Monotonic drop teacher and short residual student corrected lithium battery capacity degradation prediction method

Abstract

The application discloses a lithium battery capacity degradation prediction method of monotone drop teacher and short residual student correction, and relates to the technical field of lithium battery life prediction.The application takes a historical capacity observation sequence as input, predicts future capacity drop amounts at each step through a monotone drop teacher model, generates an overall non-increasing basic capacity trajectory through non-negative mapping and cumulative decoding, further constructs a short residual student branch, fuses an auxiliary state vector and the teacher basic trajectory, outputs a local residual correction amount with a limited amplitude, and obtains a final capacity prediction sequence through monotone post-processing.The application simultaneously considers capacity degradation main trend constraints, local error controlled compensation, rolling prediction stability and cross-condition generalization capability, and is suitable for lithium battery state of health evaluation, life end determination and remaining useful life estimation of electric vehicles, energy storage power stations and portable electronic devices.

Description

Technical Field

[0001] This invention relates to the field of lithium battery life prediction technology, specifically a lithium battery capacity degradation prediction method corrected by monotonic drop teacher and short residual student. Background Technology

[0002] With the rapid development of new energy vehicles, energy storage systems, and portable electronic devices, lithium batteries have become one of the most widely used electrochemical energy storage devices due to their advantages such as high energy density, long cycle life, and good power performance. During long-term charge-discharge cycles, irreversible aging reactions continuously occur inside lithium batteries, such as active lithium loss, electrode material structure degradation, electrolyte decomposition, and increased internal resistance. These aging processes lead to a gradual decline in the battery's usable capacity, thereby affecting the device's range, operational reliability, and safety. Therefore, accurately predicting the capacity degradation trajectory of lithium batteries is of great significance for battery health management, operation and maintenance decisions, lifespan determination, and remaining service life estimation.

[0003] Existing methods for predicting lithium battery capacity degradation are mainly divided into two categories: mechanistic models and data-driven methods. Mechanistic models rely on many prior assumptions and precise parameter identification, which limits their applicability under complex operating conditions and results in high computational costs. Data-driven methods use deep learning models to uncover nonlinear relationships in capacity sequences, exhibiting stronger fitting capabilities, but they still have the following shortcomings in practical applications: First, capacity degradation follows a physical law of overall irreversible decline. However, existing methods directly regress to future capacity points, lacking explicit constraints on the relationship between predicted steps. This can easily lead to local jaggedness, incoordination between steps, or even non-physical rebounds, affecting the stability of lifetime determination.

[0004] Second, capacity curves exhibit local fluctuations and periodic turning points, making it difficult to accurately fit key intervals by only emphasizing the overall trend. If the introduced residual correction lacks amplitude constraints, it can easily disrupt the overall degradation path, leading to over-correction.

[0005] Third, during the rolling forecasting process, the reinjection of historical forecast values ​​can lead to the accumulation and propagation of errors, resulting in trajectory deviations and misjudgments of the endpoint.

[0006] Therefore, this invention proposes a method for predicting lithium battery capacity degradation using monotonic drop teacher and short residual student correction. Summary of the Invention

[0007] The purpose of this invention is to provide a method for predicting lithium battery capacity degradation using monotonic drop teacher and short residual student correction, in order to solve the problems mentioned in the background art.

[0008] According to a first aspect of the present invention, in order to achieve the above-mentioned objective, the present invention provides the following technical solution: a method for predicting lithium battery capacity degradation based on monotonic drop teacher and short residual student correction, comprising the following steps: Obtain the capacity degradation sequence of the target lithium battery and construct a historical observation window for the current prediction time based on a sliding window; The historical observation window is input into a pre-built monotonic drop teacher model. The monotonic drop teacher model solves the capacity drop parameters by predicting the future prediction steps, and generates a basic capacity prediction trajectory that satisfies the overall non-incremental constraint through non-negative mapping and cumulative decoding. The monotonic drop teacher model is constructed based on input mapping, position encoding, local convolution module, temporal encoding module and cyclic feature aggregation module. Based on the relative position of the current predicted time in the basic capacity degradation trajectory, the lifetime stage state variables are constructed, and the local degradation intensity state variables are constructed based on the local fluctuation intensity at the tail of the historical observation window. The lifetime stage state variables and the local degradation intensity state variables are concatenated to obtain the auxiliary state vector. Construct a short residual student correction branch, input the historical observation window into the short residual student correction branch, and fuse the auxiliary state vector and the basic capacity prediction trajectory to generate a local residual correction quantity limited by amplitude; The local residual correction is superimposed on the basic capacity prediction trajectory to obtain the preliminary correction trajectory. Then, a non-incremental constraint is applied to the preliminary correction trajectory through a monotonic post-processing mechanism to obtain the final capacity prediction sequence. Based on the final capacity prediction sequence and the preset capacity failure threshold, the prediction end point is determined by the rule that multiple consecutive prediction points are all below the failure threshold, and the remaining service life prediction value is calculated based on the prediction end point and the current prediction time. Specifically, a phased training strategy is adopted to train the monotonic falling teacher model and the short residual student correction branch, and a rolling prediction method driven by real observation is adopted in the inference stage.

[0009] Furthermore, the capacity degradation sequence of the target lithium battery is obtained, and a historical observation window for the current prediction time is constructed based on a sliding window, as follows: Obtain the capacity degradation sequence of the target lithium battery, denoted as: in, This represents the capacity degradation sequence of the target lithium battery. Indicates the first The capacity value corresponding to each cycle, Indicates the cycle number. This indicates the total number of cycles for the battery; At the current forecast time The construction length is Historical observation window Its expression is: in, Indicates the current prediction time The corresponding historical observation window, Indicates the current prediction time or the current cycle position. Indicates the length of the input window. This represents the current capacity observation value; Corresponding future The actual capacity label is: in, Indicates the current prediction time The corresponding future real capacity label sequence, Indicates the future prediction step size. Indicates the number of times after the current moment. The actual capacity value corresponding to each prediction step.

[0010] Furthermore, the historical observation window is input into a pre-constructed monotonic drop teacher model. The monotonic drop teacher model solves for the capacity drop parameters of each future prediction step by predicting them, and generates a basic capacity prediction trajectory that satisfies the overall non-incremental constraint through non-negative mapping and cumulative decoding, as follows: Historical observation window The input is fed into a monotonically decreasing teacher model, which extracts capacity degradation features through input mapping, positional encoding, local convolutional modules, temporal encoding modules, and recurrent feature aggregation modules to obtain the teacher's latent representation: in, This represents the temporal latent features extracted by the monotonically falling teacher model at the current prediction time. The superscript represents the feature encoding function of the teacher model. Indicates the branch of the teacher model; Based on the teacher's implicit representation, the teacher model outputs the original fall parameter vectors for each future prediction step: in, This represents the original fall parameter vector for each future prediction step output by the teacher model. This represents the drop parameter mapping function of the teacher model. Indicates the first The original drop parameters corresponding to each prediction step; The original drop parameters are converted into future capacity drop values ​​using nonnegative mapping: in, Indicates the current prediction time Next The capacity drop corresponding to each future forecast step. This indicates the upper limit of the single-step capacity drop. This represents the Sigmoid nonlinear mapping function; Based on the last actual observation capacity of the current window By cumulatively decoding the capacity drop at each step in the future, the teacher's basic prediction trajectory is obtained: in, The teacher model represents the first The basic predicted value of the cycle capacity, This represents the actual capacity observation at the end of the current window. Indicates the first Capacity drop corresponding to each prediction step Indicates the cumulative summation index; This yields the teacher base capacity prediction sequence: in, This represents the basic capacity prediction sequence output by the teacher model. The teacher model indicates that in the future... The basic capacity prediction value corresponding to each prediction step; Due to the capacity drop in each step All values ​​are non-negative, therefore the teacher's basic prediction trajectory satisfies the overall non-increasing constraint: in, to These represent the first to the second steps of the teacher model's output, respectively. Basic capacity prediction value.

