A lithium ion battery full-frequency range electrochemical impedance spectrum reconstruction method and system

Abstract

This invention provides a method and system for reconstructing the full-band electrochemical impedance spectroscopy (EIS) of lithium-ion batteries. The method includes: performing distributed relaxation time (DRT) analysis on each group of battery EIS samples to obtain DRT spectra; aligning the DRT spectra on the logarithmic time constant axis and performing ensemble statistics, selecting peaks and / or valleys that stably appear under multiple operating conditions based on statistical stability, and mapping them to obtain a set of conditionally invariant characteristic frequencies; selecting characteristic frequency points that satisfy the sampling budget from the set of conditionally invariant characteristic frequencies, and performing sparse EIS measurements on the target battery at these characteristic frequency points to obtain sparse complex impedance inputs; generating a full-band complex impedance sequence based on the sparse complex impedance inputs using an autoregressive reconstruction model; and performing battery state estimation and fault diagnosis based on the full-band complex impedance sequence. This invention significantly improves the continuity of the spectral shape and the generalization ability across operating conditions under sparse sampling conditions, while reducing the full-spectrum testing time and sampling burden.

Description

Technical Field

[0001] This invention belongs to the field of lithium-ion battery and energy storage technology, specifically relating to a method and system for reconstructing the full-band electrochemical impedance spectroscopy of lithium-ion batteries. Background Technology

[0002] As a core component of electric vehicles and energy storage systems, lithium-ion batteries' safety and lifespan are highly dependent on operating conditions and internal electrochemical states. Battery management systems (BMS) typically need to monitor and diagnose state of charge (SOC), state of health (SOH), internal resistance growth, and potential anomalies (such as polarization anomalies, connection / contact anomalies, etc.). Electrochemical impedance spectroscopy (EIS) can characterize ohmic impedance, interfacial charge transfer processes, and diffusion processes at different frequencies, and is therefore considered one of the important information sources for battery state estimation and fault diagnosis.

[0003] Traditional EIS typically requires scanning multiple frequency points over a wide frequency range to obtain full-band impedance information. However, low-frequency testing requires long excitation and steady-state waiting times, while high-frequency testing demands high sampling synchronization accuracy and hardware bandwidth, resulting in long full-spectrum testing times and high requirements for the measurement link. In online scenarios such as automotive BMS, battery current, temperature, and SOC often change with operating conditions and are difficult to maintain stability for long periods, further reducing the feasibility and consistency of full-spectrum EIS. Therefore, engineering practices generally tend to reduce testing costs by reducing the number of frequency points or narrowing the frequency band. However, this brings about the technical requirement of "how to recover full-spectrum or key spectral features with a limited sampling budget".

[0004] Existing sparse measurements often employ empirically fixed frequency points, sample-driven point selection based on a single temperature / single SOC or a single aging stage, and point selection strategies oriented towards the observability of equivalent circuit model parameters. However, the timescale of battery impedance spectrum and its main conductive chemical processes shifts significantly with temperature, SOC, aging degree, and even cell type. This means that a frequency point that is "effective" under one operating condition may no longer correspond to key processes or sensitive features under another operating condition, leading to feature drift, unstable reconstruction, or increased diagnostic errors. Therefore, a stable and reusable sparse frequency point selection mechanism that can remain stable under multiple operating conditions is needed to provide a unified frequency point basis for online sampling.

[0005] For the recovery of full-spectrum information from sparse EIS, existing technologies typically include interpolation / curve fitting, full-spectrum generation after Equivalent Circuit Model (ECM) parameter identification, and data-driven regression / deep learning reconstruction. Interpolation / fitting methods are simple to implement but are sensitive to nonlinear changes in spectral shape and noise. When the distribution of sparse points is unreasonable, shape distortion or local oscillations are likely to occur. ECM methods have a certain degree of physical interpretability but rely on circuit structure assumptions. The model structure or parameter constraints often need to be adjusted across cells / aging stages, and parameter identification may be unstable under sparse frequency conditions. Deep learning methods can improve fitting ability when there are sufficient samples, but they are prone to non-physical cross-frequency coupling, spectral discontinuities or artifacts under sparse input conditions. They are also highly dependent on the training distribution, and their generalization performance deteriorates under distribution shifts caused by temperature or cell type changes, making it difficult to use stably in online scenarios for a long time.

[0006] In summary, current online EIS applications suffer from a chain of problems: "full-spectrum measurement is difficult to implement due to time and hardware constraints—only sparse measurement is possible—sparse frequency points are unstable across operating conditions—existing reconstruction methods are prone to distortion under sparse and distributed offset conditions." On the one hand, there is an urgent need for a sparse frequency point selection mechanism that can still be used under changes in temperature, SOC, aging, and cell type. On the other hand, there is an urgent need for a full-spectrum reconstruction method that can explicitly constrain frequency axis continuity, suppress cross-frequency artifacts, and meet the requirements of online causal inference with very few frequency point inputs. At the same time, it should also support rapid adaptation to new temperatures or new cell types with a small amount of target domain data to reduce engineering calibration costs, thereby meeting the actual deployment needs of online diagnostics and condition estimation for vehicle BMS. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a method for reconstructing the full-band impedance spectrum of lithium-ion batteries based on conditionally invariant characteristic frequency selection and Transformer-Graph autoregression.

[0008] To achieve the above objectives, the present invention provides the following solution: A method for reconstructing the full-band electrochemical impedance spectroscopy of a lithium-ion battery includes: Multiple sets of battery electrochemical impedance spectroscopy samples were collected, and distributed relaxation time (DRT) analysis was performed on each set of battery electrochemical impedance spectroscopy samples to obtain DRT spectra. The DRT spectrum is aligned on the logarithmic time constant axis and subjected to set statistics. Peaks and / or valleys that appear stably under multiple operating conditions are selected based on statistical stability and mapped to obtain a set of conditionally invariant characteristic frequencies. Select characteristic frequency points that satisfy the sampling budget from the set of conditionally invariant characteristic frequencies, and perform sparse electrochemical impedance spectroscopy measurements on the target battery at the characteristic frequency points to obtain sparse complex impedance input; Based on the sparse complex impedance input, a full-band complex impedance sequence is generated through the Transformer–Graph autoregressive reconstruction model. Based on the full-band complex impedance sequence, battery state estimation and fault diagnosis are performed.

