A Lithium-ion Battery Life Prediction Method Based on Improved ELM

Abstract

This invention discloses a lithium-ion battery lifetime prediction method based on an improved ELM (Elastic Matrix Modeling). One approach is to replace the fully connected relationship between the input and hidden layers of the ELM with a convolutional operation. Specifically, a regular-sized convolutional kernel is introduced, treated as a variation of the original connection weights between the input and hidden layers, and convolved with the input data. The extracted feature matrix is ​​then subjected to average pooling to obtain the hidden layer output matrix H. Finally, the Moore-Penrose generalized inverse H is calculated... + Multiplying the output matrix of the training set by the output matrix yields the output weight matrix β, which is then substituted into the test set data for result prediction. Another approach is to replace the fully connected relationship between the ELM input layer and hidden layer with pooling; that is, the input layer data is directly pooled to obtain the hidden layer output matrix H, and then the Moore-Penrose generalized inverse H is calculated. + The output weight matrix β is obtained by multiplying the output matrix of the training set with the output matrix of the training set, and then used to predict the result by substituting it into the test set data. This invention makes the prediction results more accurate and robust.

Description

[0001] This application is a divisional application of application number 202011518358.5, filed on December 21, 2020, entitled "A method for predicting the lifespan of a lithium-ion battery based on an improved ELM". Technical Field

[0002] This invention relates to a lithium-ion battery life prediction method based on an improved ELM (Extreme Learning Machine) algorithm, belonging to the field of lithium battery health management technology. Background Technology

[0003] Lithium-ion batteries are widely used in various industries due to their small size, light weight, high energy density, wide operating range, fast charge and discharge rate, and environmental friendliness, such as mobile phones, computers, airplanes, power tools, automobiles, and cameras. Therefore, lithium-ion batteries are ubiquitous in daily life, and their application prospects are very promising. However, due to various external and internal environmental factors, lithium-ion batteries inevitably age after a period of use, significantly affecting their performance. In severe cases, when the performance of lithium-ion batteries degrades to a certain level, battery leakage, insulation damage, and partial short circuits can lead to catastrophic accidents. Therefore, the discipline of Prognostics and Health Management (PHM) is particularly important. Remaining useful life (RUL), as an important research direction in this discipline, plays a crucial role in the accurate prediction of safety, reliability, and economy.

[0004] Generally, the rated uptime (RUL) of a lithium-ion battery is defined as the number of charge-discharge cycles remaining before performance degrades to the rated failure threshold. Lithium-ion battery degradation can be characterized by health indicators (HIs), such as current, voltage, impedance, and capacity. Among these, capacity degradation and RUL prediction have become a significant concern. Existing literature on RUL prediction for lithium-ion batteries can be broadly categorized into three types: model-based methods, data-driven methods, and hybrid methods.

[0005] In model-based methods, usable models include electrochemical models, equivalent circuit models, and empirical models. Electrochemical models are constructed based on specific physicochemical reaction processes within the battery, providing a detailed and accurate description of the intrinsic causes and complex mechanisms of battery aging. While this model offers a deep understanding of the battery's inherent characteristics, and a well-constructed model can predict RUL (Range Ultra-Long Term Indicator) well, its construction requires consideration of numerous internal factors and various external disturbances, resulting in a large number of parameters that need to be estimated, leading to high computational costs and making it difficult to implement in practical applications. Equivalent circuit models aim to simplify circuit analysis by using resistive elements such as resistors, capacitors, and voltage sources to construct a simple circuit that approximates the dynamic characteristics of the battery. Common lithium-ion battery equivalent circuit models include the Rint model, RC model, Thevenin model, and PNGV model. Furthermore, many derived parameter identification methods have further refined the models, enhancing their reliability. This model is more applicable than the electrochemical model, but it still involves a large number of parameter estimations and remains quite complex. Unlike these two models, empirical models are established by using parameters reflecting battery performance, such as capacity, internal resistance, and final discharge voltage, to obtain the trends of these state parameters over time or the recursive relationship between the state variables of the system at two different time points, thus enabling the prediction of the battery's rated capacity limit (RUL). He et al. proposed a four-parameter empirical exponential model for capacity degradation and performed curve fitting on battery capacity decay data. Based on this model, many filtering algorithms, such as extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filtering (PF), and unscented particle filtering (UPF), are widely used for RUL prediction. Xing et al. proposed a combined model to describe capacity degradation, which integrates empirical exponential and multinomial regression models, and then uses PF to adjust the model parameters online to achieve RUL prediction for lithium batteries. Miao et al. proposed an improved UPF method based on MCMC to predict the RUL of lithium batteries. Duong et al. introduced the heuristic Kalman algorithm (HKA), which, combined with power factor (PF), can accurately predict the relative uptime (RUL) of lithium batteries. Therefore, numerous studies have focused on two main improvements to this method: improvements to the empirical model and improvements to the filtering algorithm. Besides capacity-based empirical models, there are other types of empirical models, such as resistance-based exponential growth models and models with linear parameter variations.Empirical models for lithium batteries are easier to build than the previous two models, significantly reducing the workload and broadening their applicability. However, these models are susceptible to interference from external environmental conditions such as noise, resulting in poor adaptability and robustness. Furthermore, issues such as particle depletion and parameter initialization can also make it difficult to build accurate models.

