Lithium-ion battery health management method fusing fuzzy system and deep learning

Abstract

The application discloses a lithium ion battery health management method fusing a fuzzy system and deep learning, and has the following steps: step one, constructing a physical information and fuzzy hybrid deep learning model; step two, training the physical information and fuzzy hybrid deep learning model, inputting the feature of a training sample into a full connection deep neural network, obtaining a latent solution, calculating the partial differential of the latent solution to each input feature, inputting any combination of the partial differential of a non-labeled feature, the input feature and the latent solution into a TSK fuzzy system, fusing the partial differential of the latent solution to a labeled feature and the output of the TSK fuzzy system through a function F, training the physical information and fuzzy hybrid deep learning model based on a loss function, and obtaining an optimized model through training; and step three, predicting the lithium ion health state. The method replaces the deep neural network representing the non-linear dynamics of the physical information neural network with the TSK fuzzy system, and improves the accuracy of the lithium ion battery health state estimation.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of deep learning, and particularly relates to a lithium ion battery health management method fusing a fuzzy system and deep learning. BACKGROUND

[0002] Lithium ion batteries are dominant in the rechargeable battery commercial market due to their high energy density, long battery life, low self-discharge rate, strong fast charging and discharging ability, and no memory effect, especially for portable electronic products and electric vehicles. However, lithium ion batteries will age during their entire life cycle and affect their performance and life, so the prediction and health management of lithium ion batteries play a crucial role. There are various lithium ion battery models to quantify the battery health status, which can be mainly divided into three categories: equivalent circuit model, electrochemical model and data-driven model. The electrochemical model describes the electrochemical equations inside the battery and analyzes the electrochemical reactions inside the battery, but it includes complex partial differential equations with large calculation, so it is difficult to be directly used for real-time battery health management.

[0003] Data-driven models ignore the internal electrochemical reactions of lithium ion batteries and mainly rely on external data, such as external voltage and current during charging / discharging process. Data-driven models are derived from machine learning algorithms, with simple structure and high computational efficiency. In particular, the progress of deep learning promotes the development of data-driven models, and various models and algorithms for natural language understanding, image processing and computer vision have been extended to lithium ion battery health state estimation. Neural network models imitate human perception and cognitive mechanisms, such as neural networks originated from the simulation of human brain neuron networks, and attention mechanisms imitate human cognitive processes. However, human perception and cognitive mechanisms are different from the electrochemical reaction mechanism of lithium ion batteries, so it is difficult for data-driven models based on neural networks to represent the electrochemical reaction mechanism of lithium ion batteries.

[0004] The electrochemical reactions of lithium-ion batteries include partial differential equations, and physical information neural networks (PINN) involve partial differential equation (PDE) numerical solution, PINN has been used to estimate the state of health of lithium-ion batteries, using two deep neural networks (DNN) to represent two main parts thereof respectively: latent solution and nonlinear dynamics. However, lithium-ion batteries contain various electrochemical reactions, mass transport and charge transport processes, and are influenced by multiple factors such as internal electrochemical reactions and external stress in use, and there are differences between individual lithium-ion batteries, so there is uncertainty in the lithium-ion battery data. In particular, the common and recommended charging method of lithium-ion batteries is small rate constant current constant voltage charging, but the charging time is long; if large rate constant current constant voltage charging, the charging time can be shortened, but the performance of the battery will be accelerated to decay. In order to accelerate the charging and cause the performance to deteriorate, a multi-step charging method can be used, that is, the current of each step of multi-step charging is different, which further aggravates the uncertainty of the data. Moreover, neural networks are like a "black box", lacking transparency and explainability, which hinders the analysis and interpretation of the decision-making process, so there is uncertainty in the data-driven model based on DNN. The uncertainty of data and model leads to uncertainty in the estimation of the state of health of lithium-ion batteries based on PINN of DNN alone and causes the accuracy to be unstable. SUMMARY

[0005] The purpose of the present application is to provide a lithium-ion battery health management method fusing fuzzy systems and deep learning, seamlessly integrating a TSK fuzzy system into the nonlinear dynamics of a physical information neural network, constructing a physical information and fuzzy hybrid deep learning, optimizing training through a back propagation algorithm, using the ability of a TSK fuzzy system to handle uncertain systems, and improving the accuracy of lithium-ion battery health estimation.

