2 ,That like Figure 6 As shown. The two-dimensional m-order pseudo Hilbert curve divides the plane large square into two m×2 m =4 m small squares, and connect the centers of the small squares in sequence, then the length of the curve is defined recursively

[0152]

[0153] According to the boundary conditions Solved

[0154]

[0155] The curve length is related to the three-dimensional structure later in the text and will not be introduced here.

[0156] Proof of the convergence of the curve. For two-dimensional space, define

[0157]

[0158] Moreover, any point t∈[0,1] on the line segment is assumed to fall within the interval [k4 -N , (k+1)4 -N ], then All in In a small square (the side length of the square is 2 -m ),Right now

[0159]

[0160] According to Cauchy's convergence theorem, we can get Uniform convergence. If For any point (x, y)∈[0, 1] on the plane 2 , there exists a side with length 2 -m square, so that

[0161]

[0162] because Then there is

[0163]

[0164] Therefore, according to the convergence, a point on the curve gets closer and closer to a specific point on the plane as the order m increases, while for the serpentine curve, it will jump repeatedly, which also reflects the stability of the Hilbert curve.

[0165] 2) 3D-Hilbert Curve construction and properties. The 3D-Hilbert Curve construction is also based on the fractal concept for recursive iteration. Since it is a three-dimensional space construction, the process of the evolution of the first-order curve to the next-order curve will be 2-dimensional space.3 Equal division means that a cube is evenly divided into 8 small cubes. The cube is filled with a certain order three-dimensional Hilbert curve, and the adjacent first order curve is filled with 8 small cubes. For order m, there are 2 m ×2 m ×2 m For the simplest first-order curve, divide the three-dimensional space into eight equal parts, and then connect the eight cube center points in sequence according to a certain rule (numbered 1, 2, 3, 4, 5, 6, 7, 8 respectively, and the curve will be constructed in the following order). This will form a first-order curve, such as Figure 7 shown.

[0166] The high-order three-dimensional Hilbert curve is also composed of basic construction units. However, unlike the 2D-Hilbert Curve, which has only four basic construction units, 24 basic units can be constructed according to the connection order between the center points of each cube. The specific construction principle of each basic unit is as follows:

[0167]

[0168] Each element in the S matrix represents the number of the space cube mentioned above, and each row represents the corresponding curve formed by the combination of these numbers, which is recorded as S x , where x represents the xth row of the matrix. The three-dimensional first-order pseudo Hilbert curve in the figure above is constructed by S2 iteration, where S2 represents the basic curve construction unit composed of the number combination of the second row of the matrix. Through the above basic arrangement order, 24 basic three-dimensional Hilbert curve units (such as Figure 8 These curves can be combined in different ways to perform high-order iterations.

[0169] Each three-dimensional pseudo-Hilbert curve is constructed by iterating the above 24 basic units, but the iteration must be constructed according to a specific rule (the iteration relationship is shown in the following matrix E). Specifically, from low-order to high-order construction, a filling transformation must be performed at each inflection point of the low-order curve. For example, each inflection point of the m-1 order curve is divided into 8 small cubic spaces again, and iterated according to the filling rule to form an m-order curve. In other words, the m-order curve is obtained by connecting 8 m-1 order curves in a certain order (note: the 8 m-1 order curves here are not exactly the same curve). For a first-order curve, the 8 0 =1 basic unit; second-order curve, composed of 8 1 =8 basic units; the third-order curve is constructed from 8 2 = 64 basic units are constructed... and so on. The m-order curve is constructed from 8 m-1 It is composed of a basic unit structure.

[0170]

[0171] In the above matrix, each element represents a basic structural unit, and each line is a higher-order curve composed of basic units, denoted as E x , where x represents the xth row of the matrix. By iterating matrix transformation, we can construct curves from low order to high order. Take S2 ​​as an example: for a first order curve, that is, the S2 curve, the expression is The second-order curve is the E transformation corresponding to S2, that is, E2=S3+S1+S2+S 10 +S3+S2+S5+S 10 , then the expression of the second-order curve is The third-order curve continues to iterate on the basis of the second order, and is transformed by E to

[0172] By analogy, we can construct the m-order three-dimensional Hilbert curve. The above iterative process from first order to second order is as follows Figure 7 shown.

