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

Abstract

The invention discloses a lithium ion battery health management method fusing a fuzzy system and deep learning. The method comprises the following steps: 1, constructing a physical information and fuzzy mixed deep learning model; 2, training physical information and a fuzzy mixed deep learning model, and inputting features of training samples into a full-connection deep neural network to obtain a potential solution; calculating partial differential of the potential solution to each input feature; wherein the partial differential of the non-marked feature, the input feature and any combination of the potential solution are input into a TSK fuzzy system, and the partial differential of the potential solution to the marked feature and the output of the TSK fuzzy system are fused through a function F; based on the loss function, adopting a back propagation method to train physical information and a fuzzy mixed deep learning model, and obtaining an optimization model after training; and 3, predicting the lithium ion health state. According to the method, a TSK fuzzy system replaces a deep neural network to represent nonlinear dynamics of a physical information neural network, and the accuracy of lithium ion battery health state estimation is improved.

Description

Technical Field

[0001] The present invention belongs to the field of deep learning technology, and specifically relates to a lithium-ion battery health management method integrating fuzzy system and deep learning. Background Art

[0002] Lithium-ion batteries dominate the commercial rechargeable battery market, especially for portable electronics and electric vehicles, due to their high energy density, long battery life, low self-discharge rate, fast charge and discharge capabilities, and no memory effect. However, lithium-ion batteries age throughout their life cycle, affecting their performance and life, so the prediction and health management of lithium-ion batteries plays a vital role. There are various lithium-ion battery models to quantify battery health, which can be mainly divided into three categories: equivalent circuit models, electrochemical models, and data-driven models. Electrochemical models describe the electrochemical equations inside the battery and analyze the electrochemical reactions inside the battery, but they include complex partial differential equations with large computational complexity, so it is difficult to use them directly for real-time battery health management.

[0003] Data-driven models ignore the internal electrochemical reactions of lithium-ion batteries and rely mainly on external data, such as external voltage and current during the charging / discharging process. Data-driven models are derived from machine learning algorithms, with simple structures and high computational efficiency. In particular, advances in deep learning have promoted the development of data-driven models, such as a variety of models and algorithms for natural language understanding, image processing, and computer vision that have been extended to lithium-ion battery health state estimation. Neural network models imitate human perception and cognitive mechanisms. For example, neural networks originate 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 mechanisms of lithium-ion batteries, so it is difficult for data-driven models based on neural networks to represent the electrochemical reaction mechanisms of lithium-ion batteries.

[0004] The electrochemical reaction of lithium-ion batteries includes partial differential equations. Physical information neural network (PINN) involves numerical solution of partial differential equations (PDE). PINN has been used to estimate the health status of lithium-ion batteries. Two deep neural networks (DNN) are used to represent its two main parts: potential solution and nonlinear dynamics. However, lithium-ion batteries contain multiple electrochemical reactions, mass transfer and charge transfer processes, and are affected by multiple factors such as internal electrochemical reactions and external stresses during use. In addition, there are differences among individual lithium-ion batteries, so the data of lithium-ion batteries contains uncertainty. In particular, the common and recommended charging method for lithium-ion batteries is small-rate constant current and constant voltage charging, but charging takes a long time; if high-rate constant current and constant voltage charging is used, the charging time can be shortened, but the battery performance will be accelerated. In order to accelerate charging and cause accelerated performance deterioration, a multi-step charging method can be used, that is, the current of each step of multi-step charging is different, which exacerbates data uncertainty. Moreover, the neural network is like a "black box" and lacks transparency and interpretability, which hinders its analysis and explanation of the decision-making process, so the data-driven model based on DNN has uncertainty. The uncertainty of data and models leads to uncertainty in the health status of lithium-ion batteries estimated by PINN based only on DNN and leads to unstable accuracy. Summary of the invention

[0005] The purpose of the present invention is to provide a lithium-ion battery health management method that integrates fuzzy systems and deep learning, seamlessly integrates the TSK fuzzy system into the nonlinear dynamics of the physical information neural network, constructs physical information and fuzzy hybrid deep learning, performs optimization training through the back propagation algorithm, and utilizes the ability of the TSK fuzzy system to handle uncertain systems to improve the accuracy of lithium-ion battery health estimation.

