A method and system for estimating the state of health of a lithium battery in a wide temperature range based on MGPR and improved timing RBF

Abstract

The application relates to a lithium battery health state estimation method and system based on MGPR and an improved time sequence RBF, and relates to the lithium battery health state prediction technical field. In order to solve the problems that the existing lithium battery health state estimation method generally assumes that there is a linear relationship between a to-be-predicted battery and a training battery aging relationship, the universality and robustness are poor, the uncertainty of the relationship between the to-be-predicted battery and the training battery, and the shortage of the to-be-predicted battery data set and other factors, the technical points are as follows: the aging characteristics are extracted by using the depolarization process after the full charging of the battery, the dependence on specific working conditions is avoided; the multiple types of measured voltage and residual pressure characteristics are comprehensively considered, and the characteristics are screened according to the correlation; the temperature characteristics are additionally added to the screened characteristics; the differences between the batteries are considered, the aging characteristic importance of different batteries is sorted, different aging characteristics are screened, and the corresponding GPR network is trained; a residual stress measurement clamp is separately designed; the GPR network and the RBF network are ingeniously combined together, the internal propagation mechanism of the RBF network is improved, the RBF network has a memory storage function, is more suitable for processing time sequence data, and avoids the gradient disappearance and gradient explosion problems. The application is used for lithium battery health prediction.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of lithium battery state of health prediction, and particularly relates to a wide-temperature-range lithium battery state of health estimation method and system based on MGPR and improved time-series RBF. BACKGROUND

[0002] With the vigorous development of new energy automobile industry, the power battery industry also attracts much attention. As the core component of new energy vehicles, power batteries play a huge role, and their performance determines the overall performance of new energy vehicles to a large extent. Among the many batteries for vehicles, lithium-ion batteries are favored due to their high working voltage, long cycle life, high specific energy, low self-discharge, environmental friendliness, and no memory effect. They have become the main development direction of vehicle power batteries. However, as the use time of lithium-ion batteries increases, they inevitably age, and the capacity of the battery will irreversibly decline. As one of the core functions of the battery management system (BMS), lithium-ion battery state of health (SOH) estimation can intuitively reflect the aging of the battery. Accurate SOH estimation helps the BMS manage the battery throughout its life cycle, better utilize battery performance, and prolong battery life. It is also conducive to grasping the critical point of tier utilization, avoiding energy waste, reducing battery utilization costs, and improving battery reliability to prevent accidents caused by deteriorating battery performance.

[0003] Currently, the main SOH estimation methods include empirical method, model-based method and data-driven method. Empirical method uses the historical data of battery use to estimate the SOH value of the battery through statistical and fitting means. The classic empirical method includes direct measurement method, cycle count method, etc. Bao et al. established the relationship between the measured internal resistance and the capacity of the battery through online internal resistance detection and linear fitting method. Wang et al. established the relationship between the characteristic parameters of the battery and the remaining capacity through a cross-validation strategy, thereby realizing the rapid SOH estimation of the retired battery. The SOH estimation of lithium battery based on model method is usually based on electrochemical model (EM) or equivalent circuit model (ECM) to construct the state space expression, and the SOH value is taken as the state variable to be estimated. Galeotti et al. introduced the relationship between the ohmic internal resistance and the SOH of the battery after obtaining the equivalent circuit model parameters by EIS, and the maximum estimation error of SOH can be as low as 3.73%. Allam et al. constructed an adaptive observer based on the enhanced single-particle model, and the SOH estimation error was controlled within 2%. The SOH estimation of lithium battery based on data-driven method extracts the battery aging characteristics, learns the complex nonlinear aging behavior inside the battery, and establishes the mapping relationship between SOH value and aging characteristics. Zheng et al. extracted the statistical characteristics of the charging curve by segmentation to estimate SOH, and obtained good estimation results. Wang et al. extracted a total of 206 features of three types as feature selection input, and finally output 7 features for SOH estimation, with the maximum estimation error within 1%. Dr. Duan documents the SOH of the battery through VFOS-ELM algorithm, and obtains higher estimation accuracy. Dr. Wu Lingfeng realizes higher precision SOH estimation in the case of poor data quality through a method combining multi-model fusion and data-driven.

[0004] The direct measurement method measures the aging characteristic parameters of the battery in an offline state, such as internal resistance, capacity, and the like, and then obtains the SOH value of the current battery according to the SOH calculation formula. This method has accurate calculation results and is suitable for batteries of different materials and different technologies, but it must be performed in an offline state and is not suitable for online real-time estimation of SOH. However, due to the complex and variable operating conditions of electric vehicles, it is difficult to accurately estimate the SOH value using such a method. The SOH estimation based on ECM has fewer parameters, simple mathematical formulas, and low calculation complexity, and is therefore easy to implement. However, the original intention of ECM is to simulate the charging and discharging behavior of the battery, and it cannot reflect the changes in the internal state and parameters of the battery, so the accuracy and robustness are poor. The SOH estimation of the battery based on EM can simulate the internal state of the battery and capture the parameter change trajectory, and therefore has good estimation accuracy and robustness. However, EM contains a large number of important parameters, and the parameter identification process involves lengthy offline experiments that affect the service life of the battery. At the same time, the EM solving process involves complex differential equation calculations, which puts high requirements on the hardware devices of the BMS. The SOH estimation of lithium batteries based on data-driven methods does not require an understanding of the battery mechanism and can handle high-dimensional data, providing greater flexibility in model construction. However, existing data-driven SOH estimation methods still face challenges such as insufficient feature quality and dependence on specific working conditions. At the same time, since different types of lithium batteries exhibit different aging characteristics, traditional data-driven methods are only suitable for a single type or even a single batch of lithium-ion batteries, which means that existing data-driven methods need to be retrained when used for different types or different batches of lithium batteries, consuming a lot of time. At the same time, considering the processing differences, there will be inconsistencies in the aging of lithium batteries of the same type and the same batch. When the estimated battery and the training battery have a large aging difference and the data of the estimated battery are limited, the SOH estimation accuracy of the lithium battery will undoubtedly be greatly affected.