[0009] Preferred methods for obtaining DRT spectra include: Collect multiple sets of battery electrochemical impedance spectroscopy samples covering different temperatures, states of charge (SOC), aging states, and / or cell types; Obtain the complex impedance data of each group of battery electrochemical impedance spectrum samples at each frequency point, and establish a complex form DRT forward model including high-frequency ohmic resistance, relaxation contribution function integral term and series inductance term. The logarithmic time constant grid interval is determined based on the electrochemical impedance spectroscopy test frequency range. A logarithmic time constant grid is constructed within the interval, and the DRT forward model is discretized to construct a linear inversion equation for the unknown parameters. By applying a smoothing regularization constraint to the linear inversion equation and solving it using the complex impedance data, the DRT spectrum is obtained.

[0010] Preferably, a "peak-valley-interval" point selection strategy is adopted within the sampling budget to select characteristic frequency points from the set of conditionally invariant characteristic frequencies; the "peak-valley-interval" point selection strategy includes: The frequency point corresponding to the most significant peak in the DRT spectrum of the characteristic frequency set with invariant conditions is selected as the peak selection point; Select the frequency point corresponding to the peak with the largest interval on the logarithmic time constant axis that is the most significant peak, as the interval selection point; Frequency points corresponding to stable valleys are added between peak selection points and interval selection points, and the remaining selection points are alternately added between stable valleys and significant peaks.

[0011] Preferably, the structure of the Transformer-Graph autoregressive reconstruction model includes: The frequency location coding module is used to perform hybrid location coding based on the logarithmic frequencies of each frequency point in the full frequency band to obtain a frequency-aware location representation. The Transformer self-attention autoregressive decoding module is used to fuse and encode the sparse complex impedance input with the frequency-aware position representation of the corresponding frequency point, and construct an autoregressive decoding sequence in combination with the observation mask. During the decoding process, attention weights are calculated based on the dot product of the query vector and the key vector, the trainable bias term with respect to the logarithmic frequency difference, and the local window mask, thereby outputting the latent variable of the current frequency point to be predicted. The graph structure prior module is used to construct a k-nearest neighbor graph on the logarithmic frequency axis, wherein the nodes of the k-nearest neighbor graph are frequency points and the edges connect the k neighbors with the closest logarithmic frequency distance. The in-step subgraph aggregation module is used to select the observed frequency point set and the predicted frequency point set based on the k nearest neighbor graph in each autoregressive step to construct a subgraph and perform graph aggregation to obtain neighborhood consistency features. The residual fusion module is used to perform residual fusion of the neighborhood consistency features and the latent variables of the frequency point to be predicted, and then output the complex impedance prediction value of the current step frequency point.

[0012] Preferably, the method by which the frequency position encoding module obtains the frequency-aware position representation includes: Based on the total number of frequency points across the entire frequency band, the target frequency sequence to be reconstructed is obtained; Based on the target frequency sequence, calculate the logarithmic frequency variable for each frequency point; A frequency-aware location representation is constructed based on the continuous representation obtained by mapping logarithmic frequency variables, the dimension-wise gating coefficients, the learnable embedding entries corresponding to the frequency index, and the linear jump terms.

[0013] Preferably, the method by which the Transformer self-attention autoregressive decoding module obtains the latent variables of the frequency points to be predicted includes: The sparse complex impedance input is mapped to frequency content features and fused with the frequency-aware location representation of the corresponding frequency point to obtain the decoder input sequence. Based on the observation mask, the observed frequency points and the frequency points to be predicted are distinguished, and an autoregressive decoding sequence is constructed according to the preset frequency order; Based on the decoder input sequence, construct the query vector, key vector, and value vector for each frequency point; The attention score is calculated based on the dot product of the query vector and the key vector, the trainable bias term obtained by the relative logarithmic frequency difference mapping, and the local window mask. The value vector is weighted and summed based on the attention score to obtain the context features of each frequency point; The context features are averaged and pooled based on a predefined set of low-frequency indices to obtain a global summary vector. The global summary vector is concatenated or linearly fused with the context features of each frequency point to obtain the latent variables of each frequency point.

[0014] Preferably, the method by which the intra-step subgraph aggregation module obtains neighborhood consistency features includes: Based on the k-nearest neighbor graph, the global adjacency relationship and edge weight between each frequency point in the entire frequency band are obtained; At each autoregressive step t, the set of available nodes is determined based on the set of observed frequency points and the set of predicted frequency points in the current step. Based on the set of available nodes and the global adjacency relationship, extract the subgraph corresponding to the current step from the k nearest neighbor graph; Based on the edge weights of the subgraph, graph aggregation is performed on the subgraph to obtain neighborhood consistency features.

[0015] This invention also provides a full-band electrochemical impedance spectroscopy reconstruction system for lithium-ion batteries, used to implement the method, comprising: The DRT analysis module is used to collect multiple sets of battery electrochemical impedance spectroscopy samples and perform distributed relaxation time (DRT) analysis on each set of battery electrochemical impedance spectroscopy samples to obtain the DRT spectrum. The conditionally invariant feature set acquisition module is used to align the DRT spectrum on the logarithmic time constant axis and perform set statistics, filter peaks and / or valleys that appear stably under multiple operating conditions based on statistical stability, and map them to obtain a set of conditionally invariant feature frequencies. The sparse electrochemical impedance spectroscopy measurement module is used to select characteristic frequency points that satisfy the sampling budget from the set of conditionally invariant characteristic frequencies, and to perform sparse electrochemical impedance spectroscopy measurement on the target battery at the characteristic frequency points to obtain sparse complex impedance input; A full-band complex impedance sequence generation module is used to generate a full-band complex impedance sequence based on the sparse complex impedance input using a Transformer-Graph autoregressive reconstruction model. The battery state estimation module is used to perform battery state estimation and fault diagnosis based on the full-band complex impedance sequence.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The frequency selection is robust and reusable: Based on the statistical screening of stable peaks / valleys and mapping of frequency points according to the DRT set of multiple operating conditions, the characteristic frequency points are more stable under temperature, SOC, aging and cell differences compared to single operating conditions or fixed frequency point strategies, and can be used for long-term online measurement.