[0173] From the above iterative process, we can see that the three-dimensional second-order pseudo-Hilbert curve is composed of 8 first-order curve compression transformations. The ratio of the length of each line segment in the first-order and second-order curves is 2, and its compression ratio is 1 / 2. Therefore, the Hausdorff dimension is In8 / In2=3, which means that the Hilbert curve can fill three-dimensional space.

[0174] (3) Dimensionality reduction of temperature field based on 3D-2D Hilbert Curve

[0175] 1) Temperature data preprocessing

[0176] To reduce the battery temperature field's dimensionality, we need to use the temperature data from the thermal network nodes in Chapter 3 as the source data. However, this source data doesn't match the format used for dimensionality reduction. Therefore, we need to perform a series of transformations on the source data to make it compatible with the subsequent image dataset. The temperature data transformation primarily involves converting it into 24-bit decimal color values. The specific process is as follows.

[0177] First, define the temperature conversion mapping relationship:

[0178]

[0179] R=255*r (47)

[0180] G=0 (48)

[0181] B=-255*r+255 (49)

[0182] color = (R, G, B) (50)

[0183] Where r represents the relative position of the current temperature within the given temperature range, T min Indicates the minimum temperature, T max Represents the highest temperature, color represents the RGB value corresponding to the current temperature, R is the R channel value of the RGB value corresponding to the current temperature, G is the G channel value of the RGB value corresponding to the current temperature, and B is the B channel value of the RGB value corresponding to the current temperature. The present invention only uses two channels, so the G channel is set to 0 here. Therefore, the RGB value corresponding to the highest temperature is (255, 0, 0), and the RGB value corresponding to the lowest temperature is (0, 0, 255). Secondly, the RGB value corresponding to each temperature can be calculated by the above formula, but this format cannot be used directly because the temperature value is subsequently assigned to the coordinate on the Hilbert curve. The data format requires the input to be a decimal value, so the RGB value needs to be converted to a decimal color value. The conversion relationship is:

[0184] DC=R<<16+G<<8+B (51)

[0185] In the formula, DC represents the color value expressed in decimal, and << represents the left shift operator. This relationship allows us to convert the RGB color components into a 24-bit decimal number (here, color conversions at several temperature points are shown in Table 2), representing the RGB encoding of a color. At this point, the data format meets the requirements, and we can then construct the Hilbert curve in the 3D temperature field.

[0186] Table 2 Color conversion comparison table

[0187]

[0188] 2) Construction of Hilbert Curve in 3D temperature field.

[0189] From the above construction of the Hilbert curve that can fill the three-dimensional space, we can see that each inflection point can be divided into a higher-order space. When a temperature point coincides with the inflection point of the curve, the temperature at this inflection point can replace all the temperatures in the higher-order space (the temperature of the cube area centered at the inflection point). Each temperature node of the battery has a specific coordinate in the three-dimensional space. When these points are interspersed with the 3D-Hilbert Curve according to the construction rules, each temperature point also has its specific position on the curve, such as Figure 9 shown.

[0190] The specific principle of the temperature points of the three-dimensional thermal network and the points on the curve is as follows: for a point P on the curve, assuming the three-dimensional coordinates are (X, Y, Z), then the point is expressed as P = (X, Y, Z); in the thermal network, the corresponding point is represented by T P Indicates that the coordinates are (x, y, z), then the coordinates of the point can be expressed as T P =(x, y, z). When the curve passes through the battery temperature field, T P Assign to P, use represents its position on the curve, x represents the sequence number of point P according to the construction order, then the spatial position of point P on the curve can be expressed as When the temperature of the point (pre-processed) is substituted, the visual input format of the point can be expressed as Where DC is the decimal color value of the temperature data point; this completes the one-to-one correspondence between the temperature point and the inflection point of the curve, completing the visualization.

[0191] For the first point A on the curve, it is represented by 255}, the second point B is The third point C is Similarly, 255 represents blue, 0 represents black, and 8855416 represents purple. This is only for demonstration. Assign the converted temperature to the corresponding temperature point on the 3D-Hilbert curve at that moment, and the curve is constructed in the temperature field. Figure 10 As shown in Figure 2, the visualized three-dimensional temperature field can be used to generate a two-dimensional temperature field image based on the mapping relationship.

