A remote health state analysis and abnormality identification method for an electric bicycle battery

Abstract

The present application relates to the technical field of power battery health state evaluation and abnormality identification, and particularly relates to a remote health state analysis and abnormality identification method for an electric bicycle battery, which comprises: applying a small signal active excitation under an admitted working condition and synchronously collecting to form an opportunity diagnosis excitation data window; developing time-frequency coupling modeling, including equivalent impedance, harmonic and intermodulation fingerprint, Koopman operator modeling and entropy coefficient difference, and generating a multi-domain response package, a physical invariant vector and an uncertainty matrix by constructing a spectral measure geometry distance with an optimal transmission; gating and layering standardization according to the geometry distance and consistency score, obtaining a health state estimation record and an abnormal event set by using a shape-constrained health mapping model; combining the mapping Jacobian and the dual potential, generating a next-period opportunity diagnosis excitation plan by using D-optimal test design and updating the population health manifold, so as to realize remote health evaluation and early abnormality identification across environments and devices and with traceability.

Description

Technical Field

[0001] This invention relates to the field of power battery health status assessment and anomaly identification technology, and in particular to a method for remote health status analysis and anomaly identification of electric bicycle batteries. Background Technology

[0002] The large-scale ownership of electric bicycles has made battery safety, lifespan, and maintainability a shared concern for both operators and regulators. Remote health status analysis and anomaly identification are directly related to thermal runaway prevention, range degradation management, warranty assessment, and secondary circulation classification; for platform-based operations and vehicle-to-everything (V2X) services, they also determine maintenance costs, downtime rates, and user experience. Establishing a traceable health assessment baseline that spans equipment and seasons, particularly for dispersed fleets and complex operating conditions, is crucial for improving industry governance and service levels. Summary of the Invention

[0003] To address the numerous problems existing in the prior art, this invention provides a remote health status analysis and anomaly identification method for electric bicycle batteries. This invention applies a small-signal active excitation under the access condition to form an opportunity diagnostic excitation data window; constructs a multi-domain representation using equivalent impedance, harmonic and intermodulation fingerprints, Koopman operator modeling, and entropy coefficient difference; and uses the optimal transmission metric spectrum shape shift; after consistency gating and hierarchical standardization, the shape-constrained health mapping outputs the health status and abnormal events; and updates the excitation and population health manifold using a D-optimal experimental design in a closed loop, achieving remote, interpretable, and traceable health assessment.

[0004] A method for remote health status analysis and anomaly identification of electric bicycle batteries includes the following steps:

[0005] Under the condition of meeting the admission criteria, small-signal active excitation is applied, and voltage, current and temperature are simultaneously collected and preprocessed using multiple sinusoidal excitation or pseudo-random binary sequence excitation to form an opportunity diagnostic excitation data window.

[0006] Based on the opportunity diagnostic excitation data window, time-frequency coupling modeling is carried out, including equivalent impedance, harmonic and intermodulation fingerprint extraction, Koopman operator modeling and entropy coefficient difference, constructing spectral measure and using the optimal transmission calculation and the geometric distance of the group reference spectral measure to generate multi-domain response packet, physical invariant vector and uncertainty matrix.

[0007] Based on the geometric distance and consistency score gating and hierarchical standardization, a shape-constrained health mapping model is used to obtain health status estimation records and abnormal event sets;

[0008] Based on health status estimation records, abnormal event sets, and uncertainty matrices, and combined with the Jacobian and optimal transport dual potential of the shape-constrained health mapping model, D-optimal experimental design is used to determine the frequency, amplitude, direction, and window duration, generate the next cycle opportunity diagnosis incentive plan, and update the population health manifold for population reference spectrum measurement and gating threshold.

[0009] Preferably, the estimated and parameter fitting output of the equivalent impedance includes high-frequency internal resistance, charge transfer resistance, double-layer capacitance and diffusion correlation coefficient, and the equivalent impedance spectrum is obtained by multi-window cross-spectral estimation.

[0010] Preferably, the harmonic and intermodulation fingerprint extraction includes calculating the third harmonic ratio, intermodulation intensity, and directional asymmetry in the charging and discharging directions, respectively, and writing the third harmonic ratio, intermodulation intensity, and directional asymmetry into a multi-domain response packet and merging it into a physical invariant vector.

[0011] Preferably, the Koopman operator modeling adopts extended dynamic mode decomposition, and the dictionary includes current, voltage, temperature and their single-step lag terms and product terms. The output spectral radius and the difference norm between the charging direction and the discharging direction are written into the multi-domain response package.

[0012] Preferably, the entropy coefficient difference is used to estimate the entropy coefficient of the open-circuit voltage temperature coefficient by the difference in the rate of temperature change under positive and negative micro-amplitude current excitation, and an electro-thermal consistency score is generated accordingly.

[0013] Preferably, constructing the spectral measure includes normalizing the amplitude of the equivalent impedance spectrum to form the spectral measure, and using entropy regularization to calculate the geometric distance between the optimal transmission and the group reference spectral measure, and storing the optimal transmission dual potential as the gradient representation of the geometric distance with respect to the spectral measure in the multi-domain response packet.

[0014] Preferably, the uncertainty matrix is ​​obtained by bootstrapping and resampling the time window segments and frequency domain components to estimate the variance and correlation of the equivalent impedance parameters, harmonic and intermodulation fingerprints, Koopman operator modeling quantities and entropy coefficient difference components, and then assembled in the order of physical invariant vectors.

[0015] Preferably, the consistency score includes directional consistency score and electro-thermal consistency score. Environmental stratification standardization establishes the mean and standard deviation according to the temperature range and the battery state of charge range, respectively. The shape-constrained health mapping model applies monotonically non-increasing constraints to high-frequency internal resistance, charge transfer resistance, diffusion correlation coefficient and spectral geometric distance.

[0016] Preferably, the Fisher information matrix of the D-optimal experimental design is synthesized from the linear response sensitivity of the equivalent impedance parameter, the nonlinear sensitivity of harmonics and intermodulation fingerprints, and the observability of the Koopman mode, and combined with the optimal transmission dual potential to determine the frequency band weights to generate an excitation parameter set containing frequency, amplitude, direction, and window duration.

[0017] Preferably, the population health manifold is updated using hierarchical Bayesian methods. The update objects include the population reference spectrum measure and the gating threshold. The update is based on the historical sequence of the opportunity diagnosis stimulus data window, health status estimation records, and multi-domain response packets.

[0018] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows:

[0019] By unifying the acquisition of data windows through small-signal active excitation and opportunistic diagnostic excitation, frequency band identification and cross-device comparability are achieved. Through time-frequency coupling modeling and spectral measure construction, shape-level health comparison and environmental decoupling are realized. By extracting harmonic and intermodulation fingerprint directions in pairs, interface nonlinearity and connection paths are distinguished. Through Koopman operator modeling and spectral radius and difference norm output, dynamic consistency measurement within a short window is achieved. Through entropy coefficient difference and electro-thermal consistency scoring, separation and verification of reversible heat and environmental heat dissipation are achieved. Through bootstrapping resampling and error propagation of the uncertainty matrix, intervalization and credibility management of health estimation are achieved. Through monotonic constraints of the shape-constrained health mapping model, interpretable regression consistent with electrochemical mechanisms is achieved. Through a joint strategy of optimal transmission dual potential and D-optimal experimental design, closed-loop optimization of frequency, amplitude, direction, and duration is achieved. Through hierarchical Bayesian updating of the population health manifold, adaptive evolution of the population reference spectral measure and gating threshold is achieved. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0021] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation.

[0022] like Figure 1 As shown, a method for remote health status analysis and anomaly identification of electric bicycle batteries includes the following steps:

[0023] Under the condition of meeting the admission criteria, small-signal active excitation is applied, and voltage, current and temperature are simultaneously collected and preprocessed using multiple sinusoidal excitation or pseudo-random binary sequence excitation to form an opportunity diagnostic excitation data window.

[0024] This invention acquires electrical and thermal responses through small-signal active excitation during normal vehicle use, constructing an opportunity diagnostic excitation data window that can be directly consumed by subsequent algorithms. Small-signal active excitation applies a short-duration, narrow-amplitude, and controllable current disturbance to the battery without altering the drive control strategy or riding experience, causing observable changes in voltage and temperature. Compared to relying solely on passive operating condition data, this method achieves higher information density and discriminability within the target frequency band, providing a data foundation within the same time window for subsequent equivalent impedance estimation, harmonic and intermodulation analysis, Koopman operator modeling, and entropy coefficient differencing.

[0025] The entry criteria consist of operating conditions and environmental conditions. Operating conditions are used to select periods with minimal disturbance and low fluctuations, such as constant speed cruising or parking, to suppress the contamination of the response by changes in vehicle-side load. Environmental conditions are used to limit temperature and battery state of charge to within identifiable ranges, making the electrochemical process approximately linear or weakly nonlinear, thereby ensuring the effectiveness of small-signal analysis. The vehicle-side uses a state machine to manage entry, execution, and exit. Any out-of-bounds event immediately exits and records the event code, while retaining the current window for traceability.

[0026] Two excitation mechanisms are employed: multi-sinusoidal excitation and pseudo-random binary sequence excitation. Multi-sinusoidal excitation injects small currents at several discrete frequency points, facilitating direct acquisition of amplitude and phase in the frequency domain, and is suitable for precise estimation of equivalent impedance point values ​​and direction-dependent nonlinear indices. Pseudo-random binary sequence excitation jumps between two current levels in a pseudo-random sequence, enabling the injection of approximately broadband energy in a short time, suitable for cross-spectrum estimation and broadband modeling. Both mechanisms are unified under a single data contract, eliminating the need for subsequent algorithmic branching based on mechanism differences. To reduce the impact on user experience and energy consumption, the excitation amplitude is scheduled according to the battery's state of charge and temperature, limiting energy injection per unit time. For multi-sinusoidal excitation, complementary phase pairs are configured for the same frequency point within adjacent short time windows to offset net torque fluctuations.

