Prediction method of cross-granularity feature interaction and timing progressive cross-attention fusion

Abstract

The application belongs to the technical field of time series data prediction, and specifically discloses a prediction method of cross-granularity feature interaction and time series progressive cross attention fusion, comprising the following steps: extracting static features and dynamic features of original data through a multi-criteria feature selection framework; inputting the dynamic features into a time series progressive cross attention network; the time series progressive cross attention network captures multi-scale time series dependencies of time series features through a progressive window self-attention mechanism to obtain first time series features, and simultaneously performs cross attention calculation by taking the dynamic features as key-value pairs and the static features as queries through a static modulation cross attention mechanism to obtain second time series features; fusing the two to obtain time series representation with static context; inputting the time series representation with static context into a multi-scale fusion network to generate prediction results of multiple future time steps. The application can effectively improve the accuracy and stability of time series data prediction containing multiple cyclic change rules.

Description

Technical Field

[0001] This application belongs to the field of time series data prediction technology, and more specifically, relates to a prediction method that combines cross-granularity feature interaction and temporal progressive cross-attention fusion. Background Technology

[0002] Battery capacity prediction is a key technology in battery management systems. Accurate assessment of battery health and precise prediction of remaining lifespan have become core technological challenges for battery management systems. Accurate prediction of the capacity degradation curve of lithium-ion batteries is of great significance.

[0003] The importance of battery capacity prediction is multifaceted. Lithium-ion batteries may experience increased internal resistance and decreased thermal stability during aging, potentially leading to thermal runaway or even fire and explosion. The challenge in battery capacity prediction lies in the significant nonlinearity of the degradation process. It exhibits a monotonic decay trend over the long term, displays periodic fluctuations over the medium term, and is susceptible to noise disturbances in the short term. These multi-timescale degradation characteristics place higher demands on the model's prediction accuracy and robustness.

[0004] With the rise of data-driven approaches, early work primarily employed traditional machine learning algorithms such as support vector regression, Gaussian process regression, and random forests to construct predictive models by extracting statistical features from signals like voltage, current, and temperature. These methods perform well in small-sample scenarios, but feature engineering relies heavily on domain expert experience and struggles to fully extract the deeper information from raw time-series data.

[0005] In recent years, deep learning methods have made groundbreaking progress. Time series prediction models based on self-attention mechanisms achieve direct information interaction between any positions within a sequence through global self-attention, possessing the ability to capture arbitrary long-range dependencies. To address the computational complexity issue, researchers have proposed various improvement schemes, such as sparse attention, pyramid attention, or two-dimensional reshaping of time series data to improve the prediction efficiency of long sequences. Furthermore, researchers have achieved efficient long sequence modeling through frequency domain decomposition or wavelet transform, or designed cross-attention fusion mechanisms to achieve information interaction between exogenous and endogenous variables.

[0006] Despite the progress made by the above methods in time series modeling capabilities, the following limitations still exist: most existing methods adopt fixed-scale attention mechanisms or single-resolution feature extraction strategies, which are difficult to capture multi-timescale features of battery degradation; the utilization of inherent battery properties usually only involves feature concatenation or addition for fusion, failing to fully explore the differential modulation effect of static features on different degradation stages; and some high-performance models have high computational complexity, making them difficult to deploy on resource-constrained battery management system platforms.

[0007] Therefore, improving the accuracy and stability of time series forecasting is an urgent problem to be solved. Summary of the Invention

[0008] To address the shortcomings of existing technologies, the purpose of this application is to provide a prediction method that integrates cross-granularity feature interaction and temporal progressive cross-attention fusion, which can effectively improve the accuracy and stability of temporal prediction.

[0009] To achieve the above objectives, in a first aspect, this application provides a prediction method that integrates cross-granularity feature interaction and temporally progressive cross-attention fusion, comprising the following steps: S10, extract cross-granularity features through a multi-criteria feature selection framework. The cross-granularity features include static features and temporal features formed by merging the original temporal features and dynamic enhancement features. S20, the temporal features are input into a temporal progressive cross-attention network. The temporal progressive cross-attention network captures the multi-scale temporal dependencies of the dynamic features through a progressive window self-attention mechanism to obtain a first temporal feature. At the same time, through a static modulation cross-attention mechanism, the dynamic features are used as key-value pairs and the static features are used as queries to perform cross-attention calculation to obtain a second temporal feature. The first temporal feature and the second temporal feature are fused to obtain a temporal representation with static context. S30, the time-series representation with static context is input into the multi-scale fusion network to generate prediction results for multiple future time steps.

[0010] As a further preferred embodiment, in step S10, obtaining the static features includes: Candidate static features are extracted from time-series overview data using data analysis and physical modeling methods. A multi-criteria feature selection framework, incorporating mutual information, maximum information coefficient, and L1 regularized regression, is used to score the candidate static features. The scores from the three methods are then Min-Max normalized to [0,1], and the arithmetic mean is taken to obtain a comprehensive score. The top 15 dimensions are selected as static features based on their comprehensive scores in descending order. The formula for calculating mutual information is as follows: ; The formula for calculating the maximum information coefficient is as follows: ; The formula for calculating L1 regularized regression is: ; The formula for calculating the overall score is as follows: ; In the formula, x For the specific values ​​of the candidate static feature random variables; y To predict the specific values ​​of the target random variable; i The index number for the feature;X i For the first i The overall random variables of candidate static features; Y The target random variable for the prediction task; The joint probability distribution of features and targets. , For their respective marginal distributions; For a given grid, divide G Maximum mutual information; B This is an upper bound for grid complexity; m , n The number of rows and columns in the grid; These are the regularization coefficients automatically determined through 5-fold cross-validation; Let L1 norm be the coefficient vector; Indicates the first i The score after Min-Max normalization of each feature.

[0011] As a further preferred embodiment, in step S10, obtaining the time-series features includes: Original time-series features are selected from the time-series overview data, and dynamic enhancement features are extracted from the process details data of a single loop. The dynamic enhancement features include in-loop statistical features and sliding window derived features. The original time-series features and the dynamic enhancement features are aligned by identifier and number and merged to form dynamic features.

[0012] As a further preferred embodiment, the extraction of the dynamic enhancement features includes: Candidate dynamic features are constructed from the process details of a single cycle, and the candidate dynamic features are scored using lagged mutual information and Granger causality test. The scores of the two methods are mapped to [0,1] through Min-Max normalization, and the arithmetic mean is taken to obtain the comprehensive score. The comprehensive scores are sorted in descending order to select 12-dimensional dynamic enhancement features. The formula for calculating the lag mutual information is as follows: ; The formula for calculating Granger causality test is as follows: ; The formula for calculating the overall score is as follows: ; In the formula, and These are the sums of squared residuals for the restricted model and the complete model, respectively. p The lag order is minimized. p Value converted to score ; For the i-th candidate dynamic feature, the lagged mutual information score after Min-Max normalization; For the i-th candidate dynamic feature, the Granger causality test score after Min-Max normalization; k The step size is the lagging step size.

[0013] As a further preferred embodiment, in step S20, the temporal progressive cross-attention network includes a 4-layer stacked structure, in which progressive window self-attention operation and static modulation cross-attention operation are performed in each layer; the outputs of the progressive window self-attention operation and the static modulation cross-attention operation are fused and used as the input of the next layer.