[0017] (2) Significantly improved spectral continuity under sparse sampling: Under the condition of measuring only 3–9 frequency points, structural constraints are imposed on the neighborhood continuity by the logarithmic frequency k nearest neighbor graph prior, and the graph aggregation is embedded in each step of autoregression, which significantly reduces spectral discontinuity, cross-band artifacts and non-physical oscillations, and improves the consistency between Nyquist arc and Bode phase change.

[0018] (3) Online inference is reliable and feasible: the in-step subgraph only uses observed / predicted frequency points to avoid future information leakage and meet the causal requirements of online real-time autoregression generation.

[0019] (4) Reduced measurement burden: Compared with full-band scanning, sparse measurement significantly shortens the test time and reduces the requirements for hardware excitation and sampling.

[0020] (5) Easy to deploy and low adaptation cost: Transfer learning supports rapid adaptation to new temperatures or new cell types with a small amount of target domain data, reducing calibration and data acquisition costs. Attached Figure Description

[0021] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 Flowchart of the method for reconstructing the full-band electrochemical impedance spectroscopy of lithium-ion batteries; Figure 2 Flowchart for selecting DRT set statistics and conditionally invariant characteristic frequencies; Figure 3 A diagram illustrating the overall structure of the Transformer–Graph autoregressive reconstruction; Figure 4 This is a diagram illustrating the phased fine-tuning of transfer learning. Detailed Implementation

[0023] 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. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] Example 1: like Figure 1 As shown, a method for reconstructing the full-band electrochemical impedance spectroscopy of a lithium-ion battery includes: S1: Collect multiple sets of battery electrochemical impedance spectroscopy (EIS) samples, and perform distributed relaxation time (DRT) analysis on each set of EIS samples to obtain DRT spectra. DRT spectra can map different electrochemical processes in the impedance spectrum onto the logarithmic time constant axis, making cross-frequency processes easier to statistically analyze and align. A further implementation method for obtaining DRT spectra includes: Multiple sets of battery electrochemical impedance spectroscopy samples covering different temperatures, states of charge (SOC), aging states, and / or cell types were collected to form a sample set.

[0026] Complex impedance data at each frequency point were obtained for each group of battery electrochemical impedance spectroscopy samples. A complex form DRT forward model was established, including high-frequency ohmic resistance, the integral term of the relaxation contribution function, and the series inductance term. Specifically, for each sample, the complex impedance data at each frequency point were obtained. or angular frequency Complex impedance at And establish a forward model of DRT in complex form: in, It is a high-frequency ohmic resistor. For series inductors, time constant The relaxation contribution function of the distribution. When using the above complex model, the same Simultaneously characterizes the real part of the impedance. and the virtual part This avoids inconsistencies caused by fitting the real and imaginary parts separately.

[0027] Based on the frequency range of electrochemical impedance spectroscopy (EIS) measurements, a logarithmic time constant grid interval is determined. Within this interval, a logarithmic time constant grid is constructed, and the DRT forward model is discretized to construct a linear inversion equation for the unknown parameters. In practical implementation, within the interval... Built-in logarithmic time constant grid ,in and will Discretize into . and The frequency range can be determined based on the EIS test frequency range, preferably. With the highest test frequency correspond, With minimum test frequency Correspondingly, an expansion margin can be reserved at both ends to reduce boundary effects. Discretizing the above integral expression, it can be written as: This leads to the construction of information about the unknown parameters. , and The linear inversion problem is solved, and the DRT spectrum of the corresponding sample is obtained by solving based on the measured complex impedance data.

[0028] By applying a smoothing regularization constraint to the linear inversion equation and solving it using complex impedance data, the DRT spectrum is obtained.

[0029] Specifically, since DRT inversion is an ill-conditioned problem, to improve the stability of the solution, the following can be done: Applying regularization constraints, preferably using a smoothing regularization method for solving the problem, such as adding a regularization constraint to the least squares objective function. A smoothing constraint term varying along the logarithmic time constant axis is added to suppress the influence of noise on the inversion results. Furthermore, this can be adjusted according to the specific system. Apply nonnegativity constraints; for systems with non-ideal effects, also allow Take positive or negative values. The objective function can be expressed as: in, The coefficient matrix consists of the kernel function and concatenated terms. The measured complex impedance vector, It is a difference matrix. The regularization coefficient is . During the solution process, and Preferred and Simultaneous estimation is performed to avoid bias in the high-frequency DRT spectrum recovery caused by high-frequency boundary term estimation errors. Final output. or This serves as the DRT spectrum corresponding to the EIS sample, enabling subsequent alignment, statistical analysis, and peak / valley selection on a unified logarithmic time constant axis.

[0030] To further improve the adequacy of disclosure in the specification, a clear definition of the coefficient of variation can be added in subsequent statistical steps, for example: in, The set mean For the set standard deviation, To prevent positive numbers with a denominator of zero.

[0031] S2: Align the DRT spectra on the logarithmic time constant axis and perform ensemble statistics. Based on statistical stability, screen for peaks and / or valleys that stably appear under multiple operating conditions, and map them to obtain a set of conditionally invariant characteristic frequencies. Specifically, align multiple sets of DRT spectra on the logarithmic time constant axis, calculate ensemble statistics for each time constant position, and the ensemble statistics include at least the ensemble mean, ensemble standard deviation, and coefficient of variation (CV) to characterize the "significance" and "stability" of that position under multiple operating conditions. Detect peaks and / or valleys on the ensemble mean DRT spectrum and screen candidates based on stability criteria: such as peak significance not lower than a preset threshold, candidates satisfying the minimum logarithmic interval constraint, and CV less than a stability threshold. Then, map the screened time constant candidates to frequencies (e.g., mapping according to the relationship f=1 / (2πτ)) to form a candidate frequency set. Figure 2 As shown.

