CN109815995B - Method for predicting remaining life of lithium battery under condition of missing observed value - Google Patents

Abstract

The invention relates to a method for predicting the residual life of a lithium battery under the condition of missing observed values, which comprises the following steps: 1) designing a total framework of a lithium battery residual life prediction method under the condition of missing observation values; 2) designing a preprocessing module algorithm, including introducing an ELM algorithm of an extreme learning machine, an ELMSI (single-point interpolation algorithm) design and an ELMMI (multiple interpolation algorithm); 3) the prediction module algorithm design comprises a nuclear limit learning machine design and a multi-step advanced prediction algorithm design; 4) training an ELMMI multiple interpolation algorithm model; 5) and (3) carrying out model training on a multi-step advanced prediction method. The invention has the beneficial effects that: the invention provides a method for combining a multi-interpolation algorithm ELMMI with different multi-step advance prediction methods to construct a multi-step advance predictor based on the multi-interpolation algorithm, which can realize an accurate and stable estimation process.

Description

Method for predicting remaining life of lithium battery under condition of missing observed value

Technical Field

The invention relates to a method for predicting the residual service life of a lithium iron phosphate battery under the condition of a missing observation value, in particular to a method for filling the missing observation value based on a multiple interpolation technology and a method for predicting the residual service life of a single lithium battery based on multi-step advanced prediction.

Background

Lithium batteries are favored by the industry due to the advantages of high energy density, long service life, low self-discharge rate and the like, and currently occupy the main market of power batteries. During the use process, the lithium battery has the problems of rapid aging and energy exhaustion, which leads to the reduction of the overall performance of the equipment and unpredictable damage. Therefore, the life Prognosis and Health Management (PHM) of lithium batteries are increasingly gaining importance from the battery industry. The life prognosis of a lithium battery is defined as predicting the service life of a battery system according to the operating conditions and operating conditions of the system. Lithium battery remaining service life (RUL) prediction methods are mainly divided into two major categories, model-based prediction and data-driven prediction. The model-based prediction method is the most widely used RUL estimation method, but since all parameters of the prediction model need initialization and pre-adjustment, it is difficult to obtain accurate and perfect model parameters in practical applications. Meanwhile, the model parameters are difficult to update in real time under new working conditions. The above problem can be solved based on a data-driven prediction method that predicts future values using present and past observations in the battery degradation curve. The information characteristics reflected by the degradation curve, such as voltage values, capacity values, current values, and impedance values, can be extracted and used for accurate prediction of RUL. And the data driving algorithm calculates the degradation trend by learning the correlation among the information characteristics and accurately predicts the residual service life of the lithium battery.

A one-step look-ahead (OSP) method for estimating the short-term RUL of a battery uses a non-linear A-regression (NAR) structure to build a pre-decision model as shown in equation (1):

in the formula, C is the battery capacity in the discharge cycle, i is the cycle number, e is the estimation error of each cycle, n is the total number of cycles, and f is an approximate function generated by the training stage predictor and is a parameter matrix of the estimation function.

Disclosure of Invention

The invention aims to overcome the defects in the prior art and provide a method for predicting the residual life of a lithium battery under the condition of missing observed values.

The method for predicting the residual life of the lithium battery under the condition of the missing observation value comprises the following steps:

step 1: designing a total framework of a lithium battery residual life prediction method under the condition of missing observation values; calculating and predicting based on an ELM (extreme learning machine); the preprocessing module designs single-point interpolation and multiple interpolation based on an ELM algorithm, and the prediction module designs a multi-step advanced prediction method based on the traditional ELM, the nucleation ELM and the online sequential ELM;

step 2: designing an algorithm of a preprocessing module; designing single-point interpolation and multiple interpolation algorithms based on the traditional ELM algorithm;

step 2-1: introducing an ELM algorithm of an extreme learning machine; giving a group of m observation values, and randomly distributing input weight and hidden layer deviation by using ELM; ELM analyzes and adjusts output weight, and the algorithm formula is as follows:

where α is the output weight, h_iFor non-linear feature mapping, w_iTo connect the ith hidden node to the input node, b_iA threshold value of the ith hidden node; minimizing prediction error H alpha-F Y in ELM model training period²And the output weight rated value alpha is calculated according to the following formula:

wherein the content of the first and second substances,

representing an output node x_jThe error vector of (a) is calculated,

for regularization parameters, F is a function F_ELMThe solution of (1); to solve the optimization problem, the following least-norm least-squares solution of the linear system is found:

Hα＝F (4)

the least squares solution α ═ H is obtained from equation (4)^TF；H^TObtaining prior information by utilizing an orthogonal projection technology;

step 2-2: designing a single-point interpolation algorithm ELMSI: the observation data set is first divided into two distinct subsets, complete subset X_completeAnd incomplete subset X_uncomThen to the subset X_uncomAny observation vector x in (2)_nBy the use of X_completeTraining an ELM model by all complete observations in (1); finally, a target feature vector X is defined_nAnd estimating X by using the trained ELM model_nThe missing observation feature of (a);

step 2-3: design of an ELMMI (multiple interpolation algorithm): in the initial state, ELMMI divides the data set into two subsets, complete subset X_completeAnd incomplete subset X_uncom(ii) a By X_uncomEach observation vector x of_nThe loop creates p estimation sets and satisfies p e [1,5 ]]Generating a complete estimation data set with a matrix size of m multiplied by n for each estimation set; by using X_completeCircularly train the ELM model with x_nAll incomplete observation features in (1) are target vectors, the rest observation features are input vectors, and an incomplete subset X is estimated_uncomThe missing observation vector features in (1); computing recently input observations x using a similarity function λ_nAnd complete subset X_completeA similarity between each of the observations; interpolation algorithm searching complete subset X_completeSelecting the l nearest neighbors

Building a data subset X_l(ii) a With X_lUsing x as a training target_nTaking all corresponding incomplete observation features as input vectors, and training an ELM model; training the ELM model twice to obtain the final ELMMI model, and estimating X_nAnd the complete observation is obtained

Adding complete subset X_completePerforming the following steps;

and step 3: designing a prediction module algorithm; introducing one-step advanced prediction, and designing a multi-step advanced prediction algorithm as a component module of the lithium battery residual life prediction method; designing a nuclear limit learning machine based on the ELM;

step 3-1: designing a coring extreme learning machine; designing a nucleation extreme learning machine KELM based on the ELM, utilizing a kernel matrix of the ELM model, and meeting Mercer conditions, such as formula (5):

Ψ_KELM＝HH^T:f_KELM(x_i,x_j)＝h(x_i)·h(x_j) (5)

the output function of the KELM model is reconstructed as:

in the formula, Y and f_KELM(. the) respectively represents the identification matrix and the kernel function, m observed values are selected, and the formula is as follows:

training a KELM model by utilizing various kernel functions, wherein the functions meet the Mercer condition; training a KELM model by utilizing a wavelet function WAV and a radial basis function RBF, and establishing formulas of the wavelet function and the RBF respectively as follows:

wherein tau, upsilon, zeta and xi are model parameters in the algorithm training process respectively;

step 3-2: designing a multi-step advanced prediction algorithm; multi-step advanced prediction MSP is classified into three major categories: iterative, DirRec and direct; designing a new model of multi-step advanced prediction based on a multiple interpolation technology and a DirRec method, wherein the model generates a new prediction model after each calculation step;

calculating a new predicted value in the training subset, and discarding the last observation value, namely keeping the same number of observation values of the training subset in each iterative calculation process; the new predicted value formula for estimating the L lithium battery capacities is as follows:

in the formula (f)_lA prediction model for predicting step length of L order;

and 4, step 4: training an ELMMI multiple interpolation algorithm model;

step 4-1: introducing a set of missing observations in each cycle of a battery aging data set

Creating incomplete dataset X'_uncom(ii) a The missing observation values are randomly imported into different data set periods, and the import probability of the last period of the training sequence is highest;

step 4-2: selecting the voltage/current and SOC (state of charge) data of 40-50% of the front of the single battery to carry out ELMMI model training; vector X in complete subset_completeIs rewritten as

The model training formula is as follows:

in the formula, H is a hidden node matrix,

is an output weight matrix; using a model function f_ELMMIPredicted X'_uncomIncomplete vector of

x_n∈X_completeAnd introducing random missing observation values; selecting the first 40-50% sampling value to train the model, wherein the model training formula is as follows:

step 4-3: the complete observation vector is represented as

The training model selects a nonlinear model and a linear model, and compares the nonlinear model and the linear model with the real value of the target parameter;

and 5: training a multi-step advanced prediction method model; and for an incomplete data set containing less than 20% of missing observed values, performing data filling on the input subset by using a multiple interpolation algorithm.

Preferably, the method comprises the following steps: in step 2-3, the ELM-based multiple interpolation algorithm elmi further includes the following steps:

inputting: x_m×nIs an incomplete data set, is a parameter set of an ELM model;

defining: c. C^misIs a missing feature of an observed value, c^obsObservable features being an observation, d^misFor incomplete observation, d^obsFor complete observations, X is the total observation dataset, X_completeIs a complete subset of X, X_uncomIs a non-complete subset of X, X_estmationFor the estimated set of full observations,

for some two observed values x_nAnd x_mThe similarity between them;

wherein GRC is a gray correlation coefficient and is expressed as GRC (x)_nj,x_mj)＝0.5/(|x_nj-x_mj|+0.5)；

1) Decomposition of X into X_completeAnd X_uncom；

2) Mixing X_uncomBy c^misThe data sets are represented and arranged from small to large;

3) normalization of X_completeAnd X_uncom；

Within the p data sets, satisfying p ═ 1:1:5, the following steps are performed:

when n satisfies the formula

Performing steps 4) to 12);

4) using the parameter X_completeRewritten as x_nTraining an ELM model;

in the formula, H is a hidden node matrix,

to output the weight matrix, the weight matrix is output,

is an observable in a complete subset;

5) using a model function f_ELMPrediction of X_uncomIs incompletely observed value x_n，x_n∈X_uncom

Rewriting a complete observation expression as

When m satisfies

Then, step 6) and step 7) are performed;

6) calculating a weight coefficient gamma:

γ＝(2β-1)/10

in the formula, beta is a parameter coefficient;

7) calculating a similarity equation:

the value M is taken out and circulated;

8) according to the parameter X_completeWriting an equation lambda in descending order;

9) when the equation value lambda is maximum, selecting one observation value to satisfy

10) The ELM model was trained using the following formula:

11) using f_ELMEstimating missing value x_n∈X_uncomIs of the formula

Rewriting a complete observation expression as

12) Will be provided with

Instead of parameter set X_completeA medium vector;

n value cycle is finished;

13) set of return estimates X_estimation(a)＝X_complete；

And finishing the p value cycle.

