Lithium battery remaining service life prediction method based on multimode collaborative compressed sensing and IDMamba

Abstract

The invention discloses a lithium battery remaining service life prediction method based on multimode collaborative compressed sensing and IDMamba, and relates to the technical field of batteries. According to the method, a multi-mode cooperative compressed sensing (MCS) method and an IDMamba neural network model method are adopted, the advantage of data denoising is achieved, the MCS is adopted for processing sequence data, mapping the data to a low-dimensional measurement space, removing redundant information and noise and then conducting data reconstruction, in the process, a self-attention mechanism is added to pay more attention to key features, and the accuracy of data reconstruction is improved. And the stability is improved through layer normalization, so that redundant components of the original data can be removed, a clearer data view is provided, and the nature of the data can be better understood.

Description

Technical Field

[0001] This invention relates to the field of battery technology, specifically to a method for predicting the remaining lifespan of lithium batteries based on multi-mode collaborative compressed sensing and IDMamba. Background Technology

[0002] Lithium-ion batteries (LiB) are widely used energy storage devices, playing a crucial role in electric vehicles (EVs), rail transportation, and power grids. Their lightweight and high energy density have led to their widespread application. However, due to electrochemical degradation, battery performance gradually declines over time, potentially resulting in insufficient power supply or even system outages. To optimize battery performance and extend its lifespan, accurate monitoring of the degradation state is essential, involving the assessment of state of health (SOH) and remaining useful life (RUL).

[0003] State of Harshness (SOH) is a key indicator of battery aging; a decrease in SOH leads to capacity decay and increased internal resistance, directly impacting equipment performance. Rullow Life (RUL) characterizes the number of cycles a battery will have remaining before its capacity drops to 80% of its rated value. To support lifespan prediction, the accuracy of capacity and resistance estimations needs to reach at least 5%, ideally controlled within 2%. Accurate RUL prediction is crucial for enhancing the application value of battery lifecycle technologies, creating conditions for battery reuse and adapting to the future trend of demand growth exceeding raw material supply.

[0004] Currently, the prediction of the remaining useful life (RUL) of lithium-ion batteries (LiB) mainly relies on four cutting-edge technological approaches: evidence-based aging mechanism modeling, data-driven methods, feature-assisted data modeling strategies, and physical modeling methods. Among these, data-driven methods have become a key research focus due to their better suitability for real-time applications such as vehicle monitoring. These methods can be further divided into modeling approaches based entirely on raw data and hybrid strategies that rely on feature extraction.

[0005] Purely data-driven methods directly use measured data such as voltage, current, impedance, and temperature as input to machine learning models, showing promising promise in battery state of health (SOH) estimation. However, the application of this technology still has limitations: on the one hand, models such as deep long short-term memory networks (LSTM) are limited by the scale of training data—although a single cell contains hundreds of cycles of data that can be used for SOH estimation, the complete life cycle data for each battery only corresponds to a single time point, resulting in insufficient data samples; on the other hand, purely data-driven models are highly dependent on raw data input, requiring massive, comprehensive, and high-quality datasets to support training, while obtaining such data in real-world scenarios is difficult.

[0006] Existing machine learning (ML) models mostly employ a "forward simulation" strategy. By learning the correlation between short-cycle capacity decay and parameters such as current and temperature, they accumulate the capacity decay over each cycle and track when it crosses the 80% nominal capacity failure threshold (EoS) to achieve RUL prediction. While this method is convenient to operate, the model's generalization ability is limited by the quality and scale of the data.

[0007] Existing methods for predicting the remaining useful life (RUL) of lithium-ion batteries still face several bottlenecks that limit their performance and reliability. First, insufficient data quality or noise interference weakens the model's learning effect; when the degradation curves used for training are incomplete or contain outliers, the model's prediction accuracy and generalization ability both decrease significantly. Second, as the data scale increases, the complex feature engineering and model training processes often consume significant computational resources and time, making it difficult to meet the requirements of real-time updates and online deployment. Third, battery degradation involves multiple interacting factors such as temperature, charge / discharge rate, and cycle count, while existing algorithms often only capture some key features, failing to fully reflect the degradation mechanism. Finally, the battery health status changes dynamically with the usage environment and each cycle; if the model lacks an online tracking and adaptive mechanism for this evolution, the effectiveness of its RUL prediction will gradually diminish over long-term operation.

[0008] Therefore, a new solution to the above problems is urgently needed. Summary of the Invention

[0009] The purpose of this invention is to provide a method for predicting the remaining lifespan of lithium batteries based on multi-mode collaborative compressed sensing and IDMamba, so as to solve the technical deficiencies mentioned in the background art.

[0010] To achieve the above objectives, the present invention provides the following technical solution: a method for predicting the remaining lifespan of lithium batteries based on multi-mode cooperative compressed sensing and IDMamba, comprising at least the following steps:

[0011] S1: Construct the basic model, based on multi-modal collaborative compressed sensing and IDMamba;

[0012] S2: Use the basic model to predict the future trend of multiple variables, that is, use the model to make multi-variable multi-step predictions;

[0013] S3: The input data is compressed and reduced in dimensionality using MCS to remove redundant information and noise, while retaining key features, so that subsequent models can focus more on highlighting these prominent features.

[0014] S4: Use state-space model and recursion mechanism to capture the dynamic correlation between multiple variables. Input the multivariate sequence processed in S3 into the IDMamba model. For all time points of each sequence, embed the hidden state space through linear projection. The recursion mechanism of the state-space model and the gating unit work together to capture the dynamic correlation between multiple variables.

