Lithium ion battery internal short circuit fault diagnosis method based on model and data fusion

Abstract

The application discloses a lithium ion battery internal short circuit fault diagnosis method based on model and data fusion, and belongs to the technical field of lithium ion battery fault diagnosis. The method collects current, single-end voltage and average temperature data of the battery under normal working conditions and internal short circuit working conditions; an electro-thermal coupling model is established to perform state estimation, a residual sequence is generated according to a measurement value and a predicted value, multi-scale electro-thermal coupling features are extracted, and a standardized feature matrix is constructed; a random forest classification model is used to classify the battery state, and internal short circuit fault diagnosis is realized. The method provides mechanism constraints through physical modeling, combines multi-scale feature analysis and machine learning classification, realizes high-precision identification and diagnosis of the internal short circuit fault, improves the diagnosis reliability and engineering practicability, and can provide technical support for lithium ion battery safety monitoring and fault early warning.

Description

Technical Field

[0001] This invention relates to the field of lithium-ion battery fault diagnosis technology, and in particular to a method for diagnosing internal short-circuit faults in lithium-ion batteries based on model and data fusion. Background Technology

[0002] Lithium-ion batteries, with their high energy density, long cycle life, and excellent charge / discharge rate performance, are widely used in key fields such as new energy and energy storage power stations. However, during the long-term service life of lithium-ion batteries, internal short-circuit faults and other safety hazards are the core bottlenecks restricting their large-scale application. Internal short-circuit faults originate from process defects in the production stage and aging damage during use. They are initially highly concealed, but can continuously cause local micro-discharges and heat accumulation, eventually potentially inducing thermal runaway, fire, and explosion, posing a serious threat to equipment and personnel safety. Therefore, accurately and effectively detecting internal short-circuit faults in lithium-ion batteries has significant theoretical and practical value.

[0003] Existing lithium-ion battery fault diagnosis methods are mainly divided into two categories: model-based methods and data-driven methods. Model-based methods establish theoretical models such as equivalent circuits and thermal models, and combine them with algorithms such as Kalman filtering to achieve fault diagnosis. These methods have clear physical meaning and strong interpretability, but modeling under various operating conditions is cumbersome and computationally intensive, making it difficult to meet the requirements for rapid response. Data-driven methods rely on a large amount of operational data, extracting features and classifying them through machine learning algorithms. They do not require complex physical models and are highly adaptable, but they are highly dependent on data, lack physical mechanism support, and are prone to problems such as insufficient generalization and high false positive rates. Therefore, neither type of method can meet the multiple requirements of diagnostic accuracy, robustness, and practicality when applied alone.

[0004] In lithium-ion battery fault diagnosis, single-feature extraction methods typically diagnose faults by extracting the variation patterns of a specific battery parameter, offering advantages such as simplicity and intuitive calculation. However, a single feature can only reflect the battery's state changes in a specific dimension, making it difficult to comprehensively characterize the battery's overall operating state and fault evolution patterns. Therefore, fault diagnosis methods relying solely on single features struggle to simultaneously meet the practical application requirements of both fault diagnosis accuracy and robustness under complex operating conditions.

[0005] Based on this, we developed a method for detecting internal short-circuit faults in lithium-ion batteries based on multi-scale coupling features of model and data fusion. The method uses physical models to provide mechanistic constraints and data-driven methods to uncover fault patterns. By comprehensively characterizing fault evolution through multi-scale coupling features, the method improves the accuracy of fault diagnosis and has significant theoretical and engineering value for ensuring the safe operation of lithium-ion battery systems. Summary of the Invention

[0006] This invention provides a method for diagnosing internal short-circuit faults in lithium-ion batteries based on model and data fusion. This method can solve the problems of large computational load and insufficient generalization of traditional single-model methods and single-data-driven methods, and overcome the defects of incomplete characterization by single features.

[0007] To achieve the above objectives, this invention provides a method for diagnosing internal short-circuit faults in lithium-ion batteries based on model and data fusion, comprising the following steps:

[0008] S1: Collect current, single-cell terminal voltage and average single-cell temperature data of lithium-ion batteries under normal operating conditions and internal short-circuit fault conditions.

[0009] S2: Establish an electrothermal coupling model, and use the recursive least squares method with forgetting factor and adaptive extended Kalman filter algorithm to complete the model parameter identification and state estimation, and obtain the predicted values ​​of terminal voltage and average temperature.

[0010] S3: Based on the measured values ​​and model predictions, obtain the terminal voltage and average temperature residual sequences, extract multi-scale electrothermal coupling features, and generate a standardized feature matrix;

[0011] S4: Construct a random forest classification model and complete model training based on the standardized feature matrix;

[0012] S5: Use the trained random forest model to classify the state of lithium-ion batteries and realize internal short-circuit fault diagnosis.