[0006] The present application adopts the following technical solutions: a lithium-ion battery health management method fusing fuzzy systems and deep learning, comprising the following steps:

[0007] Step one, constructing a physical information and fuzzy hybrid deep learning model:

[0008] The physical information and fuzzy hybrid deep learning model comprises a fully connected deep neural network, a TSK fuzzy system and a function F, wherein the outputs of the fully connected deep neural network are connected to the inputs of the TSK fuzzy system and the function F respectively, and the output of the TSK fuzzy system is connected to the input of the function F;

[0009] Step two, training the physical information and fuzzy hybrid deep learning model in step one:

[0010] Extracting a set of feature parameters of the battery charging and discharging process as a training sample;

[0011] inputting the training sample into the full connection deep neural network to obtain a potential solution, the potential solution being a predicted value of the SOH value, and the SOH value being a lithium ion state of health value;

[0012] calculating partial derivatives of the potential solution with respect to each feature parameter in the feature parameter set to obtain a partial derivative set;

[0013] taking one of the partial derivative corresponding to the non-labeled feature parameter in the partial derivative set, the training sample, and the potential solution as a feature set, inputting the feature set into the TSK fuzzy system to obtain a description feature about the feature set, and fusing the description feature and the partial derivative corresponding to the labeled feature parameter in the partial derivative set through the function F to generate an F feature;

[0014] calculating partial derivatives of the F feature with respect to the labeled feature parameter in the feature parameter set to obtain an F t feature;

[0015] based on a loss between the potential solution and a measured SOH value, a loss of the F feature, and a loss of the F t feature obtained by the loss function, and training the physical information and fuzzy hybrid deep learning model through a back propagation method to obtain an optimized physical information and fuzzy hybrid deep learning model;

[0016] Step three, inputting the feature parameter extracted from the test battery data into the full connection deep neural network in the optimized physical information and fuzzy hybrid deep learning model to obtain a SOH predicted value of the test battery.

[0017] Further, the labeled feature parameter of the battery is t, and the non-labeled feature parameter is x;

[0018] The t is the internal resistance IR of the battery, or the minimum value of dQ / dV in the charging or discharging process of the battery;

[0019] When the t is the internal resistance IR of the battery, the x includes the average temperature, the charging time, the terminal voltage, the variance of dQ / dV in the charging or discharging process, the skewness of dQ / dV in the charging or discharging process, and the minimum value of dQ / dV in the charging or discharging process of the battery;

[0020] When the t is the minimum value of dQ / dV in the charging or discharging process of the battery, the x includes the internal resistance IR, the average temperature, the charging time, the terminal voltage, the variance of dQ / dV in the charging or discharging process, and the skewness of dQ / dV in the charging or discharging process of the battery.

[0021] Further, the loss function is L, as follows:

[0022]

[0023] wherein: L U = |U(t,x) - y| 2 is the squared error of the latent solution U(t,x) with y, which is the measured value of SOH;

[0024] L F = |F| 2 is the squared error of the function F; L Ft = |F t | 2 is the squared error of F t ; F t = U tt - G t is the first derivative of F with respect to the parameter t; U tt is the second order partial derivative of the latent solution with respect to the parameter t; G t is the first order partial derivative of the characteristic with respect to the parameter t.

[0025] Further, the function F is as follows: F := U t - G(t,x,U,U x ,U xx ,…; θ);

[0026] wherein: U t is the first order partial derivative of the latent solution with respect to the parameter t, U x is the first order partial derivative of the latent solution with respect to the parameter x; U xx is the second order partial derivative of the latent solution with respect to the parameter x; θ is the parameter of the nonlinear dynamics module, which is a real number.

[0027] Further, the TSK fuzzy system comprises a batch normalization layer, a first layer, a second layer, a third layer, a fourth layer and a fifth layer connected in sequence; wherein:

[0028] In the first layer, each neuron represents a membership function, which represents the degree of the input feature z d satisfying the fuzzy set Z r,d , r = 1, …, R, d = 1, …, D, and outputs; a Gaussian membership function is adopted, as follows:

[0029]

[0030] wherein: m r,d and σ r,d are the first premise parameter and the second premise parameter, which represent the mean and the standard deviation of the Gaussian membership function, m r,d is a real number, and σ r,d is a positive real number; the input feature z d is selected from at least one of the partial derivative corresponding to the non-label feature parameter, the training sample, and the latent solution;

[0031] In the second layer, each neuron multiplies the inputs and outputs the product as the activation strength of the corresponding fuzzy rule, as follows:

[0032]

[0033] In the third layer, each neuron calculates the normalized activation strength as:

[0034]

[0035] where R is the number of fuzzy rules.

