CN103389471B - A kind of based on the cycle life of lithium ion battery indirect predictions method of GPR with indeterminacy section - Google Patents

Abstract

An indirect prediction method for cycle life of a lithium-ion battery based on GPR with an uncertain interval, and the invention relates to a method for predicting battery life. The present invention solves the problem that the existing method cannot realize lithium battery cycle life prediction. The present invention adopts the ESN algorithm to carry out degradation modeling, adopts the Gaussian process regression modeling method, and establishes a GPR-based equal pressure drop discharge time prediction model based on ESN degradation model training and GPR-based equal pressure drop discharge time prediction model training, obtain the equal pressure drop discharge time prediction model, carry out the GPR-based equal pressure drop discharge time prediction model, and obtain the predicted value of the equal pressure drop discharge time; Based on the degradation model of ESN, the discharge capacity of the battery in the next N ₁ discharge cycles is obtained; the remaining capacity value of the battery is compared with the failure threshold of the battery capacity, and the indirect prediction of the battery cycle life is completed. The invention is suitable for battery life prediction.

Description

An Indirect Prediction Method of Lithium-ion Battery Cycle Life Based on GPR with Uncertainty Interval

technical field

The invention relates to a battery life prediction method.

Background technique

Although a lithium-ion battery is an energy storage and conversion device, it is not infinitely usable, that is, its cycle life is limited, because the performance of the battery will gradually decline as the battery is used.

Lithium-ion battery is a rechargeable battery that mainly relies on the movement of lithium ions between the positive and negative electrodes. The chemical power of the entire battery comes from the difference in the chemical potential of its two electrodes. When the battery is charging, it converts electrical energy into chemical energy and stores it in the battery, and when discharging, it converts chemical energy into electrical energy for the load to use. Due to the reversibility of the two kinds of energy conversion, it seems that the cycle process of charge and discharge is infinite, but it is not. This is because some irreversible processes will occur inside the battery during the cycle process of charge and discharge, resulting in changes in internal impedance, output current, etc. , causing the attenuation of battery capacity, thus affecting the cycle life of the battery.

During the cycle charge and discharge process of lithium-ion batteries, some irreversible chemical reaction processes will occur inside the battery, resulting in the loss of "embedded/extracted" Li+ on the electrodes, thereby increasing the internal impedance of the battery, which is directly manifested as a drop in the open circuit voltage of the battery.

The internal resistance of the battery measured by resistance impedance spectroscopy includes charge transfer resistance RCT, Warburg resistance RW and electrolyte resistance RE, among which the impact of Warburg resistance RW on the battery degradation process is negligible, so it can be ignored. NASA's PCoE Research Center has analyzed a large amount of experimental data and found that there is a high linear correlation between battery capacity and internal impedance, and the battery capacity will gradually degrade as the battery ages, that is, the battery capacity after each charge and discharge cycle Therefore, the degradation of battery capacity can be used as the main indicator of battery cycle life. However, due to the shortcomings of less historical data, difficult model establishment, and uncertainty in the prediction of lithium battery life, However, it is impossible to predict the cycle life of lithium batteries.

Contents of the invention

In order to solve the problem that the existing method cannot realize the cycle life prediction of the lithium battery, the present invention proposes an indirect prediction method for the cycle life of the lithium ion battery based on GPR with an uncertain interval.

A kind of lithium-ion battery cycle life indirect prediction method based on GPR with uncertain interval described in the present invention, the concrete steps of this method are:

Step 1. Collect the number of charge and discharge cycles x of the battery to be tested, the discharge voltage and battery capacity of each charge and discharge cycle, and the amount of electricity z released in each charge and discharge cycle.