[0013] Optionally, in step S2, an electrothermal coupling model is established, and model parameter identification and state estimation are completed based on the recursive least squares method with forgetting factor and the adaptive extended Kalman filter algorithm to obtain the predicted values ​​of terminal voltage and average temperature, including the following:

[0014] S21: Establish an electrothermal coupling model for a single lithium-ion battery cell. The electrical model adopts the following first-order resistor-capacitor (RC) equivalent circuit model:

[0015]

[0016] in, Terminal voltage, Open circuit voltage, This is the charging and discharging current. For ohm resistance, Polarization voltage, Polarization resistor, It is a polarizing capacitor.

[0017] The thermal model adopts a single-state lumped-parameter thermal model:

[0018]

[0019] in, For the rate of heat generation, The average temperature. For ambient temperature, For equivalent heat capacity, This is the equivalent thermal resistance.

[0020] S22: The parameters of the equivalent circuit model and thermal model are identified using the recursive least squares method with a forgetting factor, and the parameters of ohmic resistance, polarization resistance, polarization capacitance, equivalent thermal capacity, and equivalent thermal resistance are obtained.

[0021]

[0022] in, for The gain coefficient matrix at different times, and for and Time parameter estimates, and for and Time error covariance matrix, The forgetting factor for recursive least squares method. for Time-based observations for Time-regression vector.

[0023] S23: An adaptive extended Kalman filter algorithm is used to estimate the state of lithium-ion batteries. The state variables of the electrical model are the state of charge and polarization voltage, and the state variables of the thermal model are the temperature rise relative to the ambient temperature. The predicted values ​​of terminal voltage and average temperature are obtained.

[0024] First, based on the optimal estimate from the previous time step, the state and covariance at the current time step are predicted to obtain the prior estimate for the current time step:

[0025]

[0026] in, and for The prior state estimate and prior covariance matrix at time t. and for The state estimate and the state estimate covariance matrix at time t. for The system input vector at time step, for The noise covariance matrix at any given time step. for The state transition matrix at each time step, for Input matrix at each time step.

[0027] Secondly, by combining the prior covariance matrix, the observation matrix, and the observation noise covariance matrix, the Kalman gain matrix is ​​calculated to balance the weights of prediction and observation:

[0028]

[0029] in, for The Kalman gain matrix at each time step. for The noise covariance matrix is ​​observed at all times. for Time-based observation matrix.

[0030] Then, the prior estimate is updated using Kalman gain to correct the prediction bias and obtain the optimal posterior estimate at the current time.

[0031]

[0032] in, for The optimal posterior estimate of the state at time t. for The posterior covariance matrix at time t. for The measured value at time, for Predicted value of measurement at time, It is an identity matrix.

[0033] Finally, based on the filtered residuals, the covariance between process noise and observation noise is adaptively updated to improve the robustness of the algorithm.

[0034]

[0035] in, for The weighting of the data is updated continuously. For the adaptively updated forgetting factor, for The forgetting factor in time, for The error between the measured and predicted values ​​at any given time. for The noise covariance matrix at any given time step. for The noise covariance matrix is ​​observed at all times.

[0036] Optionally, in step S3, the residual sequence of terminal voltage and average temperature is obtained based on the measured values ​​and model predictions. Multi-scale electrothermal coupling features are extracted and a standardized feature matrix is ​​generated, including the following:

[0037] S31: Based on the measured and predicted values ​​of the individual unit terminal voltage and the average temperature of the individual unit, the voltage residual is obtained respectively. With temperature residual The specific expression is as follows:

[0038]

[0039] in, and These are the measured values ​​of the terminal voltage and average temperature of the individual cells. and These are the predicted values ​​for terminal voltage and average temperature.

[0040] S32: A multi-scale sliding window is used to extract features from the residual sequence. The sliding window includes a short window, a medium window, and a long window to extract multi-scale electrothermal coupling features.

[0041] To extract multi-scale features, a short window is set. , middle window Long window , , , These represent the number of sampling points corresponding to the short, medium, and long windows, respectively.

[0042] Based on the above definition of short window , middle window Long window Characteristics of the mean of the product of voltage residual and temperature residual The expression is as follows:

[0043]

[0044] in, For the first Voltage residual at time step For the first Temperature residual at time step For the multi-scale sliding window defined above, These correspond to short windows, medium windows, and long windows, respectively.

[0045] Furthermore, the covariance characteristics of voltage residuals and temperature residuals. The expression is as follows:

[0046]

[0047] in, and These are the average values ​​of the voltage residual and temperature residual within the window, respectively.

[0048] Based on this, the voltage residual and temperature residual stability coupling characteristics The expression is as follows:

[0049]

[0050] in, It is a function of standard deviation;

[0051] Finally, the dynamic coupling characteristics of voltage residual and temperature residual. The expression is as follows:

[0052]

[0053] in, It is a mean function. and For the first Voltage and temperature residuals at the time step.

