Battery thermal runaway pressure prediction method, device and system and storage medium

By extracting the pressure characteristics during the operation of the lithium battery and using the LSTM neural network model for prediction, the accuracy of the thermal runaway prediction of lithium battery is solved, and the safety of the battery and the performance of the management system are improved.

CN119830174APending Publication Date: 2025-04-15CHONGQING UNIV +1
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Patent Information

Application Number
CN202411887966.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-12-20
Publication Date
2025-04-15

AI Technical Summary

Technical Problem

The prior art is difficult to accurately predict the possible thermal runaway phenomenon caused by lithium batteries under extreme conditions, resulting in an increase in the risk of safety accidents.

Method used

By obtaining the pressure data of the lithium battery during operation, key pressure characteristics reflecting the battery state are extracted, and inputting them into the pre-trained LSTM deep neural network model to predict the future pressure changes of the battery.

Benefits of technology

Accurate prediction of the thermal runaway pressure of lithium batteries is achieved, time to deal with thermal runaway, and improved battery safety and management system performance.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention discloses a battery thermal runaway pressure prediction method, device and system, and a storage medium. The method comprises the following steps: S1, acquiring pressure data of a to-be-tested battery during operation; s2, extracting key pressure characteristics reflecting the state of the to-be-tested battery according to the pressure data of the to-be-tested battery during operation; and S3, inputting the key pressure characteristics into a pre-trained battery thermal runaway pressure prediction model, and predicting the future pressure change condition of the to-be-detected battery. By adopting the technical scheme provided by the invention, accurate prediction of the thermal runaway pressure of the battery can be effectively realized, prevention measures can be taken in time, and the safety and reliability of a battery system are guaranteed.
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Description

Technical Field

[0001] The present invention belongs to the technical field of battery thermal runaway, and in particular relates to a battery thermal runaway pressure prediction method and device, system, and storage medium. Background Art

[0002] With the rapid development of electric vehicles and portable electronic devices, lithium batteries have become one of the main power sources due to their high energy density, long life and lightweight. However, the safety issues of lithium batteries are becoming increasingly prominent, especially under extreme conditions (such as overcharging, short circuit, high temperature, etc.), which may cause thermal runaway, which may lead to serious safety accidents such as fire or explosion. Therefore, the development of effective lithium battery thermal runaway prediction technology is of great significance to ensure user safety and improve the performance of battery management systems.

[0003] Traditional lithium battery safety management methods mainly rely on real-time monitoring of parameters such as temperature, voltage and current, and triggering protection mechanisms through preset thresholds. However, this method has the problem of response lag and it is difficult to accurately predict the occurrence of thermal runaway. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a battery thermal runaway pressure prediction method and device, system, and storage medium, which can monitor and predict battery pressure in real time, effectively increase the time to deal with thermal runaway, and improve battery safety.

[0005] To achieve the above object, the present invention adopts the following technical solution:

[0006] A method for predicting thermal runaway pressure of a battery, comprising:

[0007] Step S1, obtaining pressure data of the battery to be tested during operation;

[0008] Step S2, extracting key pressure features reflecting the state of the battery to be tested according to the pressure data of the battery to be tested during operation;

[0009] Step S3: input the key pressure characteristics into a pre-trained battery thermal runaway pressure prediction model to predict future pressure changes of the battery to be tested.

[0010] Preferably, in step S2, key pressure features reflecting the state of the battery to be tested are extracted based on the pressure values ​​of the battery to be tested at a certain moment or multiple moments during the thermal runaway experiment in the pressure data of the battery to be tested during operation.

[0011] Preferably, the method further includes: training an LSTM deep neural network model based on pressure data of sample batteries in thermal runaway experiments to obtain a battery thermal runaway pressure prediction model, wherein the pressure data of the thermal runaway experiment is pressure data measured each time the sample battery is heated to thermal runaway at high temperature or overcharged to thermal runaway.