[0011] Furthermore, based on the relative position of the current predicted time within the basic capacity degradation trajectory, a lifetime stage state variable is constructed, and a local degradation intensity state variable is constructed based on the local fluctuation intensity at the tail of the historical observation window. The lifetime stage state variable and the local degradation intensity state variable are concatenated to obtain an auxiliary state vector, as follows: Based on the relative position of the current predicted time within the entire capacity degradation trajectory, construct the lifetime stage state variables: in, This indicates the relative position of the current prediction window within the entire battery life trajectory. Indicates the current prediction time. This represents the total number of cycles in the target battery capacity sequence; According to the latest at the end of the window The mean of the first-order differences of each capacity point is used to construct the local degradation intensity state quantity: in, Indicates the local degradation intensity near the tail of the window. This represents the window length used to calculate the local degradation intensity. and These represent the capacity values ​​of the adjacent loops near the end of the current window. Indicates the summation index; By concatenating the state variables of the lifetime stage and the state variables of the local degradation intensity, we obtain the auxiliary state vector: in, This represents the auxiliary state vector corresponding to the current prediction time. Used to characterize the degradation stage of the current prediction window. Used to characterize the intensity of local degradation fluctuations near the tail of the window.

[0012] Furthermore, a short residual student correction branch is constructed, the historical observation window is input into the short residual student correction branch, and the auxiliary state vector and the basic capacity prediction trajectory are fused to generate a local residual correction quantity limited by amplitude, as follows: Historical observation window Inputting into the short residual student branch yields the student-side temporal feature representation: in, This represents the temporal feature representation extracted by the short residual student branch at the current prediction time. The feature encoding function representing the student branch, superscript Indicates a student branch; Globally aggregate the temporal features on the student side and combine them with the auxiliary state vector. Teacher's basic prediction trajectory Feature fusion is performed to obtain local correction features: in, This represents the fused feature vector used for local residual correction. This represents the global pooling operation performed on the time-series features on the student side. Indicates feature concatenation operation; Based on the local correction feature, the student branch outputs the original residual vector for each future step: in, This represents the vector of original residual parameters for each prediction step in the future output of the student branch. The residual mapping function represents the student branch. Indicates the first The original residual parameters corresponding to each prediction step; Applying hyperbolic tangent constraints and magnitude scaling to the original residual vector yields constrained short residuals: in, Indicates the first The short residual correction amount corresponding to each prediction step Indicates the upper bound of the residual amplitude. Represents the hyperbolic tangent function; The short residual correction is superimposed onto the teacher's basic prediction trajectory to obtain the preliminary corrected trajectory: in, Represents the th after superposition of residuals Preliminary correction value for cycle capacity, Indicates the residual injection coefficient. This represents the first branch output of the student. Short residual correction for each prediction step.

[0013] Furthermore, the local residual correction is superimposed on the basic capacity prediction trajectory to obtain a preliminary correction trajectory. Then, a non-increasing constraint is applied to the preliminary correction trajectory through a monotonic post-processing mechanism to obtain the final capacity prediction sequence, as follows: For the first prediction point, the final predicted value is defined as: in, This represents the first predicted future capacity value in the final output. This represents the actual capacity observation at the end of the current window. This represents the first preliminary correction value for future capacity after residual stacking. This indicates the operation of taking the smaller value; For the remaining prediction points, the final predicted value is recursively defined as: in, This indicates the final output number. One future capacity forecast value, This represents the final capacity prediction value from the previous prediction step. Indicates the first Preliminary correction values ​​for each prediction step; This yields the final capacity prediction sequence: in, Indicates the current prediction time The final capacity prediction sequence is as follows. to These represent steps 1 to 2 respectively. The final capacity prediction for the step.

[0014] Furthermore, a phased training strategy is adopted to train the monotonically falling teacher model and the short residual student correction branch, as follows: First, a monotonic drop teacher model is trained to learn a stable baseline capacity degradation trajectory. Then, the teacher model parameters are frozen, and only the short residual student branch is trained, allowing it to learn local error compensation around the teacher's baseline prediction trajectory. In the teacher phase, construct the teacher prediction loss function: In the formula, This represents the total loss function during the teacher phase. Indicates the first Error weights for each prediction step, This represents the point-by-point prediction error function. The output of the teacher model represents the first... A basic forecast of future capacity. This represents the corresponding actual capacity value. This represents a monotonic consistency auxiliary constraint term. Indicates the weight of the monotonic consistency constraint; After the teacher model is trained, the teacher model parameters are frozen, and the difference between the teacher's base prediction and the actual capacity value is used as the target residual for student branch learning. in, Indicates the first The target residual for each prediction step Indicates the first The actual capacity value corresponding to each future prediction step. This represents the baseline capacity prediction value output by the teacher model; During the student phase, a loss function for the student phase is constructed: in, This represents the total loss function during the student's academic journey. This represents the final capacity prediction value after short residual correction and monotonic post-processing. This represents the corresponding actual capacity value. This represents the residual alignment error function. This represents the short residual correction amount output by the student branch. Indicates the target residual. Indicates the weight of the residual alignment term. This represents the weight of the residual regularization term.

[0015] Furthermore, a rolling prediction mechanism driven by real observations is constructed, as follows: When the new cycle capacity observation value Upon arrival, delete the earliest capacity point in the original history window. and the latest actual capacity observations Write to the end of the window to obtain the input window for the next prediction time: in, This indicates the historical observation window corresponding to the next prediction time. This indicates the first capacity point in the updated window. This represents the latest observed actual capacity value.

[0016] Furthermore, based on the final capacity prediction sequence and the preset capacity failure threshold, the predicted lifetime end point is determined by a rule that multiple consecutive prediction points are all below the failure threshold. The remaining lifetime prediction value is then calculated based on the predicted lifetime end point and the current prediction time, as follows: The lithium battery capacity decays to its initial capacity. preset ratio The corresponding cycle position is defined as the end of the lifespan, and the failure threshold is expressed as: in, Indicates the capacity failure threshold. This represents the capacity failure ratio. Indicates the initial capacity of the target lithium battery; During the rolling inference process, based on the current prediction time... The corresponding final capacity prediction sequence is used as input, and the final capacity prediction value corresponding to each prediction step is extracted. When there is a continuous sequence... The final capacity prediction values ​​at each cycle position are all lower than or equal to the capacity failure threshold. When the first cycle position in this continuous interval is determined as the predicted lifetime end, its expression is: in, Indicates the cycle position corresponding to the predicted end of life. Indicates the number of consecutive threshold determination points. to Indicates continuity The predicted capacity value corresponding to each cycle position; At the current forecast time The predicted remaining useful life is expressed as: in, Indicates the current prediction time The remaining useful life is predicted below. Indicates the predicted end of life. Indicates the current prediction time.

[0017] According to a second aspect of the present invention, the present invention provides a lithium battery capacity degradation prediction system with monotonic drop teacher and short residual student correction, for implementing the lithium battery capacity degradation prediction method with monotonic drop teacher and short residual student correction described in Embodiment 1, comprising: The data acquisition and window construction module is used to obtain the capacity degradation sequence of the target lithium battery and construct the historical observation window for the current prediction time based on the sliding window. The basic capacity prediction trajectory generation module is used to input the historical observation window into a pre-constructed monotonic drop teacher model. The monotonic drop teacher model solves by predicting the capacity drop parameters of each prediction step in the future, and generates a basic capacity prediction trajectory that satisfies the overall non-incremental constraint through non-negative mapping and cumulative decoding. The monotonic drop teacher model is constructed based on input mapping, position encoding, local convolution module, temporal encoding module and cyclic feature aggregation module. The auxiliary state vector construction module is used to construct the lifetime stage state quantity based on the relative position of the current prediction time in the basic capacity degradation trajectory, and to construct the local degradation intensity state quantity based on the local fluctuation intensity at the tail of the historical observation window. The lifetime stage state quantity and the local degradation intensity state quantity are concatenated to obtain the auxiliary state vector. The short residual student correction branch construction module is used to construct the short residual student correction branch. The historical observation window is input into the short residual student correction branch, and the auxiliary state vector and the basic capacity prediction trajectory are fused to generate the local residual correction amount with amplitude limitation. The monotonic post-processing module is used to superimpose the local residual correction amount onto the basic capacity prediction trajectory to obtain a preliminary correction trajectory, and then apply non-incremental constraints to the preliminary correction trajectory through the monotonic post-processing mechanism to obtain the final capacity prediction sequence. The lifetime prediction and output module is used to determine the predicted lifetime end point based on the final capacity prediction sequence and the preset capacity failure threshold, using the rule that multiple consecutive prediction points are all below the failure threshold, and to calculate the remaining lifetime prediction value based on the predicted lifetime end point and the current prediction time. The phased training module is used to train the monotonically falling teacher model and the short residual student correction branch using a phased training strategy, and adopts a rolling prediction method driven by real observations during the inference phase.