[0054] S33: Construct a feature matrix by arranging the extracted multi-scale electrothermal coupling features in chronological order, and then standardize the feature matrix to obtain a standardized feature matrix for internal short-circuit fault diagnosis.

[0055] The extracted 8-dimensional electrothermal coupling features are arranged in chronological order, and the first... The 8-dimensional electrothermal coupling features corresponding to each sample are denoted as follows: :

[0056]

[0057] Arrange the feature vectors of all normal and faulty samples in rows to construct the overall feature matrix. :

[0058]

[0059] Among them, the feature matrix Include There are 100 samples, each corresponding to an 8-dimensional feature vector. This represents the number of samples under normal operating conditions. The number of samples under faulty operating conditions is the same as the number of samples under normal operating conditions.

[0060] To eliminate the dimensional differences between different features and improve the stability of model training, the feature matrix is ​​further standardized using zero-mean (Z-score) to obtain a standardized feature matrix. :

[0061]

[0062] in, Characteristic matrix The mean vector of each column, Characteristic matrix The standard deviation vector of each column.

[0063] Optionally, in step S4, constructing a random forest classification model and training the model based on the standardized feature matrix includes the following:

[0064] S41: Constructing a random forest classification model:

[0065] 1) Bootstrap Sampling: For the current training set samples, perform bootstrap sampling with replacement to generate... A bootstrap sample set with the same number of samples as the training set.

[0066] 2) Decision tree construction and node splitting: A decision tree is constructed based on each bootstrap sample set, and nodes are randomly selected during splitting. One electrothermal coupling characteristic, The number of features randomly selected when a node splits.

[0067] Using the Gini index as the evaluation criterion for the optimal splitting feature, firstly, the current node sample set... Gini index for:

[0068]

[0069] in, For the current node's sample set, For category ( This is the normal state. (Internal short-circuit fault state) in the sample set The proportion of.

[0070] Gini index after splitting: Selecting features With threshold For nodes Perform a binary split to obtain the left child node. and right child node The weighted Gini index after splitting for:

[0071]

[0072] in, , , These represent the number of samples for each node. and left child node and right child node The Gini index;

[0073] Based on this, the amount of decline in the Gini index is defined. This is used to quantify the effect of feature splitting on improving node purity.

[0074]

[0075] Traverse all candidate features and all possible split thresholds Select to make The largest feature and threshold complete the node split.

[0076] 3) Categorized voting integration: The classification results of each decision tree are used to determine the final classification label through a majority voting mechanism, resulting in the output of the random forest model. The final classification output expression of the random forest is as follows:

[0077]

[0078] in, For the total number of decision trees, For the first decision trees for the first The classification results of each sample For candidate category labels ( This is the normal state. (This indicates an internal short-circuit fault condition). This is an indicator function (it takes the value 1 if the condition is true, and 0 otherwise). For random forests, the first The final classification label of each sample.

[0079] The beneficial effects of this invention are as follows:

[0080] 1) This invention proposes a model-data fusion method for diagnosing internal short-circuit faults in lithium-ion batteries. It obtains residuals and constructs fault features through an electrothermal coupling model and adaptive extended Kalman filtering. This method not only overcomes the shortcomings of traditional pure mechanistic models (poor generalization) and pure data-driven methods (lack of physical constraints), but also achieves complementary advantages between mechanism and data, improving the reliability of fault diagnosis.

[0081] 2) Construct multi-scale electrothermal coupling features to comprehensively characterize the electrothermal abnormal coupling relationship under faults, making up for the limitations of single-scale features and improving the sensitivity of fault identification.

[0082] 3) Multi-scale sliding window is used to extract features, capturing transient, intermediate and long-term features simultaneously, which makes up for the lack of robustness of single window and improves the classification stability of the model. Attached Figure Description

[0083] Figure 1 This is an overall flowchart of the lithium-ion battery internal short-circuit fault diagnosis method described in this invention;

[0084] Figure 2 This is a schematic diagram of the equivalent circuit model of the internal short-circuited battery in an embodiment of the present invention;

[0085] Figure 3 This is a schematic diagram of the electrothermal coupling model structure in an embodiment of the present invention;

[0086] Figure 4 This is a diagram showing the result of parameter identification of the equivalent electrical model using the recursive least squares method with forgetting factor in an embodiment of the present invention, where (a) represents the parameters. The identification result image, (b) shows the parameters. The identification result image, (c) represents the parameters. Identification result image;

[0087] Figure 5 The diagram shows the state estimation results and error results of the adaptive extended Kalman filter algorithm in this embodiment of the invention. (a) is a comparison diagram of the measured and predicted terminal voltage values, (b) is a diagram of the terminal voltage estimation error, (c) is a comparison diagram of the measured and predicted average temperature values, and (d) is a diagram of the average temperature estimation error.

