Lithium ion battery state of health estimation method based on multi-objective optimization

Abstract

The application is a lithium ion battery health state estimation method based on multi-objective optimization, first, the charging and discharging cycle data of the lithium ion battery is collected and pretreated; then, a plurality of health characteristics including the constant current charging time and the polynomial coefficient of the constant current charging voltage-time curve fitted by the Logit model are extracted from the charging and discharging cycle data; finally, the health state estimation model is established based on the extreme learning machine neural network, the health state estimation model is trained by using the charging and discharging cycle data of the lithium ion battery, in the training process, the health state estimation model is optimized by the multi-objective optimization algorithm based on the non-dominated sorting and the crowded distance, and the optimized health state estimation model is used for the estimation of the lithium ion battery health state. The polynomial coefficient extracted by the application reflects the nonlinear aging law in the constant current charging process, indirectly represents the battery degradation, the constant current charging time directly represents the battery degradation, and the model optimization considers the prediction accuracy and stability of the model.

Description

Technical Field

[0001] This invention belongs to the field of battery management system health state estimation technology, specifically relating to a lithium-ion battery health state estimation method based on multi-objective optimization. Background Technology

[0002] Lithium-ion batteries are widely used in electric vehicles due to their advantages such as high energy density, large output capacity, and cost-effectiveness. During battery cycling, their internal structure experiences phenomena such as cyclic lithium loss and current collector corrosion, leading to continuous performance degradation. To ensure the safe and stable operation of electric vehicles, a battery management system (BMS) is used to manage and control the power battery online. The battery's State of Health (SOH) reflects its current energy storage capacity relative to a new battery. Accurately predicting the battery's SOH allows for advance knowledge of its capacity level, which is crucial for optimizing electric vehicle control strategies, improving energy utilization, and reducing energy costs.

[0003] Currently, commonly used methods for assessing the health status of lithium-ion batteries are divided into model-based methods and data-driven methods. Model-based methods describe the physical processes of lithium-ion batteries by establishing mathematical models, but they suffer from drawbacks such as high model complexity, difficulty in determining parameters, and poor applicability. Data-driven methods, on the other hand, utilize historical battery data and employ machine learning and other techniques to build models and predict the battery's health status. Compared to model-based methods, they offer better prediction accuracy and robustness, but they still have the following problems: First, in terms of health feature extraction, current research mostly focuses on features such as battery capacity increment, isostatic rise time, isostatic drop time, and average voltage. However, these features cannot reflect the nonlinear aging law of the battery during constant current charging and cannot accurately characterize the degradation characteristics of the lithium-ion battery's health status. Second, regarding data-driven models, traditional single-objective optimization models in health status assessment mostly focus on improving prediction accuracy. However, during battery cycling, capacity recovery occurs, and the fluctuations caused by this recovery cannot be accurately tracked, leading to poor prediction stability. Therefore, traditional single-objective optimization models neglect the impact of capacity recovery on prediction stability.

[0004] Therefore, this invention proposes a lithium-ion battery health state estimation method based on multi-objective optimization. On the one hand, it extracts health features that reflect nonlinear aging during constant current charging, and on the other hand, it enables the model to simultaneously focus on the accuracy and stability of the prediction results. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, the technical problem to be solved by the present invention is to propose a method for estimating the health status of lithium-ion batteries based on multi-objective optimization.

[0006] The present invention solves the aforementioned technical problem by adopting the following technical solution:

[0007] A method for estimating the state of health of lithium-ion batteries based on multi-objective optimization, characterized by the following steps:

[0008] Step S1: Collect charge-discharge cycle data of the lithium-ion battery;

[0009] Step S2: Preprocess the charge-discharge cycle data and extract multiple health features from the charge-discharge cycle data. One of the health features is the constant current charging time, and the other health features are the polynomial coefficients of the constant current charging voltage-time curve fitted by the Logit model.

[0010] Step S3: Establish a health status estimation model based on the Extreme Learning Machine neural network;

[0011] Step S4: Train the health status estimation model using the collected lithium-ion battery charge-discharge cycle data. The input feature matrix of the model is F = [F 1 ;F 2 ;…;F n ;…;F N The output vector is This represents the input feature vector for the nth iteration. This represents the health characteristics extracted in the nth iteration. This represents the true health status in the nth cycle, where N represents the total number of charge-discharge cycles throughout the entire lifespan.

