Lithium-ion battery cross-temperature soh estimation method based on physical information transfer learning

Abstract

The present application relates to a lithium ion battery cross-temperature SOH estimation method based on physical information transfer learning. It uses generalized regression neural network to quickly fit electrochemical impedance spectrum to extract equivalent circuit model parameters with clear physical meaning, solves the black box defect of pure data driven method; through the trainable temperature embedding layer, the discrete temperature is coded into a high-dimensional feature vector and fused with the physical parameters, the nonlinear coupling effect of temperature on the aging characteristics is decoupled; using the generative adversarial distribution matching mechanism combined with multi-kernel maximum mean difference regularization, the feature distribution alignment across temperature domains is realized without the need for target domain labels, solving the problem of precision decline caused by domain shift; in the health state evaluation link, a temperature correction factor based on Arrhenius kinetics is introduced, the capacity estimation value is converted to a unified reference temperature baseline to peel off the reversible capacity fluctuation component, solving the problem of systematic evaluation deviation caused by the inseparability of temperature effect and aging effect.

Description

Technical Field

[0001] This invention belongs to the field of lithium-ion battery state estimation and management technology, specifically involving a method for estimating the state of equilibrium (SOH) of lithium-ion batteries across temperatures based on physical information transfer learning. Background Technology

[0002] During long-term cycling, batteries experience a gradual performance degradation due to complex electrochemical aging mechanisms, including the continuous thickening of the solid electrolyte interface film, the collapse of the lattice structure of the positive electrode active material, and the irreversible depletion of lithium reserves. Existing health status estimation methods mainly include model-based and data-driven methods. While electrochemical model-based methods can describe the internal mechanisms of batteries, they involve a large number of microscopic parameters that are difficult to measure in real time and have excessively high computational complexity. Traditional equivalent circuit models, although having lower computational requirements, have a weak mapping relationship between circuit components and the internal physical degradation process of the battery, making them difficult to adapt to complex and variable aging scenarios. Pure data-driven methods based on deep learning, while possessing strong nonlinear fitting capabilities, are generally considered black-box models lacking physical interpretability and are extremely dependent on massive amounts of labeled data. When there is a domain shift between the training temperature and the actual operating temperature, the model accuracy drops sharply. While domain adaptation techniques in transfer learning offer a novel approach to addressing cross-temperature domain shifts, existing statistical distribution matching methods suffer from high computational costs and reliance on predefined metrics. Adversarial methods exhibit significant training instability and are prone to mode collapse. More critically, most of these transfer strategies align features solely at the statistical level, neglecting the physical and electrochemical constraints batteries must adhere to at different temperatures, potentially leading to transferred features that violate physical laws. Furthermore, even when cross-temperature capacity estimates are obtained, these estimates simultaneously couple two fundamentally different effects: temperature-induced reversible capacity fluctuations and aging-induced irreversible capacity degradation. Directly comparing these estimates with the rated capacity calibrated at a single reference temperature will systematically underestimate the battery's health at low temperatures and systematically overestimate it at high temperatures, failing to accurately reflect the battery's pure aging status.

[0003] Therefore, an optimized scheme for estimating the state of oxygen (SOH) of lithium-ion batteries across temperatures based on physical information transfer learning is desired. Summary of the Invention

[0004] To address the aforementioned technical problems, this application is proposed. Embodiments of this application provide a method for estimating the state of harm (SOH) of lithium-ion batteries across temperatures based on physical information transfer learning, comprising: S1: Rapidly fit and extract parameters from the collected electrochemical impedance spectroscopy data of lithium-ion batteries under multiple temperature conditions to obtain equivalent circuit model parameters including ohmic internal resistance, solid electrolyte interface film resistance, and charge transfer resistance. S2: A trainable temperature embedding layer based on index mapping performs discrete indexing encoding and high-dimensional feature space mapping on the temperature data corresponding to each temperature condition to obtain a temperature embedding vector that can decouple the nonlinear coupling effect of temperature on battery aging characteristics. S3: The equivalent circuit model parameters and the temperature embedding vector are concatenated and fused along the feature dimension to obtain the source domain enhanced feature vector and the target domain enhanced feature vector; S4: Using the source domain enhanced feature vector, the target domain enhanced feature vector, and the source domain capacity label as input, the generator and discriminator are iteratively trained through joint optimization of adversarial loss, multi-kernel maximum mean difference regularization loss, and source domain supervision loss to obtain a transfer learning model; S5: The enhanced feature vector generated by the electrochemical impedance spectroscopy data and temperature data of the battery under test after parameter extraction and temperature embedding is input into the transfer learning model to infer the capacity and obtain the capacity estimate.

[0005] S6: Determine the battery's health status value based on the ratio of the estimated capacity to the battery's rated capacity.

[0006] Compared with existing technologies, this invention proposes a method for estimating the state of oxygen (SOH) of lithium-ion batteries across temperatures based on physical information transfer learning. First, it utilizes a generalized regression neural network to rapidly and robustly fit electrochemical impedance spectroscopy data, extracting equivalent circuit model parameters with clear physical meaning, thus solving the problem of lack of physical interpretability in traditional pure data-driven methods. Then, by constructing a trainable temperature embedding layer based on index mapping, discrete temperature information is encoded into high-dimensional feature vectors, and these vectors are fused with physical parameters to generate enhanced feature vectors, effectively decoupling the nonlinear coupling effect of temperature on battery aging characteristics. Next, a generative adversarial distribution matching mechanism combined with multi-kernel maximum mean difference regularization is employed to align the feature distributions between the source and target domains without requiring target temperature domain label data, solving the problem of decreased model accuracy caused by cross-temperature domain offset. Finally, in the health status assessment stage, a temperature correction factor based on Arrhenius dynamics is introduced to equivalently convert the capacity estimate at any operating temperature to a unified reference temperature baseline, stripping away the reversible capacity fluctuation component caused by temperature. This solves the systematic assessment bias problem caused by the inability to effectively separate temperature effects and aging effects in direct ratio calculations, enabling the health status value to truly reflect the irreversible aging degree of the battery across the entire temperature range. Attached Figure Description

[0007] Figure 1 This is a flowchart of a lithium-ion battery SOH estimation method based on physical information transfer learning according to an embodiment of this application; Figure 2This is a schematic diagram of the data flow of a lithium-ion battery SOH estimation method based on physical information transfer learning according to an embodiment of this application. Figure 3 This document describes a flowchart illustrating a method for estimating the SOH (Surface Electrochemical Harmonic) of lithium-ion batteries across temperatures based on physical information transfer learning, according to an embodiment of this application. The method involves rapidly fitting and extracting parameters from collected electrochemical impedance spectroscopy (EHS) data of lithium-ion batteries under multiple temperature conditions to obtain an equivalent circuit model parameter that includes ohmic internal resistance, solid electrolyte interface film resistance, and charge transfer resistance. Figure 4 The equivalent circuit model and corresponding electrochemical impedance spectroscopy of the lithium-ion battery cross-temperature SOH estimation method based on physical information transfer learning according to the embodiments of this application are shown below. Figure 5 This is a diagram of the GRNN network architecture for a cross-temperature SOH estimation method for lithium-ion batteries based on physical information transfer learning according to an embodiment of this application. Figure 6 This is a flowchart illustrating a trainable temperature embedding layer based on index mapping for a cross-temperature SOH estimation method for lithium-ion batteries based on physical information transfer learning, according to an embodiment of this application. The process involves discretizing and indexing the temperature data corresponding to each temperature condition and mapping it to a high-dimensional feature space to obtain a temperature embedding vector that can decouple the nonlinear coupling effect of temperature on battery aging characteristics. Figure 7 This is a diagram of an index-based temperature embedding system for a lithium-ion battery SOH estimation method based on physical information transfer learning according to an embodiment of this application. Figure 8 The flowchart of the transfer learning method for estimating the SOH of lithium-ion batteries across temperature according to the embodiment of this application is as follows: the generator and discriminator are iteratively trained to obtain the transfer learning model by taking the source domain enhanced feature vector, the target domain enhanced feature vector and the source domain capacity label as input, and by jointly optimizing the adversarial loss, the multi-kernel maximum mean difference regularization loss and the source domain supervision loss. Figure 9 This is a flowchart illustrating how a lithium-ion battery's state of health (SOH) value is determined based on the ratio of the capacity estimate to the battery's rated capacity, according to the physical information transfer learning-based lithium-ion battery cross-temperature SOH estimation method of this application. Detailed Implementation

[0008] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0009] Figure 1 This is a flowchart of a lithium-ion battery cross-temperature SOH estimation method based on physical information transfer learning according to an embodiment of this application. Figure 2 This is a schematic diagram of the data flow for a lithium-ion battery SOH estimation method based on physical information transfer learning according to an embodiment of this application. Figure 1 and Figure 2 As shown, the lithium-ion battery cross-temperature SOH estimation method based on physical information transfer learning according to an embodiment of this application includes the following steps: S1, rapidly fitting and extracting parameters from the collected electrochemical impedance spectroscopy data of the lithium-ion battery under multiple temperature conditions to obtain equivalent circuit model parameters including ohmic internal resistance, solid electrolyte interface film resistance, and charge transfer resistance; S2, based on an index-mapped trainable temperature embedding layer, discretizing and indexing the temperature data corresponding to each temperature condition and mapping it to a high-dimensional feature space to obtain a temperature embedding vector that can decouple the nonlinear coupling effect of temperature on battery aging characteristics; S3, combining the equivalent circuit model parameters and the temperature embedding vector in... S4. Feature vectors are concatenated and fused along the feature dimension to obtain source domain enhanced feature vectors and target domain enhanced feature vectors; S5. Using the source domain enhanced feature vector, target domain enhanced feature vector, and source domain capacity label as input, the generator and discriminator are iteratively trained through joint optimization of adversarial loss, multi-kernel maximum mean difference regularization loss, and source domain supervision loss to obtain a transfer learning model; S6. The enhanced feature vector generated by parameter extraction and temperature embedding processing of the electrochemical impedance spectroscopy data and temperature data of the battery under test is input into the transfer learning model for capacity inference to obtain a capacity estimate; S7. Based on the ratio of the capacity estimate to the battery's rated capacity, the battery's health status value is determined.