[0088] Figure 6 The diagram shows the confusion matrix results of ten repeated five-fold cross-validation in an embodiment of the present invention, where (a) is the ten-fold average confusion matrix result of the first fold, (b) is the ten-fold average confusion matrix result of the second fold, (c) is the ten-fold average confusion matrix result of the third fold, (d) is the ten-fold average confusion matrix result of the fourth fold, (e) is the ten-fold average confusion matrix result of the fifth fold, and (f) is the overall average confusion matrix result. Detailed Implementation

[0089] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0090] A model- and data fusion-based method for diagnosing internal short-circuit faults in lithium-ion batteries, such as Figure 1 As shown, the specific steps are as follows:

[0091] Step S1: Collect current, single-cell terminal voltage, and average single-cell temperature data of lithium-ion batteries under normal operating conditions and internal short-circuit fault conditions.

[0092] S11: This embodiment uses an experimental platform consisting of three lithium-ion batteries connected in series. The lithium-ion batteries used in the experiment are ternary lithium-ion batteries with a nominal capacity of 2.5Ah and a nominal voltage of 3.8V. An internal short-circuit fault is simulated by connecting a 100Ω resistor in parallel between the positive and negative electrodes of one of the individual cells. Data on battery pack current, three-channel individual cell terminal voltage, and three-channel individual cell average temperature are collected at a sampling frequency of 1Hz, with a total of 10186 sampling points. The ambient temperature is controlled at 25℃. The first channel of individual cell terminal voltage and the first channel of individual cell average temperature data are used for electrothermal coupling modeling, parameter identification, and state estimation. The second channel of individual cell terminal voltage and the second channel of individual cell average temperature data serve as a control sample under normal operating conditions. The third channel of individual cell terminal voltage and the third channel of individual cell average temperature data serve as an internal short-circuit fault sample.

[0093] To clearly characterize the electrothermal coupling behavior of lithium-ion batteries under internal short-circuit faults, an equivalent circuit model of the internal short circuit is constructed, such as... Figure 2 As shown, the expression is as follows:

[0094]

[0095] in, This represents the total internal current of the battery. For external load current, This is the internal short-circuit current. Terminal voltage, Open circuit voltage, For ohm resistance, Polarization voltage, For internal short-circuit resistance, Joule heating under internal short-circuit faults for and The total resistance of the components.

[0096] This invention is not limited to using a 100Ω parallel resistor to simulate an internal short-circuit fault; other equivalent resistance values ​​or fault excitation methods that can characterize internal short-circuit features are also applicable to the method of this invention.

[0097] Step S2: Establish an electrothermal coupling model, and complete the model parameter identification and state estimation based on the recursive least squares method with forgetting factor and the adaptive extended Kalman filter algorithm to obtain the model prediction value.

[0098] S21: Establish the lithium-ion battery cell model as an electrothermal coupling model.

[0099] The internal reaction mechanism of lithium-ion batteries is complex, with each component influencing the others. The charging and discharging current flowing through the battery's internal resistance generates heat, raising the battery temperature. This temperature change, in turn, affects the battery's electrical model parameters. The battery's electrical and thermal characteristics are interdependent and mutually influential, making it difficult to study them in isolation. To ensure model accuracy, this embodiment establishes an electrothermal coupling model after analyzing the relationship between the parameters of the electrical and thermal models, such as... Figure 3 As shown, this allows the parameters of the two to be passed to each other and interact with each other.

[0100] First order The equivalent circuit model parameters vary with the temperature of the lithium-ion battery. The heat production of a single-state lumped parameter thermal model changes with the changes in temperature. The magnitude and current, ohmic resistance polarization resistance This is relevant. In the electrothermal coupling model, the electrical model transmits the ohmic resistance and polarization resistance to the thermal model to calculate heat generation. In turn, the average temperature output by the thermal model affects the values ​​of the resistance parameters of the electrical model, thereby forming a closed-loop coupling and improving the model accuracy.

[0101] Calculation of battery state of charge based on ampere-hour integration method ):

[0102]

[0103] in, This represents the initial state of charge of the battery. The Coulomb efficiency coefficient is... This refers to the battery's available capacity.

[0104] The electric model uses a first-order... Equivalent circuit model:

[0105]

[0106] in, Terminal voltage, Open circuit voltage, This is the charging and discharging current. For ohm resistance, Polarization voltage, Polarization resistor, It is a polarizing capacitor.

[0107] The thermal model adopts a single-state lumped-parameter thermal model:

[0108]

[0109] in, For the rate of heat generation, The average temperature. For ambient temperature, For equivalent heat capacity, This is the equivalent thermal resistance.

