CN102798823A - Gaussian process regression-based method for predicting state of health (SOH) of lithium batteries - Google Patents

Abstract

The invention discloses a Gaussian process regression-based method for predicting state of health (SOH) of lithium batteries, relates to a method for predicting the SOH of the lithium batteries, belongs to the fields of electrochemistry and analytic chemistry and aims at the problem that the traditional lithium batteries are bad in health condition prediction adaptability. The method provided by the invention is realized according to the following steps of: I. drawing a relation curve of the SOH of a lithium battery and a charge-discharge period; II, selecting a covariance function according to a degenerated curve with a regeneration phenomenon and a constraint condition; III, carrying out iteration according to a conjugate gradient method, then determining the optimal value of a hyper-parameter and bringing initial value thereof into prior distribution; IV, obtaining posterior distribution according to the prior part; V, obtaining the mean value and variance of predicted output f' without Gaussian white noise; and VI, together bringing the practically predicted SOH of the battery and the predicted SOH obtained in the step V into training data y to obtain the f', then determining the prediction confidence interval and predicting the SOH of the lithium battery. The method provided by the invention is used for detecting lithium batteries.

Description

Lithium battery health status Forecasting Methodology based on the Gaussian process recurrence

Technical field

The present invention relates to a kind of lithium battery health status Forecasting Methodology, belong to galvanochemistry and analytical chemistry field.

Background technology

Lithium battery makes it become very potential energy source in the electronic equipment owing to have high energy dose rate and power.In electronic equipment, lithium ion battery is very important ingredient, in specific system, plays crucial effects, and its fault can cause the decline of system performance, and misoperation, more serious meeting cause catastrophic accident.

Through our effective management to the battery health situation, comprise the service condition of setting battery, map out the replacing interval of battery etc., can strengthen the reliability and stability of total system to a certain extent.Yet; Since we the health status of battery is managed and the process predicted in to rely on the integration of parameter; And directly measured value can receive the restriction of interference of noise and resolution, and the uncertainty that makes us predict increases, and the accuracy that directly causes predicting the outcome descends.

So we must show great attention to management of lithium ion battery health status and prediction; Service condition through the control battery; Change the reliability and stability that wait enhanced system at interval. battery on-line operation process is dynamic, and its performance receives the influence of surrounding environment and loading condition to a great extent.The health status of battery (SOH) prediction is a very important ingredient in the battery predictive, and it mainly is that system battery storage and energy delivered are quantitatively estimated.SOH prediction can be used for the degeneration of reaction cell system performance, through its effective prediction can avoid maybe accident generation.

At present; Estimate so long as the health status that the capacity that utilizes battery and impedance also have much other mode to come estimating battery for the SOH of lithium ion battery; Someone has proposed the prediction notion based on the SOH of the power lithium ion battery of suitable SOH definition, new technology that the SOH that also has Kim to propose the two smooth mode of utilization estimates or the like.

Gaussian process model (GPR) is flexibly a kind of; Has uncertain nonparametric model of expressing; And; GPR can come through the combination of suitable Gaussian process modeling is carried out in the behavior of arbitrary system, the final prediction that realizes based on the Bayesian forecasting framework, combination priori that can be flexible in this process.Now, it has become a very important part in the algorithm of battery status prediction and health control, and in the different predicting model, the selection of covariance function is very important, still, does not have clear and definite standard for its selection.Carry out the Gaussian process regression forecasting for time dependent inside battery parameter, utilize the relation of itself and battery capacity that it is delivered to the battery capacity field then and predict, express capacity degradation with time situation.The result is an acceptable, but in the situation of reality, resting of discharging and recharging in the lithium ion battery use can cause self-charging phenomenon, i.e. orthogenesis; So when we predicted it, the degradation trend of battery will be reacted this point.In addition, the training data that obtains when us more after a little while, the effect of prediction is not very desirable, can better not react real cell degradation situation.

Summary of the invention

The objective of the invention is problem, a kind of lithium battery health status Forecasting Methodology that returns based on Gaussian process is provided to traditional lithium battery health status prediction bad adaptability.