[0010] Specifically, in step S1, the collected electrochemical impedance spectroscopy (EIS) data of the lithium-ion battery under multiple temperature conditions is rapidly fitted and parameters are extracted to obtain equivalent circuit model parameters including ohmic internal resistance, solid electrolyte interfacial membrane resistance, and charge transfer resistance. It should be noted that, given that the performance degradation of lithium-ion batteries during long-term cycling essentially stems from the evolution of internal microscopic electrochemical processes, and that EIS can reveal the kinetic behaviors of charge transfer, mass diffusion, and interfacial membrane growth within the battery from a frequency domain perspective, the internal state information it contains is far richer than external characteristics such as voltage and current. However, the original impedance spectroscopy data is high-dimensional and has obscure physical meaning, requiring an equivalent circuit model to transform it into physical parameters with clear electrochemical correspondences to effectively serve subsequent health state estimation. Based on this, the technical solution of this application first utilizes the nonparametric estimation characteristics of a generalized regression neural network to rapidly fit and extract parameters from the collected EIS data of the lithium-ion battery under multiple temperature conditions, obtaining equivalent circuit model parameters including ohmic internal resistance, solid electrolyte interfacial membrane resistance, and charge transfer resistance. Through the above processing, the traditional least squares method can be effectively replaced by an iterative optimization process that is sensitive to initial values ​​and unstable at low signal-to-noise ratios. The equivalent circuit model parameters with clear physical meaning can be obtained quickly through a single forward propagation, so that the input features of the deep learning model directly correspond to the microscopic degradation process inside the battery. This overcomes the black box defect of pure data-driven methods and provides a feature foundation that combines physical interpretability and computational efficiency for subsequent cross-temperature transfer learning.

[0011] Figure 3 This document describes a flowchart illustrating the rapid fitting and parameter extraction of collected electrochemical impedance spectroscopy data of lithium-ion batteries under multiple temperature conditions, based on a physical information transfer learning-based method for estimating the solid electrolyte interfacial (SOH) resistance (SOH) of lithium-ion batteries according to embodiments of this application. The aim is to obtain an equivalent circuit model with parameters including ohmic internal resistance, solid electrolyte interfacial membrane resistance, and charge transfer resistance. For example... Figure 3 As shown, step S1 includes: S11, extracting the test frequency, real impedance and imaginary impedance from the electrochemical impedance spectroscopy data to construct an impedance feature input vector; S12, inputting the impedance feature input vector into a generalized regression neural network to perform pattern layer feature distance measurement to obtain a set of Euclidean distance squares; S13, performing kernel regression weighted parameter prediction on the set of Euclidean distance squares to obtain the equivalent circuit model parameters.

[0012] In step S11, the test frequency, real impedance, and imaginary impedance are extracted from the electrochemical impedance spectroscopy (EIS) data to construct an impedance feature input vector. It should be noted that since the original EIS measurement data exists in the form of a frequency scan sequence, with each frequency point corresponding to a set of complex impedance values, its data structure differs in dimensionality and organization from the standardized input format required by the subsequent generalized regression neural network. Therefore, the technical solution of this application first extracts the test frequency, real impedance, and imaginary impedance from the EIS data to construct the impedance feature input vector. Through the above processing, the multidimensional frequency domain information of the original impedance spectrum can be integrated into a structured feature representation, providing a format-adapted numerical input for the subsequent model layer distance metric of the neural network.

[0013] More specifically, in a particular example of this application, electrochemical impedance spectroscopy (EIS) data of a lithium-ion battery is first acquired after frequency sweep excitation by an electrochemical workstation under specified temperature conditions. This data includes complex impedance measurements at several discrete frequency points from the high-frequency region to the low-frequency region. The EIS can be divided into three main regions according to frequency from high to low: the high-frequency region is located at the intersection of the real axis on the left side of the impedance spectrum and the first capacitive arc, mainly exhibiting ohmic internal resistance. The subsequent semi-circular feature represents the charge transfer process at the solid electrolyte interface layer; the mid-frequency region, located in the second semi-circular arc, also exhibits semi-circular characteristics, primarily reflecting the charge transfer impedance and double-layer capacitance effect at the battery electrode interface; the low-frequency region, located at the rightmost tail of the spectrum, ideally appears as an extended straight line tilted at approximately 45 degrees, corresponding to the diffusion behavior of the active material within the electrode, as indicated by the Warburg diffusion impedance. Modeling is performed. Based on the aforementioned frequency domain characteristic distribution patterns, this application employs an equivalent circuit model containing constant-phase elements and Warburg diffusion elements to physically model the electrochemical impedance spectrum.

[0014] Figure 4 This document presents the equivalent circuit model and corresponding electrochemical impedance spectroscopy for a lithium-ion battery temperature-dependent state of harmonics (SOH) estimation method based on physical information transfer learning, according to embodiments of this application. Figure 4 As shown in (a), the Nyquist plot of the electrochemical impedance spectroscopy visually illustrates the mapping relationship between each frequency range and the corresponding electrochemical process; as shown in (a), Figure 4 As shown in (b) of this application, the equivalent circuit model includes an ohmic resistor. The resistance of the solid electrolyte interfacial membrane With the first constant phase element The first parallel circuit formed, and the charge transfer resistor Warburg diffusion element With the second constant phase element This forms the second parallel circuit. The impedance expression for the constant-phase element is: in, For constant phase elements at angular frequency The complex impedance value below, For the generalized capacitance representing the radius of a semicircle, The imaginary unit, Angular frequency, The dispersion coefficient reflects the flatness of the semicircle. The time-constant phase element behaves as an ideal capacitor and generates a standard semicircle. It behaves as a Warburg diffusion element when It behaves as a purely resistive element. The impedance expressions for each element in the equivalent circuit model are as follows: Ohmic impedance: in, For ohmic impedance, The resistance is in ohms, corresponding to the purely resistive losses of the conductive substrate and connecting components inside the battery. The impedance contributed by the solid electrolyte interface film layer is also considered. in, For the solid electrolyte interface film layer at angular frequency The complex impedance value below, For the solid electrolyte interface film resistance, The capacitance value of the first parallel circuit. The imaginary unit, Angular frequency, This represents the dispersion coefficient corresponding to the first parallel circuit. Warburg diffusion impedance: in, The Warburg diffusion impedance associated with ion transport processes, For Warburg diffusion capacitance, The imaginary unit, ω is the angular frequency, and the exponent 0.5 is the inherent dispersion coefficient of the Warburg diffuser. The combined impedance of charge transfer and diffusion: in, The combined impedance of charge transfer and diffusion at angular frequency The complex impedance value below, For charge transfer resistor, For Warburg diffusion impedance, The capacitance value of the second parallel circuit. The imaginary unit, Angular frequency, This is the dispersion coefficient corresponding to the second parallel loop. The total impedance of the equivalent circuit model formed by the series connection of the above components is calculated using the following formula: in, For the equivalent circuit model at angular frequency The total complex impedance value below, For ohmic impedance, The impedance contributed to the solid electrolyte interface film layer. The combined impedance of charge transfer and diffusion. For ohm resistance, For the solid electrolyte interface film resistance, For charge transfer resistor, , and These are the capacitors of the first parallel circuit, the second parallel circuit, and the Warburg diffusion capacitor, respectively. and These are the corresponding diffusion coefficients. The imaginary unit, Let ω be the angular frequency. For each discrete frequency point, three core physical dimensions of test features are extracted: the first dimension is the test frequency value corresponding to that frequency point; the second dimension is the real impedance value corresponding to that frequency point, which physically represents the projection component of the complex impedance onto the real axis; and the third dimension is the imaginary impedance value corresponding to that frequency point, which physically represents the projection component of the complex impedance onto the imaginary axis. After extracting the above three-dimensional features frequency-by-frequency, the test frequency, real impedance, and imaginary impedance are sequentially concatenated and combined along the feature dimensions according to a preset fixed arrangement order to form a one-dimensional numerical tensor, i.e., the impedance feature input vector. Figure 5 This is a GRNN network architecture diagram of a cross-temperature SOH estimation method for lithium-ion batteries based on physical information transfer learning, according to an embodiment of this application. Figure 5 As shown, after the impedance feature input vector is fed into the generalized regression neural network, it is processed sequentially through the input layer, mode layer, summation layer and output layer to realize the continuous calculation process from feature distance measurement to equivalent circuit model parameter prediction.