[0012] The present invention also provides a battery thermal runaway pressure prediction device, comprising:

[0013] An acquisition module, used to acquire pressure data of the battery under test during operation;

[0014] An extraction module, used for extracting key pressure features reflecting the state of the battery under test according to the pressure data of the battery under test during operation;

[0015] The prediction module is used to input key pressure characteristics into a pre-trained battery thermal runaway pressure prediction model to predict future pressure changes of the battery to be tested.

[0016] Preferably, the extraction module extracts key pressure features reflecting the state of the battery under test based on the pressure values ​​of the battery under test at a certain moment or multiple moments during the thermal runaway experiment in the pressure data of the battery under test during operation.

[0017] Preferably, it also includes: a training module for training an LSTM deep neural network model based on the pressure data of the sample battery in the thermal runaway experiment to obtain a battery thermal runaway pressure prediction model, wherein the pressure data of the thermal runaway experiment is the pressure data measured each time the sample battery is heated to thermal runaway at high temperature or overcharged to thermal runaway.

[0018] An embodiment of the present invention further provides a battery thermal runaway pressure prediction system, comprising: a memory and a processor, wherein the memory stores a computer program executed by the processor, and the computer program executes a battery thermal runaway pressure prediction method when executed by the processor.

[0019] An embodiment of the present invention further provides a storage medium, on which a computer program is stored, and the computer program executes a method for predicting thermal runaway pressure of a battery when running.

[0020] The present invention obtains the pressure data of the battery to be tested during operation; processes the pressure data during operation to extract key pressure features that can reflect the state of the battery to be tested; inputs the extracted pressure features into a pre-trained battery thermal runaway pressure prediction model to predict the future pressure changes of the battery to be tested; wherein the battery thermal runaway pressure prediction model is obtained through neural network learning, and can establish a mapping relationship between battery pressure features and future pressure. The present invention can effectively realize the accurate prediction of battery thermal runaway pressure, which helps to take preventive measures in time and ensure the safety and reliability of the battery system. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0022] Figure 1 This is a flow chart of a method for predicting thermal runaway pressure of a battery according to an embodiment of the present invention;

[0023] Figure 2 This is a flow chart of the battery thermal runaway pressure prediction model training according to an embodiment of the present invention;

[0024] Figure 3 Schematic diagram of the LSTM model structure in an embodiment of the present invention;

[0025] Figure 4 Schematic diagram of the neural network model structure in an embodiment of the present invention;

[0026] Figure 5 This is an example flow chart of a data-driven battery thermal runaway pressure prediction method in an embodiment of the present invention. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0028] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0029] Embodiment 1:

[0030] like Figure 1 As shown, an embodiment of the present invention provides a data-driven battery thermal runaway pressure prediction method for pressure changes of lithium batteries, and the lithium battery can be configured in a car or an electric car, or other devices. The execution subject of the method can be an electronic device, such as a computer, a tablet computer, an electronic device carrying a battery, etc. The method includes the following steps:

[0031] Step 101: Obtaining pressure data of the battery under test during operation

[0032] If the electronic device executing the method is equipped with an interactive display screen, the process of obtaining the pressure data of the battery to be tested during operation can be operated by relevant staff. During the operation of the battery, the staff can monitor the pressure state of the battery, input and submit the corresponding pressure data through the interactive display screen of the electronic device, so that the electronic device can obtain and record the pressure data.

[0033] If the pressure data of the battery is stored in the server, the electronic device can send a request to the server to obtain the historical pressure data of the battery under test during operation. Then, the electronic device will receive the corresponding pressure data returned by the server according to the request, thereby obtaining the required information for subsequent analysis.

[0034] It should be noted that the battery to be tested may be a battery in an actual vehicle, and the pressure data of the battery to be tested during operation may be historical pressure data of the battery in the actual vehicle during operation.

[0035] In addition, the pressure data of the battery under test during operation can be obtained by periodically sampling the pressure value before the current time at a preset time interval during operation, thereby obtaining pressure data at multiple times. For example, if the current time is 15:45:30 and the sampling interval is 5 seconds, this step will sequentially obtain the pressure values ​​at 15:45:30, 15:45:25, 15:45:20, 15:45:15, 15:45:10, etc.