[0032] S3: Select characteristic frequency points that satisfy the sampling budget from the set of conditionally invariant characteristic frequencies, and perform sparse electrochemical impedance spectroscopy measurements on the target battery at these characteristic frequency points to obtain the sparse complex impedance input; set the sampling budget nsel∈{3,4,5,6,7,8,9}, and combine it with the upper limit of online measurement time, frequency band coverage requirements, and signal-to-noise ratio constraints to select nsel characteristic frequency points from the candidate frequency set to form the set of conditionally invariant characteristic frequencies; where a minimum allowable frequency f can be set. min Low-frequency points are eliminated to avoid excessively long online measurement times. A further implementation involves employing a "peak-valley-interval" point selection strategy within the sampling budget to select characteristic frequency points from a set of conditionally invariant characteristic frequencies. The "peak-valley-interval" point selection strategy includes: The frequency point corresponding to the most significant peak in the DRT spectrum of the characteristic frequency set with invariant conditions is selected as the peak selection point; Select the frequency point corresponding to the peak with the largest interval on the logarithmic time constant axis that is the most significant peak, as the interval selection point; Frequency points corresponding to stable valleys are added between peak selection points and interval selection points, and the remaining selection points are alternately added between stable valleys and significant peaks.

[0033] During operation, EIS measurements are performed on the target battery only at 3–9 frequency points corresponding to the set of conditionally invariant characteristic frequencies to obtain sparse complex impedance inputs (real and imaginary parts).

[0034] Optionally, measurement-related operating condition information (such as temperature, SOC, etc.) can be fed into the reconstruction model along with the complex impedance as conditional input or context input to improve the reconstruction robustness in distributed offset scenarios.

[0035] In this embodiment, electrochemical impedance spectroscopy samples were collected at different temperatures, SOCs, aging states, and cell types. DRT analysis was performed on each sample to obtain γ(τ). The samples were aligned to a logarithmic τ grid, and µ(τ), σ(τ), and CV(τ) were calculated. Samples meeting the peak significance threshold, the minimum interval between adjacent candidates Δmin, and CV≤CV were retained. max Candidates are selected. Let nsel∈{3,4,5,6,7,8,9}, and fill in the gaps to nsel according to the rule of "significant peak priority—maximum interval peak—stable valley anchor point—peak-valley alternation supplementation"; and a minimum allowable frequency fmin can be set to remove excessively low frequency points to meet online duration constraints. Map τ to a frequency using f=1 / (2πτ) to obtain the set of conditionally invariant feature frequencies.

[0036] S4: Based on sparse complex impedance input, a full-band complex impedance sequence is generated through a Transformer-Graph autoregressive reconstruction model; the full-spectrum reconstruction of this invention is not a simple interpolation of sparse points, nor is it "post-processing smoothing" after the sequence model output, but rather incorporates frequency domain geometric continuity as a structural prior into the inference process. Figure 3 As shown, a further implementation of the Transformer–Graph autoregressive reconstruction model includes the following structure: A frequency location encoding module is used to perform hybrid location encoding based on the logarithmic frequencies of each frequency point in the entire frequency band to obtain a frequency-aware location representation. Specifically, a hybrid location encoding form is preferred, which includes at least: a trainable frequency point index embedding term, a nonlinear projection term of the logarithmic frequency, and a linear jump term of the logarithmic frequency. The nonlinear projection term can be weighted by gating coefficients to make the model explicitly aware of the relationship between the frequency scale and the frequency band. A further implementation method is that the frequency location encoding module obtains the frequency-aware location representation by: obtaining the target frequency sequence to be reconstructed based on the total number of frequency points in the entire frequency band; calculating the logarithmic frequency variable for each frequency point based on the target frequency sequence; and constructing the frequency-aware location representation based on the continuous representation obtained by mapping the logarithmic frequency variable, the dimension-wise gating coefficients, the learnable embedding term corresponding to the frequency index, and the linear jump term.

[0037] Specifically, this involves constructing frequency sequences and logarithmic frequency variables. Let the target frequency sequence to be reconstructed be: Where, N f This represents the total number of frequency points across the entire frequency band. For each frequency point, calculate its logarithmic frequency variable: Using logarithmic frequency coordinates helps to make the EIS spectrum change more smoothly across orders of magnitude frequency bands and facilitates subsequent relative frequency difference modeling.

[0038] Frequency-aware location representation construction. For each frequency point f i Constructing a hybrid frequency position representation p(f) i It consists of discrete embedding terms, continuous nonlinear mapping terms, and linear jump-connected terms. The continuous branch can be written as: in, It is a continuous representation obtained from the logarithmic frequency mapping, used to characterize smooth changes on the continuous frequency axis; σ(·) represents the dimension-wise gating coefficients (gating weights), used to suppress excessive amplification of continuous projected branches by unstable frequency bands. σ(·) is the Sigmoid function. This yields the frequency-aware position representation: Where p0(i) is the learnable embedding entry corresponding to the frequency index, used to represent the positional identity in the fixed frequency template; ⊙ represents Hadamard element-wise multiplication. This is a linear skip connection. Stacking the position representations of all frequency points yields the frequency position matrix P = [p(f1),...,p(f...]. {Nf} ]], and after being broadcast along the batch dimension, it is input into the decoder and used as the basic representation of frequency-aware queries and keys.

[0039] The Transformer self-attention autoregressive decoding module is used to fuse and encode the sparse complex impedance input with the frequency-aware position representation of the corresponding frequency point, and construct an autoregressive decoding sequence in combination with the observation mask. During the decoding process, attention weights are calculated based on the dot product of the query vector and the key vector, the trainable bias term with respect to the logarithmic frequency difference, and the local window mask, thereby outputting the latent variable of the current frequency point to be predicted. The graph structure prior module is used to construct a k-nearest neighbor graph on the logarithmic frequency axis. The nodes of the k-nearest neighbor graph are frequency points, and the edges connect the k neighbors that are closest to the logarithmic frequency. The in-step subgraph aggregation module is used to select the observed frequency point set and the predicted frequency point set based on the k nearest neighbor graph to construct a subgraph and perform graph aggregation in each autoregressive step to obtain neighborhood consistency features. The residual fusion module is used to perform residual fusion of neighborhood consistency features and latent variables of the frequency point to be predicted, and then output the complex impedance prediction value of the current step frequency point.