[0014] As a further preferred embodiment, in step S20, the progressive window self-attention mechanism performs the following operations on the temporal features: No. l In the layer, the temporal features Generate queries by enhancing projection through convolution. Q ,key K Sum V , among which query Q Point-to-point mapping is preserved through convolution with a kernel size of 1, key K Information from adjacent time steps is aggregated through convolutions with a kernel size of 3. V Generated in conjunction with the gating signal, and then segmented after Sigmoid activation. V and gating coefficient G The calculation formula is:

[0015]

[0016]

[0017] The time-series features are segmented into multiple non-overlapping windows, and within each window, the query is used. Q ,key K Sum V Self-attention is calculated independently, using the following formula: ,in For learnable temperature parameters, d For feature embedding dimension; For the first l In a layered network, the query vector Q The learnable projective weight matrix; The self-attention output is selectively filtered using the gating coefficient, and the filtered result is used as the first temporal feature.

[0018] As a further preferred embodiment, in step S20, the static modulation cross-attention mechanism performs the following operations: The static features are subjected to nonlinear transformation and dimensional mapping to obtain static embeddings; The static feature embedding is expanded to four tokens, which are used as tokens in each layer of temporal progressive cross-attention. K - V With Q Cross-attention calculation is performed on the temporal features:

[0019] No. l In the layer, temporal features are used as components in the cross-attention mechanism. Q Actively query static knowledge:

[0020]

[0021]

[0022] Cross-attention calculates the dependency weights of temporal features on static features through a scaled dot product mechanism:

[0023] The attention weight matrix The dependency of each time step on the four static tokens was quantified, enabling dynamic context-aware modulation; specifically, The t The row corresponds to the first t The retrieval distribution of tokens at each time step; due to The temporal representation from this time step evolves with the degradation stage, and this distribution will follow... t The token modulation effect is stage-dependent due to adaptive changes; finally, the enhanced feature representation, i.e., the second temporal feature, is obtained through weights.

[0024] In the formula, To output the projection matrix; This is a timing representation with a static context; For the first l The value matrix of layer static modulation cross-attention; B Batch size; T This represents the timing length. As a further preferred embodiment, step S20, fusing the first time-series feature with the second time-series feature, includes: The first temporal feature output by the progressive window self-attention is added to the second temporal feature output by the statically modulated cross-attention after layer normalization to obtain a dual-path fusion representation. For the first and second layers, standard residual connections are used. For the third and fourth layers, an adaptive residual gating mechanism is introduced. The adaptive residual gating mechanism learns gating coefficients from the input features through 1×1 convolution. The gating coefficients act on the feature dimension to adaptively adjust the residual connections.

[0025] As a further preferred embodiment, in step S30, the multi-scale fusion network includes three parallel time aggregation branches: the global scale branch processes all historical time steps, the mid-scale branch processes the second half of the time steps, and the short-scale branch processes the last quarter of the time steps. Each branch employs attention-weighted pooling, mapping the features of each time step to scalar attention scores through a single-layer fully connected network. After Softmax normalization, the features are weighted and summed to obtain aggregated scale features. The aggregated features of the three scales are concatenated and nonlinearly fused through a two-layer feedforward neural network, and then mapped to the capacity prediction results for multiple future cycles through a linear output layer.

[0026] Secondly, this application provides a prediction system for cross-granularity feature interaction and temporal progressive cross-attention fusion, used to implement the method described in any one of the above, comprising: A cross-granularity feature extraction module is used to extract cross-granularity features through a multi-criteria feature selection framework. The cross-granularity features include static features and temporal features formed by merging the original temporal features and dynamically enhanced features. A temporal progressive cross-attention network module is used to input the temporal features into the temporal progressive cross-attention network. The temporal progressive cross-attention network captures the multi-scale temporal dependencies of the dynamic features through a progressive window self-attention mechanism to obtain a first temporal feature. At the same time, through a static modulation cross-attention mechanism, the dynamic features are used as key-value pairs and the static features are used as queries to perform cross-attention calculation to obtain a second temporal feature. The first temporal feature and the second temporal feature are fused to obtain a temporal representation with static context. The multi-scale fusion network module is used to input the time-series representation with static context into the multi-scale fusion network to generate prediction results for multiple future time steps.

[0027] The beneficial effects of this application are as follows: This application proposes a temporal progressive cross-attention fusion network. This model, by constructing a cross-granularity feature extraction mechanism and a progressive fusion framework, achieves deep interaction modeling of static and dynamic features during battery degradation, thereby improving the accuracy and stability of temporal prediction. Specifically: 1) A feature extraction method for battery degradation processes, incorporating both static and dynamic features, is proposed. Static features extract the overall degradation trend and inherent properties of the battery from multiple mechanistic perspectives, while dynamic features capture the evolution of the battery's health state on a cycle-by-cycle basis, thus providing a dynamic representation for subsequent model predictions. Experiments show that static and dynamic features effectively complement each other in terms of time scale and information granularity.

[0028] 2) A temporal progressive cross-attention network was designed, consisting of two parts: progressive window self-attention and static modulation cross-attention. Progressive window self-attention achieves progressive feature extraction from coarse to fine through decreasing window size and introduces a gating mechanism and a learnable temperature parameter to enhance multi-scale adaptability. Static modulation cross-attention encodes static features as conditional tokens, enabling temporal features to actively query inherent attribute information. In each layer of temporal progressive cross-attention: progressive window self-attention captures intra-temporal correlations, while static modulation cross-attention introduces static priors for context modulation, allowing the model to dynamically adjust its attention pattern to features based on the battery's inherent properties.

[0029] 3) A temporal progressive cross-attention fusion network was constructed, unifying cross-granularity feature extraction, temporal progressive cross-attention encoding, and multi-scale fusion into a single prediction framework. Experimental results show that this method exhibits good performance in terms of prediction accuracy, stability, and model efficiency. Attached Figure Description

[0030] Figure 1 This is a system problem modeling description diagram provided in the embodiments of this application; Figure 2 This is a diagram of the overall structure of the temporally progressive cross-attention network provided in the embodiments of this application; Figure 3 This is a diagram illustrating the static and dynamic feature extraction process provided in the embodiments of this application; Figure 4 This is a feature trend analysis chart provided in the embodiments of this application; Figure 5 This is the first set of model prediction result comparisons provided in the embodiments of this application, including local interval prediction curves (a), long interval prediction curves (b), and scatter comparisons of predicted values ​​and true values ​​(c). Figure 6 This is a comparison of the second set of model prediction results provided in the embodiments of this application, including a local interval prediction curve (a), a long interval prediction curve (b), and a scatter comparison of the predicted value and the true value (c). Figure 7 This is a static feature dimensionality reduction analysis diagram provided in the embodiments of this application; Figure 8This is a dynamic feature evolution analysis diagram provided in the embodiments of this application; Figure 9 This is a comparison chart of different prediction steps provided in the embodiments of this application. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0032] The battery capacity prediction method provided in this application will be described in detail from the following aspects: (I) System Model Method Design 1.1 Symbolic Description and Problem Modeling Battery state of health (SOH) prediction can be formulated as a multivariate time-series regression problem. Its goal is to predict the capacity decay trajectory over multiple future cycles using historical charge-discharge cycle observation data, thereby achieving health status assessment and remaining lifetime estimation. The overall modeling process for this application is as follows: Figure 1 As shown.