[0006] The present invention adopts the following technical solution: a lithium-ion battery health management method integrating fuzzy system and deep learning, comprising the following steps:

[0007] Step 1: Build a physical information and fuzzy hybrid deep learning model:

[0008] 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 respectively connected to the input of the TSK fuzzy system and the input of the function F, and the output of the TSK fuzzy system is connected to the input of the function F;

[0009] Step 2: Train the physical information and fuzzy hybrid deep learning model in step 1:

[0010] Extract the characteristic parameter set of the battery charging and discharging process as training samples;

[0011] Inputting the training sample into the fully connected deep neural network to obtain a potential solution, wherein the potential solution is a predicted value of the SOH value, and the SOH value is a lithium ion health state value;

[0012] Calculating the partial differential of the potential solution with respect to each characteristic parameter in the characteristic parameter set to obtain a partial differential set;

[0013] Taking the partial differential corresponding to the non-marked feature parameter in the partial differential set, the training sample, and one of the potential solutions as a feature set, inputting the feature set into the TSK fuzzy system to obtain a descriptive feature about the feature set, and fusing the descriptive feature with the partial differential corresponding to the marked feature parameter in the partial differential set through the function F to generate an F feature;

[0014] Calculate the partial derivative of the F feature with respect to the marked feature parameter in the feature parameter set to obtain F t feature;

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

[0016] Step 3: After extracting characteristic parameters from the test battery data, input the optimized physical information and the fully connected deep neural network in the fuzzy hybrid deep learning model to obtain the SOH prediction value of the battery to be tested.

[0017] Further, the marking characteristic parameter of the battery is t; the non-marking characteristic parameter is x;

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

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

[0020] When t is selected as the minimum value of dQ / dV during the battery charging or discharging process, 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 charging or discharging process, and the skewness of dQ / dV during the charging or discharging process.

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

[0022]

[0023] Where: L U =|U(t,x)-y| 2 , is the square error between the potential solution module U(t,x) and y, and y is the measured value of SOH;

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

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

[0026] Among them: U t is the first-order partial differential of the potential solution with respect to parameter t, U x is the first-order partial differential of the potential solution with respect to parameter x; U xx is the second-order partial differential of the potential 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 includes 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 input feature z d Satisfy fuzzy set Z R,D r=1,...,R,d=1,...,D, and output; using Gaussian membership function, as follows:

[0029]

[0030] Where: m r,d and σ r,d are the first premise parameter and the second premise parameter, representing the mean and standard deviation of the Gaussian membership function, m r,d The value range is real number, σ r,d The value range is positive real number; input feature z d At least one selected from the group consisting of a partial differential corresponding to a non-labeled feature parameter, a training sample, and a potential solution;

[0031] In the second layer, each neuron multiplies the input 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. in

[0037] in r=1,...,R,d=0,1,...,D represents the subsequent parameters, and the value range is real number;

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

[0039]

[0040] Furthermore, the fully connected deep neural network includes N small modules BL connected in sequence, and multiple small modules BL are connected in a chain, and the back end of the chain, that is, after the last small module BL, is connected to a fully connected layer, as follows:

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

[0042] Among them, BL1, BL2…BL N-1 BL N They represent the input small module starting from the input end to the output small module at the output end; f1 is the fully connected layer.