Step 2. Calculate the corresponding equal pressure drop discharge time difference according to the number x of charge and discharge cycles of the collected battery to be tested and the discharge voltage and battery capacity of each charge and discharge cycle, and obtain the equal pressure drop discharge time series y;

Step 3: Use the ESN algorithm to perform degradation modeling using the equal pressure drop discharge time series y and the remaining capacity data z of the battery after each charge and discharge, and obtain a degradation model based on ESN;

Step 4, using the Gaussian process regression modeling method, using the number of charge and discharge cycles x and the equal pressure drop discharge time series y corresponding to the battery charge and discharge cycle to establish a GPR-based equal pressure drop discharge time prediction model;

Step 5, the data set of the equal pressure drop discharge time series data y and the electric quantity z released in each discharge cycle As a training set for ESN-based degradation model training, the data set of the number of battery charge and discharge cycles x and the equal pressure drop discharge time series y As the training data, the GPR-based equal pressure drop discharge time prediction model training is carried out to obtain the equal pressure drop discharge time prediction model, wherein N is a positive integer;

Step 6. Set the next N ₁ charge and discharge cycle times Input the GPR-based equal pressure drop discharge time prediction model to obtain the predicted value of equal pressure drop discharge time

Step 7. The predicted value of the equal pressure drop discharge time will be obtained Substitute into the degradation model based on ESN to obtain the discharge capacity of the battery for the next N ₁ discharge cycles

Step 8. Subtract the initial capacity of the battery from the discharge capacity of the battery for the next N ₁ charge and discharge cycles The remaining capacity value of the battery is compared with the failure threshold of the battery capacity to determine whether the remaining capacity of the battery is equal to the failure threshold of the battery capacity. The indirect prediction of the lithium-ion battery cycle life in the interval, otherwise perform step nine;

Step 9. Compare the remaining capacity of the battery with the failure threshold of the battery capacity. If the remaining capacity of the battery is greater than the failure threshold of the battery capacity, set N=N+N ₁ and return to step 5. If the remaining capacity of the battery If the value is less than the failure threshold of the battery capacity, set N=NN ₂ and return to step 5, where N ₂ is a positive integer smaller than N ₁ .

The present invention combines the ESN algorithm with the Gaussian process regression modeling method, adopts the GPR algorithm to establish the equal pressure drop discharge time series prediction model to predict the equal pressure drop discharge time series in the future, and finally uses the predicted equal pressure drop discharge time series Input to the degradation model of the lithium-ion battery, so as to realize the prediction of the battery capacity at the next N ₁ time, and then realize the indirect prediction of the cycle life of the lithium-ion battery.

Description of drawings

Fig. 1 is the degradation modeling verification curve of NASA lithium-ion battery based on ESN. In the figure, curve 1 is the estimated value curve, and curve 2 is the real value curve;

Fig. 2 is the error curve graph between the estimated value of lithium-ion battery capacity obtained by modeling and the actual value of measured capacity;

Figure 3 is the prediction effect diagram of model training using 30% data. In the figure, 3 is the real remaining service life at the failure threshold of 80%, 4 is the confidence interval, 5 is the predicted mean value at the failure threshold of 80%, and 6 is 80%. Failure threshold, 7 is the confidence interval, 8 is the predicted mean value at the 70% failure threshold, 9 is the 70% failure threshold, and 10 is the real remaining service life at the 80% failure threshold;

Fig. 4 is a prediction effect diagram of model training using 50% data;

Figure 5 is the prediction effect diagram of model training with 70% data.

Detailed ways

Specific Embodiments 1. A method for indirect prediction of cycle life of a lithium-ion battery based on GPR with an uncertain interval described in this embodiment, the specific steps of the method are:

Step 1. Collect the number of charge and discharge cycles x of the battery to be tested, the discharge voltage and battery capacity of each charge and discharge cycle, and the amount of electricity z released in each charge and discharge cycle.

Step 2. Calculate the corresponding equal pressure drop discharge time difference according to the number x of charge and discharge cycles of the collected battery to be tested and the discharge voltage and battery capacity of each charge and discharge cycle, and obtain the equal pressure drop discharge time series y;

Step 3: Use the ESN algorithm to perform degradation modeling using the equal pressure drop discharge time series y and the remaining capacity data z of the battery after each charge and discharge, and obtain a degradation model based on ESN;

Step 4, using the Gaussian process regression modeling method, using the number of charge and discharge cycles x and the equal pressure drop discharge time series y corresponding to the battery charge and discharge cycle to establish a GPR-based equal pressure drop discharge time prediction model;

Step 5, the data set of the equal pressure drop discharge time series data y and the electric quantity z released in each discharge cycle As a training set for ESN-based degradation model training, the data set of the number of battery charge and discharge cycles x and the equal pressure drop discharge time series y As the training data, the GPR-based equal pressure drop discharge time prediction model training is carried out to obtain the equal pressure drop discharge time prediction model, wherein N is a positive integer;