[0033] Define the original data sequence as: . in: Provide an overview of battery charge / discharge cycle data and record summary information for each cycle; This provides detailed process data for a single charge-discharge cycle. N This is the total number of cycles. M This represents the number of sampling points within a single loop.

[0034] Based on raw data X Construct the following features as model input: Original time series features :from X cycle Six key features (Q) were selected. D Q C IR, T max T min CT) is used as the basic timing input, where T This is the length of the history window.

[0035] Static features :from X cycle Static statistical features are extracted from the full life cycle data to characterize the inherent properties of the battery.

[0036] Dynamic enhancement features : From signal processing methods X detailExtracting intra-loop features captures fine-grained degradation information.

[0037] Define timing characteristics , where [;] indicates feature splicing. X time It characterizes the original key metrics of the battery and the enhanced detailed degradation information, and learns multi-scale temporal dependencies through the progressive window self-attention module.

[0038] X time Static features X S Transformed X token By combining static modulation cross-attention modules, deep fusion of static and dynamic features is achieved. Finally, a multi-scale fusion network is used to generate battery capacity prediction results.

[0039] The overall prediction framework can be represented as a composite mapping: (1) The ultimate goal of this mapping is to minimize the prediction capacity. Compared to actual capacity The error between them.

[0040] 1.2 Overall Model Structure of Temporally Progressive Cross-Attention Network To achieve deep integration of static attributes and dynamic evolution characteristics during battery degradation and effectively capture capacity degradation curves, the temporal progressive cross-attention network (TPC) model proposed in this application includes the following stages, with the overall structure as follows: Figure 2 As shown.

[0041] 1.2.1 Cross-granularity feature extraction method This module is responsible for decoupling and extracting dynamic and static heterogeneous features from battery data to construct complementary basic representations.

[0042] The static feature extraction module extracts data from the cyclic overview. X cycle Enhanced features are extracted and generated, and then mapped through a three-layer multilayer perceptron to generate a compact representation, which is then used to generate... X token A global context used for subsequent cross-attention operations.

[0043] The dynamic feature extraction module extracts data from process details. X detail Extract time-varying feature sequences and generate enhanced time-series features using feature engineering algorithms. X D , and then combine XC Formation of time series characteristics X time .

[0044] 1.2.2 Sequential Progressive Cross-Attention Network Temporally progressive cross-attention serves as the core interaction unit of the model, receiving cross-granularity features and achieving deep coupling between temporal dependency modeling and dynamic / static features. It employs a four-layer stacked structure, with each layer performing two key operations: First... X time Temporal dependencies are captured through progressive window self-attention; simultaneously X time and X token The global context of static features is injected into the progressive window self-attention dynamic feature prediction process through static modulation cross-attention computation. Finally, a multi-scale representation is generated using a feedforward neural network. .

[0045] 1.2.3 Multi-scale fusion network To address the multi-timescale characteristics of battery degradation, a multi-scale fusion network adaptively aggregates the multi-scale features from the temporally progressive cross-attention output. Specifically, X TPCA Multi-scale output is generated through three parallel aggregation branches: f 1, f 2, f 3. The system adaptively fuses data through an attention-weighted mechanism, then projects it through two layers of feedforward neural networks to generate the future... n Capacity prediction at each time step .

[0046] 1.3 Cross-granularity feature extraction method Static and dynamic feature extraction processes, such as Figure 3 As shown, static features are designed to encode the inherent properties and full life-cycle statistical characteristics of the battery; while the dynamic features extraction module is responsible for processing time-series data that changes with charge-discharge cycles to capture the evolution patterns during battery degradation.

[0047] 1.3.1 Static Feature Extraction Considering that battery degradation is affected by inherent factors such as initial capacity and material properties, this application is based on cycle overview data. X cycle Candidate static features were constructed by combining statistical methods such as frequency domain analysis, statistical aggregation, differential fluctuation characterization, and degradation trend fitting with the mechanism. To overcome the limitations of traditional linear screening methods, such as their inability to capture nonlinear relationships and their sensitivity to data distribution, this application employs an adaptive multi-criteria static feature selection module. It utilizes three complementary evaluation methods—Mutual Information (MI), Maximum Information Coefficient (MIC), and L1 regularization—to evaluate the static feature selection process. s A comprehensive score is calculated, and 15 static features are adaptively selected. X S .

[0048] Candidate features were scored using three complementary methods: Mutual information: measures the statistical dependence between features and cycle lifetime, and can capture nonlinearities. (2) Maximum information coefficient: fairly compares the correlation strength under different functional relationships (linear, nonlinear, periodic, etc.).

[0049] (3) L1 regularized regression: measures feature importance by the absolute value of the regression coefficients and automatically compresses unimportant features to zero.

[0050] (4) The three scoring methods are mapped to [0,1] using Min-Max normalization, and the arithmetic mean is taken to obtain the comprehensive score. ,according to Sort in descending order and select the top 15 features as the final static features. X S .

[0051] (5) In the formula, The joint probability distribution of features and targets. , For their respective marginal distributions; For a given grid, divide G Maximum mutual information; B This is an upper bound for grid complexity; m , n The number of rows and columns in the grid; These are the regularization coefficients automatically determined through 5-fold cross-validation; Let L1 norm be the coefficient vector; Indicates the first i The score after Min-Max normalization of each feature.

[0052] In order to generate conditional features to guide the model's attention,X S Nonlinear transformations and dimensional mappings are performed using a three-layer multilayer perceptron, mapping to 32-dimensional, 48-dimensional, and 64-dimensional hidden spaces, respectively. (6) in, The final 64-dimensional static embedding It was copied into 4 tokens: (7) These static tokens are used as key-value pairs as input in the subsequent cross-attention mechanism. They are retrieved by the query vector at different times with different attention weights, thereby providing differentiated context modulation information.

[0053] 1.3.2 Dynamic Feature Extraction The dynamic feature extraction module from X detail Constructing multidimensional time-series feature sequences Candidate dynamic features include both directly measured physical quantities and derived features constructed based on mechanism analysis and data fitting, used to characterize the local degradation rate, electrochemical activity changes, and short-term fluctuation behavior of the battery. Subsequently, this application employs lag mutual information (Lagged MI) and Granger causality tests to construct a dynamic feature screening framework to evaluate the correlation between each candidate dynamic feature and degradation indicators, selecting 12-dimensional dynamic features. X D .

[0054] In-loop statistical feature extraction extracts statistics from voltage, current, temperature, and differential capacity curves within a single loop, including descriptors such as mean, standard deviation, extreme values, and range. Sliding window derived feature extraction extracts features from adjacent... w Calculate local degradation dynamics within a window of loops: (8) (9) (10) in, , and These represent the local decay rate, local fluctuation, and local trend slope, respectively.