[0192] 3) Hilbert Curve Dimensionality Reduction of 3D Temperature Field

[0193] A three-dimensional Hilbert curve can fill a 2 m ×2 m ×2 m The three-dimensional space R 3 , since the m-order curve consists of 8 m-1 It is composed of basic units, and each basic unit is composed of 8 line segments, so the length of the three-dimensional Hilbert curve is:

[0194]

[0195] For the two-dimensional Hilbert curve, the filling is 2 m ×2 m The two-dimensional space R 2 , the m-order curve consists of 4 m-1 The two-dimensional Hilbert curve is composed of four basic units, each of which is composed of four line segments.

[0196]

[0197] The two-dimensional temperature map is the data set of the machine learning model. To produce the data set, the three-dimensional temperature field needs to be expanded into a two-dimensional picture. The generation of the two-dimensional temperature map requires dimensionality reduction. In order to project the three-dimensional temperature field onto the two-dimensional plane, we use lenH m To perform the transformation, we first need to define the mapping rule. For Euclidean space (R 3 →R 2 ),definition:

[0198] f:H 3 →H 2 (54)

[0199]

[0200] Where H 3 Represents the Hilbert curve of three-dimensional space, H 2 represents the Hilbert curve in two-dimensional space. The mapping relationship needs to satisfy the above equation to ensure a one-to-one mapping. m and n represent the order of the curve. Since the basic structural units of different dimensions are different, the lengths of curves of the same order but different dimensions must be different. Therefore, different variables are used here to distinguish the orders of different dimensions. At the same time, the curves must be in the same coordinate system, and the Cartesian coordinate system is used here.

[0201] According to the above equation, the present invention takes a three-dimensional second-order pseudo Hilbert curve and a two-dimensional third-order pseudo Hilbert curve for study, that is, m = 2, n = 3. At this time, there are 64 points in both the three-dimensional space and the two-dimensional space. According to the mapping rule, each inflection point of the coordinate transformation curve is one-to-one corresponding, such as Figure 11 shown.

[0202] After the temperature data is imported, the temperature field can be mapped to the XOY plane to obtain a two-dimensional temperature map, such as Figure 12 shown. Figure 12 The numbers on the left side of the middle represent different temperature points on the three-dimensional curve, corresponding to the 20 temperature points in the three layers of the battery mentioned above; Figure 12 The middle right part is the two-dimensional temperature map after dimensionality reduction. Each temperature point has been marked on the color block in the figure, corresponding one to one with the three-dimensional temperature point.

[0203] By using the above method, the temperature at each moment in the battery discharge process is imported, and a temperature field picture corresponding to the moment will be generated. The present invention studies 9 working conditions at 1C, 1.5C, and 2C discharge rates at three temperatures of 15°C, 25°C, and 35°C, with a total of 3568 pictures. For the 1C rate, since the discharge time is the longest and the data is the largest, in order to simplify the data, the present invention samples once every 10 seconds, calculates the temperature value and generates a temperature map at that moment; for the 1.5C and 2C rates, if sampling is also done every 10 seconds, the data set is too small, and if one temperature is sampled per second, the temperatures in adjacent two seconds are too close, and the calculated color values ​​are the same, so the present invention samples once every 5 seconds. The number of specific data set pictures under the nine working conditions is shown in Table 3.

[0204] Table 3 Two-dimensional temperature images under different working conditions

[0205]

[0206] S3: Establish a time series prediction model for two-dimensional temperature graphs.

[0207] (1) ConvLSTM convolutional long short-term memory network model structure. The convolutional long short-term memory network model (ConvLSTM) combines the advantages of both, with both the spatial processing characteristics of CNN and the temporal data processing capabilities of LSTM. It has unique advantages in temporal image sequence processing and also has good prediction effects.

[0208] The ConvLSTM neural network has three layers (such as Figure 13 As shown), the architecture is as follows:

[0209] The first layer of the network is the ConvLSTM2D layer, which extracts spatial features from the input image sequence while capturing temporal dependencies. This layer takes as input a tensor of shape (16, 128, 128, 3), with a kernel size of (3, 3) and a number of kernels of 64 to ensure sufficient feature representation. After processing by the neural network, this layer outputs a tensor of shape (16, 128, 128, 64), representing the temporal image sequence containing 64 kernels.