[0005] In view of such problems, some scholars have proposed the concept of transfer learning. Feng et al. converted the aging characteristics of the battery to be predicted into the aging characteristics of the battery used for model training through a linear feature conversion method, thereby realizing transfer learning. Wu et al. pre-constructed aging models of different training batteries, solved the weights of the aging models of different training batteries according to part of the data of the predicted battery, and linearly fitted the results of different training batteries according to the weights, thereby realizing transfer learning. However, the above methods all assume that there is a linear relationship between the aging relationship of the battery to be predicted and the training battery, and the universality and robustness are poor.

[0006] For example, the existing patent document with document number CN119087264A discloses a lithium battery health estimation method and system based on transfer learning and multi-feature fusion, which includes: obtaining a preset charge-discharge cycle dataset, performing data preprocessing to obtain a preprocessed dataset; feature extraction is performed on the preprocessed dataset to obtain fusion health features, and time series division is performed to obtain a short-term health feature information set, and then random division is performed to obtain a training set and a test set; a transfer learning base model is constructed, and the training set corresponding to the source dataset is input into the transfer learning base model for training; the pre-trained transfer learning base model is fine-tuned, and the training set corresponding to the target dataset is input into the transfer learning base model for training to obtain a lithium battery health state estimation model; the lithium battery health state estimation model is tested and verified through the test set, and then the health state of the to-be-tested lithium battery is estimated. It is used to improve the efficiency and accuracy of lithium battery health state estimation. The existing patent document with document number CN118655466A discloses a lithium battery health state SOH prediction method and device and storage medium, which includes collecting parameter data in the lithium battery operating environment and preprocessing the data; features are obtained according to the collected parameter data, a recursive feature elimination feature selection method is applied for evaluation, and features related to battery health state SOH and remaining useful life RUL are identified and extracted; according to the equivalent circuit model of the battery and the extracted features, a battery SOH prediction model is obtained; a LSTM network is established according to the extracted features, parameters are initialized using a weight initialization strategy, a learning rate decay plan and an early stopping mechanism are introduced for learning and training, and after network iteration, a battery SOH prediction model is obtained; the battery SOH prediction model and the battery SOH prediction model are fused using a weighted fusion method to obtain a final prediction model Hfusion of the battery health state SOH and the remaining useful life RUL; it combines the physical formula method and the LSTM time series prediction, and improves the accuracy of lithium battery SOH and RUL prediction.

[0007] In summary, with the rapid development of fast charging strategies, the constant current and constant voltage charging method is no longer the only charging method for lithium batteries. The health state estimation of lithium batteries should consider the influence of charge-discharge protocols on the aging characteristics of lithium batteries, the residual stress characteristics representing the irreversible expansion of lithium batteries, the uncertainty of the relationship between the to-be-predicted battery and the training battery, and the shortage of the to-be-predicted battery dataset, and other factors, so it is urgent to provide a more reliable lithium battery health state estimation scheme. SUMMARY

[0008] The technical problem to be solved by the present application is:

[0009] The present application aims at solving the problems in the prior art that the existing lithium battery state of health estimation method generally assumes that there is a linear relationship between the aging relationship of the to-be-predicted battery and the training battery, resulting in poor universality and robustness, and that the existing estimation does not consider the influence of the charge-discharge protocol on the aging characteristics of the lithium battery, the residual stress characteristics representing the irreversible expansion of the lithium battery, the uncertainty of the relationship between the to-be-predicted battery and the training battery, and the shortage of the to-be-predicted battery data set, and further provides a wide temperature range lithium battery state of health estimation method and system based on MGPR and improved time series RBF.

[0010] The technical scheme adopted by the present application to solve the above technical problems is:

[0011] A wide temperature range lithium battery state of health estimation method based on MGPR and improved time series RBF, the method comprising a training process and a prediction process;

[0012] The training process comprises a GPR1, GPR2, …, GPRN network training process corresponding to each cell, and an improved time series RBF neural network training process:

[0013] The cell 1 aging characteristics, the cell 2 aging characteristics, …, and the cell N aging characteristics obtained by extracting and screening the aging characteristics of each cell obtained by the cyclic aging experiment of each cell are used to train the GPR1, GPR2, …, and GPRN network one by one;

[0014] The to-be-predicted cell aging characteristics, the to-be-predicted cell SOH, and the trained GPR1, GPR2, …, and GPRN network are used to train the improved time series RBF network, and in this process, the improved time series RBF network is updated in the forward propagation and model parameter updating mode:

[0015] Forward propagation: the mean and standard deviation (calculated from the variance) output by the GPR network corresponding to different cells are used as the input of the improved time series RBF network;

[0016] Back propagation: the ideal output of the T time model and the model performance index function are constructed, and the parameter value is continuously updated according to the parameter adjustment amount to realize the back propagation process;

[0017] Finally, N GPR networks are trained using the aging data of the known N blocks of cells, and the improved time series RBF network is trained in combination with the partial known data of the to-be-predicted cell, to obtain an MGPR-improved RBF model;

[0018] The prediction part realizes the following process: the aging characteristics of the to-be-predicted cell extracted at the depolarization stage at the end of charging are input into the MGPR-improved time series RBF network to realize the prediction process.