[0015] S5: By stacking and improving convolution methods, the prediction performance is further improved. The entire model is constructed by stacking multiple layers. The improved cross-convolution structure contained in IDMamba can better extract the latent features in the sequence. The trend-aware weighted exponential moving average module dynamically enhances and adaptively fuses the time-series features of the parallel branch data after dynamic exponential smoothing, accurately capturing the fluctuation patterns in the time-series data, thereby improving the prediction performance of the model.

[0016] According to claim 1, the method for predicting the remaining lifespan of a lithium battery based on multi-mode cooperative compressed sensing and IDMamba is characterized in that: step S2 includes at least the following steps:

[0017] First, historical data on lithium batteries is provided:

[0018]

[0019] This indicates that there are L sequence lengths and d variables;

[0020] Historical data is used as the training data.

[0021] Finally, a fixed length k is set as the prediction window step size for prediction:

[0022]

[0023] Among them, c t+i (i = 1, 2, 3, ..., k) represents the current remaining capacity of the lithium battery.

[0024] The method for predicting the remaining lifespan of a lithium battery based on multi-mode collaborative compressed sensing and IDMamba as described in claim 2 is characterized in that: step S3 includes at least the following steps:

[0025] The lithium battery capacity degradation data is compressed and reconstructed using MCS to obtain key reconstructed data, which is then used for reinforcement learning in subsequent parts of the model.

[0026] First, generate a Weibull distribution measurement matrix. Compression measurements were then performed.

[0027] y t =Φx t

[0028] Among them, y t Represents compressed low-dimensional data; x t This represents the original data before compression; t is the current time step.

[0029] Subsequently, a fast iterative thresholding algorithm, namely FISTA, is used to sparsely decode low-dimensional observations. In each iteration, the solution vector is updated based on gradient descent and soft thresholding operations. η is a dynamically adjusted step size factor that we introduce.

[0030]

[0031] Where, x i Represents a sample of the input signal, |x i | represents the absolute value of each sample; n represents the number of signal samples; λ is the initialization step size; μ abs It is the absolute mean of the input signal, used to dynamically adjust the step size so that the step size matches the overall amplitude of the input signal, thereby improving numerical stability;

[0032] In each iteration, the update process is as follows:

[0033]

[0034] Among them, g (k) It is the current gradient direction; z (k) It is an intermediate variable that incorporates historical information under the momentum mechanism. After calculating the gradient step size, a learnable soft thresholding operation is applied, with channel adaptive scaling. T represents the matrix transpose operation. Through the iterative update mechanism of the dynamic step size factor and momentum auxiliary variable, the iterative convergence speed is improved from O(1 / k) of ISTA = to O(1 / k). 2 FISTA sparse coding can achieve fast and stable convergence, significantly improving the performance of compressed sensing models.

[0035] After sparse coding is completed, a learnable reconstruction dictionary is designed to achieve accurate signal reconstruction. To ensure initial expressive power, the dictionary is constructed using discrete cosine transform during initialization:

[0036]

[0037] Among them, D k,i It is a two-dimensional array, where k and i are the row and column indices, respectively;

[0038] When k = 0 This means that the first element of the dictionary is a constant, and its size is [value]. Where D is the dimension of the dictionary;

[0039] When k = 1, ..., D-1, D k,i A formula based on the cosine function was used, which means that the k-th row of the dictionary is generated by a cosine function, and each row has a different phase and frequency, in order to ensure that the elements of the dictionary have good distribution and spectral characteristics.

[0040] Furthermore, during the training process, the model was continuously optimized. To avoid overfitting and enhance model stability, an L2 regularization term was introduced to normalize the dictionary.

[0041] To further improve reconstruction performance, an attention mechanism module was introduced. First, the sparse encoding x of the FISTA output was processed. (k) Normalization is performed, and then the data is fed into an attention network to extract correlation information between channels and feature dimensions, forming an attention-enhanced sparse representation. Finally, it is reconstructed using a dictionary matrix, and residual connections are performed after this normalization process to retain the trend information of the original battery mid-term data, resulting in the reconstruction result:

[0042]

[0043] Where Attention represents self-attention; LN represents layer normalization; D T Represents the transpose of the dictionary matrix D

[0044] IDMamba was used to extract features from the reconstructed data and capture the features in the sequence.

[0045] The method for predicting the remaining lifespan of lithium batteries based on multi-mode collaborative compressed sensing and IDMamba as described in claim 4 is characterized in that: the cross-convolutional structure in S5 smoothly expresses the ability through interaction between the dual-branch structure and cross features;

[0046] The input is processed through two parallel standard one-dimensional convolutional branches to extract features, and after passing through the SiLu activation function and Dropout regularization, the features are cross-multiplied to generate complementary features.

[0047] Then, dilated convolution is used to expand the receptive field and capture long-range dependencies;

[0048] Finally, the dual-branch output is fused through residual connections. This module can effectively mine data features and aggregate complementary features through multi-scale feature interaction, thereby improving prediction accuracy and robustness.

[0049] The process formula for the cross structure is as follows:

[0050] O=D1(φ(Conv1(x'))⊙Conv2(x'))+D2(φ(Conv2(x'))⊙Conv1(x'))

[0051] Where φ is the SiLu activation function; Conv1 and Conv2 are two standard one-dimensional convolutional layers; D1 and D2 are two dilated convolutions; and x' represents the input.