[0210] To further enhance temporal modeling capabilities, the second layer of the network is also a ConvLSTM2D layer. This layer also uses 64 convolution kernels of size (3, 3) to further capture the temporal dependencies in the image sequence. The input shape is (16, 128, 128, 64). After passing through this layer, the output of the last time step of the image sequence is returned, with an output shape of (128, 128, 64).

[0211] The last layer is the Conv2D layer, which is responsible for decoding the extracted spatiotemporal features and converting the feature map into an output image. This layer receives an input of shape (128, 28, 64) and outputs an image of shape (128, 128, 3). The convolution kernel size is (3, 3) and the output is a three-channel RGB image. Finally, the output image is normalized to the range [0, 1] using the sigmoid activation function. Figure 13 As we can see, ConvLSTM is an improvement on LSTM. It replaces the dot multiplication in the input gate with a convolution operation. That is, CNN operation is performed in the feedforward neural network to extract spatial features. The fully connected layer in CNN is used as the input of LSTM for time series prediction. The main calculation formula involved in ConvLSTM is as follows:

[0212] f t =σ(W f *(h t-1 ,x t )+b f ) (56)

[0213] i t =σ(W i *(h t-1 ,x t )+b i ) (57)

[0214] o t =σ(W o *(h t-1 ,x t )+b o ) (58)

[0215] c t =f t ⊙c t-1 +c' t ⊙i t (59)

[0216] c' t =tanh(W c *(h t-1 , x t )+b c ) (60)

[0217] h t =o t ⊙tanh(c t ) (61)

[0218] The meanings of the symbols in the formula are:

[0219] x t-1 represents the state of the input layer at time t-1; ht represents the state of the hidden layer at time t; y t represents the state of the output layer at time t; f H represents the activation function of the hidden layer; W and U represent the weight parameters of the hidden layer; b t represents the bias parameter of the hidden layer; f o represents the activation function of the output layer; V represents the weight parameter of the output layer; b o Represents the output layer bias parameter; * represents the table convolution operation.

[0220] The Convolutional Long Short-Term Memory (ConvLSTM) model combines the advantages of CNN and LSTM to perform time series prediction of multiple frames. ConvLSTM is mainly divided into the encoding section and the prediction section. The principle is that the encoding section performs a convolution operation on the two-dimensional temperature field image to extract spatial features, and then extracts the temporal features through the long short-term memory network and saves these features in the hidden layer; the prediction section copies the hidden layer state based on the spatiotemporal features of these temperature fields, and then uses it as the initial hidden state to predict the temperature field at the next moment, such as Figure 14 As shown. The data input of ConvLSTM has five parameters, namely (batch_size, sequence_length, width, hight, channel), where batch_size represents the batch size of each training (usually set in advance, can be omitted here), sequence_length is the length of the sequence, representing the number of continuous temperature field images input, width and hight are the image size, representing the width and height of the input image, and channel represents the number of channels of the image. The present invention uses 16 consecutive frames of temperature field images corresponding to the discharge working condition as the model input, and predicts the temperature field of the 17th frame, which is the next moment (as shown in Figure 2). Figure 15 The image is an RGB image resized from 1024×1024 to 128×128, so the input format is (16, 128, 128, 3). To accelerate training and improve stability, we added a batch normalization layer after each ConvLSTM layer. Batch normalization helps the model converge faster and reduces the risk of overfitting by adjusting the mean and variance of the input at each layer. The Adam algorithm is also used to optimize the loss function.

