Soft-pack lithium-ion battery temperature field prediction method and system based on tensor Tucker decomposition

Abstract

The present invention discloses a method and system for predicting the temperature field of a soft-pack lithium-ion battery based on tensor Tucker decomposition. The method first performs spatio-temporal separation on the two-dimensional temperature field data on the battery surface by using tensor Tucker decomposition technology, then establishes a neural network prediction model to estimate the future low-order time characteristics of the nominal system, and finally reconstructs the prediction information of the future temperature field of the battery through the inverse transformation of Tucker decomposition. The present invention adopts a model reduction method based on tensor Tucker decomposition, avoiding the complex calculation problem of directly modeling high-order data one by one, and at the same time considering the two-dimensional spatio-temporal characteristics of the battery surface temperature field, greatly reducing the difficulty of prediction modeling while ensuring the model accuracy. The method of the present invention is simple and easy to implement, is particularly suitable for the temperature field prediction problem of large soft-pack lithium-ion batteries, can better meet the modeling requirements of systems with limited computing resources, and has a wide application prospect.

Description

Technical Field

[0001] The present invention belongs to the technical field of lithium-ion battery thermal management, and relates to a method for predicting the surface temperature field of a soft-pack lithium-ion battery, specifically to a method and system for predicting the temperature field of a soft-pack lithium-ion battery based on tensor Tucker decomposition. Background Art

[0002] As an energy storage and conversion component, the battery plays an important role in industries such as aerospace, electronic devices, and new energy vehicles. Among various batteries, lithium-ion batteries are widely used due to their advantages such as high energy density and long cycle life. The temperature effect is the main factor restricting the performance of lithium-ion batteries. Battery thermal management technology is a new solution based on multiple disciplines and fields such as materials science, electrochemistry, heat transfer, and molecular dynamics, aiming to address the heat dissipation or thermal runaway phenomena that occur when the battery operates under extreme temperature conditions (such as too high or too low), thereby optimizing and enhancing the overall performance and safety of the battery.

[0003] Predicting the surface temperature field of the battery is one of the key technologies in battery thermal management. Traditional prediction methods pre-embed thermocouple probes near the battery tabs to collect battery temperature data. Under different working conditions, according to the influence of temperature on battery performance, combined with the electrochemical characteristics and heat generation mechanism of the battery, the equivalent circuit model is used to simplify the temperature field model into a lumped parameter model. However, due to the decrease in battery consistency caused by environmental factors such as battery cycle aging, the lumped parameter model cannot accurately calculate the actual change of the battery temperature field.

[0004] With the introduction of technologies such as infrared thermal imaging, it is easier to set multiple temperature measurement points on the battery surface, thereby obtaining more comprehensive information on the battery surface temperature field. Currently, there are studies on data-driven battery temperature field prediction methods. However, these studies focus on simplifying the battery thermal system into a one-dimensional system for processing, and these models cannot directly characterize the two-dimensional spatial temperature characteristics of the lithium-ion battery surface, resulting in low prediction efficiency. Summary of the Invention

[0005] The present invention provides a method and system for predicting the temperature field of a soft-pack lithium-ion battery based on tensor Tucker decomposition. The tensor Tucker decomposition technology is used to reduce the order of the two-dimensional temperature field data on the battery surface. Subsequently, a neural network prediction model of the nominal system is established respectively to predict the future low-dimensional eigenvalues, and then the future information of the battery surface temperature field is predicted by reconstructing the spatio-temporal data. The present invention can significantly reduce the complexity of the prediction model and improve the model calculation efficiency while ensuring the prediction accuracy of the model.

[0006] The object of the present invention is achieved through the following technical solutions:

[0007] A temperature field prediction method for soft-pack lithium-ion batteries based on Tucker decomposition, comprising the following steps:

[0008] Step (1): Arrange a sufficient number of sensors on the battery surface. Conduct charge and discharge experiments on the lithium-ion battery for a period of time. Use the sensors to collect the temperature field data on the battery surface, and preprocess the obtained temperature data to organize and obtain the tensor form of the spatio-temporal data of the temperature field;

[0009] Step (2): Perform Tucker decomposition with an initial rank of (1, 1, 1) on the spatio-temporal data of the lithium-ion battery temperature field to obtain the spatial modal decomposition factor matrix, the time modal factor matrix, and the core tensor. Determine whether the reconstruction error between the inverse transformation result of the Tucker decomposition and the original data meets the accuracy requirements of the system; if not, discard the current decomposition result and increase the rank of the tensor decomposition, and repeat the above Tucker decomposition steps until the reconstruction error meets the accuracy requirements. Then, extract the spatial modal factor matrix as the spatial characteristic matrix of the original data and the time modal factor matrix as the low-order time characteristic matrix;

[0010] Step (3): Construct a neural network prediction model based on GRU (Gated Recurrent Unit). The neural network prediction model consists of a recurrent network module and a feature selection module, where:

[0011] The recurrent network module contains 2 GRU layers, and a Hardswish activation function is connected after each GRU layer;

[0012] The feature selection module is composed of a linear layer and an activation function. The linear layer performs weighted summation on the output of the recurrent network module, converts the features extracted by the recurrent network module into the final predicted value, and finally further improves the nonlinear expression ability of the model through the activation function;

[0013] Step (4): Given the current moment's current value, apply the low-order time characteristic matrix obtained by Tucker decomposition and the constructed neural network prediction model, and combine with the external input variable sequence for prediction modeling to predict the low-order time characteristic matrix at a future moment, and perform dimensionality elevation reconstruction on it with the spatial characteristic matrix and the core tensor to obtain the high-order temperature field prediction tensor at the future moment.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] 1. The model establishment process of the present invention is divided into three stages: model reduction, predictive modeling, and upscaling reconstruction. In the model reduction stage, as the rank selected for Tucker decomposition increases, the number of columns in the decomposition factor matrices continuously increases. By examining the reconstruction error, as the rank increases, the decomposition algorithm can better capture the spatial and temporal characteristics of the system, thereby improving the accuracy of the neural network prediction model. The neural network prediction model is trained based on the low-order time characteristics and the external input variable sequence. Finally, the predicted low-order time characteristic matrix is reconstructed through the inverse transformation of Tucker decomposition to obtain the high-dimensional temperature field prediction tensor.

[0016] 2. The present invention adopts a model reduction method based on tensor Tucker decomposition, avoiding the complex calculation problems of directly modeling high-order data one by one, and at the same time considering the two-dimensional spatio-temporal characteristics of the battery surface temperature field, greatly reducing the difficulty of predictive modeling while ensuring the model accuracy.

[0017] 3. The method of the present invention is simple and easy to implement, and is particularly suitable for the temperature field prediction problem of large soft-pack lithium-ion batteries. Both theoretical analysis and experimental results prove that the predictive modeling method of the present invention is a temperature field modeling method with high efficiency, which can better meet the modeling requirements of systems with limited computing resources and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a schematic diagram of tensor Tucker decomposition;

[0019] Figure 2 is the structure diagram of the time series prediction neural network;

[0020] Figure 3 is the computational graph of the gated recurrent unit;

[0021] Figure 4 is the battery system control process;

[0022] Figure 5 is the heat transfer coefficient h(t);

[0023] Figure 6 is the charge and discharge current i(t);

[0024] Figure 7 is the visualization of the original tensor sliced along the time dimension;

[0025] Figure 8 is the visualization of the reconstruction error slices of tensor Tucker decomposition;

[0026] Figure 9 is the visualization of the time mode decomposition factor matrix;

[0027] Figure 10 is the prediction effect diagram of time mode t1;

[0028] Figure 11 It is the prediction effect diagram of the time mode t2;

[0029] Figure 12 It is the prediction effect diagram of the time mode t3;

[0030] Figure 13 It is the visualization of the modeling error slice. Specific implementation manner

[0031] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings, but it is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.

[0032] The present invention provides a soft-pack lithium-ion battery temperature field prediction method based on tensor Tucker decomposition. First, the spatio-temporal separation of the two-dimensional temperature field data on the battery surface is performed by using the tensor Tucker decomposition technology. Subsequently, a neural network prediction model is established to estimate the future low-order time characteristics of the nominal system. Then, the prediction information of the future temperature field of the battery is reconstructed through the inverse transformation of Tucker decomposition. The specific steps are as follows:

[0033] Step (1) Arrange a sufficient number of sensors on the battery surface. During a period of time, charge and discharge experiments are carried out on the lithium-ion battery. The temperature field data on the battery surface is collected by using the sensors, and the obtained temperature data is preprocessed to organize and obtain the tensor form of the temperature field spatio-temporal data. The specific steps are as follows:

[0034] Step (11) During a period of time, charge and discharge experiments are carried out on the lithium-ion battery. Assume that there are sufficient temperature sensors arranged on the battery surface. Without loss of generality, assume that m×n temperature sensors are evenly arranged on the x-axis and y-axis, and the total number of time steps during the charge and discharge process is k. Given the charge and discharge current as Battery surface heat transfer coefficient The temperature data set of m×n temperature sensors on the battery at k moments is collected as T temp (x, y, t), where m is the number of temperature sensors on the x-axis and n is the number of temperature sensors on the y-axis.

[0035] Step (12) Preprocess the temperature data set T temp (x, y, t). The preprocessing includes the following three steps:

[0036] First, check whether there are missing values in the data. If so, fill them with the mean value of the current moment temperature matrix.

[0037] Secondly, check whether there are outliers in the elements of the tensor. Since the temperature field has a hysteresis characteristic, the temperature point data between adjacent moments and adjacent positions will not mutate. Therefore, if the data contains noise data greater than 3 times the standard deviation, it will be replaced with the mean value of the temperature matrix at the current moment.