[0019] Further, the GPR network training process specifically comprises:

[0020] The GPR network input quantity is the extracted lithium battery aging feature, and the output quantity is the battery SOH value; assuming that there are N training samples, and the input feature is p, then the training sample input feature X, the output feature Y, and the sample data Data can be represented as follows:

[0021] X = (x1, x2,..., x N ) T N×P (1)

[0022] Y = (y1, y2,..., y N ) T (2)

[0023]

[0024] Assume that y i = f(x i ) + ε i (ε i ~ N(0, σ 2 )), where f(x i ) is a Gaussian process function, and ε i represents noise (assuming it is Gaussian white noise); at this time, the model output is shown in (4), where m(X) is the mean function, and K(X, X) is the covariance kernel function;

[0025] F = f(X) = (f(x1), f(x2),... f(x N )) T ~ N(m(X), K(X, X)) (4)

[0026] At this time, the training sample output feature Y can be represented as shown in (4), where I is the unit matrix;

[0027] Y = f(X) + ε ~ N(m(X), K(X, X) + σ 2 I) (5)

[0028] Prediction: given then at this time Y * = f(X * ) + ε, and the joint Gaussian distribution of Y and f(X * ) is shown in equation (6).

[0029]

[0030] Given the joint Gaussian distribution, the conditional probability can be obtained as shown in equation (7):

[0031] P(f(X * )|Y, X, X* ) ~ N(m * , σ *2 )(7)

[0032] where m * , σ *2 satisfy the following calculation formula:

[0033] m * = K(X * , X)[K(X, X) + σ 2 I] -1 [Y - m(X)] + m(X * )(8)

[0034] σ *2 = K(X * , X * ) - K(X * , X)[K(X, X) + σ 2 I] -1 K(X, X * )(9)

[0035] Considering Y * = f(X * ) + ε, then

[0036] P(Y * | Y, X, X * ) ~ N(m * , σ *2 + σ 2 I)(10)

[0037] Based on the fact that there is no obvious function relationship between SOH and aging characteristics, the GPR mean function is set to 0; the automatic relevance determination (ARD) exponential kernel function is selected as the GPR kernel function to reduce the model complexity while improving the model performance; the specific expression of the ARD exponential kernel function is shown in formula (11), where is the covariance, and l F is the length scale corresponding to the Fth feature. x iF is the Fth feature of the ith sample;

[0038]

[0039] The GPR model hyperparameters θ = {σ, σ f , l1, l 2, ..., l p}; in order to accurately express the relationship between the input features X and the output features Y, the maximum likelihood estimation method is used to find a set of hyperparameters θ, so that the value of the likelihood p(Y|X, θ) reaches the maximum; that is, The GPR model is completed.

[0040] Further, the improved timing RBF neural network training process is specifically:

[0041] The improved timing RBF network is used to realize the migration learning process of SOH estimation between different battery cells, and the input of the improved timing RBF network is improved respectively represent the estimated mean and standard deviation of the SOH output by the GPR network corresponding to the i-th block of battery cells at time T; the hidden layer selects a Gaussian basis function, b m,T ,C m,T respectively represent the base width and center vector of the m-th node at time T; ω represents the weight between the hidden layer and the output layer; Y T , that is, the final output of the improved RBF network is the migration learning result; the proposed improved timing RBF network is updated in terms of forward propagation and model parameter updating method, and the implementation process is as follows:

[0042] (1) Forward propagation: the mean and standard deviation (calculated from the variance) output by the GPR network corresponding to different battery cells are used as the input of the improved timing RBF network; the hidden layer selects a Gaussian basis function, and the base width and center vector of each node in the hidden layer are initialized as the vector composed of the mean square deviation and mean value of the output of each GPR network at the initial time; the hidden layer parameters of the improved timing RBF network at time T+1 are composed of the hidden layer parameters at time T and the network input parameters at time T+1; the linear mapping between the hidden layer and the output layer, and the weight of each hidden layer is different;

[0043] The input of the improved timing RBF network is consistent with the number of hidden layer nodes, and the output layer is a single node (SOH), which is specifically:

[0044] Assuming that the GPR network corresponding to m blocks of battery cells has been pre-trained, the input of the improved RBF network at time T is shown in equations (12) and (13), wherein X T is the mean value of the SOH estimation of each GPR network output at time T, and X_σ T is the standard deviation of the SOH estimation of each GPR network output at time T;

[0045]

[0046] The radial basis vector H T of the hidden layer at time T can be represented as shown in equation (14), wherein h i,T is the Gaussian basis function corresponding to the i-th hidden layer node at time T, and the expression is shown in equation (15);

[0047] H T = [h 1,T , h 2,T ,..., h i,T ,..., h m,T ] (14)

[0048]

[0049] The central vector C of the i-th node at time T in formula (15) i,T The expandable formula (16) is shown as follows:

[0050] C i,T = [c i1,T ,c i2,T ,...,c ii,T ,...,c im,T ] (16)

[0051] The base width vector expression at time T is introduced as shown in formula (17):

[0052] B T = [b 1,T ,b 2,T ,...b i,T ,...,b m,T ] (17)

[0053] Then the improved timing RBF network output value Y at time T is T The formula (18) is shown as follows:

[0054] Y T = h 1,T ω1+h 2,T ω2+...+h i,T ω i +...+h m,T ω m (18)

[0055] Where ω i represents the connection weight between the i-th hidden layer node and the output layer;

[0056] The hidden layer state information at the next time is calculated from the hidden layer state information at the previous time and the input layer input information at the next time, and the specific expression is as follows:

[0057]

[0058] Where X_σ T , represents the SOH standard deviation of the GPR network output at time T, X T , represents the SOH mean value of the GPR network output at time T; ω B , ω C are the weight matrices occupied by the introduced input SOH standard deviation and mean value, respectively, and the forward propagation process ends;

[0059] (2) Back propagation: assuming that the ideal output of the model at time T is The model performance index function can be represented as formula (21):

[0060]

[0061] According to the performance index function, the adjustment amount of the parameters ω i , ω B,i , and ω C,ii is as follows:

[0062]

[0063] b i,T represents the base width of the i-th node at time T, represents the input value of the i-th node at time k c ii,T represents the base width of the i-th input corresponding to the i-th node at time T, represents the input value of the i-th input corresponding to the i-th node at time k η represents the network learning rate;

[0064] The back propagation process can be realized by continuously updating the parameter values according to the parameter adjustment amount. Thus, the improved time-series RBF network is built.