[0221] (2) Dataset processing

[0222] The ConvLSTM dataset in this paper contains multiple time-series images. To meet the input requirements of the model, each image needs to be preprocessed. First, the images are uniformly scaled to a resolution of 128×128 to improve the training speed and convergence of the model. Secondly, since the images are color images, the RGB channels are required. Therefore, the pixel values ​​of the three channels of the image are extracted and normalized to the range of [0, 1]. The calculation formula is as follows:

[0223]

[0224] Where pixel is the current pixel value, pixel_norm is the normalized value, pixel_max is the maximum value of the pixel in the channel, which is 255 here, and pixel_min is the minimum value of the pixel in the channel, which is 0 here. Therefore, the above formula (5.21) can also be written as:

[0225]

[0226] The dataset of the present invention is divided into a training set, a validation set, and a test set. The training set accounts for 80% of the total dataset, the validation set accounts for 10%, and the test set accounts for 10%. To improve the generalization ability of the model, data augmentation techniques such as random cropping, horizontal flipping, and rotation are also applied during the training process. These methods can increase the diversity of the training data and reduce overfitting.

[0227] (3) Image processing and temperature inversion calculation

[0228] The ConvLSTM model described above has predicted the battery's temperature field, but this temperature field is still a two-dimensional image. To obtain specific temperature values, an inverse operation must be performed on the two-dimensional image. This requires knowledge of image recognition, and the predicted temperature can be calculated based on the temperature conversion mapping equation defined in Chapter 4. The image in this invention uses RGB channels, with each channel ranging from 0 to 255. To extract RGB pixels, this invention utilizes Python graphics processing libraries such as Pillow and Numpy. Pillow is a Python image processing library based on PIL (Python Imaging Library) and offers powerful image processing functions such as image opening, cropping, and scaling. Pillow allows for convenient access to image pixel data and saving in a variety of formats. NumPy is a Python array library suitable for processing large amounts of numerical data. As mentioned above, the RGB values ​​of an image can be viewed as a three-dimensional matrix, so each pixel can be accessed using the matrix subscript. The NumPy library efficiently accesses and manipulates image pixel data by converting images into NumPy arrays.

[0229] For each picture, not all pixels are meaningful. This paper selects 20 temperature points to study the discrete temperature field of power batteries. These 20 points have their specific position coordinates and color channel values ​​on the picture. Therefore, in the process of pixel extraction, the color channel extraction area must be determined first. Here, it is necessary to crop the picture area and crop the 20 temperature point areas separately to facilitate the determination of pixel coordinates and pixel values. Figure 16 shown.

[0230] For a 128×128 image, the position cropping region format is as follows:

[0231] regions=(x1,y1,x2,y2) (64)

[0232] In the formula, regions represents the cropping area, x1 and y1 represent the coordinate values ​​of the lower left corner, and x2 and y2 represent the coordinate values ​​of the upper right corner. The cropping area of ​​each temperature map is shown in Table 4:

[0233] Table 4 Coordinates of the cropping area of ​​the 2D temperature map

[0234]

[0235] After cropping each temperature region, the RGB value corresponding to each region is obtained through the Python library, and the inverse calculation of the temperature can be performed. There are two ways to perform the inverse calculation. One is to calculate the average RGB value of the pixels in the cropped area and then inversely calculate the temperature of the temperature point; the other is to inversely calculate the temperature of each pixel point, then average the temperature, and use the average value to replace the temperature value of the point. By comparison, the former has a smaller error. This invention adopts the first method, and the calculation formula is as follows:

[0236]

[0237] According to equations (65), (66), and (67), the mean values ​​of the RGB channels of the cropped area are obtained. Combined with the color mapping formula, the following temperature inverse calculation formula is obtained:

[0238]

[0239] T=r average ×(T max -T min )+T min (71) In the formula, r1 represents the position of the pixel value in the R channel, r2 represents the position of the pixel value in the B channel, and r_average represents the overall relative position of the pixel value. For the inverse calculation of temperature, the pixel value is first normalized to between 0 and 1, and the position of the current pixel in each channel is calculated separately. Since the G channel is set to 0, it is not included in the calculation here. Then, the relative position of the pixel is substituted into formula (71) to calculate the temperature value corresponding to the current area.

[0240] S4: ConvLSTM model validation analysis.