[0006] Data-driven prediction methods rely on historical data to analyze and mine lithium-ion battery performance degradation data through various data processing methods. Based on this data, corresponding relationships are established to predict the relative uptime (RUL). Commonly used data-driven methods include Support Vector Machine (SVM), Relevance Vector Machine (RVM), Autoregressive Integrated Moving Average (ARIMA) model, Hidden Markov Model (HMM), and Neural Networks (NN) methods. Neural networks, an important branch of artificial intelligence, have received significant attention in data-driven RUL prediction. Wu et al. used feedforward neural networks (FFNN) to simulate the relationship between the battery charging curve and RUL under constant current. Considering the nonlinearity of the curve, the input sampling points of the FFNN were obtained from importance sampling (IS), thus achieving online estimation of lithium-ion battery RUL. Xing et al. used battery impedance as input data and battery capacity as output data, employing an adaptive neural network to establish the relationship between battery impedance and capacity, obtaining more accurate and competitive prediction results. Liu et al. proposed an adaptive recurrent neural network (ARNN) for predicting the remaining lifespan of lithium-ion batteries. This method, through adaptive and recursive feedback, fully utilizes the previous states of the system, improving prediction accuracy. Experimental results outperform classical recurrent neural networks (RNNs) and recurrent neural fuzzy systems (RNFs). Since RNNs cannot handle long-term dependencies, the Long Short-Term Memory (LSTM) network proposed by Hochreiter et al. has become a focus of RUL prediction research. Zhang et al. used LSTM RNNs to learn the long-term dependencies between lithium battery capacity degradation and employed the Root Mean Square Propagation (RMSprop) technique for adaptive optimization of the constructed neural network, as well as packet loss techniques to address overfitting. Results demonstrate that its prediction performance surpasses that of support vector machine models, particle filter models, and simple RNN models.Yu et al. proposed a novel network model averaging method to address network model uncertainty in RUL prediction for non-lifecycle labeled datasets. The effectiveness of the proposed method was validated on a bidirectional LSTM (Bi-L-STM) network, proposed by Huang et al., which simultaneously learns forward and backward time-related information. Ren et al. combined autoencoders with deep neural networks (DNNs) for RUL prediction of lithium-ion batteries. Shen et al. utilized deep convolutional neural networks (DCNNs) to estimate lithium-ion battery capacity online, achieving higher accuracy and robustness in capacity estimation.

[0007] Hybrid approaches primarily combine two or more model-based or data-driven methods to improve prediction performance.

[0008] In recent years, data-driven methods for discovering the relationship between monitored system data and corresponding right-to-limit (RUL) predictions have received increasing attention. Numerous researchers have proposed neural network-based methods to improve RUL prediction accuracy, with deep learning networks showing particular potential in both prognostic symptom monitoring (PHM) and RUL estimation. While deep networks have well-structured architectures, their complexity due to numerous hidden layers and interconnections leads to significant time and memory consumption during training. Furthermore, network design and parameter tuning present substantial challenges. Therefore, finding a cost-effective method for accurately predicting RUL is increasingly desired by researchers.

[0009] ELM (Extreme Learning Machine) is a special type of single-hidden-layer feedforward neural network. It has only one hidden layer, a simple network structure, and does not require backpropagation to update parameter values. It learns quickly, has strong generalization ability, and can perform classification and prediction, making it widely used in computer vision, bioinformatics, environmental science, and other fields. Jiang et al. extracted the isobaric discharge time as an indirect lifetime characteristic parameter of lithium batteries and used ELM to construct a model of the relationship between this parameter and battery capacity, indirectly predicting the RUL (Relative Lifetime Limit) of lithium batteries. Wu et al. introduced the Glowworm Swarm Optimization (GSO) algorithm to optimize the randomly generated input weights and hidden layer bias values ​​of ELM, using isobaric discharge time series for indirect RUL prediction, reducing the algorithm's prediction error. Razavi-Far et al. used one-step and multi-step advance prediction in Extreme Learning Machine as a prediction module, employing various prediction strategies to estimate RUL using constant current experimental capacity data. Ma et al. introduced the idea of ​​generalized learning (BL) and developed the generalized learning-extreme learning machine (BL-ELM). This method continuously expands the input layer and increases the number of nodes in the input layer, which greatly improves the network's ability to capture effective feature information in the data.