[0018] The present invention has at least the following beneficial effects: 1. This invention constructs a monotonically decreasing teacher model that, instead of directly regressing future capacity values, predicts the non-negative capacity drop in each future step and performs cumulative decoding based on the current actual capacity. This ensures that the basic prediction trajectory naturally satisfies the overall non-increasing constraint in its mathematical structure. This design fundamentally suppresses common phenomena in multi-step prediction, such as local jaggedness, inter-step inconsistency, and non-physical recovery, guaranteeing that the prediction results conform to the fundamental physical law of irreversible capacity degradation in lithium batteries.

[0019] 2. This invention introduces a short residual student correction branch to perform localized corrections on the teacher's baseline trajectory with limited amplitude. By restricting the residual output range through the hyperbolic tangent function and the upper bound of the amplitude, the correction amount is always kept within a small range. This effectively compensates for prediction biases near local fluctuation intervals, stage inflection points, and the end of the lifespan, without excessively disturbing the overall degradation trend, thus achieving a synergy between maintaining global monotonicity and improving local fitting accuracy.

[0020] 3. This invention further incorporates a monotonic post-processing mechanism after residual superposition, forcibly restoring the non-incremental nature of the predicted trajectory through a recursive minimum operation. This mechanism ensures that even if the student branch produces a slight upward adjustment, the final output capacity sequence still strictly satisfies the requirement that the capacity does not increase with the progression of the loop, eliminating the risk of non-physical rebound that may be caused by the correction process, and making the prediction results more reliable in engineering.

[0021] 4. This invention employs a phased strategy of first training the teacher, then freezing the teacher model, and finally training the student model. The teacher model prioritizes learning stable principal degradation trends, while the student model only learns local residual compensation based on a fixed teacher model, avoiding mutual interference between principal trend modeling and local detail fitting. This training method significantly improves the convergence stability and prediction reliability of the joint model while reducing its sensitivity to hyperparameters.

[0022] 5. This invention employs a real-observation-driven rolling inference mechanism. During the online application phase, only the latest real capacity observations are used to update the historical input window, strictly prohibiting the backfeeding of historical model predictions to subsequent inputs. This design blocks the propagation and amplification path of prediction errors along the time axis, significantly reducing the risk of error accumulation during multi-step rolling prediction. Simultaneously, this invention combines continuous threshold crossing rules for lifespan endpoint determination, avoiding misjudgments caused by single-point capacity fluctuations, and providing more stable support for lithium battery health status assessment, lifespan early warning, and operation and maintenance decisions.

[0023] 6. This invention constructs an auxiliary description vector containing lifetime stage state variables and local degradation intensity state variables, and integrates it into the student branch. This mechanism enables the student branch to perceive whether the current sample is in the early, middle, or late degradation stage, as well as the intensity of local fluctuations near the end of the window, thereby applying differentiated residual corrections to samples under different operating conditions and at different degradation stages, improving the adaptability and accuracy of the correction.

[0024] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a schematic diagram of the prediction method described in this invention; Figure 2 This is a schematic diagram of the collaborative capacity prediction framework for monotonic drop teachers and students with short residuals in this invention. Figure 3 This is a diagram showing the capacity prediction results under the same-domain verification conditions of this invention; Figure 4 This is a graph showing the capacity prediction results under cross-dataset migration conditions of the present invention; Figure 5 This is a graph showing the capacity prediction results under cross-temperature migration conditions of the present invention; Figure 6 The diagram shows the effect of additional error recovery under different fixed step size conditions of the present invention. Detailed Implementation

[0027] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0028] Example 1: This embodiment takes the historical capacity observation sequence of the target lithium battery as input, predicts the capacity drop in each future step through a monotonic drop teacher model, and generates the overall non-increasing basic capacity degradation trajectory using a cumulative decoding method. On this basis, a short residual student correction branch is further constructed to compensate for the local residual of the teacher basic trajectory with limited amplitude. A monotonic post-processing mechanism is used to ensure that the final output trajectory still meets the capacity degradation direction constraint. This embodiment also combines an auxiliary state description, a phased training and a rolling inference mechanism driven by real observations to achieve stable prediction of the future capacity degradation trajectory, life end and remaining service life of the lithium battery.