Step 6. Set the next N ₁ charge and discharge cycle times Input the GPR-based equal pressure drop discharge time prediction model to obtain the predicted value of equal pressure drop discharge time

Step 7. The predicted value of the equal pressure drop discharge time will be obtained Substitute into the degradation model based on ESN to obtain the discharge capacity of the battery for the next N ₁ discharge cycles

Step 8. Subtract the initial capacity of the battery from the discharge capacity of the battery for the next N ₁ charge and discharge cycles The final remaining capacity value of the battery is compared with the failure threshold of the battery capacity to determine whether the remaining capacity _of the battery is equal to the failure threshold of the battery capacity. Determine the indirect prediction of the lithium-ion battery cycle life of the interval, otherwise perform step nine;

Step 9. Compare the remaining capacity of the battery with the failure threshold of the battery capacity. If the remaining capacity of the battery is greater than the failure threshold of the battery capacity, set N=N+N ₁ and return to step 5. If the remaining capacity of the battery If the value is less than the failure threshold of the battery capacity, set N=NN ₂ and return to step 5, where N ₂ is a positive integer smaller than N ₁ .

In this embodiment, the GPR algorithm is used to establish an equal pressure drop discharge time series prediction model to predict the equal pressure drop discharge time series in the future, and finally the predicted equal pressure drop discharge time series is input into the degradation model of the lithium-ion battery, so as to achieve Forecast of capacity in the future moment,.

Specific embodiment 2. This embodiment is a further description of the indirect prediction method for lithium-ion battery cycle life based on GPR with an uncertain interval described in specific embodiment 1. In step 3, the ESN algorithm is used, and the equal pressure is used. The method of degrading the discharge time series y and the remaining capacity data z of the battery is as follows:

Step 31. Using the method of cross-validation, obtain the output weight of the ESN by obtaining the reserve pool size N, the spectral radius sr, the input unit scale and the input unit displacement;

Step 32. Use the quadratic programming equation with monotonic constraints to train the output weight of the ESN so that the battery capacity estimate The sum of squares of the error with the true value y(n) is the smallest, and the degradation modeling is completed.

ESN is a black-box method, and its modeling results are not given in the form of specific expressions. Its modeling process includes two parts: one is the ESN training process, that is, part of the input data: constant pressure drop discharge time series x(n), output data: battery capacity y(n) is used as the training set, and ESN training is carried out, so as to obtain the Degradation model of ESN. In the ESN model, there are four parameters that affect the modeling performance, namely the reserve pool size N, the spectral radius sr, the input unit scale (InputScaling, IS) and the input unit displacement (InputShift, IF). The training process is to use the cross-validation method to obtain the optimal value of the above four parameters, and use the quadratic programming equation with monotone constraints to train the output weight of the ESN, so that the battery capacity estimate The sum of squares of the error with the true value y(n) is the smallest. The second is the model verification process, which is to bring the remaining input data into the degradation model, calculate the estimated value of battery capacity, and compare and analyze the estimated value with the real data to verify the accuracy of the degradation model.

To sum up, the battery degradation modeling process based on ESN is the process of determining the optimal value of the four parameters of ESN according to the training data, namely the reserve pool size N, spectral radius sr, input unit scale (InputScaling, IS) and input unit Shift(InputShift, IF). Once these four parameters are determined, the degradation model is also determined, but its specific expression cannot be given.

The model error described in this embodiment: use root mean square error (RootMeanSquaredError, RMSE) as the evaluation index of approximation performance, such as the formula:

$\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; =</span>\sqrt{\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; no</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula, n is the length of training data or test data, is the output value of the ESN, that is, the predicted value of the remaining capacity of the battery, and y(i) is the real value of the remaining capacity of the ith battery

Overall fitting effect ^: using the overall fitting effect of the R2 evaluation function, when the fitting effect of the model is very poor, the sum of the squares of the error between the model output value and the true value will be greater than the error between the model output value and the mean value of the true value The sum of squares, that is, R ² may have a negative value; such as the formula, in the formula, for mean value.

${\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Degradation modeling results:

Table 1 shows the parameters of the degradation model obtained according to the above modeling process and the evaluation results of the degradation model during the training process.