[0065] Further, the cycle aging experiment of each battery cell, the extraction and selection of aging characteristics of each battery cell are as follows:

[0066] Cycle aging experiment of each battery cell: In the interval of 100% to 80% SOH, different battery cells are subjected to aging characteristic extraction at different temperatures every fixed cycle interval; the characteristics are extracted from the voltage curve and residual stress curve in the depolarization process after the end of charging of the battery cell, including physical characteristics: ECM (equivalent circuit model) parameters; original characteristics: maximum and minimum measured voltage, maximum and minimum residual stress; statistical characteristics: mean and variance of measured voltage, mean and variance of residual stress; and temperature characteristics that will affect the above aging characteristics;

[0067] SOH is calibrated by the ratio of the current cycle capacity to the initial capacity measured at 25℃ environment, i.e. the SOH values at different temperatures at a certain cycle are all equal by default; the aging characteristic extraction at different temperatures at a certain cycle should be performed in the order of 35℃-25℃-15℃;

[0068] Pearson correlation analysis is used for aging characteristic selection: the Pearson coefficients of different aging characteristics of different battery cells at different temperatures are calculated, the average values of the Pearson coefficients of the same aging characteristics of different battery cells at different temperatures are calculated, the importance of the characteristics is sorted according to the absolute values of the average values, and the aging characteristics of different battery cells are selected respectively.

[0069] Further, in each battery cycle aging experiment, high temperature accelerated aging cycle experiment is adopted, the battery is placed in 40 DEG C environment and continuously charged and discharged, every 10 cycles is interval, until the SOH value of the battery is lower than 80%.

[0070] Further, the residual stress is completed by an experimental device comprising three plates, a pressure sensor and a fastener, the initial surface pressure is 0.05 Mpa, which is a lower initial stress for prolonging the battery life; after the battery is installed with the pressure measuring experimental device, the initial stress (Mpa) of different batteries is kept consistent until the cycle life is reached.

[0071] A lithium battery state of health estimation system based on MGPR and improved time sequence RBF in a wide temperature range has program modules corresponding to the steps of the above technical solutions, and when running, the steps in the lithium battery state of health estimation method based on MGPR and improved time sequence RBF in a wide temperature range are executed.

[0072] A computer readable storage medium stores a computer program, and the computer program is configured to realize the steps of the lithium battery state of health estimation method based on MGPR and improved time sequence RBF in a wide temperature range when called by a processor.

[0073] The present application has the following beneficial technical effects:

[0074] The lithium battery SOH estimation method based on MGPR and improved time sequence RBF network effectively solves the problems of the above-mentioned various methods. With the rapid development of fast charging strategy, the constant current and constant voltage charging method is not the only charging method for lithium batteries. The present application considers the influence of the charging and discharging protocol on the aging characteristics of lithium batteries, and selects the depolarization process after full charging of lithium batteries which is irrelevant to the charging and discharging protocol for aging characteristic extraction. Considering that the residual stress feature represents the irreversible expansion of lithium batteries, it can better reflect the aging condition of lithium batteries. In order to enrich the aging characteristics of lithium batteries, the residual stress feature is additionally introduced on the basis of measuring voltage, physical, statistical and original aging characteristics. After preliminary preparation of the aging characteristics, the aging characteristics with stronger correlation are selected for model training. Considering that some aging characteristics of lithium batteries are affected by temperature, the temperature should be added to the training features. In terms of model selection, the GPR neural network which can reflect the mean and variance of SOH estimation results is selected.

[0075] In terms of transfer learning, considering the uncertainty of the relationship between the predicted battery and the training battery and the shortage of the predicted battery dataset, the RBF neural network with strong generalization ability and suitable for small sample estimation is selected for transfer learning. The mean and variance of the SOH estimation of the GPR network output corresponding to different lithium batteries are used as the center and bandwidth of each hidden layer of the RBF network, so as to enhance the approximation and generalization ability of the RBF network and avoid overfitting. At the same time, considering that the SOH value of the lithium battery has a time sequence feature, the propagation path and parameter updating method of the RBF network are improved to have a memory storage function.

[0076] The time sequence-based hidden layer state updating formula designed in the application avoids the gradient disappearance and gradient explosion problems caused by the application of the chain rule, and makes the network more suitable for small sample SOH estimation. Therefore, high-precision SOH estimation of the whole life cycle of the battery can be realized according to a small amount of battery data to be estimated. It should be noted that different battery cells are subjected to aging feature screening, so the input features of each GPR network are not completely consistent. The application realizes good prediction results with as little data as possible. BRIEF DESCRIPTION OF DRAWINGS

[0077] Figure 1 The overall flowchart of the SOH estimation method of the application, Figure 2 The flowchart of the cycle aging experiment, Figure 3 The schematic diagram of the residual stress measuring device, Figure 3 The single battery cell is placed between the two upper plates), Figure 4 The flowchart of the aging feature screening, Figure 5 The improved time sequence RBF network diagram. DETAILED DESCRIPTION

[0078] The application is described in detail as follows in combination with the accompanying Figures 1-5 The implementation of the wide-temperature-range lithium battery health state estimation method based on MGPR and improved time sequence RBF according to the application is described in detail as follows:

[0079] As Figure 1 The overall flowchart of the SOH estimation method of the application is shown, which includes two training processes and one prediction process.

[0080] The training process 1 includes the cycle aging experiment of each battery cell, the aging feature extraction and screening of each battery cell, and the training process of the GPR network corresponding to each battery cell.