[0027] Synchronous sampling covers three physical quantities: voltage, current, and temperature. Voltage and current are sampled synchronously at a high frequency and strictly aligned with the excitation timing, while temperature is sampled at a lower frequency, recording the average value and rate of change within a window. Anti-aliasing filtering is implemented in the sampling link. Before data is entered into the database, DC removal and edge smoothing are performed to reduce spectral leakage, and median filtering is used to remove isolated spikes. All frames are timestamped with a hardware clock to ensure that the three data streams are aligned on the same time base.

[0028] The opportunity diagnostic excitation data window is a complete package of data and metadata corresponding to a small-signal active excitation. The data portion includes preprocessed voltage, current, and temperature sequences. The metadata portion includes frequency set, phase set, amplitude set, excitation direction, start and end timestamps, battery state-of-charge statistics and temperature statistics, execution results, and quality markers. A unique identifier is assigned to each window after generation, facilitating consistency verification, traceability, and correlation with subsequent health estimation results at the remote end. The window serves as the sole input source for subsequent calculations, avoiding mismatches and biases caused by cross-window splicing.

[0029] The benefits of this step are threefold. First, the one-to-one correspondence response to the target frequency band significantly improves the stability of equivalent impedance estimation and spectral shape measurement, reducing bias and variance when relying on random operating condition data. Second, paired charging and discharging direction excitations within the same time window provide the information needed for directional consistency, enabling direct evidence for identifying interface nonlinearity and lithium plating tendency. Third, temperature and battery state of charge are bound to each response as window metadata, facilitating hierarchical standardization and gating at the remote end based on temperature and battery state of charge, suppressing the impact of environmental differences on population modeling.

[0030] To ensure the availability and security of remote deployment, the vehicle-side implements failure rollback and retry logic. When a low signal-to-noise ratio, sampling saturation, or a perceptible torque risk is detected, the current window is not discarded. Instead, a failure flag is written to the window metadata, and adjustment suggestions for the next cycle are generated, including reducing the amplitude, shortening the frequency, or switching the excitation system. This suggestion is submitted along with the window and is uniformly decided by the test design strategy in subsequent cycles, thereby maintaining the consistency of the diagnostic closed loop.

[0031] Example: After an electric bicycle equipped with a lithium-ion battery meets the access criteria on a straight, uniform-speed urban commuting route, the system issues a multi-sinusoidal excitation covering low to mid-frequency frequencies for several seconds. Voltage and current are recorded synchronously at high frequency, and temperature is recorded as average value and rate of change. After the window ends, the data undergoes DC removal, edge smoothing, and glitch removal, generating an opportunistic diagnostic excitation data window and uploading it. If the same vehicle meets the access criteria again during a nighttime parking period, the system uses a pseudo-random binary sequence excitation to form a second window. The remote end performs unified time-frequency coupling modeling on the two windows, outputting a multi-domain response packet, a physical invariant vector, and an uncertainty matrix. Subsequently, gating and hierarchical standardization are performed based on geometric distance and consistency scores, and a health status estimate is provided by a shape-constrained health mapping model, generating an abnormal event set. The experimental design strategy is then used to schedule high-information-frequency band excitations for the next cycle, achieving a closed loop of diagnosis and planning. The above example demonstrates that this step not only meets the safety and operability requirements of remote scenarios but also provides structured and high-quality input for subsequent core algorithms, thereby supporting the accuracy and traceability of health estimation and anomaly identification.

[0032] Based on the opportunity diagnostic excitation data window, time-frequency coupling modeling is carried out, including equivalent impedance, harmonic and intermodulation fingerprint extraction, Koopman operator modeling and entropy coefficient difference, constructing spectral measure and using the optimal transmission calculation and the geometric distance of the group reference spectral measure to generate multi-domain response packet, physical invariant vector and uncertainty matrix.

[0033] This invention employs time-frequency coupled modeling of the opportunity diagnostic excitation data window under a unified data contract. It jointly processes voltage, current, and temperature sequences with excitation metadata within the same time window to obtain an interpretable and cross-condition stable multi-domain representation. This processing chain covers equivalent impedance estimation, harmonic and intermodulation fingerprint extraction, Koopman operator modeling, and entropy coefficient differencing. Subsequently, a spectral measure is constructed, and the geometric distance between the optimal transmission and the population reference spectral measure is calculated. Finally, a multi-domain response packet, a physical invariant vector, and an uncertainty matrix are generated for subsequent health mapping and anomaly identification.

[0034] The equivalent impedance is estimated by obtaining the frequency response within a window using the cross-spectral method. Let the voltage time series be V(t) and the current time series be I(t). The cross-spectrum and auto-spectrum are obtained by performing a Fourier transform on the windowed piecewise segments. in For equivalent impedance estimation, S VI (ω) is the cross spectrum of voltage and current, S II (ω) represents the autospectral density of the current. Based on For the characteristic shapes at high, mid, and low frequencies, high-frequency internal resistance, charge transfer resistance, double-layer capacitance, and diffusion correlation coefficients are fitted, respectively, and passive and approximate causality checks are performed to eliminate distortion windows. Harmonic and intermodulation fingerprint extraction are performed separately for multi-sinusoidal excitation and pseudo-random binary sequence excitation. For multi-sinusoidal excitation, complex amplitudes are extracted at each fundamental frequency and its higher integer harmonics to form the third harmonic ratio. in and These represent the voltage amplitudes of the third harmonic and the fundamental frequency, respectively. For combinations with multiple frequency points, the intensity and directional asymmetry of the third-order intermodulation components are statistically analyzed, providing directional sensitivity evidence for interface nonlinearity and contact anomalies. Koopman operator modeling employs extended dynamic mode decomposition, mapping a dictionary consisting of current, voltage, temperature, and their hysteresis and products to linear evolution. The observation matrices X and Y are constructed, and the following values ​​are obtained: Where K is the Koopman operator estimate, γ is the regularization coefficient, and I is the identity matrix. The operator difference norm between the spectral radius and the charging and discharging directions is extracted to measure hysteresis and dynamic consistency. The entropy coefficient difference is used to estimate the temperature coefficient of the open-circuit voltage. For micro-excitations with the same amplitude but opposite directions within the same window, the temperature change rate difference is calculated and the Joule heating term is eliminated to obtain... Where α T C is the entropy coefficient. th For equivalent heat capacity, T avg The average temperature of the window. and ΔI represents the temperature change rate under forward and reverse micro-excitation, respectively, and ΔI is the amplitude of the micro-excitation current. The entropy coefficient, combined with the mid-to-low frequency equivalent impedance change, can be used for electrothermal uniformity gating and intrinsic temperature correction. In frequency domain geometric modeling, the equivalent impedance amplitude is normalized to the spectral measure p(ω). i Let p be the spectral measure of the reference healthy group. ref (ω j The optimal transmission distance is defined using entropy regularization: Where Γ represents the transmission plan, and C ij The distance represents the frequency cost, ε is the regularization coefficient, and KL is the relative entropy. This distance characterizes the degree of deviation of the spectral shape of this window from the healthy baseline, and outputs the dual potential as a gradient approximation of the distance to the spectral measure for use in subsequent experimental design.

[0035] The uncertainty matrix was obtained through bootstrapping resampling in the frequency and time domains. The cross-spectral bands, harmonic amplitudes, Koopman operator estimates, and entropy coefficients were repeatedly sampled, and their variances and correlations were calculated separately. These were then assembled into a covariance matrix in a fixed order of the physical invariant vectors. This matrix was subsequently used for health state uncertainty propagation and gating confidence calculation.

[0036] The multi-domain response package encapsulates all intermediate quantities for decision-making, including equivalent impedance spectrum, high-frequency internal resistance, charge transfer resistance, double-layer capacitance, diffusion correlation coefficient, third harmonic ratio, intermodulation intensity, directional asymmetry, spectral radius, operator difference norm, entropy coefficient, spectral geometric distance, and window-level quality markers. The physical invariant vector selects a subset of these quantities that is monotonic and stable across operating conditions, serving as direct input to the shape-constrained health map. The uncertainty matrix and the multi-domain response package together ensure that subsequent estimates have interval and confidence representations, rather than single-point values.

[0037] For example, a single multi-sinusoidal excitation window covers several discrete points at low and mid frequencies. The cross-spectral method is used to obtain the equivalent impedance estimate for the continuous frequency band. The high-frequency internal resistance is fitted at the high-frequency end, the charging transfer resistance and double-layer capacitance are fitted at the mid-frequency arc, and the diffusion correlation coefficient is regressed at the low-frequency end. The fundamental frequency and third harmonic are extracted from the same window to obtain the third harmonic ratio and directional asymmetry. Extended dynamic mode decomposition is used to calculate the Koopman operator estimate and output the spectral radius and difference norm. The entropy coefficient is obtained by differencing the temperature change rates of the forward and reverse micro-excitations. The normalized equivalent impedance amplitude is used to construct a spectral measure, which is compared with the group reference spectral measure to calculate the optimal transmission geometry distance and preserve the dual potential. Finally, an uncertainty matrix is ​​formed using a bootstrapping method. The output of this window is written into a multi-domain response packet and a physical invariant vector for subsequent gating, health mapping, and anomaly detection.

[0038] Example: A vehicle on a road section with stable temperature and load receives one multi-sinusoidal excitation window and one pseudo-random binary sequence excitation window. The two windows respectively complete the aforementioned modeling process, generating two sets of multi-domain response packets and physical invariant vectors. The two sets of results are filtered by a consistency rule at the remote end and merged into the same health estimation period. Spectral geometric distance shows that the vehicle has a low-to-mid-frequency offset relative to the group reference, the third harmonic ratio is higher in the charging direction than in the discharging direction, and the entropy coefficient is consistent with the temperature dependence of the equivalent impedance. After comprehensive judgment, a health state estimation record and anomaly event set are output, and dual potential and sensitivity information are provided to the experimental design module for arranging the frequency band and amplitude configuration for the next period.

[0039] Preferably, the estimated and parameter fitting output of the equivalent impedance includes high-frequency internal resistance, charge transfer resistance, double-layer capacitance and diffusion correlation coefficient, and the equivalent impedance spectrum is obtained by multi-window cross-spectral estimation.

[0040] This invention performs multi-window cross-spectral estimation on voltage, current, and temperature sequences within the same time window to obtain the equivalent impedance spectrum. It then robustly fits key parameters of the equivalent circuit within the frequency band, outputting high-frequency internal resistance, charge transfer resistance, double-layer capacitance, and diffusion correlation coefficient as core physical quantities for subsequent health mapping and anomaly identification. The cross-spectral estimation employs piecewise windowing and averaging to reduce variance, ensuring a stable frequency response even under short-time, small-signal conditions.