[0012] The input weights from the input layer to the hidden layer and the hidden layer bias of the health status estimation model are used as parameters to be optimized. A multi-objective optimization algorithm based on non-dominated ranking and crowding distance is used to optimize the health status estimation model. The fitness function of the multi-objective optimization algorithm includes the mean square error and the stability index, as shown in the following formula:

[0013]

[0014]

[0015] Where MSE is the mean squared error, SDEX is the stability index, K is the sample size, and y i , Let be the true health status and the predicted health status of the i-th sample, respectively, and std(·) represent the standard deviation.

[0016] Step S5: Use the optimized health status estimation model to estimate the health status of the lithium-ion battery.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0018] 1. This invention utilizes the Logit model to fit the voltage-time curve during constant current charging and extracts the polynomial coefficients of the Logit model as health features. Compared with traditional health features such as capacity increment, isostatic rise time, isostatic drop time, and average voltage, the polynomial coefficients can fully reflect the nonlinear aging law of the battery during constant current charging and can indirectly characterize the degradation of lithium-ion batteries. At the same time, the constant current charging time, which directly characterizes the degradation of lithium-ion batteries, is also used as a health feature, thereby improving the accuracy of SOH estimation.

[0019] 2. By employing a multi-objective whale optimization algorithm based on non-dominated sorting and crowding distance calculation to optimize the health status estimation model, and using the mean square error and stability index (SDEX) as the objective functions of the multi-objective optimization, the model can simultaneously consider both prediction accuracy and stability. This effectively solves the problem that traditional single-objective optimization models only consider prediction accuracy and ignore the poor prediction stability caused by battery capacity recovery. It can achieve relatively high prediction accuracy and stability in the health status estimation of lithium-ion batteries throughout their entire life cycle. Attached Figure Description

[0020] Figure 1 This is an overall flowchart of the present invention;

[0021] Figure 2 The SOH degradation curves of three batteries in the Maryland dataset;

[0022] Figure 3 For charging voltage-time curves;

[0023] Figure 4 The graph shows the variation of the third-order fitting accuracy of the voltage curve over the entire life cycle of the CS35 battery.

[0024] Figure 5 A graph showing the relationship between the four normalized health characteristics and the number of cycles;

[0025] Figure 6 This is a structural diagram of the ELM neural network;

[0026] Figure 7(a) shows the health state estimation curves of the CS37 battery under different models;

[0027] Figure 7(b) shows the relationship between the relative error and the number of cycles for different models;

[0028] Figure 8(a) shows the relative error histogram of the PSO-ELM model;

[0029] Figure 8(b) shows the relative error histogram of the WOMOA-ELM model. Detailed Implementation

[0030] Specific embodiments are given below with reference to the accompanying drawings. These specific embodiments are only used to illustrate the technical solutions of the present invention in detail, and are not intended to limit the scope of protection of this application.

[0031] This invention provides a method for estimating the state of health of lithium-ion batteries based on multi-objective optimization, comprising the following steps:

[0032] Step S1: Collect charge-discharge cycle data during the lithium-ion battery aging test and construct a dataset;

[0033] This example uses the University of Maryland aging dataset, which includes aging test data for three batteries: CS2_35 (CS35), CS2_36 (CS36), and CS2_37 (CS37). All batteries use lithium cobalt oxide (LiCoO2) as the positive electrode material and have a nominal capacity of 1.1 Ah. The charge / discharge standard for the battery aging test is as follows: at room temperature (24°C), constant current charging is initiated at 3.8V and then charged at 0.5C until the charging cutoff voltage of 4.2V is reached. Subsequently, charging continues in constant voltage mode until the current drops to 50mA. Finally, constant current discharge is performed at 1C until the discharge cutoff voltage of 2.7V is reached.

[0034] Step S2: Data preprocessing and health feature extraction;

[0035] S2.1: Remove noise and complete data preprocessing;

[0036] S2.2: The state of health (SOH) is defined by the full discharge capacity, as shown in equation (1); each battery retains charge-discharge cycle data from 100% SOH down to 70% SOH, and the three batteries retain 641, 635, and 708 charge-discharge cycle data respectively. The health status degradation curves of the three batteries throughout their entire life cycle are shown in equation (1). Figure 2 As shown;

[0037]

[0038] In the formula, SOH n C represents the SOH value in the nth cycle. n C0 represents the capacity value in the nth cycle, where C0 is the rated capacity of the battery.