[0036] Step 102: Process the pressure data during operation to extract key pressure features that can reflect the state of the battery to be tested.

[0037] In the embodiment of the present invention, step 102 includes the following steps: extracting pressure characteristic values ​​of the battery to be tested according to pressure values ​​of the battery to be tested at a certain moment or multiple moments during operation, and using the pressure characteristic values ​​as pressure characteristic data.

[0038] For the operation process of the battery, the pressure characteristic value is the pressure value of the battery under test at one or more moments during the operation process. The pressure characteristic value can be expressed by formula (1):

[0039] X=(x 1 , x 2 , …, x N ) (1)

[0040] where x t is the battery pressure value at time t, and N is the total number of input times.

[0041] Step 103: input the extracted pressure characteristics into a pre-trained battery thermal runaway pressure prediction model to predict future pressure changes of the battery to be tested; wherein the battery thermal runaway pressure prediction model is obtained through neural network learning, and can establish a mapping relationship between the battery pressure characteristics and future pressure.

[0042] In an embodiment of the present invention, the battery thermal runaway pressure prediction model can be obtained by training based on the LSTM model, or it can be obtained by training using other neural network models based on actual needs, and this application does not limit this.

[0043] The LSTM deep neural network model is trained based on the pressure characteristic data of the battery to be tested in the thermal runaway experiment, so that the neural network model can learn the mapping function between historical pressure characteristics and future pressure characteristics, thereby establishing the correlation between the two, and finally obtaining a trained battery thermal runaway pressure prediction model.

[0044] According to the data-driven battery thermal runaway pressure prediction method of the embodiment of the present invention, the pressure data of the battery to be tested during operation is obtained, and the key pressure characteristics that can reflect the state of the battery to be tested are extracted, and the pressure characteristic data is input into the pre-trained battery thermal runaway pressure prediction model to predict the future pressure changes of the battery to be tested. This method can effectively realize the accurate prediction of battery thermal runaway pressure, which helps to take preventive measures in time to ensure the safety and reliability of the battery system.

[0045] As an implementation method of the embodiment of the present invention, Figure 2 As shown, the training of the battery thermal runaway pressure prediction model includes the following steps:

[0046] Step 201: Establish LSTM as a deep neural network model

[0047] In the embodiment of the present invention, Figure 3 As shown in the figure, the LSTM model consists of a cell state, an input gate, a forget gate, and an output gate. Its main principles are as follows:

[0048] Forget gate: The forget gate determines which information needs to be removed from the cell state. The forget gate calculates a value between 0 and 1 through a sigmoid activation function, indicating whether the existing information of each part needs to be retained. By calculating:

[0049] f t =σ(W f ·[h t-1 , x t ]+b f ) (2)

[0050] where f t is the output of the forget gate, W f and b f are the weight matrix and bias term, respectively, h t-1 is the hidden state at the previous moment, x t is the input at the current moment.

[0051] Input gate: Next, the input gate determines what new information will be added to the cell state. At the same time, the candidate cell states are calculated

[0052] i t =σ(W i ·[h t-1 , x t ]+b i ) (3)

[0053]

[0054] Among them, i t is the output of the input gate, is the candidate cell state, W i 、b i , W C and b C are the corresponding weight matrix and bias term respectively.

[0055] Update cell state: Combine the results of the forget gate and the input gate to update the cell state C t :

[0056]

[0057] where ⊙ represents element-wise multiplication.

[0058] Output Gate: Finally, the output gate determines what information in the cell state is output:

[0059] o t =σ(W o ·[h t-1 , x t ]+b o ) (6)

[0060] h t =o t ⊙tanh(C t) (7)

[0061] Among them, t is the output of the output gate, h t is the hidden state at the current moment, W o and b o are the weight matrix and bias term respectively.