[0055] This application constructs a dynamic feature adaptive screening framework, employing two time-series analysis methods: hysteresis mutual information and Granger causality test. d A comprehensive score is used to evaluate the predictive ability of each candidate feature for capacity degradation: Lag mutual information: Calculating the statistical dependence between historical feature values ​​and future degradation indicators at multiple lag steps. (11) Granger causality test: Verifies whether historical values ​​of features have a statistically significant incremental contribution to the prediction of degradation indicators. Compare the sum of squared residuals between the restricted and complete models: (12) in and These are the sums of squared residuals for the restricted model and the complete model, respectively. p Let this be the lag order. Minimize... p Value converted to score .

[0056] The scores from both methods are mapped to [0,1] using Min-Max normalization, and the arithmetic mean is taken to obtain the overall score. (13) according to Sort in descending order, and finally select 12-dimensional dynamic features. X D The screening results showed that 10 out of the 12 selected features passed the Granger significance test (…). p <0.05) indicates that the screening results have good methodological consistency. Original features X C and enhanced features X D Aligned by battery ID and cycle number, the final matrix is ​​formed as an 18-dimensional time-series feature matrix. X time .

[0057] 1.4 Sequential Progressive Cross-Attention Network Fixed-window attention mechanisms often struggle to account for key dependencies at different temporal granularities and are highly complex. Furthermore, many existing methods simply concatenate or add static features, failing to fully utilize their phased modulation effect on the degradation process. Therefore, this application proposes a temporally progressive cross-attention network, which consists of four stacked layers, each performing two core operations: progressive window self-attention and static modulation cross-attention.

[0058] 1.4.1 Asymptotic Window Self-Attention While the standard Transformer's global self-attention can capture long-term dependencies in data, it is costly in long-sequence scenarios and assigns the same receptive field to all time steps, making it difficult to capture multi-timescale features in the battery degradation process. To address this, this application proposes a progressive window self-attention strategy. In the four-layer structure of temporally progressive cross-attention, the window size follows a design rule of decreasing layer by layer and finally global integration: the first layer uses a larger window to capture the long-term trend of capacity decay and low-frequency degradation information; the second and third layers progressively shrink the window to enhance the modeling ability of mid-term stage changes and short-term local fluctuations; the fourth layer uses global attention to integrate complete sequence information, thereby establishing global dependencies across stages. The reason for using a decreasing rather than increasing window strategy is that shallow features are closer to the original input and are more suitable for perceiving macroscopic degradation trends with a larger receptive field; as the network depth increases, the feature representation gradually becomes more abstract, and at this point, using a smaller window is beneficial for highlighting local stage changes and fine-grained degradation patterns, and finally, global attention completes the unified modeling across scales. This design enables the model to achieve progressive temporal modeling, from coarse-grained trend perception to fine-grained fluctuation characterization, and then to global semantic fusion.

[0059] No. l In the layer, the input sequence First, the projection is enhanced using convolution to generate the query. Q ,key K Sum V : (14) (15) (16) in, For the Sigmoid function, G (l) is the gating coefficient.

[0060] The self-attention calculation process within the window is as follows: (17) in For learnable temperature parameters, This represents element-wise product.

[0061] Sliding window attention divides the input sequence into multiple non-overlapping windows, calculating attention weights independently within each window. This reduces computational complexity to... ( (To decrease the window size), a linear speedup is achieved compared to global attention. To enhance the ability to capture local temporal patterns while maintaining the flexibility of the attention mechanism, this application further introduces convolutional enhancement. QKVGeneration mechanism: Q Point-to-point mapping is preserved through convolution with a kernel size of 1; K Use convolutions with a kernel size of 3 to aggregate information from adjacent time steps; V The matrix and gated signal are jointly generated, and after Sigmoid activation, the signal is divided into... V and gating coefficient G Gating mechanisms selectively filter attention output: (18) 1.4.2 Static Modulation of Cross-Attention The degradation trajectory of a battery depends not only on its historical state evolution but also on its inherent properties. For example, batteries with higher initial capacity typically have longer cycle life, batteries with lower baseline internal resistance degrade more slowly, and early capacity decay rates often predict subsequent aging trends. Traditional methods often incorporate static features into the model through simple concatenation or addition, which ignores the differentiated dependence of different stages of degradation on inherent properties.

[0062] This application designs a static feature modulation cross-attention mechanism to achieve more refined feature fusion. This mechanism expands the static feature embedding into four tokens, which are used as tokens in each layer of temporal progressive cross-attention. K - V With time series characteristics (as) Q Perform cross-attention calculation: (19) This asymmetric attention design enables temporal features to adaptively retrieve intrinsic attribute information most relevant to the current degradation stage at each time step.

[0063] No. l In the layer, temporal features are used as components in the cross-attention mechanism. Q Actively query static knowledge: (20) (twenty one) (twenty two) Cross-attention calculates the dependency weights of temporal features on static features through a scaled dot product mechanism: (twenty three) The attention weight matrix The dependency of each time step on the four static tokens was quantified, enabling dynamic context-aware modulation. Specifically, The t The row corresponds to the first t The retrieval distribution of tokens at each time step; due to The temporal representation from this time step evolves with the degradation stage, and this distribution will follow... t The token's modulation effect is stage-dependent due to adaptive changes. Finally, the enhanced feature representation is obtained through weights. (twenty four) in This is for outputting the projection matrix. This is a timing representation with a static context.

[0064] 1.4.3 Dual-path fusion and residual connectivity Self-attention output Adding this to the cross-attention output after layer normalization, a dual-path fusion representation is formed: (25) For shallow layers (layers 1 and 2), standard residual connections are used to maintain gradient flow: (26) For deeper layers (layers 3 and 4), an adaptive residual gating mechanism is introduced to enhance training stability: (27) Among them, the gating coefficient It is learned from the input features through 1×1 convolution. It operates on the feature dimension and can adaptively adjust the information flow according to the input content. It encodes rich multi-scale temporal features and context-aware static information.

[0065] In each temporally progressive cross-attention stacking layer, the attention is computed and then fed into the feedforward neural network, along with residual connections and layer normalization to improve representational power and training stability. The feedforward neural network consists of two layers of linear transformation and nonlinear activation, used to perform position-wise nonlinear mapping and reparameterization of the attention output.

[0066] (28) Through four layers of progressive cross-attention, the model achieves hierarchical representation learning from local to global and from low-level features to high-level semantics. Using progressive window self-attention and statically modulated cross-attention, the temporal progressive cross-attention network achieves a linear time complexity of O(n log n). T This is significantly better than the quadratic complexity O(n log n) of global attention. T ²). Final output The system encodes multi-scale temporal patterns guided by static features, providing high-quality feature representations for subsequent multi-scale fusion networks and supporting accurate capacity prediction tasks.

[0067] 1.5 Multi-scale Fusion Network Traditional simple aggregation strategies such as global average pooling or last time step selection are insufficient to fully utilize the hierarchical information of temporal features. Therefore, this application introduces an adaptive multi-scale fusion network. This network aims to integrate degradation features at different temporal granularities to achieve accurate capacity prediction by processing features at different time scales in parallel and learning their optimal combined weights.

[0068] The multi-scale fusion network receives the output from the 4th layer of the temporally progressive cross-attention layer. The paper proposes a method for dividing battery capacity into three parallel time-scale branches. The division of these branches is primarily based on the multi-time-scale characteristics of battery degradation and the hierarchical modeling requirements of the input history window. Battery capacity evolution typically includes an overall degradation trend over a long-term timescale, phased changes over a medium-term timescale, and inter-cycle fluctuations and random disturbances over a short-term timescale. Therefore, this application adopts a progressive time-scale division method from global to local, with a fixed history window length. Create three branches: Global scale f 1: Process all T Each time step corresponds to the macroscopic aging pattern of the battery's entire life cycle, such as long-term deterministic processes like monotonically increasing internal resistance and exponential capacity decay.