[0081] The flowchart of the cycle aging experiment is shown in Figure 2The aging feature extraction operation at different temperatures is performed every interval fixed cycle number for different battery cells in the 100% to 80% SOH interval. The features are extracted from the voltage curve and the residual stress curve in the depolarization process after the end of charging of the battery cell, including physical features: ECM (equivalent circuit model) parameters; original features: maximum and minimum measured voltage, maximum and minimum residual stress; statistical features: mean and variance of the measured voltage, mean and variance of the residual stress; and temperature features that will affect the above aging features. It should be noted that the SOH is calibrated by the ratio of the current cycle capacity to the initial capacity measured at 25°C, that is, the SOH values at different temperatures at a certain cycle are all equal by default. Therefore, in order to reduce the influence of the battery aging caused by different aging feature extraction experiments on the inaccuracy of the aging feature-SOH correspondence, the aging feature extraction at different temperatures at a certain cycle should be performed in the order of 35°C-25°C-15°C (according to the order from low to high of the acceleration degree of the cycle to aging at different temperatures). The specific flow chart is shown in Figure 2 .

[0082] In the experimental details part, the present application adopts high-temperature accelerated aging cycle experiment, places the battery cell in a 40°C environment for continuous charging and discharging cycles, every 10 cycles, performs the test process as shown in Figure 2 . The residual stress is measured by the experimental device as shown in Figure 3 . The experimental device is composed of three plates, a pressure sensor and a fastener. The initial surface pressure is 0.05Mpa, which is a lower initial stress that is beneficial to prolong the life of the battery through research. It should be noted that in order to avoid the influence of the friction between the bolt and the second plate on the measurement accuracy of the pressure sensor, the hole of the second plate should be larger than the diameter of the bolt. Threaded connection is used between the sensor and the plate, in order to avoid the influence of the screw cap on the measurement of the battery swelling force, a groove is provided at the fixed threaded hole of the sensor. In order to avoid the loosening of the bolt caused by the swelling of the battery and ensure the accuracy of the sensor measurement data, a lock nut is used for fastening. In order to make the experimental conditions more consistent with the actual use conditions, the battery cell is not disassembled after the pressure measurement experimental device is installed, until the cycle life is reached, and the initial stress (Mpa) applied to different battery cells remains consistent. In order to speed up the experimental progress, the present application adopts 6 sets of completely consistent experimental equipment for synchronous experiment.

[0083] In the aging feature screening aspect, the present application adopts Pearson correlation analysis. The Pearson coefficients of different aging features of each battery cell at different temperatures are calculated, the average value of the Pearson coefficients of the same aging feature at different temperatures of different battery cells is obtained, the feature importance is sorted according to the absolute value of the average value, and the aging features of different battery cells are selected respectively. It should be noted that considering that temperature will affect the aging features, it is directly added to the selected features. The specific flow chart is shown in Figure 4F1 to F5 respectively represent the ohmic internal resistance R0, the activation polarization resistance R1, the activation polarization capacitance C1, the concentration polarization resistance R2, and the concentration polarization capacitance C2 of the second-order ECM; F6 to F9 respectively represent the maximum measured voltage, the minimum measured voltage, the average of the measured voltage, and the variance of the measured voltage; F 10 to F 13 respectively represent the maximum residual stress, the minimum residual stress, the average of the residual stress, and the variance of the residual stress.

[0084] In the network training part, the present application selects GPR, i.e., Gaussian Process Regression. Gaussian Process is a random process composed of an infinite number of Gaussian random variables defined on a continuous domain, and the random process can be represented by the mean and the variance between the random variables. At this time, the mean and the covariance matrix are changed from constants to functions (function space angle). Of course, from the weight space angle, GPR can also be regarded as a nonlinear prediction realized by the kernel function (inner product) method after the high-dimensional space mapping of the Bayesian linear regression.

[0085] Regression: In the present application, the input quantity of the GPR network is the extracted lithium battery aging feature, and the output quantity is the battery SOH value. Assuming that there are N training samples and p input features, the training sample input feature X, the output feature Y, and the sample data Data can be represented as follows:

[0086] X=(x1,x2,...,xp) N ) T N×P (1)

[0087] Y=(y1,y2,...,yp) N ) T (2)

[0088]

[0089] Assume that y i =f(x i )+ε i (ε i ~N(0,σ 2 )), where f(x i ) is a Gaussian process function, and ε i represents noise (assuming it is Gaussian white noise). At this time, the model output is shown in (4), where m(X) is the mean function, and K(X,X) is the covariance kernel function.

[0090] F=f(X)=(f(x1),f(x2),...f(x N )) T~N(m(X),K(X,X)) (4)

[0091] At this point, the output feature Y of the training sample can be represented as shown in (4), where I is the identity matrix.

[0092] Y=f(X)+ε~N(m(X),K(X,X)+σ 2 I) (5)

[0093] Prediction: Given Then Y * =f(X) * )+ε, Y and f(X) * The joint Gaussian distribution of is shown in equation (6).

[0094]

[0095] Given the joint Gaussian distribution, the conditional probability can be calculated as shown in equation (7).

[0096] P(f(X * )|Y,X,X * )~N(m * ,σ *2 (7)

[0097] Where m * σ *2 The following calculation formula is satisfied:

[0098] m * =K(X) * ,X)[K(X,X)+σ 2 I] -1 [Ym(X)]+m(X * (8)

[0099] σ *2 =K(X) * ,X * )-K(X * ,X)[K(X,X)+σ 2 I] -1 K(X,X * (9)

[0100] Considering Y * =f(X) * If )+ε, then

[0101] P(Y * |Y,X,X * )~N(m * ,σ *2 +σ 2 I)(10)

[0102] Considering that there is no obvious function relationship between SOH and aging characteristics, and for the convenience of calculation, the mean function of GPR in the application is set to 0. At the same time, in order to further screen out the characteristics with greater contribution to the model and ignore the unimportant characteristics, the automatic relevance determination (ARD) exponential kernel function is selected as the GPR kernel function in the application, so as to improve the model performance while reducing the model complexity. The specific expression of the ARD exponential kernel function is shown in formula (11), wherein is the covariance, l F is the length scale corresponding to the Fth feature. x iF is the Fth feature of the ith sample.