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

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

[0045] The first premise parameter m in the TSK fuzzy system r,d , the second premise parameter σ r,d and subsequent parameters

[0046] The beneficial effects of the present invention 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, and the TSK fuzzy system and the physical information neural network are regarded as one for back-propagation optimization training, 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 and its partial differential 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 jointly linked to the function F. This architecture is close to the form of the partial differential equation group of the lithium-ion battery electrochemical model; therefore, through the back-propagation algorithm, the model parameters are optimized using data, thereby improving the model accuracy and the accuracy of the lithium ion health state estimation. 3. Use TSK fuzzy system to replace deep neural network to represent physical information and nonlinear dynamics of fuzzy hybrid deep learning. Because TSK fuzzy system has fuzzy if-then rules and membership functions, it is better at handling uncertainty and ambiguity than deep neural network. Lithium-ion batteries are complex and uncertain systems. Experiments on large-scale public lithium-ion battery data sets show that the physical information and fuzzy hybrid deep learning method proposed in the present invention can more accurately predict the health status of lithium-ion batteries. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Schematic diagram of physical information and fuzzy hybrid deep learning;

[0048] Figure 2 Deep learning graphs for physical information and fuzzy hybrids;

[0049] Figure 3 Fast charging conditions and battery life for lithium-ion battery datasets;

[0050] Figure 4 The health status of the four test batteries is estimated where t selects the minimum value of the characteristic dQ / dV;

[0051] Figure 5 The characteristic IR is selected for the four test battery health state estimates. DETAILED DESCRIPTION

[0052] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0053] The present invention discloses a lithium-ion battery health management model integrating fuzzy system and deep learning, such as Figure 1 and 2 As shown, it includes two connected modules: the potential solution module U(t,x) and the nonlinear dynamics module G(t,x,U x ,U xx,...; θ); the output of the potential solution module U(t,x) is connected to the nonlinear dynamics module G(t,x,U x ,U xx ,...;θ) and the input of the function F, the nonlinear dynamics module G(t,x,U x ,U xx ,...;θ)'s output connects the input of function F;

[0054] Where: t is a one-dimensional real number; x=[x1,...,x n ] T is an n-dimensional real number, t and x are both input features, n is a positive integer; θ is a parameter of nonlinear dynamics, which is a real number;

[0055] For simplicity, partial differentials can be expressed not only in general mathematical expressions, but also by subscripts to indicate differentials or partial derivatives with respect to t or x. Therefore, the first-order partial differential can be expressed as U t and U x , the second-order partial differential is expressed 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) constructs a physical information and fuzzy hybrid deep learning architecture as:

[0057]

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

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

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

[0061]

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

[0063] The partial differentials in the physical information and fuzzy hybrid deep learning architecture are solved using automatic differentiation, which is to decompose a complex mathematical operation process into a series of simple basic operations through the chain derivation method of calculus. Each basic operation can be obtained through the partial differential table.

[0064] The above potential solution U(t,x) is represented by a fully connected deep neural network. The fully connected deep neural network is a composite chain structure formed by linking a fully connected layer, an activation function, and a batch normalization layer. The composite chain structure is to combine multiple related functions together. Let function f1 represent the fully connected layer. Each fully connected layer has parameter weight coefficients and biases, which can be trained through the back propagation algorithm of the entire network. The number of parameters is related to the number of neurons. 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, and Leaky ReLU function. Each neuron in 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 and second adjustable parameters, respectively, which can be trained by the back propagation algorithm, μ B and They are the mean and variance of a small batch of data sets, respectively. A small batch can be represented by a mini-batch; ε is an extremely small value added to prevent the denominator from being zero.

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

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

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

[0070] Among them, BL1, BL2…BL N-1 BL N It represents the input small module starting from the input end to the output small module at the output end.

[0071] The parameter set consisting of the parameter weight coefficients and bias of all fully connected layers f1 and the parameters β and γ of the normalization layer is expressed as Ω, where Ω is a real number, which is the trainable parameter set of this fully connected deep neural network.