[0040] A further implementation method involves the Transformer self-attention autoregressive decoding module obtaining the latent variables of the frequency points to be predicted, including: The sparse complex impedance input is mapped to frequency content features and fused with the frequency-aware location representation of the corresponding frequency point to obtain the decoder input sequence. Based on the observation mask, observed frequencies and frequencies to be predicted are distinguished, and an autoregressive decoding sequence is constructed according to a preset frequency order. Based on the decoder input sequence, query vectors, key vectors, and value vectors for each frequency point are constructed. Based on the frequency-aware location representation, query vectors, key vectors, and value vectors for each frequency point are constructed. Based on the dot product of the query vector and the key vector, the trainable bias term obtained from the relative logarithmic frequency difference mapping, and the local window mask, the attention score is calculated.

[0041] Specifically, given the sparse complex impedance observations x_obs obtained at characteristic frequency points and the external condition information c, the full-band complex impedance reconstruction is modeled as a conditional autoregressive generation problem. Let the full-band sequence to be reconstructed corresponding to the target frequency template be x1:T, where x_t represents the complex impedance to be predicted at the t-th frequency point. Let T represent the frequency subsequence that has been observed or generated before this frequency point, and T be the total number of target frequency points. Then, the conditional probability decomposition of the full-band complex impedance sequence can be expressed as: Where x_obs represents the sparse complex impedance observations obtained at the corresponding frequency points of the conditionally invariant characteristic frequency set, and c represents external condition information, which includes one or more of temperature, state of charge (SOC), aging state, cycle count, and cell type. During training, a teacher-forced input of prior true values ​​is preferred; during inference, subsequent frequency point results are generated recursively according to a preset frequency order.

[0042] Self-attention computation with relative frequency offset. For the i-th query position and the j-th key position, first construct the query vector q based on the frequency position representation. i and key vector k j Then, based on the standard dot product attention, a relative logarithmic frequency difference bias and a local window mask are superimposed to obtain the attention score: Where, d h For single-head attention dimension, For relative logarithmic frequency difference The trainable bias term obtained from the mapping is used to explicitly reflect the relative distance relationship between different frequency points on the logarithmic frequency axis. The local window mask mask(i,j) is preferably defined as follows: when |ij| does not exceed the preset window width w, it takes the value of 0; when |ij| is greater than w, it takes the value of negative infinity or a sufficiently large negative value, so as to retain only the attention connection within a finite neighborhood, thereby suppressing unreasonable long-distance coupling under sparse conditions.

[0043] mask{i,j} = { 0, when |ij| ≤ w; -∞, when |ij| > w.} in, This represents the attention score between the i-th query position and the j-th key position; q i and k j These represent the query vector and key vector at the corresponding positions, respectively; d h The feature dimension representing single-head attention; The relative frequency difference between the i-th and j-th frequency points on the logarithmic frequency axis is represented by mask(i,j); mask(i,j) represents the local window mask item; w represents the preset local window width.

[0044] The attention scores are used to weight and sum the value vectors to obtain the contextual features of each frequency point. Specifically, after scoring, Softmax normalization is performed along the key dimension for each query position to obtain attention weights, and the value vectors are then weighted and summed to form the contextual features of the current position. In this way, the decoder can utilize the local smooth correlation between adjacent frequency points and retain the global dependencies between cross-frequency band processes by using trainable relative frequency difference biases.

[0045] The context features are average-pooled based on a predefined low-frequency index set to obtain a global summary vector. The global summary vector is then concatenated or linearly fused with the context features of each frequency point to obtain the latent variables for each frequency point. Specifically, to further inject low-frequency global information into each frequency point, preferably, the predefined low-frequency index set... The global summary vector s is constructed by averaging the decoded features on the vector. Among them, h i This represents the hidden feature of the i-th frequency point after being updated by the attention module. This represents the number of elements in the low-frequency index set. Subsequently, this global summary vector is broadcast to all frequency points and concatenated or linearly fused with the local features of each frequency point to obtain the node representation n used in subsequent graph or regression branches. i It can be written as: Among them, [h i ; s] represents vector concatenation, W n and b n These are the linear projection parameters and the bias term, respectively. Through this local-global fusion process, the decoder can simultaneously perceive local frequency neighborhood information and low-frequency global background information during frequency-by-frequency reconstruction.

[0046] After the above self-attention with relative frequency offset and local-global fusion, the latent representation n corresponding to each frequency point is obtained. i For complex impedance reconstruction tasks, it is preferable to set up real and imaginary output heads to regress each frequency point separately, obtaining the predicted real and predicted imaginary parts: in, Let W_r and b represent the predicted complex impedance at the i-th frequency point. r For the real part regression head parameters, W_q and b q These are the parameters for the imaginary part of the regression head. During the inference phase, the prediction results for each frequency point are output sequentially according to a preset frequency order, and the generated frequency points are used as the conditional context for subsequent frequency points until the recursive reconstruction of the impedance spectrum across the entire frequency band is completed.

[0047] The above decoding process introduces relative logarithmic frequency offset and local window mask into the standard Transformer autoregressive framework. On the one hand, the relative frequency offset allows the model to explicitly utilize physical distance information between frequency points, improving the ability to model the correlation between electrochemical processes at different time scales. On the other hand, the local window mask constrains attention to a finite neighborhood, helping to avoid non-physical coupling across too far frequency bands under sparse measurement conditions, thereby improving the stability, physical consistency, and generalization ability of full-band EIS reconstruction.

[0048] A further implementation method involves obtaining neighborhood consistency features using the intra-step subgraph aggregation module. This method includes: acquiring the global adjacency relationships and edge weights between frequency points across the entire frequency band based on a k-nearest neighbor graph; the graph edge weights can be determined by a monotonically decaying function of the logarithmic frequency difference, the function parameters of which can be trained or adaptively estimated to reflect the effective frequency resolution under different battery cells / operating conditions. In each autoregressive step t, a set of available nodes is determined based on the observed and predicted frequency point sets of the current step; based on the available node set and the global adjacency relationships, the subgraph corresponding to the current step is extracted from the k-nearest neighbor graph; based on the edge weights of the subgraph, graph aggregation is performed on the subgraph to obtain neighborhood consistency features. Specifically, to further constrain the spectral continuity between adjacent frequency points, a k-nearest neighbor graph is constructed using frequency points on the full-frequency template as graph nodes and logarithmic frequency distance as the adjacency metric on the graph. For nodes... Its nearest neighbor nodes The edge weight is defined as: in, Represents a node The k nearest neighbor set on the logarithmic frequency axis The width of the frequency difference attenuation kernel. and It can be set as a fixed hyperparameter, or it can be adjusted during training using a trainable or adaptive update method.