Table 1 Degradation model results and model evaluation indicators

Degradation model validation:

As shown in the above table, the four parameters of the ESN-based lithium-ion battery degradation model are obtained, and the degradation model of the lithium-ion battery is obtained, and the evaluation index of the training process model is obtained by calculation. To verify the accuracy of the degradation modeling, the equal voltage drop discharge time series Bring in the battery degradation model, estimate the capacity value of the battery through the model, and compare and analyze the estimated value with the real value to verify the accuracy of the model. The verification is shown in Figure 1.

Curve 1 in Figure 1 is the estimated value curve of the lithium-ion battery capacity calculated based on the ESN degradation model, and the dotted line 2 represents the actual value curve of the battery capacity. Fig. 2 is a curve diagram of the error between the estimated value of the lithium-ion battery capacity obtained by modeling and the actual value of the measured capacity.

The root mean square error and R2 results between the calculated capacity estimate and the true value are shown in Table ² .

Table 2 Evaluation index of degradation model verification based on ESN

To sum up, the discharge time series with equal pressure drop proposed by the present invention can characterize the capacity of the battery, and realize the degradation modeling of the battery through the ESN algorithm. Figure 1 verifies the accuracy of the battery degradation model. From Figure 2 It can be seen that the model error is between -0.04 and 0.12. The root mean square error and the overall fitting effect of the model given in Table 2 can also show the validity of the degradation state modeling method proposed in this paper.

Specific Embodiment 3. This embodiment is a further explanation of the indirect prediction method for lithium-ion battery cycle life based on GPR with an uncertainty interval described in Specific Embodiment 1. The model method, using the number of charge and discharge cycles x and the battery charge and discharge cycle corresponding to the equal pressure drop discharge time y sequence, the method to obtain the prediction model of equal pressure drop discharge time based on GPR is as follows:

Step 41. Extract the number of charge and discharge cycles x of the battery to be tested, the discharge voltage of each charge and discharge cycle, and a partial data set of battery capacity Carry out prediction model training, where N is a positive integer;

Step 42, input the training data into the GPR model, carry out the GPR prediction model training, and obtain the GPR prediction model;

Step 43: According to the obtained GPR prediction model, the charging and discharging cycle at the future moment Input the prediction model to get the capacity prediction value at the next N time And the variance, get the discharge time prediction model based on GPR equal pressure drop.

Equal pressure drop discharge time series prediction is to use the known number of charge and discharge cycles and the equal pressure drop discharge time series data corresponding to the charge and discharge cycle to carry out prediction model training to obtain an optimal prediction model, and then use this model to extrapolate the future The constant voltage drop discharge time of the cycle. Because noise will inevitably be introduced in the data collection process, making the data uncertain, fully considering this point, the present invention uses Gaussian process regression (GPR) algorithm for data testing and prediction experiments. The Gaussian Process Regression Model (GPR) is a flexible, non-parametric model with uncertainty expression, and GPR can model the behavior of any system through the combination of appropriate Gaussian process kernel functions, and finally realize Forecasting based on the Bayesian forecasting framework, prior knowledge can be combined flexibly and conveniently in this process. The prediction result of the Gaussian process can also give the variance of the prediction while outputting the prediction result, that is, the prediction confidence interval is determined, which increases the accuracy of the prediction. Now, it has become a very important part of battery state prediction and health management algorithms.

The input data of the GPR model is the number of charge and discharge cycles, and the input data is the discharge time of the voltage drop. The GPR prediction model has two key steps, one is model training, and the other is model prediction, which will be introduced separately below.

GPR model training

The idea of Gaussian process modeling is that there is no need to give the parametric or non-parametric form of f(x) in y=f(x), and the value of f(x) is directly regarded as a random variable in the function space. Think of the prior probability distribution p(f(x)) of f(x) as a Gaussian distribution. Given a data set And define the input data matrix X∈R ^d×N , and the output data vector y∈R ^N×1 . In the finite data set of a given data set D, f(x ₁ ),...,f(x _n ) can constitute a set of random variables (each set is regarded as a random variable), and have a joint Gaussian distribution, the random process they form is called a Gaussian process. Right now

f(x)～GP(m(x),k(x _i ,x _j ))(3)

Among them, m(x)=E[f(x)], k(x _i , x _j )=E[(f(x _i )-m(x _i )(f(x _j )-m(x _j ) )], the symbol E represents the mathematical expectation. m(x) is the mean function, and k( _xi , x _j ) is the covariance function.