[0072] Nonlinear dynamics module G(t,x,U x ,U xx ,...; θ) is represented by a TSK fuzzy system, whose input can be flexibly adjusted and can be any combination of the four variables {t, x, U, Ux}. In the embodiment of the present invention, all of these four variables are selected as inputs for greater representativeness. Let [t, x, U, Ux] T Represents 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 the input space is divided into R fuzzy subspaces, each subspace is controlled by a fuzzy if-then rule, and R is a positive integer. A batch normalization layer is connected to the input of the TSK fuzzy system to perform normalization processing, z = BN ([t, x, U, Ux] T ), so z is a D-dimensional column vector, D is a positive integer; where z d It represents the d-th dimension element of z, and then enters the first layer of the TSK fuzzy system. t is the marked characteristic parameter of the battery, and x is the non-marked characteristic parameter of the battery.

[0073] The TSK fuzzy system includes 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 input feature z d Satisfy fuzzy set Z R,D r=1,...,R,d=1,...,D, and output; input feature z d At least one selected from the group consisting of a partial differential corresponding to a non-labeled feature parameter, a training sample, and a potential solution;

[0075] Different membership functions can be used. The Gaussian membership function is used in the present invention as follows:

[0076]

[0077] Where: m r,d and σ r,dare the first premise parameter and the second premise parameter, representing the mean and standard deviation of the Gaussian membership function, m r,d The value range is real number, σ r,d The value range is positive real numbers.

[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:

[0081]

[0082] Where: R is the number of fuzzy rules.

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

[0084] in r=1, ..., R, d=0, 1, ..., D represents subsequent parameters, and the value range is real numbers.

[0085] The fifth layer of the TSK system is the output layer, which is used for summation, as follows:

[0086]

[0087] The present invention mainly includes two main submodules: the potential solution U represented by a deep neural network and the nonlinear dynamics G represented by a TSK fuzzy system. The potential solution U is obtained by automatic differentiation to obtain partial differentials Ux, which is then combined with the input (t, x) to form the input vector [t, x, U, Ux] of the nonlinear dynamics G. T The output of the nonlinear dynamics G is linked to the potential solution U through the function F as shown in formula (2), so that the input and output of the two submodules are seamlessly linked. Finally, the loss function is calculated as shown in formula (3). The potential solution U represented by the deep neural network and the nonlinear dynamics G represented by the TSK fuzzy system constitute the overall model of physical information and fuzzy hybrid deep learning through the basic architecture of physical information and fuzzy hybrid deep learning.

[0088] The method in the present invention mainly includes two steps: training and prediction. After the model is built, it needs to be trained, and then the trained parameters are saved and can be used for prediction. The training step mainly includes two parts: forward propagation to calculate the loss function and back propagation to adjust the parameters. These two parts are iteratively cycled, and finally the parameters are adjusted to meet the conditions, and the parameters and model are saved. After the model and parameters are saved, the test sample is input, and the SOH can be predicted by calculating the forward propagation stage.

[0089] Step A: Input (x, t) first calculates the potential solution U through equation (5), and then solves the partial differential through automatic differentiation to obtain Ux.

[0090] Step B: [t, x, U, Ux] T The input vectors that constitute the nonlinear dynamics G are calculated using equations (6)-(10).

[0091] Step C: The output of the nonlinear dynamics G is linked to the potential solution U by function F as shown in formula (2), and then the loss function is calculated as shown in formula (3).

[0092] The present invention trains these adjustable parameters by back propagation method, written as BP: the potential solution U represented by the fully connected deep neural network includes the adjustable parameter set Ω; and the nonlinear dynamics G represented by the TSK fuzzy system includes the adjustable parameters: the first premise parameter m r,d and the second premise parameter σ r,d r=1,...,R,d=1,...,D and subsequent parameters r=1,...,R,d=0,1,...,D。 The back propagation method is based on the gradient descent method and is a neural network optimization method. It is currently widely used in neural network training. As follows:

[0093] First, calculate the input to the forward propagation, and forward propagate step A to step B as described above;

[0094] The error calculated for the loss function of a sample is as shown in formula (3); if it is a batch or mini-batch sample training, the error is the sum of the loss function formula (3) of these samples, that is, the loss function sum;

[0095] Calculate the gradient of the adjustable parameters. The calculation process is to advance from the last layer forward, that is, the error is back-propagated;

[0096] The adjustable parameters are updated according to the gradient descent rule, with the goal of reducing the error.