[0062] like Figure 4 As shown in the figure, on the basis of a single-layer LSTM model, the same LSTM model is added for superposition, so that the output of the first-layer LSTM model is used as the input of the second-layer LSTM model, and so on, until the output of the n-th layer LSTM is used as the overall output of the model. Based on the output of the n-th layer LSTM, the original input sequence is introduced, and the original input sequence is added element by element with the output of the n-th layer through residual connection. This multi-layer neural network model can be expressed as:

[0063]

[0064] The multi-layer LSTM model can learn more complex feature representations through multi-layer nonlinear transformations. Each layer of LSTM can extract abstract features at different levels, thereby improving the model's expressiveness. Deep networks help the model maintain more stable memory and information transfer when processing long sequence data. Multi-layer LSTM models can achieve higher prediction accuracy than single-layer LSTM models. This is because multi-layer models can better fit complex nonlinear relationships and time dependencies. By directly passing input information to the subsequent layers, residual connections provide a shortcut path that allows gradients to flow to shallow layers more easily, which effectively enhances the model's training capabilities. Even if the features learned by some layers are not accurate enough, the existence of residual paths can make the model rely on the original information of the input, thereby improving robustness. Therefore, a global residual connection is added to the output and input sequences of the top-level LSTM to simplify the learning process.

[0065] The parameters of the LSTM deep neural network model are defined, including input feature dimension, output dimension, number of hidden layers, number of neurons, learning rate, dropout rate, and number of iterations, as shown in Table 1.

[0066] Table 1

[0067]

[0068]

[0069] Step 202, constructing training data based on the pressure data of the sample battery in the thermal runaway experiment; wherein the pressure data of the thermal runaway experiment includes: pressure data measured each time the sample battery is heated to thermal runaway at high temperature or overcharged to thermal runaway.

[0070] It should be noted that the sample battery can be the same battery as the battery to be tested, or can be the same type of battery as the battery to be tested, but not the same battery.

[0071] In an embodiment of the present invention, the specific implementation process of step 202 includes: obtaining the pressure characteristic value of the battery to be tested according to the pressure data of the thermal runaway experiment of the sample battery, and using the pressure characteristic value as the pressure characteristic data; obtaining the historical pressure characteristic data and future pressure characteristic data corresponding to each experiment of the sample battery under the thermal runaway experimental conditions; using the experimental historical pressure characteristic data and future pressure data as the training data, wherein the future pressure data is the label value.

[0072] Under experimental conditions, the pressure of the sample battery is available, so the pressure characteristic data can be used as training data to train the constructed LSTM deep learning model, so that the neural network model can learn the mapping relationship between historical pressure characteristics and future pressure characteristics.

[0073] In addition, based on the thermal runaway experimental pressure data, the specific implementation process of extracting the experimental pressure characteristic data can be consistent with the implementation method in the above embodiment, and will not be repeated here.

[0074] Step 203: Train the LSTM deep neural network model based on the training data to obtain a trained LSTM model, and use the model as a battery thermal runaway pressure prediction model.

[0075] In an embodiment of the present invention, in order to unify the dimension of the data and improve the training efficiency, the training data may be normalized, and then the LSTM deep neural network model may be trained based on the normalized data.

[0076] During model training, if the learning rate is too large, the model parameters will jump over the global optimal point during optimization, causing optimization oscillation or even failure to converge. If the learning rate is too small, the model will converge too slowly, increase training time, or even fall into a local optimum. Therefore, dynamic learning rate technology is used to decide whether to adjust the learning rate based on the performance of the model on the validation set (such as loss value, accuracy, and other indicators) or the progress of the training phase. At the same time, by monitoring the performance of the validation set, the training can be terminated in advance when the model performance is no longer improved, preventing the model from overfitting the training set, avoiding redundant training iterations, and reducing time and computing costs.

[0077] In LSTM, the gradient in the back propagation process accumulates continuously, resulting in numerical instability. Gradient clipping may cause gradient explosion by limiting the back propagation process, affecting the model training effect. Therefore, gradient clipping is used to prevent gradient explosion by limiting the size of the gradient in the back propagation process.

[0078] In order to evaluate the training effect and prediction accuracy of the model, the thermal runaway experimental pressure characteristic data can be divided into a training set and a test set. For example, the training set and the test set can be divided in a ratio of 7:3 or 8:2.