[0110] S22: The parameters of the equivalent circuit model and thermal model are identified using the recursive least squares method with a forgetting factor, and the parameters of ohmic resistance, polarization resistance, polarization capacitance, equivalent thermal capacity, and equivalent thermal resistance are obtained.

[0111] First, regarding the first order... In the equivalent circuit model, a regression vector is constructed using terminal voltage data. Compared with observed values The estimated parameters are obtained by iterative updating using the recursive least squares method with forgetting factor. Its expanded form is as follows:

[0112]

[0113] in, for The equivalent circuit model regression vector at time step 1 contains the voltage difference from the previous time step. Current at the current moment Current at the previous moment ; for The observed value at time, i.e., the voltage difference at the current time. ; Let be the coefficient vector of the electric model to be identified, where The voltage difference autoregressive coefficient, The regression coefficient of the current on the voltage difference is denoted as . The regression coefficient of historical current on voltage difference.

[0114] Based on the identification Further refinement and derivation yielded the physical parameters of the equivalent electrical model, and the analytical expressions are shown below:

[0115]

[0116] Electrical parameters include , and , It is a time constant. The sampling time interval determines the identification result, which varies with the battery. It exhibits nonlinear characteristics due to changes, such as Figure 4 As shown. Among them, Figure 4 In the diagrams (a), (b), and (c), the internal resistances correspond to ohmic resistances, respectively. Polarization resistance and polarization capacitor The identification results. (From) Figure 4 It can be seen that the differences Under certain conditions, the internal electrochemical reactions and polarization effects of the battery dynamically influence its impedance and capacitance parameters, indicating that the battery's equivalent circuit parameters are not fixed constants, but rather change with the environment. Time-varying parameters that change and are updated.

[0117] For parameter identification of single-state lumped parameter thermal models, a regression vector is constructed based on average temperature data. and observed values The estimated parameters are obtained by iterative updating using the recursive least squares method with forgetting factor. Its detailed expansion is as follows:

[0118]

[0119] in, for The thermal model regression vector at time step 1 contains the temperature change at the previous time step. The rate of heat generation compared to the previous moment ; for The observed value at a given time, i.e., the change in temperature at the current time. ; Let be the vector of thermal model coefficients to be identified, where The regression coefficient for temperature change. This is the regression coefficient of the heat generation rate on temperature change.

[0120] Based on the identification The analytical expressions for the thermal model parameters are derived by simplification:

[0121]

[0122] S23: An adaptive extended Kalman filter algorithm is used to estimate the electrical and thermal states. The electrical model state variables include the state of charge (SOC) and polarization voltage, while the thermal model state variables are the temperature rise relative to the ambient temperature. The predicted values ​​of terminal voltage and average temperature are obtained through state estimation.

[0123] When performing state estimation of the electrothermal coupling model using the adaptive extended Kalman filter algorithm, the equivalent circuit model and the lumped parameter thermal model are processed separately. The state-space equation of the equivalent circuit model is as follows:

[0124]

[0125] in, for Discharge current at all times for The difference between the terminal voltage and the open-circuit voltage at any given time. for The state transition matrix at each time step, for Input matrix at each time step, for Output matrix at each time step for The matrix is ​​passed directly at any time. , for and The battery's internal state vector at time t, containing the remaining charge. With polarization voltage .

[0126] Based on the state-space equations of the equivalent circuit model, the system matrix is ​​further derived. , , , The specific expression is:

[0127]

[0128] After completing the state estimation of the circuit model, the state-space equations are further constructed for the single-state lumped parameter thermal model:

[0129]

[0130] in, for The rate of heat generation at any given time for The temperature rise of the battery relative to the ambient temperature at any given time. for The state transition matrix at each time step, for Input matrix at each time step, for Output matrix at each time step for The matrix is ​​passed directly at any time. , for and The battery thermal state vector at time t, including the relative temperature rise. , This represents the temperature rise of the battery relative to the ambient temperature.

[0131] Based on the state-space equations of the thermal model, the system matrix is ​​derived. , , , The specific expression is:

[0132]

[0133] After performing state estimation using the adaptive extended Kalman filter algorithm, the estimated results of the single-unit terminal voltage and the single-unit average temperature are obtained, such as... Figure 5 As shown. Among them, Figure 5 In Figures (a) and (b), the measured and predicted values ​​of the single-unit terminal voltage are compared, along with the estimation error. Figures (c) and (d) show the measured and predicted values ​​of the single-unit average temperature, along with the estimation error. Figure 5 It can be seen that the estimated values ​​of the single-unit terminal voltage and the single-unit average temperature can track the corresponding measured values ​​well, and the overall estimation error is small and the fluctuation is stable. This indicates that the adaptive extended Kalman filter algorithm can accurately obtain the predicted values ​​of the single-unit terminal voltage and the single-unit average temperature, thus providing a reliable basis for constructing voltage residual sequences and temperature residual sequences based on the measured values ​​and predicted values.