[0103]

[0104] At this time, the GPR model hyperparameters θ = {σ, σ f , l1, l 2, ..., l p}. In order to accurately express the relationship between the input features X and the output features Y, the maximum likelihood estimation method is used to find a set of hyperparameters θ, so that the value of the likelihood p(Y|X, θ) reaches the maximum. That is At this time, the GPR model hyperparameters θ = {σ, σ f , l1, l 2, ..., l p}. In order to accurately express the relationship between the input features X and the output features Y, the maximum likelihood estimation method is used to find a set of hyperparameters θ, so that the value of the likelihood p(Y|X, θ) reaches the maximum. That is

[0105] The training process 2 is the transfer learning process of using the improved time sequence RBF network to realize the SOH estimation of different battery cells, and the specific implementation manner is as shown in Figure 5

[0106] Figure 5 The input quantity of the improved RBF network in the application is respectively represent the estimated mean value and the standard deviation of the SOH of the GPR network output corresponding to the ith battery cell at time T. The hidden layer selects the Gaussian basis function, b m,T , C m,T respectively represent the basis width and the center vector of the mth node at time T. ω represents the weight between the hidden layer and the output layer. Y T is the final output of the improved RBF network. Different from the classical RBF network, the improved time sequence RBF network proposed in the application is updated in the aspects of forward propagation and model parameter updating manner. The specific implementation process is as follows:

[0107] (1) Forward propagation: the mean value and standard deviation (calculated from the variance) output by the GPR network corresponding to different battery cells are taken as the input of the improved time-series RBF network. The Gaussian basis function is selected for the hidden layer, and the basis width and center vector initialization values of each node in the hidden layer are selected as the vectors composed of the mean square deviation and mean value of each GPR network output at the initial moment. The hidden layer parameters of the improved time-series RBF network at T+1 moment are composed of the hidden layer parameters at T moment and the network input parameters at T+1 moment. The linear mapping between the hidden layer and the output layer, and the different weights of each hidden layer are different. It should be noted that in the present application, the input of the improved time-series RBF network is consistent with the number of hidden layer nodes, and the output layer is a single node (SOH). The specific formula derivation is as follows:

[0108] Assuming that the GPR network corresponding to the m block battery cells has been pre-trained, the input of the improved RBF network at T moment is shown in formula (12) and formula (13). Wherein X T is the SOH estimation mean value of each GPR network output at T moment, and X_σ T is the SOH estimation standard deviation of each GPR network output at T moment.

[0109]

[0110] The radial basis vector H T of the hidden layer at T moment can be represented as shown in formula (14), wherein h i,T is the Gaussian basis function corresponding to the i-th hidden layer node at T moment, and the expression is shown in formula (15).

[0111] H T =[h 1,T ,h 2,T ,...,h i,T ,...,h m,T ] (14)

[0112]

[0113] The center vector C i,T of the i-th node at T moment in formula (15) can be expanded as shown in formula (16).

[0114] C i,T =[c i1,T ,c i2,T ,...,c ii,T ,...,c im,T ] (16)

[0115] The expression of the basis width vector at T moment is shown in formula (17).

[0116] B T =[b 1,T ,b 2,T ,...bi,T ..., b m,T ] (17)

[0117] The output value Y of the improved timing RBF network at time T T may be represented as shown in equation (18):

[0118] Y T = h 1,T ω1+ h 2,T ω2+... + h i,T ω i +... + h m,T ω m (18)

[0119] where ω i represents the connection weight between the i-th hidden layer node and the output layer.

[0120] It should be noted that in the present application, the hidden layer state information at the next moment is calculated from the hidden layer state information at the previous moment and the input layer input information at the next moment, and the specific expression is as follows:

[0121]

[0122]

[0123] where i.e. X_σ T , represents the SOH standard deviation of the GPR network output at time T, i.e. X T , represents the SOH mean value of the GPR network output at time T. ω B , ω C are the weight matrices of the input SOH standard deviation and mean value introduced in the present application, respectively. Thus, the forward propagation process ends.

[0124] (2) Back propagation: assuming that the ideal output of the model at time T is The model performance index function can be represented as shown in equation (21).

[0125]

[0126] Now, according to the performance index function, the adjustment amount of parameters ω i , ω B,i , ω C,ii is solved in turn as follows.

[0127]

[0128] It should be noted that b i,T represents the base width of the i-th node at time T, Input value of the i-th node at the k-th moment c ii,T Base width of the i-th input corresponding to the i-th node at the T-th moment Input value of the i-th input corresponding to the i-th node at the k-th moment

[0129] Then, the parameter value is continuously updated according to the parameter adjustment amount, and the back propagation process is realized.

[0130] The implementation process of the prediction part is as follows: N GPR networks are trained by using the aging data of N known battery cells, and the improved time sequence RBF network is trained in combination with part of the known data of the battery cell to be predicted. The aging characteristics of the battery cell to be predicted are extracted at the depolarization stage at the end of charging, the GPR output results are input into the improved time sequence RBF network, and thus the prediction process is realized.

[0131] Thus, the complete process of the method of the application ends.

[0132] The key points and points to be protected of the application include:

[0133] (1) The aging characteristics are extracted by using the depolarization process after the battery is fully charged, which is independent of the charging and discharging protocol, and the dependence on specific working conditions is avoided. Multiple types of measured voltage and residual pressure characteristics are comprehensively considered, and are screened according to the correlation. The temperature characteristics are additionally added to the screened characteristics.

[0134] (2) The differences between battery cells are considered, the importance of the aging characteristics of different battery cells is sorted, different aging characteristics are screened, and the corresponding GPR networks are trained.

[0135] (3) In order to ensure the measurement accuracy of the residual stress and make the experimental working condition more consistent with the actual application working condition, a separate residual stress measurement clamp is designed.

[0136] (4) The GPR network and the RBF network are combined together, the internal propagation mechanism of the RBF is improved, the RBF has the memory storage function, is more suitable for processing time sequence data, and avoids the problems of gradient disappearance and gradient explosion.