Applying the Gaussian process to the general regression modeling problem, the observed target value y containing noise can be considered, that is,

y=f(x)+ε(4)

Where ε is an additional independent Gaussian white noise uncorrelated with f(x), that is, the mean is zero and the variance is The normal distribution of , can be written as For formula (4), since the noise ε is Gaussian white noise independent of f(x), if f(x) is a Gaussian process, then y also obeys a Gaussian distribution, and the joint distribution of its finite observations can form a Gaussian process ,Right now

$\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ~</span>\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Among them, m(x) is the mean value function, δ _ij is the Dirac function, when i=j, the function δ _ij =1; i and j are the i-th and j-th input variables respectively.

y=f(x)+ε is a function expression used for prediction. Unlike general regression problems, f(x) cannot be expressed in the form of parameters or non-parameters, and the known is f(x ) is a Gaussian process, in which each variable f(x ₁ ),...,f(x _n ) obeys the joint Gaussian distribution, so the obtained prediction model is to bring each training point into the obtained matrix So the predictive model is written in the form of a matrix as follows:

$\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ~</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

In formula 6, I represents the unit matrix of N×N, C(X,X) represents the covariance matrix of N×N, K(X,X) represents the kernel matrix of N×N, which is called the Gram matrix, and its element k _ij =k(x(i),x(j)).

Here, formula (6) can be understood as the relationship between y and x (equivalent to y=ax+b in unary linear regression). where m(x) and All contain unknown parameters, collectively referred to as hyperparameters, such as m(x)=a+bx, $k(x_i,x_j)+{\mathrm{\&sigma;}}_{\mathrm{no}}^2{\mathrm{\&delta;}}_{ij}={\mathrm{\&upsi;}}_0\exp \{-\frac{1}{2}\underset{l=1}{\overset{d}{\&Sigma;}}{\mathrm{\&omega;}}_l{(x_i-x_j)}^2\}+{\mathrm{\&sigma;}}_{\mathrm{no}}^2{\mathrm{\&delta;}}_{ij},$ The hyperparameters are Θ=[a,b,υ ₀ ,ω _l ,σ _n ] these hyperparameters are similar to unary linear regression, a and b are unknowns determined by the training data, υ ₀ is the variance of the covariance function, and ω _l is The distance dimension of the covariance function, σ _n is the variance of the noise.

GPR model prediction

In the functional space defined by the prior distribution of the Gaussian process, the function prediction output value of the posterior distribution can be calculated under the Bayesian framework. When making predictions, for a collection of N ^* input data (charge and discharge cycles) The input data matrix X _* ∈ R ^d×N* is composed of the input, and the corresponding predicted output has the mean and variance The Gaussian distribution of

$\begin{array}{c}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{<span\; class="notranslate">\; *</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{<span\; class="notranslate">\; *</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}_{<span\; class="notranslate">\; *</span>}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

It can be seen from Equation 7 that the GPR model can also give the confidence level or uncertainty of the model prediction while giving the output prediction value, where is the covariance function matrix of test data and training data, is the covariance function matrix of the training data, y is the target vector of the training data, and k _* =k(x _* ,x _* ) is the covariance function of the test data.

Specific Embodiment 4. This embodiment is a further description of the indirect prediction method of lithium-ion battery cycle life based on GPR with an uncertainty interval described in Specific Embodiment 3. The variance covered in step 43 Areas are 95% confidence intervals.

Verification and Analysis

IPC10 (cycle2) battery verification and analysis

30%, 50% and 70% of the total data were used for prediction model training, and the remaining data was used as a verification set for comparative analysis with the predicted value. Since the ICIP10 battery only performs a capacity test every 500 cycles, this embodiment only conducts a comparative analysis at the corresponding time;

The experimental process is as follows:

Data set: Collect IIPC10 (cycle2) battery data and the corresponding number of charge and discharge cycles to build a data set x is the charge and discharge cycle, y is the equal pressure drop discharge time, and z is the battery capacity;

Model training: will As a training set for ESN-based degradation model training, and then As the training data, the GPR-based equal pressure drop discharge time prediction model is trained to obtain the equal pressure drop discharge time prediction model.