[0036] In the fourth layer, each neuron corresponds to a fuzzy rule and outputs the normalized activation strength as: where

[0037] where represents the subsequent parameter, and the value range is a real number;

[0038] The fifth layer is the output layer, which is used for summation, as follows:

[0039]

[0040] Further, the fully connected deep neural network includes N small modules BL connected in sequence, and the plurality of small modules BL are connected in a chain, and a fully connected layer is connected at the rear end of the chain, i.e., after the last small module BL, as follows:

[0041] U(t,x)=f1(BL N (BL N-1 (...BL2(BL1(t,x)))));

[0042] where BL1, BL2, …, BL N-1 , BL N represent the input small module from the input end to the output small module to the output end in sequence; f1 is a fully connected layer.

[0043] Further, the physical information and fuzzy hybrid deep learning model parameters include the following:

[0044] The parameter set Ω composed of the parameter weight coefficient and the bias quantity of the fully connected layer f1, and the parameters β and γ of the normalization layer;

[0045] The first premise parameter m r,d , the second premise parameter σ r,d , and the subsequent parameter

[0046] The beneficial effects of the present application are: 1. The TSK fuzzy system is seamlessly integrated into the nonlinear dynamics of the physical information neural network. "Seamless" means that the input and output can be directly connected, so the forward calculation is simple and efficient. In addition, the TSK fuzzy system and the physical information neural network are optimized and trained by back propagation, so the TSK fuzzy system and the physical information neural network are integrated to coordinate efficient training and prediction. 2. The potential solution represented by the deep neural network, its partial derivative and input features are used as the input of the fuzzy system, and the output of the deep neural network and the output of the fuzzy system are linked together in function F. This architecture is close to the form of the partial differential equation set of the lithium ion battery electrochemical model. Therefore, by using the back propagation algorithm to optimize the model parameters with data, the model accuracy and the accuracy of the lithium ion state of health estimation are improved. 3. The TSK fuzzy system is used to replace the deep neural network to represent the nonlinear dynamics of the physical information and fuzzy hybrid deep learning. Because the TSK fuzzy system has fuzzy if-then rules and membership functions, it is better than the deep neural network in handling uncertainty and fuzziness. Lithium ion batteries are complex and uncertain systems. Experiments on a large public lithium ion battery dataset show that the physical information and fuzzy hybrid deep learning method proposed in the present application can more accurately predict the state of health of lithium ion batteries. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 is a physical information and fuzzy hybrid deep learning schematic diagram;

[0048] Figure 2 is a physical information and fuzzy hybrid deep learning diagram;

[0049] Figure 3 is a fast charging condition and battery life of a lithium ion battery dataset;

[0050] Figure 4 is a state of health estimation of four test batteries, where the feature dQ / dV minimum is selected;

[0051] Figure 5 is a state of health estimation of four test batteries, where the feature IR is selected; DETAILED DESCRIPTION

[0052] The present application will be described in detail below in conjunction with the drawings and specific embodiments.

[0053] The present application discloses a lithium ion battery health management model that fuses a fuzzy system and deep learning, as shown in Figure 1 and 2 , which includes two modules connected in series: a potential solution module U(t,x) and a nonlinear dynamics module G(t,x,U x ,U xxThe outputs of the latent solution module U(t,x) are connected to the nonlinear dynamics module G(t,x,U). x U xx The inputs of ,...;θ) and the input of the function F, the nonlinear dynamics module G(t,x,U) x U xx The output of ,...;θ) connects to the input of the function F;

[0054] Where: t is a one-dimensional real number; x = [x1,...,x] n ] T Let t and x be n-dimensional real numbers, where t and x are input features and n is a positive integer; θ is a parameter of the nonlinear dynamics, which takes the value of a real number.

[0055] For simplicity, partial differentials can be expressed not only with general mathematical expressions, but also with subscripts to represent differentiation or partial derivatives with respect to t or x. Therefore, a first-order partial differential can be expressed as U t and U x The second-order partial differential is represented as U tt and U xx .

[0056] like Figure 1 As shown, the potential solution U(t,x) and the nonlinear dynamics G(t,x,U) x U xx ,...;θ) Construct a hybrid deep learning architecture for physical information and fuzzy information as follows:

[0057]

[0058] According to equation (1), the function F is defined as:

[0059] F:=U t -G(t,x,U,U x U xx ;…;θ) (2);

[0060] Take the partial derivative of F with respect to t: F t =U tt -G t Therefore, the loss function L is:

[0061]

[0062] Where: L U =|U(t,x)-y| 2 It is the squared error between the latent solution module U(t,x) and y; L F =|F| 2 L is the squared error of the function F; Ft =|F t | 2 For Ft The square error of y is a one-dimensional real number, which represents the measured value of SOH corresponding to the input features. The function F is a fusion module.

[0063] The partial derivative in the physical information and fuzzy hybrid deep learning architecture is solved by automatic differentiation, which decomposes a complex mathematical operation process into a series of simple basic operations through the chain rule of calculus, and each basic operation can be obtained through partial differentiation.