[0039] Figure 3 The charging voltage-time curve under constant current charging conditions shows that the constant current charging time gradually shortens with the increase of the number of cycles. Therefore, the constant current charging time reflects battery degradation. The constant current charging time is considered a health characteristic, denoted as HF1, and its expression is:

[0040] ΔT=T (4.2V) -T (3.8V)(2)

[0041] In the formula, T (4.2V) T (3.8V) These represent the charging time when the battery is charged to the constant current charging start voltage of 3.8V and the charging cutoff voltage of 4.2V, respectively.

[0042] S2.3: From Figure 3 It can be seen that the charging voltage-time curve under constant current charging conditions is nonlinear, and the curve gradually shifts to the left as the number of cycles increases. The charging voltage-time curve under constant current charging conditions contains health characteristics that characterize battery aging. The Logit model of Equation (3) is used to fit the voltage and charging time during constant current charging. The polynomial coefficients of the fitted curve can reflect the nonlinear aging law of the battery. Therefore, the polynomial coefficients of the fitted curve are regarded as health characteristics and used to estimate the health status of the battery.

[0043]

[0044] In the formula, U represents voltage. represents the polynomial coefficients, T represents the charging time, c represents the intercept, n represents the number of cycles, and m represents the fitting order.

[0045] Select the coefficient of determination (R²) 2 The accuracy of the Logit model at different fitting orders is evaluated by two indicators: root mean square error (RMSE). The calculation formulas are shown in equations (4) and (5).

[0046]

[0047]

[0048] Among them, U j , Let these represent the j-th true voltage and the fitted voltage, respectively. This represents the average value of the actual voltage, where S is the number of sampling points;

[0049] The results show that when the fitting order is greater than or equal to 3, R0 2 With an accuracy of ≥0.996 and RMSE≤0.0063, the required precision is met. Therefore, the fitting order is set to 3rd order. The coefficients of the first, second, and third terms of the Logit model are used as health features HF2~HF4 to estimate the battery's health status. For the variation in the 3rd order fitting accuracy of the CS35 battery's full life-cycle voltage curve, please refer to [link to documentation]. Figure 4 ;

[0050] S2.4: The correlation between health features HF1-HF4 and battery SOH was verified using equation (6). The Pearson correlation coefficients between the four health features and battery SOH are shown in Table 1. The absolute values ​​of the Pearson correlation coefficients are all above 0.97, so the four selected health features are reasonable and can reflect the health status of the battery. The relationship between the four normalized health features and the number of cycles is as follows: Figure 5 As shown;

[0051]

[0052] In the formula, Pearson is the Pearson correlation coefficient, E(·) is the expected value, α represents the health feature vector, and θ represents the battery SOH vector;

[0053] Table 1. Pearson correlation coefficients between health characteristics and SOH.

[0054]

[0055] Step S3: Establish a health status estimation model based on an Extreme Learning Machine (ELM) neural network; such as... Figure 6 As shown, the health status estimation model consists of an input layer, a hidden layer, and an output layer. The input layer has 4 nodes, the hidden layer has 9 nodes, and the output layer has 1 node. It is assumed that there are K sample data points. The health status estimation model can be expressed as follows:

[0056]

[0057] In the formula, L is the number of hidden layer nodes, h(·) is the Sigmoid activation function, and ω r =[ω r1 ,ω r2 ,…,ω rK ] T b represents the input weights from the input layer to the hidden layer. r =[b r1 ,b r2 ,…,b rK ] T For the hidden layer bias, β r =[β r1 ,β r2 ,…,β rK [] represents the output layer weights;

[0058] The output of a trained health state estimation model can approximate the true value infinitely. In this case, the health state estimation model can be equivalent to Hβ = Y, with output weights β = H. + Y, H +The inverse of the output matrix H of the health state estimation model is shown below:

[0059]

[0060] Step S4: Train the health status estimation model and optimize it using a multi-objective optimization algorithm to obtain the optimized health status estimation model;

[0061] S4.1: Use CS35 and CS36 battery data as the training set and CS37 battery data as the test set; the model's input feature matrix is ​​F = [F 1 ;F 2 ;…;F n ;…;F N The output vector is in, This represents the input feature vector for the nth iteration. This represents the four health features extracted in the nth iteration. This represents the true health status in the nth cycle, where N represents the total number of charge-discharge cycles throughout the entire lifespan.