[0010] The ELM algorithm first provides training samples, the number of hidden nodes, and the activation function type. Then, it randomly generates the weights between the input and hidden layers and the biases of the hidden layer neurons. Generally, the weights are uniformly distributed between [-1, 1], and the biases are uniformly distributed between [0, 1]. Once all initial parameter values ​​are set, the hidden layer output matrix can be calculated. The optimal output weights are calculated by minimizing the squared error of the training samples. At this point, the ELM learning algorithm is complete, yielding the optimal parameters and minimum training error. For subsequent result prediction, the input matrix of the test set is then input into the first fully connected layer of the ELM network. The result is multiplied by the output weight β to obtain the final prediction result. Its structure is as follows: Figure 1 As shown.

[0011] Analysis of previous research reveals that traditional ELMs for predicting the RUL (Relative Limiting Value) of lithium-ion batteries often fail to perform well with commonly used activation functions such as the sigmoid function, Gaussian function, polynomial function, hard limit function, and sine function. While the popular ReLU function can predict RUL at certain times, uncertainties remain, leading to divergence and low accuracy, significantly weakening the algorithm's robustness and generalization ability. Current ELM improvements primarily focus on increasing or decreasing the number of hidden layer nodes according to certain rules, optimizing parameter algorithms, and introducing kernel functions. Their input and hidden layers remain fully connected, and locally connected ELM structures have not received widespread attention. However, these improvements all increase computational complexity, and many parameters still require initialization; improper selection can negatively impact prediction results. Furthermore, the single-layer convolutional squared pooling architecture with random weights proposed by Andrew M. Saxe et al., and the Local Receptive Fields Based Extreme Learning Machine (ELM-LRF) proposed by Huang et al., both demonstrate that constructing a specific network structure can significantly improve system performance, exhibiting better results than some deep learning algorithms and greatly increasing training speed. Lin et al. proposed replacing fully connected layers with global average pooling, that is, performing global average pooling on each feature map obtained from the last multi-layer perceptron convolutional layer. This allows each feature map to obtain an output, saving parameters, reducing network complexity, and avoiding overfitting. Summary of the Invention

[0012] The purpose of this invention is to address the aforementioned problems by proposing an improved ELM-based lithium-ion battery life prediction method. This method incorporates two classic techniques: convolutional neural networks (CNNs) and global average pooling, improving ELM in two different ways. First, to address the lack of widespread attention given to the locally connected ELM structure, the first improved algorithm replaces the fully connected relationship between the input and hidden layers with convolution and pooling. Considering that in traditional ELM algorithms and their improved implementations, input layer nodes are fully connected to hidden layer nodes, failing to learn local dependencies, and that CNNs, as a special type of deep feedforward neural network, share convolutional kernel parameters and have sparse local connections between layers, significantly reducing parameter redundancy caused by fully connected layers, the fully connected relationship between the input and hidden layers of ELM is replaced with convolution and pooling operations. The subsequent method for obtaining the output weight matrix β is consistent with traditional ELM. Second, because the values ​​of the convolutional kernels and biases in the first improved algorithm are randomly generated according to the common methods used in traditional ELM, the results of each run are uncertain, easily leading to inconsistent predictions and poor algorithm robustness. Based on the above reasons, inspired by the idea of ​​global average pooling, the second improved algorithm of this invention directly replaces the fully connected relationship between the input layer and hidden layer of ELM with pooling. Similarly, the acquisition of the output weight matrix β is the same as that of standard ELM. Since there is no random generation of values ​​and no arbitrary selection of activation functions, this method eliminates the uncertainty of the prediction results. It is worth noting that since the input layer data is only a matrix, equivalent to a feature map, it is necessary to use traditional average pooling methods to reduce the dimensionality of the matrix instead of directly performing global average pooling on this matrix. This invention uses two sets of lithium-ion battery experimental data provided by the University of Maryland's Advanced Life Cycle Engineering Center and NASA's Ames Center of Excellence for Prediction to verify the effectiveness of the improved ELM algorithm.