[0064] The above potential solution U(t,x) is represented by a fully connected deep neural network, which is a composite chain structure formed by linking fully connected layers, activation functions and batch normalization layers. The composite chain structure is to composite multiple related functions together. Let f1 represent the fully connected layer, each fully connected layer has parameter weight coefficients and bias, which can be trained through the back propagation algorithm of the entire network, and the number of parameters is related to the number of neurons. The function f2 represents the activation function, including but not limited to activation functions such as Sigmoid function, Tanh function, ReLU function, Softmax function, Mish function, Swish function, SELU function, ELU function, PReLU function, Leaky ReLU function. Each neuron of the batch normalization layer can be represented as:

[0065]

[0066] Where: x bn is the input of the batch normalization layer, β and γ are the first adjustable parameter and the second adjustable parameter, which can be trained by the back propagation algorithm, μ B and are the mean and variance of the mini-batch data set respectively, and mini-batch can be used to represent the mini-batch; ε is a very small value added to prevent the denominator from being zero.

[0067] The fully connected deep neural network includes N small modules BL connected in sequence, and multiple small modules BL are connected in a chain. The back end of the chain, that is, after the last small module BL, a fully connected layer is linked; each small module BL includes a fully connected layer f1(·), an activation function f2(·) and a batch normalization layer BN(·) connected in sequence, and the small module is as follows: BL=BN(f2(f1(x in )), where x N represents the input of the frontmost small module;

[0068] Specifically, the above fully connected deep neural network is as follows:

[0069] U(t,x)=f1(BL N-1 (BL N-1 (...BL2(BL1(t,x))))) (5);

[0070] where BL1, BL2, …, BL N-1 , BL N represent input sub-modules from the input end to output sub-modules to the output end, respectively.

[0071] The parameter set composed of the parameter weight coefficients and bias of all the full connection layers f1 and the parameters β and γ of the normalization layer is denoted as Ω, Ω takes real values, and is the trainable parameter set of the full connection deep neural network.

[0072] The nonlinear dynamics module G(t, x, U x , U xx ,...; θ) is expressed by a TSK fuzzy system, the input of which can be flexibly adjusted and can be any combination of the four variables {t, x, U, Ux}, in the embodiment of the application, all the four variables are selected as the input, and [t, x, U, Ux] T denotes the input of the TSK fuzzy system. The TSK fuzzy system performs input-output mapping based on R fuzzy rules, and each membership function is associated with each input, so that the input space is divided into R fuzzy subspaces, each of which is controlled by a fuzzy if-then rule, and R is a positive integer. A batch normalization layer is linked at the input end of the TSK fuzzy system to perform normalization processing, z = BN([t, x, U, Ux] T ), so that z is a D-dimensional column vector, and D is a positive integer; wherein z d denotes the dth element of z, and then enters the first layer of the TSK fuzzy system. t is a labeled feature parameter of the battery, and x is an unlabelled feature parameter of the battery.

[0073] The TSK fuzzy system comprises a batch normalization layer, a first layer, a second layer, a third layer, a fourth layer and a fifth layer connected in sequence; wherein:

[0074] In the first layer, each neuron represents a membership function, which represents the degree of the input feature z d satisfying the fuzzy set Z r,d , r = 1,..., R, d = 1,..., D, and outputs; the input feature z d is selected from at least one of the partial derivative corresponding to the unlabelled feature parameter, the training sample and the potential solution;

[0075] Different membership functions can be used, and in the application, a Gaussian membership function is used, as follows:

[0076]

[0077] wherein: m r,d and σ r,dThe first premise parameter and the second premise parameter represent the mean value and the standard deviation of the Gaussian membership function, m r,d The value range is a real number, and sigma r,d The value range is a positive real number.

[0078] In the second layer, each neuron multiplies the input and outputs the product as the activation strength of the corresponding fuzzy rule, as follows:

[0079]

[0080] In the third layer, each neuron calculates the normalized activation strength as follows:

[0081]

[0082] Wherein, R is the number of fuzzy rules.

[0083] In the fourth layer, each neuron corresponds to a fuzzy rule, and the Wherein:

[0084]

[0085] Wherein The subsequent parameters represent real numbers.

[0086] The fifth layer of the TSK system is the output layer, which is used for summation, as follows:

[0087]

[0088] The present application mainly includes two main sub-modules: a latent solution U represented by a deep neural network and a nonlinear dynamics G represented by a TSK fuzzy system. The latent solution U is solved by automatic differentiation to obtain Ux, and then an input vector [t, x, U, Ux] of the nonlinear dynamics G is formed with the input (t, x). T The output of the nonlinear dynamics G is linked with the latent solution U through a function F as shown in equation (2), so that the input and output of the two sub-modules are seamlessly linked. Finally, the loss function is calculated as shown in equation (3), and the latent solution U represented by the deep neural network and the nonlinear dynamics G represented by the TSK fuzzy system form a physical information and fuzzy hybrid deep learning basic architecture to constitute a physical information and fuzzy hybrid deep learning overall model.