[0062] S4.2: The parameters ω of the health status estimation model r and b r The parameters to be optimized in the multi-objective optimization algorithm are initialized; the population size of the multi-objective optimization algorithm is Agents_no=20, the maximum number of iterations is Max_iter=10, the current iteration number is defined as GEN, and GEN is initialized to 1.

[0063] The mean squared error (MSE) and the stability index (SDEX) are used as two fitness functions, and the calculation formulas are as follows:

[0064]

[0065]

[0066] Among them, y i , Let be the true health status and the predicted health status of the i-th sample, respectively, and std(·) represent the standard deviation.

[0067] S4.3: Taking the Multi-Objective Whale Optimization Algorithm (MOWOA) as an example, this paper uses MOWOA to perform multi-objective trade-off optimization on the two parameters to be optimized in the health status estimation model. MOWOA is a multi-objective optimization algorithm based on non-dominated sorting and crowding distance calculation. Specifically, after merging the parents and offspring of the whale population, firstly, non-dominated sorting is used to divide all individuals into several non-dominated fronts; secondly, the solutions for each non-dominated front are sorted from maximum to minimum according to the crowding distance; finally, individuals are selected as the next population group based on the non-dominated front level and crowding distance. The specific optimization process includes the following steps:

[0068] S4.3.1: Calculate the fitness value of the initial whale individuals in the target space; perform a non-dominated ranking of all whale individuals based on their fitness values, and treat two whale individuals as two known decision variables e = (e1, e2, ..., e...). d ) and o=(o1,o2,···,o d ), if and only if satisfying Then ePareto dominates o, denoted as e>o; if a decision variable e=(e1,e2,···,e d )satisfy Then e = (e1, e2, ..., e d A solution is a Pareto optimal solution, and the set of all Pareto optimal solutions is called the optimal solution set.

[0069] The main purpose of non-dominated sorting is to find a set of solutions such that, among all possible solutions, this set of solutions is not dominated by other solutions. Based on the dominance relationship, the population is divided into M layers, where the first layer is the set of non-dominated individuals in the whale population, the second layer is the set of non-dominated individuals in the remaining population obtained after removing the individuals in the first layer, and so on, with the Mth layer being the set of non-dominated individuals in the remaining population obtained after removing the individuals in the first M-1 layers.

[0070] S4.3.2: Divide all solutions into several layers, ensuring that solutions within each layer are non-dominated; calculate the crowding distance for each solution to help select a set of excellent non-dominated solutions, ensuring that the solutions on the Pareto front have a certain distribution. The specific calculation formula is as follows:

[0071]

[0072] In the formula: V u (k-1) and V u (k+1) represents the u-th function value of the solution preceding and following the k-th solution. and These are the maximum and minimum values ​​of the u-th function, respectively;

[0073] S4.3.3: Update the position of each whale according to the predefined movement rules and evaluate the new solution. The movement process includes three parts: encirclement and hunting, spiral update and prey search.

[0074] Encirclement hunting: During the search, each whale searches its surroundings based on its current position and speed, looking for the direction most likely to contain prey. The mathematical model is shown in the following formula:

[0075] D = |C·X P (t)-X(t)| (12)

[0076] X(t+1)=X P (t)-A·D (13)

[0077] In the formula, X P X(t) represents the prey's position, X(t) represents the current position of the whale, D represents the distance between the whale and the prey, t represents the current iteration number, and A and C represent the vector coefficients, defined as follows:

[0078]

[0079] Where a is the convergence factor, which decreases linearly from 2 to 0; r is a random number, ranging from 0 to 1.

[0080] Spiral Update: When an individual whale is close to the optimal solution but cannot reach it, it will move along a spiral path to increase its exploration range. The mathematical model is as follows:

[0081] X t-1 =D3·e bl ·cos(2πl)+X * (t) (15)

[0082] In the formula, b is a constant whose value affects the spiral shape; l is a random number with a value range of [-1, 1]; in addition, when the probability is less than 0.5, it is in the spiral contraction stage; when it is greater than 0.5, it is in the spiral renewal stage.