[0029] Please see Figure 1 This invention provides a technical solution: a method for predicting lithium battery capacity degradation using monotonic drop teacher and short residual student correction, comprising the following steps: Step 1: Obtain the capacity degradation sequence of the target lithium battery, and construct a historical observation window for the current prediction time based on a sliding window. This window is used to organize the capacity degradation data of the target lithium battery into supervised learning samples that can be input into the model, as follows: Capacity observation data of the target lithium battery during the cycle aging process are obtained to form a capacity degradation sequence, denoted as: in, This represents the capacity degradation sequence of the target lithium battery. Indicates the first The capacity value corresponding to each cycle, Indicates the cycle number. This indicates the total number of cycles for the battery; At the current forecast time Extract the nearest value from the capacity sequence Construct a historical observation window using continuous capacity observations. Its expression is: in, Indicates the current prediction time The corresponding historical observation window, Indicates the current prediction time or the current cycle position. Indicates the length of the input window. This represents the capacity observation at the end of the current window; The future corresponding to this historical observation window The actual capacity label is recorded as follows: in, Indicates the current prediction time The corresponding future real capacity label sequence, Indicates the future prediction step size. Indicates the number of moments after the current prediction time. The actual capacity value corresponding to each prediction step; Through the above-described sliding window construction method, this embodiment converts the entire capacity degradation sequence into multiple training samples from historical capacity windows to future capacity trajectories, enabling the model to learn the mapping relationship between the historical capacity state of the target lithium battery and the future capacity degradation trend. Step 2: Input the historical observation window into the pre-constructed monotonic drop teacher model. The monotonic drop teacher model solves by predicting the capacity drop parameters of each future prediction step, and generates a basic capacity prediction trajectory that satisfies the overall non-incremental constraint through non-negative mapping and cumulative decoding. This is used to generate a basic capacity prediction trajectory that conforms to the overall capacity decay law of lithium batteries, as detailed below: Historical observation window The input is a monotonically decreasing teacher model. The teacher model extracts capacity degradation features through input mapping, positional encoding, local convolutional modules, temporal encoding modules, and recurrent feature aggregation modules to obtain the teacher-side temporal latent representation: in, This indicates that the monotonically falling teacher model is at the current prediction time. Extracted temporal latent features, The superscript represents the feature encoding function of the teacher model. Indicates the branch of the teacher model; Based on the teacher-side temporal implicit representation, the teacher model further outputs the original fall parameter vectors corresponding to each future prediction step: in, This represents the original fall parameter vector for each future prediction step output by the teacher model. This represents the drop parameter mapping function of the teacher model. Indicates the first The original drop parameters corresponding to each future prediction step; To ensure that the predicted trajectory conforms to the overall decline pattern of capacity degradation, this invention does not directly regress future capacity values, but instead first predicts the capacity drop at each future step. The original drop parameters are converted into capacity drop amounts through a non-negative mapping: in, Indicates the current prediction time Next The capacity drop corresponding to each future forecast step. This indicates the upper limit of the single-step capacity drop. This represents the Sigmoid nonlinear mapping function. Since the Sigmoid function outputs a non-negative value, therefore... Not less than zero; Subsequently, the actual capacity observation at the end of the current window was used. Starting from this point, the cumulative capacity drop in each future step is decoded to obtain the basic capacity prediction value of the teacher model: in, The teacher model represents the first The basic predicted value of the cycle capacity, This represents the actual capacity observation at the end of the current window. Indicates the first Capacity drop corresponding to each prediction step Indicates the cumulative summation index; This yields the teacher base capacity prediction sequence: in, This represents the basic capacity prediction sequence output by the teacher model. to These represent steps 1 to 2 respectively. The predicted value of the teacher base capacity in the step; Due to the capacity drop in each step All are non-negative, therefore the teacher's basic prediction trajectory satisfies the overall non-increasing constraint: in, to This represents the continuous future capacity baseline prediction value output by the teacher model. Through this design, the teacher model can structurally suppress local jaggedness, inter-step inconsistency, and non-physical rebound phenomena in multi-step prediction, providing a stable baseline degradation trajectory for subsequent local corrections; Step 3: Based on the relative position of the current predicted time in the basic capacity degradation trajectory, construct the lifetime stage state variables, and construct the local degradation intensity state variables based on the local fluctuation intensity at the tail of the historical observation window. Concatenate the lifetime stage state variables and the local degradation intensity state variables to obtain the auxiliary state vector. This stage is used to provide the student correction branch with information on the current degradation stage and local degradation intensity. Since the capacity error performance is different under different lifetime stages and different local fluctuations, relying solely on the historical capacity window may not be sufficient to fully characterize the current sample state. Therefore, an auxiliary state description vector is constructed. First, based on the relative position of the current predicted time within the entire capacity degradation trajectory, the lifetime stage state variables are constructed: in, This indicates the relative position of the current prediction window within the entire battery life trajectory. Indicates the current prediction time. This represents the total number of cycles in the target battery capacity sequence. This state variable is used to describe whether the current sample is in the early, middle, or late degradation stage. Secondly, based on the nearest window tail The mean of the first-order differences of each capacity point is used to construct the local degradation intensity state quantity: in, Indicates the local degradation intensity near the tail of the window. This represents the window length used to calculate the local degradation intensity. and These represent the capacity values ​​of the adjacent loops near the end of the current window. Indicates the summation index; By concatenating the state variables of the lifetime stage and the state variables of the local degradation intensity, an auxiliary state vector is obtained: in, This represents the auxiliary state vector corresponding to the current prediction time. Used to characterize the degradation stage of the current prediction window. Used to characterize the intensity of local degradation fluctuations near the tail of the window; By introducing this auxiliary state vector, the short residual student branch can perform more targeted error compensation by combining the current degradation stage and the intensity of local changes; Step 4: Construct a short residual student correction branch, input the historical observation window into the short residual student correction branch, and fuse the auxiliary state vector and the basic capacity prediction trajectory to generate a local residual correction amount limited by amplitude; This stage is used to correct local errors with limited amplitude based on the teacher's basic predicted trajectory. Although the monotonically falling teacher model can ensure that the basic capacity trajectory is non-increasing overall, there may still be some prediction bias in local fluctuation ranges, stage transition ranges, and near the end of life. Therefore, this embodiment constructs a short residual student correction branch to locally compensate for the teacher's basic trajectory, as follows: Historical observation window Input the short residual student branch to obtain the student-side temporal feature representation: in, This represents the temporal feature representation extracted by the short residual student branch at the current prediction time. The feature encoding function representing the student branch, superscript Indicates a student branch; Subsequently, the temporal features on the student side are globally aggregated and compared with the auxiliary state vector. Teacher's basic prediction trajectory By fusing the data, local correction features are obtained: in, This represents the fused feature vector used for local residual correction. This represents the global pooling operation performed on the time-series features on the student side. Indicates feature concatenation operation; Based on the local correction feature, the student branch outputs the original residual parameter vectors for each future step: in, This represents the vector of original residual parameters for each prediction step in the future output of the student branch. The residual mapping function represents the student branch. Indicates the first The original residual parameters corresponding to each prediction step; To avoid excessive corrections from the student branch, hyperbolic tangent constraints and magnitude scaling are applied to the original residual parameters to obtain constrained short residuals: in, Indicates the first The short residual correction amount corresponding to each prediction step Indicates the upper bound of the residual amplitude. This represents the hyperbolic tangent function. Through this constraint, the residual correction amount of the student branch output is limited to a finite range, avoiding excessive disturbance of the overall degradation trend by local corrections. The short residual correction is superimposed onto the teacher's basic prediction trajectory to obtain the preliminary corrected trajectory: in, Represents the th after superposition of residuals Preliminary correction value for cycle capacity, The output of the teacher model represents the first... One future forecast step of basic capacity forecast value Indicates the residual injection coefficient. This represents the first branch output of the student. Short residual correction for each prediction step; Through the aforementioned short residual student correction branch, this invention can improve local prediction accuracy by providing small-amplitude, constrained compensation for local biases while preserving the main degradation trend of the teacher model. Step 5: Superimpose the local residual correction amount onto the basic capacity prediction trajectory to obtain the preliminary correction trajectory, and then apply non-incremental constraints to the preliminary correction trajectory through a monotonic post-processing mechanism to obtain the final capacity prediction sequence. Since the short residual student branch will locally compensate the teacher's basic trajectory, the residual superposition may produce a slight non-physical rebound at individual prediction points. In this stage, a recursive monotonic post-processing is applied to the preliminary correction trajectory to ensure that the final prediction trajectory after student residual correction still satisfies the capacity degradation direction constraint. For the first future forecast point, the final capacity forecast is defined as: in, This represents the first predicted future capacity value in the final output. This represents the actual capacity observation at the end of the current window. This represents the first preliminary correction value for future capacity after residual stacking. This indicates the operation of taking the smaller value; For the remaining future prediction points, the final prediction value is determined using the following recursive method: in, This indicates the final output number. One future capacity forecast value, This represents the final capacity prediction value from the previous prediction step. Indicates the first Preliminary correction values ​​for each prediction step; This yields the final capacity prediction sequence: in, Indicates the current prediction time The final capacity prediction sequence is as follows. to These represent steps 1 to 2 respectively. The final capacity prediction for the step; Through the above monotonic post-processing mechanism, the final predicted trajectory remains non-increasing overall after short residual local correction, thus simultaneously satisfying the requirements of local error compensation and the rationality of degradation trend. Step 6: Train the monotonically falling teacher model and the short residual student correction branch using a phased training strategy; This embodiment does not use a fully synchronous training method for the teacher model and the student branch, but instead adopts a phased training strategy to improve the optimization stability of the teacher model and the student model. First, the monotonic falling teacher model is trained to learn a stable basic capacity degradation trajectory; then, the teacher model parameters are frozen and only the short residual student branch is trained to learn local error compensation around the teacher's basic prediction trajectory. In the teacher phase, construct the teacher prediction loss function: in, This represents the total loss function during the teacher phase. Indicates the first Error weights for each prediction step, This represents the point-by-point prediction error function. The output of the teacher model represents the first... A basic forecast of future capacity. This represents the corresponding actual capacity value. This represents a monotonic consistency auxiliary constraint term. Indicates the weight of the monotonic consistency constraint; After the teacher model is trained, the teacher model parameters are frozen, and the difference between the teacher's base prediction and the actual capacity value is used as the target residual for student branch learning. in, Indicates the first The target residual for each prediction step Indicates the first The actual capacity value corresponding to each future prediction step. This represents the baseline capacity prediction value output by the teacher model; During the student phase, a loss function for the student phase is constructed: in, This represents the total loss function during the student's academic journey. This represents the final capacity prediction value after short residual correction and monotonic post-processing. This represents the corresponding actual capacity value. This represents the residual alignment error function. This represents the short residual correction amount output by the student branch. Indicates the target residual. Indicates the weight of the residual alignment term. Indicates the weight of the residual regularization term; Through this phased training method, the teacher model prioritizes learning the main trend path that conforms to the capacity degradation law, while the student branch then learns the local errors that the teacher model cannot cover, thereby reducing the mutual interference between main trend modeling and local correction and improving the stability of the overall prediction framework. Step 7: Constructing a Real Observation-Driven Rolling Inference Mechanism In practical applications, the target lithium battery will continuously generate new capacity observations as the cycle progresses. This embodiment uses a real observation-driven rolling inference mechanism to update the historical window, in order to reduce the risk of error accumulation in multi-step rolling prediction during the online or testing phase. When the new cycle capacity observation value Upon arrival, delete the earliest capacity point in the original history window. and the latest actual capacity observations Write to the end of the window to obtain the input window for the next prediction time: in, This indicates the historical observation window corresponding to the next prediction time. This indicates the first capacity point in the updated window. This represents the latest observed actual capacity value; In this rolling inference process, the input window consists only of the actual capacity observations or the preprocessed capacity observations, and the model's historical predictions are not used as subsequent inputs. This design can prevent prediction errors from propagating and amplifying along the rolling input link, thereby improving the stability of the multi-step prediction process. Step 8: Establishment of the mechanism for determining end-of-life and calculating remaining useful life This stage is used to further convert the capacity degradation prediction results into end-of-life and remaining useful life results; The lithium battery capacity decays to its initial capacity. preset ratio The corresponding cycle position is defined as the end of the lifespan, and the failure threshold is expressed as: in, Indicates the capacity failure threshold. This represents the capacity failure ratio. Indicates the initial capacity of the target lithium battery; To reduce the impact of fluctuations at a single prediction point on the determination of the lifespan end, this invention employs continuous... The rule that a predicted lifetime end is determined when the predicted point is below the failure threshold. During the rolling inference process, the final capacity prediction sequence corresponding to each prediction time t is used as input to extract the final capacity prediction value of each prediction step. When there are M consecutive cycle positions where the final capacity prediction value is below the capacity failure threshold, the prediction is considered complete. At that time, output the predicted end of lifetime: in, Indicates the cycle position corresponding to the predicted end of life. Indicates the number of consecutive threshold determination points. to Indicates continuity The predicted capacity value corresponding to each cycle position; At the current forecast time The predicted remaining useful life is expressed as: in, Indicates the current prediction time The remaining useful life is predicted below. Indicates the predicted end of life. Indicates the current prediction time; Through the above-mentioned end-of-life determination and remaining lifespan calculation mechanism, this embodiment can further transform the capacity degradation trajectory prediction results into lifespan indicators that can be used for battery health management, lifespan early warning, and operation and maintenance decisions.