[0052] The method for predicting the remaining lifespan of lithium batteries based on multi-mode collaborative compressed sensing and IDMamba as described in claim 5 is characterized in that: the trend-sensing weighted exponential moving average module in S5 is the DEMA module.

[0053] The DEMA module, by fusing first-order and second-order differences and dynamically adjusting smoothing weights, achieves sensitive capture of local fluctuations and trend accelerations. The DEMA module enhances the modeling ability of cross-period features, thereby improving the model's adaptability to complex time series and its predictive performance. The expression is as follows:

[0054] First, calculate the difference between adjacent time steps:

[0055] d t =|x t -x t-1 |

[0056] This difference measure reflects the degree of short-term fluctuation in the sequence at each time point. To more accurately perceive changes in the sequence trend, the rate of change of difference, i.e., second-order difference, is further introduced:

[0057] d' t =|d t -d t-1 |

[0058] This step can be seen as a measure of the "acceleration" of trend changes, reflecting whether the sequence change is intensifying or stabilizing;

[0059] Then, the first-order difference d is fused. t Second-order difference d' t Construct a difference metric that integrates trend perception:

[0060]

[0061] Here, δ is a hyperparameter used to adjust the degree of influence of trend changes on the overall difference, and then the difference is mapped to a dynamic weighting factor using an exponential decay method:

[0062] scale t =exp(-β·((1-δ)·|x t -x t-1 |+δ·|x t -2x t-1 +x t-2 |)

[0063] Here, β is a dynamically adjusted intensity hyperparameter that controls the degree to which the magnitude of the difference suppresses the weights; the larger the difference, the more drastic the fluctuation, and the corresponding scale... t The smaller the value, the lower the impact at that moment; the smaller the difference, the greater the scale. t The closer it is to 1, the more information about that moment is retained;

[0064] The dynamic weights are calculated as follows:

[0065]

[0066] Here, α is a hyperparameter that determines the degree to which the weight decreases over time at each moment;

[0067] The final expression is:

[0068]

[0069] Finally, the output is completed after all processing. The process is as follows:

[0070]

[0071] Will The input is fed into the linear mapping layer to produce the final predicted output C.

[0072] Compared with the prior art, the beneficial effects of the present invention are:

[0073] 1. This invention employs a multimodal collaborative compressed sensing (MCS) and IDMamba neural network model, which has the advantage of data denoising. MCS is used to process sequential data, mapping the data to a low-dimensional measurement space to remove redundant information and noise. Subsequently, data reconstruction is performed. In this process, a self-attention mechanism is added to focus more on key features, and layer normalization is used to improve stability. This compressed reconstruction helps to remove redundant components of the original data, providing a clearer data view and helping to better understand the essence of the data.

[0074] 2. This invention possesses feature interaction and nonlinear transformation capabilities. ICDB constructs a feature interaction network through multi-branch convolution operations, mapping the input sequence to the hidden layer space via convolution. Nonlinear characteristics are introduced through the SiLU activation function, and element-wise multiplication is used to achieve cross-channel feature fusion. Dilated convolution is then used to capture long-distance dependencies. This architecture effectively extracts local features and global dependencies from sequence data, and smooths the model's ability to express temporal patterns through dynamic feature interaction, providing more discriminative feature representations for subsequent sequence modeling.

[0075] 3. This invention possesses dynamic exponential weighting and sequence feature enhancement capabilities. DEMA constructs an adaptive weighted model for time series signals by integrating a basic exponential moving average mechanism with a dynamic weight adjustment strategy. This module first generates exponentially decaying basic weights based on the alpha parameter, and then calculates first- and second-order dynamic adjustment factors based on the differences between adjacent time steps to achieve adaptive correction of the weights. This architecture can capture the local variation characteristics of sequence data, enhance the response capability to abrupt signals, and simultaneously retain the long-term dependence of historical information through weighted accumulation and calculation, providing a feature representation for subsequent time series modeling that combines dynamic adaptability and historical memory.

[0076] 4. This invention features multivariate multi-step prediction. The model is a multivariate multi-step prediction model that combines MCS processing sequence and IDMamba prediction. This combination utilizes the characteristics of MCS and uses the IDMamba model for prediction to achieve the prediction of the remaining lifespan of lithium batteries. Attached Figure Description

[0077] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0078] Figure 1 This is a schematic diagram of the CIDMamba model framework of the present invention;

[0079] Figure 2 This is a battery capacity degradation roadmap from NASA and CALCE, in which... Figure 2 (a) shows three batteries from NASA. Figure 2 (b) are the four batteries of CALCE;

[0080] Figure 3 This is a prediction graph of the capacity degradation curves of four batteries in the CALCE system of this invention. Figure 3 (a) is CS2_35. Figure 3 (b) is CS2_36. Figure 3 For (c)CS2_37, Figure 3 (d) is CS2_38.