[0089] The method in the present application mainly includes two links: training and prediction. After the model is constructed, it needs to be trained, and then the trained parameters are saved, which can be used for prediction. The training step mainly includes two parts: forward propagation to calculate the loss function and backward propagation to adjust the parameters, and the two parts are iteratively cycled, and finally the parameters are adjusted to meet the conditions, and the parameters and the model are saved. The saved model and parameters are input into the test sample, and the forward propagation stage can be used to predict the SOH.

[0090] Step A, input (x, t) first calculates the potential solution U by formula (5), and then solves the partial derivative Ux by automatic differentiation.

[0091] Step B, the input vector of the nonlinear dynamics G is composed of [t, x, U, Ux] T , which is calculated by formulas (6)-(10).

[0092] Step C, the output of the nonlinear dynamics G is linked to the potential solution U by the function F as formula (2), and then the loss function is calculated as formula (3).

[0093] The present application trains these adjustable parameters by the back propagation method, written as BP: the potential solution U represented by the fully connected deep neural network includes a set of adjustable parameters Ω; and the adjustable parameters in the nonlinear dynamics G represented by the TSK fuzzy system include the first premise parameter m r,d and the second premise parameter σ r,d r=1,...,R,d=1,...,D and subsequent parameters The back propagation method is based on the gradient descent method, which is a neural network optimization method and is widely used in neural network training. As follows:

[0094] First, calculate the input to the forward propagation, i.e. the forward propagation steps A to B as described above;

[0095] Calculate the error of the loss function for one sample as formula (3); if it is a batch or small batch of samples for training, the error is the sum of the loss functions of these samples, i.e. the loss function sum;

[0096] Calculate the gradient of the adjustable parameters, and the calculation process is from the last layer to the front, i.e. the error is back propagation;

[0097] Update the adjustable parameters according to the gradient descent rule, and the goal is to reduce the error.

[0098] Specifically as follows: training the physical information and fuzzy hybrid deep learning model in step one:

[0099] Extract a set of feature parameters of the battery charging and discharging process as training samples;

[0100] Input the training samples into the fully connected deep neural network to obtain a potential solution, and the potential solution is a predicted value of the SOH value, and the SOH value is a lithium ion state of health value;

[0101] Calculate the partial derivative of the potential solution to each feature parameter in the set of feature parameters to obtain a set of partial derivatives.

[0102] At least one of the partial derivative corresponding to the non-labeled feature parameter in the partial derivative set, the training sample and the potential solution is taken as a feature set, and the feature set is input into the TSK fuzzy system to obtain a description feature about the feature set, and the description feature is fused with the partial derivative corresponding to the labeled feature parameter in the partial derivative set to generate a F feature through the function F;

[0103] The partial derivative of the F feature to the labeled feature parameter in the feature parameter set is calculated to obtain a F t feature.

[0104] The loss of the error between the potential solution obtained based on the loss function and the SOH measured value, the loss of the F feature and the loss of the F t feature are obtained, and a trained full-connection deep neural network is obtained through a back propagation algorithm.

[0105] The above steps are iterated until a stop criterion is met, for example, the difference between the errors of adjacent two iterations is small, or the iteration reaches a set number of times. The potential solution U represented by the full-connection deep neural network and the nonlinear dynamics G represented by the TSK fuzzy system are not only seamlessly linked in input and output, but also form a whole physical information and fuzzy hybrid deep learning, which can coordinate efficient integrated training and prediction.

[0106] The present application is supported by the National Natural Science Foundation (Grant No. 62263006) and the Guangxi Science and Technology Plan Project (Grant No. Guike AD21220095).

[0107] The experimental verification in the present application uses a public data set selected from the literature "Data-driven prediction of battery cycle life before capacity degradation". The data set consists of 124 A123 Systems batteries, each with a nominal capacity of 1.1 Ah and a nominal voltage of 3.3 V. The batteries are cycled to failure by one-step or two-step fast charging strategies and are discharged at 4C rate. As shown in the figure, Figure 3 The fast charging strategy has three main parameters: the first step charging current, the second step charging current and the battery conversion state of charge.

[0108] The state of charge is represented by SOC%, and after the SOC% reaches the battery conversion state of charge, the first step charging current is switched to the second step charging current. The present application ignores some data abnormal cycles, and a total of about 96,700 valid cycles are collected, i.e., 96,700 data samples are collected.