[0038] Finally, in order to make the Tucker decomposition process and the backpropagation process in the prediction model more stable, the data needs to be normalized by the maximum-minimum method, so that the data range is scaled between 0 and 1, and the tensor form of the temperature data is obtained. The formula for maximum-minimum normalization is:

[0039]

[0040] where max(T temp ) and min(T temp ) represent the maximum and minimum values in the dataset T temp (x, y, t), respectively.

[0041] In step (2), perform Tucker decomposition with an initial rank of (1, 1, 1) on the spatio-temporal data of the lithium-ion battery temperature field to obtain the spatial mode decomposition factor matrix, the time mode factor matrix, and the core tensor. Determine whether the reconstruction error between the inverse transformation result of the Tucker decomposition and the original data meets the accuracy requirements of the system; if not, discard the current decomposition result and increase the rank of the tensor decomposition, and repeat the above Tucker decomposition steps until the reconstruction error meets the accuracy requirements. Then, extract the spatial mode factor matrix as the spatial characteristic matrix of the original data and the time mode factor matrix as the low-order time characteristic matrix. The specific steps are as follows:

[0042] In step (21), according to the tensor Tucker decomposition theory, the rank r (r x ×r y ×r t ) ∈ N + needs to be determined during the decomposition, where r x , r y , and r t are the ranks on the three modes.

[0043] In step (22), start the Tucker decomposition with the initial rank r x = r y = r t = 1, and determine whether the reconstruction error between the inverse transformation result of the Tucker decomposition and the original data meets the accuracy requirements of the system; if not, discard the current decomposition result and increase the rank of the tensor decomposition, and repeat the above Tucker decomposition steps until the reconstruction error meets the accuracy requirements. Then, obtain the final r x , r y and rt , the high-order spatio-temporal tensor Z(x, y, t) can be decomposed into the product of the core tensor and the factorization matrices on each mode. The schematic diagram of Tucker decomposition is as Figure 1 shown. Therefore, the expression of Tucker decomposition for the third-order tensor Z(x, y, t) is:

[0044]

[0045] where represents the approximate tensor obtained after the reconstruction of the original tensor Z(x, y, t) by Tucker decomposition; g is called the core tensor, and each of its elements represents the interaction degree between different components; and represent the factorization matrices of the original tensor Z(x, y, t) in three modes. The factorization matrices are usually orthogonal and can be regarded as the principal components along the corresponding modes.

[0046] In formula (1), the operation of "× n " is the n-mode product of tensors, which is used to represent the product between tensors and matrices. Its mathematical definition is to multiply each slice of the tensor in the n-th mode by the matrix, that is:

[0047]

[0048] In the formula, represents the r t -th component of the time-mode factor matrix T, The operation represents the outer product. The outer product is an operation that combines two vectors into a higher-dimensional tensor. The elements of the tensor outer product are represented as follows:

[0049]

[0050] Step (23) extracts the spatial-mode factor matrix as the spatial feature matrix of the original data and the time-mode factor matrix as the low-order time feature matrix.

[0051] Step (3) constructs a neural network prediction model based on GRU (Gated Recurrent Unit).

[0052] Step (4) Given the current current value, apply the low-order time feature matrix obtained by Tucker decomposition and the constructed neural network prediction model, and combine with the external input variable sequence for prediction modeling to predict the low-order time feature matrix at the future moment, and perform dimensionality-raising reconstruction with the spatial feature matrix and the core tensor to obtain the high-order temperature field prediction tensor at the future moment.

[0053] In the present invention, the process of predictive modeling is to construct a retrospective window of size w at each sampling moment k, and build a dataset based on the true values of the time components from the k-th moment to the (k - w)-th moment before and the external factors of the system to iteratively update the neural network prediction model. The purpose is to enable the model to obtain the predicted temperature field prediction tensor of single-step prediction from the input of the system and the current state of the controlled object. Let the value of the time modal factor matrix T(t, r) at the point (p, γ) be t

[0054] (p), where γ represents the γ-th component in the matrix T(t, r), and p represents the p-th time step, then 1 ≤ p ≤ k and 1 ≤ γ ≤ r. γ (p), where γ represents the γ-th component in the matrix T(t, r), and p represents the p-th time step, then 1 ≤ p ≤ k and 1 ≤ γ ≤ r. t The prediction process considers the charge and discharge current i(t) of the battery system, the battery surface heat transfer coefficient h(t), and the r-th t component of the low-order time characteristic matrix to form the following external input sequence dataset sample

[0055]

[0056] where w is the size of the retrospective window. To establish a time series prediction dataset, let w < p < k, then the feature window constructed at the p-th moment is u(p) = [t γ (p)...t γ (p - w), i(p)...i(p - w), h(p)...h(p - w)]. Through the neural network prediction model modeling, the following functional relationship is obtained:

[0057]

[0058] In the formula, is a set of neural network prediction models obtained through time series prediction, representing the predicted value of the time characteristic matrix component at the next moment using the time characteristic matrix component t γ and the first w historical values in the external input variable sequence. Summarize and combine all r t components of to form the predicted low-order time matrix obtained which is expanded into the following form:

[0059]

[0060] Finally, through the inverse transformation of Tucker, the high-order temperature prediction tensor at the future moment is obtained and is expressed as:

[0061]

[0062] Inverse-normalize the predicted tensor to obtain the high-order temperature field data in the original feature space and the predicted value at the future time of p + 1. Inverse-normalization formula:

[0063]

[0064] In the present invention, the spatio-temporal modeling process can be described as follows:

[0065] 1. Tucker decomposition for spatio-temporal separation:

[0066] In this step, the Tucker decomposition can be written in the following matrix form:

[0067]

[0068] where Z (n) represents the matricization of tensor Z in the n-th mode. For an n-th order tensor with n = 1, 2, 3,..., the matricization of a tensor is also called tensor unfolding or tensor flattening, which is the process of unfolding a high-order tensor along a certain mode into a matrix. For example, Z (1) is the first-mode unfolding of Z. The first dimension of the tensor is kept as the row index of the matrix, and the second and third dimensions form the column matrix of the matrix. The resulting matrix The operation represents the Kronecker product, also known as the direct product or tensor product. For a matrix t with shape t×r and a matrix y with shape y×r the result of the Kronecker product is a matrix with shape ty×r t r y and is defined as:

[0069]

[0070] Since the ultimate goal of the Tucker decomposition is to minimize the reconstruction error between the reconstructed tensor and the original tensor Z, the process of solving the decomposition factors can be written as an optimization problem:

[0071]

[0072] where ||·|| represents the norm of the tensor, similar to the Frobenius norm of a matrix, that is, taking the square root after summing the squares of all elements:

[0073]

[0074] In the above formula, the tensor E is the reconstructed tensor The error representation obtained by subtracting from the original tensor Z, (E) αβγ is the element representation of the tensor E.

[0075] If you want to iteratively solve the factorization matrix using an optimization method, you need to first convert the minimum value optimization problem into a maximum value optimization problem and write the objective function formula (12) in a squared form:

[0076]

[0077] According to the definition formula (2) of Tucker decomposition, the core tensor g satisfies:

[0078] g = Z ×1X T ×2Y T ×3T T (15)

[0079] Substituting the core tensor g into the result of formula (14), we can get:

[0080]

[0081] Since ||Z|| is a constant, the minimum value optimization objective of formula (12) can be redefined as a series of sub-problems containing the following maximization problems:

[0082] max g,X,Y,T ||Z ×1X T ×2Y T ×3T T || (17)

[0083] Furthermore, the above formula can be written in matrix form:

[0084]

[0085] Using the alternating least squares method to solve the above optimization problem, the initial solution of the factorization matrix can be determined by singular value decomposition. We only need to define the factorization factors as the first r left singular vectors of W to solve. Next, update the factor matrix of each mode in turn until convergence. This step is cyclic, that is, in each iteration, update the factor matrix of the first mode, then update the second mode, and so on until the factor matrices of all modes are updated. Finally, the core tensor g is determined by formula (15). This method will converge to a solution where the objective function no longer decreases.

[0086] 2. Low-order time characteristic prediction modeling

[0087] The present invention adopts the Figure 2 neural network prediction model constructed Identify the low-order time characteristics of the temperature identification system. In the Tucker decomposition stage, the decomposition result includes the low-order time characteristic matrix is the r t th column vector in the low-order time characteristic matrix T(t,r). Construct a backtracking window of size w, then the prediction modeling process can be described as: combining the charge and discharge current i(t), the battery surface heat transfer coefficient h(t) and the r t th component of the low-order time characteristic matrix to construct the external input sequence dataset sample u(t), and train a neural network prediction model with a recurrent network module and a feature selection module The prediction process expression is:

[0088]

[0089] Neural network prediction model consists of two modules: a recurrent network module and a feature selection module. Among them, the recurrent network module contains 2 GRU layers, and a Hardswish activation function is connected after each GRU layer. The recurrent network module introduces a gating mechanism through the GRU layer to solve the problems of gradient vanishing and gradient explosion in traditional recurrent neural networks and provide an effective method to capture long-term dependencies. Combining the characteristic of the Hardswish activation function to smooth the gradient enables the low-order model in the present invention to better capture long-term dependencies when processing long sequence data. The calculation formula of the Hardswish function:

[0090]

[0091] The feature selection module consists of a linear layer and an activation function. The features output by the GRU layer have a high dimension, and the network contains multiple hidden layers and a large number of hidden units. Finally, these high-dimensional features need to be mapped to the dimension of single-step prediction. Secondly, the output of the GRU layer contains rich temporal information and features, but this information is often distributed in multiple time steps and hidden layer units. The linear layer can integrate these scattered temporal features by performing a weighted sum on the output of the recurrent network module and provide a comprehensive output. In other words, the linear layer can be regarded as a "decision-making layer" that transforms the features extracted by the recurrent network module into the final prediction value. Finally, the model capacity is further enhanced through the activation function.