[0013] This invention is a lithium-ion battery lifetime prediction method based on an improved ELM. The technical solution adopted to solve the aforementioned problems is as follows: The first improved algorithm first changes the fully connected relationship between the input layer and hidden layer of the ELM to a convolution operation. Specifically, a regular-sized convolution kernel is introduced, which is considered a variation of the original hidden layer weights and convolved with the input layer data. Then, the extracted feature matrix is ​​subjected to average pooling to obtain the hidden layer output matrix H. Finally, the Moore-Penrose generalized inverse H is calculated... +The output weight matrix β is obtained by multiplying the output matrix of the training set with the output matrix of the training set, completing the learning process of the algorithm. Finally, the result is predicted by inputting the test set data. The second improved algorithm first changes the fully connected relationship between the input layer and the hidden layer of ELM to pooling. That is, the input layer data can be directly processed by pooling to obtain the hidden layer output matrix H. Similarly, the Moore-Penrose generalized inverse H is then calculated... + The output weight matrix β is obtained by multiplying it with the output matrix of the training set, thus completing the learning process of the algorithm. Finally, the result is predicted by substituting it into the test set data.

[0014] This invention is a lithium-ion battery lifetime prediction method based on an improved ELM (Elastic Module Model), specifically including the following steps:

[0015] Step 101. Data Preprocessing;

[0016] Step 102. Initialize parameters;

[0017] Step 103. Perform a convolution operation on the input matrix of the training set to obtain the feature matrix tempH of the training set;

[0018] Step 104. Using the feature matrix tempH extracted in Step 103, calculate the nonlinear feature output matrix tH and the hidden layer output matrix H of the training set;

[0019] Step 105. Using the hidden layer output matrix H of the training set obtained in Step 104, calculate its Moore-Penrose generalized inverse H. + ;

[0020] Step 106. Calculate the output weight matrix β; the output weight matrix β is obtained by combining the training set output matrix T_train with the generalized inverse H. + Multiplying them together, we get: β = H + T_train.

[0021] Step 107. Using the test set input matrix P_test obtained in Step 101, calculate the feature matrix of the test set.

[0022] Step 108. The feature matrix extracted in Step 107 Calculate the nonlinear feature output matrix of the test set. With hidden layer output matrix

[0023] Step 109. The hidden layer output matrix of the test set obtained in Step 108. Multiplying the result by the output weight matrix β obtained in Step 106 yields the final prediction result, i.e.:

[0024] Specifically, Step 101 data preprocessing involves: starting from cycle period k=1, using data from every 10 consecutive cycles as a set of inputs, and the data from the next cycle as the output. This process is repeated for both sets of lithium battery data. After the construction is complete, a prediction starting point T is selected to obtain P_train; T_train; P_test; T_test, where P_train is the training set input matrix, T_train is the training set output matrix, P_test is the test set input matrix, and T_test is the test set output matrix.

[0025] The parameters initialized in Step 102 include: initializing IW; B, where IW is the convolution kernel and B is the bias.

[0026] Specifically, Step 103 involves using the preprocessed training set input matrix from Step 101 as the data for the input layer, and performing a convolution operation with the convolution kernel to obtain the feature matrix tempH of the training set, where tempH = P_train*IW + BiasMatrix, and BiasMatrix is ​​the copy expansion matrix of the bias B.

[0027] Specifically, Step 104 involves: obtaining the nonlinear feature output matrix tH by inputting the feature matrix tempH of the training set into an activation function for nonlinear feature mapping, i.e., tH = g(tempH), where g(x) is the activation function. The hidden layer output matrix H of the training set is obtained by average pooling tH.

[0028] Specifically, Step 107 involves performing a convolution operation on the test set input matrix using the same convolution kernel and bias as in Step 103 to obtain the feature matrix of the test set. The specific steps are the same as in Step 103.

[0029] Step 108 yields the nonlinear feature output matrix of the test set. With hidden layer output matrix The specific steps are the same as in Step 104.

[0030] Furthermore, the inventors provide a lithium-ion battery lifetime prediction method based on an improved ELM, specifically including the following steps:

[0031] Step 201. Data Preprocessing;

[0032] Step 202. Calculate the hidden layer output matrix H of the training set;

[0033] Step 203. Using the hidden layer output matrix H of the training set obtained in Step 202, calculate its Moore-Penrose generalized inverse H. + ;

[0034] Step 204. Calculate the output weight matrix β; use the training set output matrix T_train and the generalized inverse H... + Multiplying them together, we get: β = H + T_train;

[0035] Step 205. Using the test set input matrix P_test obtained in Step 201, calculate the hidden layer output matrix of the test set.

[0036] Step 206. Obtain the final prediction result Y, using the hidden layer output matrix of the test set obtained in Step 205. Multiplying the result by the output weight matrix β obtained in Step 204 yields the final prediction result, i.e.:

[0037] Specifically, Step 201, the data preprocessing, involves: starting from cycle period k=1, using data from every 10 consecutive cycles as a set of inputs, and the data from the next cycle as the output. This process is repeated for both sets of lithium battery data. After the construction is complete, a prediction starting point T is selected to obtain P_train; T_train; P_test; T_test, where P_train is the training set input matrix, T_train is the training set output matrix, P_test is the test set input matrix, and T_test is the test set output matrix.