[0041] Let the terminal voltage be V(t) and the terminal current be I(t). Divide the opportunity diagnostic excitation data window into M equal-length segments, and let the signal of the m-th segment be v. m (t), i m Given a segment w(t) with a window function w(t) and an angular frequency ω, perform a Fourier transform on each segment and calculate the average to obtain the cross spectrum and the autospectrum. in They are conjugates. The equivalent impedance estimate is: Direct reading at discrete frequency points under multi-sine excitation Point values ​​are used to form continuous band estimates under pseudo-random binary sequence excitation. To suppress systematic errors, DC removal, time alignment, and anti-aliasing filtering are performed beforehand, and a smoothing window is applied to the window edges to reduce spectral leakage. Parameter fitting follows physical banding constraints from high frequency to low frequency. The high-frequency internal resistance is obtained by extrapolating the real part at the high-frequency end, and is defined as follows: In practice, at several of the highest frequency points... Weighted linear extrapolation is performed, and a robust loss is employed to suppress isolated noise. The mid-frequency region is characterized by Randle-type interface branches, and the model is as follows: Where R ct For the charge transfer resistor, C dl Let be the double-layer capacitance, and j be the imaginary unit. Complex least squares is used to fit both the real and imaginary parts simultaneously, with weights assigned to different frequency bands to avoid bias in the mid-frequency fitting caused by local frequency impedance. A semi-infinite diffusion approximation is used in the low-frequency region; let the diffusion correlation coefficient be σ, then Z... W (ω)=σ(1-j)ω -1 / 2 ,by With ω -1 / 2 The regression slope σ is estimated, and the fit is performed only within the linear segment when there are signs of finite-length diffusion. The three fitting segments are fitted sequentially in the order of high frequency, mid frequency, and low frequency to lock the parameters and avoid squeezing each other's degrees of freedom.

[0042] To ensure the availability and traceability of the estimates, this invention implements two types of physical consistency checks on the equivalent impedance spectrum. First, a passive check, requiring... Second, an approximate causality check is performed, using the frequency domain Hilbert consistency residual to measure the Kramers–Kronig bias. If the check fails, a quality flag is written into the opportunity diagnostic stimulus data window, and the contribution of that window to the health estimate is limited in subsequent gating steps.

[0043] In remote health status analysis and anomaly identification scenarios, the above parameters play a clear role: high-frequency internal resistance reflects the total series impedance drift of the current collector, busbar, and electrode, and is sensitive to connection contact anomalies and high-frequency admittance changes; charge transfer resistance characterizes the interface charge exchange rate and is closely related to temperature, aging, and interface state; double-layer capacitance reflects changes in effective interface area and roughness; and diffusion correlation coefficient characterizes the degree of ion diffusion restriction and plays a decisive role in low-frequency shape. These four quantities constitute the monotonically increasing principal term in the physical invariant vector. Subsequent shape-restricted health mapping imposes a monotonically non-increasing constraint on them, causing the health status to decrease as impedance and diffusion restriction worsen, ensuring interpretability.

[0044] Uncertainty assessment employs segment-level bootstrapping and frequency resampling. Sampling with replacement is performed on M window segments, and the calculations are repeated. The results are then propagated to R0, charge transfer resistance, double-layer capacitance, and diffusion correlation coefficient to form parameter variances and correlations, which are then summarized into an uncertainty matrix. This matrix is ​​subsequently used for health state interval estimation and gating confidence measurement, enabling remote decision-making to be independent of single-point estimations.

[0045] For example, a multi-sinusoidal opportunity diagnostic excitation covered several points from low to mid-frequency. After obtaining the equivalent impedance spectrum through cross-spectral estimation, high-frequency internal resistance was obtained through linear extrapolation in the high-frequency band, charge transfer resistance and double-layer capacitance were obtained through complex fitting in the mid-frequency band, and diffusion correlation coefficients were obtained through slope regression in the low-frequency band. Passivity and approximate causality checks were both passed. Compared with the historical window under the same temperature and battery state of charge stratification one month ago, the high-frequency internal resistance increased slightly, while the increase in charge transfer resistance was more significant. The multi-domain response packet and physical invariant vector generated by this window were entered into the health mapping, and the output health state estimation record showed a downward trend; the abnormal event set did not trigger connection contact anomalies, but indicated the risk of interface dynamic degradation. Subsequently, the experimental design strategy was to increase the density of mid-frequency points in the next cycle to improve the identification of changes in charge transfer resistance. The above examples show that multi-window cross-spectral estimation and zonal fitting can reliably extract health-related electrochemical parameters under short-term excitation and remain stable and interpretable in remote environments.

[0046] Preferably, the harmonic and intermodulation fingerprint extraction includes calculating the third harmonic ratio, intermodulation intensity, and directional asymmetry in the charging and discharging directions, respectively, and writing the third harmonic ratio, intermodulation intensity, and directional asymmetry into a multi-domain response packet and merging it into a physical invariant vector.

[0047] This invention performs harmonic and intermodulation fingerprint extraction on voltage and current sequences within the opportunity diagnostic excitation data window to obtain directional sensitive quantities indicating the nonlinearity of the electrode interface and the connection state, and writes them into a multi-domain response packet and a physical invariant vector as key inputs for health mapping and anomaly identification.

[0048] For multi-sinusoidal excitation systems, coherent demodulation or discrete Fourier transform is used to extract complex amplitudes at each fundamental frequency and the third integer harmonic. Let the window duration be T, the angular frequency be ω, the voltage be V(t), and the current be I(t), then the complex amplitude of the voltage at ω and 3ω is defined as follows: Where j is the imaginary unit. The third harmonic ratio is calculated using this: The corresponding values ​​were obtained in the charging and discharging directions respectively, forming nonlinear intensity quantities with paired directions. To improve robustness, linear extrapolation correction was used for phase drift at adjacent frequency points, and robust averaging was used for amplitude to suppress isolated noise points.

[0049] For intermodulation components, let the set of input frequency points be Ω={ω i}, take unordered pairs from Ω to form a set For each pair (ω) a ,ω b The third-order intermodulation frequency 2ω was detected on the output spectrum. a -ω b With 2ω b -ω a complex amplitude Define the normalized third-order intermodulation intensity: And on The arithmetic mean is used to obtain the aggregation intermodulation strength: Under the pseudo-random binary sequence excitation system, Ω is first constructed based on the spectral peak set of the input current, and then the intermodulation amplitude is calculated on the output spectrum according to the same frequency relationship, while the above definition remains unchanged.

[0050] To measure the nonlinear difference in the electrochemical interface along the charge-discharge direction, directional asymmetry is constructed. Let the third harmonic ratios of the charging and discharging directions be (H3 / H1). chg (H3 / H1) dis The polymerization intermodulation strengths were IM3. chg IM3 dis .definition The logarithm is the natural logarithm. This definition is insensitive to amplitude scaling and measurement gain, facilitating cross-device comparisons. Orientation asymmetry serves as the core input to the orientation consistency criterion and is also fed into the physical invariant vector for monotonic constraints and anomaly scoring in shape-constrained health mapping.

[0051] To reduce noise impact and spectral leakage, this invention performs windowing, DC removal, and edge smoothing on the opportunity diagnostic excitation data window; the spectral search for harmonics and intermodulations uses a fixed frequency deviation tolerance and takes a weighted average across multiple windows. For paired windows of charging and discharging directions, time-adjacent pairing is preferred to reduce temperature and battery state-of-charge drift. For the uncertainty of the third harmonic ratio and intermodulation intensity, segment-level bootstrapping resampling is used to form a variance estimate, which is written into the multi-domain response packet along with the principal values.

[0052] The role of harmonics and intermodulation fingerprints in remote health status analysis and anomaly identification is reflected in three aspects. First, the third harmonic is sensitive to nonlinear admittance induced by interfacial nonlinearity and local lithium plating, and the increase in the charging direction reveals deposition trends more clearly than that in the discharging direction. Second, intermodulation intensity is more sensitive to nonlinear terms caused by multi-frequency interactions, providing early risk warnings before harmonics become prominent. Third, directional asymmetry unifies the above two types of fingerprints into dimensionally consistent scalars within the framework of paired charge and discharge, facilitating joint gating with temperature, equivalent impedance, and entropy coefficient information.

[0053] For example, a small current is injected into a single multisine window at two frequencies, 0.5Hz and 1.0Hz. Third-order intermodulation components are detected on the output spectrum at 1.5Hz and 0Hz, respectively. The IM3 of this window is calculated according to the definition. agg Simultaneously, the third harmonic ratio (HMR) was estimated at 0.5Hz and 1.5Hz. Then, paired windows for the discharge direction were acquired in adjacent time periods, and the discharge direction indices were repeatedly calculated. The directional asymmetry was calculated from the two pairs of windows, showing that the HMR and aggregation intermodulation intensity in the charging direction were higher than those in the discharging direction. The HMR, aggregation intermodulation intensity, directional asymmetry, and corresponding uncertainties of this window were written into a multi-domain response packet and selected into the physical invariant vector. In the subsequent health mapping stage, the combined change in directional asymmetry and charging transfer resistance led to a decrease in the estimated health status. In the anomaly identification stage, the lithium plating tendency score was set high, triggering the next cycle's opportunity diagnostic excitation configuration in the low-to-mid frequency band to verify and track the interface nonlinear evolution.

[0054] Example: A vehicle completes a set of paired window acquisitions under low-temperature conditions. The third harmonic ratio (HMR) in the charging direction increases around 0.8Hz, the aggregation intermodulation intensity increases, and the directional asymmetry reaches above a preset threshold. Combined with the increase in the mid-frequency arc radius of the equivalent impedance and the positive entropy coefficient in the same window, the system schedules a probabilistic diagnostic excitation plan that night, primarily using multi-sine excitations from 0.5Hz to 2.0Hz, and reviews the high-frequency transient connectivity indicators. Subsequent window displays show that the HMR remains high while connectivity jitter is not abnormal. Based on this, the remote terminal confirms the anomaly type dominated by interface nonlinearity and shortens the health status assessment cycle. The above process demonstrates the synergistic effect of harmonics and intermodulation fingerprints in directional sensitivity, cross-condition robustness, and closed-loop test design.