[0241] The present invention uses a convolutional long short-term memory neural network model to perform time series prediction of the two-dimensional temperature field and conducts comparative analysis on the prediction of 20 points in the temperature field. Due to limited space, a total of 10 points inside and outside the battery are shown here, including 4 points inside and 6 points outside. For the four temperature points inside the battery, they are T9, T 10 、T 11 、T 12 The model has the highest degree of fit at a discharge rate of 1C. At a discharge rate of 1.5C, the model is most accurate in the middle stage of discharge, with some deviations at the beginning and end of discharge, but the overall fit is very high. For a constant current discharge rate of 2C, the model prediction is very accurate at the beginning of discharge, with some deviations in the middle and late stages of discharge, but within an acceptable range. Overall, the data-driven temperature field prediction model can predict internal points of the temperature field at different temperatures and discharge rates, accurately describing the temperature evolution of points within the battery.

[0242] For the battery surface temperature, a temperature point is selected for each surface. Here, six points, T1, T7, T14, T16, T18, and T20, are selected for analysis. 14 、T 16 、T 18 、T 20These four points are more accurate than the predictions at points T1 and T7. While the predictions for the front and back surfaces aren't as good as for the top, bottom, and left / right surfaces, they can still describe the surface points outside the temperature field. At a constant current discharge rate of 1C, the predictions are better than those at 1.5C and 2C, but the overall discharge trend remains accurate. According to Table 5, when the ambient temperature is 15°C, the maximum average absolute error occurs at the constant current condition with a discharge rate of 2C. The average absolute error of the temperature point T2 under this condition is 1.162°C, and the average relative error is 5.08%. In addition to point T2, the average absolute errors of points T3 and T6 exceed 1°C, which are 1.035°C and 1.033°C respectively. The maximum average relative error is 5.42%, which occurs at point T2 under the discharge rate of 1C. The average relative errors of T3 and T6 are also greater than those of other points, which are 4.82% and 4.81% respectively, just like the absolute error. The average absolute errors of the remaining temperature points do not exceed 0.60°C, and the average relative errors do not exceed 2.1%.

[0243] Table 5 Prediction error when the ambient temperature is 15℃

[0244]

[0245] Table 6 shows the prediction errors at an ambient temperature of 25°C. Compared to 15°C, the maximum mean absolute error (MAE) decreases slightly, reaching 1.124°C at T2. The MAEs at T3 and T6 also decrease, but still exceed 1°C. These errors occur under a 2C constant current discharge rate. The MAEs at all other points are within 0.7°C. At a 1C discharge rate, the MAEs decrease to below 0.19°C. The maximum mean relative error occurs at T2 under the 1C condition, where the error increases to 7.58% compared to 15°C. The MAEs at T3 and T6 are 6.86% and 6.85%, respectively, while those at all other points are within 3%.

[0246] Table 6 Prediction error when the ambient temperature is 25℃

[0247]

[0248]

[0249] Measurements show that when the ambient temperature is 35°C, the mean absolute error and mean relative error at temperature point T2 are both the largest, at 1.070°C and 10.24%, respectively. The former occurs at a 2°C magnification rate, and the latter occurs at a 1°C magnification rate. The mean absolute errors at temperature points T3 and T6 drop below 1°C for the first time, reaching 0.977°C and 0.975°C, respectively. The mean absolute errors at the remaining points are within 0.5°C, and the mean relative errors are within 3.7%.

[0250] For all of the above operating conditions, the overall prediction accuracy is within acceptable limits. In particular, for the 1C rate at 15°C, 25°C, and 35°C, the maximum absolute error is within 0.8°C. Only at T2, T3, and T6 does the adaptability show slightly poorer performance, but the error remains within 1.2°C. The remaining points are within 0.7°C. These results demonstrate that the model's predicted temperature field is sufficiently accurate, demonstrating that this data-driven model can be used to predict and estimate the temperature field of power batteries.

[0251] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A data-driven battery temperature field prediction method based on Hilbert curve order reduction, characterized by: The following steps are involved: S1. Establish a battery thermal model based on a three-dimensional thermal network to generate temperature data at each moment of the battery discharge process; S2. Using a three-dimensional Hilbert curve, the three-dimensional temperature field corresponding to the temperature data is reduced in dimension and mapped to a two-dimensional plane to generate a two-dimensional temperature map sequence; S3. Using a Convolutional Long Short-Term Memory (ConvLSTM) model to perform time series prediction on the two-dimensional temperature map sequence, and output a predicted temperature map at a future moment; S4. Perform image processing and temperature inverse calculation on the predicted temperature map to obtain predicted temperature values ​​of each point in the battery temperature field.