[0137] (5) In the aspect of transfer learning, the RBF has the characteristics of strong nonlinear fitting ability, strong generalization ability and being suitable for small samples, which solves the problem of single stacking mode of the existing transfer learning model, and improves the transfer learning accuracy.

[0138] (6) The center quantity and the base width of the RBF network are calculated based on the mean and variance of the GPR network output, which solves the difficulty of selecting the center quantity and the base width of the RBF network.

[0139] Other alternative schemes capable of achieving the object of the application

[0140] There are a large number of neural network models applied to lithium battery SOH estimation to obtain good results, and the neural network model can be replaced to realize the purpose of the application in combination with feature conversion, combined training, difference value filling and other transfer learning methods.

[0141] It has been verified that the method proposed in the application solves the technical problems proposed in the application, and the method described in the application has been verified by simulation experiments and practical applications, and the technical effects described in the application have been verified.

[0142] The algorithm (method) proposed in the application is the underlying technical core of the application, and various products can be derived based on the algorithm. Based on the algorithm (method) proposed in the application, a wide temperature range lithium battery health state estimation system based on MGPR and improved time sequence RBF is developed by using a program language, the system has a program module corresponding to the steps of the above technical solution, and when running, the steps in the above method for estimating the health state of a wide temperature range lithium battery based on MGPR and improved time sequence RBF are executed.

[0143] The computer program of the developed system (software) is stored on a computer readable storage medium, and the computer program is configured to be called by a processor to realize the steps of the above method for estimating the health state of a wide temperature range lithium battery based on MGPR and improved time sequence RBF. That is, the application is materialized on a carrier to become a computer program product.

[0144] A wide temperature range lithium battery health state estimation device based on MGPR and improved time sequence RBF, the device comprises at least one processor, and a memory in communication connection with the at least one processor, wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the above method for estimating the health state of a wide temperature range lithium battery based on MGPR and improved time sequence RBF, and realize scientific and effective prediction of the health state of the wide temperature range lithium battery.

[0145] Various implementations of the systems and techniques described here can be realized in digital electronic circuitry, integrated circuitry, specially designed ASICs (application specific integrated circuits), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include implementation in one or more computer programs that are executable and / or interpretable on a programmable system including at least one programmable processor, which can be special or general purpose, coupled to receive data and instructions from, and to transmit data and instructions to, a storage system, at least one input device, and at least one output device. The computer programs (also referred to as programs, software, software applications, or code) include machine instructions for the programmable processor, and can be implemented in a high-level process and / or object-oriented programming language, and / or in assembly / machine language. As used in this disclosure, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, apparatus and / or device (e.g., magnetic discs, optical disks, memory, Programmable Logic Devices (PLDs)) used to provide machine instructions and / or data to a programmable processor, including a machine-readable medium that receives machine instructions as a machine-readable signal. The term "machine-readable signal" refers to any signal used to provide machine instructions and / or data to a programmable processor.

[0146] It should be understood that the various forms of flow shown above can be re-ordered, added to, or deleted from without departing from the scope of the present disclosure. For example, the steps recited in the present disclosure can be executed in parallel, executed in series, or executed in different orders, as long as the desired results of the technology disclosed in the present disclosure are achieved, and are within the scope of the present disclosure.