[0038] Step 202 involves using the preprocessed training set input matrix P_train from Step 201 as the input layer data, and obtaining the hidden layer output matrix H from the training set input matrix P_train by directly performing average pooling.

[0039] The hidden layer output matrix of the test set obtained in Step 205 is... The test set input matrix P_test is pooled using the same method as in Step 202, with the specific steps being the same as in Step 202.

[0040] This invention discloses an improved ELM-based lithium-ion battery lifetime prediction method. Its advantages and benefits are as follows: The first improved algorithm introduces the concept of local receptive field, altering the fully connected relationship between the input layer and hidden layers. This reduces parameter redundancy and significantly lowers the computational load, making the prediction results more accurate than traditional ELM. The second improved algorithm builds upon the first, abandoning convolution and directly pooling the input layer data. Because parameter initialization and activation function selection are eliminated, the algorithm's prediction results are more stable and robust. Attached Figure Description

[0041] Figure 1 The following is a flowchart of the traditional ELM algorithm.

[0042] Figure 2a The flowchart shown is for the improved algorithm 1 (Example 1) of the present invention.

[0043] Figure 2b The flowchart shown is for the improved algorithm 2 (Example 2) of this invention.

[0044] Figure 3a The image shows the capacity variation curves of four lithium-ion battery data sets (A3, A5, A8, and A12) from the University of Maryland's Center for Advanced Life Cycle Engineering.

[0045] Figure 3b The image shows capacity variation curves for four sets of lithium-ion battery data (B5, B6, B7, and B18) from NASA's Ames Center of Excellence for Predictive Computing.

[0046] Figure 4a The image shows a comparison between the actual A12 battery data and the results of the three algorithms.

[0047] Figure 4b The figure shown is a graph comparing the actual A12 battery data with the absolute error of the three algorithms.

[0048] Figure 5a The image shows a comparison between the actual data of the B5 battery and the results of the three algorithms.

[0049] Figure 5b The figure shown is a graph comparing the actual data of the B5 battery with the absolute error of the three algorithms.

[0050] Figure 6a The image shown is an RMSE chart of A12 battery data.

[0051] Figure 6b The image shown is a MAPE graph of A12 battery data.

[0052] Figure 7a The image shown is the RMSE graph of the B5 battery data.

[0053] Figure 7b The image shown is a MAPE graph of the B5 battery data.

[0054] Figure 8a The figure shows the RMSE values ​​of each algorithm under different lithium battery data in the CALCE group.

[0055] Figure 8b The figure shows the RMSE values ​​of each algorithm under different lithium battery data from NASA.

[0056] Figure 8c The figure shows the MAPE values ​​of each algorithm under different lithium battery data in the CALCE group.

[0057] Figure 8d The figure shows the MAPE values ​​of various algorithms under different lithium battery data from NASA.

[0058] Figure 8e The figure shows the RUL values ​​of each algorithm under different lithium battery data in the CALCE group.

[0059] Figure 8f The figure shows the RUL values ​​of various algorithms under different lithium battery data from NASA. Detailed Implementation

[0060] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0061] Example 1

[0062] This invention presents an improved ELM-based method for predicting the lifetime of lithium-ion batteries, the specific process of which is as follows:

[0063] like Figure 2a As shown, the first improved algorithm:

[0064] Step 1: Data Preprocessing. Specifically, starting from cycle period k=1, data from every 10 consecutive cycles is used as a set of inputs, and data from the next cycle is used as the output. This process is repeated for both sets of lithium battery data. After construction, selecting the prediction starting point T yields P_train; T_train; P_test; T_test, where P_train is the training set input matrix, T_train is the training set output matrix, P_test is the test set input matrix, and T_test is the test set output matrix.

[0065] Step 2: Initialize parameters, including: initialize IW; B, where IW is the convolution kernel and B is the bias.

[0066] Step 3: Perform a convolution operation on the training set input matrix to obtain the feature matrix tempH of the training set. Specifically, use the preprocessed training set input matrix from Step 1 as the data for the input layer, and perform a convolution operation with the convolution kernel to obtain the feature matrix tempH of the training set, where tempH = P_train*IW + BiasMatrix, and BiasMatrix is ​​the copy expansion matrix of the bias B.