[0097] The details are as follows: Train the physical information and fuzzy hybrid deep learning model in step 1:

[0098] Extract the characteristic parameter set of the battery charging and discharging process as training samples;

[0099] Inputting the training sample into the fully connected deep neural network to obtain a potential solution, wherein the potential solution is a predicted value of the SOH value, and the SOH value is a lithium ion health state value;

[0100] Calculating the partial differential of the potential solution with respect to each characteristic parameter in the characteristic parameter set to obtain a partial differential set;

[0101] Taking the partial differential corresponding to the non-marked feature parameter in the partial differential set, the training sample, and at least one of the potential solutions as a feature set, inputting the feature set into the TSK fuzzy system, obtaining a descriptive feature about the feature set, and fusing the descriptive feature with the partial differential corresponding to the marked feature parameter in the partial differential set through the function F to generate an F feature;

[0102] Calculate the partial derivative of the F feature with respect to the marked feature parameter in the feature parameter set to obtain F t feature;

[0103] The loss of the error between the potential solution and the measured SOH value obtained based on the loss function, the loss of F features and F t The feature loss is calculated and the trained fully connected deep neural network is obtained through the back propagation algorithm.

[0104] Iterate the above steps until the stopping criteria are met, such as the difference between the errors of two consecutive iterations is very small, or the number of iterations reaches the set number. The potential solution U represented by the fully connected 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 constitute a whole physical information and fuzzy hybrid deep learning, which can coordinate efficient integrated training and prediction.

[0105] This invention was supported by the National Natural Science Foundation of China (fund number: 62263006) and the Guangxi Science and Technology Plan Project (fund number: Guike AD21220095).

[0106] The experimental verification in this invention 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 1.1Ah and a nominal voltage of 3.3V. The battery fails in a one-step or two-step fast charging strategy and is discharged under 4x rate conditions. Figure 3 As shown, the fast charging strategy has three main parameters: the first step charging current, the second step charging current and the charging state of the battery during conversion.

[0107] The charging state is expressed by SOC%, and after SOC% reaches the charging state when the battery is switched, the first step charging current switches to the second step charging current. The present invention ignores some cycles with abnormal data, and collects about 96,700 valid cycles, that is, 96,700 data samples.

[0108] Compared with the traditional constant current constant voltage charging, which is expressed by CCCV, the fast charging strategy is complex and flexible, making SOH estimation more difficult. External data such as terminal voltage, current and temperature are collected during the charging and discharging process.

[0109] Features are extracted from the above effective cycles, and the extracted features should have a strong correlation with SOH, which is the key to deep learning. In the present invention, internal resistance, average temperature and charging time are extracted as features, and internal resistance is represented by IR because they have an impact on battery capacity and are related to SOH.

[0110] In order to identify and quantify the electrochemical characteristics of batteries, incremental capacity analysis is a widely used electrochemical method. Incremental capacity analysis is represented by ICA, which is based on the voltage change during the charge / discharge stage. ICA is defined as the rate of change of capacity with voltage dQ / dV, so the minimum value, variance and skewness of dQ / dV during discharge are extracted as features. The six features of internal resistance, average temperature and charging time, as well as the minimum value, variance and skewness of dQ / dV during discharge, are linearly scaled to [0,1] through minimum-maximum normalization.