[0083] Searching for prey: When |A|>1, the whale cannot obtain useful information and enters the search phase through a random walk. The mathematical model is as follows:

[0084] D = |C × X rand (t)-X(t)| (16)

[0085] X(t+1)=X rand (t)-A·D (17)

[0086] In the formula, Xrand (t) represents a whale location randomly selected from the current population;

[0087] S4.3.4: Perform non-dominated sorting and calculate the crowding distance for the new solution, and decide whether to accept it based on the layer to which it belongs and the crowding distance;

[0088] S4.3.5: Repeat steps S4.3.3 and S4.3.4 until the iteration terminates, and obtain a set of optimal solutions. These solutions are evenly distributed on the Pareto front and have a certain degree of diversity and feasibility. The health status estimation model corresponding to the optimal solution is the optimized health status estimation model.

[0089] Step S5: Use the optimized health status estimation model to estimate the health status of the lithium-ion battery, that is, estimate the health status of the CS37 battery throughout its entire life cycle.

[0090] The model estimation accuracy is evaluated using relative error (RE), mean absolute error (MAE), and root mean square error (RMSE), and the calculation formulas are shown in equations (18) to (20); the stability of the model estimation is evaluated using the stability index (SDEX), as shown in equation (10).

[0091]

[0092]

[0093]

[0094] Figures 7(a) and (b) show the health state estimation curves and relative error curves of the LSTM, PSO-ELM, and WOMOA-ELM models for the CS37 battery, respectively. Figures 8(a) and (b) show the relative error histograms of the PSO-ELM and WOMOA-ELM models, respectively. The WOMOA-ELM model is the health state estimation model of this invention. As can be seen from the figures, the relative error of the WOMOA-ELM model of this invention is significantly smaller than that of the PSO-ELM model, and it exhibits higher stability. This is because the multi-objective whale optimization algorithm based on non-dominated sorting and crowding distance calculation is used to optimize the parameters of the health state estimation model through multi-objective trade-offs. Therefore, the WOMOA-ELM model demonstrates higher prediction accuracy and stability in the overall prediction interval, while the PSO-ELM model, although having higher overall estimation accuracy, shows poor estimation accuracy and unstable estimation results in certain local intervals.

[0095] Any aspects not covered in this invention are applicable to existing technologies.

Claims

1. A method for estimating the state of health of lithium-ion batteries based on multi-objective optimization, characterized in that, The method includes the following steps: Step S1: Collect charge-discharge cycle data of the lithium-ion battery; Step S2: Preprocess the charge-discharge cycle data and extract multiple health features from the charge-discharge cycle data. One of the health features is the constant current charging time, and the other health features are the polynomial coefficients of the constant current charging voltage-time curve fitted by the Logit model. Step S3: Establish a health status estimation model based on the Extreme Learning Machine neural network; Step S4: Train the health status estimation model using the collected lithium-ion battery charge-discharge cycle data. The input feature matrix of the model is F = [F 1 ;F 2 ;…;F n ;…;F N The output vector is This represents the input feature vector for the nth iteration. This represents the health characteristics extracted in the nth iteration. This represents the true health status in the nth cycle, where N represents the total number of charge-discharge cycles throughout the entire lifespan. The input weights from the input layer to the hidden layer and the hidden layer bias of the health status estimation model are used as parameters to be optimized. A multi-objective optimization algorithm based on non-dominated ranking and crowding distance is used to optimize the health status estimation model. The fitness function of the multi-objective optimization algorithm includes the mean square error and the stability index, as shown in the following formula: Where MSE is the mean squared error, SDEX is the stability index, K is the sample size, and y i , Let be the true health status and the predicted health status of the i-th sample, respectively, and std(·) represent the standard deviation. Step S5: Use the optimized health status estimation model to estimate the health status of the lithium-ion battery.

2. The lithium-ion battery health state estimation method based on multi-objective optimization according to claim 1, characterized in that, In step S2, the accuracy of the Logit model at different fitting orders is evaluated by the coefficient of determination and the root mean square error. When the fitting order is greater than or equal to 3, the accuracy can meet the requirements. Therefore, the coefficients of the first, second, and third terms of the Logit model are selected as health features.

3. The lithium-ion battery health state estimation method based on multi-objective optimization according to claim 1 or 2, characterized in that, The multi-objective optimization algorithm is the multi-objective whale optimization algorithm.

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