[0015] In step S12, the impedance feature input vector is input into a generalized regression neural network to perform a pattern layer feature distance metric to obtain a set of Euclidean distance squares. It should be noted that the kernel regression prediction mechanism of the generalized regression neural network relies on a quantitative evaluation of the spatial similarity between the input sample and the historical training samples, and this similarity metric presupposes that the geometric distance calculation between feature vectors is performed in the pattern layer. Therefore, the technical solution of this application further inputs the impedance feature input vector into the generalized regression neural network to perform a pattern layer feature distance metric to obtain a set of Euclidean distance squares. Through the above processing, the vector positional relationships in the high-dimensional feature space can be transformed into scalar distance values ​​that can be processed by the subsequent Gaussian kernel function, providing a numerical basis for the nonlinear similarity weighting of the summation layer.

[0016] More specifically, in a concrete example of this application, the impedance feature input vector constructed in the previous step is imported into the pattern layer of the generalized regression neural network. This pattern layer pre-stores feature vectors of all historical samples from the training phase. Each stored feature vector corresponds to a set of known electrochemical impedance spectroscopy measurement data after being extracted and concatenated in the same dimension. The number of neurons in the pattern layer corresponds one-to-one with the total number of training samples. During the forward computation of the pattern layer, for the current input impedance feature vector, element-wise difference operations are performed with each pre-stored training sample feature vector in the pattern layer to obtain the difference vector between the two vectors. Then, the inner product operation of the transpose and itself is performed on this difference vector, i.e., the transpose of the difference vector is multiplied by the difference vector itself. The resulting scalar value is the squared Euclidean distance between the current input and the training sample in the multidimensional feature space. The mathematical expression for the above distance metric is: ,in, The impedance characteristic input vector is the current input. The first one pre-stored in the pattern layer The feature vectors of each training sample, with superscript... This represents the vector transpose operation. For the calculated first Each element represents a squared Euclidean distance. After performing the above distance calculation on the input vector and all training samples one by one, all squared distance values ​​are aggregated into an ordered scalar set, namely the Euclidean distance square set, according to the storage order of the training samples. Each element in this set reflects the degree of difference in relative position in the feature space between the impedance characteristics of the current battery under test and the corresponding historical sample. The smaller the squared distance value, the more similar the impedance characteristics of the two are; the larger the squared distance value, the more obvious the difference in their electrochemical states.

[0017] In step S13, kernel regression weighted parameter prediction is performed on the Euclidean distance square set to obtain the equivalent circuit model parameters. It should be noted that since the Euclidean distance square set output by the mode layer only represents the geometric distance relationship between the input sample and each training sample, a mapping path from distance metric to physical parameter prediction has not yet been established. Based on this, the technical solution of this application further performs kernel regression weighted parameter prediction on the Euclidean distance square set to obtain the equivalent circuit model parameters. Through the above processing, an end-to-end mapping from impedance characteristics to physical parameters can be completed through non-parametric estimation, outputting equivalent circuit model parameters with a clear electrochemical correspondence.

[0018] More specifically, in a concrete example of this application, the set of squared Euclidean distances output from the pattern layer is transmitted to the summation layer of the generalized regression neural network. In the summation layer, for each squared distance value in the set, it is substituted into a Gaussian kernel function for nonlinear activation. This involves exponentiation using the natural constant as the base and the negative value of the squared distance divided by twice the square of the smoothing factor as the exponent, mapping the geometric distance to a similarity weight value between 0 and 1. Training samples with smaller squared distance values ​​receive weight values ​​closer to 1 after Gaussian kernel mapping, indicating a closer similarity to the impedance characteristics of the current input and a greater contribution to the final prediction result. Conversely, training samples with larger squared distance values ​​receive weight values ​​closer to 0, effectively suppressing their influence on the prediction result. After calculating the similarity weights for all training samples, the weight values ​​are used to linearly weight and sum the corresponding real physical parameter labels for each training sample. Then, in the output layer, the weighted sum is divided by the sum of all weight values ​​for probability normalization, ultimately outputting the predicted equivalent circuit model parameters. The complete formula for calculating the above kernel regression nonparametric estimation is as follows: in, For input vector The equivalent circuit model parameter vector of the predicted output. For the first The true label values ​​of the physical parameters corresponding to each training sample. For the square set of Euclidean distances One element, To control the smoothing factor of the receptive field width of the Gaussian kernel function, This represents the total number of training samples. The equivalent circuit model parameters output through the above calculations must include at least an ohmic internal resistance. Solid electrolyte interfacial membrane resistance Charge transfer resistance The first parallel circuit capacitor Second parallel circuit capacitor Warburg diffusion capacitor and the corresponding diffusion coefficient and The above parameters are the total impedance formula for the aforementioned equivalent circuit model. All the variables to be identified in the data correspond to the contact conductivity loss, interfacial membrane ion transport resistance, electrode reaction kinetics, double-layer energy storage effect and solid-state diffusion behavior inside the battery, respectively. They can accurately reflect the loss of active materials and kinetic degradation process inside the battery from the microscopic electrochemical level.

[0019] Specifically, in step S2, a trainable temperature embedding layer based on index mapping is used to perform discrete indexed encoding and high-dimensional feature space mapping on the temperature data corresponding to each temperature condition to obtain a temperature embedding vector that can decouple the nonlinear coupling effect of temperature on battery aging characteristics. It should be noted that, given the nonlinear coupling effect of ambient temperature fluctuations on the electrochemical reaction rate and aging trajectory of lithium-ion batteries, the decrease in electrolyte ionic conductivity at low temperatures leads to an increase in polarization impedance, and the thermal excitation acceleration of active material reaction kinetics at high temperatures leads to an intensification of side reactions. If temperature values ​​are directly input into the model as scalar values, the single-dimensional numerical information cannot fully express the complex regulatory effect of temperature on multiple battery aging mechanisms, and it is easy to cause dimensional and order-of-magnitude interference with the parameters of the equivalent circuit model. Therefore, the technical solution of this application further uses a trainable temperature embedding layer based on index mapping to perform discrete indexed encoding and high-dimensional feature space mapping on the temperature data corresponding to each temperature condition to obtain a temperature embedding vector that can decouple the nonlinear coupling effect of temperature on battery aging characteristics. Through the above processing, discrete temperature operating condition information can be transformed into a dense vector representation in the same high-dimensional feature space as the parameters of the equivalent circuit model. This enables the subsequent transfer learning model to adaptively learn and identify feature distribution patterns related to a specific temperature domain, providing temperature sensing capability for feature alignment across temperature domains.

[0020] Figure 6 This document describes a flowchart illustrating a trainable temperature embedding layer based on index mapping in a lithium-ion battery cross-temperature SOH estimation method based on physical information transfer learning, according to an embodiment of this application. The process involves discretizing and indexing the temperature data corresponding to each temperature condition and mapping it to a high-dimensional feature space to obtain a temperature embedding vector that decouples the nonlinear coupling effect of temperature on battery aging characteristics. For example... Figure 6 As shown, step S2 includes: S21, based on the mapping rules from the physical temperature domain to the discrete state space defined in the preset global temperature mapping dictionary, the temperature data is discretized and indexed to obtain the temperature index; S22, the temperature index is input to a trainable embedding layer for lookup addressing mapping to output the temperature embedding vector corresponding to the current temperature condition.

[0021] In step S21, based on the mapping rules from the physical temperature domain to the discrete state space defined in the preset global temperature mapping dictionary, the temperature data is discretized and indexed to obtain a temperature index. It should be noted that since temperature data exists in the form of continuous physical quantities, its physical dimensions and numerical range are incompatible with the discrete integer index input format required by the subsequent embedding layer. Therefore, a mapping relationship from the physical temperature domain to the discrete state space needs to be established. Based on this, the technical solution of this application further discretizes and indexes the temperature data based on the mapping rules from the physical temperature domain to the discrete state space defined in the preset global temperature mapping dictionary to obtain a temperature index. Through the above processing, the differences in physical dimensions of the original temperature data can be eliminated, and continuous temperature information can be converted into standardized integer identifiers that can be looked up and addressed by the embedding layer.

[0022] More specifically, in a concrete example of this application, a global temperature mapping dictionary is first pre-constructed during the data preprocessing stage. This dictionary defines a one-to-one mapping rule between all discrete temperature conditions involved in the experiment or actual operation and their corresponding integer indices in the form of key-value pairs. Taking three typical temperature conditions involved in lithium-ion battery aging experiments as an example, this mapping dictionary maps 25 degrees Celsius to integer index 0, 35 degrees Celsius to integer index 1, and 45 degrees Celsius to integer index 2. The above mapping relationship remains fixed after the dictionary is established, ensuring that the same temperature always corresponds to the same index value in the training and inference stages. During actual execution, temperature data under the current battery operating conditions or experimental measurement conditions is obtained. This temperature value is used as the search key to perform key-value matching in the global temperature mapping dictionary. After a corresponding entry is found, its mapped integer index value is extracted as the output. The output integer scalar is the temperature index. It no longer carries the Celsius unit information of the original temperature data, but identifies the current temperature condition category in a categorized discrete encoding form, thus providing format-adapted input for subsequent table lookup and addressing mapping in the embedding layer.