Based on the lithium battery health status Forecasting Methodology that Gaussian process returns, it is realized by following steps:

Step 1, with lithium battery emptying of newly dispatching from the factory to be detected; And be full of again; Repeat to discharge and recharge N time, wherein N is more than or equal to 20 integer, the battery capacity of this lithium battery in the record cycle; Draw the health status SOH and the relation curve that discharges and recharges the cycle, the degenerated curve that promptly has orthogenesis of the battery of this lithium battery then;

Step 2, basis have the degenerated curve constraints of orthogenesis and select covariance function; This constraint condition is that the covariance matrix that selected covariance function constituted satisfies nonnegative definite;

Covariance function is k (x _i, x _j)=k _f(x _i, x _j)+k _n(x _i, x _j), wherein, k _fBe used for describing the function part in the unknown system model, k _nRepresent the noise section of unknown system, x _iBe an input point, x _jBe another input point, i is the positive integer more than or equal to 0, and j is the positive integer more than or equal to 0; Weigh input point x with its covariance function value _iWith input point x _jBetween distance; [numerical value is big more, explains that this correlativity of 2 is big more]

Step 3, setting ultra parameter Θ=[l ₁, σ _y, l ₂, σ _f, w, σ _n] initial value, set earlier any initial value, obtaining the likelihood function local derviation according to the method for conjugate gradient iteration then is 0 optimal value; [our optimal value should make that likelihood function is 0 to the local derviation of each hyper-function; This is the target that we finally will reach; But calculate complicated like this; So do not knowing under the situation of optimal value, set earlier any initial value, obtaining the likelihood function local derviation according to the method for conjugate gradient iteration then is 0 optimal value.】

Step 4, confirmed the form of covariance function after, with training data (x, y) | i=1 ..., in n} and the prediction input substitution covariance function, it is following with the prior distribution of prediction output to obtain the training objective value,

$\left(\begin{array}{c}y\\ f^{\′}\end{array}\right)~(0,\left(\begin{array}{cc}k(x,x)+{\mathrm{\σ}}_n^2& k(x,x^{\′})\\ {k(x,x^{\′})}^T& k(x^{\′},x^{\′})\end{array}\right))$

According to theorem and the prior distribution that obtained, then obtain corresponding posteriority and be distributed as:

$\stackrel{\‾}{f^{\′}}|x,y,x^{\′}~N(f^{\′},\mathrm{cov}\left(f^{\′}\right)),$

Wherein, $\stackrel{\‾}{f^{\′}}=E{\left[f^{\′}\right|x,y,x^{\′}]=k(x,x^{\′})[k(x,x)+{\mathrm{\σ}}_n^{2}I]}^{-1}y,$

$\mathrm{cov}\left(f^{\′}\right)=k(x^{\′},x^{\′})-{[k(x^{\′},x)+{\mathrm{\σ}}_n^{2}I]}^{-1}k(x,x^{\′}),$

In the formula,

Be the variance of noise, I is a unit matrix, and x, x ' are different input points; Y is the desired value of training data, and the model that Gaussian process returns is: y=f (x)+ε, ε are white Gaussian noise, its distribution be N (0, σ _n);

Be the mean prediction output of not noisy; σ _nIt is the variance of noise;

Said theorem is: suppose that d is the sample that from obey the finite dimension Gaussian distribution, extracts, d～(0, D), D is a covariance matrix, and we are divided into two parts [a, b] to d now, promptly $\left(\begin{array}{c}a\\ b\end{array}\right)~N(0,\left(\begin{array}{cc}A& C^T\\ C& B\end{array}\right))$ This moment, we obtained distributing:

b/a～N(CA ^-1a，B-CA ^-1C ^T)；

Step 5, distribute according to resulting posteriority in the step 4, with after the respective value substitution with average

and the variance cov (f ') of the prediction output f ' of white Gaussian noise;

The health status SOH of step 6, the battery that will newly record is brought among the training data y; What must make new advances does not export f ' with the prediction of white Gaussian noise, confirms the prediction fiducial interval, dopes the health status of lithium battery; Step 6 is carried out in circulation, obtains the dynamic data forecast model.

Advantage of the present invention is: the employed Gaussian process regression model of this paper; Be flexibly a kind of; Have the nonparametric model that probability is expressed, can when providing mean prediction, provide fiducial interval, be used for noise and the uncertainty introduced in the descriptive system with it.In order to assess the feasibility of this model, we predict that for the health status of lithium ion battery experimental result has proved the Gaussian process model, and prediction has excellent adaptability and validity for lithium ion battery health status.Concrete experiment comprises the prediction effect contrast of different training data, and the contrast of dynamic model and static model.

Description of drawings

Fig. 1 is a process flow diagram of the present invention;

Fig. 2 is the degenerated curve figure of the health status SOH of battery from the degenerate case in the cycle of discharging and recharging 0 to 168;

The prediction effect figure of Fig. 3 for beginning to predict at N=100;

The prediction effect figure of Fig. 4 for beginning to predict at N=80;

Fig. 5 is the prediction output effect figure behind the actual N=20 that records of adding.

