Battery aging trajectory adaptive extrapolation method fusing physical timing prior

Abstract

The application discloses a battery aging trajectory adaptive extrapolation method fusing physical time sequence priori, and comprises the following steps: collecting full-life cycle constant-current charging data of a battery, extracting an incremental capacity curve and constructing a feature peak evolution to form a multi-dimensional physical time sequence priori; introducing a state space backbone network to realize trend perception by initializing an implicit state with the priori; constructing an attention abnormality detection module to distinguish real relaxation from noise; releasing monotonic constraints through a differentiable relaxation layer for relaxation events, and correcting data through Kalman filtering for noise; constructing a dynamic trade-off loss function to adaptively adjust the strength of physical constraints, and iteratively training the model based on the corrected data to realize stable extrapolation prediction. The application effectively solves the problems in the prior art that real physical relaxation and measurement noise cannot be distinguished, and that the rigidity of physical constraints leads to prediction deviation.

Description

Technical Field

[0001] This invention relates to the field of battery testing technology, and in particular to an adaptive extrapolation method for battery aging trajectory that integrates physical time priors. Background Technology

[0002] Lithium-ion batteries, due to their high energy density and long cycle life, have become the core carrier for electric vehicles and large-scale energy storage systems. Accurate assessment of battery aging status and prediction of remaining life are crucial for ensuring system safety and reducing operation and maintenance costs. Among these methods, data-driven battery aging trajectory extrapolation has received widespread attention in recent years because it does not require the construction of complex electrochemical models.

[0003] However, purely data-driven methods have inherent limitations when extrapolating long sequences: errors accumulate exponentially as the prediction step size increases, and the model's ability to generalize to conditions outside the training data distribution is insufficient. To overcome this limitation, researchers have proposed incorporating prior physical knowledge into deep learning models. By imposing physical constraints (such as the monotonicity of capacity decay, the Arrhenius temperature acceleration factor, and impedance growth boundaries), the model is guided to learn solutions that conform to physical laws, thereby improving the rationality of predictions and the stability of extrapolation.

[0004] Existing physical constraint methods are mainly divided into two categories: one is based on hard constraint model structure design, such as restricting the output layer weights to be positive to ensure monotonicity; the other is based on soft constraint loss function penalty terms, which add penalties for deviations from physical laws to the training objective. These methods improve the physical consistency of predictions to a certain extent, and typical examples include the LiRUL framework and the LSTM-PINN hybrid model.

[0005] However, in practical applications, existing physical constraint methods face two major technical bottlenecks:

[0006] First, the constraints are overly simplistic. Current methods primarily employ monotonic penalties or single empirical formulas (such as the square root time model) as physical priors, essentially reducing the complex aging process to a single mathematical expression. However, battery aging is a nonlinear dynamic process involving multiple coupled mechanisms, including the interaction of various aging modes such as solid electrolyte interphase (SEI) film growth, active material loss, and lithium deposition. For example, the square root time model can only describe the early aging stage dominated by the SEI film, lacking the ability to characterize later nonlinear transitions such as accelerated active material loss and lithium deposition triggering. Research using the LiRUL framework clearly indicates that while constraint-based methods improve rationality, they are often overly simplistic for nonlinear, multi-factor aging dynamics.

[0007] Second, there is a conflict between physical priors and real-world data. Batteries exhibit capacity regeneration during actual operation—a brief increase in capacity can be observed after prolonged periods of inactivity or low-rate charging and discharging. This is a genuine relaxation effect caused by physical mechanisms such as lithium-ion concentration redistribution and polarization mitigation. However, strict monotonicity constraints cause models to forcibly ignore these physically possible capacity rebounds, treating them as noise or outliers and suppressing them. Studies using LSTM-PINN have found that the model's maximum prediction error at capacity regeneration events can reach 8.38% SOH. Analysis indicates that the root cause is the model's application of very strict monotonicity constraints to maintain physical plausibility. When the true ground value violates the physical degradation law, the physically constrained model appropriately rejects these non-physical signals.

[0008] The essence of the above problem lies in the fact that existing physical priors adopt rigid constraints, lacking the ability to distinguish between true anomalies (measurement noise, sensor failure) and false anomalies (real physical relaxation effects) in the data. When the real phenomenon conflicts with the preset rules, the model is caught in a dilemma—if it strictly follows the physical constraints, it will lose real information and increase local prediction errors; if it relaxes the physical constraints, it may be misled by noise and lose the stability of long-sequence extrapolation.

[0009] In summary, how to construct a multimodal physical time series prior that can distinguish between real physical relaxation effects and measurement noise during the extrapolation of battery aging trajectories, and how to achieve adaptive dynamic adjustment of the rigid physical constraint strength according to data characteristics, so as to ensure the physical consistency of long-sequence extrapolation while avoiding the false suppression of real physical phenomena such as capacity regeneration and reducing local prediction errors, has become an urgent problem to be solved. Summary of the Invention

[0010] To address the issue that existing rigid physical constraints cannot distinguish between real physical relaxation and noise anomalies, leading to prediction bias at capacity regeneration events, an extrapolation method that can adaptively distinguish between real and false anomalies and dynamically balance physical consistency and data fidelity needs to be designed.

[0011] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0012] This invention discloses an adaptive extrapolation method for battery aging trajectory based on physical time priors, comprising the following steps:

[0013] Step 1: Collect constant current charging segment data of the battery cell under test throughout its entire life cycle, extract the incremental capacity curve from the constant current charging segment data, and track the peak position shift trajectory and peak area decay trajectory of the characteristic peak in the incremental capacity curve, thereby constructing a multi-dimensional physical time sequence prior template characterizing the battery aging mechanism evolution process.

[0014] Step 2: Introduce a state-space backbone network with temporal inductive bias capability, and use the multi-dimensional physical temporal prior template as the implicit state initialization parameter of the state-space backbone network, so that the state-space backbone network has physical cognition of the battery aging trajectory evolution trend in the initial training stage.

[0015] Step 3: Construct a physical anomaly detection module based on an attention mechanism. The physical anomaly detection module calculates the local deviation between the current input data sequence and the multi-dimensional physical time-series prior template in real time, and dynamically determines whether the current input data sequence belongs to a real physical relaxation event or a measurement noise anomaly event based on the magnitude and duration of the local deviation.

[0016] Step 4: When the physical anomaly detection module determines that the current input data sequence belongs to a real physical relaxation event, a differentiable relaxation effect containment layer is constructed. The differentiable relaxation effect containment layer temporarily releases the monotonicity constraint weights in the state space backbone network, so that the state space backbone network can fit the capacity recovery characteristics corresponding to the real physical relaxation event.

[0017] Step 5: When the physical anomaly detection module determines that the current input data sequence belongs to a measurement noise anomaly event, the noise suppression unit based on Kalman filtering is activated. The noise suppression unit based on Kalman filtering corrects the abnormal data points corresponding to the measurement noise anomaly event in real time according to the degradation trend reference value provided by the multi-dimensional physical time series prior template.

[0018] Step 6: Construct a dynamic trade-off loss function for physical consistency. The dynamic trade-off loss function for physical consistency includes a data fidelity term and a physical prior deviation penalty term. Based on the discrimination result output by the physical anomaly detection module, the weight coefficient of the physical prior deviation penalty term is adaptively adjusted so that the weight of the physical prior deviation penalty term is automatically reduced during real physical relaxation events to accommodate real physical phenomena, and automatically increased during measurement noise anomaly events to strengthen physical constraints.

[0019] Step 7: Using the training data that has been jointly corrected by the differentiable relaxation effect containment layer and the noise suppression unit based on Kalman filtering, iteratively train the state space backbone network loaded with the multi-dimensional physical time-series prior template until the physical consistency dynamic trade-off loss function converges, and output a battery aging trajectory prediction model that can adaptively distinguish between real physical relaxation events and measurement noise anomaly events and realize long sequence extrapolation.

[0020] Furthermore, step 1 includes the following sub-steps:

[0021] Step 1-1: Charge the battery cell under test with a constant current at a preset constant current rate. Collect charging voltage and charging capacity data in real time through a high-precision data acquisition device. The sampling frequency is not less than 1Hz until the charging voltage reaches the preset cutoff voltage, thereby obtaining constant current charging segment data.

[0022] Steps 1-2: Perform numerical differentiation calculation on the capacity-voltage relationship in the constant current charging segment data to obtain the initial incremental capacity curve, and use the Savitzky-Golay convolution smoothing algorithm to denoise the initial incremental capacity curve to eliminate the interference of measurement noise on subsequent feature peak identification, and obtain the smoothed incremental capacity curve.