Prediction: the next N _* time charging cycle data set Input the equal pressure drop discharge time prediction model to predict the equal pressure drop discharge time Then substitute the predicted value into the battery degradation model to get the predicted value of battery capacity

Model analysis: predicting capacity with actual value conduct comparative analysis;

Experimental results:

In order to verify the effectiveness and adaptability of the method proposed in this paper, 30%, 50% and 70% of all data are used as training data for modeling, and the results are the capacity prediction value, confidence interval and prediction error corresponding to each cycle .

The experimental results are shown in Table 3-5.

Table 330% battery capacity prediction of training data

Table 450% battery capacity prediction for training data

Table 5. Battery capacity prediction for 70% training data

As can be seen from Table 3-5, the indirect prediction method of lithium-ion battery cycle life based on GPR with uncertainty interval proposed by the present invention realizes the prediction of battery capacity, and also provides the confidence interval of the prediction result while predicting , and verified the adaptability of the method through different training sets.

Specific Embodiment 5. This embodiment is a further explanation of the indirect prediction method for lithium-ion battery cycle life based on GPR with an uncertain interval described in Embodiment 1. The failure threshold of battery capacity in step 8 is the battery capacity 70% or 80% of initial capacity.

The battery RUL prediction method is consistent with the capacity prediction method, but the output results are different. 70% and 80% of the initial capacity were used as failure thresholds, respectively. When modeling the prediction model, 30%, 50% and 70% of all the data are used for modeling, and the RUL prediction value, confidence interval and error of the battery are given. The prediction effect of model training with 30% data is shown in Figure 3, and the prediction effect of model training with 50% data is shown in Figure 4. The prediction effect of using 70% data for model training is shown in Figure 5. Since 80% of the failure thresholds have been included in the training data, only 70% of the failure predictions can be made for RUL prediction. The RUL prediction results of three training data lengths are shown in Table 6.

Table 6 RUL prediction results of three training data lengths

NASA battery verification and analysis

Experimental verification is carried out using the 18th battery of the BatteryDataSet experimental data provided by NASA.

The data set comes from the lithium-ion battery test bed built by the NASA CoE Research Center, battery charging, discharging and impedance measurement experiments, run at room temperature 25 ℃:

Charge at a constant current of 1.5A until the battery voltage reaches 4.2V;

Discharge in the mode of constant current 2A until the battery voltage drops to 2.5V;

The battery impedance is measured by EIS, and the frequency sweep ranges from 0.1Hz to 5kHz.

The No. 18 battery data set has a total of 132 capacity data. In order to verify the effectiveness of the prediction method proposed by the present invention, the training sets of three lengths of 30%, 50% and 70% of the total capacity data are used to train the prediction model, and the remaining The data are used for model validation and comparative analysis.

1. Battery capacity prediction

The battery capacity is predicted by the method of the present invention, and the prediction results are shown in Table 7-Table 9.

Table 7. Capacity prediction results of 30% training data

Table 850% capacity prediction results of training data

Table 970% capacity prediction results of training data

2. Prediction of remaining battery life

The prediction method of the remaining life of NANSA battery is to use 70% and 80% of the initial capacity as the failure threshold respectively, and use 30%, 50% and 70% of the total data to model the prediction model, and give the RUL of the battery Predicted value, confidence interval, error. The RUL prediction results of three training data lengths are shown in Table 10.

Table 10 RUL prediction results of three training data lengths

The method of the present invention solves the problem that the capacity prediction and remaining life prediction of the lithium-ion battery in online application cannot be realized; the method can not only provide the point estimated value of the prediction result, but also provide the confidence interval of the prediction result, so that the prediction result is more accurate Reasonable, the guiding significance for users is greater.