Embodiment

Embodiment one, this embodiment is described below in conjunction with Fig. 1,

Based on the lithium battery health status Forecasting Methodology that Gaussian process returns, it is realized by following steps:

Step 1, with lithium battery emptying of newly dispatching from the factory to be detected; And be full of again; Repeat to discharge and recharge N time, wherein N is more than or equal to 20 integer, the battery capacity of this lithium battery in the record cycle; Draw the health status SOH and the relation curve that discharges and recharges the cycle, the degenerated curve that promptly has orthogenesis of the battery of this lithium battery then;

Step 2, basis have the degenerated curve constraints of orthogenesis and select covariance function; This constraint condition is that the covariance matrix that selected covariance function constituted satisfies nonnegative definite;

Covariance function is k (x _i, x _j)=k _f(x _i, x _j)+k _n(x _i, x _j) wherein, k _fBe used for describing the function part in the unknown system model, k _nRepresent the noise section of unknown system, x _iBe an input point, x _jBe another input point, i is the positive integer more than or equal to 0, and j is the positive integer more than or equal to 0; Weigh input point x with its covariance function value _iWith input point x _jBetween distance; Numerical value is big more, explains that this correlativity of 2 is big more.

Step 3, setting ultra parameter Θ=[l ₁, σ _y, l ₂, σ _f, w, σ _n] initial value, set earlier any initial value, obtaining the likelihood function local derviation according to the method for conjugate gradient iteration then is 0 optimal value; Our optimal value should make that likelihood function is 0 to the local derviation of each hyper-function; This is the target that we finally will reach; But calculate complicated like this; So do not knowing under the situation of optimal value, set earlier any initial value, obtaining the likelihood function local derviation according to the method for conjugate gradient iteration then is 0 optimal value.

Step 4, confirmed the form of covariance function after, with training data (x, y) | i=1 ..., in n} and the prediction input substitution covariance function, it is following with the prior distribution of prediction output to obtain the training objective value,

$\left(\begin{array}{c}y\\ f^{\′}\end{array}\right)~(0,\left(\begin{array}{cc}k(x,x)+{\mathrm{\σ}}_n^2& k(x,x^{\′})\\ {k(x,x^{\′})}^T& k(x^{\′},x^{\′})\end{array}\right))$

According to theorem and the prior distribution that obtained, then obtain corresponding posteriority and be distributed as:

$\stackrel{\‾}{f^{\′}}|x,y,x^{\′}~N(f^{\′},\mathrm{cov}\left(f^{\′}\right)),$

Wherein, $\stackrel{\‾}{f^{\′}}=E{\left[f^{\′}\right|x,y,x^{\′}]=k(x,x^{\′})[k(x,x)+{\mathrm{\σ}}_n^{2}I]}^{-1}y,$

$\mathrm{cov}\left(f^{\′}\right)=k(x^{\′},x^{\′})-{[k(x^{\′},x)+{\mathrm{\σ}}_n^{2}I]}^{-1}k(x,x^{\′}),$

In the formula,

Be the variance of noise, I is a unit matrix, and x, x ' are different input points; Y is the desired value of training data, and the model that Gaussian process returns is: y=f (x)+ε, ε are white Gaussian noise, its distribution be N (0, σ _n);

Be the mean prediction output of not noisy; σ _nIt is the variance of noise;

Said theorem is: suppose that d is the sample that from obey the finite dimension Gaussian distribution, extracts, d～(0, D), D is a covariance matrix, and we are divided into two parts [a, b] to d now, promptly $\left(\begin{array}{c}a\\ b\end{array}\right)~N(0,\left(\begin{array}{cc}A& C^T\\ C& B\end{array}\right))$ This moment, we obtained distributing:

b/a～N(CA ^-1a，B-CA ^-1C ^T)；

Step 5, distribute according to resulting posteriority in the step 4, with after the respective value substitution with average

and the variance cov (f ') of the prediction output f ' of white Gaussian noise;

The health status SOH of step 6, the battery that will newly record is brought among the training data y; What must make new advances does not export f ' with the prediction of white Gaussian noise, confirms the prediction fiducial interval, dopes the health status of lithium battery; Carry out with this step cycle, then obtain the dynamic data forecast model.