[0055] Preferably, the Koopman operator modeling adopts extended dynamic mode decomposition, and the dictionary includes current, voltage, temperature and their single-step lag terms and product terms. The output spectral radius and the difference norm between the charging direction and the discharging direction are written into the multi-domain response package.

[0056] Koopman operator modeling is used to characterize the temporal evolution of current, voltage, and temperature within a short time window, thereby measuring the dynamic differences in slow mode strength and charge / discharge direction of the system without introducing high-order nonlinear differential equations. This invention employs extended dynamic mode decomposition to establish a discrete-time linear up-dimensional representation, mapping the current, voltage, and temperature sequences in the opportunistic diagnostic excitation data window to a feature space. The linear mapping matrix is ​​estimated using ridge regression, and then the spectral radius and directional difference norm are calculated as quantitative indicators of dynamic consistency and hysteresis.

[0057] Let the sampling period be a fixed interval, and the time index be an integer sequence. A state vector is constructed using the current, voltage, and temperature at the current moment. A dictionary function is defined to increase the dimensionality of the state vector. Dictionary entries include linear terms, single-step lag terms, and quadratic interaction terms, such as the square of current, the product of current and voltage, and the product of voltage and temperature. The dictionary is evaluated point-by-point within a window to obtain the feature matrix and its single-step shifted feature matrix. The linear operator φ(z) is estimated using the following formula. k+1 )≈Kφ(z k ), Where φ(·) is a dictionary mapping, z k Let X be a state vector consisting of current, voltage, and temperature, where X = [φ(z1), ..., φ(z2)]. M-1 )],Y=[φ(z2),…,φ(z M [], K is the finite-dimensional approximation of the Koopman operator on the dictionary basis, γ>0 is the regularization coefficient, and I is the identity matrix. Zero-mean and unit-variance standardization is first applied to each column of the dictionary to ensure comparable contributions of different dimensions to the estimation; robust weights are used for outliers to reduce the impact of sudden noise. Spectral analysis is performed on the estimated Koopman operator. Let its eigenvalues ​​be {λ i Define the spectral radius. A spectral radius closer to 1 indicates a slower decay mode or near-amplitude-preserving cycling mode within the window, corresponding to a slow recovery or hysteresis in the electrochemical process. A spectral radius significantly lower than 1 indicates that the dynamics within that window are dominated by rapid decay. To characterize the dynamic differences in the charge and discharge directions, two operators, denoted as K, are estimated independently for the charging and discharging windows respectively. (chg) With K (dis) Define the directional difference norm: Δ K =||K (chg) -K (dis) || F , where ||·|| F This is the Frobenius norm. The directional difference norm reflects the degree of inconsistency in the linearization dynamics of charge and discharge operations under similar environmental conditions; the larger the value, the stronger the hysteresis or asymmetric behavior.

[0058] To ensure estimation stability, time alignment, DC removal, and edge smoothing are first performed on voltage and current within the window. A consistent dictionary and lag order are selected based on the opportunistic diagnostic excitation system. For pseudo-random binary sequence excitations, the number of lag terms in the dictionary can be appropriately increased to capture short-term memory effects driven by jumps; for multi-sinusoidal excitations, the weight of interaction terms can be increased to highlight amplitude-phase coupling information. Regularization coefficients are selected offline on the training set using unsupervised criteria and kept fixed online to ensure consistency across remote scenarios.

[0059] Spectral radius and directional difference norm are incorporated into the multi-domain response package and, together with equivalent impedance parameters, harmonic and intermodulation indices, and entropy coefficients, are used to construct the physical invariant vector and uncertainty matrix. In practical applications, the spectral radius is used for dynamic consistency scoring and frequency band preference selection in experimental design: when the spectral radius is close to 1 and the uncertainty is large, low-to-mid-frequency energy is preferentially allocated in the next cycle to distinguish slow mode sources; when the spectral radius is far from 1, the experimental design adds high-frequency snapshots to confirm changes on the connection side. The directional difference norm, along with directional asymmetry and the third harmonic ratio, is used for anomaly classification: when the directional difference norm increases and the harmonic fingerprint is significantly amplified in the charging direction, it points to interface-related asymmetric nonlinearity; when the directional difference norm increases while the harmonic index is low, and high-frequency real part jitter is enhanced, it is more likely to indicate changes in the connection contact path.

[0060] For example, on a weekday evening with stable temperatures, a vehicle obtains two adjacent windows: the first for the charging direction and the second for the discharging direction. Extended dynamic mode decomposition is performed using the same dictionary configuration to obtain K. (chg) With K (dis) Spectral analysis results show that the spectral radius in the charging direction is close to 1, while the spectral radius in the discharging direction is slightly lower, and the directional difference norm is significantly higher than the historical average. In harmonic and intermodulation analysis within the same period, the third harmonic ratio and aggregated intermodulation intensity in the charging direction are both high; the mid-frequency arc radius of the equivalent impedance increases, and the entropy coefficient is positive. Considering these quantities, this invention labels this period as a risk dominated by interface nonlinearity in anomaly identification, and the decrease range of the health status estimate output by the health mapping becomes wider. The experimental design arranges low-to-mid-frequency multi-sinusoidal excitation and reduces the single-point amplitude in the next period to improve the observability of slow modes without increasing the impact on the user experience. The implementation results show that the spectral radius and directional difference norm provided by the Koopman operator modeling can stably capture dynamic characteristics in remote scenarios and, in conjunction with frequency domain and thermal information, improve the reliability of health assessment and anomaly classification.

[0061] Preferably, the entropy coefficient difference is used to estimate the entropy coefficient of the open-circuit voltage temperature coefficient by the difference in the rate of temperature change under positive and negative micro-amplitude current excitation, and an electro-thermal consistency score is generated accordingly.

[0062] This invention utilizes forward and reverse micro-amplitude current excitations within the same opportunity diagnostic excitation data window to extract the entropy coefficient of the open-circuit voltage temperature coefficient, and constructs an electro-thermal consistency score accordingly. This step centers on the odd symmetry of the reversible thermal term with respect to the current sign in energy balance, using paired directional measurements to offset the uncertainties of Joule heating and environmental heat dissipation, achieving a robust estimate of the entropy coefficient. The consistency of the electro-thermal link is then determined based on the synergistic relationship between this estimate and frequency domain characteristics.

[0063] The thermal equilibrium of a battery under small-signal conditions can be written as the sum of reversible and irreversible heat. Let the temperature be T and the ambient temperature be T.amb The current is I, the equivalent internal resistance is R, and the equivalent heat capacity is C. th The combined convective heat transfer coefficient and radiation coefficient are represented by h. The rate of temperature change approximately satisfies: in U is the entropy coefficient. oc This is the open-circuit voltage. In this formula, I... 2 R and the heat transfer term are evenly symmetric about the current sign, while ITα T Regarding the odd symmetry of the current sign. This invention sets up two micro-excitations with equal amplitude but opposite directions within the same environmental layer, and denotes the temperature change rate as... and The current amplitude is ΔI, and the average temperature of the window is T. avg Subtracting the two equations, we get: This leads to the estimation formula for the entropy coefficient. Among them, C th To obtain the equivalent heat capacity calibration value through in-plant bench or vehicle-side offline calibration, T avg The value is the arithmetic mean of the temperatures in the two windows, and ΔI is the amplitude of the micro-excitation. This estimation formula is the core calculation expression for this step.

[0064] To ensure α T To assess the effectiveness of the estimation, the data processing link employs a directional pairing and time proximity strategy: the execution time interval of the forward and reverse micro-excitations is limited to the same running segment, ensuring that T and the environmental flow field change slowly; temperature change rate The slope of local polynomial regression within the window is calculated, and the edges are smoothed to reduce jitter caused by spectral leakage; when |T + -T - When the preset tolerance is exceeded, the window is marked as low confidence and its weight is reduced in the gating. The impact of temperature and current measurement noise is assessed using segment-level self-liftback resampling to evaluate uncertainty, and the result is obtained according to the error propagation law. in The variance of the entropy coefficient, and The variance of the temperature change rate is estimated. This uncertainty is written into the uncertainty matrix and included in the multi-domain response package along with the principal value. The electro-thermal consistency score is quantified based on the coherence of the entropy coefficient's sign and magnitude, the equivalent impedance temperature sensitivity, and the directional fingerprint. Let the reference entropy coefficient of the population prior at a given temperature and battery state of charge stratification be . The consistency residual is then Simultaneously, the empirical slope of the mid-frequency equivalent impedance parameter with respect to temperature and the degree of directional asymmetry are used as supporting parameters, and a score is generated through weighted normalization. Among them, b α To be according to With respect to the scale determined by the population distribution, q dirq is a standardized quantity for the degree of directional asymmetry. Z λ is a standardized quantity representing the temperature sensitivity of the equivalent impedance. dir With λ Z The weights are denoted by α, and clip(·) is the clipping operator. A score closer to 1 indicates that electrical and thermal information corroborate each other; a lower score suggests inconsistencies in the electrothermal link, potentially stemming from sensor offset, changes in connection paths, or abnormal side reactions. The score is related to α. T The estimate and its uncertainty are included in the gating and health mapping.

[0065] This step is effective in remote health status analysis and anomaly identification in three aspects. First, by using directional parity decomposition to separate reversible heat from Joule heating and heat transfer terms, it significantly reduces the bias caused by heat transfer in unknown environments. Second, α T The environmental stratification records enable comparability of cross-day comparisons of the same vehicle, providing continuous quantification of slowly evolving interface changes. Third, the electro-thermal consistency score integrates temperature, equivalent impedance, and directional fingerprints into a single scale, facilitating clear pass or deweighting decisions in gating.