[0092] The calculation process of the GRU layer is as Figure 3 shown, which contains two key gates: the update gate λ and the reset gate z. The update gate determines how much old information the model needs to remember and integrate in the current step while receiving new information. The calculation formula of the update gate is:

[0093]

[0094] where x t is the input vector at the t-th time step, i.e., the t-th component of the input sequence and will undergo a linear transformation, i.e., multiply with the weight matrix W (z) . The hidden state h t-1 stores the information of the previous time step t - 1 and will also undergo a linear transformation. We add these two parts of information and feed them into the Sigmoid activation function, so the result is compressed between 0 and 1. The formula of the Sigmoid activation function is:

[0095]

[0096] The reset gate determines how much old information the model needs to ignore and resets the hidden state at the current step. h t-1 and x t first go through a linear transformation, then are added and fed into the Sigmoid activation function to output the activation value. The calculation formula of the reset gate is:

[0097]

[0098] In the use of the reset gate, the new memory content will use the reset gate to store past relevant information. Calculate the Hadamard product of λ t and h t-1 , that is, the element-wise product. Since the reset gate calculated above is a vector consisting of 0s and 1s, it will measure the size of the gated opening. This Hadamard product will determine the information to be retained from the past, the current memory content:

[0099] h t ' = tanh(x t W x +(λ t ⊙h t-1 )W h +b) (24)

[0100] According to the above formula, if z = 0, the new hidden state h t ' only depends on the input x t , that is, the past hidden state will be completely ignored and no past memory will be retained. To calculate the final memory, the update gate λ is used to determine the information to be collected from the current memory content h t ' and the hidden state h t-1 of the previous time step. This process can be expressed as:

[0101] h t = λ t ⊙ht-1 +(1 - λ t ) ⊙ h t ' (25)

[0102] where λ t is the activation result of the update gate, which controls the inflow of information in a gated manner. λ t and the Hadamard product of h t-1 represent the information retained from the previous time step to the final memory, weighting the newly added information, and the sum of this information and the information retained in the memory to the final memory is equal to the content output by the final GRU layer. The GRU layer does not clear previous information over time. It retains relevant information and passes it to the next unit. Therefore, it utilizes all the information and avoids the vanishing gradient problem.

[0103] Since the time series prediction method used in the present invention is single-step prediction with multiple input variables, the input features are n = 2 (n depends on the number of external input variables considered in the prediction modeling), the number of features predicted and output by the GRU layer depends on the size of the hidden layer, and the output of the prediction model in single-step prediction is a single value. Therefore, as shown in Figure 2 the model structure diagram, a feature selection module composed of linear layers needs to be connected after the recurrent network module for feature reduction, so as to obtain the output of single-step prediction and increase the non-linear expression ability of model F.

[0104] In the present invention, the definitions of the above parameters are shown in Table 1:

[0105] Table 1

[0106]

[0107]

[0108] The present invention also provides a soft-pack lithium-ion battery temperature field prediction system based on tensor Tucker decomposition for implementing the above method. The system includes a data acquisition module, a neural network prediction model construction module, a temperature field prediction module, a spatio-temporal coupling module, and a battery charge and discharge control module, where:

[0109] The data acquisition module is used to acquire battery surface temperature field data and preprocess it to obtain a battery temperature field spatio-temporal tensor;

[0110] The neural network prediction model construction module is used to construct a neural network prediction model;

[0111] The temperature field prediction module is used to predict a newly given input current using the established neural network prediction model to obtain a future low-order time characteristic prediction matrix;

[0112] The spatio-temporal coupling module is used to perform tensor Tucker decomposition and inverse transformation on the temperature field data to obtain future temperature field data;

[0113] The battery charge and discharge control module is used to control the battery charge and discharge process.

[0114] Embodiment:

[0115] This embodiment provides a prediction modeling method based on tensor Tucker decomposition - gated recurrent structure. The method includes the following steps:

[0116] Step (1): Collect the surface temperature dataset of the lithium-ion battery, preprocess the data, and organize it into a tensor form.

[0117] Step (2): Perform Tucker decomposition with an initial rank of (1, 1, 1) on the spatio-temporal data of the lithium-ion battery temperature field to obtain the spatial modal decomposition factor matrix, the temporal modal factor matrix, and the core tensor. Determine whether the reconstruction error between the inverse transformation result of the Tucker decomposition and the original data meets the accuracy requirements of the system; if not, discard the current decomposition result and increase the rank of the tensor decomposition, and repeat the above steps until the reconstruction error meets the accuracy requirements. Then, extract two spatial modal factor matrices as the spatial characteristic matrix of the original data, and the temporal modal factor matrix as the low-order temporal characteristic matrix.