[0067] Step 4: Using the feature matrix tempH extracted in Step 3, calculate the nonlinear feature output matrix tH and the hidden layer output matrix tH of the training set. Specifically, the nonlinear feature output matrix tH is obtained by inputting the feature matrix tempH of the training set into the activation function for nonlinear feature mapping, i.e., tH = g(tempH), where g(x) is the activation function. The hidden layer output matrix H of the training set is obtained by average pooling tH.

[0068] Step 5: Using the hidden layer output matrix H of the training set obtained in Step 4, calculate its Moore-Penrose generalized inverse H. + ;

[0069] Step 6: Calculate the output weight matrix β. Use the training set output matrix T_train and the generalized inverse H... + Multiplying them yields the output weight matrix β, i.e.: β = H + T_train.

[0070] Step 7: Using the test set input matrix P_test obtained in Step 1, calculate the feature matrix of the test set. Specifically, the test set input matrix is ​​convolved using the same kernel and bias as in step three to obtain the feature matrix of the test set. Right now: The values ​​of IW and B are the same as in step three.

[0071] Step 8: The feature matrix extracted in Step 7 Calculate the nonlinear feature output matrix and hidden layer output matrix of the test set. Specifically, similar to step four, the feature matrix tempH of the training set is input into the activation function for nonlinear feature mapping to obtain the nonlinear feature output matrix. Right now: Where g(x) is the activation function. The hidden layer output matrix of the training set. Depend on Obtained through average pooling.

[0072] Step 9: Obtain the final prediction result Y. Specifically, this involves the hidden layer output matrix of the test set obtained in Step 8. Multiplying the result by the output weight matrix β obtained in step six yields the final prediction result, i.e.:

[0073] Step 10: Evaluate the algorithm.

[0074] Example 2

[0075] like Figure 2b As shown, the second improved algorithm:

[0076] Step 1: Data Preprocessing. Specifically, starting from cycle period k=1, data from every 10 consecutive cycles is used as a set of inputs, and data from the next cycle is used as the output. This process is repeated for both sets of lithium battery data. After construction, a prediction starting point T is selected, resulting in P_train; T_train; P_test; T_test, where P_train is the training set input matrix, T_train is the training set output matrix, P_test is the test set input matrix, and T_test is the test set output matrix.

[0077] Step 2: Calculate the hidden layer output matrix H of the training set. Specifically, use the preprocessed training set input matrix P_train from Step 1 as the input layer data, and obtain the hidden layer output matrix H of the training set directly by average pooling from the training set input matrix P_train.

[0078] Step 3: Using the hidden layer output matrix H of the training set obtained in Step 2, calculate its Moore-Penrose generalized inverse H. + .

[0079] Step 4: Calculate the output weight matrix β. Use the training set output matrix T_train and the generalized inverse H... + Multiplying them yields the output weight matrix β, i.e.: β = H + T_train.

[0080] Step 5: Using the test set input matrix P_test obtained in Step 1, calculate the hidden layer output matrix of the test set. Specifically: the hidden layer output matrix of the test set. The test set input matrix P_test is averaged using the same method as in step two.

[0081] Step Six: Obtain the final prediction result Y. Specifically, this involves using the hidden layer output matrix of the test set obtained in Step Five. Multiplying the result by the output weight matrix β obtained in step four yields the final prediction result, i.e.:

[0082] Step 7: Evaluate the algorithm.

[0083] This experiment uses MATLAB R2020b software for simulation, based on lithium-ion battery experimental data from the University of Maryland's Center for Advanced Life Cycle Engineering and NASA's Ames Center of Excellence for Prediction. The experimental data are selected from sets A3, A5, A8, A12, and B5, B6, B7, B18. These two sets of lithium-ion battery experimental data are shown below. Figure 3a and Figure 3b As shown.

[0084] The lithium batteries provided by the CALCE center were four identical models from the same manufacturer, all featuring graphite carbon anodes and lithium cobalt oxide cathodes. Multiple charge-discharge tests were conducted at room temperature using an Arbin BT2000 battery testing system. A charge-discharge cycle was considered complete when the charging or discharging voltage reached the specified cutoff voltage. The batteries had a rated capacity of 0.9 Ah and a constant discharge current of 0.45 A.

[0085] The lithium-ion battery data provided by NASA Ames PCoE is based on second-generation 18650-sized lithium-ion batteries manufactured at Idaho National Laboratory, operated at room temperature (24°C) under three different operating conditions (charge, discharge, and impedance). Charging was performed in constant current (CC) mode at 1.5A until the battery voltage reached 4.2V, followed by charging in constant voltage (CV) mode until the charging current dropped to 20mA. Discharging was conducted in constant current mode at 2A until the voltages of batteries B5, B6, B7, and B18 dropped to 2.7V, 2.5V, 2.2V, and 2.5V, respectively. Impedance measurements were performed using electrochemical impedance spectroscopy (EIS) frequency scanning from 0.1Hz to 5kHz. Repeated charge and discharge cycles lead to accelerated battery degradation, and the impedance measurements provide insight into how internal battery parameters change. Although the cycle discharge conditions of these four batteries differed slightly, their rated capacity is considered to be 2Ah.