[0030] The technical solution of this invention will be further elaborated below with specific examples: The following description, using data from NASA's lithium battery aging dataset, the Center for Advanced Life Cycle Engineering (CALCE) lithium battery aging dataset from a university, and the Oxford Battery Degradation Dataset, further illustrates the specific implementation of this invention.

[0031] This implementation plan mainly focuses on the prediction of capacity degradation in the same domain, the prediction of migration across datasets and across temperatures, and the ablation verification of student modules with fixed step size and short residuals, so as to illustrate the applicability and engineering application potential of the present invention under different degradation modes, different data sources and distribution offset scenarios.

[0032] A. Unified Description of Experimental Datasets Step 1: Selection of Experimental Dataset and Description of Subjects This implementation scheme selects three publicly available lithium battery aging datasets—NASA, CALCE, and Oxford—as experimental data sources. The NASA dataset uses four lithium batteries (B0005, B0006, B0007, and B0018) that exhibit significant local fluctuations and non-stationary changes during capacity degradation, which can be used to verify the invention's ability to predict complex fluctuating degradation trajectories. The CALCE dataset uses four lithium batteries (CS2_35, CS2_36, CS2_37, and CS2_38) whose capacity degradation process is relatively stable, which can be used to verify the invention's ability to track stable degradation trends. The Oxford dataset uses Cell1 to Cell4 as representative test objects. This dataset operates under high temperature conditions and can be used to verify the invention's generalization performance across temperature ranges and complex operating conditions. These three datasets differ significantly in capacity degradation morphology, temperature conditions, and data distribution, providing diverse verification scenarios for the invention's in-domain prediction, cross-dataset transfer, and cross-temperature prediction.

[0033] To make the experimental subjects and uses clearer, Table 1 provides basic information about the dataset used in this implementation plan.

[0034] Table 1 Overview of the lithium battery aging dataset used in the examples Step 2: Standardize data processing and evaluation criteria To ensure the comparability of experimental results across different datasets, this implementation plan uniformly uses the capacity degradation sequence as the characterization of battery health status, and uses a sliding window approach to construct historical observation inputs and future capacity labels. During the model training phase, the capacity sequence is normalized based on the statistics of the training set, and the same normalization parameters are used for transformation during the testing phase to avoid leakage of test information. The evaluation metrics include root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²), which are used to measure the fitting accuracy between the capacity prediction curve and the actual capacity curve. At the same time, the absolute error at the end of life (AE) and the relative error at the end of life (RE) are used to measure the prediction deviation at the end of life, so as to comprehensively evaluate the capacity trajectory prediction capability and life determination reliability of the present invention.

[0035] B. Experimental Verification and Result Analysis Step 1: Validation of Co-domain Capacity Degradation Prediction This step is used to verify the capacity degradation prediction performance of the present invention under the same data distribution conditions. Experiments were conducted using the leave-one-out method within three datasets: NASA, CALCE, and Oxford. For each dataset, one battery was reserved as the test case, and the remaining batteries were used as training data, thus constructing independent test scenarios within the dataset. The training, validation, and test sets employed a consistent data processing flow, and capacity prediction results were generated during the testing phase using a rolling inference method driven by real observations.

[0036] Figure 2 The present invention provides a collaborative capacity prediction framework for monotonic falling teachers and students with short residuals.

[0037] Figure 3 Capacity prediction results for representative test cells under the same-domain verification condition are presented.

[0038] Specifically, Figure 3 The solid blue line represents the actual capacity degradation trajectory, the dashed orange line represents the capacity prediction trajectory obtained by this invention, the horizontal dashed blue line represents the 80% capacity failure threshold, and the magnified area is used to display the capacity fluctuation range and prediction details near the end of the lifetime. Figure 3 As can be seen, under the three same-domain test scenarios of NASA, CALCE, and Oxford, the predicted curves generally follow the downward direction of the actual capacity curve and maintain good trend consistency in the range close to the failure threshold. For samples with significant local fluctuations, although the prediction results show slight deviations near individual abrupt change points, no obvious non-physical rebound phenomenon is observed overall. This indicates that the present invention can effectively track local changes while maintaining the monotonic trend of capacity degradation. To further verify the above prediction effect from a quantitative perspective, Table 2 presents the capacity degradation prediction results under the same-domain verification conditions.

[0039] Table 2. Capacity degradation prediction results under co-domain verification conditions. As shown in Table 2, the present invention can track the actual capacity degradation trajectory well in the same-domain validation of the three datasets. For the CALCE dataset, where the capacity degradation process is relatively smooth, the differences in indicators among the tested batteries are small, indicating that the present invention has good fitting consistency under stable degradation scenarios. For the NASA dataset, which exhibits local fluctuations and non-stationary changes, the errors of B0006 and B0018 are relatively large, indicating that local fluctuations increase the prediction difficulty, but the present invention still maintains good overall trend tracking ability. For the Oxford dataset, Cell1, Cell3, and Cell4 show good prediction results, while Cell2 has a relatively low R², indicating that the local degradation pattern of this sample places higher demands on the model. Overall, the present invention can maintain relatively stable capacity trajectory prediction ability under the same-domain conditions and maintain relatively consistent judgment results near the end of the lifespan.

[0040] Step 2: Cross-dataset migration prediction validation This step is used to verify the generalization ability of the present invention when transferring data between different data sources. Two cross-dataset transfer tasks are constructed: NASA→CALCE and CALCE→NASA. NASA→CALCE means using the NASA dataset as the source domain training set and the CALCE dataset as the target domain test set; CALCE→NASA means using the CALCE dataset as the source domain training set and the NASA dataset as the target domain test set. During the testing phase, the model parameters are frozen, and inference is performed one by one on the target domain test cells.