[0109] Compared with the traditional constant current constant voltage charging, the constant current constant voltage adopts CCCV, the fast charging strategy is complex and flexible, and the SOH estimation is more difficult. The external data such as terminal voltage, current and temperature are collected during charging and discharging.

[0110] The features are extracted from the above effective cycles, and the extracted features should have a strong correlation with SOH, which is the key of deep learning. In the present application, the internal resistance, average temperature and charging time are extracted as features, and the internal resistance is represented by IR, because they have an impact on the battery capacity and are related to SOH.

[0111] In order to identify and quantify the electrochemical characteristics of the battery, incremental capacity analysis is a widely used electrochemical method, which adopts ICA, based on the voltage change during charging / discharging phase. ICA is defined as the rate of change of capacity with respect to voltage dQ / dV, so the minimum value, variance and skewness of dQ / dV during discharging process are extracted as features. The internal resistance, average temperature and charging time, and the minimum value, variance and skewness of dQ / dV during discharging process, these six features are linearly scaled to [0, 1] by min-max normalization.

[0112] All lithium ion batteries are cycled under multiple fast charging conditions, and the charging strategy will also affect SOH, so the first step charging current, the second step charging current and the state of charge when the battery is converted, and the cycle number are extracted as features. The first step charging current and the second step charging current are linearly scaled at the highest charging rate of 8 times, and the cycle number is also linearly scaled at the maximum cycle number. A total of 10 features are extracted for each battery cycle. In order to avoid the fact that some features are superior to others due to the difference in scale, the present application uses Z-Score standardization, also known as zero mean normalization, to convert the data into standard scores with zero mean and unit variance, and rescale the features extracted from the training data set. The 10 features extracted are input variables (t, x).

[0113] The state of health of lithium ion is represented by SOH, and there are various definitions of the state of health of lithium ion. The commonly used definition is the capacity of the i th cycle C i The ratio between the nominal capacity C nom , that is, the measured value SOH i As follows:

[0114]

[0115] Where: SOH i is the measured value, represented by y as described above.

[0116] To obtain better generalization performance, the training validation data includes 115 batteries from #1 to #115, i.e., the training involves approximately 86,600 cycles. In each experiment, 10% of the training validation data is randomly selected for validation, and the other data is trained. In addition to the 115 batteries used for training validation, there are 9 batteries left in the dataset, of which 4 batteries are selected as test batteries, i.e., #116, #117, #121 and #124 batteries. Four sets of test experiments are performed on the four batteries respectively, each experiment repeats the training and testing process three times, and the results are averaged to reduce randomness. All experiments are performed on a workstation equipped with Intel(R) Core(TM) i9-10900X CPU @ 3.70 GHz and NVIDIA GeForce RTX 3080 GPU.

[0117] The backpropagation method of the present application adopts the classic optimization settings as shown in Table 1:

[0118] Table 1 Optimization Settings

[0119]

[0120] In the present application, the inputs t and x are different because t has a significant impact on U t , while x does not. From the 10 extracted features, one feature is selected as t, and the other 9 features are selected as x. Because dQ / dV is an electrochemical method to identify the electrochemical properties of the battery, and IR is related to SOH according to the electrochemical model, two choices of t are tested: the minimum value of dQ / dV or IR. The specific selection principle is as follows:

[0121] When the t is selected as the internal resistance IR of the battery, the x includes: the average temperature of the battery, the charging time, the terminal voltage, the variance of dQ / dV during the discharging process, the skewness of dQ / dV during the discharging process and the minimum value of dQ / dV during the discharging process;

[0122] When the t is selected as the minimum value of dQ / dV during the discharging process of the battery, the x includes: the internal resistance IR of the battery, the average temperature, the charging time, the terminal voltage, the variance of dQ / dV during the discharging process and the skewness of dQ / dV during the discharging process.

[0123] In the case of two t choices, four experiments are performed on #116, #117, #121 and #124 batteries respectively. Each experiment trains and tests two choices of t, and each choice has two series of hyperparameter settings, so four experiments are performed in each group, and the experiment labels are PIFHDL1T, PIFHDL2T, PIFHDL1R and PIFHDL2R, as shown in Table 2 for detailed information of the hyperparameters of each experiment.