[0049] The prior diagram is not used to replace sequence modeling, but to impose structural consistency constraints on the local neighborhood of the frequency axis, so that the model can maintain the local smoothness and geometric continuity of the spectral lines at the high-frequency end, the mid-frequency arc region and the low-frequency diffusion tail.

[0050] The key improvement in this embodiment is that the graph structure branches do not propagate in parallel all at once across the entire frequency graph, but rather on the [missing information - likely a specific timeframe or sequence]. Each autoregressive step only aggregates the causal subgraph composed of "observed frequency points and predicted frequency points", thereby avoiding future information leakage.

[0051] Let the first The set of available nodes corresponding to the step is in, It is a sparse set of measured frequency points. This is the set of frequency points that have been predicted before the current step. Graph aggregation is performed only on the subgraph induced by this set to obtain the [number of]th [step]. Neighborhood consistency feature of the step: in, For the first Step Node The input representation, The transformation matrix of the graph. For the right of the border The normalized aggregate weights are then used to fuse the graph aggregation output with the Transformer latent variables using residuals, forming the final latent representation for the current step. in, For Transformer in the 1st Hidden variables in the step output, These are either fixed coefficients or gated fusion coefficients. Subsequently, the real and imaginary predicted values ​​for the current frequency point are obtained using a dual-output regression head. Through the above-mentioned "intra-step subgraph aggregation + residual fusion" mechanism, the global context information provided by Transformer and the local geometric continuity information provided by graph structure can be used simultaneously in each prediction step, which is different from the conventional structure combination method of simply connecting Transformer and graph network in series or parallel.

[0052] Optional enhancements: frequency domain gating and multi-scale spectral shape fusion.

[0053] To further suppress local artifacts and cross-scale distortion under sparse sampling conditions, a frequency-domain gated branch can be added to the latent variable sequence. Let the feature sequence arranged along the frequency point dimension be... Then, first perform a real-number fast Fourier transform: Apply a learnable bandpass gate vector to the frequency domain coefficients. : Then, the frequency domain is restored through inverse transformation: The above processing can modulate different frequency band components as a whole with a low number of parameters, thereby enhancing global spectral coherence.

[0054] Following frequency domain gating, multi-scale one-dimensional convolutional branches can be set, employing multiple convolutional kernel scales. Local spectral patterns at different scales are extracted and fused using adaptive gating: in, For the first Each frequency point in scale The integration scoring on the platform This represents the normalized scale weights. Through this branch, the model can simultaneously take into account sharp local transitions, semi-circular changes, and low-frequency tail structures, further improving the smoothness and fidelity of the reconstructed spectrum.

[0055] Specifically, at the t-th autoregressive step, the reconstructed model constructs a subgraph based solely on the "set of observed frequency points and the set of predicted frequency points". Graph aggregation is performed on this subgraph to obtain neighborhood consistency features. The neighborhood consistency features are then residually fused with the latent variables generated by Transformer decoding to output the complex impedance prediction value at the t-th frequency point.

[0056] Through the "in-step subgraph" mechanism, the graph prior continuously applies local geometric continuity constraints during the inference process, rather than being used as a smoothing process after the output; through the subgraph construction rule of "only observed / predicted frequencies", the use of future frequency information that has not yet been predicted is avoided, ensuring the causality and online availability of autoregressive inference.

[0057] S5: Based on the full-band complex impedance sequence, perform battery state estimation and fault diagnosis.

[0058] It outputs a full-band complex impedance sequence and can further generate Nyquist and Bode curves for applications such as SOC / SOH estimation, fault diagnosis, and internal resistance / arc radius feature extraction.

[0059] To improve deployability across temperature and cell types, the Transformer-Graph autoregressive reconstruction model can employ transfer learning adaptation: after pre-training on source domain data, a phased fine-tuning strategy is used on the target domain (e.g., first updating the output layer, then fine-tuning the decoding and fusion modules, and finally unfreezing the entire network depending on the amount of data) to complete adaptation with a small amount of data while maintaining reconstruction performance. Figure 4 As shown.

[0060] The above frequency-point autoregressive generation results are combined according to a predetermined frequency template to obtain a full-band complex impedance sequence: Based on this full-spectrum complex impedance sequence, Nyquist and Bode plots can be further generated and used for battery state estimation, fault diagnosis, life assessment, or online management decisions.

[0061] Example 2 In this embodiment, the complex impedance is decomposed into a real part sequence and an imaginary part sequence for dual-stream autoregressive decoding. The two streams share the prior of the k-nearest neighbor graph structure and maintain amplitude-phase consistency through cross-attention or gating coupling, thereby reducing inconsistencies caused by independent prediction of real and imaginary parts.

[0062] (1) Construction of dual-stream input sequence. Let the target frequency sequence of the entire frequency band be... ,in This represents the total number of frequencies to be reconstructed. The complex impedance is decomposed into a sequence of real parts. With imaginary part sequence These serve as the reconstruction targets for the real and imaginary decoded streams, respectively. A logarithmic frequency variable is defined for each frequency point. The two decoded streams share the frequency axis definition, frequency-aware position representation, and conditional coding memory, thereby ensuring that the real and imaginary parts are aligned and modeled under the same frequency reference system.

[0063] (2) Dual-stream parallel autoregressive decoding. A Transformer decoder with causal constraints is constructed for both the real and imaginary streams. In the first... At each target frequency point, the real part stream constructs a query vector, key vector, and value vector based on previously known or generated real part features, and the imaginary part stream constructs corresponding features similarly. Both streams use the same frequency position encoding and the same autoregressive masking rule at each layer to enable parallel generation at the same frequency order. Preferably, the attention score for the real part stream can be written as... The attention score for the imaginary flow can be written as: in The above notation indicates that, despite differences in content characteristics, the two streams share the same relative logarithmic frequency difference offset form and local window mask constraint, thereby ensuring that the real and imaginary parts maintain consistency in their frequency neighborhood relationships.