[0111] 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, the charging state during battery conversion, and the number of cycles are extracted as features. The first step charging current and the second step charging current are linearly scaled with the maximum charging rate of 8 times, and the number of cycles is also linearly scaled with the maximum number of cycles. A total of 10 features are extracted for each battery cycle. In order to avoid some features being superior to other features due to differences in scale, the present invention uses Z-Score normalization, also known as zero mean normalization, to convert the data into a standard score with zero mean and unit variance, and rescale the features extracted from the training data set. The 10 extracted features are the input variables (t, x).

[0112] The health status of lithium ions is represented by SOH. There are many definitions of the health status of lithium ions. The commonly used definition is the capacity C of the i-th cycle. i Ratio C to the nominal capacity nom , that is, the measured value SOH i as follows:

[0113]

[0114] Among them: SOH i is the measured value, represented by y as before.

[0115] To obtain better generalization performance, the training validation data includes 115 batteries, from #1 to #115, that is, the training involves approximately 86,600 cycles. In each experiment, 10% of the training validation data is randomly selected for validation, and the rest of the data is used for training. In addition to the 115 batteries used for training validation, there are 9 batteries left in the data set, of which 4 batteries are selected as test batteries, namely #116, #117, #121 and #124 batteries. Four groups of test experiments were performed on the four batteries respectively, and the training and testing processes were repeated 3 times in each experiment, and the results were averaged to reduce randomness. All experiments were performed on a workstation equipped with an Intel(R) Core(TM) i9-10900X CPU@3.70GHz and an NVIDIAGeForce RTX 3080GPU.

[0116] The back propagation method of the present invention adopts the classic optimization settings, as shown in Table 1:

[0117] Table 1 Optimization settings

[0118]

[0119] In the present invention, the inputs t and x are different because t has no effect on U t has a significant effect, while x does not. From the 10 extracted features, one feature is selected as t and the other 9 features are 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 options for t are tested in the experiment: the minimum value of dQ / dV or IR. The specific selection principles are as follows:

[0120] When t is selected as the internal resistance IR of the battery, x includes: the average temperature of the battery, the charging time, the terminal voltage, the variance of dQ / dV during the discharge process, the skewness of dQ / dV during the discharge process, and the minimum value of dQ / dV during the discharge process;

[0121] When t is selected as the minimum value of dQ / dV during the battery discharge process, x includes: the battery's internal resistance IR, average temperature, charging time, terminal voltage, variance of dQ / dV during the discharge process, and skewness of dQ / dV during the discharge process.

[0122] Four sets of experiments were conducted for cells #116, #117, #121, and #124, respectively, with two choices of t. Each set of experiments trained and tested two choices of t, and each choice had two series of hyperparameter settings, so four experiments were implemented in each set, and the experimental labels were recorded as PIFHDL1T, PIFHDL2T, PIFHDL1R, and PIFHDL2R, as shown in Table 2 for the detailed information of the hyperparameters of each set of experiments.

[0123] Table 2 Detailed information of experimental hyperparameters

[0124]

[0125] The experimental effect of the present invention is compared with three existing PINN methods, such as the three algorithms PINN-DeepHPM (AdpBal), PINN-Verhulst (Sum) and PINN-Verhulst (AdpBal) in Example A of "Physics-Informed Neural Networks for Prognostics and Health Management of Lithium-Ion Batteries". The data of #91 and #100 batteries are used for training, and then tested on #124 batteries. The present invention is not only tested on #124 batteries, but also on three other test batteries: #116, #117, and #121 to verify the prediction effect.