[0023] Steps 1-3: Identify multiple characteristic peaks corresponding to different aging mechanisms on the smoothed incremental capacity curve using the local maximum search algorithm, and record the peak position voltage value and peak area integral value of each characteristic peak in each charge-discharge cycle, thereby forming the peak position offset trajectory and peak area decay trajectory.

[0024] Steps 1-4: Time-scale normalization is performed on the peak position offset trajectory and peak area decay trajectory to eliminate the influence of cycle life differences between different battery cells. The normalized trajectories are then statistically averaged to construct a multi-dimensional physical time-series prior template that reflects the common evolution law of battery aging mechanism.

[0025] Furthermore, step 2 includes the following sub-steps:

[0026] Step 2-1: Construct a temporal backbone network based on a state-space model. The temporal backbone network based on a state-space model includes learnable implicit state vectors and state transition matrices. Implicit state vectors are used to carry instantaneous state information of the battery aging process, and state transition matrices are used to control the evolution of implicit state vectors between different time steps.

[0027] Step 2-2: Vectorize the multi-dimensional physical time series prior template constructed in Step 1-4, and map the statistical mean of the peak position offset trajectory and the statistical mean of the peak area decay trajectory to the initial value of the implicit state vector. At the same time, map the statistical variance of the peak position offset trajectory and the statistical variance of the peak area decay trajectory to the initial confidence of the implicit state vector.

[0028] Steps 2-3: Use the implicit state vector carrying multi-dimensional physical time-series prior template information as the initial implicit state of the time-series backbone network based on the state-space model, so that the time-series backbone network based on the state-space model can grasp the general law of the evolution of feature peaks during battery aging before it comes into contact with any training data.

[0029] Steps 2-4: Set the state transition matrix as a diagonal matrix with temporal inductive bias capability. The diagonal elements of the diagonal matrix are initialized with forgetting factors calculated based on the average rate of change of peak position offset and peak area decay between adjacent cycles in the multi-dimensional physical temporal prior template, so that the implicit state vector can evolve according to the aging rate revealed by the physical prior as the time step moves forward.

[0030] Furthermore, step 3 includes the following sub-steps:

[0031] Step 3-1: At each time step of the state space backbone network, calculate the difference between the battery capacity observation value input at the current time step and the capacity prediction value generated by the state space backbone network based on the multi-dimensional physical time series prior template at the time step to obtain the instantaneous residual at the current time step, and combine the instantaneous residuals of multiple consecutive time steps into a sliding window residual sequence.

[0032] Step 3-2: Construct a local deviation calculation unit based on multi-head self-attention mechanism. Input the sliding window residual sequence into the local deviation calculation unit based on multi-head self-attention mechanism. Calculate the Mahalanobis distance between each residual element in the sliding window residual sequence and the template residual statistical distribution at the corresponding time position in the multi-dimensional physical time-series prior template through the local deviation calculation unit based on multi-head self-attention mechanism. Use the Mahalanobis distance as the quantized value of local deviation.

[0033] Step 3-3: Set the duration counter and deviation accumulator. When the local deviation exceeds the preset anomaly judgment threshold, the duration counter is triggered to start counting, and the deviation accumulator is triggered to start accumulating the value of the local deviation that exceeds the anomaly judgment threshold.

[0034] Steps 3-4: When the count value of the duration counter reaches the preset minimum duration threshold of the relaxation event and the accumulated value of the deviation accumulator exceeds the preset energy threshold of the relaxation event, the physical anomaly detection module determines that the data interval corresponding to the currently input sliding window residual sequence belongs to the real physical relaxation event and outputs the first control signal.

[0035] Steps 3-5: When the count value of the duration counter is lower than the minimum duration threshold of the relaxation event or the accumulated value of the deviation accumulator is lower than the energy threshold of the relaxation event, the physical anomaly detection module determines that the data interval corresponding to the currently input sliding window residual sequence belongs to the measurement noise anomaly event, and outputs the second control signal, while clearing the duration counter and the deviation accumulator to zero.

[0036] Furthermore, step 4 includes the following sub-steps:

[0037] Step 4-1: Embed a differentiable relaxation effect containment layer in the loss function calculation path of the state space backbone network. The differentiable relaxation effect containment layer receives the first control signal output by the physical anomaly detection module as the trigger input and has built-in learnable relaxation gating parameters.

[0038] Step 4-2: When the differentiable relaxation effect containment layer receives the first control signal, the differentiable relaxation effect containment layer calculates the monotonic constraint release coefficient proportional to the local deviation based on the current value of the learnable relaxation gating parameter, and applies the monotonic constraint release coefficient to the monotonic penalty term in the loss function of the state space backbone network, so that the weight of the monotonic penalty term is multiplied by the monotonic constraint release coefficient to obtain the decayed monotonic penalty term.

[0039] Step 4-3: The differentiable relaxation effect containment layer calculates the difference between the implicit state vector of the state space backbone network at the current time step and the template state vector at the corresponding time position in the multi-dimensional physical time-series prior template to obtain the state offset vector. The state offset vector is used as an additional input to the differentiable relaxation effect containment layer, so that the state space backbone network can use the state offset vector as a reference when fitting the capacity recovery characteristics corresponding to the real physical relaxation event, and avoids excessive deviation from the long-term degradation trend revealed by the multi-dimensional physical time-series prior template.

[0040] Step 4-4: When the real physical relaxation event ends and the physical anomaly detection module stops outputting the first control signal, the differentiable relaxation effect containment layer gradually restores the monotonic constraint release coefficient to the initial value of 1.0 according to the preset decay rate of the learnable relaxation gating parameters, so that the monotonic penalty term of the state space backbone network is restored to the original constraint strength, thereby maintaining the overall physical consistency in the long sequence extrapolation process while containing the real physical relaxation event.

[0041] Furthermore, step 5 includes the following sub-steps:

[0042] Step 5-1: Deploy a noise suppression unit based on Kalman filtering in parallel at the input of the state space backbone network in advance. The noise suppression unit based on Kalman filtering maintains the state estimation vector and the error covariance matrix. The state estimation vector is used to store the optimal capacity estimate after filtering at the current time step, and the error covariance matrix is ​​used to characterize the uncertainty of the state estimation vector.

[0043] Step 5-2: When the noise suppression unit based on Kalman filtering receives the second control signal output by the physical anomaly detection module, the noise suppression unit based on Kalman filtering immediately reads the template capacity reference value corresponding to the current time step from the multi-dimensional physical time series prior template, and uses the template capacity reference value as the prediction benchmark value of the external observation model in the Kalman filtering framework.

[0044] Step 5-3: The noise suppression unit based on Kalman filtering calculates the optimal capacity estimate for the current time step based on the state estimation vector and error covariance matrix, combined with the external observation information provided by the template capacity reference value. The size of the Kalman gain matrix is ​​automatically adjusted according to the local deviation of the measurement noise anomaly event, so that the greater the local deviation, the higher the weight of the template capacity reference value in the fusion.

[0045] Step 5-4: The Kalman filter-based noise suppression unit uses the calculated optimal capacity estimate as the corrected capacity data for the current time step, replaces the original abnormal data points corresponding to the measurement noise abnormal events, and simultaneously outputs the optimal capacity estimate to the input of the state space backbone network and feeds it back to the state estimation vector update module inside the Kalman filter-based noise suppression unit for prediction update in the next time step.

[0046] Step 5-5: When the measurement noise anomaly event ends and the physical anomaly detection module stops outputting the second control signal, the noise suppression unit based on Kalman filtering automatically switches to pass-through mode, directly transmitting the uncorrected original input data to the state space backbone network, while maintaining continuous updates to the state estimation vector and error covariance matrix, so as to be able to respond quickly when the next measurement noise anomaly event occurs.

[0047] Furthermore, step 6 includes the following sub-steps:

[0048] Step 6-1: Construct a physical consistency dynamic trade-off loss function that includes a data fidelity term and a physical prior deviation penalty term. The data fidelity term uses the mean square error form to calculate the deviation between the capacity prediction value output by the state space backbone network and the actual capacity observation value. The physical prior deviation penalty term uses the KL divergence form to calculate the distribution difference between the implicit state vector of the state space backbone network and the template state vector at the corresponding time position in the multi-dimensional physical time-series prior template.

[0049] Step 6-2: Set adaptively adjustable weight coefficients in the physical consistency dynamic tradeoff loss function. Weighting coefficient Used to control the proportion of the physical prior deviation penalty term in the total loss. The value range of is limited to between 0 and 1, when A value of 1 indicates that the physical prior is completely followed; when... A value of 0 indicates that physical priors are completely ignored;

[0050] Step 6-3: Establish weighting coefficients The mapping relationship between the results and the judgment results output by the physical anomaly detection module is established. When the physical anomaly detection module outputs the first control signal indicating that the current data interval belongs to a real physical relaxation event, the weighting coefficients are adjusted. Set to the preset low weight value This reduces the contribution of the physical prior deviation penalty term to accommodate the capacity recovery feature corresponding to real physical relaxation events.