[0041] Table 3 shows the experimental setup for cross-condition verification.

[0042] Table 3. Cross-condition verification experiment setup Specifically, Figure 4 The top-middle row shows the capacity prediction curves for B0005, B0006, B0007, and B0018 under the CALCE→NASA migration condition, while the bottom row shows the capacity prediction curves for CS2_35, CS2_36, CS2_37, and CS2_38 under the NASA→CALCE migration condition. In the figures, the solid blue line represents the actual capacity degradation trajectory, the dashed orange line represents the predicted trajectory, the horizontal dashed blue line represents the 80% capacity failure threshold, and the magnified boxes are used to show prediction details near the end of the lifespan and within local fluctuation ranges. Figure 4It can be seen that even when the training and test data sources are different, this invention can still maintain good consistency between the predicted trajectory and the actual capacity degradation direction. For the local fluctuations and short-term capacity rebounds observed in the NASA test battery, the predicted curve can follow the main degradation trend. For the relatively stable degradation process in the CALCE test battery, the predicted trajectory generally matches the actual trajectory well and can maintain a stable downward trend near the capacity failure threshold. This result, from a curve perspective, demonstrates that this invention still possesses good trend preservation and local tracking capabilities under cross-dataset migration conditions. To further quantify the above migration prediction performance, Table 4 presents the capacity degradation prediction results under cross-dataset migration conditions.

[0043] Table 4. Capacity degradation prediction results under cross-dataset migration conditions. As shown in Table 4, in the NASA→CALCE migration scenario, this invention maintains a high coefficient of determination and a small capacity prediction error across all tested cells in CALCE, indicating that it can learn transferable capacity degradation features from NASA data and maintain stable trend fitting ability in a relatively stable target domain. In the CALCE→NASA migration scenario, the errors for B0006 and B0018 are relatively large, indicating that the model's prediction difficulty increases when the target domain's capacity trajectory has stronger local fluctuations and non-stationary characteristics. Overall, this invention can still provide relatively stable capacity prediction results and lifetime end-of-life judgment results under normal temperature cross-dataset migration conditions.

[0044] Step 3: Validation of cross-temperature migration predictions This step is used to verify the predictive stability of the present invention under varying temperature conditions and degradation modes. Four types of cross-temperature transfer tasks are constructed: NASA→Oxford, CALCE→Oxford, Oxford→NASA, and Oxford→CALCE. The Oxford dataset is used as the target or source domain under 40°C conditions to examine the adaptability of the present invention when transferring between different temperature conditions.

[0045] Specifically, Figure 5The first two rows show the capacity prediction curves for Cell1 to Cell4 under the CALCE→Oxford and NASA→Oxford migration conditions, respectively. The last two rows show the capacity prediction curves for each test cell under the Oxford→CALCE and Oxford→NASA migration conditions, respectively. In the figures, the solid blue line represents the actual capacity degradation trajectory, the dashed orange line represents the predicted trajectory, the horizontal dashed blue line represents the 80% capacity failure threshold, and the magnified boxes are used to show the prediction details in the range approaching the failure threshold and in local fluctuation ranges. Figure 5 It can be seen that, even with different temperature conditions in the source and target domains, this invention can still maintain good consistency between the predicted trajectory and the actual capacity degradation direction. For the migration task with Oxford as the target domain, the prediction curve generally follows the capacity degradation trend, but Cell2 shows some deviation in local inflection points and near-threshold regions, indicating that this type of sample has a higher modeling difficulty under cross-temperature conditions. For the migration tasks from Oxford to CALCE and NASA, the prediction results generally maintain a stable downward trend and can maintain good trend tracking ability when there are local fluctuations in the target battery. This result, from the curve level, shows that this invention still has good degradation trend preservation ability and rolling prediction stability in cross-temperature migration scenarios. To further verify the above cross-temperature migration effect from the perspective of quantitative indicators, Table 5 shows the capacity degradation prediction results under cross-temperature migration conditions.

[0046] Table 5. Predicted capacity degradation under cross-temperature migration conditions Table 5 shows that, in the two types of tasks with Oxford as the target domain, the prediction results of Cell1, Cell3, and Cell4 are relatively stable, while Cell2 shows a more significant fitting deviation in both CALCE→Oxford and NASA→Oxford settings, indicating that this sample is more difficult to model under cross-temperature conditions. The results of Oxford→CALCE are generally stable, with small differences in indicators among the tested cells; the error fluctuations of Oxford→NASA are relatively more obvious, especially the relatively high lifetime endpoint errors for B0005 and B0007. The above results indicate that, under cross-temperature migration scenarios, the present invention can still maintain a good capacity trend fitting ability, but the local degradation morphology of the target domain will have a certain impact on the lifetime endpoint determination.

[0047] Step 4: Ablation verification of student modules with fixed step size and short residuals This step analyzes the impact of fixed submission step size variations and the short residual student correction module on prediction performance. Representative test subjects were selected for the experiment, and two modes were constructed: one using only the monotonically decreasing teacher model and the other incorporating the short residual student correction branch. Here, Teacher(T) represents rolling prediction using only the monotonically decreasing teacher backbone without student residual correction; TeacherShortResidual(TSR) represents adding a short residual student module to the teacher backbone to perform limited amplitude correction on the teacher output. The numbers 1, 3, and 6 represent fixed submission step sizes of 1, 3, and 6, respectively.

[0048] Table 6 shows the ablation experiment setup for student modules with fixed step size and short residuals.

[0049] Table 6 Ablation Experiment Setup for Fixed Step Size and Short Residual Student Modules Table 7 presents the capacity prediction error results under different fixed step size settings.

[0050] Table 7. Capacity prediction error results under different fixed step size settings To further analyze the compensation effect of the student module on the additional error brought about by the increase of fixed step size, Table 8 presents the results of the additional error recovery analysis under different fixed step size conditions.

[0051] Table 8 Results of Additional Error Recovery Analysis under Different Fixed Step Sizes Figure 6 The results of additional error recovery under different fixed step sizes are presented.

[0052] From Tables 6 to 8 and Figure 6 It can be seen that as the fixed submission step size increases, the overall rolling prediction error tends to increase, indicating that a longer step size exacerbates the accumulation of errors during the prediction process. After introducing the short residual student module, it can recover some of the additional errors under fixed step sizes of 3 and 6, with a more significant recovery effect at a fixed step size of 6. This suggests that the short residual student module mainly functions to compensate for the new errors in long-step rolling predictions. While its gain is relatively limited under short-step conditions, it has certain application value in long-step prediction scenarios that are closer to actual deployments.

[0053] C. Summary of Implementation Results The above experiments demonstrate that this invention possesses the following characteristics: First, it maintains relatively stable capacity degradation trajectory fitting capabilities on three datasets with different degradation modes: NASA, CALCE, and Oxford, indicating its applicability to capacity prediction tasks under conditions of stable degradation, local fluctuations, and complex temperatures. Second, it maintains good trend tracking capabilities across datasets and temperature transitions, demonstrating that the monotonically falling teacher model and short residual student correction mechanism contribute to improving cross-condition generalization. Third, ablation experiments show that the short residual student module can compensate for the increased prediction errors under longer fixed step sizes to a certain extent, thereby enhancing rolling prediction stability. In summary, this invention can provide effective technical support for lithium battery health status assessment, lifespan determination, remaining lifespan prediction, and lifespan early warning applications in battery management systems.