[0126] 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. In order to distinguish these samples, the variables are added with subscripts to indicate the sample numbers. For example, y m represents the mth SOH measurement value, and the corresponding mth input variable is (x m ,t m ), U(x m ,t m ) is simplified as U m The present invention uses two widely used indicators to evaluate the experimental performance: root mean square error and mean absolute error. The root mean square error RMSE formula is:

[0127]

[0128] Where M is a positive integer, indicating the total number of samples involved. The mean absolute error MAE formula is:

[0129]

[0130] Table 3 RMSE test results

[0131]

[0132] Table 4 MAE test results

[0133]

[0134] Tables 3 and 4 list the RMSE and MAE results of four groups of test experiments respectively. The smaller the value, the smaller the error, that is, the better the prediction accuracy. The black value represents the minimum error obtained by testing each battery. The physical information and fuzzy hybrid deep learning proposed in the present invention adopts four different hyperparameter settings. After training 4 models, the prediction error RMSE and MAE on the #116, #117 and #121 test batteries are smaller than the three existing PINN methods. Only when testing the #124 battery, only PIFHDL1T has better prediction error RMSE and MAE than the three existing PINN methods, and PIFHDL1R and PIFHDL2R have better prediction error RMSE and MAE than a PINN method PINN-Verhulst (Sum). On the first three test batteries, the physical information and fuzzy hybrid deep learning proposed in the present invention achieve higher prediction accuracy than the three existing PINN methods; tested on the #124 battery, the physical information and fuzzy hybrid deep learning proposed in the present invention achieves prediction accuracy comparable to the three existing PINN methods.

[0135] The three existing PINN methods are trained with data from #91 and #100 batteries, and only achieve good prediction performance on #124 battery, because the three batteries #91, #100 and #124 use the same fast charging strategy. However, the four test batteries use different fast charging strategies. Based on the test results of the four batteries, the model and algorithm proposed by the present invention have relatively average errors on the four test batteries, while on the test batteries using different fast charging strategies, the performance of the three existing PINN methods is degraded, and the performance of the four test batteries varies greatly. For example, the RMSE of PINN-Verhulst (AdpBal) is 0.104 on the #116 battery test, but 0.00465 on the #124 battery test.

[0136] On battery #116, PIFHDL1R achieved the best prediction performance with 0.00474RMSE and 0.00326MAE. On battery #117, PIFHDL2R outperformed other methods with 0.00587RMSE and 0.00518MAE. On battery #121, PIFHDL2R achieved the best prediction performance with 0.00537RMSE and 0.00483MAE. On battery #124, PIFHDL1T achieved the best prediction performance with 0.00376RMSE and 0.00282MAE. It can be seen that the methods with the smallest prediction errors on the above four test batteries are all the physical information and fuzzy hybrid deep learning proposed in the present invention, so the physical information and fuzzy hybrid deep learning proposed in the present invention can more accurately predict the health status of lithium-ion batteries.

[0137] like Figure 4As shown, the health status of four test batteries is estimated, and the minimum value of the characteristic dQ / dV is selected; Figure 5 For the health status estimation of the four test batteries, the feature IR is selected. As can be seen from the figure, using the method of the present invention, under different parameter settings, the predicted value of SOH is close to the measured value curve, that is, 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 system and deep learning, characterized in that: The steps include: Step 1: Build a physical information and fuzzy hybrid deep learning model: 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 respectively connected to the input of the TSK fuzzy system and the input of the function F, 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 in step 1: Extract the characteristic parameter set of the battery charging and discharging process as training samples; Inputting the training sample into the fully connected deep neural network to obtain a potential solution, wherein the potential solution is a predicted value of the SOH value, and the SOH value is a lithium ion health state value; Calculating the partial differential of the potential solution with respect to each characteristic parameter in the characteristic parameter set to obtain a partial differential set; Taking the partial differential corresponding to the non-marked feature parameter in the partial differential set, the training sample, and at least one of the potential solutions as a feature set, inputting the feature set into the TSK fuzzy system, obtaining a descriptive feature about the feature set, and fusing the descriptive feature with the partial differential corresponding to the marked feature parameter in the partial differential set through the function F to generate an F feature; Calculate the partial derivative of the F feature with respect to the marked feature parameter in the feature parameter set to obtain F t feature; The loss between the potential solution and the measured SOH value obtained based on the loss function, the loss of F features and F t The feature loss is obtained by back-propagation training to obtain a fully connected deep neural network after training; Step 3: After the characteristic parameters of the test battery are input into the trained fully connected deep neural network, the SOH prediction value of the battery to be tested is obtained.