[0051] Step 6-4: When the physical anomaly detection module outputs a second control signal indicating that the current data interval belongs to a measurement noise anomaly event, the weighting coefficient is adjusted. Set to the preset high weight value This increases the contribution of the physical prior deviation penalty term to strengthen the constraint effect of the multi-dimensional physical time-series prior template on anomalous data points, forcing the implicit state vector of the state-space backbone network to move closer to the template state vector.

[0052] Step 6-5: During the normal aging phase when the physical anomaly detection module does not output any control signals, adjust the weighting coefficients. Set as an intermediate weight value that is dynamically adjusted based on the current number of aging cycles. intermediate weight value Preferring higher weight values ​​in the early stages of aging To strengthen physical prior guidance, the model is gradually reduced in the later stages of aging to increase the degree of freedom of the model to fit data features;

[0053] Step 6-6: The weighted coefficients are then... The physical prior deviation penalty term, which is dynamically weighted, is added to the data fidelity term to obtain the final loss value at the current time step. The final loss value is then backpropagated to each trainable parameter of the state space backbone network to achieve a dynamic trade-off between physical consistency and data fidelity.

[0054] The technological advancements achieved by this invention compared to existing technologies are as follows:

[0055] This invention extracts the peak position shift trajectory and peak area decay trajectory of characteristic peaks from the incremental capacity curve, constructing a multi-dimensional physical time-series prior template with a clear electrochemical mechanism orientation. This allows the physical prior to no longer rely on a single empirical formula, but rather to characterize the battery aging process in a multi-mechanism coupling manner, significantly improving the ability to express nonlinear, multi-stage aging behavior, thus overcoming the problem of overly simplified physical constraints in existing methods. Furthermore, by embedding the multi-dimensional physical time-series prior template into the implicit state initialization and state transition process of the state-space backbone network, the model possesses the ability to perceive evolutionary trends that conform to physical laws from the initial training stage. This avoids the error accumulation and trajectory drift problems caused by the lack of prior constraints in long-sequence extrapolation of traditional data-driven methods, thereby improving the overall extrapolation stability and physical consistency.

[0056] Furthermore, by constructing a physical anomaly detection module based on an attention mechanism, starting from the temporal structure and statistical distribution of the residuals, a fine distinction is made between real physical relaxation events and measurement noise anomalies. This enables the model to distinguish different types of anomalies in the data, breaking through the technical bottleneck of existing methods that cannot distinguish between real and false anomalies.

[0057] For different anomaly types, this invention designs a differentiable relaxation effect containment layer and a noise suppression unit based on Kalman filtering. When a real physical relaxation event occurs, the monotonicity constraint weights are dynamically released, enabling the model to fit real physical phenomena such as capacity regeneration. When a measurement noise anomaly event occurs, the abnormal disturbance is suppressed by prior-guided data correction. Thus, the preservation of the real signal and the suppression of noise are achieved within the same framework, avoiding the false suppression of real physical phenomena by existing rigid constraints.

[0058] Meanwhile, by constructing a dynamic trade-off loss function for physical consistency and adaptively adjusting the weight coefficient of the physical prior deviation penalty term based on the anomaly detection results, the model can automatically adjust the strength of physical constraints under different operating conditions. In the real physical relaxation stage, the constraints are reduced to improve the data fitting ability; in the noise interference stage, the constraints are strengthened to maintain physical consistency; and in the normal aging stage, a smooth transition is achieved, thereby realizing a dynamic balance between physical consistency and data fidelity.

[0059] In summary, this invention effectively solves the problems in the prior art of being unable to distinguish between real physical relaxation and measurement noise, as well as the prediction bias caused by physical constraint rigidity. While ensuring the physical rationality of long sequence extrapolation, it significantly reduces the local prediction error in key intervals such as capacity regeneration, and improves the accuracy of battery aging trajectory prediction. Attached Figure Description

[0060] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0061] In the attached diagram:

[0062] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0063] The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of the present invention will now be described with reference to the accompanying drawings.

[0064] like Figure 1 As shown, this invention discloses an adaptive extrapolation method for battery aging trajectory based on physical time priors, including:

[0065] Step 1: Collect constant current charging segment data of the battery cell under test throughout its entire life cycle, extract the incremental capacity curve from the constant current charging segment data, and track the peak position shift trajectory and peak area decay trajectory of the characteristic peak in the incremental capacity curve, thereby constructing a multi-dimensional physical time sequence prior template characterizing the battery aging mechanism evolution process.

[0066] Step 2: Introduce a state-space backbone network with temporal inductive bias capability, and use the multi-dimensional physical temporal prior template as the implicit state initialization parameter of the state-space backbone network, so that the state-space backbone network has physical cognition of the battery aging trajectory evolution trend in the initial training stage.

[0067] Step 3: Construct a physical anomaly detection module based on an attention mechanism. The physical anomaly detection module calculates the local deviation between the current input data sequence and the multi-dimensional physical time-series prior template in real time, and dynamically determines whether the current input data sequence belongs to a real physical relaxation event or a measurement noise anomaly event based on the magnitude and duration of the local deviation.

[0068] Step 4: When the physical anomaly detection module determines that the current input data sequence belongs to a real physical relaxation event, a differentiable relaxation effect containment layer is constructed. The differentiable relaxation effect containment layer temporarily releases the monotonicity constraint weights in the state space backbone network, so that the state space backbone network can fit the capacity recovery characteristics corresponding to the real physical relaxation event.

[0069] Step 5: When the physical anomaly detection module determines that the current input data sequence belongs to a measurement noise anomaly event, the noise suppression unit based on Kalman filtering is activated. The noise suppression unit based on Kalman filtering corrects the abnormal data points corresponding to the measurement noise anomaly event in real time according to the degradation trend reference value provided by the multi-dimensional physical time series prior template.

[0070] Step 6: Construct a dynamic trade-off loss function for physical consistency. The dynamic trade-off loss function for physical consistency includes a data fidelity term and a physical prior deviation penalty term. Based on the discrimination result output by the physical anomaly detection module, the weight coefficient of the physical prior deviation penalty term is adaptively adjusted so that the weight of the physical prior deviation penalty term is automatically reduced during real physical relaxation events to accommodate real physical phenomena, and automatically increased during measurement noise anomaly events to strengthen physical constraints.

[0071] Step 7: Using the training data that has been jointly corrected by the differentiable relaxation effect containment layer and the noise suppression unit based on Kalman filtering, iteratively train the state space backbone network loaded with the multi-dimensional physical time-series prior template until the physical consistency dynamic trade-off loss function converges, and output a battery aging trajectory prediction model that can adaptively distinguish between real physical relaxation events and measurement noise anomaly events and realize long sequence extrapolation.

[0072] Specifically, step 1 includes:

[0073] The core of Step 1 lies in extracting information carriers from the constant current charging segment that can stably characterize the evolution of the battery's internal aging mechanism, and transforming the discrete cyclic data into a physical time-series prior template with statistical commonalities. This process is not a simple data preprocessing, but rather maps electrochemical behavior into a structured prior expression that can be used for subsequent model initialization and constraint adjustment.

[0074] During the data acquisition phase, a constant current rate is applied to the battery cells under test for charging, ensuring that the charging process is under quasi-steady-state conditions. This allows the voltage response to be primarily driven by electrode reaction kinetics and diffusion processes. Voltage and capacity data are synchronously recorded using a high-precision acquisition device at a sampling frequency of at least 1 Hz until a preset cutoff voltage is reached, resulting in a complete constant-current charging segment data sequence. This data sequence is continuous in the time dimension and covers key reaction intervals in the voltage dimension, providing a foundation for subsequent feature extraction.

[0075] In the feature construction stage, the relationship between capacity and voltage is numerically differentiated to obtain the incremental capacity curve, which is mathematically expressed as: ,in Indicates charging capacity. This represents the terminal voltage. The incremental capacity curve essentially reflects the capacity increment corresponding to a unit voltage change and is highly sensitive to electrode phase transitions and the electrochemical reaction activity range. Since measurement noise is unavoidable in the original data, direct differentiation would amplify high-frequency disturbances. Therefore, the Savitzky Golay convolution smoothing algorithm is introduced to perform local polynomial fitting on the curve, which suppresses noise interference while preserving the peak structure, thus obtaining a smoothed incremental capacity curve.