2. The data-driven battery temperature field prediction method based on Hilbert curve order reduction according to claim 1 is characterized in that: The S2 specifically includes: S21, constructing a three-dimensional second-order pseudo Hilbert curve to traverse the nodes of the three-dimensional temperature field of the battery, and constructing a two-dimensional third-order pseudo Hilbert curve to fill the two-dimensional plane; S22, through length equivalence relation \text{len} establishes a one-to-one mapping between the node coordinates of the 3D curve and the node coordinates of the 2D curve; S23. Generate RGB values ​​according to the temperature value T according to the preset color mapping rule: R＝255*r G＝0 B＝-255*r+255 Where T min 、T max are the lower and upper limits of the temperature range, respectively, and R, G, B are the RGB channel values; S24. Convert the RGB value into a decimal color value DC=R<<16+G<<8+B, and assign the value to the corresponding two-dimensional coordinate point to generate a two-dimensional temperature map.

3. The data-driven battery temperature field prediction method based on Hilbert curve order reduction according to claim 2, characterized in that: In S3, the input data format of the ConvLSTM model is: (batch size, sequence length, image width, image height, number of channels) = (batch_size, 16, 128, 128, 3), the output is a 128 × 128 pixel RGB temperature image at the next moment.

4. The data-driven battery temperature field prediction method based on Hilbert curve reduction according to claim 1, characterized in that: In S4, the temperature inverse calculation includes: S41, cropping 20 preset temperature point areas in the predicted temperature map, with the coordinates of each area defined as a rectangular box (x1, y1, x2, y2); S42, calculate the RGB mean of the pixels in each cropping area S43. Calculate the temperature value T according to the inverse mapping formula:

5. The data-driven battery temperature field prediction method based on Hilbert curve reduction according to claim 3 is characterized in that: The ConvLSTM model consists of three layers: First layer: ConvLSTM2D layer, input size (16,128,128,3), convolution kernel (3×3), output channels 64; Second layer: ConvLSTM2D layer, input size (16, 128, 128, 64), convolution kernel (3×3), output last time step feature map (128, 128, 64); The third layer is Conv2D layer, with input size (128, 128, 64), convolution kernel (3×3), and output three-channel image (128, 128, 3), which is normalized by Sigmoid function.

6. The data-driven battery temperature field prediction method based on Hilbert curve order reduction according to claim 1 is characterized in that: In S1, the three-dimensional thermal network model construction includes: S11. Calculate the heat production rate per unit volume based on the Bernardi heat production formula Where I is the current, V is the battery volume, R T is the total internal resistance, U OCV is the open circuit voltage; S12. Divide the battery into internal nodes and surface nodes, and solve the temperature of each node by discretizing the heat transfer differential equation: Internal node temperature update formula: Surface node temperature update formula: Among them, F(P), F(P d ) is the heat transfer coefficient function, T A is the ambient temperature, Q' P Heat production per unit volume.

7. The data-driven battery temperature field prediction method based on Hilbert curve order reduction according to claim 6, characterized in that: The three-dimensional thermal network model includes 20 nodes, including 8 internal nodes and 12 surface nodes, and the node spacing is determined according to the battery geometric size.

8. The data-driven battery temperature field prediction method based on Hilbert curve reduction according to claim 1 is characterized in that: The step S4 further includes: verifying the predicted temperature value using mean absolute error (MAE) and mean relative error (MRE): Where T pred,i To predict the temperature, T sim,i is the simulation temperature, and N is the number of samples.

9. A battery temperature field prediction system for implementing the method according to any one of claims 1 to 8, characterized in that: include: Thermal network modeling module: configured to execute S1 and generate three-dimensional temperature field data; Dimensionality reduction processing module: configured to execute S2 and output a two-dimensional temperature map sequence; Time Series Forecasting Module: This module is configured to execute S3 and contains a trained ConvLSTM model. Temperature Inversion Module: Configured to execute S4, extracting temperature values ​​from the predicted temperature map.

10. The battery temperature field prediction system according to claim 9, characterized in that: The time series prediction module integrates a batch normalization layer to accelerate the training convergence of the ConvLSTM model.

Images