[0069] Mid-scale f 2: Focus on the second half T / 2 time steps, sensitive to medium-term nonlinear effects such as temperature accumulation and the effects of multiple overcharge and discharge.

[0070] short-term scale f 3: Focus on the end T / 4 time steps, quickly adapting to short-term random disturbances such as cyclical fluctuations and sudden capacity drops.

[0071] For each time scale This approach replaces simple average pooling with attention-weighted pooling. The mechanism first maps the features at each time step to scalar attention scores using a single-layer fully connected network, and then applies softmax normalization to generate the attention weight distribution. : (29) Finally by The aggregated scale features are obtained by weighted summation of the features. : (30) in h t Indicates the firstt The feature vectors at each time step. Multi-scale temporal aggregation enables the model to adaptively assign higher weights to important time steps within each time scale. The aggregated features at three scales are concatenated to form a multi-scale representation. To achieve nonlinear interaction between different scales, a two-layer feedforward fusion network is implemented using the following formula: (31) Features after fusion Information from multiple scales, including global, medium-term, and short-term, is then mapped to the future through a linear output layer. Capacity prediction for each cycle: (32) By integrating feature representations across three scales, the model simultaneously models multi-scale data fluctuations and long-term trends. In the early stages when battery health is high, the global scale may dominate, while in the decay phase nearing failure, the weight of the short-term scale increases significantly to capture signals of rapid degradation.

[0072] (II) Experimental Results and Analysis 2.1 Dataset This application utilizes the lithium-ion battery fast-charging dataset jointly released by MIT and Stanford University. This dataset is a standard benchmark dataset in the field of battery prediction, containing the complete degradation trajectory of 125 commercial lithium iron phosphate / graphite batteries under fast-charging conditions from cycling to failure. Each battery sample has an average of 586 cycles, with an average of 1042 sampling points per cycle, including cycle-level features. X cycle Loop characteristics X detail Two levels of data. All batteries were tested in a 30°C constant temperature convection chamber using a 48-channel Arbin LBT potentiostat, with a nominal capacity of 1.1Ah, a nominal voltage of 3.3V, and a voltage cutoff range of 2.0-3.6V.

[0073] The objective of this application is to predict the discharge capacity for the next 10 cycles based on the characteristics of the past 20 charge-discharge cycles. Q D The curve is shown. After generating training samples using the sliding window method, they are randomly divided into training, validation, and test sets in a 7:2:1 ratio. Each sample contains the input sequence. , as well as (Covering historical data from the past 60 hours, 3 hours per step) and target sequence (extract Q D (The column is used as the prediction target). Figure 4 The time series of six representative features from this dataset are presented, allowing observation of discharge capacity. Q D and charging capacitor Q C As the number of charge-discharge cycles increases, the curve shows a downward trend.

[0074] Tables 1 and 2 present the overall loop features and process detail features of the dataset.

[0075] Table 1 Overview of Cyclic Data Characteristics

[0076] Table 2. Characteristics of Process Details Data

[0077] 2.2 Evaluation Indicators This application employs four commonly used regression evaluation indicators to measure the difference between predicted and actual values ​​from different perspectives. Let the predicted value be... The actual value is The mean of the true values ​​is The sample size is n. The definitions of each evaluation index are shown in Table 3.

[0078]

[0079] Among the above indicators, the smaller the values ​​of MAE, MSE, RMSE, and MAPE, the higher the prediction accuracy of the model. This study calculated all indicators on the test set and averaged the results through five independent experiments to ensure the stability and reliability of the results.

[0080] 2.3 Comparative Analysis of Overall Prediction Models To verify the effectiveness of the temporally progressive cross-attention network, this application selected several representative models as benchmarks for comparison (see Table 4). Each model was independently repeated 5 times, and the average value was taken as the final result (see Table 5). Among all the compared models, the temporally progressive cross-attention network achieved the best prediction performance while maintaining low parameters.

[0081] Table 4. Experimental Comparison with Benchmark Model

[0082] Table 5 Comparison of Evaluation Indicators for Model Prediction Results

[0083] In contrast, while fusion and frequency domain models such as TimeXer and WPMixer have the ability to handle multiple variables, their prediction accuracy is generally lower than that of models based on self-attention mechanisms. Informer and Pyraformer, which use Transformer as a baseline, perform well on some metrics, but their overall performance is still lower than that of temporal progressive cross-attention networks, and their model overhead is relatively large.

[0084] The results show that the temporal progressive cross-attention network, while maintaining lightweight design and deployability, demonstrates an efficient joint modeling capability for temporal and static features. The multi-scale temporal aggregation mechanism and cross-attention structure effectively enhance the model's ability to capture cross-granularity feature correlations, thereby achieving better prediction performance and generalization stability.

[0085] Figure 5 and Figure 6 The comparison results of the two sets of models in the battery capacity degradation prediction task are presented, including local interval prediction curves, long interval prediction curves, and scatter plot comparisons of predicted and actual values. Overall, all models can follow the basic law of capacity decreasing with cycle number to some extent, but there are significant differences in their ability to capture local degradation processes, long-term fitting accuracy, and prediction consistency.

[0086] exist Figure 5 (a) and Figure 6 In the magnified region of (a), the differences in prediction curves among different models are quite pronounced. Frequency domain models (FiLM, WPMixer) perform poorly, attention-based models (Informer, Pyraformer) are overly smoothed during the degradation acceleration phase, while TimesNet's response to sudden capacity changes is insufficient, and TimeXer exhibits significant lag. In contrast, the temporal progressive cross-attention network's prediction curve more closely matches the actual capacity change trajectory in several key fluctuation phases, maintaining a good fit, especially during periods of abrupt degradation or increased volatility.

[0087] In addition, from Figure 5 (c) and Figure 6 The comparison in (c) further verifies the differences in model prediction accuracy. The scatter distribution of the temporal progressive cross-attention network is more concentrated near the diagonal, with less dispersion, indicating lower prediction error and stronger generalization stability. Other models all exhibit varying degrees of dispersion or bias, especially in the mid-to-late degeneration stage (around 0.9).

[0088] Based on the above analysis, the temporal progressive cross-attention network can capture short-term fluctuations while predicting long-term downward trends, making it the best performing model among the comparison models.

[0089] 2.4 Feature Extraction Experimental Analysis To verify the effectiveness of the multimodal feature engineering proposed in this application, this application examines the extracted static features. X S With dynamic characteristics X D Perform the analysis.

[0090] 2.4.1 Static Feature Extraction Analysis This application is for X S A comprehensive evaluation was conducted. Table 6 shows the results. X S The overall score is obtained by selecting the framework based on static features.

[0091] These characteristics are not only statistically highly correlated with cycle life, but also have clear explanatory significance in electrochemical mechanisms. For example, the capacity curve spectrum reflects the dominant degradation frequency, and the rate of change of internal resistance quantifies degradation instability. Compared with methods that use a single correlation coefficient for selection, adaptive multi-criteria selection more comprehensively considers linear and nonlinear dependencies, improving the discriminative power of static characteristics.