[0076] During the feature extraction stage, a local maximum search is performed on the smoothed incremental capacity curve to identify multiple characteristic peaks. Each characteristic peak corresponds to the main conductive chemical reaction within a specific voltage range, such as the lithium insertion / extraction process at the positive and negative electrodes or a phase transition plateau. For each cycle, the peak position voltage value and peak area integral value of the characteristic peak are recorded, where the peak position reflects the drift of the reaction potential, and the peak area reflects the effective active material mass participating in the reaction. The peak area can be expressed as... in and For the first The left and right boundary voltages of each characteristic peak. As the cycle progresses, the peak position usually exhibits a systematic shift, and the peak area gradually decreases. These two types of trajectories correspond to aging mechanisms such as polarization enhancement and loss of active materials, respectively.

[0077] During the trajectory construction phase, the peak positions and peak areas extracted from each cycle are concatenated according to the cycle number to form multiple sequences that evolve over time, namely peak position shift trajectories and peak area decay trajectories. These trajectories depict the dynamic evolution of different aging mechanisms throughout the entire life cycle, have clear physical orientation, and can maintain a relatively consistent trend of change across individual batteries.

[0078] In the prior template construction stage, the trajectories of different battery cells are normalized over time, mapping their respective cycle lifetimes to a unified scale to eliminate time alignment bias caused by differences in lifespan. The normalized trajectories are then statistically fused on the same time axis. The evolutionary patterns at the population level are obtained by calculating the mean and variance. Specifically, the process of statistically fusing the normalized trajectories on a unified time axis includes: mapping the peak position shift trajectory and peak area decay trajectory of each battery cell to the interval [0,1] according to the normalized cycle lifetime, and constructing a unified time grid within this interval using an equal-interval sampling method. For each time node By using linear interpolation or spline interpolation methods, the corresponding trajectory values ​​are obtained from the original trajectories of each battery cell, forming a sample set at that time node.

[0079] Based on this, for the same time point Statistical calculations were performed on all sample values ​​to obtain the population mean and variance, which are expressed as follows:

[0080]

[0081]

[0082] in Indicates the number of individual battery cells. Indicates the first The trajectory values ​​of each battery at the normalized time node (t_k).

[0083] The above statistical process is performed on the peak position shift trajectory and peak area decay trajectory respectively to obtain the corresponding mean trajectory and variance trajectory. These are then concatenated along the feature dimension to form a unified multi-dimensional physical time series prior template. To avoid the influence of outliers on the statistical results, a quantile-based truncation mechanism or a weighted average mechanism can be introduced before statistical calculations, assigning lower weights to samples with large deviations. The mean describes the typical aging path, while the variance reflects individual differences and uncertainties. The final multi-dimensional physical time series prior template includes both peak position shift information and peak area decay information, and statistically encodes the common evolutionary characteristics of the battery aging mechanism.

[0084] This multi-dimensional physical time-series prior template is not a static set of curves, but a prior knowledge carrier with time-dependent structure and uncertainty expression capabilities. It provides initial state distribution and evolution reference for the subsequent state-space backbone network, enabling the model to have the ability to perceive evolutionary trends in accordance with electrochemical laws in the early stages of training.

[0085] Specifically, step 2 includes:

[0086] The goal of step 2 is to transform the multi-dimensional physical time-series prior template constructed in step 1 from a statistically significant trajectory description into an internal state representation of the model that can participate in dynamic inference, so that the model possesses the initial evolutionary conditions that conform to the battery aging mechanism before parameter learning. Essentially, this process transforms the physical prior from an external constraint into an endogenous state, thereby embedding a temporal inductive bias at the structural level.

[0087] At the network structure construction level, a temporal backbone network based on a state-space model is adopted as the unified modeling framework. This structure characterizes the intrinsic aging state of the system at the current time step by introducing implicit state vectors, and describes the recursive relationship of states in the time dimension through a state transition matrix. The implicit state vector can be represented as... Each dimension corresponds to a potential aging factor, used to comprehensively characterize the multi-mechanism coupling effect reflected by peak position shift and peak area decay. The state evolution process can be formalized as follows: ,in Here is the state transition matrix. This represents the observation-driven input perturbation term. This expression enables the model to evolve continuously over time and is naturally suited for long-sequence extrapolation tasks.

[0088] At the prior encoding level, the multi-dimensional physical temporal prior template obtained in step 1 is vectorized. Specifically, the statistical mean sequence of the peak position offset trajectory and the statistical mean sequence of the peak area decay trajectory are aligned on the same time axis and concatenated to form a unified feature vector, which is then mapped to the implicit state space as the initial state value. This mapping can be represented as follows: ,in The statistical mean of the peak position offset trajectory. The statistical mean of the peak area decay trajectory is represented. It represents a linear or nonlinear mapping function, and its specific implementation includes linear mapping or feedforward mapping structure with nonlinear activation.

[0089] When a linear mapping is used, the mapping function can be expressed as:

[0090]

[0091] in This represents the input feature vector formed by concatenating the statistical mean of the peak position offset trajectory and the statistical mean of the peak area decay trajectory. This is the weight matrix. This is the bias vector. This form realizes a linear projection from the prior feature space to the implicit state space.

[0092] When a nonlinear mapping is used, the mapping function can employ a single-layer or multi-layer feedforward structure, expressed as follows:

[0093]

[0094] in To represent a nonlinear activation function, either the ReLU function or the hyperbolic tangent function can be chosen. , This is the weight matrix. , This is the bias vector. This structure is used to enhance the ability to express the nonlinear coupling between different aging mechanism characteristics.

[0095] Meanwhile, the corresponding statistical variance sequence is encoded as an uncertainty measure of the implicit state vector, used to characterize the confidence level of the prior in different dimensions. The smaller the variance, the stronger the consistency of the aging pattern in the population, and the corresponding dimension should have a higher constraint weight in subsequent training.

[0096] At the initialization mechanism level, the encoded implicit state vector is directly used as the initial implicit state of the state space backbone network, so that the model is in a state distribution that conforms to the physical laws of battery aging before training begins, rather than traditional random initialization. This initialization method allows the model to refine and adjust based on existing physical knowledge without having to learn the aging trend from scratch, thereby significantly reducing the drift risk during long sequence extrapolation and improving convergence stability.

[0097] At the state evolution constraint level, the state transition matrix is ​​structurally designed, constrained to a diagonal matrix form, to introduce an explicit temporal inductive bias. Each diagonal element of the diagonal matrix corresponds to an autoregressive coefficient of a certain dimension of the implicit state, whose physical meaning can be interpreted as the forgetting factor or retention rate of that aging factor. These diagonal elements are not randomly assigned, but initialized based on the average rate of change between adjacent cycles in the multi-dimensional physical temporal prior template. If the peak position of a certain characteristic peak drifts slowly and steadily with the cycle, the diagonal element of the corresponding dimension is close to 1, indicating that the state has strong inertia; if the peak area of ​​a certain characteristic peak decays rapidly, the diagonal element of the corresponding dimension is less than 1, indicating that the state decays rapidly over time.

[0098] This initialization method based on the prior rate of change ensures that the state transition matrix possesses reasonable dynamic properties from the early stages of model training. As time progresses, the implicit state no longer evolves unconstrainedly, but rather follows the average aging rate revealed by the physical prior. When subsequent input data aligns with the prior, the state evolution remains smooth and stable; when deviations occur, the model can adaptively correct itself without producing drastic oscillations.

[0099] Through the aforementioned structural design and parameter initialization, the multi-dimensional physical time-series prior template is internalized as the initial conditions and evolution rules of the state-space backbone network, enabling the model to possess a physical understanding of the overall trend of battery aging trajectory before encountering training data. This endogenous prior embedding method provides a unified state representation foundation for subsequent anomaly detection, constraint adjustment, and long-sequence extrapolation.

[0100] Specifically, step 3 includes:

[0101] The goal of step 3 is to introduce a discriminative physical anomaly detection module based on the multi-dimensional physical time-series prior template constructed in step 1 and the state-space backbone network established in step 2. This module further subdivides deviations from the physical prior into real physical relaxation events and measurement noise anomaly events, thereby providing reliable control signals for subsequent constraint adjustment. This process no longer simply relies on single-point errors but characterizes the nature of deviation behavior from both temporal structure and statistical distribution perspectives.

[0102] At the residual construction level, the capacity prediction value generated by the state-space backbone network at each time step is used as a reference benchmark. The difference between the current input capacity observation value and the prediction value is calculated to obtain the instantaneous residual, which is expressed as follows: ,in This represents the capacity observation at the current time step. This represents the capacity prediction value generated based on a multi-dimensional physical time-series prior template. The residual not only reflects the deviation between the data and the model output but also implicitly reflects the degree of deviation of the observed data from the physical prior. To avoid interference from single-point fluctuations in the discrimination results, the instantaneous residuals from multiple consecutive time steps are concatenated in chronological order to form a sliding window residual sequence, allowing the deviation behavior to exhibit overall structural characteristics within a local time range.