[0064] (3) Low-frequency global context sharing. To enhance the overall consistency of the two streams in the low-frequency region, a predefined low-frequency index set can be used. The two stream features are average pooled separately to obtain the low-frequency summary vector. Preferably, the two low-frequency summary vectors can be concatenated or added together and then broadcast to the features of each frequency point, so that the real flow and the imaginary flow can share background information in terms of low-frequency tail trend, diffusion tail response and overall spectral shape change.

[0065] (4) Shared k-nearest neighbor graph structure prior. Construct a k-nearest neighbor graph based on the logarithmic frequency axis, for any frequency node Select its nearest frequency in the logarithmic frequency space Each neighbor forms an adjacency set. Edge weight optimization is defined as follows: in, `x` represents the graph kernel width parameter. The real and imaginary flows share the same graph topology and edge weight definition, and graph convolution or graph attention aggregation are performed on this graph respectively, followed by residual fusion with their respective Transformer decoded features. This can be written as... By sharing graph structure priors, both streams can simultaneously utilize local smoothness within the frequency neighborhood and cross-frequency band structural relationships, reducing the risk of frequency mismatch that occurs when the real and imaginary parts are modeled independently.

[0066] (5) Two-stream coupling maintains amplitude and phase consistency. To avoid inconsistencies between the Nyquist trajectory and Bode phase caused by completely independent prediction of the real and imaginary parts, preferably, after prior fusion of the shared graph, cross-attention or gated coupling is introduced between the two streams.

[0067] A preferred method for implementing gated coupling is to first concatenate the fusion features of the two streams at the same frequency point to obtain the gate coefficients. Then, the two-stream information is bidirectionally modulated using this gating coefficient to obtain... in, Indicates feature splicing, For the Sigmoid function, This represents element-wise multiplication. Through the above coupling, the real flow can perceive the phase correlation characteristics of the imaginary flow at the same frequency, and the imaginary flow can also perceive the amplitude correlation characteristics of the real flow at the same frequency, thus maintaining the consistency of the overall complex impedance trajectory. If cross-attention is used, the features of one flow can be used as the query, and the features of another flow can be used as the key and value, performing cross-flow attention aggregation at the same frequency or in the local frequency domain neighborhood. Its essential function is consistent with the above-mentioned gating coupling.

[0068] (6) Dual-head regression output. The features after dual-current coupling are input into the real part regression head and the imaginary part regression head respectively to obtain the predicted values ​​of the impedance spectrum at each frequency point across the entire frequency band. Preferably, it can be written as: in, , These are the output mapping parameters for the real part regression head and the imaginary part regression head, respectively. , This is the bias term. The model outputs all target frequency points one by one according to a predetermined autoregressive order, and finally obtains the complete complex impedance reconstruction spectrum.

[0069] To further suppress cross-band artifacts, an RFFT can be performed along the frequency dimension on the decoded latent variables to obtain the frequency domain representation. After applying learnable gating coefficients to each spectral band in the frequency domain, the result is inversely transformed back to the sequence domain. Furthermore, multi-scale one-dimensional convolutional branches are used to extract spectral features at different scales and adaptively fuse them to improve cross-band consistency and local smoothness.

[0070] Example 3: This invention also provides a full-band electrochemical impedance spectroscopy reconstruction system for lithium-ion batteries, used to implement the method of Example 1, comprising: The DRT analysis module is used to collect multiple sets of battery electrochemical impedance spectroscopy samples and perform distributed relaxation time (DRT) analysis on each set of battery electrochemical impedance spectroscopy samples to obtain DRT spectra. The conditionally invariant feature set acquisition module is used to align the DRT spectrum on the logarithmic time constant axis and perform set statistics. Based on statistical stability, it filters peaks and / or valleys that appear stably under multiple operating conditions and maps them to obtain the conditionally invariant feature frequency set. The sparse electrochemical impedance spectroscopy measurement module is used to select characteristic frequency points that satisfy the sampling budget from the set of conditionally invariant characteristic frequencies, and to perform sparse electrochemical impedance spectroscopy measurement on the target battery at the characteristic frequency points to obtain the sparse complex impedance input. The full-band complex impedance sequence generation module is used to generate a full-band complex impedance sequence based on sparse complex impedance input through a Transformer–Graph autoregressive reconstruction model. The battery state estimation module is used to perform battery state estimation and fault diagnosis based on the full-band complex impedance sequence.

[0071] To facilitate implementation and broaden the scope of protection, the present invention may adopt the following preferred ranges (none of which constitute a limitation on the present invention): (1) Sampling budget: nsel is an integer of 3–9, which can be adaptively determined according to the upper limit of online duration and SNR.

[0072] (2) Graph structure: k-nearest neighbor number k can be 2–10; edge weight decay function can be Gaussian kernel, exponential kernel or equivalent transformation thereof; parameters can be trained or adaptively estimated.

[0073] (3) Subgraph rule: Each autoregressive step contains only observed / predicted nodes to avoid future leakage; the graph aggregation operator can be graph convolution, graph attention or its equivalent structure.

[0074] (4) Complex modeling: real / imaginary part two-stream shared graph prior, and amplitude-phase consistency is maintained by gating or cross-attention coupling.

[0075] (5) Enhancement modules: FFT gating and multi-scale convolution are optional modules that can be enabled according to computing power and accuracy requirements.

[0076] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for reconstructing the full-band electrochemical impedance spectroscopy of a lithium-ion battery, characterized in that, include: Multiple sets of battery electrochemical impedance spectroscopy samples were collected, and distributed relaxation time (DRT) analysis was performed on each set of battery electrochemical impedance spectroscopy samples to obtain DRT spectra. The DRT spectrum is aligned on the logarithmic time constant axis and subjected to set statistics. Peaks and / or valleys that appear stably under multiple operating conditions are selected based on statistical stability and mapped to obtain a set of conditionally invariant characteristic frequencies. Select characteristic frequency points that satisfy the sampling budget from the set of conditionally invariant characteristic frequencies, and perform sparse electrochemical impedance spectroscopy measurements on the target battery at the characteristic frequency points to obtain sparse complex impedance input; Based on the sparse complex impedance input, a full-band complex impedance sequence is generated through the Transformer–Graph autoregressive reconstruction model. Based on the full-band complex impedance sequence, battery state estimation and fault diagnosis are performed.