[0023] Figure 7 This is a diagram of an index-based temperature embedding system for a lithium-ion battery cross-temperature SOH estimation method based on physical information transfer learning, according to an embodiment of this application. Figure 7 As shown, the temperature embedding process includes temperature catalog establishment, temperature index mapping, and embedding layer table lookup addressing, which transforms discrete temperature conditions into multidimensional temperature feature representations that can participate in subsequent joint modeling.

[0024] In step S22, the temperature index is input to a trainable embedding layer for lookup table addressing and mapping to output the temperature embedding vector corresponding to the current temperature condition. It should be noted that since the temperature index is only a discrete integer scalar without any semantic information, it cannot directly express the differentiated impact of different temperature conditions on battery aging characteristics. Therefore, it needs to be converted into a continuous feature vector with rich representational capabilities. Based on this, the technical solution of this application further inputs the temperature index to a trainable embedding layer for lookup table addressing and mapping to output the temperature embedding vector corresponding to the current temperature condition. Through the above processing, each discrete temperature condition can obtain a high-dimensional dense feature representation that is continuously optimized during training, providing a temperature-dimensional semantic encoding for subsequent feature fusion and transfer learning.

[0025] More specifically, in a specific example of this application, the temperature index is input to a trainable embedding layer for lookup addressing mapping to output a temperature embedding vector corresponding to the current temperature condition, including: converting the temperature index into a one-hot encoded vector; and based on the one-hot encoded vector, extracting the row vector corresponding to the temperature index from the trainable weight matrix of the embedding layer as the temperature embedding vector.

[0026] In other words, more specifically, a trainable embedding layer is first constructed within the deep learning framework. This embedding layer maintains a trainable weight matrix with rows equal to the total number of discrete temperature categories defined in the global temperature mapping dictionary, and columns equal to the preset embedding vector dimension. All elements in the weight matrix are randomly assigned during initialization and continuously updated and optimized through backpropagation during subsequent end-to-end training. When performing table lookup mapping, the temperature index output from the previous step is received and logically converted into a one-hot encoded vector, generating a sparse vector with a length equal to the total number of temperature categories. Only the element at the temperature index is 1, and all other elements are 0. This one-hot encoded vector is then multiplied by the trainable weight matrix of the embedding layer. Physically, this operation is equivalent to directly extracting the corresponding row vector from the weight matrix using the temperature index as the row address. The mathematical expression for the above feature mapping process is: ,in, The output temperature embedding vector, This is the trainable weight matrix for the embedding layer. This is a one-hot encoding conversion function. The input temperature index is used. Taking three temperature conditions and an embedding dimension of 8 as an example, when the input temperature index is 1, the second element of the one-hot encoded vector is 1. After matrix multiplication, the second row of the weight matrix is ​​extracted, outputting a dense temperature embedding vector of length 8. This embedding layer is essentially a learnable lookup table. During the training phase, through joint optimization with the subsequent transfer learning model, it adaptively learns the optimal feature representation corresponding to each temperature condition, so that the spatial distribution of the embedding vectors mapped by different temperature indices can reflect the inherent differences in battery aging characteristics under the corresponding temperature conditions.

[0027] Specifically, for the training process of the trainable embedding layer, the weight matrix within this layer is assigned random values ​​during the initialization phase and is jointly trained end-to-end with the subsequent transfer learning model. During model iterative training, the total loss function calculated by the front end, consisting of a weighted sum of source domain supervision loss, adversarial loss, and multi-core maximum mean difference regularization loss, is used to calculate the corresponding gradient information through the backpropagation algorithm. This gradient information is continuously propagated back to the temperature embedding layer along the network computation graph, driving the optimizer to continuously update and adjust the specific element values ​​in the weight matrix along the gradient descent direction. Through the above end-to-end optimization mechanism, the embedding layer can overcome the limitations of static lookup tables, adaptively learning and mining the nonlinear coupling law of each discrete temperature condition on the battery electrochemical aging trajectory during training. This allows the values ​​of the weight matrix to dynamically evolve with the training process until the overall network converges and solidifies into the optimal temperature feature space. This ensures that the same temperature index can be stably mapped to a high-dimensional temperature embedding vector that best expresses the physical parameters of the equivalent circuit model.

[0028] Specifically, in step S3, the equivalent circuit model parameters and the temperature embedding vector are concatenated and fused along the feature dimension to obtain source domain enhanced feature vectors and target domain enhanced feature vectors. It should be noted that since the equivalent circuit model parameters and the temperature embedding vector respectively carry information about the internal electrochemical degradation state of the battery and the external environmental temperature distribution, they may differ in data structure and tensor shape. They need to be unified into the same feature space for joint encoding to provide a complete input for subsequent transfer learning models that simultaneously includes physical mechanisms and environmental information. Based on this, the technical solution of this application further concatenates and fuses the equivalent circuit model parameters and the temperature embedding vector along the feature dimension to obtain source domain enhanced feature vectors and target domain enhanced feature vectors. Through the above processing, a comprehensive feature representation that simultaneously encodes the internal degradation state of the battery and the external temperature distribution can be constructed, guiding subsequent models to identify feature distribution patterns related to specific temperature domains.

[0029] More specifically, in a concrete example of this application, the equivalent circuit model parameters output by the front-end generalized regression neural network are first processed using tensor formatting. The equivalent circuit model parameters include eight independent microscopic physical variables: ohmic internal resistance, solid electrolyte interface film resistance, charge transfer resistance, first parallel loop capacitance, second parallel loop capacitance, Warburg diffusion capacitance, and two diffusion coefficients. These physical variables are flattened in a predetermined fixed order to form a one-dimensional numerical tensor of length 8, i.e., the aligned physical feature vector. Subsequently, the temperature embedding vector output by the temperature embedding layer undergoes dimension reshaping. Tensor shape adjustment ensures its rank matches the aligned physical feature vector, generating an aligned temperature feature vector. Taking an embedding dimension of 8 as an example, the length of the aligned temperature feature vector is also 8. After completing the format alignment of the two features, a linear concatenation operation is performed along the feature channel dimension on the aligned physical feature vector and the aligned temperature feature vector. That is, the aligned temperature feature vector is directly appended to the aligned physical feature vector, generating a joint tensor with a dimension equal to the sum of the dimensions of the two inputs. The mathematical expression for this concatenation operation is: ,in, The output is the enhanced feature vector. To align physical feature vectors, To align the temperature feature vector, This is a concatenation operator on the feature dimensions. Taking the above values ​​as an example, the length of the enhanced feature vector generated after concatenation is 16. Its first 8 dimensions encode the internal electrochemical degradation state information of the battery, and the last 8 dimensions encode the external environmental temperature distribution information. In the actual training process, the source domain data and the target domain data independently execute the above complete parameter extraction, temperature embedding, and feature concatenation processing flow. The source domain data is processed to generate the source domain enhanced feature vector, and the target domain data is processed to generate the target domain enhanced feature vector. Both have the same feature dimensions and data structure, and are used as dual inputs for the subsequent adversarial training of the transfer learning model.

[0030] Specifically, in step S4, the generator and discriminator are iteratively trained using the source domain enhanced feature vector, the target domain enhanced feature vector, and the source domain capacity label as inputs, through joint optimization of adversarial loss, multi-kernel maximum mean difference regularization loss, and source domain supervision loss, to obtain a transfer learning model. It should be noted that although the enhanced feature vectors of the source and target domains are generated through the same physical parameter extraction and temperature embedding process, their probability distributions in the feature space still exhibit domain shifts due to temperature differences because they are collected from different temperature conditions. Directly applying the prediction model trained in the source domain to the target domain leads to a decrease in estimation accuracy, and the target domain lacks capacity label data, making supervised training impossible. Therefore, the technical solution of this application further uses the source domain enhanced feature vector, the target domain enhanced feature vector, and the source domain capacity label as inputs, and iteratively trains the generator and discriminator through joint optimization of adversarial loss, multi-kernel maximum mean difference regularization loss, and source domain supervision loss to obtain a transfer learning model. Through the above processing, the overlapping alignment of feature distributions between the source and target domains can be achieved through the synergistic effect of adversarial game mechanism and distribution alignment constraint without the need for target temperature domain label data. At the same time, source domain supervised loss is used to prevent catastrophic forgetting during the transfer process, so that the trained model has the ability to transfer unsupervised knowledge from laboratory fixed temperature data to actual variable temperature conditions.