[0103] At the level of local deviation modeling, a multi-head self-attention mechanism is introduced to model the sliding window residual sequence. This mechanism enables the model to automatically identify key patterns in the residual sequence by weighted aggregation of correlations between time steps within the sequence, rather than simple averaging or fixed-window statistics. Specifically, each attention head projects the residual sequence from different subspaces, extracts multi-scale deviation features, and obtains an enhanced representation through weighted summation. Based on this, the enhanced residual representation is compared with the template residual statistical distribution at the corresponding time position in the multi-dimensional physical time-series prior template, using Mahalanobis distance as the deviation metric, expressed as: ,in This represents the residual vector of the current sliding window. and These represent the mean and covariance matrix of the residuals at the corresponding time positions obtained from the multi-dimensional physical time-series prior template, respectively. This metric can simultaneously consider the correlation between the residual magnitude and each dimension, enabling the local deviation to have statistical consistency and scale adaptability.

[0104] At the level of the anomaly triggering mechanism, to avoid misjudging transient noise as physical events, a duration counter and a deviation accumulator are introduced to integrate the deviation behavior over time. When the local deviation exceeds a preset anomaly judgment threshold, the duration counter begins recording the duration of continuous deviations exceeding the threshold, while the deviation accumulator integrates and accumulates the deviation portion, thus quantifying and distinguishing between short-term spikes and long-term offsets. The duration counter reflects the temporal scale characteristics of the deviation behavior, while the deviation accumulator reflects the energy intensity of the deviation behavior; together, they constitute a dual constraint on the anomaly pattern.

[0105] At the event discrimination level, when the duration counter reaches the preset minimum duration threshold for a relaxation event and the deviation accumulator exceeds the preset energy threshold for a relaxation event, it indicates that the current deviation behavior is continuous and significant. Its time structure conforms to the characteristics of slow release of internal physical processes in the battery, and it is judged as a real physical relaxation event, and the first control signal is output. This type of event usually corresponds to the capacity recovery caused by lithium-ion concentration redistribution or polarization mitigation, and its residual sequence shows a smooth and continuous deviation trend.

[0106] At the noise discrimination level, when the duration is insufficient or the accumulated energy is low, it indicates that the deviation behavior lacks persistence or has limited overall strength, consistent with the characteristics of random disturbances or measurement errors. This is judged as a measurement noise anomaly event, and a second control signal is output. Simultaneously, the duration counter and deviation accumulator are reset to prevent historical residues from interfering with subsequent discrimination. This type of anomaly typically manifests as a single-point mutation or short-term oscillation, and its residual structure lacks stable time correlation.

[0107] Through the above mechanism, the physical anomaly detection module achieves fine-grained discrimination from whether there is a deviation to the type of deviation. It integrates and compares the statistical prior in step 1 with the dynamic prediction results in step 2, introduces structural constraints in the time dimension and distribution measures in the statistical dimension, thereby providing clear and reliable control basis for the subsequent differentiable relaxation effect containment layer and Kalman filter-based noise suppression unit.

[0108] Specifically, step 4 includes:

[0109] The core of step 4 lies in the fact that when step 3 determines that the current data interval belongs to a real physical relaxation event, the original rigid monotonicity constraint is no longer simply maintained. Instead, while ensuring that the overall degradation trend is not destroyed, the local constraint strength is continuously and controllably released, enabling the state space backbone network to express the physical phenomenon of a brief capacity rebound. This process is achieved by introducing a differentiable relaxation effect containment layer into the loss function path, thereby maintaining the consistency and optimizability of end-to-end training.

[0110] At the structural embedding level, a differentiable relaxation effect containment layer is placed in the loss function calculation path of the state-space backbone network, allowing it to directly act on the constraint terms rather than the original data or network structure. This containment layer receives the first control signal output by the physical anomaly detection module as a trigger input, and simultaneously incorporates learnable relaxation gating parameters to adjust the magnitude and response speed of constraint release. Since these gating parameters participate in backpropagation, their values ​​are not fixed but adaptively optimized during training based on data characteristics and the degree of prior conflict, thereby achieving differentiated responses for different batteries and different stages.

[0111] At the constraint release mechanism level, when the first control signal is received, it indicates that the current residual deviation is persistent and structural, corresponding to the actual physical relaxation process. At this point, the differentiable relaxation effect containment layer calculates the monotonic constraint release coefficient based on the relaxation gating parameter and the local deviation. This coefficient can be expressed as... ,in This represents the local deviation obtained in step 3. Indicates the relaxation gating parameter. This represents the compression mapping function. This expression makes the release coefficient continuously change with the degree of deviation; the more significant the deviation, the higher the degree of release. This release coefficient is then applied to the monotonicity penalty term in the loss function, causing the original constraint weights to decay proportionally. This allows the model to deviate from a strictly monotonically decreasing trend within a local time period, achieving a fit to the capacity recovery characteristics.

[0112] At the state reference mechanism level, to prevent the model from completely deviating from the physical prior trajectory due to constraint release, a state offset vector is introduced as an additional adjustment signal. Specifically, the implicit state vector at the current time step is differentially calculated with the template state vector at the corresponding time position in the multi-dimensional physical time-series prior template constructed in step 1, resulting in:

[0113]

[0114] in This represents the implicit state vector of the backbone network in the state space at the current time step, reflecting the current aging state of the battery learned by the model based on the data. This represents the template state vector at the same time location, given by a multi-dimensional physical time-series prior template, reflecting the state under an ideal physical degradation path. This represents the difference between the two, i.e., the state offset vector. This offset vector is a multi-dimensional quantity, with each dimension corresponding to a deviation in a specific aging mechanism direction, such as peak position drift deviation or peak area decay deviation. This state offset vector reflects the direction and magnitude of the deviation of the current model state from the physical prior; it indicates how much the current battery state has deviated from the normal aging trajectory, and in which direction it has deviated. When this occurs, it indicates that the current state is highly consistent with the physical prior, and the system is in a typical aging path. A larger value indicates a significant deviation of the current state from the physical prior, potentially corresponding to two scenarios: genuine physical relaxation, such as capacity recovery, or measurement noise or anomalous perturbations. Therefore, this quantity serves as a bridge connecting data performance and physical understanding. In the differentiable relaxation effect containment layer, this offset vector is used as an auxiliary input in loss modulation, allowing the model to adjust using this offset as a reference boundary when fitting capacity recovery, rather than drifting without constraints. This approach both accommodates genuine physical relaxation and prevents over-correction after local constraint release, maintaining consistency with the long-term degradation trend.

[0115] At the constraint recovery mechanism level, when the actual physical relaxation event ends, the physical anomaly detection module stops outputting the first control signal, indicating that the data has reverted to the normal degradation trajectory. At this point, the differentiable relaxation effect containment layer does not immediately restore the original constraint strength. Instead, based on the decay rate set by the relaxation gating parameters, it smoothly increases the monotonic constraint release coefficient, gradually bringing it closer to 1. This gradual recovery process avoids training oscillations caused by sudden changes in constraint strength, allowing the implicit state vector to smoothly transition back to the constrained evolutionary trajectory, thereby maintaining stability during long-sequence extrapolation.

[0116] Through the above mechanism, the differentiable relaxation effect containment layer achieves dynamic adjustment of physical constraints. It uses the multi-dimensional physical temporal priors extracted in step 1 as a long-term evolution benchmark, the continuous evolution of the implicit states in step 2 as an expression carrier, and combines the anomaly discrimination results from step 3 to selectively contain local non-monotonic phenomena. This process introduces the ability to model real physical relaxation effects without compromising overall physical consistency, thereby effectively reducing the prediction bias of the capacity regeneration interval.

[0117] Specifically, step 5 includes:

[0118] The core of step 5 lies in the fact that when step 3 determines that the current deviation belongs to an abnormal event of measurement noise, instead of fitting through constraint release, the abnormal observation is structurally corrected so that the input data reverts to the degradation trend described by the multi-dimensional physical time-series prior constructed in step 1, while maintaining dynamic consistency with the state-space backbone network in step 2. This process is achieved by introducing a noise suppression unit based on Kalman filtering in parallel at the input, moving the data correction forward to the model entry point and suppressing noise propagation from the source.