[0092] 15-dimensional static features extracted and filtered using static features X S It can reflect the overall attributes of the battery degradation process. Figure 7 For all battery samples X S Dimensionality reduction was performed using the t-SNE (t-distributed stochastic neighbor embedding) algorithm. As a nonlinear dimensionality reduction technique, t-SNE can reveal the local neighborhood structure of high-dimensional data. Results show that samples form regions of different densities in two-dimensional space, and long-lifetime and short-lifetime batteries exhibit significant separation in the feature space.

[0093] Table 6. Correlation Analysis of Static Features

[0094] The above analysis shows that static features have nonlinear representation capabilities in battery prediction tasks, providing rich inputs for the model.

[0095] 2.4.2 Dynamic Feature Extraction and Analysis This application provides a comprehensive evaluation of XD. Table 7 shows the comprehensive score obtained by XD based on the dynamic feature selection framework.

[0096] Table 7 shows the 12 dynamic features selected.

[0097] Among them, the peak value of the differential capacity curve and the correlation characteristics of dQ / dV are closely related to the electrode reactivity, while the local decay rate and local fluctuations reflect the short-term degradation rate and instability. Therefore, dynamic characteristics, to a certain extent, carry information about the battery degradation mechanism. Although XD8 and XD9 did not pass the Granger causality test (p>0.05), they still scored highly in the hysteresis mutual information analysis, indicating that they have a nonlinear dependence on future capacity. This suggests that the cycling current intensity and fluctuations can provide information on capacity evolution, helping the model capture degradation modes.

[0098] To quantitatively assess the temporal discriminative ability of dynamic features, this study selected two representative samples for comparison: the long-lived sample b1c5 and the short-lived sample b1c31. The evolution trajectories of key features are as follows: Figure 8 As shown.

[0099] The evolution curves of short-life samples exhibit higher volatility variance and steeper negative gradients, reflecting the instability of the battery during degradation. This difference may stem from the different dominant degradation mechanisms, such as the varying rates of solid electrolyte interfacial film thickening and activity loss patterns. The above analysis demonstrates that dynamic characteristics provide a fine-grained, dynamic representation of the cycle-by-cycle evolution of battery health.

[0100] 2.5 Ablation Experiment This application analyzes the effectiveness of the proposed model through systematic ablation experiments across multiple dimensions. All experiments were conducted under the same dataset partitioning, training configuration, and random seed to ensure the comparability of results.

[0101] 2.5.1 Feature Usage Strategy To systematically evaluate the impact of different feature combinations on model performance, this study designed four feature configuration schemes, as shown in Table 8. This experiment investigates the contributions of XS and XD to model performance and their complementarity. The basic configuration (C1) contains only XC, C2 adds XS, C3 introduces XD, and C4 integrates all features to achieve fusion modeling.

[0102] Table 8. Detailed Description of Feature Configuration Scheme

[0103] Table 9 presents a performance comparison of the model using different feature configurations, thereby verifying the effectiveness of introducing static and dynamic features. As feature information is gradually enhanced, the model prediction error gradually decreases. Introducing XS and XD on top of C1 improves performance, with C4 showing the best performance across all features. The results indicate that XD effectively enhances the model's ability to capture time dependencies; XS has a positive gain on overall performance; and the two are synergistic.

[0104] Table 9 Performance Comparison of Different Feature Configurations

[0105] 2.5.2 Feature Fusion Methods Different fusion strategies affect the model's expressive power and generalization performance. Based on the different fusion timing and mechanisms, this application's model architecture employs four fusion methods at the attention level: 1) no fusion of static features; 2) conditional encoding fusion; 3) gating fusion; and 4) cross-attention fusion. Simultaneously, the output layer selects whether to fuse XS, thus constituting eight fusion strategies, as shown in Table 10.

[0106] Table 10 Classification System of Feature Fusion Strategies

[0107] Conditional coding fusion uses parameters generated from static features (XS) to perform affine transformations on temporal features. The gated fusion strategy introduces an adaptive gating mechanism, dynamically controlling the contribution of static features through learned gating weights. Static modulation cross-attention enables dynamic interaction between temporal and static features, adaptively allocating feature weights based on the temporal context.

[0108] Based on the C4 feature configuration (XC+XS+XD), this study systematically evaluated the performance of eight fusion strategies. All experiments used the same main model architecture and training configuration, changing only the fusion strategy to ensure fairness in the comparison. The final ablation results are shown in Table 11.

[0109] Table 11 Performance Comparison of Different Fusion Methods

[0110] The results show that S8 achieves the best performance across all metrics. This success is not solely due to the introduction of static features, but also to the adoption of a fusion mechanism more suited to battery degradation modeling. Specifically, conditional coding fusion generates modulation parameters from static features and performs a uniform transformation on the features; gated fusion controls the injection intensity of static features through gating weights. While these two methods can introduce static information, they are essentially still static modulation methods, lacking modeling of the fine-grained matching relationship between temporal states and static attributes at different times. In contrast, static modulation cross-attention uses temporal features as queries and static features as keys and values, enabling the model to adaptively select the most relevant static information for modulation based on the temporal context of the current degradation stage. Therefore, it can more effectively model the feature coupling relationship in the battery degradation process.

[0111] Comparing S7 and S8 reveals that, even with static modulation cross-attention already employed, fusing static features again at the output layer actually degrades performance. This indicates that static modulation cross-attention has already achieved sufficient information exchange in the intermediate layers, and subsequent linear layer fusion introduces information redundancy. Therefore, static features are more suitable as contextual information for dynamic modulation. In conclusion, this application adopts the S8 strategy as the static feature fusion scheme for the temporally progressive cross-attention network.

[0112] 2.5.3 Progressive Window Self-Attention Window Configuration Strategy To verify the effectiveness of the progressive window self-attention module's layer-by-layer window reduction strategy, this application designed a window strategy ablation experiment. This application systematically evaluates the rationality of the design through a comparative experiment with ten sets of window configurations, and the experimental results are shown in Table 12.

[0113] Table 12 Window Strategy Ablation Experiments

[0114] Where [6,4,2,0] is the default layer-by-layer decreasing strategy (0 represents global attention); [0,0,0,0] is the global attention baseline; [0,2,4,6], [0,4,7,10] and [10,7,4,0] are the extended verifications of the increasing and decreasing strategies, respectively.

[0115] Experimental results show that the default progressively decreasing window strategy [6,4,2,0] in this application achieves optimal performance on multiple metrics. In the fixed window strategy, as the window size increases, RMSE initially decreases and then stabilizes; however, when the window is too large, all metrics deteriorate significantly, indicating that an excessively large local window may lead to underfitting of the global trend. Notably, the increasing strategy performs poorly on both RMSE and MAPE, verifying that the decreasing window strategy outperforms the increasing reverse design.

[0116] From a computational efficiency perspective, the decreasing window strategy maintains good computational efficiency while preserving optimal performance. In summary, there is a good correspondence between the layer-by-layer decreasing window strategy and the degenerate multi-scale characteristics.