[0031] Figure 8 The flowchart illustrates the process of iteratively training the generator and discriminator to obtain the transfer learning model based on the physical information transfer learning-based lithium-ion battery temperature-dependent state-of-the-art (SOH) estimation method according to embodiments of this application. The method takes source domain enhanced feature vectors, target domain enhanced feature vectors, and source domain capacity labels as inputs, and employs joint optimization of adversarial loss, multi-kernel maximum mean difference regularization loss, and source domain supervision loss. Figure 8 As shown, step S4 includes: S41, inputting the source domain enhanced feature vector and the target domain enhanced feature vector into the generator for deep feature mapping to obtain the mapped source features and the mapped target features, and calculating the source domain supervision loss based on the predicted value of the mapped source features and the mean square error of the source domain capacity label; S42, inputting the mapped source features and the mapped target features into the discriminator to calculate the adversarial loss; S43, measuring the distribution difference between the two domains in the regenerating kernel Hilbert space based on a combination of multiple Gaussian kernel functions with different bandwidths to obtain the multi-kernel maximum mean difference regularization loss; S44, constructing the total loss function by weighting and summing the source domain supervision loss, adversarial loss, and multi-kernel maximum mean difference regularization loss through preset weight coefficients, and then fixing the network weights after backpropagation iterative optimization until convergence to obtain the transfer learning model.

[0032] In step S41, the source domain enhanced feature vector and the target domain enhanced feature vector are input into the generator for deep feature mapping to obtain mapped source features and mapped target features. The source domain supervision loss is then calculated based on the mean squared error of the predicted value of the mapped source features and the source domain capacity label. It should be noted that since the enhanced feature vector is still in the original concatenation space and has not yet undergone domain-invariant nonlinear feature extraction, and if there is a lack of constraints on the source domain prediction performance during transfer learning, the model may lose its memory of learned source domain knowledge when aligning with the target domain distribution. Therefore, the technical solution of this application further inputs the source domain enhanced feature vector and the target domain enhanced feature vector into the generator for deep feature mapping to obtain mapped source features and mapped target features, and calculates the source domain supervision loss based on the mean squared error of the predicted value of the mapped source features and the source domain capacity label. Through the above processing, transfer-oriented deep feature extraction and the establishment of source domain knowledge anchoring constraints can be completed simultaneously.

[0033] More specifically, in a concrete example of this application, the source domain enhanced feature vector and the target domain enhanced feature vector are respectively input into the generator network of the transfer learning model. The generator network consists of multiple layers of fully connected layers and nonlinear activation functions stacked alternately. The source domain enhanced feature vector is transformed layer by layer nonlinearly by each layer of the generator to output mapped source features, and the target domain enhanced feature vector is processed by the same network structure and shared weight parameters of the same generator to output mapped target features. Both features obtain feature representations optimized for domain invariance in the same deep latent space. After feature mapping, the mapped source features are used to predict capacity through a regression prediction head connected to the end of the generator. The regression prediction head maps the mapped source features to scalar capacity prediction values ​​through fully connected layers. Then, the predicted value is compared with the corresponding source domain capacity label sample by sample, and the mean squared error between the two is calculated as the source domain supervision loss. The mathematical expression for this loss is: in, For source domain monitoring loss, This is a composite mapping function between the generator and the regression prediction head. For the first Enhance feature vectors from source domains For the first The actual value of the source domain capacity label. The total number of samples in the source domain. The source domain supervision loss acts as an anchor constraint throughout the training process, forcing the generator to retain its memory of the source domain capacity prediction task while fitting the target domain distribution, thus preventing catastrophic forgetting caused by overfitting to the target domain and resulting in degradation of source domain performance.

[0034] In step S42, the source and target features are input into the discriminator to calculate the adversarial loss. It should be noted that although the source and target features are processed by the same generator, residual inter-domain differences may still exist in their distribution in the deep latent space. Therefore, an adversarial game mechanism is needed to drive the generator to actively eliminate this distribution shift. Based on this, the technical solution of this application further inputs the source and target features into the discriminator to calculate the adversarial loss. Through the above processing, the competitive game between the generator and the discriminator forces the two domain features to become indistinguishable in the latent space, achieving the extraction of domain-invariant features.

[0035] More specifically, in a concrete example of this application, the source and target mapping features output by the generator are fed into a discriminator network for domain classification. The discriminator network consists of multiple fully connected layers and nonlinear activation functions, with a probability prediction node at its end whose output value is between 0 and 1. An output value of 1 indicates that the discriminator determines the input feature originates from the source domain, and an output value of 0 indicates that the input feature originates from the target domain. The goal of optimizing the discriminator is to distinguish the domain affiliation of the source and target mapping features as accurately as possible. The corresponding discriminator loss is defined as: in, For discriminator loss, This is the discriminator function, which outputs a probability value between 0 and 1. A value of 1 indicates that the input features originate from the source domain, and a value of 0 indicates that the input features originate from the target domain. The source domain mapping function has its parameters fixed during the pre-training phase and does not participate in adversarial optimization. This is the target domain mapping function, which is used as a generator for parameter optimization during the adversarial training phase. For source domain dataset A single sample in the, For the target domain dataset A single sample in the, For mathematical expectation operators, The loss function is the natural logarithm. The first term of this loss term drives the discriminator to map features from the source domain. The output probability is pushed towards 1, and the second term drives the discriminator to map the target domain to features. The output probability is pushed towards 0, thereby enhancing the discriminator's ability to distinguish features between the two domains. The generator's optimization direction is opposite to that of the discriminator, namely, to minimize the discriminator's misclassification of target domain features as source domain features. The corresponding generator loss is defined as: in, For generator loss, , , , and The definition is consistent with that in the discriminator loss. By minimizing this loss, the generator is encouraged to adjust the target domain mapping function. The parameters enable the discriminator to map the target domain to features. The output probability is misclassified as close to 1, even though the discriminator believes the target domain feature comes from the source domain, thus deceiving the discriminator. During training, the discriminator enhances its domain discrimination ability by minimizing its discriminator loss, while the generator weakens the discriminator's discrimination ability by minimizing its generator loss; the two form an adversarial game. When training reaches equilibrium, the discriminator's output probability for any input feature approaches 0.5, indicating that it can no longer distinguish which temperature domain the feature comes from. At this point, the distributions of the mapped source feature and the mapped target feature in the deep latent space are aligned. The discriminator loss and the generator loss together constitute the adversarial loss, which participates in joint optimization as part of the subsequent total loss function.

[0036] In step S43, the distribution difference between the two domains in the regenerating kernel Hilbert space is measured by combining multiple Gaussian kernel functions with different bandwidths to obtain the multi-kernel maximum mean difference regularization loss. It should be noted that since the adversarial loss only indirectly drives feature alignment through the classification probability of the discriminator, its training process is subject to the risk of gradient vanishing or mode collapse. Therefore, an additional explicit distribution distance metric is needed as a regularization constraint to stabilize the alignment process. Based on this, the technical solution of this application further measures the distribution difference between the two domains in the regenerating kernel Hilbert space by combining multiple Gaussian kernel functions with different bandwidths to obtain the multi-kernel maximum mean difference regularization loss. Through the above processing, explicit alignment constraints can be imposed on the feature distributions of the source and target domains at the statistical distribution level, complementing the adversarial loss to improve the stability and sufficiency of cross-temperature feature alignment.

[0037] More specifically, in a specific example of this application, the multi-kernel maximum mean difference regularization loss is obtained by measuring the distribution difference between two domains in the regenerating kernel Hilbert space based on a combination of multiple Gaussian kernel functions with different bandwidths. This includes: constructing Gaussian kernel functions with multiple different bandwidth parameters, and linearly combining the multiple Gaussian kernel functions to form a multi-kernel kernel function; using the multi-kernel kernel function to map the mapping source features and mapping target features to the regenerating kernel Hilbert space; in the regenerating kernel Hilbert space, extracting the mean kernel function values ​​between sample pairs in the source domain, sample pairs in the target domain, and cross-domain sample pairs, respectively, and evaluating the distance between the feature distributions of the two domains based on the mean kernel function values ​​to obtain the multi-kernel maximum mean difference regularization loss.

[0038] In other words, a set of Gaussian kernel functions with different bandwidth parameters is first constructed. Each Gaussian kernel function corresponds to a specific bandwidth value. Kernel functions with different bandwidths are sensitive to structural differences in the feature distribution at different scales. Small-bandwidth kernel functions focus on capturing local detail differences in the distribution, while large-bandwidth kernel functions focus on capturing global structural differences in the distribution. These multiple Gaussian kernel functions are linearly combined to form a multi-kernel kernel function. This multi-kernel kernel function implicitly maps the source and target features from the original feature space to the regenerating kernel Hilbert space. In the regenerating kernel Hilbert space, the mean kernel function values ​​between source domain sample pairs, between target domain sample pairs, and between cross-domain sample pairs are calculated. The distance between the means of the embedding distributions of the two domains is calculated by adding the mean within the source domain to the mean within the target domain and subtracting twice the cross-domain mean. The unbiased estimation formula for the maximum mean difference of the multi-kernel kernel is as follows: in, The loss is the maximum mean difference regularization loss for multi-core processors. A multi-kernel kernel function is a linear combination of multiple Gaussian kernel functions with different bandwidths. and For the first feature in the mapping source The and the first One sample, and For the first feature in the mapping target The and the first One sample, The number of samples in the source domain. The number of samples in the target domain is denoted as . A larger loss value indicates a greater distance between the feature distributions of the two domains in the regenerating kernel Hilbert space. During training, minimizing this loss value forces the feature distributions of the source and target domains to be closer, working in conjunction with adversarial loss to achieve multi-granularity cross-temperature domain feature distribution alignment.