[0119] At the structural deployment level, a Kalman filter unit is connected in parallel at the input of the state-space backbone network, forming a dual-path structure with the original data path. This unit internally maintains a state estimation vector and an error covariance matrix. The state estimation vector represents the optimal capacity estimate at the current time step, and the error covariance matrix characterizes the uncertainty of this estimate and its evolution over time. The introduction of the Kalman filter framework allows data correction to no longer rely on simple smoothing, but rather on a recursive estimation mechanism based on the fusion of state prediction and observation.

[0120] At the prior guidance level, when the second control signal output by the physical anomaly detection module is received, it indicates that the deviation of the current data point lacks persistence and structure, and should be considered as measurement noise. At this point, the Kalman filter unit reads the template capacity reference value corresponding to the current time position from the multi-dimensional physical time-series prior template constructed in step 1, and uses it as the reference benchmark for the external observation model. This reference value is not a single prediction result, but rather a degradation trend position given by the statistical mean trajectory, possessing global consistency and physical rationality, and is used to form correction constraints for anomaly observations.

[0121] At the optimal estimation level, the Kalman filter unit performs prediction updates based on the current state estimation vector and the error covariance matrix, and combines this with the template capacity reference value for observation updates. The core lies in the calculation of the Kalman gain matrix, which is expressed as:

[0122]

[0123] in This represents the prediction error covariance. This represents the observation noise covariance. To achieve linkage with step 3, local deviation is introduced. The model is constructed to dynamically change with the degree of deviation. When the local deviation is large, the observation noise covariance increases, leading to a decrease in the Kalman gain, thereby reducing the weight of the original observations in the fusion and increasing the dominant role of the template capacity reference value. When the deviation is small, the observation noise covariance decreases, retaining more original observation information. In this way, an adaptive response to the degree of anomaly is achieved.

[0124] At the data correction and feedback level, Kalman gain is used to weight and fuse the predicted values ​​and reference observations to obtain the optimal capacity estimate for the current time step. This estimate replaces the original outlier data points and is fed into the state-space backbone network as the corrected input data, thus avoiding noise directly affecting implicit state updates. Simultaneously, this optimal capacity estimate is fed back into the Kalman filter unit to update the state estimation vector and error covariance matrix, ensuring the filtering process maintains continuity and memory over time. This bidirectional coupling mechanism keeps data correction consistent with state evolution, avoiding the problem of input-internal state mismatch.

[0125] At the mode switching level, when the measurement noise anomaly event ends, the physical anomaly detection module stops outputting the second control signal, indicating that the data has returned to the normal fluctuation range. At this time, the Kalman filter unit automatically switches to direct-pass mode, and the original input data enters the state space backbone network directly without correction. However, the state estimation vector and error covariance matrix inside the filter unit are continuously updated to maintain the characterization of the system state uncertainty. When the next noise anomaly occurs, estimation can be quickly completed based on the latest state without re-initialization.

[0126] Through the above mechanism, the noise suppression unit based on Kalman filtering achieves real-time identification and adaptive correction of measurement noise anomalies. It uses the physical time prior in step 1 as a global reference benchmark, the state evolution in step 2 as the basis for dynamic prediction, and combines the anomaly detection results from step 3 to selectively replace and fuse abnormal data. This process avoids the cumulative amplification of noise in long-sequence extrapolation while not interfering with the representation of real physical relaxation events. It complements step 4, jointly ensuring the stability and accuracy of the model under complex conditions.

[0127] Specifically, step 6 includes:

[0128] The core of step 6 lies in unifying the multi-dimensional physical temporal priors constructed in step 1, the implicit state evolution in step 2, and the anomaly detection and data correction mechanisms formed in steps 3 to 5 into a single optimization objective. By constructing a physically consistent dynamic tradeoff loss function, an adaptive balance between physical constraints and data fitting is achieved during training. This loss function is no longer a static weight combination but dynamically adjusted over time and according to data features, enabling the model to possess differentiated learning strategies under different circumstances.

[0129] At the loss function construction level, the total loss is divided into two parts: a data fidelity term and a physical prior deviation penalty term. The data fidelity term measures the deviation between the capacity prediction output by the state-space backbone network and the capacity observation after correction in step 5, and is expressed as:

[0130]

[0131] This term directly drives the model to fit the observed data, ensuring the numerical accuracy of the prediction results. The physical prior deviation penalty term is used to constrain the consistency between the implicit state vector and the multi-dimensional physical time-series prior template constructed in step 1. It characterizes the degree of deviation through a distribution-level difference measure, and is expressed as:

[0132]

[0133] in Represents the current implicit state vector. This represents the template state vector at the corresponding time position. This term ensures that the implicit state always fluctuates around the physical prior distribution during evolution, avoiding unconstrained drift.

[0134] At the level of weight adjustment mechanism, a weight coefficient is introduced. The physical prior deviation penalty term is dynamically adjusted so that the total loss function is expressed as:

[0135]

[0136] This weighting coefficient is limited to between 0 and 1, and its physical meaning is the degree to which the model depends on physical priors. A value closer to 1 indicates that the model emphasizes physical consistency; a value closer to 0 indicates that the model emphasizes its ability to fit the data. By... Set it as a time-varying parameter so that it can respond to different data states and anomaly types.

[0137] At the level of regulating real physical relaxation events, when step 3 outputs the first control signal and step 4 has partially released the monotonicity constraint, it indicates that there is a real capacity recovery phenomenon in the current data interval. Maintaining a high level of physical prior constraints will suppress the model's representation of this phenomenon. Therefore, the weight coefficients are set to a preset low weight value. This reduces the contribution of the physical prior deviation penalty term, thereby expanding the model's tolerance range for implicit state shifts, enabling it to deviate from the template state within a local time period and achieve fitting of the real physical relaxation process.

[0138] In the noise anomaly adjustment stage, when the second control signal is output in step 3 and the abnormal data is corrected in step 5, it indicates that the current deviation originates from non-physical factors. At this point, it is necessary to strengthen the constraint effect of physical priors on the model to avoid erroneous updates to the implicit state due to noise interference. Therefore, the weight coefficients are set to preset high weight values. This increases the proportion of the physical prior deviation penalty term in the total loss, forcing the implicit state to converge to the template state, thereby stabilizing the state evolution trajectory.

[0139] At the normal aging stage adjustment level, when the physical anomaly detection module does not output any control signal, it indicates that the system is in a typical degradation process. In this case, the weighting coefficient is set to an intermediate weight value. And it changes dynamically with the aging process. In the early stages of aging, due to the limited observable data and significant individual differences, Set to near This strengthens the guiding role of physical priors, enabling the model to converge quickly to a reasonable trajectory; as the cycle progresses, the data gradually becomes richer, individual characteristics gradually emerge, and the [various limitations] gradually decrease. This improves the model's ability to fit data details, thereby achieving a smooth transition from prior-driven to data-driven approaches.

[0140] At the joint optimization level, the dynamically weighted physical prior deviation penalty term is superimposed with the data fidelity term to obtain the final loss at the current time step. This loss is then applied to the state space backbone network parameters, the relaxation gating parameters in step 4, and related learnable modules via backpropagation. Due to the weight coefficients... Directly related to the discrimination result in step 3, the entire optimization process forms a closed-loop structure. The anomaly detection result not only affects data correction and constraint release, but also directly regulates the shape of the loss function, thereby continuously adjusting the learning direction of the model during the training process.

[0141] Through the above mechanism, the physical consistency dynamic tradeoff loss function achieves unified scheduling of each module from step 1 to step 5, coupling physical priors, data features, and anomaly types within the same optimization framework. It avoids over-constraints in real physical relaxation scenarios, strengthens physical guidance in measurement noise scenarios, and achieves a smooth transition in normal degradation stages, thus ensuring both physical consistency and prediction accuracy in long-sequence extrapolation tasks.

[0142] Specifically, step 7 includes:

[0143] The goal of step 7 is to unify and integrate the multi-dimensional physical time-series priors, state-space modeling mechanisms, anomaly detection strategies, and constraint and data correction mechanisms developed in steps 1 to 6, ultimately obtaining a battery aging trajectory prediction model capable of stably performing long-sequence extrapolation and possessing anomaly adaptive capabilities. This process is not only a parameter optimization process but also a convergence process for the multi-module collaborative mechanism.

[0144] At the sample construction level, based on the training data jointly corrected by the differentiable relaxation effect containment layer in step 4 and the Kalman filter-based noise suppression unit in step 5, sliding window data blocks are extracted according to the time sequence of charge-discharge cycles. Each data block includes continuous... The sequence of capacity observations from each cycle is used as the input sample, and subsequent consecutive values ​​are also selected. The cyclical sequence of capacity observations serves as the prediction label. This construction method allows the model to predict the future from a known historical context during the training phase, thus aligning with real-world extrapolation scenarios. The sliding window moves progressively along the timeline, forming a training sample set covering the entire lifecycle, enabling the model to learn dynamic features at different aging stages.