[0086] from Figure 3a and Figure 3bAs can be seen from the graph, the capacity stored in a lithium battery gradually decreases with the increase of charge-discharge cycles. However, when the lithium battery is in a static state during charge-discharge, the reaction products dissipate, allowing the electrochemical performance of the lithium battery to recover relatively compared to the previous cycle during degradation. Obviously, the usable capacity increases in the next cycle, hence the term "capacity regeneration" in lithium batteries. For batteries of the same type, their capacities have different degradation rates. The horizontal axis in the graph represents the number of charge-discharge cycles, while the vertical axis represents the actual capacity value of the lithium battery after each charge-discharge cycle. Furthermore, it is generally considered that when the discharge capacity of a lithium battery drops to 60%–80% of its rated capacity, it indicates the end of its life (EOL). Therefore, setting 80% of the rated capacity of the first group of batteries as the end of life point... Figure 3a The failure threshold shown by the purple dashed line is 0.72 Ah. Similarly, 71% of the rated capacity of the second set of batteries is set as the end-of-life point. Figure 3b The failure threshold shown by the dashed line is 1.42 Ah. Therefore, the lifespan termination points (i.e., actual RUL values) for the first group of lithium batteries A3, A5, A8, and A12 are 47, 188, 131, and 208, respectively; and the lifespan termination points (i.e., actual RUL values) for the second group of lithium batteries B5, B6, B7, and B18 are 115, 105, 159, and 89, respectively.

[0087] In the experiment, traditional ELM and two improved ELM algorithms were used to train and predict sample data. In the traditional ELM, the number of hidden layer nodes was equal to the number of training samples. The weights w between the input and hidden layers and the biases b of the hidden layer neurons were randomly and uniformly generated, and a sine function was used as the activation function. In the first improved algorithm, the convolutional part was configured as follows: the convolutional kernel size was 3×3, the kernel and bias values ​​were randomly and uniformly initialized, the stride was 1, and zero-padding was used. The activation function was also a sine function. The pooling part was configured as follows: the pooling kernel size was 2×1, the stride was 1, and average pooling was used. Meanwhile, the pooling part in the second improved algorithm was configured the same as the first method. However, unlike the commonly used pooling kernels with consistent width and height, a 2×1 pooling kernel was used here. This size was chosen to allow for the calculation of the subsequent output weight matrix β. After the training and test sets are divided and the prediction starting point is selected, the size of the output matrix Y of the training data is fixed. In order to obtain the value of β, the hidden layer output matrix H obtained after pooling operation needs to match the size of Y so that the calculation can continue.

[0088] Example 1: The specific process of the first improved algorithm is as follows:

[0089] 1. Normalize the divided training and test sets to obtain:

[0090]

[0091] Tn_train=[1.00000.95180.78770.7840…-0.7051-1.00000.7966-0.8837]

[0092]

[0093] Tn_test=[-1.0227-0.9287-1.0667-1.0456…-34.3215-34.5820-34.6421-34.6118]

[0094] T_test=[0.86340.86560.86240.8629…0.07920.07310.07170.0724]2.

[0095] 3. 4.

[0096]

[0097] 5.

[0098] 6.

[0099] 7. 8.

[0100]

[0101] 9. Inverse normalization yields the predicted value.

[0102]

[0103] Example 2, the specific process of the second improved algorithm is as follows:

[0104] 1. Normalize the divided training and test sets to obtain:

[0105]

[0106] Tn_train=[1.00000.95180.78770.7840…-0.7051-1.00000.7966-0.8837]

[0107]

[0108] Tn_test=[-1.0227-0.9287-1.0667-1.0456…-34.3215-34.5820-34.6421-34.6118]

[0109] T_test=[0.86340.86560.86240.8629…0.07920.07310.07170.0724]

[0110] 2.

[0111] 3.

[0112] 4.

[0113] 5.

[0114] 6. Inverse normalization yields the predicted value:

[0115]

[0116] The effectiveness of the two improved ELM algorithms of this invention is verified by using lithium battery experimental data from the University of Maryland's Center for Advanced Life Cycle Engineering and NASA's Ames Center of Excellence for Prediction, and compared with the traditional ELM algorithm.

[0117] This experiment compares the improved ELM algorithm with the traditional ELM algorithm to demonstrate the accuracy of the prediction results.