[0039] In step S44, a total loss function is constructed by weighting and summing the source domain supervision loss, adversarial loss, and multi-kernel maximum mean difference regularization loss using preset weight coefficients. This function is then iteratively optimized through backpropagation until convergence, after which the network weights are solidified to obtain the transfer learning model. It should be noted that since the adversarial loss, multi-kernel maximum mean difference regularization loss, and source domain supervision loss serve different optimization objectives, they need to be integrated into a unified optimization direction through reasonable weight allocation to coordinate the balance between adversarial confusion, distribution alignment, and source domain knowledge preservation. Based on this, the technical solution of this application further constructs a total loss function by weighting and summing the source domain supervision loss, adversarial loss, and multi-kernel maximum mean difference regularization loss using preset weight coefficients. This function is then iteratively optimized through backpropagation until convergence, after which the network weights are solidified to obtain the transfer learning model. Through the above processing, cross-temperature domain feature alignment and source domain prediction performance preservation can be simultaneously achieved within a unified optimization framework, outputting a transfer learning model with cross-temperature generalization capabilities.

[0040] More specifically, in a concrete example of this application, the adversarial loss, multi-core maximum mean difference regularization loss, and source domain supervision loss calculated by the front end are first weighted and summed using preset weighting coefficients to construct the total loss function. The mathematical expression of this total loss function is: in, For the total loss function, To combat the losses, The loss is the maximum mean difference regularization loss for multi-core processors. For source domain monitoring loss, , and These are the corresponding weight coefficients. The optimal allocation of these weight coefficients is determined through a grid search combined with cross-validation. Specifically, the source domain supervised loss weights are... The value is fixed at 0.01 to ensure the stability of the source domain knowledge, and an adversarial loss weight is set. The candidate values ​​are 10 discrete values: 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1, 2, 5, and 10. The multi-core maximum mean difference regularization loss weight is set. The candidate values ​​are 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, and 100, a total of 10 discrete values. This constructs 100 weight combinations. 30-fold cross-validation is used to train and evaluate the model for each weight combination. The mean relative error, root mean square error, and mean absolute error are used as comprehensive evaluation indicators. The weight combination that optimizes the comprehensive indicators is selected as the hyperparameter of the final model.

[0041] Based on the above grid search and 30-fold cross-validation evaluation, the comprehensive performance indicators of the model under some representative weight combinations in the target temperature domain are shown in Table 1 below: Table 1 The above evaluation results show that when the adversarial loss weight When the size is too small, the generator lacks sufficient adversarial drive for domain alignment, resulting in a large estimation error in the target domain; when... When the value is too large, the adversarial training process becomes unstable. An overly strong discriminator gradient signal causes oscillations in the generator's optimization direction, ultimately reducing estimation accuracy. Similarly, when the multi-core maximum mean difference regularization loss weights... When the size is too small, explicit distribution alignment constraints are insufficient to compensate for the local instability of adversarial training; when... When the value is too large, an overly strong distribution matching constraint can suppress the effective transmission of source domain supervision signals, leading to a degradation in the model's predictive ability in the source domain and indirectly affecting the estimation accuracy in the target domain. Considering the three indicators—mean relative error, root mean square error, and mean absolute error—when... =1、 =20、 When the weight ratio is 0.01, the model achieves the best overall performance in 30-fold cross-validation with a mean relative error of 1.24%, a root mean square error of 0.0243 Ah, and a mean absolute error of 0.0192 Ah. All three metrics are superior to the other 99 weight combinations. Therefore, the final selected weight coefficients for the total loss function are: adversarial loss weights. =1, Multi-core maximum mean difference regularization loss weight =20, source domain supervised loss weight =0.01.

[0042] After determining the weight coefficients, the gradients of all trainable parameters in the generator and discriminator are calculated using the backpropagation algorithm based on the total loss function. An optimizer iteratively updates the network weight parameters in the direction of gradient descent, alternately optimizing the parameters of the discriminator and generator in each iteration until the total loss function converges and the feature distributions of the source and target domains are fully aligned. After training, all network weight parameters of the generator and discriminator are frozen, and the overall output encapsulating the complete network structure and fixed weights is presented as a transfer learning model for direct use in subsequent inference stages.

[0043] Specifically, in step S5, the enhanced feature vector generated from the electrochemical impedance spectroscopy data and temperature data of the battery under test after parameter extraction and temperature embedding is input into the transfer learning model for capacity inference to obtain a capacity estimate. It should be noted that since the transfer learning model has already completed the feature distribution alignment between the source and target domains during the training phase and possesses cross-temperature generalization capability, the real-time operating data of the battery under test needs to be fed into the model after undergoing the same feature processing procedure for online capacity inference. Based on this, the technical solution of this application further inputs the enhanced feature vector generated from the electrochemical impedance spectroscopy data and temperature data of the battery under test after parameter extraction and temperature embedding into the transfer learning model for capacity inference to obtain a capacity estimate. Through the above processing, real-time estimation of the maximum usable capacity of the battery under test under its current operating conditions can be achieved without the need for target temperature domain label data.

[0044] More specifically, in a concrete example of this application, the electrochemical impedance spectroscopy (EIS) data and temperature data of the lithium-ion battery under test are first acquired in real time under the current operating conditions. The EIS data is input into a generalized regression neural network with pre-defined parameters to extract equivalent circuit model parameters. The temperature data is converted into a temperature index using a global temperature mapping dictionary and then input into a temperature embedding layer pre-defined during the training phase to obtain a temperature embedding vector. Subsequently, the equivalent circuit model parameters and the temperature embedding vector are aligned in dimension and concatenated to generate an enhanced feature vector for the battery under test. The above feature processing flow is completely consistent with the training phase, ensuring that the data structure and distribution characteristics of the input features meet the inference requirements of the model. After feature preparation is completed, the network running state of the transfer learning model is set to inference mode, gradient calculation and parameter update functions are disabled, and the enhanced feature vector of the battery under test is fed as an input tensor into the generator network entry point of the model. The enhanced feature vector is calculated through layer-by-layer forward propagation of multiple fully connected layers and nonlinear activation functions inside the generator to extract deep latent variable features with domain invariant properties. This feature is then mapped by the fully connected layer of the terminal regression prediction head to output a scalar value, which is the capacity estimate of the battery under test under the current operating temperature condition. Its physical meaning is the maximum amount of usable charge that the battery can hold under the current condition.

[0045] In step S6, the battery's health status value is determined based on the ratio of the capacity estimate to the battery's rated capacity. It should be noted that since the capacity estimate output by the transfer learning model is an absolute capacity value in ampere-hours (AH), its magnitude is affected by the battery model and specifications, making it incomparable between different batteries. It needs to be converted into a normalized relative indicator to uniformly measure the degree of battery degradation and serve the battery management system's safety warning and lifespan management decisions. Based on this, the technical solution of this application further determines the battery's health status value based on the ratio of the capacity estimate to the battery's rated capacity. Through the above processing, the absolute capacity value can be converted into a dimensionless percentage indicator between 0 and 100%, intuitively reflecting the proportion of the battery's current usable capacity relative to its factory-nominated capacity. This provides a quantitative basis for the battery management system to determine whether the battery meets the industry's accuracy requirement of an average health status estimation error of less than 5%.

[0046] Figure 9 This is a flowchart illustrating how a lithium-ion battery's state of health (SOH) value is determined based on the ratio of the estimated capacity to the battery's rated capacity, according to an embodiment of this application's physical information transfer learning-based method for estimating SOH across temperature ranges in lithium-ion batteries. Figure 9 As shown, step S6 includes: S61, using the reference absolute temperature at the factory calibration as the baseline anchor point, performing temperature scale conversion and kinetic offset calculation on the temperature data to obtain a temperature correction factor; S62, performing cross-temperature capacity normalization conversion on the capacity estimate based on the temperature correction factor to remove the reversible capacity fluctuation component caused by temperature, and obtaining the reference temperature normalized capacity; S63, using the reference temperature normalized capacity as the numerator and the battery rated capacity calibrated at the same reference temperature as the denominator to obtain the health status value.

[0047] In step S61, the temperature data is converted to a temperature scale and kinetic offset is calculated using the reference absolute temperature at the factory calibration as the baseline anchor to obtain the temperature correction factor. It should be noted that since the capacity estimate is a dynamic estimate inferred by the transfer learning model at the current actual operating temperature, while the battery's rated capacity is a fixed benchmark value calibrated at the standard reference temperature at the factory, the two are on different temperature benchmarks. The capacity estimate simultaneously couples two fundamentally different effect components: reversible capacity fluctuations caused by temperature and irreversible capacity degradation caused by aging. Directly performing a ratio calculation cannot distinguish the contribution ratio of the two. Based on this, the technical solution of this application further uses the reference absolute temperature at the factory calibration as the baseline anchor to perform temperature scale conversion and kinetic offset calculation on the temperature data to obtain the temperature correction factor. Through the above processing, the capacity baseline offset rate caused by the current operating temperature deviating from the reference temperature can be quantified based on the physical mechanism of electrochemical kinetics, providing a correction basis for subsequent removal of the reversible capacity fluctuation component.