[0079] The training set can be input into the LSTM deep neural network model, and the mean square error loss function (MeanSquared Error Loss) and Adam (Adaptive Moment Estimation) optimization algorithm are used to better adapt to the training data and improve the accuracy and generalization ability of the model in sequence tasks. The calculation process is shown in formula (9).

[0080]

[0081] Among them, y i represents the real data at the i-th moment in the model, is the predicted value at the i-th moment in the model.

[0082] Adaptive moment estimation (Adam) optimizer and mean square error loss function are used to update model parameters, so that the model can more accurately predict pressure changes at subsequent moments. Through back propagation and optimization update, the input, output, learning rate, number of iterations and other hyperparameters of the LSTM deep learning model are adjusted, and network training is repeated until the model achieves the ideal prediction accuracy, and finally a trained LSTM model is obtained.

[0083] In order to clearly express the technical solution of this application, Figure 5 Taking the sample battery and the battery to be tested as an example, the sample battery and the battery to be tested are the same type of battery, and the data-driven battery thermal runaway pressure prediction method is introduced in the form of an example.

[0084] (1) Obtain experimental pressure data under thermal runaway experimental conditions;

[0085] (2) Process the experimental pressure and extract key pressure characteristic data;

[0086] (3) Divide the key pressure feature data into a training set and a test set, and train the LSTM deep neural network model to obtain a battery thermal runaway pressure prediction model;

[0087] (4) During the application process, obtain the pressure data of the battery under test during operation;

[0088] (5) Processing the pressure data of the battery under test during operation and extracting key pressure characteristic data;

[0089] (6) The key pressure characteristics of the battery to be tested are used as the input of the LSTM deep neural network model to predict the future pressure of the battery.

[0090] According to the data-driven battery thermal runaway pressure prediction method of the embodiment of the present invention, the training data is first determined through experimental pressure data, and then the LSTM deep neural network model is trained to obtain a battery thermal runaway pressure prediction model. This method uses deep learning technology to effectively predict the future thermal runaway pressure changes of batteries in actual application scenarios, which helps to improve the accuracy and timeliness of battery warnings, thereby providing a solid guarantee for the safe and stable operation of the battery system.

[0091] The present invention monitors and predicts battery pressure in real time, which can effectively increase the time to deal with thermal runaway and improve battery safety. The following steps are taken: First, the pressure data of the battery during operation is collected in real time by a pressure sensor installed on the battery. These data provide an important reference for identifying potential risks and predicting future pressure change trends. Next, according to the pressure value of the battery to be tested at a certain moment or multiple moments during the thermal runaway experiment, the key pressure features that can reflect the state of the battery to be tested are extracted. Among them, the key pressure features may include the current pressure value, the pressure change rate, the pressure peak, the minimum pressure, the average pressure, etc. These extracted pressure feature data will be used as the input of the thermal runaway pressure prediction model to predict the future pressure changes of the battery. Then, the extracted pressure feature data is input into the preset battery thermal runaway pressure prediction model. The prediction model is constructed as a battery thermal runaway pressure neural network model based on deep learning. Through training a large amount of historical data, the model has learned to identify the laws and characteristics of battery pressure changes, so the future pressure of the battery can be predicted based on the input pressure feature data. Through the present invention, the future pressure value of the battery to be tested can be predicted, and the future pressure change trend of the battery can be identified in advance, so as to take protective measures in time to avoid pressure anomalies or thermal runaway problems. The data-driven battery thermal runaway pressure model has a high degree of prediction accuracy and real-time performance, which can effectively identify potential safety risks, significantly improve the battery's pressure warning capability, and ensure its safe operation. In summary, by collecting and analyzing the battery's historical pressure data, extracting key pressure features, and using the thermal runaway pressure prediction model built with deep learning for analysis, accurate prediction of the battery's thermal runaway pressure can be achieved, which helps the battery operate safely and stably.