[0081] Figure 4 This is a prediction graph of the capacity degradation curves of four NASA batteries in this invention, where... Figure 4 (a) is B0005. Figure 4 (b) is B0006. Figure 4 (c) is B0007. Figure 4 (d) is B0018. Detailed Implementation

[0082] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0083] Please see Figure 1 The method for predicting the remaining lifespan of lithium batteries based on multi-mode collaborative compressed sensing and the IDMamba lithium battery includes at least the following steps:

[0084] S1: Construct the basic model, based on multi-modal collaborative compressed sensing and IDMamba;

[0085] S2: Use the basic model to predict the future trend of multiple variables, that is, use the model to make multi-variable multi-step predictions;

[0086] S3: The input data is compressed and reduced in dimensionality using MCS to remove redundant information and noise, while retaining key features, so that subsequent models can focus more on highlighting these prominent features.

[0087] S4: Use state-space model and recursion mechanism to capture the dynamic correlation between multiple variables. Input the multivariate sequence processed in S3 into the IDMamba model. For all time points of each sequence, embed the hidden state space through linear projection. The recursion mechanism of the state-space model and the gating unit work together to capture the dynamic correlation between multiple variables.

[0088] S5: By stacking and improving convolution methods, the prediction performance is further improved. The entire model is constructed by stacking multiple layers. The improved cross-convolution structure contained in IDMamba can better extract the latent features in the sequence. The trend-aware weighted exponential moving average module dynamically enhances and adaptively fuses the time-series features of the parallel branch data after dynamic exponential smoothing, accurately capturing the fluctuation patterns in the time-series data, thereby improving the prediction performance of the model.

[0089] According to claim 1, the method for predicting the remaining lifespan of a lithium battery based on multi-mode cooperative compressed sensing and IDMamba is characterized in that: step S2 includes at least the following steps:

[0090] First, historical data on lithium batteries is provided:

[0091]

[0092] This indicates that there are L sequence lengths and d variables;

[0093] Historical data is used as the training data.

[0094] Finally, a fixed length k is set as the prediction window step size for prediction:

[0095]

[0096] Among them, c t+i (i = 1, 2, 3, ..., k) represents the current remaining capacity of the lithium battery.

[0097] The method for predicting the remaining lifespan of a lithium battery based on multi-mode collaborative compressed sensing and IDMamba as described in claim 2 is characterized in that: step S3 includes at least the following steps:

[0098] The lithium battery capacity degradation data is compressed and reconstructed using MCS to obtain key reconstructed data, which is then used for reinforcement learning in subsequent parts of the model.

[0099] First, generate a Weibull distribution measurement matrix. Compression measurements were then performed.

[0100] y t =Φx t

[0101] Among them, y t Represents compressed low-dimensional data; x t This represents the original data before compression; t is the current time step.

[0102] Subsequently, a fast iterative thresholding algorithm, namely FISTA, is used to sparsely decode low-dimensional observations. In each iteration, the solution vector is updated based on gradient descent and soft thresholding operations. η is a dynamically adjusted step size factor that we introduce.

[0103]

[0104]

[0105] Where, x i Represents a sample of the input signal, |x i | represents the absolute value of each sample; n represents the number of signal samples; λ is the initialization step size; μ abs It is the absolute mean of the input signal, used to dynamically adjust the step size so that the step size matches the overall amplitude of the input signal, thereby improving numerical stability;

[0106] In each iteration, the update process is as follows:

[0107]

[0108] Among them, g (k) It is the current gradient direction; z (k)It is an intermediate variable that incorporates historical information under the momentum mechanism. After calculating the gradient step size, a learnable soft thresholding operation is applied, with channel adaptive scaling. T represents the matrix transpose operation. Through the iterative update mechanism of the dynamic step size factor and momentum auxiliary variable, the iterative convergence speed is improved from O(1 / k) of ISTA = to O(1 / k). 2 FISTA sparse coding can achieve fast and stable convergence, significantly improving the performance of compressed sensing models.

[0109] After sparse coding is completed, a learnable reconstruction dictionary is designed to achieve accurate signal reconstruction. To ensure initial expressive power, the dictionary is constructed using discrete cosine transform during initialization:

[0110]

[0111] Among them, D k,i It is a two-dimensional array, where k and i are the row and column indices, respectively;

[0112] When k = 0 This means that the first element of the dictionary is a constant, and its size is [value]. Where D is the dimension of the dictionary;

[0113] When k = 1, ..., D-1, D k,i A formula based on the cosine function was used, which means that the k-th row of the dictionary is generated by a cosine function, and each row has a different phase and frequency, in order to ensure that the elements of the dictionary have good distribution and spectral characteristics.

[0114] Furthermore, the model was continuously optimized during training. To avoid overfitting and enhance model stability, an e2 regularization term was introduced to normalize the dictionary.

[0115] To further improve reconstruction performance, an attention mechanism module was introduced. First, the sparse encoding x of the FISTA output was processed. (k) Normalization is performed, and then the data is fed into an attention network to extract correlation information between channels and feature dimensions, forming an attention-enhanced sparse representation. Finally, it is reconstructed using a dictionary matrix, and residual connections are performed after this normalization process to retain the trend information of the original battery mid-term data, resulting in the reconstruction result:

[0116]

[0117] Where Attention represents self-attention; LN represents layer normalization; D T Represents the transpose of the dictionary matrix D

[0118] IDMamba was used to extract features from the reconstructed data and capture the features in the sequence.

[0119] The method for predicting the remaining lifespan of lithium batteries based on multi-mode collaborative compressed sensing and IDMamba as described in claim 4 is characterized in that: the cross-convolutional structure in S5 smoothly expresses the ability through interaction between the dual-branch structure and cross features;

[0120] The input is processed through two parallel standard one-dimensional convolutional branches to extract features, and after passing through the SiLu activation function and Dropout regularization, the features are cross-multiplied to generate complementary features.