[0054] Example 2: This embodiment provides a lithium battery capacity degradation prediction system with monotonic drop teacher and short residual student correction, used to implement the lithium battery capacity degradation prediction method with monotonic drop teacher and short residual student correction described in Embodiment 1, including: The data acquisition and window construction module is used to obtain the capacity degradation sequence of the target lithium battery and construct the historical observation window for the current prediction time based on the sliding window. The basic capacity prediction trajectory generation module is used to input the historical observation window into a pre-constructed monotonic drop teacher model. The monotonic drop teacher model solves by predicting the capacity drop parameters of each prediction step in the future, and generates a basic capacity prediction trajectory that satisfies the overall non-incremental constraint through non-negative mapping and cumulative decoding. The monotonic drop teacher model is constructed based on input mapping, position encoding, local convolution module, temporal encoding module and cyclic feature aggregation module. The auxiliary state vector construction module is used to construct the lifetime stage state quantity based on the relative position of the current prediction time in the basic capacity degradation trajectory, and to construct the local degradation intensity state quantity based on the local fluctuation intensity at the tail of the historical observation window. The lifetime stage state quantity and the local degradation intensity state quantity are concatenated to obtain the auxiliary state vector. The short residual student correction branch construction module is used to construct the short residual student correction branch. The historical observation window is input into the short residual student correction branch, and the auxiliary state vector and the basic capacity prediction trajectory are fused to generate the local residual correction amount with amplitude limitation. The monotonic post-processing module is used to superimpose the local residual correction amount onto the basic capacity prediction trajectory to obtain a preliminary correction trajectory, and then apply non-incremental constraints to the preliminary correction trajectory through the monotonic post-processing mechanism to obtain the final capacity prediction sequence. The lifetime prediction and output module is used to determine the predicted lifetime end point based on the final capacity prediction sequence and the preset capacity failure threshold, using the rule that multiple consecutive prediction points are all below the failure threshold, and to calculate the remaining lifetime prediction value based on the predicted lifetime end point and the current prediction time. The phased training module is used to train the monotonically falling teacher model and the short residual student correction branch using a phased training strategy, and adopts a rolling prediction method driven by real observations during the inference phase.

[0055] In the description of this specification, the references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0056] The foregoing has shown and described the basic principles, main features, and advantages of this application. Those skilled in the art should understand that this application is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of this application. Various changes and modifications can be made to this application without departing from the spirit and scope thereof, and all such changes and modifications fall within the scope of the claims of this application.

Claims

1. A method for predicting lithium battery capacity degradation using monotonic drop teacher and short residual student correction, characterized in that, Includes the following steps: Obtain the capacity degradation sequence of the target lithium battery and construct a historical observation window for the current prediction time based on a sliding window; The historical observation window is input into a pre-built monotonic drop teacher model. The monotonic drop teacher model solves the capacity drop parameters by predicting the future prediction steps, and generates a basic capacity prediction trajectory that satisfies the overall non-incremental constraint through non-negative mapping and cumulative decoding. The monotonic drop teacher model is constructed based on input mapping, position encoding, local convolution module, temporal encoding module and cyclic feature aggregation module. Based on the relative position of the current predicted time in the basic capacity degradation trajectory, the lifetime stage state variables are constructed, and the local degradation intensity state variables are constructed based on the local fluctuation intensity at the tail of the historical observation window. The lifetime stage state variables and the local degradation intensity state variables are concatenated to obtain the auxiliary state vector. Construct a short residual student correction branch, input the historical observation window into the short residual student correction branch, and fuse the auxiliary state vector and the basic capacity prediction trajectory to generate a local residual correction quantity limited by amplitude; The local residual correction is superimposed on the basic capacity prediction trajectory to obtain the preliminary correction trajectory. Then, a non-incremental constraint is applied to the preliminary correction trajectory through a monotonic post-processing mechanism to obtain the final capacity prediction sequence. Based on the final capacity prediction sequence and the preset capacity failure threshold, the prediction end point is determined by the rule that multiple consecutive prediction points are all below the failure threshold, and the remaining service life prediction value is calculated based on the prediction end point and the current prediction time. Specifically, a phased training strategy is adopted to train the monotonic falling teacher model and the short residual student correction branch, and a rolling prediction method driven by real observation is adopted in the inference stage.

2. The lithium battery capacity degradation prediction method based on monotonic drop teacher and short residual student correction according to claim 1, characterized in that: Obtain the capacity degradation sequence of the target lithium battery, and construct a historical observation window for the current prediction time based on a sliding window, as follows: Obtain the capacity degradation sequence of the target lithium battery, denoted as: in, This represents the capacity degradation sequence of the target lithium battery. Indicates the first The capacity value corresponding to each cycle, Indicates the cycle number. This indicates the total number of cycles for the battery; At the current forecast time The construction length is Historical observation window Its expression is: in, Indicates the current prediction time The corresponding historical observation window, Indicates the current prediction time or the current cycle position. Indicates the length of the input window. This represents the current capacity observation value; Corresponding future The actual capacity label is: in, Indicates the current prediction time The corresponding future real capacity label sequence, Indicates the future prediction step size. Indicates the number of times after the current moment. The actual capacity value corresponding to each prediction step.

3. The lithium battery capacity degradation prediction method based on monotonic drop teacher and short residual student correction according to claim 1, characterized in that: The historical observation window is input into a pre-built monotonic drop teacher model. The monotonic drop teacher model solves for the capacity drop parameters by predicting each future prediction step, and generates a basic capacity prediction trajectory that satisfies the overall non-increasing constraint through non-negative mapping and cumulative decoding, as follows: Historical observation window The input is fed into a monotonically decreasing teacher model, which extracts capacity degradation features through input mapping, positional encoding, local convolutional modules, temporal encoding modules, and recurrent feature aggregation modules to obtain the teacher's latent representation: in, This represents the temporal latent features extracted by the monotonically falling teacher model at the current prediction time. The superscript represents the feature encoding function of the teacher model. Indicates the branch of the teacher model; Based on the teacher's implicit representation, the teacher model outputs the original fall parameter vectors for each future prediction step: in, This represents the original fall parameter vector for each future prediction step output by the teacher model. This represents the drop parameter mapping function of the teacher model. Indicates the first The original drop parameters corresponding to each prediction step; The original drop parameters are converted into future capacity drop values ​​using nonnegative mapping: in, Indicates the current prediction time Next The capacity drop corresponding to each future forecast step. This indicates the upper limit of the single-step capacity drop. This represents the Sigmoid nonlinear mapping function; Based on the last actual observation capacity of the current window By cumulatively decoding the future capacity drop, we can obtain the teacher's basic prediction trajectory: in, The teacher model represents the first The basic predicted value of the cycle capacity, This represents the actual capacity observation at the end of the current window. Indicates the first Capacity drop corresponding to each prediction step Indicates the cumulative summation index; This yields the teacher base capacity prediction sequence: in, This represents the basic capacity prediction sequence output by the teacher model. Indicates the teacher model in the future The basic capacity prediction value corresponding to each prediction step; Due to the capacity drop in each step All values ​​are non-negative, therefore the teacher's basic prediction trajectory satisfies the overall non-increasing constraint: in, to These represent the first to the second steps of the teacher model output, respectively. Basic capacity prediction value.

4. The lithium battery capacity degradation prediction method based on monotonic drop teacher and short residual student correction according to claim 1, characterized in that: Based on the relative position of the current predicted time within the basic capacity degradation trajectory, a lifetime stage state variable is constructed, and a local degradation intensity state variable is constructed based on the local fluctuation intensity at the tail of the historical observation window. The lifetime stage state variable and the local degradation intensity state variable are concatenated to obtain an auxiliary state vector, as follows: Based on the relative position of the current predicted time within the entire capacity degradation trajectory, construct the lifetime stage state variables: in, This indicates the relative position of the current prediction window within the entire battery life trajectory. Indicates the current prediction time. This represents the total number of cycles in the target battery capacity sequence; According to the latest at the end of the window The mean of the first-order differences of each capacity point is used to construct the local degradation intensity state quantity: in, Indicates the local degradation intensity near the tail of the window. This represents the window length used to calculate the local degradation intensity. and These represent the capacity values ​​of the adjacent loops near the end of the current window. Indicates the summation index; By concatenating the state variables of the lifetime stage and the state variables of the local degradation intensity, we obtain the auxiliary state vector: in, This represents the auxiliary state vector corresponding to the current prediction time. Used to characterize the degradation stage of the current prediction window. Used to characterize the intensity of local degradation fluctuations near the tail of the window.