[0092] Embodiment 2:

[0093] The embodiment of the present invention further provides a battery thermal runaway pressure prediction device, comprising:

[0094] An acquisition module, used to acquire pressure data of the battery under test during operation;

[0095] An extraction module, used for extracting key pressure features reflecting the state of the battery under test according to the pressure data of the battery under test during operation;

[0096] The prediction module is used to input key pressure characteristics into a pre-trained battery thermal runaway pressure prediction model to predict future pressure changes of the battery to be tested.

[0097] As an implementation of an embodiment of the present invention, the extraction module extracts key pressure features reflecting the state of the battery under test based on the pressure values ​​of the battery under test at a certain moment or multiple moments during the thermal runaway experiment in the pressure data of the battery under test during operation.

[0098] As an implementation mode of an embodiment of the present invention, it also includes: a training module, which is used to train an LSTM deep neural network model according to the pressure data of the sample battery in the thermal runaway experiment to obtain a battery thermal runaway pressure prediction model, wherein the pressure data of the thermal runaway experiment is the pressure data measured each time the sample battery is heated to thermal runaway at high temperature or overcharged to thermal runaway.

[0099] Embodiment 3:

[0100] An embodiment of the present invention further provides a battery thermal runaway pressure prediction system, comprising: a memory and a processor, wherein the memory stores a computer program executed by the processor, and the computer program executes a battery thermal runaway pressure prediction method when executed by the processor.

[0101] Embodiment 4:

[0102] An embodiment of the present invention further provides a storage medium, on which a computer program is stored, and the computer program executes a method for predicting thermal runaway pressure of a battery when running.

[0103] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for predicting battery thermal runaway pressure, characterized in that: include: Step S1, obtaining pressure data of the battery to be tested during operation; Step S2, extracting key pressure features reflecting the state of the battery to be tested according to the pressure data of the battery to be tested during operation; Step S3: input the key pressure characteristics into a pre-trained battery thermal runaway pressure prediction model to predict future pressure changes of the battery to be tested.

2. The battery thermal runaway pressure prediction method according to claim 1, characterized in that: In step S2, key pressure features reflecting the state of the battery to be tested are extracted based on the pressure values ​​of the battery to be tested at a certain moment or multiple moments during the thermal runaway experiment in the pressure data of the battery to be tested during operation.

3. The battery thermal runaway pressure prediction method according to claim 2, characterized in that: Also includes: The LSTM deep neural network model is trained according to the pressure data of the sample battery in the thermal runaway experiment to obtain the battery thermal runaway pressure prediction model, wherein the pressure data of the thermal runaway experiment is the pressure data measured each time the sample battery is heated to thermal runaway at high temperature or overcharged to thermal runaway.

4. A battery thermal runaway pressure prediction device, characterized in that: include: An acquisition module, used to acquire pressure data of the battery under test during operation; An extraction module, used to extract key pressure features reflecting the state of the battery under test according to the pressure data of the battery under test during operation; The prediction module is used to input key pressure characteristics into a pre-trained battery thermal runaway pressure prediction model to predict future pressure changes of the battery to be tested.

5. The battery thermal runaway pressure prediction device according to claim 4, characterized in that: The extraction module extracts key pressure features reflecting the state of the battery under test according to the pressure values ​​of the battery under test at a certain moment or multiple moments during the thermal runaway experiment in the pressure data of the battery under test during operation.

6. The battery thermal runaway pressure prediction device according to claim 5, characterized in that: Also includes: The training module is used to train the LSTM deep neural network model according to the pressure data of the sample battery in the thermal runaway experiment to obtain the battery thermal runaway pressure prediction model, wherein the pressure data of the thermal runaway experiment is the pressure data measured each time the sample battery is heated to thermal runaway at high temperature or overcharged to thermal runaway.

7. A battery thermal runaway pressure prediction system, characterized in that: include: A memory and a processor, wherein the memory stores a computer program executed by the processor, and when the computer program is executed by the processor, the battery thermal runaway pressure prediction method according to any one of claims 1 to 3 is executed.

8. A storage medium, characterized in that: The storage medium stores a computer program, which, when running, executes the battery thermal runaway pressure prediction method according to any one of claims 1 to 3.