[0117] 2.5.4 Sensitivity Analysis of Scale Division in Multi-Scale Fusion Networks To verify the rationality of the multi-scale branch design in the multi-scale fusion network module, this application conducts sensitivity analysis on different scale partitioning schemes. This application defaults to the scale partitioning scheme [T, T / 2, T / 4]. To evaluate the effectiveness of this configuration, this application sets up two comparative schemes: [T, 2T / 3, T / 3] concentrates short-to-medium scales over a longer time span, while [T, T / 3, T / 6] further narrows the coverage of short-to-medium scales. Experimental results are shown in Table 13.

[0118] Table 13 Sensitivity Analysis of Scale Division

[0119] Experimental results show that the geometrically decreasing scale partitioning scheme achieves optimal performance across all metrics. When the short- and medium-scale branches are overly concentrated over longer or shorter time spans, the model's ability to control the error distribution decreases. The geometrically decreasing configuration retains a global view of long-term trends while also capturing fine-grained changes in the medium term and fluctuations in the short term. In contrast, [T,2T / 3,T / 3] concentrates the short- and medium-scale branches over longer time spans, resulting in insufficient modeling ability for local fluctuations; [T,T / 3,T / 6] overemphasizes short-term features, weakening its ability to perceive medium-term degradation changes.

[0120] In summary, scale division needs to cover the complete time span from global to local in order to achieve balanced modeling of characteristics of different degradation stages.

[0121] 2.5.5 Comparison of Pooling Methods in Multi-Scale Fusion Networks To verify the effectiveness of the attention-weighted pooling strategy in multi-scale fusion networks, this application compares and analyzes it with two traditional pooling methods. The experimental results are shown in Table 14.

[0122] Table 14 Ablation Experiments Using Pooling Method

[0123] Experimental results show that attention-weighted pooling outperforms the two traditional pooling methods on all evaluation metrics. Max pooling performs the worst on all metrics because battery degradation is mainly a smooth, gradual trend, and retaining only peak features would lose contextual information representing the degradation trend. Average pooling's equal weighting of all time steps limits the model's ability to distinguish between critical degradation stages and stable stages. Attention-weighted pooling in multi-scale fusion networks, through a learnable weight allocation mechanism, effectively enhances the perception of critical time steps such as degradation acceleration and capacity drop through adaptive weight allocation, achieving the best performance in both overall prediction accuracy and extreme error control. These results experimentally validate the effectiveness of the attention-weighted pooling mechanism in battery degradation prediction tasks.

[0124] 2.5.6 Comparison of different prediction steps To verify the effectiveness of the model under different prediction step sizes, Figure 9 The results of the temporally progressive cross-attention network are shown in the predictions from single-step to multi-step.

[0125] As the prediction step size increases, although the fluctuation of the predicted value increases, the overall accuracy does not decrease significantly and remains within the confidence interval. This indicates that the temporal progressive cross-attention network exhibits strong robustness and stability when dealing with long-term predictions and can effectively support prediction tasks over a longer time range.

[0126] 2.6 Model Performance Analysis To verify the model's overall performance and practical application potential, this application analyzes it from two dimensions: spatiotemporal efficiency and noise robustness. By evaluating the model's computational overhead and prediction stability under noise interference, the feasibility of deploying the model in a BMS and its engineering application value are further verified.

[0127] 2.6.1 Spatiotemporal Efficiency Analysis This application analyzes the spatiotemporal efficiency of the temporal progressive cross-attention model in the task of predicting battery capacity degradation, and evaluates the actual deployment feasibility of the model from the dimensions of time complexity and memory usage efficiency, as shown in Table 15.

[0128] Table 15 Spatiotemporal Efficiency Analysis of Temporally Progressive Cross-Attention Networks

[0129] From a time efficiency perspective, the temporal progressive cross-attention network exhibits excellent training efficiency. The entire training process takes only 391.66 seconds (approximately 6.5 minutes). Thanks to the linear complexity design of the temporal progressive cross-attention, the model's parameter count is controlled at 0.67M, and inference can be completed in just 3.17 seconds during the prediction phase, achieving a memory efficiency of 706.47MB / s. The memory change during the inference phase is only 7.94MB, significantly lower than during the training phase, demonstrating the model's memory-friendly characteristics during inference. This feature enables the model to be effectively deployed in resource-constrained edge computing environments, meeting the demand for rapid response in industrial applications. Overall, the temporal progressive cross-attention network demonstrates excellent spatiotemporal efficiency suitable for practical deployment, providing a feasible technical solution for real-time capacity prediction in battery management systems.

[0130] 2.6.2 Noise Robustness Analysis In practical battery management systems (BMS), the acquired data is inevitably affected by factors such as sensor errors, communication interference, and sampling inconsistencies. To evaluate the robustness of the model in noisy environments, this application conducted experimental analysis by injecting Gaussian noise of different intensities into the original input features. Specifically, four noise levels were set: 0.01%, 0.05%, 0.1%, and 0.2%, with the prediction performance under noise-free (0%) conditions serving as the baseline. The experimental results are shown in Table 16.

[0131] Experimental results show that the temporally progressive cross-attention network maintains stable prediction performance under different noise levels. At the highest noise level of 0.2%, MAE and MAPE only increase by 2.2% and 5.3% respectively compared to the baseline, indicating that the model has strong noise robustness overall. This is mainly attributed to the statically modulated cross-attention mechanism and the multi-scale fusion network attention weighted pooling, which can adaptively adjust the importance weights at different time steps, thereby effectively suppressing the interference of noise on prediction.

[0132] Table 16 Noise Robustness Analysis

[0133] Notably, under low noise levels, some of the model's metrics actually outperform the noise-free baseline. The RMSE under 0.01% noise conditions is 8.5% lower than the baseline. This phenomenon is related to the regularization effect: moderate noise acts as data augmentation during training, helping to alleviate overfitting of the model to the training data and thus improving generalization ability. As the noise level further increases, the regularization effect is gradually offset by information loss, and prediction performance begins to decline, but the overall degradation is limited. These results demonstrate that the temporally progressive cross-attention network exhibits good adaptability to noise interference that may exist in real-world BMS systems, proving its feasibility for industrial deployment.

[0134] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A prediction method that combines cross-granularity feature interaction and temporal progressive cross-attention fusion, characterized in that, Includes the following steps: S10, extract cross-granularity features through a multi-criteria feature selection framework. The cross-granularity features include static features and temporal features formed by merging the original temporal features and dynamic enhancement features. S20, the temporal features are input into a temporal progressive cross-attention network. The temporal progressive cross-attention network captures the multi-scale temporal dependencies of the dynamic features through a progressive window self-attention mechanism to obtain a first temporal feature. At the same time, through a static modulation cross-attention mechanism, the dynamic features are used as key-value pairs and the static features are used as queries to perform cross-attention calculation to obtain a second temporal feature. The first temporal feature and the second temporal feature are fused to obtain a temporal representation with static context. S30, the time-series representation with static context is input into the multi-scale fusion network to generate prediction results for multiple future time steps.