[0048] More specifically, in a concrete example of this application, the temperature data under the current target operating condition is first obtained and converted from the Celsius scale to the thermodynamic absolute temperature scale to obtain the operating absolute temperature in Kelvin. In the electrochemical system of a lithium-ion battery, both the exchange current density of the charge transfer reaction and the solid-state diffusion coefficient of lithium ions in the electrode material follow the Arrhenius temperature dependence, that is, the reaction rate constant changes exponentially with temperature. This law determines the nonlinear fluctuation characteristics of the battery's usable capacity with temperature at the microscopic level. Based on this physical mechanism, using the reference absolute temperature at the factory rated capacity calibration as the baseline anchor point, the electrochemical kinetic offset caused by the current operating absolute temperature deviating from the reference absolute temperature is calculated, and this offset is mapped to a dimensionless scaling factor, i.e., the temperature correction factor, through an exponential function. The formula for calculating the temperature correction factor is: in, This is the temperature correction factor, representing the capacity baseline offset ratio of the current operating temperature relative to the reference temperature. The equivalent activation energy for capacity-temperature response, expressed in joules per mole, was obtained through Arrhenius fitting and pre-calibration of full-charge and discharge experimental data at multiple discrete temperature points. It reflects the sensitivity of the battery's usable capacity to temperature changes. The universal gas constant is 8.314 joules / (molar Kelvin). The reference absolute temperature used when calibrating the factory rated capacity, in Kelvin. For example, 298.15 Kelvin corresponds to 25 degrees Celsius. This is the current absolute operating temperature, obtained by converting temperature data to a temperature scale, in Kelvin. When the operating temperature is lower than the reference temperature... The value is positive, the exponent is greater than 0, the temperature correction factor is greater than 1, and the low capacity caused by low temperature is compensated; when the operating temperature is higher than the reference temperature, the difference is negative, the exponent is less than 0, the temperature correction factor is less than 1, and the false capacity increase caused by high temperature is deducted; when the operating temperature is exactly equal to the reference temperature, the exponent is zero, the temperature correction factor degenerates to 1, the correction mechanism automatically fails, and it remains consistent with the original mechanism, ensuring backward compatibility. Taking a lithium-ion battery with a rated capacity of 2 amp-hours at 25 degrees Celsius as an example, when the battery operates at 0 degrees Celsius, due to the decrease in electrolyte ionic conductivity and the increase in charge transfer impedance, the capacity estimate output by the transfer learning model may only be 1.7 amp-hours. At this time, the operating absolute temperature is 273.15 Kelvin, and the reference absolute temperature is 298.15 Kelvin. The temperature correction factor calculated by the above formula is greater than 1, which can compensate the lower capacity observation value at low temperature to the reference temperature level. However, when the battery operates at 45 degrees Celsius, due to the thermal excitation acceleration of the reaction kinetics of the active material, the capacity estimate may reach 2.05 amp-hours. At this time, the calculated temperature correction factor is less than 1, which can correct the artificially inflated capacity observation value at high temperature to the reference temperature level.

[0049] In step S62, the capacity estimate is normalized across temperature based on a temperature correction factor to remove the reversible capacity fluctuation component caused by temperature, resulting in a reference temperature-normalized capacity. It should be noted that since the capacity estimate reflects the actual maximum usable capacity of the battery at the current operating temperature, it includes both irreversible degradation caused by aging and reversible fluctuation deviations caused by deviations from the reference temperature. Therefore, a temperature correction factor is needed to separate these two effects. Based on this, the technical solution of this application further performs a cross-temperature capacity normalization based on a temperature correction factor to remove the reversible capacity fluctuation component caused by temperature, resulting in a reference temperature-normalized capacity. Through the above processing, the capacity observation value under any operating temperature baseline can be equivalently projected back to the reference temperature baseline, retaining only the irreversible capacity loss caused by pure aging.

[0050] More specifically, in a concrete example of this application, the capacity estimate output by the transfer learning model is multiplied and scaled using the temperature correction factor calculated in the previous step. Physically, the capacity estimate reflects the actual maximum usable capacity of the battery at the current operating temperature, including both irreversible degradation caused by aging and reversible fluctuations due to deviations from the reference temperature. Multiplying by the temperature correction factor is equivalent to projecting the capacity observation at the current temperature baseline back to the reference temperature baseline along the Arrhenius curve, thereby removing the temperature-induced reversible capacity fluctuation component from the total capacity and retaining only the pure aging capacity caused by irreversible electrochemical mechanisms such as the thickening of the solid electrolyte interface film, loss of active lithium, and degradation of the cathode structure, thus generating the reference temperature normalized capacity. The formula for this normalization is: in, Reference temperature normalized capacity, i.e., the pure aging capacity value equivalently mapped to the reference temperature base, in ampere-hours. This is a capacity estimate, specifically the battery capacity at the current operating temperature, directly output by the forward inference of the transfer learning model. The temperature correction factor is used. Taking the lithium-ion battery operating at 0 degrees Celsius as an example, the capacity estimate output by the transfer learning model is 1.7 amp-hours. This value includes the reversible capacity compression effect caused by low temperature. At this time, the temperature correction factor is greater than 1. Multiplying 1.7 amp-hours by this temperature correction factor, the capacity observation is compensated upward to the reference temperature level. Assuming that the reference temperature normalized capacity obtained after correction is 1.9 amp-hours, it indicates that the battery has lost 0.1 amp-hours of capacity due to the pure aging mechanism after excluding the influence of temperature. When operating at 45 degrees Celsius, the capacity estimate is 2.05 amp-hours. This value includes the reversible capacity gain effect caused by high temperature. At this time, the temperature correction factor is less than 1. Multiplying 2.05 amp-hours by this temperature correction factor, the capacity observation is corrected downward to the reference temperature level. Assuming that the reference temperature normalized capacity is also 1.9 amp-hours after correction, it indicates that the actual aging degree of the battery is consistent under the two temperature conditions, verifying the effectiveness of the temperature decoupling mechanism.

[0051] In step S63, the health status value is obtained by using the reference temperature normalized capacity as the numerator and the battery rated capacity calibrated at the same reference temperature as the denominator. It should be noted that since the reference temperature normalized capacity has already undergone temperature effect stripping, and the battery rated capacity is also calibrated at the reference temperature, both are strictly on the same temperature baseline. This overcomes the evaluation bias caused by the numerator and denominator being at different temperature baselines in existing mechanisms, which leads to a systematic underestimation of the health status value under low-temperature conditions and a systematic overestimation under high-temperature conditions. Based on this, the technical solution of this application further uses the reference temperature normalized capacity as the numerator and the battery rated capacity calibrated at the same reference temperature as the denominator to obtain the health status value. Through the above processing, the systematic interference caused by operating temperature deviation can be completely eliminated, purely and accurately reflecting the degree of irreversible capacity loss caused by internal electrochemical aging of the battery.

[0052] More specifically, in a concrete example of this application, the normalized capacity at the reference temperature after temperature decoupling is used as the numerator, and the rated capacity of the battery calibrated at the same reference temperature is used as the denominator for a division ratio calculation. Since both the numerator and denominator are strictly above the same reference temperature baseline, their ratio can completely eliminate systematic interference caused by operating temperature deviations, purely and accurately reflecting the degree of irreversible capacity loss caused by internal electrochemical aging of the battery. This ratio is converted into a percentage form, and the final health status value is output. The formula for accurately assessing the health status after temperature decoupling is: in, This represents the health status value after temperature decoupling, expressed as a percentage indicating the remaining capacity of the battery due to pure aging factors. Normalized capacity for reference temperature The rated capacity of the battery is the factory-statistical capacity calibrated at a reference temperature. By embedding a temperature-capacity baseline correction step based on Arrhenius dynamics before the health state ratio calculation, the capacity estimate is equivalently converted from any operating temperature baseline to a reference temperature baseline identical to the rated capacity before comparison, ensuring strict consistency between the numerator and denominator in the temperature reference system. Under low-temperature conditions, the temperature correction factor is greater than 1, compensating the capacity observation value compressed by the low temperature back to the reference temperature level, preventing healthy batteries from being misjudged as severely degraded and triggering unnecessary maintenance and retirement operations. Under high-temperature conditions, the temperature correction factor is less than 1, correcting the capacity observation value artificially inflated by the high temperature back to the reference temperature level, preventing the true aging degree of degraded batteries from being masked by temperature effects and delaying safety intervention. Taking the aforementioned 2 Ah lithium-ion battery as an example, regardless of whether the battery operates at 0°C or 45°C, the reference temperature normalized capacity after temperature decoupling is 1.9 Ah. Dividing 1.9 Ah by 2 Ah and then multiplying by 100% yields a health status value of 95%. This value accurately reflects the 5% capacity loss due to the battery's aging mechanism, independent of operating temperature. After this correction mechanism, the health status value can accurately and consistently reflect the proportion of irreversible capacity loss caused by the battery's inherent aging mechanisms, such as the continuous thickening of the solid electrolyte interface film, irreversible depletion of lithium reserves, and degradation of the positive electrode active material structure, across the entire operating temperature range. This eliminates the systematic assessment bias in the original mechanism that is positively correlated with operating temperature, improves the physical accuracy and engineering reliability of health status estimation across temperature conditions, and provides a reliable data foundation for battery management systems to formulate precise safety warning strategies and lifespan optimization management decisions in complex temperature environments.