[0124] Table 2. Details of experimental hyperparameters

[0125] Experiment label PIFHDL1T PIFHDL2T PIFHDL1R PIFHDL2R Number of DNN fully connected hidden layers in U 8 12 8 12 Number of neurons per layer 64 64 64 64 Number of fuzzy rules 64 128 64 128 t selection input features dQ / dV minimum dQ / dV minimum IR IR

[0126] The experimental results of the present application are compared with three existing PINN methods, as in Example A of “Physics-Informed Neural Networks for Prognostics and Health Management of Lithium-Ion Batteries”, which are PINN-DeepHPM(AdpBal), PINN-Verhulst(Sum) and PINN-Verhulst(AdpBal). The data of #91 and #100 batteries are used for training, and then the test is performed on #124 battery. The present application not only tests on #124 battery, but also checks the prediction effect on another 3 test batteries: #116, #117, #121.

[0127] The above variables (x, t) and y represent the input and output of any sample, but there are a large number of samples in training and testing, so the following variables are added with subscripts to distinguish these samples. For example, y m represents the mth SOH measurement value, and the corresponding input variable is (x m ,t m ), and U(x m ,t m ) is simplified as U m . The present application uses two widely used indicators to evaluate the experimental performance: root mean square error and mean absolute error. The formula of root mean square error RMSE is:

[0128]

[0129] where M is a positive integer, representing the total number of samples involved. The formula of mean absolute error MAE is:

[0130]

[0131] Table 3. RMSE test results

[0132]

[0133] Table 4. MAE test results

[0134]

[0135] Table 3 and Table 4 list the RMSE and MAE results of the four groups of test experiments respectively, the smaller the value, the smaller the error, that is, the better the prediction accuracy, and the black value indicates the minimum error obtained on each battery test. The physical information and fuzzy hybrid deep learning proposed in the present application adopts four different hyperparameter settings, and after training four models, the prediction error RMSE and MAE on the #116, #117 and #121 test batteries are all smaller than the existing three PINN methods. Only in the #124 battery test, only PIFHDL1T prediction error RMSE and MAE are better than the existing three PINN methods, and PIFHDL1R and PIFHDL2R prediction error RMSE and MAE are better than one PINN method PINN-Verhulst(Sum). On the first three test batteries, the physical information and fuzzy hybrid deep learning proposed in the present application achieves higher prediction accuracy than the existing three PINN methods; in the #124 battery test, the physical information and fuzzy hybrid deep learning proposed in the present application achieves comparable prediction accuracy to the existing three PINN methods.

[0136] The existing three PINN methods are trained with the data of #91 and #100 batteries, and only good prediction performance is achieved on #124 battery, because the three batteries #91, #100 and #124 use the same fast charging strategy. But the four test batteries use different fast charging strategies, and the test results of the four batteries are comprehensive, the error of the model and algorithm proposed in the present application is more average on the four test batteries, while the existing three PINN methods degrade in performance on the test batteries using different fast charging strategies, and lead to large performance changes of the four test batteries, for example, PINN-Verhulst(AdpBal) has a RMSE of 0.104 on #116 battery test, but a RMSE of 0.00465 on #124 battery test.

[0137] On #116 battery, PIFHDL1R achieves the best prediction performance with 0.00474 RMSE and 0.00326 MAE. On #117 battery, PIFHDL2R outperforms other methods with 0.00587 RMSE and 0.00518 MAE. On #121 battery, PIFHDL2R achieves the best prediction performance with 0.00537 RMSE and 0.00483 MAE. On #124 battery, PIFHDL1T achieves the best prediction performance with 0.00376 RMSE and 0.00282 MAE. It can be seen that the method with the smallest prediction error on the above four test batteries is the physical information and fuzzy hybrid deep learning proposed in the present application, so the physical information and fuzzy hybrid deep learning proposed in the present application can more accurately predict the state of health of lithium ion batteries.

[0138] As Figure 4As shown, four test battery state of health estimates, t select feature dQ / dV minimum; Figure 5 For four test battery state of health estimates, t select feature IR. As can be seen from the figure, using the method in the application, under different parameter settings, the predicted value of SOH is close to the measured value, and the prediction accuracy is high.

Claims

1. A lithium-ion battery health management method integrating fuzzy systems and deep learning, characterized in that, Includes the following steps: Step 1: Construct a deep learning model that combines physical information and fuzzy logic. The physical information and fuzzy hybrid deep learning model includes a fully connected deep neural network, a TSK fuzzy system, and a function F, wherein the output of the fully connected deep neural network is connected to the input of the TSK fuzzy system and the input of the function F, respectively, and the output of the TSK fuzzy system is connected to the input of the function F; Step 2: Train the physical information and fuzzy hybrid deep learning model from Step 1: Extract the set of characteristic parameters of the battery charging and discharging process as training samples; The training samples are input into the fully connected deep neural network to obtain potential solutions, which are the predicted values ​​of SOH, and the SOH value is the lithium ion health status value. Calculate the partial derivative of the latent solution with respect to each feature parameter in the feature parameter set to obtain the partial derivative set; The partial differentials corresponding to the unlabeled feature parameters in the partial differential set, training samples, and at least one potential solution are used as a feature set. The feature set is input into the TSK fuzzy system to obtain descriptive features about the feature set. The descriptive features are then fused with the partial differentials corresponding to the labeled feature parameters in the partial differential set through the function F to generate F features. Calculate the partial derivative of the F feature with respect to the labeled feature parameters in the feature parameter set to obtain F. t feature; The loss between the latent solution derived from the loss function and the measured SOH value, the loss of the F feature, and F... t The feature loss is used, and the fully connected deep neural network is trained by backpropagation. Step 3: Input the feature parameters of the test battery into the trained fully connected deep neural network to obtain the SOH prediction value of the test battery.