[0134] To further quantify the accuracy of state estimation, the root mean square error is used. and mean absolute error The two indicators are used for error assessment, and their expressions are as follows:

[0135]

[0136]

[0137] in, The total number of samples, For the first The predicted value for each sample, For the first The actual measured value of each sample;

[0138] Calculations show that the terminal voltage is estimated as follows: 3.15mV The value is 2.80 mV, and the temperature is estimated to be... The temperature is 0.0045℃. The result was 0.0028℃, verifying the high accuracy and reliability of the adaptive extended Kalman filter algorithm for state estimation of the electrothermal coupling model.

[0139] Step S3: Based on the measured values ​​and model predictions, obtain the terminal voltage and average temperature residual sequences, extract multi-scale electrothermal coupling features, and generate a standardized feature matrix, including the following:

[0140] S31: Based on the measured and predicted values ​​of the individual unit terminal voltage and the average temperature of the individual unit, the voltage residual is obtained respectively. With temperature residual The specific expression is as follows:

[0141]

[0142] in, and These are the measured values ​​of the terminal voltage and average temperature of the individual cells. and These are the predicted values ​​for terminal voltage and average temperature.

[0143] S32: The electrothermal coupling features are extracted using a multi-scale sliding window. In this embodiment, the sampling frequency is 1Hz, and the short window is set to 15 sampling points, the medium window to 30 sampling points, and the long window to 60 sampling points. The short, medium, and long windows are used to characterize local rapid disturbances, medium-term fluctuations, and long-term cumulative trends, respectively.

[0144] Based on the multi-scale sliding window, eight-dimensional electrothermal coupling features are extracted from the voltage residual sequence and the temperature residual sequence, as follows:

[0145] Characteristics of the mean of the product of short-window voltage residual and temperature residual;

[0146] Characteristics of the mean of the product of voltage residual and temperature residual in the middle window;

[0147] Characteristics of the mean of the product of voltage residual and temperature residual over a long window;

[0148] Characteristics of the covariance between voltage and temperature residuals within the middle window;

[0149] Characteristics of the product of the standard deviation of the short-window voltage residual and the standard deviation of the temperature residual;

[0150] Characteristics of the product of the standard deviation of the voltage residual and the standard deviation of the temperature residual within the middle window;

[0151] The mean characteristics of the dynamic coupling between the first-order difference of the short-window voltage residual and the temperature residual;

[0152] The mean characteristics of the dynamic coupling between the first-order difference of the temperature residual and the voltage residual in the long window.

[0153] S33: Based on the predicted values, extract the above 8-dimensional features from the normal operating condition control unit and the internal short-circuit fault unit respectively to obtain the normal sample feature matrix and the fault sample feature matrix. Concatenate the two types of feature matrices in order to obtain the total feature matrix, and construct the corresponding label vector. The label for normal samples is 0, and the label for faulty samples is 1.

[0154] The total feature matrix is ​​Z-score standardized to obtain the standardized feature matrix. The standardized feature matrix is ​​used for subsequent training of the random forest classification model and fault diagnosis.

[0155] Step S4: Construct a random forest classification model. Based on the standardized feature matrix, construct a random forest classification model and complete its training, including the following:

[0156] S41: Constructing a random forest classification model:

[0157] Bootstrap sampling: Perform bootstrap sampling with replacement on the current training set samples to generate 300 bootstrap sample sets with the same number of samples as the training set.

[0158] Decision tree construction and node splitting: Decision trees are constructed based on each bootstrap sample set. When splitting nodes, three electrothermal coupling features are randomly selected. The Gini index is used as the evaluation criterion for the optimal splitting feature. The termination condition for decision tree training is: the number of node samples is less than or equal to 5 or the maximum depth of a single decision tree is set to 100 to avoid model overfitting.

[0159] Classification voting fusion: Integrate the classification results of 300 decision trees and determine the final classification label through a majority voting mechanism. That is, for each sample, the classification results of all decision trees are counted, and the category with the most votes is the final classification result of that sample.

[0160] Step S5: To reduce the randomness of a single random partition, improve the stability of model performance evaluation, and verify the generalization ability of the random forest classification model, this embodiment uses a ten-fold repeated five-fold cross-validation method to evaluate the model performance, including the following:

[0161] S51: Dataset partitioning: Standardizing the feature matrix With label vector Randomly divided into 5 mutually exclusive subsets Each time, four subsets are selected as the training set and the remaining one subset is selected as the validation set to complete one five-fold cross-validation. The above partitioning and validation process is repeated 10 times, and the average result of the 10 five-fold cross-validations is used as the model performance evaluation index.