Claims (5)

1., based on the cycle life of lithium ion battery indirect predictions method of GPR with indeterminacy section, it is characterized in that, the concrete steps of the method are:

The electricity z that step one, the collection charging-discharging cycle number of times x of mesuring battary, the sparking voltage of each charging-discharging cycle and battery capacity and each charging-discharging cycle are released,

Step 2, according to gathering the charging-discharging cycle number of times x of mesuring battary and the sparking voltage of each charging-discharging cycle and battery capacity, to calculate the pressure drop such as corresponding poor for discharge time, y such as sequence data discharge time such as pressure drop such as acquisition grade;

Step 3, adopt ESN algorithm, the residual capacity data z of the battery after pressure drop sequences y discharge time such as utilization and each discharge and recharge carries out degeneration modeling, obtains the degradation model based on ESN;

Step 4, adopt Gaussian process return modeling method, utilize charging-discharging cycle number of times x and the battery charging and discharging cycle corresponding wait pressure drop sequences y discharge time foundation based on GPR etc. pressure drop forecast model discharge time;

Step 5, by etc. pressure drop sequence data discharge time y and each discharge cycle data set of electricity z of releasing carry out training based on the degradation model of ESN as training set, by the charging-discharging cycle number of times x of battery and the data set waiting pressure drop sequences y discharge time carry out training based on pressure drop forecast model discharge time that waits of GPR as training data, acquisition waits pressure drop forecast model discharge time, and wherein N is positive integer;

Step 6, by lower N ₁individual charging-discharging cycle time manifold input forecast model discharge time such as pressure drop such as grade based on GPR, acquisition waits the predicted value of pressure drop discharge time

Step 7, by the predicted value of the pressure drop such as acquisition discharge time substitute into the degradation model based on ESN, obtain lower N ₁the discharge capacity of the battery of individual discharge cycle

Step 8, the initial capacity of battery is deducted lower N ₁the discharge capacity of the battery of individual charging-discharging cycle after the remaining capacity value of battery and the failure threshold of battery capacity compare, judge whether the remaining capacity value of battery equals the failure threshold of battery capacity, then using the residual life of charging-discharging cycle N as battery, complete based on the indirect predictions of GPR with the cycle life of lithium ion battery of indeterminacy section, otherwise perform step 9;

Step 9, the remaining capacity value of battery and the failure threshold of battery capacity to be compared, if the remaining capacity value of battery is greater than the failure threshold of battery capacity, then make N=N+N ₁, return execution step 5, if the remaining capacity value of battery is less than the failure threshold of battery capacity, then make N=N-N ₂, return execution step 5, wherein N ₂for being less than N ₁positive integer.

2. according to claim 1 a kind of based on the cycle life of lithium ion battery indirect predictions method of GPR with indeterminacy section, it is characterized in that, adopt ESN algorithm described in step 3, the method that the residual capacity data z of the battery after the pressure drop sequence data discharge time y such as utilization and each discharge and recharge carries out degeneration modeling is:

The method of step 3 one, employing cross validation, utilizes and obtains deposit pond scale N, spectral radius sr, input block yardstick and input block displacement, and obtain the output weights of ESN;

Step 3 two, use with Monotone constraint quadratic programming equation training ESN output weights, make battery capacity estimation value and the error sum of squares between actual value y (n) is minimum, complete degeneration modeling.

3. according to claim 1 a kind of based on the cycle life of lithium ion battery indirect predictions method of GPR with indeterminacy section, it is characterized in that, the modeling method that employing Gaussian process described in step 4 returns, utilize charging-discharging cycle number of times x and the battery charging and discharging cycle corresponding etc. the data of pressure drop y discharge time sequence, the method for pressure drop forecast model discharge time that waits obtained based on GPR is:

Step 4 one, the charging-discharging cycle number of times x extracting mesuring battary, the sparking voltage of each charging-discharging cycle and the partitioned data set (PDS) of battery capacity carry out forecast model training, wherein N is positive integer;

Step 4 two, training data is inputted GPR model, carry out the training of GPR forecast model, obtain GPR forecast model;

Step 4 three, basis obtain GPR forecast model, by the charging-discharging cycle of future time instance input prediction model, obtains the capacity predict value in lower N number of moment and variance, obtain forecast model discharge time such as pressure drop such as grade based on GPR.

4. according to claim 3 a kind of based on the cycle life of lithium ion battery indirect predictions method of GPR with indeterminacy section, it is characterized in that, the region that the variance described in step 4 three covers is the fiducial interval of 95%.

5. according to claim 1ly a kind ofly to it is characterized in that based on the cycle life of lithium ion battery indirect predictions method of GPR with indeterminacy section, in step 8, the failure threshold of battery capacity is 70% or 80% of the initial capacity of battery.