[0066] For example, when the battery is at 60% state of charge and the temperature is 25°C, the vehicle obtains a set of paired micro-excitation windows with a current amplitude of ΔI. Regression is performed on both windows to obtain... and Substituting into the entropy coefficient estimation formula, we get α T Its variance is given by the above formula. Within the same period, multiple sinusoidal windows give the positive slope of the mid-frequency equivalent impedance with temperature, and the directional asymmetry is higher in the charging direction. The electro-thermal consistency score is therefore close to 1, passing through the gating process. The shape-constrained health mapping will α T Combined with charge transfer resistance and diffusion correlation coefficient, it was used for health status estimation. Repeated measurements at low temperature conditions the following week showed α. T As the directional asymmetry increases, the score decreases, triggering a new, more sophisticated excitation scheme in the low-to-mid frequency band for the next cycle. This scheme tracks the interplay between interface nonlinearity and reversible thermal properties. The results demonstrate that entropy coefficient difference and electro-thermal consistency scoring can provide stable, interpretable, and quantifiable invariants and gating criteria in remote scenarios.

[0067] Preferably, constructing the spectral measure includes normalizing the amplitude of the equivalent impedance spectrum to form the spectral measure, and using entropy regularization to calculate the geometric distance between the optimal transmission and the group reference spectral measure, and storing the optimal transmission dual potential as the gradient representation of the geometric distance with respect to the spectral measure in the multi-domain response packet.

[0068] This invention transforms the amplitude shape of the equivalent impedance spectrum into a measurable and differentiable spectral geometry, used to stably characterize the changing trends of electrochemical states under long-range environments and provide frequency band guidance for experimental design. The method involves normalizing the equivalent impedance amplitude into a spectral measure on the same frequency grid, calculating the geometric distance between the optimal transmission (with entropy regularization) and the group reference spectral measure, and simultaneously extracting the dual potential of the optimal transmission as the gradient representation of the geometric distance with respect to the spectral measure, which is then written into the multi-domain response packet along with the distance.

[0069] Frequency grid is denoted as The magnitude of the equivalent impedance estimate is denoted as Spectral measure obtained by amplitude normalization Where i = 1, ..., N, p i For at frequency ω i Spectral quality distribution at the location, For the equivalent impedance at ω i Complex estimation at the location. This definition uses only shape information, naturally eliminating the scaling effects caused by differences in gain and range across devices. The population reference spectral measure is derived from a set of historical windows of healthy samples at the same temperature and battery state of charge stratification, denoted as q. j Its construction is accomplished through hierarchical statistics and Dirichlet smoothing to avoid zero mass at sparse frequency points.

[0070] Spectral geometric distance is defined as optimal transmission with entropy regularization. Let the cost matrix be C. ij Using logarithmic frequency distance C with stable logarithmic dimensions ij =(logω) i -logω j ) 2 Distance from writing Where Γ is the transport plan matrix, p is the spectral measure, q is the group reference spectral measure, ε>0 is the entropy regularization coefficient, and 1 represents a vector with all components equal to 1. This objective measures the minimum "transport cost" of the two spectral shapes under mass conservation constraints, while using entropy regularization to improve numerical stability and suppress noise-induced spikes. It can be solved efficiently using Sinkhorn scaling. The KKT conditions for the above problem give the dual potentials α and β, and Γ... * =diag(u)Kdiag(v), K ij =exp(-C ij / ε), α * =εlogu,β * =εlogv, where u and v are the Sinkhorn scaling vectors, α * With β * Let α be the dual potential between the source and the target. According to the duality relation of entropy-normalized optimal transmission, α *It is the first-order gradient representation of geometric distance with respect to spectral measure p, used to indicate which frequency band contributes the most to the current deviation.

[0071] The multi-domain response package records the spectral geometric distance and dual potential: the spectral geometric distance reflects the scale of the overall shape shift, while the distribution of the dual potential on the frequency grid reflects the direction of the shift and local sensitivity. The spectral geometric distance is selected as the monotonic term from the physical invariant vector; the uncertainty matrix is ​​bootstrapping through cross-spectral band and frequency resampling, propagating to the spectral measure and spectral geometric distance, providing an interval representation. Since the spectral measure depends only on shape and uses logarithmic frequencies as the ground metric, comparability across devices, platforms, and time periods is guaranteed; the locality of the dual potential allows subsequent experimental design to focus finite excitation energy on the frequency band with the highest information density.

[0072] In remote health status analysis and anomaly identification, this construct offers three key advantages. First, it is highly sensitive to the translation and stretching of low-to-mid-frequency arcs, enabling early detection of the synergistic changes in charge transfer resistance and diffusion correlation coefficients. Second, it exhibits a clear high-frequency bias for the mass spillover of high-frequency real-part jitter, facilitating differentiation from connection contact anomalies. Third, it provides a relative measurement of the health reference spectrum after temperature and battery state of charge stratification, effectively suppressing the interference of environmental differences on the conclusions.

[0073] For example, a vehicle obtains an opportunity diagnostic excitation data window within a stratified area at a temperature of 25°C and a battery state of charge of 60%. After equivalent impedance estimation, an amplitude sequence is formed on a preset grid. Normalization yields the spectral measure p, and the stratified health library is used to obtain q. C is constructed at a log frequency cost, and the transmission scheme Γ and dual potential α are obtained through Sinkhorn iteration. * Spectral geometric distance D ε (p,q) is higher than the historical mean. The dual potential shows a positive peak in the 0.2 to 2.0 frequency band, indicating that the excess quality in this band comes from the current window. The multi-domain response packet records the spectral geometric distance and dual potential curve accordingly, adds the physical invariant vector to the spectral geometric distance, and records its variance in the uncertainty matrix. The experimental design reads the dual potential, prioritizes the allocation of the frequency points of the next cycle's multi-sinusoidal excitation to cover the 0.2 to 2.0 frequency band, and reduces the high-frequency energy. The window of subsequent cycles shows that the spectral geometric distance decreases and the peak value of the dual potential falls back, and the estimated value and interval of the health map tend to stabilize. This implementation shows that the joint modeling of spectral measure and optimal transmission provides shape-robust, cross-domain comparable, and usable geometric information for closed-loop scheduling in long-range scenarios.

[0074] Preferably, the uncertainty matrix is ​​obtained by bootstrapping and resampling the time window segments and frequency domain components to estimate the variance and correlation of the equivalent impedance parameters, harmonic and intermodulation fingerprints, Koopman operator modeling quantities and entropy coefficient difference components, and then assembled in the order of physical invariant vectors.

[0075] This invention uses uncertainty modeling as a fundamental step in remote health status analysis and anomaly identification. Through hierarchical bootstrap resampling in the time and frequency domains, it uniformly measures the statistical fluctuations of equivalent impedance parameters, harmonics and intermodulation fingerprints, Koopman operator modeling quantities and entropy coefficient difference components, and assembles them into an uncertainty matrix in a fixed order of physical invariant vectors. The uncertainty matrix is ​​used for gating, health status interval estimation and experimental design.

[0076] The opportunity diagnostic stimulus data window is first divided into several equal-length time intervals and a frequency grid is established. Moving block bootstrapping is used in the time domain to maintain short-range correlation, and zone-based bootstrapping is used in the frequency domain to maintain spectral locality. Let the number of time intervals be M, the block length be L, the number of bootstrapping rounds be B, and the frequency grid be... In each round of bootstrapping, the time domain changes from... In each adjacent block, sampling is performed with replacement until the original length is covered; in the frequency domain, frequency point index sets are sampled in three sub-bands (low frequency, mid frequency, and high frequency) according to a fixed proportion to ensure coverage of the arc, diffusion, and high-frequency real parts regions. To maintain the paired structure of charging and discharging directions, direction-related quantities are sampled using paired windows as the basic sampling unit; temperature and battery state of charge are used as layer labels, and all sampling is completed within the same layer.

[0077] In the b-th round of bootstrapping, the parameters are re-estimated and vectorized using the same method as the main process:

[0078] Where R0 is the high-frequency internal resistance, R ct For the charge transfer resistor, C dl Let be the electric double-layer capacitance, and σ be the diffusion correlation coefficient, (H3 / H1). chg With (H3 / H1) dis IM3 is the third harmonic ratio between the charging and discharging directions. chg With IM3 dis The polymerization intermodulation intensity is given by ρ(K), where K is the spectral radius of the Koopman operator, and Δ is the spectral radius. K Let α be the directional difference norm. T The entropy coefficient is used to calculate the bootstrap mean. With covariance matrix The matrix ∑ is the core numerical representation of the uncertainty matrix. To suppress the influence of outliers, each round of bootstrapping uses quality weights to further weight the blocks and frequencies. These weights are derived from the window's signal-to-noise ratio, passive verification, and approximate causality verification results. The uncertainty matrix is ​​assembled in a fixed order of physical invariant vectors and stored together with the multi-domain response package to ensure dimensionality and semantic consistency during multi-period comparisons and group aggregations at the remote end. The uncertainty matrix has three main applications: First, gating: combining the standardized residuals of key quantities with their diagonal variances, and reducing the weight of low-confidence windows in gating. Second, interval estimation: employing first-order error propagation on the health state mapping g(θ). in The shape-constrained health mapping at the current point is obtained by offline calibration and interpolation during the online phase. Third, experimental design: the information value of the target frequency band is calculated using ∑ sensitivity weights, preferentially allocated to directions that contribute significantly to the variance of the health estimation.

[0079] To ensure cross-system consistency, the time domain block length and frequency domain banding are set separately under the multi-sinusoidal excitation and pseudo-random binary sequence excitation systems, but the output θ (b) The ∑ structure remains unchanged. For direction-dependent harmonics and intermodulation fingerprints, paired vectors of charging and discharging directions are used when calculating the correlation coefficient, which preserves the directional differences and avoids mistaking directional coupling as independent degrees of freedom. For windows with slow temperature drift, interpolation correction is used before bootstrapping to avoid amplifying variance due to slow thermal changes.

[0080] The effects of the uncertainty matrix are reflected in three aspects. First, by simultaneously modeling time and frequency domain correlations through moving blocks and segmented bootstrapping, the variance estimation becomes closer to the real noise structure. Second, by maintaining the physical structure through directional pairing and environmental stratification, the correlation coefficient can reflect the degree of coupling between interface dynamics and diffusion-limited conditions, rather than calculating spurious correlations. Third, the matrix-level output, along with the health mapping and optimal transmission dual potential, enters the experimental design objective, and can directly apply the D-type criterion or the upper confidence bound criterion to the frequency and amplitude allocation of the next cycle.