[0162] S52: Construct a confusion matrix based on the prediction results of the validation set samples, such as... Figure 6 As shown. Among them, Figure 6 (a) to (e) represent the confusion matrix results for folds 1 to 5 in the five-fold cross-validation, respectively. Figure 6 In the matrix (f), the average performance result after ten repeated five-fold cross-validation is shown. In the confusion matrix, the elements on the main diagonal represent the number of correctly classified samples, and the elements off-diagonal represent the number of misclassified samples. Specifically, true positives... This represents the number of samples that were actually internal short-circuit faults but were correctly identified as faults; true negatives. This represents the number of samples that were actually in a normal state and were correctly identified as normal; false positives. This represents the number of samples that were actually in a normal state but were mistakenly identified as faulty; false negatives. This represents the number of samples that were actually internal short-circuit faults but were misclassified as normal. Based on this, the model's fault diagnosis performance is quantitatively evaluated using three metrics: accuracy, precision, and recall. The expressions for each metric are as follows:

[0163]

[0164] in, For accuracy, For accuracy, For recall, in this embodiment, the average performance metrics of ten repeated 50% cross-validation runs are: accuracy 97.89%, precision 98.76%, and recall 97.00%. Figure 6 As shown by the above evaluation indicators, the correctly classified samples in the confusion matrix are mainly concentrated on the main diagonal, while the number of misclassified samples is small. This indicates that the proposed random forest classification model can effectively distinguish between normal states and internal short-circuit fault states. This result verifies that the model and data fusion diagnostic method proposed in this invention has high fault identification accuracy, a low false diagnosis rate, and strong false negative suppression capability, providing reliable technical support for lithium-ion battery safety monitoring and internal short-circuit fault early warning.

Claims

1. A method for diagnosing internal short-circuit faults in lithium-ion batteries based on model and data fusion, characterized in that, Includes the following steps: S1: Collect current, single-cell terminal voltage and average single-cell temperature data of lithium-ion batteries under normal operating conditions and internal short-circuit fault conditions. S2: Establish a lithium-ion battery electrothermal coupling model, use the recursive least squares method with forgetting factor to identify the parameters of the electrothermal coupling model online, and use an adaptive extended Kalman filter algorithm to estimate the state of the lithium-ion battery; wherein, in the adaptive extended Kalman filter algorithm, the terminal voltage prediction value and the average temperature prediction value are obtained based on the adaptive update process noise covariance and observation noise covariance of the filter residual. S3: The voltage residual is obtained based on the measured and predicted terminal voltage values ​​of the individual units, and the temperature residual is obtained based on the measured and predicted average temperature values ​​of the individual units. The voltage residual and temperature residual are used as a set of electrothermal coupling residual variables. Multi-scale sliding window joint analysis is performed using short, medium, and long windows to extract the 8-dimensional multi-scale electrothermal coupling features calculated by the voltage residual and temperature residual. The 8-dimensional multi-scale electrothermal coupling features are then used to construct a feature matrix in chronological order. The feature matrix is ​​then Z-score standardized to obtain a standardized feature matrix. The voltage residual With temperature residual The specific expression is as follows: ， in, and These are the measured values ​​of the terminal voltage and average temperature of the individual cells. and These are predicted values ​​for terminal voltage and average temperature; Set short window , middle window Long window , , , These represent the number of sampling points corresponding to the short, medium, and long windows, respectively. Based on the above definition of short window , middle window Long window Characteristics of the mean of the product of voltage residual and temperature residual The expression is as follows: ， in, For the first Voltage residual at time step For the first Temperature residual at time step For the multi-scale sliding window defined above, These correspond to short windows, medium windows, and long windows, respectively. Furthermore, the covariance characteristics of voltage residuals and temperature residuals. The expression is as follows: ， in, and These are the average values ​​of the voltage residual and temperature residual within the window, respectively. Based on this, the stability coupling characteristics of voltage residual and temperature residual are... The expression is as follows: ， in, It is a function of standard deviation; Finally, the dynamic coupling characteristics of voltage residual and temperature residual. The expression is as follows: ， in, It is a mean function. and For the first Voltage and temperature residuals at the time step; The extracted 8-dimensional electrothermal coupling features are arranged in chronological order, and the first... The 8-dimensional electrothermal coupling features corresponding to each sample are denoted as follows: : ， Arrange the feature vectors of all normal and faulty samples in rows to construct the overall feature matrix. : ， Among them, the feature matrix Include There are 10 samples, each corresponding to an 8-dimensional feature vector. The number of samples under normal operating conditions is the same as the number of samples under fault conditions. To eliminate the dimensional differences between different features and improve the stability of model training, the feature matrix is ​​further standardized using zero-mean (Z-score) to obtain a standardized feature matrix. : ， in, Characteristic matrix The mean vector of each column, Characteristic matrix The standard deviation vector of each column; S4: Construct a random forest classification model and complete model training based on the standardized feature matrix; S5: Use the trained random forest model to classify the state of lithium-ion batteries and realize internal short-circuit fault diagnosis.