[0145] At the sequence generation level, input samples are fed into a state-space backbone network loaded with multi-dimensional physical time-series prior templates. The implicit state vector, starting from the prior states initialized in step 2, evolves progressively under the control of the state transition matrix and is updated in conjunction with the current input data to generate capacity prediction values ​​corresponding to the input time segment. After completing the prediction of the input segment, the model continues to rely on the state transition mechanism for forward recursion, generating extrapolation results corresponding to the predicted label time segment without additional input observations, thus forming a complete capacity prediction sequence. This process demonstrates the advantages of state-space models in long-sequence extrapolation, namely, achieving continuous generation of future trends through internal state evolution.

[0146] At the loss-driven optimization level, the generated capacity prediction sequence and the corresponding true capacity labels are input into the physical consistency dynamic tradeoff loss function constructed in step 6. At each time step, the loss function dynamically adjusts the weight of the physical prior deviation penalty term based on the presence of real physical relaxation events or measurement noise anomalies, thereby changing the gradient propagation direction. Through backpropagation, the loss gradient is simultaneously transmitted to the state-space backbone network parameters and the relaxation gating parameters in the differentiable relaxation effect containment layer, enabling both to perform collaborative optimization under a unified objective. This process allows the model to not only learn data fitting capabilities but also to learn constraint adjustment strategies under different anomaly conditions.

[0147] At the convergence control level, to avoid overfitting and training oscillations, a validation mechanism is introduced after each training epoch. An independent validation set is input into the current model, and the mean absolute percentage error is calculated, expressed as:

[0148]

[0149] By continuously monitoring the trend of this indicator, when it stops decreasing within a preset number of rounds, it indicates that the model has reached its optimal generalization state, triggering an early stopping mechanism to terminate training. Finally, the model parameters corresponding to the lowest validation error are selected as the convergence result, thus ensuring the model's stability on unseen data.

[0150] At the system integration level, the converged state-space backbone network, physical anomaly detection module, differentiable relaxation effect containment layer, and Kalman filter-based noise suppression unit are uniformly encapsulated to form a complete battery aging trajectory prediction model. This model internally embeds the statistical parameters of the multi-dimensional physical time-series prior template, while retaining the relaxation gating parameters and state transition matrix obtained during training, enabling each module to operate according to the collaborative mechanism formed during training during the inference phase.

[0151] At the inference application level, early cycle capacity data of the individual battery cells to be predicted are input into the model. The input data first undergoes real-time discrimination by a physical anomaly detection module, distinguishing between potential real physical relaxation events and measurement noise anomalies. Subsequently, based on the discrimination results, the data is adaptively processed through either a differentiable relaxation effect containment layer or a Kalman filter-based noise suppression unit, ensuring that the input sequence possesses physical consistency and noise suppression characteristics before entering the state-space backbone network. Building upon this, the state-space backbone network utilizes implicit state evolution and fixed physical time-series prior templates to progressively extrapolate future capacity, generating a complete aging trajectory until the end of the battery's lifespan.

[0152] At the output level, the model not only outputs the capacity prediction value at each time step, but also provides the corresponding confidence interval based on the uncertainty propagation of the implicit state and the error covariance estimation, thus providing a quantitative description of the prediction reliability. This output format enables the model results to not only have numerical accuracy, but also interpretability and risk assessment capabilities.

[0153] Through the above training and inference process, step 7 realizes the closed-loop construction from multi-module design to unified model output, so that the various mechanisms in steps 1 to 6 work together in the same framework, and finally form a battery aging trajectory prediction model that can distinguish between real physical relaxation and measurement noise and has stable long sequence extrapolation capability.

[0154] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. An adaptive extrapolation method for battery aging trajectory based on physical time priors, characterized in that, Includes the following steps: Step 1: Collect constant current charging segment data of the battery cell under test throughout its entire life cycle, extract the incremental capacity curve from the constant current charging segment data, and track the peak position shift trajectory and peak area decay trajectory of the characteristic peak in the incremental capacity curve, thereby constructing a multi-dimensional physical time sequence prior template characterizing the battery aging mechanism evolution process. Step 2: Introduce a state-space backbone network with temporal inductive bias capability, and use the multi-dimensional physical temporal prior template as the implicit state initialization parameter of the state-space backbone network, so that the state-space backbone network has physical cognition of the battery aging trajectory evolution trend in the initial training stage. Step 3: Construct a physical anomaly detection module based on an attention mechanism. The physical anomaly detection module calculates the local deviation between the current input data sequence and the multi-dimensional physical time-series prior template in real time, and dynamically determines whether the current input data sequence belongs to a real physical relaxation event or a measurement noise anomaly event based on the magnitude and duration of the local deviation. Step 4: When the physical anomaly detection module determines that the current input data sequence belongs to a real physical relaxation event, a differentiable relaxation effect containment layer is constructed. The differentiable relaxation effect containment layer temporarily releases the monotonicity constraint weights in the state space backbone network, so that the state space backbone network can fit the capacity recovery characteristics corresponding to the real physical relaxation event. Step 5: When the physical anomaly detection module determines that the current input data sequence belongs to a measurement noise anomaly event, the noise suppression unit based on Kalman filtering is activated. The noise suppression unit based on Kalman filtering corrects the abnormal data points corresponding to the measurement noise anomaly event in real time according to the degradation trend reference value provided by the multi-dimensional physical time series prior template. Step 6: Construct a dynamic trade-off loss function for physical consistency. The dynamic trade-off loss function for physical consistency includes a data fidelity term and a physical prior deviation penalty term. Based on the discrimination result output by the physical anomaly detection module, the weight coefficient of the physical prior deviation penalty term is adaptively adjusted so that the weight of the physical prior deviation penalty term is automatically reduced during real physical relaxation events to accommodate real physical phenomena, and automatically increased during measurement noise anomaly events to strengthen physical constraints. Step 7: Using the training data that has been jointly corrected by the differentiable relaxation effect containment layer and the noise suppression unit based on Kalman filtering, iteratively train the state space backbone network loaded with the multi-dimensional physical time-series prior template until the physical consistency dynamic trade-off loss function converges, and output a battery aging trajectory prediction model that can adaptively distinguish between real physical relaxation events and measurement noise anomaly events and realize long sequence extrapolation.

2. The adaptive extrapolation method for battery aging trajectory based on fusion of physical time priors as described in claim 1, characterized in that, Step 1 includes the following sub-steps: Step 1-1: Charge the battery cell under test with a constant current at a preset constant current rate. Collect charging voltage and charging capacity data in real time through a high-precision data acquisition device. The sampling frequency is not less than 1Hz until the charging voltage reaches the preset cutoff voltage, thereby obtaining constant current charging segment data. Steps 1-2: Perform numerical differentiation calculation on the capacity-voltage relationship in the constant current charging segment data to obtain the initial incremental capacity curve, and use the Savitzky-Golay convolution smoothing algorithm to denoise the initial incremental capacity curve to eliminate the interference of measurement noise on subsequent feature peak identification, and obtain the smoothed incremental capacity curve. Steps 1-3: Identify multiple characteristic peaks corresponding to different aging mechanisms on the smoothed incremental capacity curve using the local maximum search algorithm, and record the peak position voltage value and peak area integral value of each characteristic peak in each charge-discharge cycle, thereby forming the peak position offset trajectory and peak area decay trajectory. Steps 1-4: Time-scale normalization is performed on the peak position offset trajectory and peak area decay trajectory to eliminate the influence of cycle life differences between different battery cells. The normalized trajectories are then statistically averaged to construct a multi-dimensional physical time-series prior template that reflects the common evolution law of battery aging mechanism.

3. The adaptive extrapolation method for battery aging trajectory based on fusion of physical time priors as described in claim 2, characterized in that, Step 2 includes the following sub-steps: Step 2-1: Construct a temporal backbone network based on a state-space model. The temporal backbone network based on a state-space model includes learnable implicit state vectors and state transition matrices. Implicit state vectors are used to carry instantaneous state information of the battery aging process, and state transition matrices are used to control the evolution of implicit state vectors between different time steps. Step 2-2: Vectorize the multi-dimensional physical time series prior template constructed in Step 1-4, and map the statistical mean of the peak position offset trajectory and the statistical mean of the peak area decay trajectory to the initial value of the implicit state vector. At the same time, map the statistical variance of the peak position offset trajectory and the statistical variance of the peak area decay trajectory to the initial confidence of the implicit state vector. Steps 2-3: Use the implicit state vector carrying multi-dimensional physical time-series prior template information as the initial implicit state of the time-series backbone network based on the state-space model, so that the time-series backbone network based on the state-space model can grasp the general law of the evolution of feature peaks during battery aging before it comes into contact with any training data. Steps 2-4: Set the state transition matrix as a diagonal matrix with temporal inductive bias capability. The diagonal elements of the diagonal matrix are initialized with forgetting factors calculated based on the average rate of change of peak position offset and peak area decay between adjacent cycles in the multi-dimensional physical temporal prior template, so that the implicit state vector can evolve according to the aging rate revealed by the physical prior as the time step moves forward.