[0118] Step (3): Use the low-order temporal characteristic matrix obtained by Tucker decomposition, and combine it with the external input variable sequence to train the neural network prediction model, and then predict the low-order temporal characteristic matrix of the system in the future.

[0119] Step (4): Perform dimensionality-raising reconstruction on the predicted low-order temporal characteristic matrix, the spatial modal factor matrix, and the core tensor to obtain the high-order temperature prediction tensor at future moments. Finally, compare this prediction tensor with the true value tensor of the temperature field to verify the accuracy of the modeling method.

[0120] To prove the effectiveness of the modeling method based on tensor Tucker decomposition combined with gated recurrent structure in this embodiment, taking a large soft-pack lithium-ion battery as an example, study the temperature field control problem during the charge and discharge process under different current conditions in an environment with variable thermal coefficients, and illustrate that this method has the advantages of high efficiency and stability in dealing with such problems.

[0121] The test conditions are described as follows:

[0122] Consider a two-dimensional surface temperature field system of a large square pouch lithium-ion battery simulated by a pseudo-two-dimensional model, with dimensions of 180mm * 240mm. During the experiment, the initial charge of the battery is 0.1C and the initial temperature is 20°C. The finite element analysis method is used to solve the time domain for 3600s. With a period of 1s, a total of 20×20 temperature probes are arranged on the battery surface. The control process of the battery system is as Figure 4 shown. A bidirectional electronic load is connected to the lithium-ion battery, and the surface temperature of the battery is measured by a thermal imager. After compensation, it is input into the data acquisition and processing device for modeling, and finally the current i(t) is fed back to the bidirectional electronic load.

[0123] Charge and discharge experiments are carried out on the battery, and the heat transfer coefficient h(t) on the battery surface is given, as Figure 5 shown, and the charge and discharge current i(t) is given, as Figure 6 shown. The battery is numerically simulated by the finite element method to obtain the two-dimensional temperature field data T temp (x, y, t), which is preprocessed and organized into a third-order tensor data The obtained tensor Z(x, y, t) is sliced along the time dimension, and the visualization result is as Figure 7 shown.

[0124] Result analysis:

[0125] First, given a reconstruction error requirement of less than 0.9°C, the original tensor Z(x, y, t) is decomposed by the Tucker decomposition of tensors. The rank is determined by the method of checking the reconstruction error used in the present invention to be (4, 4, 3), that is, r x = 4, r y = 4, r t = 3, and its reconstruction error is 0.15°C, which exactly meets the accuracy requirement. The visualization of the reconstruction error slices obtained after the inverse transformation and dimension elevation of the Tucker decomposition is as Figure 8 shown. It can be analyzed from Figure 8 that although the Tucker algorithm belongs to a linear algorithm, the reconstruction accuracy still meets the requirements, and the maximum reconstruction error value is 0.15°C. The errors are concentrated at the lower left boundary point in the spatial position and the time node with a sudden increase in temperature in the time change.

[0126] Secondly, the decomposition factor matrix T(t, r) of the Tucker decomposition in the time mode is as Figure 9 shown. By observing the first component of the time decomposition factor matrix, it can be seen that the algorithm captures the overall trend of the temperature change of all probes in the entire space over time. The second and third components show the trends of the temperature change with the input current and the heat convection coefficient change in the spatial domain.

[0127] Then, the three time modal components t1, t2 and t3 are modeled separately to obtain the predicted low-order time matrix The results of time series prediction for the three time components are as follows Figures 10 - 12 As shown in the experimental results, it can be clearly seen that the model designed by the present invention The time modal factor matrix obtained by Tucker decomposition was effectively predicted. The red dotted line in the figure represents the prediction result of the training set, the blue dotted line represents the prediction result of the test set, and the black solid line represents the true value. Judging from the performance of the training set, the red dotted line and the black solid line are basically consistent, indicating that the model effectively captured the main features of the time series during the training process and successfully learned the dynamic changes of the time modal factor matrix. In the prediction results of the test set, although the blue dotted line has certain deviations and fluctuations from the true value (black solid line) in some time periods, especially in some intervals with drastic short-term changes, the overall trend is still relatively consistent. This shows that the model Not only does it perform well on the training data, it also demonstrates good generalization capabilities on the test set.