2. The lithium-ion battery health management method integrating fuzzy system and deep learning as claimed in claim 1, characterized in that: The marking characteristic parameter of the battery is t; the non-marking characteristic parameter is x; The t is the internal resistance IR of the battery, or the minimum value of dQ / dV during the battery charging or discharging process; When t is selected as the internal resistance IR of the battery, x includes: the average temperature of the battery, the charging time, the terminal voltage, the variance of dQ / dV during the charging or discharging process, the skewness of dQ / dV during the charging or discharging process, and the minimum value of dQ / dV during the charging or discharging process; When t is selected as the minimum value of dQ / dV during the battery charging or discharging process, 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 charging or discharging process, and the skewness of dQ / dV during the charging or discharging process.

3. The lithium-ion battery health management method integrating fuzzy system and deep learning as claimed in claim 2, characterized in that: The loss function is L, as follows: Where: L U =|U(t,x)-y| 2 is the square error between the potential solution module U(t,x) and y, where y is the measured value of SOH; L F =|F| 2 is the square error of function F; L Ft =|F t | 2 F t The square error of t =U tt -G t Find the partial derivative of F with respect to parameter t; U tt is the second-order partial differential of the potential solution with respect to parameter t; G t is the first-order partial differential describing the characteristic with respect to parameter t.

4. The lithium-ion battery health management method integrating fuzzy system and deep learning as claimed in claim 3, characterized in that: The function F is as follows: F:=U t -G(t,x,U,U x , U xx ,…;θ); Among them: U t is the first-order partial differential of the potential solution with respect to parameter t, U x is the first-order partial differential of the potential solution with respect to parameter x; U xx is the second-order partial differential of the potential solution with respect to the parameter x; θ is the parameter of the nonlinear dynamics module, which is a real number.

5. The lithium-ion battery health management method integrating fuzzy system and deep learning as claimed in claim 4, 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 Satisfy fuzzy set Z R,D r=1,...,R,d=1,...,D, and output; using Gaussian membership function, as follows: Where: m r,d and σ r,d are the first premise parameter and the second premise parameter, representing the mean and standard deviation of the Gaussian membership function, m r,d The value range is real number, σ r,d The value range is positive real number; input feature z d At least one selected from the group consisting of a partial differential corresponding to a non-labeled feature parameter, a training sample, and a potential solution; In the second layer, each neuron multiplies the input and outputs the product as the activation strength of the corresponding fuzzy rule, as follows: In the third layer, each neuron calculates the normalized activation strength as: Where: R is the number of fuzzy rules. In the fourth layer, each neuron corresponds to a fuzzy rule. in in Represents subsequent parameters, the value range is real number; The fifth layer is the output layer, which is used for summation, as follows:

6. The lithium-ion battery health management method integrating fuzzy system and deep learning as claimed in claim 5, characterized in that: The fully connected deep neural network includes N small modules BL connected in sequence, and multiple small modules BL are connected in a chain. At the back end of the chain, a fully connected layer is connected after the last small module BL, as follows: U(t,x)=f1(BL N (BL N-1 (...BL2(BL1(t,x))))); Among them, BL1, BL2…BL N-1 BL N They represent the input small module starting from the input end to the output small module at the output end; f1 is the fully connected layer.

7. The lithium-ion battery health management method integrating fuzzy system and deep learning as claimed in claim 6, characterized in that: The physical information and fuzzy hybrid deep learning model parameters include the following: The parameter set Ω consisting of the parameter weight coefficient and bias of the fully connected layer f1 and the parameters β and γ of the normalization layer; The first premise parameter m in the TSK fuzzy system r,d , the second premise parameter σ r,d and subsequent parameters

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