2. The lithium-ion battery health management method integrating fuzzy systems and deep learning as described in claim 1, characterized in that, The battery's labeled characteristic parameter is t; its unlabeled characteristic parameter is x; The t is the internal resistance IR of the battery, or the minimum value of dQ / dV during the charging or discharging process of the battery; When t is selected as the internal resistance IR of the battery, x includes: the average temperature of the battery, charging time, terminal voltage, variance of dQ / dV during charging or discharging, skewness of dQ / dV during charging or discharging, and minimum value of dQ / dV during charging or discharging. When t is selected as the minimum value of dQ / dV during battery charging or discharging, x includes: the battery's internal resistance IR, average temperature, charging time, terminal voltage, variance of dQ / dV during charging or discharging, and skewness of dQ / dV during charging or discharging.

3. The lithium-ion battery health management method integrating fuzzy systems and deep learning as described in claim 2, characterized in that, The loss function is L, as follows: Where: L U =|U(t,x)-y| 2 Let y be the squared error between the potential solution module U(t,x) and y, where y is the measured value of SOH; L F =|F| 2 Let F be the squared error of the function F; =|F t | 2 For F t The squared error; F t =U tt -G t Take the partial derivative of F with respect to parameter t; U tt G is the second partial derivative of the potential solution with respect to the parameter t; t To describe the first-order partial derivative of the feature with respect to the parameter t; The function F is as follows: F := U t -G(t,x,U,U x U xx ,θ); Among them: U t For the first-order partial derivative of the potential solution with respect to parameter t, U x The first-order partial derivative of the potential solution with respect to the parameter x; U xx θ is the second-order partial derivative of the potential solution with respect to the parameter x; θ is the parameter of the nonlinear dynamics module, taking real values.

4. The lithium-ion battery health management method integrating fuzzy systems and deep learning as described in claim 3, characterized in that, The TSK fuzzy system comprises a batch normalization layer, a first layer, a second layer, a third layer, a fourth layer, and a fifth layer connected in sequence; wherein: In the first layer, each neuron represents a membership function, which represents the input feature z. d Satisfying the fuzzy set Z r,d The degree of membership is determined, r = 1, ..., R, d = 1, ..., D, and output; a Gaussian membership function is used, as follows: Where: m r,d and σ r,d Let m be the first and second prerequisite parameters, representing the mean and standard deviation of the Gaussian membership function. r,d The range of values ​​is real numbers, σ r,d The value range is positive real numbers; input feature z d It is selected from at least one of the partial derivatives corresponding to the unlabeled feature parameters, training samples, and potential solutions; In the second layer, each neuron multiplies its input and uses the product output as the activation strength of the corresponding fuzzy rule, as follows: In the third layer, the normalized activation intensity of each neuron is calculated as follows: Where: R is the number of fuzzy rules; In the fourth layer, each neuron corresponds to a fuzzy rule, which will... in in This indicates the subsequent parameter, whose value range is real numbers; The fifth layer is the output layer, used for summation, as follows:

5. The lithium-ion battery health management method integrating fuzzy systems and deep learning as described in claim 4, characterized in that, The fully connected deep neural network comprises N sequentially connected small modules (BLs), with multiple BLs connected to a chain. At the end of the chain, after the last BL, a fully connected layer is linked, as follows: U(t,x)=f1(BL N (BL N-1 (...BL2(BL1(t,x))))); Among them, BL1, BL2...BL N-1 BL N The input modules are sequentially represented from the input end to the output module; f1 is a fully connected layer.

6. The lithium-ion battery health management method integrating fuzzy systems and deep learning as described in claim 5, characterized in that, The physical information and fuzzy hybrid deep learning model parameters include the following: The parameter set Ω consists of the parameter weights and biases of the fully connected layer f1, and the parameters β and γ of the normalized layer. The first prerequisite parameter m in the TSK fuzzy system r,d Second prerequisite parameter σ r,d and subsequent parameters

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