[0121] Then, dilated convolution is used to expand the receptive field and capture long-range dependencies;

[0122] Finally, the dual-branch output is fused through residual connections. This module can effectively mine data features and aggregate complementary features through multi-scale feature interaction, thereby improving prediction accuracy and robustness.

[0123] The process formula for the cross structure is as follows:

[0124] O=D1(φ(Conv1(x'))⊙Conv2(x'))+D2(φ(Conv2(x'))⊙Conv1(x'))

[0125] Where φ is the SiLu activation function; Conv1 and Conv2 are two standard one-dimensional convolutional layers; D1 and D2 are two dilated convolutions; and x' represents the input.

[0126] The method for predicting the remaining lifespan of lithium batteries based on multi-mode collaborative compressed sensing and IDMamba as described in claim 5 is characterized in that: the trend-sensing weighted exponential moving average module in S5 is the DEMA module.

[0127] The DEMA module, by fusing first-order and second-order differences and dynamically adjusting smoothing weights, achieves sensitive capture of local fluctuations and trend accelerations. The DEMA module enhances the modeling ability of cross-period features, thereby improving the model's adaptability to complex time series and its predictive performance. The expression is as follows:

[0128] First, calculate the difference between adjacent time steps:

[0129] d t =|x t -x t-1 |

[0130] This difference measure reflects the degree of short-term fluctuation in the sequence at each time point. To more accurately perceive changes in the sequence trend, the rate of change of difference, i.e., second-order difference, is further introduced:

[0131] d't =|d t -d t-1 |

[0132] This step can be seen as a measure of the "acceleration" of trend changes, reflecting whether the sequence change is intensifying or stabilizing;

[0133] Then, the first-order difference d is fused. t Second-order difference d' t Construct a difference metric that integrates trend perception:

[0134]

[0135] Here, δ is a hyperparameter used to adjust the degree of influence of trend changes on the overall difference, and then the difference is mapped to a dynamic weighting factor using an exponential decay method:

[0136] scale t =exp(-β·((1-δ)·|x t -x t-1 |+δ·|x t -2x t-1 +x t-2 |)

[0137] Here, β is a dynamically adjusted intensity hyperparameter that controls the degree to which the magnitude of the difference suppresses the weights; the larger the difference, the more drastic the fluctuation, and the corresponding scale... t The smaller the value, the lower the impact at that moment; the smaller the difference, the greater the scale. t The closer it is to 1, the more information about that moment is retained;

[0138] The dynamic weights are calculated as follows:

[0139]

[0140] Here, α is a hyperparameter that determines the degree to which the weight decreases over time at each moment;

[0141] The final expression is:

[0142]

[0143] Finally, the output is completed after all processing. The process is as follows:

[0144]

[0145] Will The input is fed into the linear mapping layer to produce the final predicted output C.

[0146] A brief introduction to the specific solution based on the above embodiments:

[0147] 1. Introduction to the model framework:

[0148] This invention proposes a model based on multimodal collaborative compressed sensing and interactive smoothing Mamba to predict the remaining lifespan of lithium batteries. The model consists of three main parts: an MCS processing sequence, IDMamba prediction, and improved cross-convolution and dynamic exponential smoothing within the model. The proposed model is a multivariate, multi-step prediction model that compresses and reconstructs lithium battery capacity degradation data to obtain denoised reconstructed data containing key features of the original data. Then, it uses the IDMamba neural network model for prediction, employing its innovative cross-convolution and dynamic exponential smoothing methods to capture features from the data. The model architecture of this invention is as follows: Figure 1 As shown.

[0149] 2. MCS:

[0150] In lithium battery capacity degradation data sequences, besides obvious features such as degradation and capacity regeneration information, there are also some potential time-series related features that are often difficult to discover. First, this invention applies multi-modal collaborative compressed sensing technology, using a measurement matrix constructed through a Weibull distribution to map high-dimensional time-series data to a low-dimensional measurement space, obtaining compressed low-dimensional data. This process not only effectively reduces dimensionality but also removes a large amount of redundant information and noise from the original data, retaining key features. Second, this invention uses an improved IDMamba to extract features from the reconstructed data, capturing the features within the reconstructed data, which helps extract salient features from multiple variables.

[0151] Cross-convolution ICDB

[0152] To effectively utilize the information features in a sequence, this invention constructs a novel cross-convolutional structure, which is a cross-structure. Traditional convolution uses the output of the previous layer as input to the next convolution. While simple convolutional layers can improve the trainability of the network model, their feature extraction capabilities may be insufficient. Therefore, we propose a cross-convolutional structure that outputs by cross-combining the results of two paths. The proposed cross-structure has two convolutional branches, such as... Figure 1 As shown.

[0153] Dynamic Exponential Smoothing DEMA

[0154] To enhance the ability of state-space models to model time-series features, this invention constructs a novel Dynamic Exponential Moving Average (DEMA) structure in the residual branch of the Mamba module. While residual connections in Mamba can alleviate the training problems of deep networks, their ability to dynamically capture time-series features is limited. Therefore, we propose a dynamically adjusted moving average structure with a time complexity of O(n). This structure adaptively adjusts the weight distribution of the residual branch by calculating the exponential decay of the first-order and second-order differences at each time step. Combined with selective state space and interactive convolutional modules, this structure enhances the modeling ability for dynamic time-series features while maintaining the model's expressive power, thereby improving overall prediction performance.