[0053] In summary, a method for estimating the state of harmonics (SOH) of lithium-ion batteries across temperatures based on physical information transfer learning, according to embodiments of this application, is elucidated. First, an equivalent circuit model incorporating constant-phase elements and Warburg diffusion elements is constructed. Then, a generalized regression neural network is used to rapidly and robustly fit the electrochemical impedance spectroscopy data, extracting model parameters with clear physical meaning. This allows the input features of the subsequent deep learning model to directly correspond to the microscopic electrochemical degradation process within the battery, thereby endowing the entire framework with clear physical interpretability. Subsequently, a trainable temperature embedding layer based on index mapping is constructed to encode discrete temperature conditions into high-dimensional feature vectors. These vectors are then concatenated with physical parameters to form an enhanced feature vector that integrates physical and environmental information, effectively decoupling the nonlinear coupling between temperature and aging characteristics. Based on this, a generative adversarial distribution matching mechanism combined with a multi-kernel maximum mean difference regularization term is employed to align the feature distributions between the source and target domains without requiring target temperature domain label data, overcoming the domain offset problem between different temperature conditions. Furthermore, a temperature correction mechanism based on Arrhenius dynamics is introduced before calculating the health status ratio. This mechanism converts the capacity estimate at any operating temperature to an equivalent reference temperature baseline that is the same as the rated capacity, thus removing the reversible capacity fluctuation component caused by temperature. This ensures that the health status value truly and consistently reflects the proportion of irreversible capacity loss caused by the battery's inherent aging mechanism across the entire temperature range, eliminating systematic evaluation bias that is positively correlated with operating temperature.

[0054] Those skilled in the art will understand that the steps, measures, and schemes in the various operations, methods, and processes discussed in this application can be alternated, modified, combined, or deleted; furthermore, other steps, measures, and schemes in the various operations, methods, and processes discussed in this application can also be alternated, modified, rearranged, decomposed, combined, or deleted; furthermore, the steps, measures, and schemes in the prior art that are similar to those disclosed in this application can also be alternated, modified, rearranged, decomposed, combined, or deleted. The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. The above-described embodiments are merely illustrative of several implementation methods of this disclosure, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of the patent for the embodiments of this disclosure. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the embodiments of this disclosure, and these all fall within the protection scope of the embodiments of this disclosure. Therefore, the protection scope of the embodiments of this disclosure should be determined by the appended claims. As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes in form and detail can be made without departing from the spirit and scope of the present invention as defined in the appended claims.

[0055] The present invention and its embodiments have been described above. This description is not restrictive, and the accompanying drawings are only one embodiment of the present invention; the actual structure is not limited thereto. In conclusion, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the present invention, such designs should fall within the protection scope of the present invention.

Claims

1. A method for estimating the state of harm (SOH) of lithium-ion batteries across temperatures based on physical information transfer learning, characterized in that, include: S1: Rapidly fit and extract parameters from the collected electrochemical impedance spectroscopy data of lithium-ion batteries under multiple temperature conditions to obtain equivalent circuit model parameters including ohmic internal resistance, solid electrolyte interface film resistance, and charge transfer resistance. S2: A trainable temperature embedding layer based on index mapping performs discrete indexing encoding and high-dimensional feature space mapping on the temperature data corresponding to each temperature condition to obtain a temperature embedding vector that can decouple the nonlinear coupling effect of temperature on battery aging characteristics. S3: The equivalent circuit model parameters and the temperature embedding vector are concatenated and fused along the feature dimension to obtain the source domain enhanced feature vector and the target domain enhanced feature vector; S4: Using the source domain enhanced feature vector, the target domain enhanced feature vector, and the source domain capacity label as input, the generator and discriminator are iteratively trained through joint optimization of adversarial loss, multi-kernel maximum mean difference regularization loss, and source domain supervision loss to obtain a transfer learning model; S5: The enhanced feature vector generated by the electrochemical impedance spectroscopy data and temperature data of the battery under test after parameter extraction and temperature embedding is input into the transfer learning model to infer the capacity and obtain the capacity estimate. Step S2 includes: Based on the mapping rules from the physical temperature domain to the discrete state space defined in the preset global temperature mapping dictionary, the temperature data is discretized and indexed to obtain the temperature index. The temperature index is input into a trainable embedding layer for lookup addressing and mapping to output a temperature embedding vector corresponding to the current temperature condition. This includes: converting the temperature index into a one-hot encoded vector; and extracting the row vector corresponding to the temperature index from the trainable weight matrix of the embedding layer as the temperature embedding vector based on the one-hot encoded vector.

2. The method for estimating the state of harmonic oxygen (SOH) of lithium-ion batteries across temperatures based on physical information transfer learning according to claim 1, characterized in that, Also includes: S6: Determine the battery's health status value based on the ratio of the estimated capacity to the battery's rated capacity.

3. The method for estimating the state of harmonic oxygen (SOH) of lithium-ion batteries across temperatures based on physical information transfer learning according to claim 1, characterized in that, Step S1 includes: The test frequency, real impedance, and imaginary impedance are extracted from electrochemical impedance spectroscopy data to construct an impedance feature input vector. The impedance feature input vector is input into a generalized regression neural network to perform pattern layer feature distance measurement to obtain the Euclidean distance square set. Kernel regression weighted parameter prediction is performed on the squared Euclidean distance set to obtain the parameters of the equivalent circuit model.

4. The method for estimating the state of harmonic oxygen (SOH) of lithium-ion batteries across temperatures based on physical information transfer learning according to claim 1, characterized in that, Step S3 includes: The microscopic physical variables in the parameters of the equivalent circuit model are flattened in a preset order to obtain the aligned physical feature vector. The temperature embedding vector is redimensionally reshaped to obtain an aligned temperature feature vector; Along the feature channel dimension, the aligned physical feature vector and the aligned temperature feature vector are linearly concatenated and fused to obtain the enhanced feature vector, wherein the source domain and the target domain independently generate corresponding enhanced feature vectors as the source domain enhanced feature vector and the target domain enhanced feature vector, respectively.

5. The method for estimating the state of harmonic oxygen (SOH) of lithium-ion batteries across temperatures based on physical information transfer learning according to claim 1, characterized in that, Step S4 includes: The source domain enhanced feature vector and the target domain enhanced feature vector are input into the generator for deep feature mapping to obtain the mapped source features and the mapped target features. The source domain supervision loss is calculated based on the predicted value of the mapped source features and the mean square error of the source domain capacity label. The source and target features of the mapping are input into the discriminator to calculate the adversarial loss; The multi-kernel maximum mean difference regularization loss is obtained by combining multiple Gaussian kernel functions with different bandwidths to measure the distribution difference between the two domains in the regenerating kernel Hilbert space. The total loss function is constructed by weighting and summing the source domain supervision loss, adversarial loss, and multi-kernel maximum mean difference regularization loss by pre-setting weight coefficients. After backpropagation and iterative optimization until convergence, the network weights are solidified to obtain the transfer learning model.

6. The method for estimating the state of harmonic oxygen (SOH) of lithium-ion batteries across temperatures based on physical information transfer learning according to claim 1, characterized in that, Step S5 includes: The enhanced feature vector of the battery under test is input into the generator of the transfer learning model. In inference mode, forward propagation calculation is performed through a multi-layer nonlinear network and mapped through the terminal regression prediction head to obtain the capacity estimate under the current operating condition.

7. The method for estimating the state of oxygen (SOH) of lithium-ion batteries across temperatures based on physical information transfer learning according to claim 2, characterized in that, Step S6 includes: Using the reference absolute temperature at the factory calibration as the baseline anchor point, the temperature data is converted to a temperature scale and the dynamic offset is calculated to obtain the temperature correction factor. Based on the temperature correction factor, the capacity estimate is normalized across temperature to remove the reversible capacity fluctuation component caused by temperature, and the reference temperature normalized capacity is obtained. The health status value is obtained by using the normalized capacity at the reference temperature as the numerator and the rated capacity of the battery calibrated at the same reference temperature as the denominator.

8. The method for estimating the state of harmonic oxygen (SOH) of lithium-ion batteries across temperatures based on physical information transfer learning according to claim 5, characterized in that, The multi-kernel maximum mean difference regularization loss is obtained by combining multiple Gaussian kernel functions with different bandwidths to measure the distribution difference between two domains in the reproducing kernel Hilbert space, including: Construct a Gaussian kernel function containing multiple different bandwidth parameters, and linearly combine the multiple Gaussian kernel functions to form a multi-kernel kernel function; The source and target features are mapped to the regenerating kernel Hilbert space using a multi-kernel kernel function. In the regenerating kernel Hilbert space, the mean kernel function values ​​of sample pairs in the source domain, sample pairs in the target domain, and cross-domain sample pairs are extracted respectively. The distance between the feature distributions of the two domains is evaluated based on the mean kernel function values ​​to obtain the multi-kernel maximum mean difference regularization loss.

Images