[0128] Although there are some fluctuations on the test set, the model It can still capture the long-term trend of the data well, especially on a larger time scale, the predicted value of the model maintains a high degree of consistency with the true value. This is an important advantage of the prediction model structure in this invention, which can effectively capture long-term dependencies through the gating mechanism and show good robustness when dealing with possible noise in the time series. In this experiment, the prediction model The reason why it can achieve good performance is mainly due to the following reasons: First, the present invention regulates the flow of information through its gating mechanism, which can effectively avoid the problem of gradient disappearance, thereby maintaining the memory of information for longer time steps, which is particularly important when processing spatiotemporal data with long-term dependencies; Second, the present invention uses the Bayesian optimization method to systematically tune the hyperparameters to ensure that the model can be trained under the optimal combination of various hyperparameters. The Bayesian hyperparameter optimizer searches for the key parameters of the model, such as the learning rate, hidden layer dimension, and regularization coefficient, and makes fine adjustments, thereby effectively improving the convergence speed of the model and the final prediction performance; Third, in the model The Hardswish activation function used in [1] is a new type of activation function that has been widely used in recent years. It not only has the nonlinear advantages of the ReLU activation function, but also has lower computational cost and better smoothing properties. This function can provide a more stable gradient flow during model training, making the model more robust when learning complex data.

[0129] Finally, the three models Time component of the forecast and are combined into a predicted low-order time matrix and an outer product is performed with the spatial decomposition factor matrices X, Y, and the core tensor g obtained from the previous Tucker decomposition to obtain the predicted high-order data Define the spatio-temporal error function ζ, RMSE (Root Mean Square Error), and MER (Mean Error Rate) as follows:

[0130]

[0131] MER is the ratio of the maximum absolute error between the predicted tensor and the original tensor to the numerical range of the original tensor. This metric particularly focuses on the performance of the model in the worst-case scenario. In this embodiment, the MER between the algorithm-predicted tensor and the true-value tensor is only 4.90031%. It is proved that even considering the data points with the greatest modeling difficulty, the model can still make good predictions. In the battery temperature field prediction task, the prediction results do not show phenomena that violate the hysteresis characteristics, such as sudden changes in temperature distribution. RMSE is one of the commonly used metrics for evaluating the accuracy of a prediction model. It measures the degree of deviation between the predicted value and the true value. In this embodiment the root mean square error between and Z(x, y, t) is 0.05823. It is proved that the prediction error at each point is very small and the overall modeling accuracy is high.

[0132] Model prediction tensor The slice visualization of the error tensor ζ(x, y, t) obtained by subtracting the true-value tensor Z(x, y, t) is as Figure 13 shown. By observing Figure 13 the errors in, the maximum error is only 0.8 °C, and the running time of the complete algorithm is only 98 s, which exactly meets the design intention of the modeling method. Both theoretical analysis and experimental results prove that the method of the present invention has very high computational efficiency and takes into account good prediction accuracy, and can better meet the requirements of online modeling of the spatial distribution process in a system with limited computing resources.

Claims

1. A method for predicting the temperature field of a soft-pack lithium-ion battery based on tensor Tucker decomposition, characterized in that The method includes the following steps: Step (1): Arrange a sufficient number of sensors on the battery surface. Conduct charge and discharge experiments on the lithium-ion battery for a period of time. Use the sensors to collect the temperature field data on the battery surface, and preprocess the obtained temperature data to organize and obtain the tensor form of the spatio-temporal data of the temperature field; Step (2): Perform Tucker decomposition with an initial rank of (1, 1, 1) on the spatio-temporal data of the lithium-ion battery temperature field to obtain the spatial modal decomposition factor matrix, the time modal factor matrix, and the core tensor. Determine whether the reconstruction error between the inverse transformation result of the Tucker decomposition and the original data meets the accuracy requirements of the system; if not, discard the current decomposition result and increase the rank of the tensor decomposition, and repeat the above Tucker decomposition steps until the reconstruction error meets the accuracy requirements. Then, extract the spatial modal factor matrix as the spatial characteristic matrix of the original data and the time modal factor matrix as the low-order time characteristic matrix; Step (3): Construct a neural network prediction model based on GRU. The neural network prediction model consists of a recurrent network module and a feature selection module, where: The recurrent network module contains 2 GRU layers, and a Hardswish activation function is connected after each GRU layer; The feature selection module consists of a linear layer and an activation function. The linear layer performs weighted summation on the output of the recurrent network module, converts the features extracted by the recurrent network module into the final predicted value, and finally further improves the nonlinear expression ability of the model through the activation function; Step (4): Given the current current value, apply the low-order time characteristic matrix obtained by Tucker decomposition and the constructed neural network prediction model, and combine with the external input variable sequence for prediction modeling to predict the low-order time characteristic matrix at a future time, and perform dimensionality elevation reconstruction with the spatial characteristic matrix and the core tensor to obtain the high-order temperature field prediction tensor at a future time.