[0081] For example, a vehicle obtains a multi-sine window and a pseudo-random binary sequence window within a stratified temperature range of 25°C and a battery state of charge of 60%. The system is set to B=500, with a time domain block length covering 0.5 seconds, and frequency domain sampling in a 4:3:3 ratio for low, mid, and high frequencies. The bootstrapping results show that the correlation coefficient between the diffusion correlation coefficient and the charging transfer resistance is positive and has a high amplitude. The variance of the third harmonic ratio in the charging direction is greater than that in the discharging direction, and the uncertainty of the spectral radius is relatively large in this cycle. Therefore, gating is passed but the weight of directional asymmetry is reduced; the health state interval is expanded according to the above formula; the experimental design concentrates the energy in the 0.2 to 2.0 frequency band in the next cycle and increases the mid-frequency sampling density. In subsequent cycles, the above variance converges, and the health state estimation interval narrows. This example shows that the uncertainty matrix can provide a calculable, traceable error structure consistent with the physical mechanism in remote scenarios, providing a quantitative basis for health assessment and closed-loop scheduling.

[0082] Based on the geometric distance and consistency score gating and hierarchical standardization, a shape-constrained health mapping model is used to obtain health status estimation records and abnormal event sets;

[0083] This invention, based on the same opportunity diagnostic stimulus data window, uses geometric distance and consistency score as gating criteria, and completes standardization within the temperature and battery state of charge stratification. Then, it generates health status estimation records and a set of abnormal events through a shape-constrained health mapping model. The purpose of gating is to eliminate windows with insufficient physical consistency or significant environmental drift, ensuring that the physical invariant vectors entering the mapping model remain comparable and interpretable.

[0084] The gating coefficients aggregate geometric distance, electrothermal consistency score, and directional consistency score in the form of a logistic function. Let the spectral geometric distance be D. ε The electrothermal consistency score is S. ET The directional asymmetry is D. dir The directional consistency score is defined as S. dir =exp(-D dir / b dir ), where b dir The scaling constant is used. The gating coefficient is defined as w = σ(a) D (τ D -D ε )+a ET (S ET -τ ET )+a dir (S dir -τ dir ), where σ(·) is a logical function, a D a ET a dir For the weight, τ D τET τ dir The threshold is used. When w is below the set threshold, the window enters the deweighted channel, which is only used for early warning of abnormalities and does not participate in the principal value calculation of health mapping; when w reaches the threshold, the window enters the mapping channel.

[0085] Stratified normalization is implemented in a two-dimensional stratification based on temperature and battery state of charge. Let the current stratum be l, and the mean of the physical invariant vector within this stratum be μ. l The scale is σ l Standardized transformation is written as z = Λ l (x-μ l ), Λ l =diag(1 / σ) l ), where x is the gated vector of physical invariants and z is the standardized input. The mean and scale are obtained using robust statistics and are periodically updated to ensure consistency across seasons and vehicle fleets.

[0086] The shape-constrained health mapping model maps standardized inputs to health state point estimates and provides an uncertainty interval. Let the health state be H. The model employs a piecewise smooth monotonic spline basis function set to ensure the monotonicity of core invariants: the partial derivatives with respect to high-frequency internal resistance, charge transfer resistance, diffusion correlation coefficient, and spectral geometric distance are non-positive; and the entropy coefficient is smoothed within the piecewise range. The mapping is written as follows: Where β0 is the intercept, s m (·) and s n (·) represents the spline basis functions. For a set of monotonically non-increasing constraints, For a piecewise smooth set, η m ≤0 to ensure monotonicity. The variance of health status is calculated using error propagation. in Let be the Jacobian at the current point, and ∑ be the uncertainty matrix. The output health status estimate record includes: timestamp, stratification number, gating coefficient, health status point estimate, confidence interval, and data source index, used for longitudinal comparison and tracing. The abnormal event set constructs a risk score based on directional and frequency-selective indicators and is classified according to thresholds. Three types of results are identified: lithium plating tendency, abnormal connection contact, and leakage or micro-short circuit. The normalized quantity of the third harmonic ratio of the charging direction is denoted as z. H3,chg The normalized quantity of the aggregation intermodulation intensity in the charging direction is z. IM3,chg The standardized quantity of the high-frequency real part jitter index is z. HF An example of a risk score is shown below. Li =σ(c1z) H3,chg +c2z IM3,chg +c3D dir +c4D ε ), Where c1 to c4 and d1 to d3 are weights. This is the spectral geometric distance calculated in the high-frequency subband. Various risk scores and their uncertainties are entered into anomaly event sets. These event sets record the event type, score, classification, and evidence fields, and are associated with a unique identifier for the corresponding opportunity diagnostic incentive data window.

[0087] The effects of this step are as follows: First, gating combines frequency domain geometric quantities and directional thermal consistency into a single weight, significantly reducing the impact of environmental and institutional differences on health estimation; second, hierarchical standardization makes cross-day and cross-seasonal comparisons of the same vehicle comparable, while ensuring the robustness of group modeling; third, shape-constrained mapping explicitly constrains the physical relationship between health status and core invariants, avoiding regression results that contradict common sense in electrochemistry; and fourth, the set of anomalous events uses directional and frequency band sensitive quantities as evidence sources, enabling early warnings before health status has significantly declined.

[0088] Example: A vehicle uploads data through two windows within a stratified temperature range of 25°C and a battery state of charge of 60%. In the first window, the spectral geometric distance relative to the stratified reference increases, directional asymmetry increases, the electrothermal consistency score approaches its upper limit, and the gating coefficient exceeds the threshold, entering the mapping channel. After standardization, the health mapping yields a health state estimate lower than the vehicle's historical median, with the interval range moderately expanded based on the uncertainty matrix. Anomalies are concentrated, with the lithium plating tendency score increasing due to the increased third harmonic ratio of the charging direction and the intensity of polymerization intermodulation, while the connection contact anomaly score remains low. The second window has a slightly lower gating coefficient but still passes, and the health state estimate is consistent with the first window. Based on this, the experimental design increases the low-to-mid-frequency excitation density in the next cycle to track interface changes while maintaining the high-frequency energy upper limit to control the user experience. The entire process completes a closed loop from gating to mapping to anomaly classification, and the output health state estimate record and anomaly event set are used for remote operation and maintenance decision-making.

[0089] Preferably, the consistency score includes directional consistency score and electro-thermal consistency score. Environmental stratification standardization establishes the mean and standard deviation according to the temperature range and the battery state of charge range, respectively. The shape-constrained health mapping model applies monotonically non-increasing constraints to high-frequency internal resistance, charge transfer resistance, diffusion correlation coefficient and spectral geometric distance.

[0090] This invention, within the same opportunity diagnostic stimulus data window, first uses a consistency score for gating, then performs standardization within the stratification of temperature and battery state of charge, and finally outputs health status estimation records and a set of abnormal events through a shape-constrained health mapping model. This process unifies frequency domain geometric quantities, direction-sensitive quantities, and electrothermal quantities into computable weights and standardized inputs, avoiding interference from environmental and systemic differences on health estimation, and constrains the mapping results with physical monotonic relationships.

[0091] The consistency score consists of a directional consistency score and an electro-thermal consistency score. The directional consistency score uses directional asymmetry as the independent variable, which is derived from the logarithmic difference between the third harmonic ratio and the aggregation intermodulation intensity of the paired windows in the charging and discharging directions. Definition Among them, D dir For directional asymmetry, b dir Let z be a scaling constant. The standardized quantities of the electro-thermal consistency score's comprehensive entropy coefficient relative to the group reference's residual and equivalent impedance temperature sensitivity are denoted by z. α With z Z Then S ET =σ(k α z α +κ Z z Z +κ0), where σ(·) is a logical function, κ α ,κ Z κ0 represents the weights and biases. The two types of scores are aggregated into a gated weight W = σ(λ). dir (S dir -τ dir )+λ ET (S ET -τ ET ), where λ dir ,λ ET For aggregate weights, τ dir ,τ ET Window W is set as the threshold. Windows with W below the threshold enter the deweighted channel, used only for early anomaly alerts; windows with W reaching the threshold enter the mapping channel. Environmental stratification normalization is implemented in a two-dimensional grid of temperature and battery state of charge. The mean μ of the physical invariant vector is established for each stratum l. l With standard deviation σ l Transform the gated physical invariant vector x into z = Λ l (x-μ l ), Λ l =diag(1 / σ) l ), where z is the standardized input. This hierarchical approach eliminates the differences in seasonal temperature variations and state of charge distribution at the source, making windows for different vehicles and different days comparable. The shape-constrained health mapping model maps the standardized input to a health state H and applies monotonically non-increasing constraints to key physical quantities. Let the components involved in the monotonically constrained model be the high-frequency internal resistance R0 and the charge transfer resistance R ct The diffusion correlation coefficient σ and the spectral geometric distance D ε A piecewise smooth additive model is adopted. Among them, f j With g k For a smooth function of a spline basis, the set This includes components that do not have monotonic constraints but require smoothing correction (such as entropy coefficients, Koopman spectral radii, and polymerization intermodulation intensities). Monotonic non-increasing is achieved by the derivative inequality f′. j (t)≤0 In terms of implementation, let Apply the difference non-increase constraint Dθ to the coefficients j ≤0, and solved through quadratic optimization with inequality constraints. This ensures that the health state varies with R0 and R... ct σ and D ε The fact that the health status variance increases without rising further aligns with the physical understanding that "a decline in impedance and diffusion limitation leads to a decrease in health." The health status variance is calculated using first-order error propagation. Where ∑ is the uncertainty matrix, The value is the Jacobian of the current point. The output health status estimate record includes a timestamp, stratification number, gating weight W, health point estimate and confidence interval, and is associated with a window unique identifier.

[0092] The effects of the above design are as follows: First, the directional consistency score suppresses false nonlinearity caused by slight connection jitter or load fluctuation, highlighting interface-related directional differences; Second, the electro-thermal consistency score combines the temperature sensitivity of the entropy coefficient and equivalent impedance for joint testing, which can proactively reduce weights when sensor offset or thermal coupling anomalies occur; Third, hierarchical standardization stabilizes the comparison criteria across days and vehicles, significantly reducing the health estimation bias caused by differences in temperature and state of charge distribution; Fourth, the shape-constrained health mapping replaces "black box fitting" with constraints, avoiding inverse relationships that contradict physical laws in sparse data regions.