2. The prediction method for cross-granularity feature interaction and temporal progressive cross-attention fusion as described in claim 1, characterized in that, In step S10, obtaining static features includes: Candidate static features are extracted from time-series overview data using data analysis and physical modeling methods. A multi-criteria feature selection framework, incorporating mutual information, maximum information coefficient, and L1 regularized regression, is used to score the candidate static features. The scores from the three methods are then Min-Max normalized to [0,1], and the arithmetic mean is taken to obtain a comprehensive score. The top 15 dimensions are selected as static features based on their comprehensive scores in descending order. The formula for calculating mutual information is as follows: ; The formula for calculating the maximum information coefficient is as follows: ; The formula for calculating L1 regularized regression is: ; The formula for calculating the overall score is as follows: ; In the formula, x For the specific values ​​of the candidate static feature random variables; y To predict the specific values ​​of the target random variable; i The index number for the feature; X i For the first i The overall random variables of candidate static features; Y The target random variable for the prediction task; The joint probability distribution of features and targets. , For their respective marginal distributions; For a given grid, divide G Maximum mutual information; B This is an upper bound for grid complexity; m , n The number of rows and columns in the grid; These are the regularization coefficients automatically determined through 5-fold cross-validation; Let L1 norm be the coefficient vector; Indicates the first i The score after Min-Max normalization of each feature.

3. The prediction method for cross-granularity feature interaction and temporal progressive cross-attention fusion as described in claim 1, characterized in that, In step S10, obtaining time-series features includes: Original time-series features are selected from the time-series overview data, and dynamic enhancement features are extracted from the process details data of a single loop. The dynamic enhancement features include in-loop statistical features and sliding window derived features. The original time-series features and the dynamic enhancement features are aligned by identifier and number and merged to form dynamic features.

4. The prediction method for cross-granularity feature interaction and temporal progressive cross-attention fusion as described in claim 3, characterized in that, The extraction of the dynamic enhancement features includes: Candidate dynamic features are constructed from the process details of a single cycle, and the candidate dynamic features are scored using lagged mutual information and Granger causality test. The scores of the two methods are mapped to [0,1] through Min-Max normalization, and the arithmetic mean is taken to obtain the comprehensive score. The comprehensive scores are sorted in descending order to select 12-dimensional dynamic enhancement features. The formula for calculating the lag mutual information is as follows: ; The formula for calculating Granger causality test is as follows: ; The formula for calculating the overall score is as follows: ; In the formula, and These are the sums of squared residuals for the restricted model and the complete model, respectively. p The lag order is minimized. p Value converted to score ; For the i-th candidate dynamic feature, the lagged mutual information score after Min-Max normalization; For the i-th candidate dynamic feature, the Granger causality test score after Min-Max normalization; k The step size is the lagging step size.

5. The prediction method for cross-granularity feature interaction and temporal progressive cross-attention fusion as described in claim 1, characterized in that, In step S20, the temporal progressive cross-attention network includes a 4-layer stacked structure, in which progressive window self-attention operation and static modulation cross-attention operation are performed in each layer. The outputs of the progressive window self-attention operation and the static modulation cross-attention operation are fused together and used as the input for the next layer.

6. The prediction method for cross-granularity feature interaction and temporal progressive cross-attention fusion as described in claim 5, characterized in that, In step S20, the progressive window self-attention mechanism performs the following operations on the temporal features: No. l In the layer, the temporal features Generate queries by enhancing projection through convolution. Q ,key K Sum V , among which query Q Point-to-point mapping is preserved through convolution with a kernel size of 1, key K Information from adjacent time steps is aggregated through convolutions with a kernel size of 3. V Generated in conjunction with the gating signal, and then segmented after Sigmoid activation. V and gating coefficient G ; The calculation formula is: The time-series features are segmented into multiple non-overlapping windows, and within each window, the query is used. Q ,key K Sum V Self-attention is calculated independently, using the following formula: ,in For learnable temperature parameters, d For feature embedding dimension; For the first l In a layered network, the query vector Q The learnable projective weight matrix; The self-attention output is selectively filtered using the gating coefficient, and the filtered result is used as the first temporal feature.

7. The prediction method for cross-granularity feature interaction and temporal progressive cross-attention fusion as described in claim 5, characterized in that, In step S20, the static modulation cross-attention mechanism performs the following operations: The static features are subjected to nonlinear transformation and dimensional mapping to obtain static embeddings; The static feature embedding is expanded to four tokens, which are used as tokens in each layer of temporal progressive cross-attention. K - V With Q Cross-attention calculation is performed on the temporal features: No. l In the layer, temporal features are used as components in the cross-attention mechanism. Q Actively query static knowledge: Cross-attention calculates the dependency weights of temporal features on static features through a scaled dot product mechanism: The attention weight matrix The dependency of each time step on the four static tokens was quantified, enabling dynamic context-aware modulation; specifically, The t The row corresponds to the first t The retrieval distribution of tokens at each time step; due to The temporal representation from this time step evolves with the degradation stage, and this distribution will follow... t The token modulation effect is stage-dependent due to adaptive changes; finally, the enhanced feature representation, i.e., the second temporal feature, is obtained through weights. In the formula, To output the projection matrix; This is a timing representation with a static context; For the first l The value matrix of layer static modulation cross-attention; B Batch size; T This represents the timing length.

8. The prediction method for cross-granularity feature interaction and temporal progressive cross-attention fusion as described in claim 5, characterized in that, In step S20, fusing the first time-series feature with the second time-series feature includes: The first temporal feature output by the progressive window self-attention is added to the second temporal feature output by the statically modulated cross-attention after layer normalization to obtain a dual-path fusion representation. For the first and second layers, standard residual connections are used. For the third and fourth layers, an adaptive residual gating mechanism is introduced. The adaptive residual gating mechanism learns gating coefficients from the input features through 1×1 convolution. The gating coefficients act on the feature dimension to adaptively adjust the residual connections.

9. The prediction method for cross-granularity feature interaction and temporal progressive cross-attention fusion as described in claim 1, characterized in that, In step S30, the multi-scale fusion network includes three parallel time aggregation branches: the global scale branch processes all historical time steps, the mid-scale branch processes the second half of the time steps, and the short-scale branch processes the last quarter of the time steps. Each branch employs attention-weighted pooling, mapping the features of each time step to scalar attention scores through a single-layer fully connected network. After Softmax normalization, the features are weighted and summed to obtain aggregated scale features. The aggregated features at three scales are concatenated, then nonlinearly fused through a two-layer feedforward neural network, and finally mapped to the capacity prediction results for multiple future cycles through a linear output layer.

10. A prediction system that integrates cross-granularity feature interaction and temporal progressive cross-attention fusion, characterized in that, To implement the method of any one of claims 1 to 9, comprising: A cross-granularity feature extraction module is used to extract cross-granularity features through a multi-criteria feature selection framework. The cross-granularity features include static features and temporal features formed by merging the original temporal features and dynamically enhanced features. A temporal progressive cross-attention network module is used to input the temporal features into the temporal progressive cross-attention network. The temporal progressive cross-attention network captures the multi-scale temporal dependencies of the dynamic features through a progressive window self-attention mechanism to obtain a first temporal feature. At the same time, through a static modulation cross-attention mechanism, the dynamic features are used as key-value pairs and the static features are used as queries to perform cross-attention calculation to obtain a second temporal feature. The first temporal feature and the second temporal feature are fused to obtain a temporal representation with static context. The multi-scale fusion network module is used to input the time-series representation with static context into the multi-scale fusion network to generate prediction results for multiple future time steps.

Images