Claims

1. A method for estimating the state of health of lithium batteries in a wide temperature range based on MGPR and improved timing RBF, characterized in that, The method comprises a training process and a prediction process; The training process comprises a GPR1, GPR2,..., GPRN network training process corresponding to each battery cell, and an improved time-series RBF neural network training process: After extracting and screening the aging characteristics of each battery cell obtained by the cycle aging experiment of each battery cell, the aging characteristics of battery cell 1, the aging characteristics of battery cell 2,..., and the aging characteristics of battery cell N are obtained, and the GPR1, GPR2,..., GPRN network is trained one by one; Using the to-be-predicted battery cell aging characteristics, the to-be-predicted battery cell SOH, and the above trained GPR1, GPR2,..., GPRN network, the improved time-series RBF network is trained, and in this process, the improved time-series RBF network is updated in the forward propagation and model parameter updating mode: Forward propagation: the mean and standard deviation output by the GPR network corresponding to different battery cells are used as the input of the improved time-series RBF network; Back propagation: construct the model ideal output at time T and the model performance index function, and continuously update the parameter value according to the parameter adjustment amount to realize the back propagation process; Finally, N GPR networks are trained using the aging data of the known N battery cells, and the improved time-series RBF network is trained combined with the known data of the to-be-predicted battery cell, and the MGPR-improved RBF model is obtained. The cycle aging experiment of each battery cell and the extraction and screening of the aging characteristics of each battery cell are as follows: Cycle aging experiment of each battery cell: in the interval of 100% to 80% SOH, the aging characteristics of different battery cells are extracted at different temperatures every fixed cycle interval; the characteristics are extracted from the voltage curve and residual stress curve in the depolarization process after the end of charging, including physical characteristics: ECM equivalent circuit model parameters; original characteristics: maximum and minimum measured voltage, maximum and minimum residual stress; statistical characteristics: mean and variance of measured voltage, mean and variance of residual stress; and temperature characteristics that will affect the above aging characteristics; SOH is calibrated by the ratio of the current cycle capacity to the initial capacity measured at 25°C, i.e. the SOH value at different temperatures at a certain cycle is equal by default; the aging characteristics extraction at different temperatures at a certain cycle should be performed in the order of 35°C-25°C-15°C; Pearson correlation analysis is used for aging characteristic screening: the Pearson coefficients of different aging characteristics of each battery cell at different temperatures are calculated, the average value of the Pearson coefficients of the same aging characteristics of different battery cells at different temperatures is calculated, the importance of the characteristics is sorted according to the absolute value of the average value, and the aging characteristics of different battery cells are screened respectively; The prediction process is as follows: input the aging characteristics of the to-be-predicted battery cell extracted in the depolarization stage at the end of charging into the MGPR-improved time-series RBF network to realize the prediction process. 2.The method of claim 1, wherein, The GPR network training process is as follows: The input of the GPR network is the extracted lithium battery aging characteristics, and the output is the battery SOH value; assuming that there are N training samples, the input characteristics are p, then the training sample input characteristics X, output characteristics Y, and sample data Data can be represented as follows: (1) (2) (3) Assume where is a Gaussian process function, denotes Gaussian white noise; the model output is then given by equation (4), where is a mean function, is a covariance kernel function; (4) The training sample output feature Y at this time can be represented as shown in equation (5), wherein I is a unit matrix; (5) Prediction: Given , then at this time , and the joint Gaussian distribution of X and Y is given by equation (6): Given the joint Gaussian distribution, the conditional probability can be obtained as shown in equation (7): (7) wherein , satisfy the following calculation formula: (8) (9) With regard to then (10) Based on the fact that there is no obvious function relationship between SOH and aging characteristics, the mean function of GPR is set to 0; the automatic relevance determination (ARD) exponential kernel function is selected as the kernel function of GPR to improve the performance of the model while reducing the complexity of the model; the specific expression of the ARD exponential kernel function is shown as formula (11), wherein is the covariance, is the length scale corresponding to the Fth feature, is the Fth feature of the ith sample. GPR model hyperparameters In order to accurately express the relationship between the input features X and the output features Y, the maximum likelihood estimation method is used to find a set of hyperparameters , so that the value of the likelihood reaches the maximum; that is , the GPR model is completed. 3.The method of claim 2, wherein, The improved timing RBF neural network training process is as follows: The improved time series RBF network is used to realize the migration learning process of SOH estimation between different battery cells, and the input of the improved time series RBF network is improved respectively represent the estimated mean and standard deviation of the SOH of the GPR network output corresponding to the i-th block of battery cells at time T; the hidden layer selects a Gaussian basis function, respectively represent the base width and center vector of the m-th node at time T; represent the weight between the hidden layer and the output layer; That is, the improved time series RBF network finally outputs the migration learning result; the proposed improved time series RBF network is updated in terms of forward propagation and model parameter updating method, and the implementation process is as follows: (1) Forward propagation: the mean value output by the GPR network corresponding to different battery cells and the standard deviation calculated from the variance The improved timing RBF network is used as the input; the Gaussian basis function is selected for the hidden layer, and the basis width and center vector initialization values of each node in the hidden layer are selected as the vector composed of the mean square deviation and mean value output by the GPR network at the initial time; the hidden layer parameters of the improved timing RBF network at time T+1 are composed of the hidden layer parameters at time T and the network input parameters at time T+1; the linear mapping between the hidden layer and the output layer, and the weights of each hidden layer are different; The improved timing RBF network input and the number of hidden layer nodes are consistent, and the output layer is a single node, which is specifically: Assuming that the GPR network corresponding to the m block battery cells has been pre-trained, the improved timing RBF network input at time T is shown in equations (12) and (13) as follows: is the SOH estimation mean value of each GPR network output at time T, is the SOH estimation standard deviation of each GPR network output at time T. (12) (13) Radial basis vector of hidden layer at time T may be represented as shown in equation (14) is the Gaussian basis function corresponding to the i-th hidden layer node at time T, expressed as shown in equation (15) (14) (15) The center vector of the i-th node at time T in formula (15) The expandable as shown in formula (16): (16) The expression of the basis width vector at time T is introduced as shown in equation (17): (17) The output value of the improved time series RBF network at time T is may be represented as shown in equation (18): (18) wherein represents the connection weight between the i-th hidden layer node and the output layer; The hidden layer state information at the next time is calculated from the hidden layer state information at the previous time and the input layer input information at the next time, and the specific expression is as follows: (19) (20) wherein i.e. , represents the standard deviation of the GPR network output SOH at time T, i.e. , represents the mean value of the GPR network output SOH at time T; , are the weight matrices of the introduced output SOH standard deviation and mean value, respectively, and the forward propagation process ends. (2) Back propagation: assuming the ideal output of the model at time T is The model performance index function can be represented as shown in equation (21): (21) The performance index function is used to solve the parameters in turn , , The adjustment amount of the performance index function is as follows: (22) (23) (24) denotes the base width of the i-th node at time T, denotes the input value of the i-th node at time k ; denotes the base width of the i-th input corresponding to the i-th node at time T, denotes the input value of the i-th input corresponding to the i-th node at time k ; denotes the network learning rate; Then, the parameter value is continuously updated according to the parameter adjustment amount to realize the back propagation process, and thus the improved timing RBF network is built.

4. The wide temperature range lithium battery state of health estimation method based on MGPR and improved timing RBF of claim 1, wherein In the cycle aging experiment of each battery cell, high temperature accelerated aging cycle experiment is used, the battery cell is placed in a 40℃ environment for continuous charging and discharging cycle, and the aging characteristics of each battery cell are extracted and selected every 10 cycles, until the SOH value of the battery cell is lower than 80%.

5. The method of claim 4, wherein the method is based on MGPR and improved timing RBF for wide temperature range lithium battery state of health estimation. The residual stress is completed by an experimental device including three plates, a pressure sensor, and a fastener, and the initial surface pressure is applied to a lower initial stress of 0.05Mpa for prolonging the battery life; after the battery cell is equipped with the pressure measurement experimental device, the initial stress of different battery cells is kept consistent until the cycle life is reached.

6. A system for estimating the state of health of a lithium battery in a wide temperature range based on MGPR and improved timing RBF, characterized in that: The system has program modules corresponding to the steps of any one of claims 1-3, and when running, executes the steps of the wide temperature range lithium battery state of health estimation method based on MGPR and improved timing RBF.

7. A computer-readable storage medium, characterized in that: The computer readable storage medium stores a computer program, and the computer program is configured to realize the steps of the wide temperature range lithium battery state of health estimation method based on MGPR and improved timing RBF of any one of claims 1-3 when called by the processor.

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