2. The method according to claim 1, characterized in that, Methods for obtaining DRT spectra include: Collect multiple sets of battery electrochemical impedance spectroscopy samples covering different temperatures, states of charge (SOC), aging states, and / or cell types; Obtain the complex impedance data of each group of battery electrochemical impedance spectrum samples at each frequency point, and establish a complex form DRT forward model including high-frequency ohmic resistance, relaxation contribution function integral term and series inductance term. The logarithmic time constant grid interval is determined based on the electrochemical impedance spectroscopy test frequency range. A logarithmic time constant grid is constructed within the interval, and the DRT forward model is discretized to construct a linear inversion equation for the unknown parameters. By applying a smoothing regularization constraint to the linear inversion equation and solving it using the complex impedance data, the DRT spectrum is obtained.

3. The method according to claim 1, characterized in that, Within the sampling budget, a "peak-valley-interval" point selection strategy is adopted to select characteristic frequency points from the set of conditionally invariant characteristic frequencies; The "peak-valley-interval" point selection strategy includes: The frequency point corresponding to the most significant peak in the DRT spectrum of the characteristic frequency set with invariant conditions is selected as the peak selection point; Select the frequency point corresponding to the peak with the largest interval on the logarithmic time constant axis that is the most significant peak, as the interval selection point; Frequency points corresponding to stable valleys are added between peak selection points and interval selection points, and the remaining selection points are alternately added between stable valleys and significant peaks.

4. The method according to claim 1, characterized in that, The structure of the Transformer–Graph autoregressive reconstruction model includes: The frequency location coding module is used to perform hybrid location coding based on the logarithmic frequencies of each frequency point in the full frequency band to obtain a frequency-aware location representation. The Transformer self-attention autoregressive decoding module is used to fuse and encode the sparse complex impedance input with the frequency-aware position representation of the corresponding frequency point, and construct an autoregressive decoding sequence in combination with the observation mask. During the decoding process, attention weights are calculated based on the dot product of the query vector and the key vector, the trainable bias term with respect to the logarithmic frequency difference, and the local window mask, thereby outputting the latent variable of the current frequency point to be predicted. The graph structure prior module is used to construct a k-nearest neighbor graph on the logarithmic frequency axis, wherein the nodes of the k-nearest neighbor graph are frequency points and the edges connect the k neighbors with the closest logarithmic frequency distance. The in-step subgraph aggregation module is used to select the observed frequency point set and the predicted frequency point set based on the k nearest neighbor graph in each autoregressive step to construct a subgraph and perform graph aggregation to obtain neighborhood consistency features. The residual fusion module is used to perform residual fusion of the neighborhood consistency features and the latent variables of the frequency point to be predicted, and then output the complex impedance prediction value of the current step frequency point.

5. The method according to claim 4, characterized in that, The method by which the frequency position encoding module obtains the frequency-aware position representation includes: Based on the total number of frequency points across the entire frequency band, the target frequency sequence to be reconstructed is obtained; Based on the target frequency sequence, calculate the logarithmic frequency variable for each frequency point; A frequency-aware location representation is constructed based on the continuous representation obtained by mapping logarithmic frequency variables, the dimension-wise gating coefficients, the learnable embedding entries corresponding to the frequency index, and the linear jump terms.

6. The method according to claim 4, characterized in that, The method by which the Transformer self-attention autoregressive decoding module obtains the latent variables of the frequency points to be predicted includes: The sparse complex impedance input is mapped to frequency content features and fused with the frequency-aware location representation of the corresponding frequency point to obtain the decoder input sequence. Based on the observation mask, the observed frequency points and the frequency points to be predicted are distinguished, and an autoregressive decoding sequence is constructed according to the preset frequency order; Based on the decoder input sequence, construct the query vector, key vector, and value vector for each frequency point; The attention score is calculated based on the dot product of the query vector and the key vector, the trainable bias term obtained by the relative logarithmic frequency difference mapping, and the local window mask. The value vector is weighted and summed based on the attention score to obtain the context features of each frequency point; The context features are averaged and pooled based on a predefined set of low-frequency indices to obtain a global summary vector. The global summary vector is concatenated or linearly fused with the context features of each frequency point to obtain the latent variables of each frequency point.

7. The method according to claim 4, characterized in that, The method for obtaining neighborhood consistency features by the in-step subgraph aggregation module includes: Based on the k-nearest neighbor graph, the global adjacency relationship and edge weight between each frequency point in the entire frequency band are obtained; At each autoregressive step t, the set of available nodes is determined based on the set of observed frequency points and the set of predicted frequency points in the current step. Based on the set of available nodes and the global adjacency relationship, extract the subgraph corresponding to the current step from the k nearest neighbor graph; Based on the edge weights of the subgraph, graph aggregation is performed on the subgraph to obtain neighborhood consistency features.

8. A full-band electrochemical impedance spectroscopy reconstruction system for lithium-ion batteries, used to implement the method described in any one of claims 1-7, characterized in that, include: The DRT analysis module is used to collect multiple sets of battery electrochemical impedance spectroscopy samples and perform distributed relaxation time (DRT) analysis on each set of battery electrochemical impedance spectroscopy samples to obtain the DRT spectrum. The conditionally invariant feature set acquisition module is used to align the DRT spectrum on the logarithmic time constant axis and perform set statistics, filter peaks and / or valleys that appear stably under multiple operating conditions based on statistical stability, and map them to obtain a set of conditionally invariant feature frequencies. The sparse electrochemical impedance spectroscopy measurement module is used to select characteristic frequency points that satisfy the sampling budget from the set of conditionally invariant characteristic frequencies, and to perform sparse electrochemical impedance spectroscopy measurement on the target battery at the characteristic frequency points to obtain sparse complex impedance input; A full-band complex impedance sequence generation module is used to generate a full-band complex impedance sequence based on the sparse complex impedance input using a Transformer-Graph autoregressive reconstruction model. The battery state estimation module is used to perform battery state estimation and fault diagnosis based on the full-band complex impedance sequence.

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