4. The adaptive extrapolation method for battery aging trajectory based on fusion of physical time priors as described in claim 1, characterized in that, Step 3 includes the following sub-steps: Step 3-1: At each time step of the state space backbone network, calculate the difference between the battery capacity observation value input at the current time step and the capacity prediction value generated by the state space backbone network based on the multi-dimensional physical time series prior template at the time step to obtain the instantaneous residual at the current time step, and combine the instantaneous residuals of multiple consecutive time steps into a sliding window residual sequence. Step 3-2: Construct a local deviation calculation unit based on multi-head self-attention mechanism. Input the sliding window residual sequence into the local deviation calculation unit based on multi-head self-attention mechanism. Calculate the Mahalanobis distance between each residual element in the sliding window residual sequence and the template residual statistical distribution at the corresponding time position in the multi-dimensional physical time-series prior template through the local deviation calculation unit based on multi-head self-attention mechanism. Use the Mahalanobis distance as the quantized value of local deviation. Step 3-3: Set the duration counter and deviation accumulator. When the local deviation exceeds the preset anomaly judgment threshold, the duration counter is triggered to start counting, and the deviation accumulator is triggered to start accumulating the value of the local deviation that exceeds the anomaly judgment threshold. Steps 3-4: When the count value of the duration counter reaches the preset minimum duration threshold of the relaxation event and the accumulated value of the deviation accumulator exceeds the preset energy threshold of the relaxation event, the physical anomaly detection module determines that the data interval corresponding to the currently input sliding window residual sequence belongs to the real physical relaxation event and outputs the first control signal. Steps 3-5: When the count value of the duration counter is lower than the minimum duration threshold of the relaxation event or the accumulated value of the deviation accumulator is lower than the energy threshold of the relaxation event, the physical anomaly detection module determines that the data interval corresponding to the currently input sliding window residual sequence belongs to the measurement noise anomaly event, and outputs the second control signal, while clearing the duration counter and the deviation accumulator to zero.

5. The adaptive extrapolation method for battery aging trajectory based on fusion of physical time priors as described in claim 1, characterized in that, Step 4 includes the following sub-steps: Step 4-1: Embed a differentiable relaxation effect containment layer in the loss function calculation path of the state space backbone network. The differentiable relaxation effect containment layer receives the first control signal output by the physical anomaly detection module as the trigger input and has built-in learnable relaxation gating parameters. Step 4-2: When the differentiable relaxation effect containment layer receives the first control signal, the differentiable relaxation effect containment layer calculates the monotonic constraint release coefficient proportional to the local deviation based on the current value of the learnable relaxation gating parameter, and applies the monotonic constraint release coefficient to the monotonic penalty term in the loss function of the state space backbone network, so that the weight of the monotonic penalty term is multiplied by the monotonic constraint release coefficient to obtain the decayed monotonic penalty term. Step 4-3: The differentiable relaxation effect containment layer calculates the difference between the implicit state vector of the state space backbone network at the current time step and the template state vector at the corresponding time position in the multi-dimensional physical time-series prior template to obtain the state offset vector. The state offset vector is used as an additional input to the differentiable relaxation effect containment layer, so that the state space backbone network can use the state offset vector as a reference when fitting the capacity recovery characteristics corresponding to the real physical relaxation event, and avoids excessive deviation from the long-term degradation trend revealed by the multi-dimensional physical time-series prior template. Step 4-4: When the real physical relaxation event ends and the physical anomaly detection module stops outputting the first control signal, the differentiable relaxation effect containment layer gradually restores the monotonic constraint release coefficient to the initial value of 1.0 according to the preset decay rate of the learnable relaxation gating parameters, so that the monotonic penalty term of the state space backbone network is restored to the original constraint strength, thereby maintaining the overall physical consistency in the long sequence extrapolation process while containing the real physical relaxation event.

6. The adaptive extrapolation method for battery aging trajectory based on fusion of physical time priors as described in claim 1, characterized in that, Step 5 includes the following sub-steps: Step 5-1: Deploy a noise suppression unit based on Kalman filtering in parallel at the input of the state space backbone network in advance. The noise suppression unit based on Kalman filtering maintains the state estimation vector and the error covariance matrix. The state estimation vector is used to store the optimal capacity estimate after filtering at the current time step, and the error covariance matrix is ​​used to characterize the uncertainty of the state estimation vector. Step 5-2: When the noise suppression unit based on Kalman filtering receives the second control signal output by the physical anomaly detection module, the noise suppression unit based on Kalman filtering immediately reads the template capacity reference value corresponding to the current time step from the multi-dimensional physical time series prior template, and uses the template capacity reference value as the prediction benchmark value of the external observation model in the Kalman filtering framework. Step 5-3: The noise suppression unit based on Kalman filtering calculates the optimal capacity estimate for the current time step based on the state estimation vector and error covariance matrix, combined with the external observation information provided by the template capacity reference value. The size of the Kalman gain matrix is ​​automatically adjusted according to the local deviation of the measurement noise anomaly event, so that the greater the local deviation, the higher the weight of the template capacity reference value in the fusion. Step 5-4: The Kalman filter-based noise suppression unit uses the calculated optimal capacity estimate as the corrected capacity data for the current time step, replaces the original abnormal data points corresponding to the measurement noise abnormal events, and simultaneously outputs the optimal capacity estimate to the input of the state space backbone network and feeds it back to the state estimation vector update module inside the Kalman filter-based noise suppression unit for prediction update in the next time step. Step 5-5: When the measurement noise anomaly event ends and the physical anomaly detection module stops outputting the second control signal, the noise suppression unit based on Kalman filtering automatically switches to pass-through mode, directly transmitting the uncorrected original input data to the state space backbone network, while maintaining continuous updates to the state estimation vector and error covariance matrix, so as to be able to respond quickly when the next measurement noise anomaly event occurs.

7. The adaptive extrapolation method for battery aging trajectory based on fusion of physical time priors as described in claim 1, characterized in that, Step 6 includes the following sub-steps: Step 6-1: Construct a physical consistency dynamic trade-off loss function that includes a data fidelity term and a physical prior deviation penalty term. The data fidelity term uses the mean square error form to calculate the deviation between the capacity prediction value output by the state space backbone network and the actual capacity observation value. The physical prior deviation penalty term uses the KL divergence form to calculate the distribution difference between the implicit state vector of the state space backbone network and the template state vector at the corresponding time position in the multi-dimensional physical time-series prior template. Step 6-2: Set adaptively adjustable weight coefficients in the physical consistency dynamic tradeoff loss function. Weighting coefficient Used to control the proportion of the physical prior deviation penalty term in the total loss. The value range of is limited to between 0 and 1, when A value of 1 indicates that the physical prior is completely followed; when... A value of 0 indicates that physical priors are completely ignored; Step 6-3: Establish weighting coefficients The mapping relationship between the results and the judgment results output by the physical anomaly detection module is established. When the physical anomaly detection module outputs the first control signal indicating that the current data interval belongs to a real physical relaxation event, the weighting coefficients are adjusted. Set to the preset low weight value This reduces the contribution of the physical prior deviation penalty term to accommodate the capacity recovery feature corresponding to real physical relaxation events. Step 6-4: When the physical anomaly detection module outputs a second control signal indicating that the current data interval belongs to a measurement noise anomaly event, the weighting coefficient is adjusted. Set to the preset high weight value This increases the contribution of the physical prior deviation penalty term to strengthen the constraint effect of the multi-dimensional physical time-series prior template on anomalous data points, forcing the implicit state vector of the state-space backbone network to move closer to the template state vector. Step 6-5: During the normal aging phase when the physical anomaly detection module does not output any control signals, adjust the weighting coefficients. Set as an intermediate weight value that is dynamically adjusted based on the current number of aging cycles. intermediate weight value Preferring higher weight values ​​in the early stages of aging To strengthen physical prior guidance, the model is gradually reduced in the later stages of aging to increase the degree of freedom of the model to fit data features; Step 6-6: The weighted coefficients are then... The physical prior deviation penalty term, which is dynamically weighted, is added to the data fidelity term to obtain the final loss value at the current time step. The final loss value is then backpropagated to each trainable parameter of the state space backbone network to achieve a dynamic trade-off between physical consistency and data fidelity.

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