[0093] For example, within a stratification of temperature 25°C and battery state of charge 60%, a vehicle uploads data to two windows. The spectral geometric distance of the first window is higher than the reference, with moderate directional asymmetry, and the entropy coefficient is consistent with the temperature sensitivity of the equivalent impedance, yielding S. dir With S ET Both are relatively high, and the gate weight W enters the mapping channel through the threshold. After standardization, R0 and R... ct Slight increase, σ increases, D ε The health status output of the shape-constrained mapping is lower than the historical median of the vehicle, and the confidence interval is given by ∑. In the second window, the entropy coefficient deviation is lowered, the gating weight decreases, and the window enters a reduced-weight channel, but still generates anomaly event sets to indicate nonlinear changes in the interface. The subsequent experimental design allocates the energy of the next cycle to the frequency band from 0.2 to 2.0 to verify the changes in the low-to-mid-frequency arc. The health status trajectory continues to decline in subsequent cycles, accompanied by an increase in the lithium plating tendency fraction, forming a traceable remote diagnostic link.

[0094] Based on health status estimation records, abnormal event sets, and uncertainty matrices, and combined with the Jacobian and optimal transport dual potential of the shape-constrained health mapping model, D-optimal experimental design is used to determine the frequency, amplitude, direction, and window duration, generate the next cycle opportunity diagnosis incentive plan, and update the population health manifold for population reference spectrum measurement and gating threshold.

[0095] This invention takes health status estimation records, abnormal event sets and uncertainty matrices as inputs, combines the Jacobian and optimal transport dual potential of the shape-constrained health mapping model, generates the next cycle opportunity diagnosis incentive plan through D-optimal experimental design, and simultaneously updates the population health manifold for population reference spectrum measurement and gating threshold.

[0096] The health status estimation record provides the health status point estimate and confidence interval within the temperature and battery state of charge stratification of the previous cycle. The anomalous event set provides risk evidence of directional and band selectivity. The uncertainty matrix characterizes the variance and correlation of the physical invariant vector at the current point. The Jacobian of the shape-constrained health mapping model at this point is used to measure the local sensitivity of the health status to each physical invariant. The distribution of the optimal transmission dual potential on the frequency grid characterizes the gradient of the spectral geometric distance with respect to the quality allocation of each frequency band. Together, these determine the "information orientation" of the experimental design.

[0097] Let the vector of physical invariants be... The healthy state is H = g(x), and the Jacobian is... Let the candidate incentive set be Each candidate u k It consists of a set of frequency points, amplitude, direction, and window duration. For candidate u... k Linearize the observation model at the current operating point and construct a set of sensitivity vectors from x to observable features: frequency domain feature sensitivity. (z i (Equivalent impedance at the i-th frequency point or its derivative), directional fingerprint sensitivity (ξ p (This refers to the third harmonic ratio, aggregation intermodulation intensity, or directional asymmetry). Utilizing the optimal transport dual potential α... * The amplitude of the frequency grid is used as the frequency band weight to form the task-related Fisher information matrix. in and Let be the observation variances of the i-th frequency point and the p-th directional fingerprint, respectively, estimated from the uncertainty matrix and historical residuals, where η is the directional channel weight. Incorporating the prior uncertainty into the information matrix, we obtain... ∑ -1 +F(u k ), where ∑ is the uncertainty matrix. Taking health status as the task quantity, the D-optimal criterion is adopted. λ>0 represents a numerically stable ridge term. This criterion maximizes the expected information gain of the health status in the next cycle, automatically allocating energy to the frequency band and direction that best distinguishes health changes, while suppressing over-investment in high-variance, low-signal-to-noise-ratio channels.

[0098] Candidate generation is constrained by safety and user experience: the amplitude upper limit is scheduled according to temperature and battery state of charge; directions are paired to support directional consistency discrimination; window duration and the number of frequency points are limited to control energy injection and riding disturbances. The solution employs the Fedorov exchange method on discrete candidates: a set of feasible candidates is initialized, and iterative replacements monotonically increase the aforementioned objective until the gain falls below a threshold or reaches the iteration upper limit. The output opportunity diagnostic stimulus plan includes frequency point, amplitude, direction, and window duration, along with the following basis fields: the band weight comes from the dual potential, the direction weight comes from the risk scores in the anomalous event set, and the duration comes from a trade-off between the objective information gain and energy budget.

[0099] After execution, the system updates the population health manifold within each layer. The population health manifold uses a hierarchical Bayesian approach to perform hierarchical regression on the health state trajectory and the physical invariant vector: the individual layer updates the posterior distribution of individual health trajectories, and the population layer updates the stratified mean and covariance, used to generate new population reference spectrum measures and gating thresholds. The population reference spectrum measures are updated within each layer using exponential weighting in the logarithmic frequency domain and Dirichlet smoothing; the gating thresholds are updated using stratified posterior quantiles to ensure stable throughput and alarm sensitivity under environmental changes and fleet structure evolution.

[0100] The effects of this step are reflected in two aspects: First, the dual potential of experimental design, health mapping, and spectral geometry forms a closed loop, and the plan no longer distributes frequency points evenly, but focuses on the information frequency bands and directions that contribute to health judgment; Second, ∑ -1 The introduction of [a certain method] ensures priority access to information in dimensions with high uncertainty, thereby accelerating interval convergence; third, the continuous updating of the population health manifold enables the population reference spectrum measure and gating threshold to adapt to seasonal and fleet operation characteristics, avoiding long-term drift.

[0101] For example, within a stratum of 25°C temperature and 60% battery state of charge, a vehicle's health status estimation record shows a slow decline over the past two weeks. The abnormal event set indicates a higher lithium plating tendency score in the charging direction, and the uncertainty matrix shows that the variance of the charging transfer resistance and diffusion correlation coefficient dominates the health variance. A positive peak appears in the 0.2–2.0 frequency band. After Fedorov swapping, an opportunity diagnostic stimulus plan is obtained: frequency points are concentrated at 0.3, 0.6, 1.2, and 1.8, with the charging direction as the primary direction and the discharging direction as secondary. The amplitude is set according to energy budget and comfort constraints, and the window duration is 6 seconds. After execution, the multi-domain response packet of the new window confirms the mid-frequency arc amplification trend, and the health status range narrows. A stratified Bayesian update simultaneously adjusts the vehicle's health trajectory and the group stratum parameters. The mass distribution of the group reference spectrum measure is increased in the 0.5–1.5 range, and the gating threshold is tightened accordingly. Subsequent vehicles within the same stratum will receive higher experimental design priority in this frequency band, forming a remote closed loop of "identification-focusing-re-identification".

[0102] Preferably, the Fisher information matrix of the D-optimal experimental design is synthesized from the linear response sensitivity of the equivalent impedance parameter, the nonlinear sensitivity of harmonics and intermodulation fingerprints, and the observability of the Koopman mode, and combined with the optimal transmission dual potential to determine the frequency band weights to generate an excitation parameter set containing frequency, amplitude, direction, and window duration.

[0103] This invention couples experimental design with health estimation and spectral geometry information. It selects frequency points, amplitudes, directions, and window durations on a discrete candidate set using the D-optimal criterion, aiming to maximize the gain on health status in the next cycle under constraints. The core idea is to aggregate the sensitivity of three types of observable channels using a Fisher information matrix. These channels include the linear response sensitivity of the equivalent impedance parameter, the nonlinear sensitivity of harmonics and intermodulation fingerprints, and the observability of the Koopman mode. The optimal transmission dual potential is used to assign band weights, concentrating energy input in frequency bands with higher information density.

[0104] Let the vector of physical invariants be... (Including high-frequency internal resistance, charge transfer resistance, double-layer capacitance, diffusion correlation coefficient, spectral geometric distance, entropy coefficient, directional asymmetry, Koopman spectral radius and directional difference norm, etc., in a fixed order), the health state is mapped as H = g(x), and its Jacobian at the current point is... For a candidate excitation u (consisting of a set of frequencies, amplitude, direction, and window duration), a linearized observation model is used at the operating point of the opportunity diagnostic excitation data window, defining three types of sensitivity: frequency ω. i The gradient of the equivalent impedance derivative at x The gradient of the p-th harmonic or intermodulation pointer with respect to x No. Gradients of the Koopman modes with respect to x The dual potential obtained from optimal transmission is α * Its components on the frequency grid Used to construct frequency band weights. Let the frequency domain observation variance be... fingerprint variance is Modal observability is (Obtained by the square of the inner product of the output vector and the right eigenvector), the candidate Fisher information matrix is ​​then defined as follows: Where Ω(u) is the set of candidate frequency points, Let L(u) be the set of harmonics and intermodulations generated by this candidate, and L(u) be the set of modes that can be effectively excited and observed under this candidate. η>0 and ζ>0 are the channel weights. Incorporating the existing uncertainties in a priori form, we obtain... ∑ represents the uncertainty matrix. The D-optimal criterion uses health tasks as the quantification object, and the objective function is... λ>0 indicates a numerically stable term. Multiple candidate combinations. The choice is made by solving on a discrete library. It also satisfies constraints such as energy budget, upper limit of amplitude, direction pairing, and upper limit of window duration. The solution uses Fedorov exchange: a set of feasible candidates is initialized, and the inferior candidates in the current set are replaced iteratively with candidates that bring gains to the objective function until the gain is less than a threshold or the iteration upper limit is reached.

[0105] Frequency point from The peak value is prioritized for inclusion in the candidate library, while also considering the coverage of the equivalent impedance mid-frequency arc, low-frequency diffusion section, and high-frequency real part. The amplitude is determined by... and The function is adjusted downwards or upwards, with the goal of increasing the projection of the main diagonal element of F(u) onto the healthy gradient direction without altering the driving experience. Direction selection is based on the classification results of the anomalous event set and the degree of directional asymmetry; the charging direction is prioritized for testing interface nonlinearity hypotheses, while the discharging direction is used for falsification. The window duration is jointly determined by the frequency resolution requirements and energy budget for a given frequency point.