2. The method for predicting the temperature field of a soft-pack lithium-ion battery based on tensor Tucker decomposition according to claim 1, wherein The specific steps of step (1) are as follows: Step (11) sets m×n temperature sensors evenly arranged on the x-axis and y-axis. The total number of time steps in the charge and discharge process is k, and the given charge and discharge current is Battery surface heat transfer coefficient The temperature dataset of the m×n temperature sensors of the battery at k moments is T temp (x, y, t), where m is the number of temperature sensors on the x-axis and n is the number of temperature sensors on the y-axis; Step (12) preprocesses the temperature dataset T temp (x, y, t): First, check whether there are missing values in the data. If so, fill them with the mean value of the temperature matrix at the current time; Second, check whether there are outliers in the elements of the tensor. If it is determined that there is noise data greater than 3 times the standard deviation in the data, replace it with the mean value of the temperature matrix at the current time; Finally, perform min-max normalization on the data to scale the data range between 0 and 1, obtaining the tensor form of the temperature data 3. The method for predicting the temperature field of a soft-pack lithium-ion battery based on tensor Tucker decomposition according to claim 1, wherein The specific steps of step (2) are as follows: Step (21) According to the tensor Tucker decomposition theory, when decomposing, it is necessary to determine the rank r (r x ×r y ×r t ) ∈ N + , where r x , r y and r t are the ranks on three modes; Step (22) starts the Tucker decomposition from the initial rank r x = r y = r t = 1, and determines whether the reconstruction error between the inverse transformation result of the Tucker decomposition and the original data meets the accuracy requirements of the system; if not, discard the current decomposition result and increase the rank of the tensor decomposition, and repeat the above Tucker decomposition steps until the reconstruction error meets the accuracy requirements, then obtain the final r x , r y and r t , then Z(x, y, t) is decomposed into the product of the core tensor and the decomposition factor matrices on each mode; Step (23): Extract the spatial modal factor matrix as the spatial characteristic matrix of the original data and the time modal factor matrix as the low-order time characteristic matrix.

4. The method for predicting the temperature field of a soft-pack lithium-ion battery based on tensor Tucker decomposition according to claim 3, wherein In step (22), the expression of the Tucker decomposition of Z(x, y, t) is: Among them, represents the approximate tensor obtained after the Tucker decomposition and reconstruction of the original tensor Z(x, y, t); and represent the factor matrices of the original tensor Z(x, y, t) in three modes; "× n " operation is the n-mode product of tensors, used to represent the product between tensors and matrices. Its mathematical definition is to multiply each slice of the tensor in the n-th mode by the matrix, that is: where t rt represents the r t -th component of the time mode factor matrix T, The operation represents the outer product, and the elements of the tensor outer product are expressed as follows:

5. The method for predicting the temperature field of a soft-pack lithium-ion battery based on tensor Tucker decomposition according to claim 1, wherein The specific steps of step (4) are as follows: Step (41) sets the value of the time-modal factor matrix T(t, r) at the point (p, γ) to be t γ (p), where γ represents the γ-th component in the T(t, r) matrix, and p represents the p-th time step, so 1 ≤ p ≤ k and 1 ≤ γ ≤ r t ; Step (42) considers the charge and discharge current i(t) of the battery system, the battery surface heat transfer coefficient h(t), and the r-th t component to form the following external input sequence data set sample where w is the size of the backtracking window; Step (43) establishes a time series prediction data set. Let w < p < k, then the feature window constructed at time p is u(p) = [t γ (p)...t γ (p - w), i(p)...i(p - w), h(p)...h(p - w)]; Step (44): Model through the neural network prediction model to obtain the following modeling function relationship: In the formula, is a neural network prediction model, representing the use of the time feature matrix component t γ to predict the predicted value of the time feature matrix component at the next moment using the first w historical values in the external input variable sequence Step (45) combines all the prediction sequences of r t components and aggregates them into a predicted low-order time matrix obtained which is expanded into the following form: Step (46) performs an inverse Tucker transformation for dimensionality-increasing reconstruction to obtain a high-order temperature prediction tensor at a future time which is expressed as: Step (47) performs inverse normalization on the prediction tensor to obtain the high-order temperature field data in the original feature space which is the predicted value at the future p+1 moment.

6. A soft-pack lithium-ion battery temperature field prediction system based on tensor Tucker decomposition for implementing the method according to any one of claims 1-5, characterized in that The system includes a data acquisition module, a neural network prediction model construction module, a temperature field prediction module, a spatio-temporal coupling module, and a battery charge and discharge control module, where: The data acquisition module is used to acquire the battery surface temperature field data and preprocess it to obtain the battery temperature field spatio-temporal tensor; The neural network prediction model construction module is used to construct a neural network prediction model; The temperature field prediction module is used to predict the newly given input current using the established neural network prediction model to obtain the future low-order time characteristic prediction matrix; The spatio-temporal coupling module is used to perform tensor Tucker decomposition and inverse transformation of the temperature field data to obtain the future temperature field data; The battery charge and discharge control module is used to control the battery charge and discharge process.

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