[0118] Figures 4 and 5 correspond to battery data A12 and B5, respectively. Figure 4a 4b presents the prediction results and absolute errors of A12 when the prediction starting point is T = 80. Figure 5a Figure 5b presents the prediction results and absolute errors of B5 when the prediction starting point is T = 70.

[0119] In the graph, solid lines represent the true values; dashed lines represent the prediction results of ELM; dotted lines represent the prediction results of the first improved algorithm; dotted curves represent the prediction results of the second improved algorithm; horizontal dashed lines represent the battery capacity failure threshold; and vertical solid lines represent the prediction starting point. With the improvement of the algorithm, the prediction performance has been significantly enhanced. Figure 4a and Figure 5a As can be seen, the lines represented by the two improved algorithms are closer to the true value than the lines represented by the traditional ELM algorithm. (Absolute error) Figure 4b and Figure 5bIt can be seen that the absolute errors of both improved algorithms are very small, and the second improved algorithm is the most stable and robust.

[0120] This experiment was performed for 101 complete cycles. The RMSE and MAPE values ​​obtained after each cycle were recorded and plotted as a line graph as shown below. Figures 6a to 7b As shown in the figure, the closer the RMSE and MAPE values ​​are to 0, the more accurate the prediction method is. It can be seen from the figure that, for different datasets A12 and B5, and with different initial parameter values, the RMSE and MAPE of the two improved algorithms are smaller than those of the traditional ELM algorithm. In particular, the prediction results of the second improved algorithm are the most stable; its results remain unchanged in each iteration without any fluctuations. Therefore, the two improved ELM algorithms of this invention have better prediction performance than the traditional ELM algorithm.

[0121] from Figures 8a to 8f As can be seen, the traditional ELM algorithm's prediction performance for these eight sets of battery data is not ideal, and sometimes it even fails to reach the failure threshold. The two improved ELM algorithms of this invention outperform the traditional ELM algorithm in prediction performance across different datasets. Furthermore, as the prediction starting point increases, both improved algorithms not only show smaller RMSE and MAPE values, but their predicted RUL values ​​also become closer to the true RUL values. The first improved ELM algorithm mitigates the significant filtering divergence of the traditional ELM algorithm, reducing the error. The second improved ELM algorithm further refines the first, because even though the first improved algorithm significantly improves the accuracy of the prediction results, it still has uncertainties. These uncertainties cause the prediction results to be sometimes accurate and sometimes less than ideal. Therefore, based on this, the second improved ELM algorithm was developed, and its prediction results are the most stable and robust.

Claims

1. A lithium-ion battery lifetime prediction method based on improved ELM, characterized in that: The method first changes the fully connected relationship between the input layer and the hidden layer of ELM to pooling, that is, the data of the input layer is directly pooled to obtain the output matrix H of the hidden layer; then the Moore-Penrose generalized inverse H of the matrix H is... + The output weight matrix β is obtained by multiplying it with the output matrix of the training set, thus completing the learning process of the algorithm; finally, the test set data is used to predict the result.

2. The lithium-ion battery lifetime prediction method based on improved ELM according to claim 1, characterized in that: The specific steps of this method are as follows: Step 201. Data Preprocessing; Step 202. Calculate the hidden layer output matrix H of the training set; Step 203. Using the hidden layer output matrix H of the training set obtained in Step 202, calculate its Moore-Penrose generalized inverse H. + ; Step 204. Calculate the output weight matrix β: using the training set output matrix T_train and the generalized inverse H... + Multiplying them together, we get: β = H + T_train; Step 205. Using the test set input matrix P_test obtained in Step 201, calculate the hidden layer output matrix of the test set. Step 206. Obtain the final prediction result Y: the hidden layer output matrix of the test set obtained in Step 205. Multiplying the result by the output weight matrix β obtained in Step 204 yields the final prediction result, i.e.:

3. The lithium-ion battery lifetime prediction method based on improved ELM according to claim 1, characterized in that: The data preprocessing in Step 201 is as follows: starting from the cycle period k=1, the data of every 10 consecutive cycles is used as a set of inputs, and the data of the next cycle is used as the output. This process is repeated for the two sets of lithium battery data. After the construction is completed, the prediction starting point T is selected to obtain P_train. T_train; P_test; T_test, where P_train is the input matrix of the training set, T_train is the output matrix of the training set, P_test is the input matrix of the test set, and T_test is the output matrix of the test set.

4. The lithium-ion battery lifetime prediction method based on improved ELM according to claim 1, characterized in that: The specific process of Step 202 is as follows: the input matrix P_train of the training set preprocessed in Step 201 is used as the data of the input layer, and the output matrix H of the hidden layer of the training set is obtained by directly performing average pooling on the input matrix P_train of the training set.

Images