5. The lithium battery capacity degradation prediction method based on monotonic drop teacher and short residual student correction according to claim 1, characterized in that: A short residual student correction branch is constructed, the historical observation window is input into the short residual student correction branch, and the auxiliary state vector and the basic capacity prediction trajectory are fused to generate a local residual correction quantity with amplitude limitations, as follows: Historical observation window Inputting into the short residual student branch yields the student-side temporal feature representation: in, This represents the temporal feature representation extracted by the short residual student branch at the current prediction time. The feature encoding function representing the student branch, superscript Indicates a student branch; Globally aggregate the temporal features on the student side and combine them with the auxiliary state vector. Teacher's basic prediction trajectory Feature fusion is performed to obtain local correction features: in, This represents the fused feature vector used for local residual correction. This represents the global pooling operation performed on the time-series features on the student side. Indicates feature concatenation operation; Based on the local correction feature, the student branch outputs the original residual vector for each future step: in, This represents the vector of original residual parameters for each prediction step in the future output of the student branch. The residual mapping function represents the student branch. Indicates the first The original residual parameters corresponding to each prediction step; Applying hyperbolic tangent constraints and magnitude scaling to the original residual vector yields constrained short residuals: in, Indicates the first The short residual correction amount corresponding to each prediction step Indicates the upper bound of the residual amplitude. Represents the hyperbolic tangent function; The short residual correction is superimposed onto the teacher's basic prediction trajectory to obtain the preliminary corrected trajectory: in, Represents the th after superposition of residuals Preliminary correction value for cycle capacity, Indicates the residual injection coefficient. This represents the first branch output of the student. Short residual correction for each prediction step.

6. The lithium battery capacity degradation prediction method based on monotonic drop teacher and short residual student correction according to claim 5, characterized in that: The local residual correction is superimposed onto the basic capacity prediction trajectory to obtain a preliminary correction trajectory. Then, a non-increasing constraint is applied to the preliminary correction trajectory through a monotonic post-processing mechanism to obtain the final capacity prediction sequence, as follows: For the first prediction point, the final predicted value is defined as: in, This represents the first predicted future capacity value in the final output. This represents the actual capacity observation at the end of the current window. This represents the first preliminary correction value for future capacity after residual stacking. This indicates the operation of taking the smaller value; For the remaining prediction points, the final predicted value is recursively defined as: in, This indicates the final output number. One future capacity forecast value, This represents the final capacity prediction value from the previous prediction step. Indicates the first Preliminary correction values ​​for each prediction step; This yields the final capacity prediction sequence: in, Indicates the current prediction time The final capacity prediction sequence is as follows. to These represent steps 1 to 2 respectively. The final capacity prediction for the step.

7. The lithium battery capacity degradation prediction method based on monotonic drop teacher and short residual student correction according to claim 1, characterized in that: A phased training strategy is adopted to train the monotonically falling teacher model and the short residual student correction branch, as follows: First, a monotonic drop teacher model is trained to learn a stable baseline capacity degradation trajectory. Then, the teacher model parameters are frozen, and only the short residual student branch is trained, allowing it to learn local error compensation around the teacher's baseline prediction trajectory. In the teacher phase, construct the teacher prediction loss function: In the formula, This represents the total loss function during the teacher phase. Indicates the first Error weights for each prediction step, This represents the point-by-point prediction error function. The output of the teacher model represents the first... A basic forecast of future capacity. This represents the corresponding actual capacity value. This represents a monotonic consistency auxiliary constraint term. Indicates the weight of the monotonic consistency constraint; After the teacher model is trained, the teacher model parameters are frozen, and the difference between the teacher's base prediction and the actual capacity value is used as the target residual for student branch learning. in, Indicates the first The target residual for each prediction step Indicates the first The actual capacity value corresponding to each future prediction step. This represents the baseline capacity prediction value output by the teacher model; During the student phase, a loss function for the student phase is constructed: in, This represents the total loss function during the student's academic journey. This represents the final capacity prediction value after short residual correction and monotonic post-processing. This represents the corresponding actual capacity value. This represents the residual alignment error function. This represents the short residual correction amount of the student branch output. Indicates the target residual. Indicates the weight of the residual alignment term. This represents the weight of the residual regularization term.

8. The lithium battery capacity degradation prediction method based on monotonic drop teacher and short residual student correction according to claim 7, characterized in that, A rolling prediction mechanism driven by real observations is constructed, as follows: When the new cycle capacity observation value Upon arrival, delete the earliest capacity point in the original history window. and the latest actual capacity observations Write to the end of the window to obtain the input window for the next prediction time: in, This indicates the historical observation window corresponding to the next prediction time. This indicates the first capacity point in the updated window. This represents the latest observed actual capacity value.

9. The lithium battery capacity degradation prediction method based on monotonic drop teacher and short residual student correction according to claim 1, characterized in that, Based on the final capacity prediction sequence and the preset capacity failure threshold, the predicted lifetime end is determined by the rule that multiple consecutive prediction points are all below the failure threshold. The remaining lifetime prediction value is then calculated based on the predicted lifetime end and the current prediction time, as follows: The lithium battery capacity decays to its initial capacity. preset ratio The corresponding cycle position is defined as the end of the lifespan, and the failure threshold is expressed as: in, Indicates the capacity failure threshold. This represents the capacity failure ratio. Indicates the initial capacity of the target lithium battery; During the rolling inference process, based on the current prediction time... The corresponding final capacity prediction sequence is used as input, and the final capacity prediction value corresponding to each prediction step is extracted. When there is a continuous sequence... The final capacity prediction values ​​at each cycle position are all lower than or equal to the capacity failure threshold. When the first cycle position in this continuous interval is determined as the predicted lifetime end, its expression is: in, Indicates the cycle position corresponding to the predicted end of life. Indicates the number of consecutive threshold determination points. to Indicates continuity The predicted capacity value corresponding to each cycle position; At the current forecast time The predicted remaining useful life is expressed as: in, Indicates the current prediction time The remaining useful life is predicted below. Indicates the predicted end of life. Indicates the current prediction time.

10. A lithium battery capacity degradation prediction system with monotonic drop teacher and short residual student correction, used to implement the lithium battery capacity degradation prediction method with monotonic drop teacher and short residual student correction as described in any one of claims 1 to 9, characterized in that, include: The data acquisition and window construction module is used to obtain the capacity degradation sequence of the target lithium battery and construct the historical observation window for the current prediction time based on the sliding window. The basic capacity prediction trajectory generation module is used to input the historical observation window into a pre-constructed monotonic drop teacher model. The monotonic drop teacher model solves by predicting the capacity drop parameters of each prediction step in the future, and generates a basic capacity prediction trajectory that satisfies the overall non-incremental constraint through non-negative mapping and cumulative decoding. The monotonic drop teacher model is constructed based on input mapping, position encoding, local convolution module, temporal encoding module and cyclic feature aggregation module. The auxiliary state vector construction module is used to construct the lifetime stage state quantity based on the relative position of the current prediction time in the basic capacity degradation trajectory, and to construct the local degradation intensity state quantity based on the local fluctuation intensity at the tail of the historical observation window. The lifetime stage state quantity and the local degradation intensity state quantity are concatenated to obtain the auxiliary state vector. The short residual student correction branch construction module is used to construct the short residual student correction branch. The historical observation window is input into the short residual student correction branch, and the auxiliary state vector and the basic capacity prediction trajectory are fused to generate the local residual correction amount with amplitude limitation. The monotonic post-processing module is used to superimpose the local residual correction amount onto the basic capacity prediction trajectory to obtain a preliminary correction trajectory, and then apply non-incremental constraints to the preliminary correction trajectory through the monotonic post-processing mechanism to obtain the final capacity prediction sequence. The lifetime prediction and output module is used to determine the predicted lifetime end point based on the final capacity prediction sequence and the preset capacity failure threshold, using the rule that multiple consecutive prediction points are all below the failure threshold, and to calculate the remaining lifetime prediction value based on the predicted lifetime end point and the current prediction time. The phased training module is used to train the monotonically falling teacher model and the short residual student correction branch using a phased training strategy, and adopts a rolling prediction method driven by real observations during the inference phase.

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