[0155] 4. Dataset:

[0156] To evaluate the method proposed in this invention, two datasets that have been widely used in the field of lithium battery remaining life prediction in recent years were used: the NASA lithium battery dataset and the University of Maryland CALCE lithium battery dataset.

[0157] The NASA lithium-ion battery dataset includes aging data for four different types of lithium-ion batteries: B0005, B0006, B0007, and B0018. These datasets record the charging, discharging, and impedance measurement processes. During charging, a constant current (CC) mode of 1.5A was used until the battery voltage reached 4.2V, then switched to a constant voltage (CV) mode until the charging current dropped to 20mA. The discharging process was performed in a constant current (CC) mode of 2A until the battery voltage dropped to 2.7V, 2.5V, and 2.2V, respectively. The NASA dataset defines the failure threshold as 70% of the rated capacity (i.e., 2.0Ah to 1.4Ah). Figure 2 This shows the capacity degradation curves of four different types of lithium batteries from NASA as the number of cycles increases.

[0158] The CALCE lithium battery dataset includes four identically numbered batteries: CS2_35, CS2_36, CS2_37, and CS2_38. These datasets were collected at a constant temperature of 1°C. The charging process is similar to the NASA dataset, using constant current (CC) mode until the battery voltage reaches 4.2V, then switching to constant voltage (CV) mode until the charging current drops to 20mA. The discharging process is performed in constant current (CC) mode until the battery voltage drops to 2.7V and then stops. The fault threshold for the CALCE dataset is the same as that for the NASA dataset, at 70% of the rated capacity (i.e., from 1.1Ah to 0.77Ah). The capacity degradation curves for the CALCE lithium battery dataset are shown below. Figure 2 As shown:

[0159] The CALCE dataset has undergone more than 800 charge-discharge cycles, which is more than five times that of the NASA dataset. It can represent long-life and short-life lithium batteries respectively. For the capacity degradation of batteries with different lifespans, it can better reflect the ability of the method of this invention to mine diverse features.

[0160] 5. Evaluation Indicators:

[0161] To evaluate the performance of the proposed method, this invention selected the mean absolute error (MAE) and root mean square error (RMSE). The smaller the values ​​of MAE and RMSE, the higher the accuracy of the proposed method in predicting the lifespan of lithium batteries. The calculation formulas are as follows:

[0162]

[0163] y i Actual capacity The capacity is predicted by the proposed method, and n is the number of predicted iterations.

[0164] Secondly, this invention uses absolute error (AE) to evaluate the remaining capacity of a lithium battery when it drops to its end-of-life (EOL). The difference between the actual number of cycles and the predicted number of cycles is defined as follows:

[0165] AE = |T RUL -P RUL |,

[0166] This example combines Multimodal Collaborative Compressed Sensing (MCS) and IDMamba techniques. This method improves the accuracy of predicting remaining battery life (RUL) through compression denoising and feature capture. MCS effectively processes battery degradation data, compressing it into low-dimensional data, removing redundant information, and reconstructing it into its original dimensionality. IDMamba then effectively utilizes this data for RUL prediction. In this way, the present invention can more accurately assess the battery's health status and remaining life, providing more reliable support for battery management systems. Compared to traditional data-driven methods, the method of the present invention has better robustness and predictive performance, and can handle large-scale data without sacrificing computational efficiency and real-time performance. Therefore, the method of this patent effectively addresses the objective shortcomings of existing technologies in RUL prediction, providing important support for improving the performance and reliability of battery management systems.

[0167] This invention employs various testing methods to compare the prediction results of the proposed method with those of existing technologies, which include at least baseline models such as LSTM, Transformer, Pathformer, and TDANet, thereby verifying the accuracy and effectiveness of the proposed method.

[0168] In addition, to explore the effectiveness of different modules of the proposed method, this invention was compared with hybrid models such as LSTM, Transformer, FBAME, and TDANet, all using the NASA lithium battery dataset and the CALCE lithium battery dataset.

[0169] This invention performs a grid search on all investigateable parameters on the validation set of each dataset. Table 2 reports the final hyperparameters for all methods on the datasets. This invention uses the ADAM optimizer with decaying learning rate to train the model and sets an early stopping training strategy to avoid overfitting.

[0170] Table 1. Detailed information on different datasets and CIDMamba model parameters.

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[0173] According to Table 2, this invention demonstrates that, in two different datasets, the model of this invention outperforms the baseline model in predicting the remaining lifespan of lithium batteries, indicating that the method of this invention can effectively extract time-series features and use them for modeling. Furthermore, the superior performance of the Mamba model in battery degradation prediction compared to other baseline models shows that dynamic global features are crucial for capturing degradation trends. This is because Mamba utilizes a synergistic design of a state-space model (SSM) architecture and a gating mechanism: it models long-term time-series dependencies with a state transition matrix of linear complexity, efficiently capturing global dynamic correlations in the lithium battery degradation process; the parallel state update network can synchronously fuse the potential coupling relationships of multiple variables such as voltage and current, and adaptively weight the feature contributions of different variables through dynamic gating; the combination of state-space mapping and gating activation can also filter periodic noise in charge-discharge cycles and enhance the propagation of degradation-sensitive features such as capacity decay. The model of this invention, on the other hand, considers the potential correlations between variables and the global features of different variables, thus achieving better predictive performance than the Mamba model.