2. The method for diagnosing internal short-circuit faults in lithium-ion batteries based on model and data fusion as described in claim 1, characterized in that: In step S2, an electrothermal coupling model is established. Based on the recursive least squares method with forgetting factor and the adaptive extended Kalman filter algorithm, the model parameters are identified and the state is estimated to obtain the predicted values ​​of terminal voltage and average temperature. This includes the following steps: S21: Establish an electrothermal coupling model for a single lithium-ion battery cell. The electrical model adopts the following first-order resistor-capacitor (RC) equivalent circuit model: ， in, Terminal voltage, Open circuit voltage, This is the charging and discharging current. For ohmic resistance, Polarization voltage, Polarization resistor, Polarizing capacitor; The thermal model adopts a single-state lumped-parameter thermal model: ， in, For the rate of heat generation, The average temperature. For ambient temperature, For equivalent heat capacity, Equivalent thermal resistance; S22: The parameters of the equivalent circuit model and thermal model are identified using the recursive least squares method with a forgetting factor, and the parameters of ohmic resistance, polarization resistance, polarization capacitance, equivalent thermal capacity, and equivalent thermal resistance are obtained. ， in, for The gain coefficient matrix at different times, and for and Time parameter estimates, and for and Time error covariance matrix, The forgetting factor for recursive least squares method. for Time-based observations for Time-regression vector; S23: An adaptive extended Kalman filter algorithm is used to estimate the state of lithium-ion batteries. The state variables of the electrical model are the state of charge and polarization voltage, and the state variables of the thermal model are the temperature rise relative to the ambient temperature. The predicted values ​​of terminal voltage and average temperature are obtained. First, based on the optimal estimate from the previous time step, the state and covariance at the current time step are predicted to obtain the prior estimate for the current time step: ， in, and for The prior state estimate and prior covariance matrix at time t. and for The state estimate and the state estimate covariance matrix at time t. for The system input vector at time step, for The noise covariance matrix at any given time step. for The state transition matrix at each time step, for Input matrix at each time step; Secondly, by combining the prior covariance matrix, the observation matrix, and the observation noise covariance matrix, the Kalman gain matrix is ​​calculated to balance the weights of prediction and observation: ， in, for The Kalman gain matrix at each time step. for The noise covariance matrix is ​​observed at all times. for Time-based observation matrix; Then, the prior estimate is updated using Kalman gain to correct the prediction bias and obtain the optimal posterior estimate at the current time step. ， in, for The optimal posterior estimate of the state at time t. for The posterior covariance matrix at time t. for The measured value at time, for Predicted value of measurement at time, It is the identity matrix; Finally, based on the filtered residuals, the covariance between process noise and observation noise is adaptively updated to improve the robustness of the algorithm. ， in, for The weighting of the data is updated continuously. For the adaptively updated forgetting factor, for The forgetting factor in time, for The error between the measured and predicted values ​​at any given time. for The noise covariance matrix at any given time step. for The noise covariance matrix is ​​observed at all times.

3. The method for diagnosing internal short-circuit faults in lithium-ion batteries based on model and data fusion according to claim 1, characterized in that: In step S4, a random forest classification model is constructed, and model training is completed based on the standardized feature matrix, including the following steps: S41: Constructing a random forest classification model: 1) Bootstrap Sampling: For the current training set samples, perform bootstrap sampling with replacement to generate... A bootstrap sample set with the same number of samples as the training set; 2) Decision tree construction and node splitting: A decision tree is constructed based on each bootstrap sample set, and nodes are randomly selected during splitting. One electrothermal coupling characteristic, The number of features randomly selected during node splitting; Using the Gini index as the evaluation criterion for the optimal splitting feature, firstly, the current node sample set... Gini index for: ， in, For the current node's sample set, For category ( This is the normal state. (Internal short-circuit fault state) in the sample set The proportion in; Gini index after splitting: Selecting features With threshold For nodes Perform a binary split to obtain the left child node. and right child node The weighted Gini index after splitting for: ， in, , , These represent the number of samples for each node. and left child node and right child node The Gini index; Based on this, the decrease in the Gini index is defined. This is used to quantify the effect of feature splitting on improving node purity. ， Traverse all candidate features and all possible split thresholds Select The maximum feature and threshold are used to complete node splitting; 3) Categorized voting integration: The classification results of each decision tree are used to determine the final classification label through a majority voting mechanism, resulting in the output of the random forest model. The final classification output expression of the random forest is as follows: ， in, For the total number of decision trees, For the first decision trees for the first The classification results of each sample For candidate category labels ( This is the normal state. (This indicates an internal short-circuit fault condition). This is an indicator function (it takes the value 1 if the condition is true, and 0 otherwise). For random forests, the first The final classification label of each sample.

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