[0106] The effects of this step are as follows: band weighting guides energy distribution to the frequency band that contributes most to the spectral geometric shift; three-channel sensitivity synthesis ensures simultaneous identification of interface dynamics, diffusion, and connectivity changes; and the D-optimal criterion adjusts the health state variance along the J-axis. g The direction converges fastest, thus obtaining a narrower healthy interval within the same period and improving the confidence of abnormal classification.

[0107] For example, within a temperature stratification of 25°C and a battery state of charge of 60%, the estimated health status of a vehicle in the previous cycle decreased. The uncertainty matrix shows that the variance of the charging transfer resistance and diffusion correlation coefficient dominates, and the optimal transfer dual potential shows a positive peak in the frequency band from 0.3 to 1.5. A candidate library is constructed containing frequencies of 0.3, 0.6, 1.2, and 1.8, paired with charging and discharging directions, with amplitudes constrained by the energy budget and a window duration of 6 seconds. The F(u) and objective function gain of each candidate are calculated, and Fedorov exchange is used to obtain... It is composed of three points: 0.3, 0.6, and 1.2, and is dominated by the charging direction. After execution, the new window... The determinant of the matrix increased significantly compared to the previous period, the healthy state range narrowed, and the concentration of abnormal events in lithium plating tendency was verified. Subsequently, the population health manifold was updated with hierarchical Bayesian methods, the mass distribution of the population reference spectrum measure was increased from 0.5 to 1.0, and the gating threshold was tightened simultaneously, forming a traceable experimental design-estimation-update closed loop.

[0108] Preferably, the population health manifold is updated using hierarchical Bayesian methods. The update objects include the population reference spectrum measure and the gating threshold. The update is based on the historical sequence of the opportunity diagnosis stimulus data window, health status estimation records, and multi-domain response packets.

[0109] This invention defines the population health manifold as a joint family of priors and posteriors for health-related statistics, stratified by temperature and battery state of charge. The update targets include two types of objects: population reference spectrum measures and gating thresholds. The updates are based on historical sequences of opportunity diagnostic stimulus data windows, health state estimation records, and multi-domain response packets. Through hierarchical Bayesian inference, population references and individual observations converge within the same statistical framework, maintaining population stability while adapting to vehicle fleet and seasonal operational characteristics.

[0110] Within each layer l, the equivalent impedance magnitude is normalized on a preset logarithmic frequency grid to obtain the spectral measure vector. in The superscript n identifies the window. The group reference spectrum measure uses the Dirichlet prior, and the parameter vector is denoted as... For the t-th update cycle, a forgetting coefficient ρ∈(0,1) is introduced to control the historical weights, and a sample weight w is introduced. n The values ​​∈[0,1] are obtained by mapping the gate weights to the diagonal elements of the uncertainty matrix. The Dirichlet posterior parameters are updated as follows: s n =w m N0, where The set of windows falling into stratum l in this period, where N0>0 is the scale that maps weights to equivalent counts. The population reference spectrum measure is the posterior mean. For i = 1, ..., N, the update absorbs the spectral shape information of the new window in a hierarchical manner, and for windows with high noise, it uses w n Automatic weight reduction. Dirichlet structure guarantees q. l A strict probability distribution is used across the entire frequency band, facilitating alignment with the optimal transmission geometry and dual potential. The gating threshold establishes hierarchical priors for spectral geometry, directional consistency score, and electro-thermal consistency score, respectively. Taking spectral geometry as an example, assuming the mean and variance of this layer are unknown, a normal-inverse gamma prior is used, with parameters... Let the weighted sample mean and sum of squares for this period be denoted as . Where m n Let be the spectral geometric distance of the nth window. The posterior update is... Gating thresholds are taken from posterior quantiles in Let v be the quantile function of the student distribution with degrees of freedom v, and π∈(0,1) be the target false alarm control level. The directional consistency score and the electro-thermal consistency score each maintain a set of (μ,κ,a,b) within the same framework and output the corresponding thresholds. Thus, the gating threshold and the population reference spectrum measure are updated over time within the same layer.

[0111] The update process forms a closed loop with health estimation, optimal transport duality, and experimental design. The confidence interval of the health state estimation record and the uncertainty of the multi-domain response packet constitute w. n The source of this information is used to incorporate "observation confidence" into the population health manifold using Bayesian natural weights; the band shift of the optimal transmission dual potential indicator is in q. l The cumulative effect in the posterior timeframes leads to adjustments in the quality allocation of the group reference spectrum measure in information-dense frequency bands; the experimental design is based on a new round of q l The threshold generation opportunity diagnostic incentive plan will be used, and the results will be fed back into the above update equation in the next cycle.

[0112] The design's effectiveness is manifested in three aspects. First, the Dirichlet-polynomial structure unifies the group prior of the spectral shape with individual observations within the same probability space, ensuring stable and traceable updates. Second, the normal-inverse gamma hierarchy provides an explicit characterization of the gating threshold's uncertainty; the threshold adaptively tightens or loosens with the amount of data within each layer, maintaining a balance between pass rate and alarm sensitivity. Third, the forgetting coefficient and sample weights jointly control the trade-off between "historical memory" and "fresh information," suppressing short-term noise while tracking the actual migration of seasonality and vehicle structure.

[0113] For example, within a stratified range of 25°C and 60% battery state of charge, 28 opportunity diagnostic excitation data windows were collected over 14 consecutive days. After gating and standardization, paired charge / discharge direction samples were constructed, and spectral geometric distance and consistency scores were calculated, with weights w.n It is derived by mapping the gating weights to the width of the health state interval. After the update, η l Significant increments are observed in the 0.5–1.5 frequency band, with an upward adjustment in the mass distribution of the group reference spectral measure in this band; the threshold τ of the spectral geometric distance... l As the sample size increases and variance converges, the threshold decreases, making the pass criteria for this stratum more stringent. The subsequent week's experimental design prioritized multi-sinusoidal excitation at frequencies of 0.5, 0.8, and 1.2, further narrowing the range for health status estimation. The concentration of abnormal events showed consistency between the lithium plating tendency score and the directional asymmetry. Thus, the two classes of subjects in the population health manifold, along with individual observations, formed a stable "update-design-re-observation-re-update" closed loop, providing a calculable, verifiable, and traceable population baseline for remote health assessment and anomaly identification.

[0114] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for remote state of health analysis and anomaly identification of an electric bicycle battery, characterized in that, Comprising the following steps: Applying small-signal active excitation under the satisfaction of admission conditions, synchronously collecting voltage, current, temperature and preprocessing to form an opportunity diagnostic excitation data window using multi-sine excitation or pseudo-random binary sequence excitation; wherein the opportunity diagnostic excitation data window is a complete packaging unit of data and metadata corresponding to one small-signal active excitation, the data part includes preprocessed voltage sequence, current sequence and temperature sequence, and the metadata part includes frequency set, phase set, amplitude set, excitation direction, start and end time stamp, battery state of charge statistics and temperature statistics, execution result and quality label; Based on the opportunity diagnostic excitation data window, time-frequency coupling modeling is carried out, including equivalent impedance, harmonic and intermodulation fingerprint extraction, Koopman operator modeling and entropy coefficient difference, wherein the harmonic and intermodulation fingerprint extraction includes: calculating the third harmonic ratio, intermodulation intensity and direction asymmetry in the charging direction and the discharging direction respectively, and writing the third harmonic ratio, intermodulation intensity and direction asymmetry into the multi-domain response package and into the physical invariant vector; Wherein, the entropy coefficient difference estimates the entropy coefficient of the open circuit voltage temperature coefficient by the difference of the temperature change rate under positive and negative small current excitation, and generates the electro-thermal consistency score accordingly; Spectral measures are constructed and the geometric distance of the optimal transport calculation and the group reference spectral measure is calculated to generate the multi-domain response package, the physical invariant vector and the uncertainty matrix; Wherein, the physical invariant vector is a subset selected from the intermediate quantities packaged in the multi-domain response package, which is used as the input of the shape-constrained health mapping model and is stable across operating conditions; Wherein, the uncertainty matrix estimates the variance and correlation of the equivalent impedance parameters, the harmonic and intermodulation fingerprints, the Koopman operator modeling quantities and the entropy coefficient difference quantities by self-booting resampling of the time window segmentation and the frequency domain components, and is assembled in the order of the physical invariant vector; According to the geometric distance and the consistency score, the health state estimation record and the abnormal event set are obtained by using the shape-constrained health mapping model; wherein the shape-constrained health mapping model implements monotonic non-increasing constraints on high-frequency internal resistance, charging transfer resistance, diffusion correlation coefficient and spectral geometric distance; Based on the health state estimation record, the abnormal event set and the uncertainty matrix, the Jacobian of the shape-constrained health mapping model and the optimal transport dual potential are combined, wherein the optimal transport dual potential is the gradient representation of the geometric distance to the spectral measure, and is saved in the multi-domain response package for subsequent test design; the D-optimal test design is used to determine the frequency, amplitude, direction and window length to generate the next cycle opportunity diagnostic excitation plan and update the group health manifold for group reference spectral measure and gating threshold; Wherein, the group health manifold is updated by hierarchical Bayesian method, and the update objects include group reference spectral measure and gating threshold, and the update basis is the historical sequence of opportunity diagnostic excitation data window, health state estimation record and multi-domain response package.

2. The method of claim 1, wherein, The estimation and parameter fitting of equivalent impedance output include high-frequency internal resistance, charging transfer resistance, double-layer capacitance and diffusion correlation coefficient, and the equivalent impedance spectrum is obtained by multi-window cross-spectrum estimation.

3. The method of claim 1, wherein, The constructed spectral measure includes normalizing the amplitude of the equivalent impedance spectrum to form a spectral measure, and calculating the geometric distance with the population reference spectral measure using entropy-regularized optimal transport.

4. The method of claim 1, wherein, The consistency score includes the directional consistency score and the electro-thermal consistency score, and the environmental stratification standardization establishes the mean value and the standard deviation according to the temperature interval and the battery state of charge interval respectively.

5. The method of claim 1, wherein, The Fisher information matrix of the D-optimal experimental design is composed of the linear response sensitivity of the equivalent impedance parameters, the nonlinear sensitivity of the harmonic and intermodulation fingerprints, and the Koopman modal observability, and the frequency band weight is determined by the optimal transport dual potential to generate the excitation parameter set containing the frequency point, the amplitude, the direction and the window length.

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