[0174] Table 2 compares the prediction results of different baseline models for lithium battery data, with 50% of the training samples used.

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[0176] The following points can be drawn from Table 2:

[0177] 1) The model of this invention outperforms other hybrid models in most cases. For the CALCE dataset, the MAEs and RMSEs obtained by the method of this invention are 0.0129 and 0.0214, respectively, which are improvements of 32.6% and 9.4% compared with the second-best method. For the NASA dataset, the MAE and RMSE of our method are improved by 29.3% and 26.2%, respectively. Moreover, for RUL prediction, the RUL prediction error of the proposed method is stronger than that of other hybrid models.

[0178] 2) In most cases, the model using MCS for data compression and reconstruction performs better than the model without compression and reconstruction. However, in a few slightly rare cases, it performs slightly better than the model without signal compression and reconstruction. This invention notes that in the first three NASA datasets, the model without MCS performed slightly worse than the model in this invention. This is because NASA's lithium battery dataset is too small, and MCS relies on the assumption of signal sparsity and the compression sampling mechanism to extract features. When the dataset size is limited, resulting in insufficient sparse representation of the signal and poor fit between the sparse basis and the battery signal characteristics, MCS struggles to accurately capture signal features. Therefore, the prediction results after using MCS for sequence compression and reconstruction in the NASA dataset are similar to those in Mamba.

[0179] Figure 3 Results from the CACLE dataset show that the method proposed in this invention provides the closest prediction of the battery capacity degradation curve to the actual degradation curve. Specifically, the RUL predictions for both datasets use 50% as the prediction starting point, indicating that the model using dynamic exponential smoothing better predicts the capacity degradation trend among several models. Furthermore, compared with the prediction curves of other hybrid models, the model of this invention has stronger adaptability to random fluctuations in battery capacity.

[0180] Figure 4 In NASA, where the data volume is much smaller, most models can effectively uncover degradation features and make predictions. However, the method of this invention processes the original data through multi-modal collaborative compressed sensing (MCS), which can uncover the potential features (such as capacity regeneration feature information or other potential features) contained in the compressed and reconstructed data, thereby making the model's capacity degradation prediction closer to the real capacity degradation process.

[0181] In summary:

[0182] This invention is used to predict the remaining lifespan of lithium batteries and has the following advantages:

[0183] Sparse representation: Multi-mode collaborative compressed sensing is used to process battery data. It maps high-dimensional data to a low-dimensional space through sparse basis transformation. This representation can accurately reconstruct the original signal from a small amount of sampled data, effectively reducing data redundancy while retaining key features, providing a simpler and more information-rich data foundation for subsequent prediction.

[0184] Dynamic time-series modeling: Building upon the advantages of Mamba's linear state-space model and gating mechanism, we innovatively incorporate deep interaction and dynamic modulation module mechanisms. IDMamba can more efficiently capture long-distance dependencies and dynamic change patterns in the battery degradation process. Its unique update mechanism can adaptively handle features at different time scales, and has a stronger ability to characterize nonlinear trends and sudden anomalies in battery performance degradation, which helps to improve the accuracy and robustness of remaining service life prediction.

[0185] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A method for predicting the remaining lifespan of lithium batteries based on multi-mode collaborative compressed sensing and IDMamba, characterized in that: At least the following steps are included: S1: Construct the basic model, based on multi-modal collaborative compressed sensing and IDMamba; S2: Use the basic model to predict the future trend of multiple variables, that is, use the model to make multi-variable multi-step predictions; S3: The input data is compressed and reduced in dimensionality using MCS to remove redundant information and noise, while retaining key features, so that subsequent models can focus more on highlighting these prominent features. S4: Use state-space model and recursion mechanism to capture the dynamic correlation between multiple variables. Input the multivariate sequence processed in S3 into the IDMamba model. For all time points of each sequence, embed the hidden state space through linear projection. The recursion mechanism of the state-space model and the gating unit work together to capture the dynamic correlation between multiple variables. S5: By stacking and improving convolution methods, the prediction performance is further improved. The entire model is constructed by stacking multiple layers. The improved cross-convolution structure contained in IDMamba can better extract the latent features in the sequence. The trend-aware weighted exponential moving average module dynamically enhances and adaptively fuses the time-series features of the parallel branch data after dynamic exponential smoothing, accurately capturing the fluctuation patterns in the time-series data, thereby improving the prediction performance of the model.

2. The method for predicting the remaining lifespan of a lithium battery based on multi-mode collaborative compressed sensing and IDMamba as described in claim 1, characterized in that: S2 includes at least the following steps: First, historical data on lithium batteries is provided: This indicates that there are L sequence lengths and d variables; Historical data is used as the training data. Finally, a fixed length k is set as the prediction window step size for prediction: Among them, c t+i (i = 1, 2, 3, ..., k) represents the current remaining capacity of the lithium battery.