The mode that prior distribution in this embodiment obtains the posteriority distribution is: in prior distribution:

$\left(\begin{array}{c}y\\ f^{\′}\end{array}\right)~(0,\left(\begin{array}{cc}k(x,x)+{\mathrm{\σ}}_n^2& k(x,x^{\′})\\ {k(x,x^{\′})}^T& k(x^{\′},x^{\′})\end{array}\right))$ Concrete form about its formula is following:

To train input (x1, x2, x3, ', xn) be brought into the form that just can obtain the covariance matrix of training data in the covariance function

$k(x,x)+{\mathrm{\σ}}_n^2=\left[\begin{array}{cccc}k(x_1,x_1)& k(x_1,x_2)& ...& k(x_1,x_n)\\ k(x_2,x_1)& k(x_2,x_2)& ...& k(x_2,x_n)\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ k(x_n,x_1)& k(x_n,x_2)& ...& k(x_n,x_n)\end{array}\right]$

To predict that input x ' substitution just obtains the covariance vector of training data and predicted data:

k(x，x′)＝[k(x′，x ₁)，k(x′，x ₂)，...，k(x′，x _n)]

The covariance value of prediction input self: k (x ', x ').

Embodiment two, below in conjunction with Fig. 1 to Fig. 5 this embodiment is described, this embodiment is for to the further specifying of the health status SOH of the battery of embodiment one, the concrete expression of the health status SOH of the described battery of this embodiment as shown in the formula:

$\mathrm{SOH}=\frac{C_i}{C_0}\×100\%$

C wherein _iBe i capability value that discharges and recharges the cycle, C ₀Be initial capacity, i is the positive integer more than or equal to 0.

Embodiment three, this embodiment is described below in conjunction with Fig. 1 to Fig. 5; This embodiment is for being further specifying of periodic function to the function of selecting in the step 2 in the embodiment one, and the function that the described step 2 of this embodiment is selected is that the combination of periodic function, square exponential function and constant covariance function is as covariance function; Wherein a square index covariance function is:

$k_f={\mathrm{\σ}}_y^2\exp (-\frac{{(x-x^{\′})}^2}{2l^2})$

The cycle covariance function is:

$k_f={\mathrm{\σ}}_f^2\exp (-\frac{2}{l_2^2}{\sin }^2\left(\frac{\mathrm{\ω}}{2\mathrm{\π}}(x-x^{\′})\right))$

The constant covariance function

k(x _i，x _j)＝v ₀

Wherein the constant covariance function is represented the white Gaussian noise in the system.

Embodiment four, below in conjunction with Fig. 1 to Fig. 5 this embodiment is described, this embodiment is to setting ultra parameter Θ=[l in the step 3 in the embodiment one ₁, σ _y, l ₂, σ _f, w, σ _n] the further specifying of initial value, set ultra parameter Θ=[l in the said step 3 of this embodiment ₁, σ _y, l ₂, σ _f, w, σ _n] initial value, described ultra parameter is through adopting the maximization likelihood function to confirm that the ultra parameter in the covariance function realizes;

Likelihood function is following:

$\log p\left(y\right|x,\mathrm{\θ})=-\frac{1}{2}{y}^T{k}^{-1}y-\frac{1}{2}\log \left|k\right|-\frac{n}{2}\log 2\mathrm{\π};$

Be that the ultra parameter in the above-mentioned function is asked local derviation, the k in the formula is a covariance matrix, is to Θ=[f ₁, σ _y, l ₂, σ _f, w, σ _n] ask local derviation, making it is 0, then ultra parameter value to the end.

The present invention is not limited to above-mentioned embodiment, can also be the reasonable combination of technical characterictic described in above-mentioned each embodiment.

Claims (4)

1. the lithium battery health status Forecasting Methodology that returns based on Gaussian process, it is characterized in that: it is realized by following steps:

Step 1, with lithium battery emptying of newly dispatching from the factory to be detected; And be full of again; Repeat to discharge and recharge N time, wherein N is more than or equal to 20 integer, the battery capacity of this lithium battery in the record cycle; Draw the health status SOH and the relation curve that discharges and recharges the cycle, the degenerated curve that promptly has orthogenesis of the battery of this lithium battery then;

Step 2, basis have the degenerated curve constraints of orthogenesis and select covariance function; This constraint condition is that the covariance matrix that selected covariance function constituted satisfies nonnegative definite;

Covariance function is k (x _i, x _j)=k _f(x _i, x _j)+k _n(x _i, x _j) wherein, k _fBe used for describing the function part in the unknown system model, k _nRepresent the noise section of unknown system, x _iBe an input point, x _jBe another input point, i is the positive integer more than or equal to 0, and j is the positive integer more than or equal to 0; Weigh input point x with its covariance function value _iWith input point x _jBetween distance;

Step 3, setting ultra parameter Θ=[l ₁, σ _v, l ₂, σ _f, w, σ _n] initial value, set earlier any initial value, obtaining the likelihood function local derviation according to the method for conjugate gradient iteration then is 0 optimal value;