3. The method for predicting the remaining lifespan of a lithium battery based on multi-mode collaborative compressed sensing and IDMamba as described in claim 2, characterized in that: The S3 includes at least the following steps: The lithium battery capacity degradation data is compressed and reconstructed using MCS to obtain key reconstructed data, which is then used for reinforcement learning in subsequent parts of the model. First, generate a Weibull distribution measurement matrix. Compression measurements were then performed. y t =Φx t Among them, y t Represents compressed low-dimensional data; x t This represents the original data before compression; t is the current time step. Subsequently, a fast iterative thresholding algorithm, namely FISTA, is used to sparsely decode low-dimensional observations. In each iteration, the solution vector is updated based on gradient descent and soft thresholding operations. η is a dynamically adjusted step size factor that we introduce. Where, x i Represents a sample of the input signal, |x i | represents the absolute value of each sample; n represents the number of signal samples; λ is the initialization step size; μ abs It is the absolute mean of the input signal, used to dynamically adjust the step size so that the step size matches the overall amplitude of the input signal, thereby improving numerical stability; In each iteration, the update process is as follows: Among them, g (k) It is the current gradient direction; z (k) It is an intermediate variable that incorporates historical information under the momentum mechanism. After calculating the gradient step size, a learnable soft thresholding operation is applied, with channel adaptive scaling. T represents the matrix transpose operation. Through the iterative update mechanism of the dynamic step size factor and momentum auxiliary variable, the iterative convergence speed is improved from O(1 / k) of ISTA = to O(1 / k). 2 FISTA sparse coding can achieve fast and stable convergence, significantly improving the performance of compressed sensing models. After sparse coding is completed, a learnable reconstruction dictionary is designed to achieve accurate signal reconstruction. To ensure initial expressive power, the dictionary is constructed using discrete cosine transform during initialization: Among them, D k,i It is a two-dimensional array, where k and i are the row and column indices, respectively; When k = 0 This means that the first element of the dictionary is a constant, and its size is [value]. Where D is the dimension of the dictionary; When k = 1, ..., D-1, D k,i A formula based on the cosine function was used, which means that the k-th row of the dictionary is generated by a cosine function, and each row has a different phase and frequency, in order to ensure that the elements of the dictionary have good distribution and spectral characteristics. Furthermore, during the training process, the model was continuously optimized. To avoid overfitting and enhance model stability, an L2 regularization term was introduced to normalize the dictionary. To further improve reconstruction performance, an attention mechanism module was introduced. First, the sparse encoding x of the FISTA output was processed. (k) Normalization is performed, and then the data is fed into an attention network to extract correlation information between channels and feature dimensions, forming an attention-enhanced sparse representation. Finally, it is reconstructed using a dictionary matrix, and residual connections are performed after this normalization process to retain the trend information of the original battery mid-term data, resulting in the reconstruction result: Where Attention represents self-attention; LN represents layer normalization; D T This represents the transpose of the dictionary matrix D. IDMamba was used to extract features from the reconstructed data and capture the features in the sequence.

4. The method for predicting the remaining lifespan of a lithium battery based on multi-mode collaborative compressed sensing and IDMamba as described in claim 4, characterized in that: The S5 cross-convolutional structure smoothly expresses capabilities through the interaction of a dual-branch structure and cross features. The input is processed through two parallel standard one-dimensional convolutional branches to extract features, and after passing through the SiLu activation function and Dropout regularization, the features are cross-multiplied to generate complementary features. Then, dilated convolution is used to expand the receptive field and capture long-range dependencies; Finally, the dual-branch output is fused through residual connections. This module can effectively mine data features and aggregate complementary features through multi-scale feature interaction, thereby improving prediction accuracy and robustness. The process formula for the cross structure is as follows: O=D1(φ(Conv1(x'))⊙Conv2(x'))+D2(φ(Conv2(x'))⊙Conv1(x')) Where φ is the SiLu activation function; Conv1 and Conv2 are two standard one-dimensional convolutional layers; D1 and D2 are two dilated convolutions; and x' represents the input.

5. The method for predicting the remaining lifespan of a lithium battery based on multi-mode collaborative compressed sensing and IDMamba as described in claim 5, characterized in that: The trend-aware weighted exponential moving average module in S5 is the DEMA module. The DEMA module, by fusing first-order and second-order differences and dynamically adjusting smoothing weights, achieves sensitive capture of local fluctuations and trend accelerations. The DEMA module enhances the modeling ability of cross-period features, thereby improving the model's adaptability to complex time series and its predictive performance. The expression is as follows: First, calculate the difference between adjacent time steps: d t =|x t -x t-1 | This difference measure reflects the degree of short-term fluctuation in the sequence at each time point. To more accurately perceive changes in the sequence trend, the rate of change of difference, i.e., second-order difference, is further introduced: d' t =|d t -d t-1 | This step can be seen as a measure of the "acceleration" of trend changes, reflecting whether the sequence change is intensifying or stabilizing. Then, the first-order difference d is fused. t Second-order difference d' t Construct a difference metric that integrates trend perception: Here, δ is a hyperparameter used to adjust the degree of influence of trend changes on the overall difference, and then the difference is mapped to a dynamic weighting factor using an exponential decay method: scale t =exp(-β·((1-δ)·|x t -x t-1 |+δ·|x t -2x t-1 +x t-2 |) Here, β is a dynamically adjusted intensity hyperparameter that controls the degree to which the magnitude of the difference suppresses the weights; the larger the difference, the more drastic the fluctuation, and the corresponding scale... t The smaller the value, the lower the impact at that moment; the smaller the difference, the greater the scale. t The closer it is to 1, the more information about that moment is retained; The dynamic weights are calculated as follows: Here, α is a hyperparameter that determines the degree to which the weight at each time point decreases over time; The final expression is: Finally, the output is completed after all processing. The process is as follows: Will The input is fed into the linear mapping layer to produce the final predicted output C.

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