Step 4, confirmed the form of covariance function after, with training data (x, y) | i=1 ..., in n} and the prediction input substitution covariance function, it is following with the prior distribution of prediction output to obtain the training objective value,

$\left(\begin{array}{c}y\\ f^{\′}\end{array}\right)~(0,\left(\begin{array}{cc}k(x,x)+{\mathrm{\σ}}_n^2& k(x,x^{\′})\\ {k(x,x^{\′})}^T& k(x^{\′},x^{\′})\end{array}\right))$

According to theorem and the prior distribution that obtained, then obtain corresponding posteriority and be distributed as:

$\stackrel{\‾}{f^{\′}}|x,y,x^{\′}~N(f^{\′},\mathrm{cov}\left(f^{\′}\right)),$

Wherein, $\stackrel{\‾}{f^{\′}}=E{\left[f^{\′}\right|x,y,x^{\′}]=k(x,x^{\′})[k(x,x)+{\mathrm{\σ}}_n^{2}I]}^{-1}y,$

$\mathrm{cov}\left(f^{\′}\right)=k(x^{\′},x^{\′})-{[k(x^{\′},x)+{\mathrm{\σ}}_n^{2}I]}^{-1}k(x,x^{\′}),$

In the formula,

Be the variance of noise, I is a unit matrix, and x, x ' are different input points; Y is the desired value of training data, and the model that Gaussian process returns is: y=f (x)+ε, ε are white Gaussian noise, its distribution be N (0, σ _n);

Be the mean prediction output of not noisy; σ _nIt is the variance of noise;

Said theorem is: suppose that d is the sample that from obey the finite dimension Gaussian distribution, extracts, d～(0, D), D is a covariance matrix, and we are divided into two parts [a, b] to d now, promptly $\left(\begin{array}{c}a\\ b\end{array}\right)~N(0,\left(\begin{array}{cc}A& C^T\\ C& B\end{array}\right))$ This moment, we obtained distributing:

b/a～N(CA ^-1a，B-CA ^-1C ^T)；

Step 5, distribute according to resulting posteriority in the step 4, with after the respective value substitution with average

and the variance cov (f ') of the prediction output f ' of white Gaussian noise;

The health status SOH of step 6, the battery that will newly record is brought among the training data y; What must make new advances does not export f ' with the prediction of white Gaussian noise, confirms the prediction fiducial interval, dopes the health status of lithium battery; Step 6 is carried out in circulation then, obtains the dynamic data forecast model.

2. the lithium battery health status Forecasting Methodology that returns based on Gaussian process according to claim 1 is characterized in that: the concrete expression of the health status SOH of described battery as shown in the formula:

$\mathrm{SOH}=\frac{C_i}{C_0}\×100\%$

C wherein _iBe i capability value that discharges and recharges the cycle, C ₀Be initial capacity, i is the positive integer more than or equal to 0.

3. the lithium battery health status Forecasting Methodology that returns based on Gaussian process according to claim 1; It is characterized in that: said step 2, to select covariance function, the covariance function of its selection according to the degenerated curve constraints with orthogenesis be that the combination of periodic function, square exponential function and constant covariance function is as covariance function; Wherein a square index covariance function is:

$k_f={\mathrm{\σ}}_y^2\exp (-\frac{{(x-x^{\′})}^2}{2{l_1}^2})$

The cycle covariance function is:

$k_f={\mathrm{\σ}}_f^2\exp (-\frac{2}{l_2^2}{\sin }^2\left(\frac{\mathrm{\ω}}{2\mathrm{\π}}(x-x^{\′})\right))$

The constant covariance function

k(x _i，x _j)＝σ _n

Wherein the constant covariance function is represented the white Gaussian noise in the system.

4. the lithium battery health status Forecasting Methodology that returns based on Gaussian process according to claim 1 is characterized in that: set ultra parameter Θ=[l in the said step 3 ₁, σ _y, l ₂, σ _f, w, σ _n] initial value, described ultra parameter is through adopting the maximization likelihood function to confirm that the ultra parameter in the covariance function realizes;

Likelihood function is following:

$\log p\left(y\right|x,\mathrm{\θ})=-\frac{1}{2}{y}^T{k}^{-1}y-\frac{1}{2}\log \left|k\right|-\frac{n}{2}\log 2\mathrm{\π};$

Be that the ultra parameter in the above-mentioned function is asked local derviation, the k in the formula is a covariance matrix, is to Θ=[l ₁, σ _y, l ₂, σ _f, w, σ _n] ask local derviation, making it is 0, then ultra parameter value to the end.

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