The invention has the beneficial effects that: the invention provides a method for combining a multi-interpolation algorithm ELMMI with different multi-step advance prediction methods to construct a multi-step advance predictor based on the multi-interpolation algorithm, which can realize an accurate and stable estimation process.

Drawings

FIG. 1 is an overall frame diagram of the present invention;

FIG. 2 is a graph of the results of a comparison of the linear regression model, the non-linear prediction model, and the true values of the target parameters, trained using the first 40% observations;

FIG. 3 is a graph of the results of RMSE values calculated by 5 OS predictors in conjunction with different step lead predictors.

Detailed Description

The present invention will be further described with reference to the following examples. The following examples are set forth merely to aid in the understanding of the invention. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention.

The invention carries out pretreatment, estimation and prediction on the residual life of the lithium iron phosphate battery under the condition of missing observed values, innovatively provides a prediction method based on one-step advanced prediction and multi-step advanced prediction algorithms, and the overall framework comprises two modules: a preprocessing module and a prediction module. The preprocessing module includes two new techniques, namely an extreme learning machine-based single point interpolation technique (elsim) and a multiple interpolation technique (EMMI).

Step 1: and (3) designing the overall framework of the lithium battery residual life prediction method under the condition of missing observation values. As shown in fig. 1, the new method is based on dynamic Extreme Learning Machine (ELM) to make predictions and estimations. Since the hidden nodes of the ELM are randomly generated and the lost observation values can be classified, the algorithm can accurately predict the short-term and long-term life states of the lithium battery. The preprocessing module designs single-point interpolation and multiple interpolation based on an ELM algorithm, and the prediction module designs a multi-step advanced prediction method based on traditional ELM, nucleation ELM (KELM) and online sequential ELM (OS-ELM).

Step 2: and designing an algorithm of a preprocessing module. A preprocessing module in the lithium battery residual life prediction method mainly completes the task of filling missing observed values.

Step 2-1: an extreme learning machine ELM algorithm is introduced. Given a set of m observations, the ELM randomly assigns input weights and hidden layer biases, reducing computation time while maintaining overall prediction accuracy. ELM analyzes and adjusts output weight, and the algorithm formula is as follows:

where α is the output weight, h_iFor non-linear feature mapping, w_iTo connect the ith hidden node to the input node, b_iIs the threshold value of the ith hidden node. Minimizing prediction error H alpha-F Y in ELM model training period²And the output weight rated value alpha is calculated according to the following formula:

wherein the content of the first and second substances,

representing an output node x_jThe error vector of (a) is calculated,

for the regularization parameters to balance the above optimization formula, F is a function F_ELMThe solution of (1). To solve the optimization problem, the minimum norm least squares solution of the following linear system can be found:

Hα＝F (4)

the least squares solution α ═ H is obtained from equation (4)^TF, the solution has good generalization ability, minimal error, and fast convergence. H^TThe prior information is obtained using an orthogonal projection technique.

Step 2-2: and (4) designing a single-point interpolation algorithm. The invention designs a new single-point interpolation algorithm (ELMSI), firstly, an observation data set is divided into two different subsets, namely a complete subset X_completeAnd incomplete subset X_uncomThen to the subset X_uncomAny observation vector x in (2)_nBy the use of X_completeAll perfect observations in (a) train the ELM model. Finally, a target feature vector X is defined_nAnd estimating X by using the trained ELM model_nThe missing observation feature of (1).

Step 2-3: and (4) designing a multiple interpolation algorithm. The invention designs a multi-interpolation algorithm (ELMMI) based on single-point interpolation, and the algorithm is a novel multi-filling technology. The relevant formula and calculation flow of the new algorithm are given below: (1) in the initial state, ELMMI divides the data set into two subsets, complete subset X_completeAnd incomplete subset X_uncom(ii) a (2) By X_uncomEach observation vector x of_nThe loop creates p estimation sets and satisfies p e [1,5 ]]Generating a complete estimation data set with a matrix size of m multiplied by n for each estimation set; (3) by using X_completeCircularly train the ELM model with x_nAll incomplete observation features in (1) are target vectors, the rest observation features are input vectors, and an incomplete subset X is estimated_uncomThe missing observation vector features in (1); (4) computing recently input observations x using a similarity function λ_nAnd complete subset X_completeThe similarity between each observation value in (the weighting coefficient of the similarity function is gamma, and gamma is 0.1-0.9); (5) interpolation algorithm searching complete subset X_completeSelecting the l nearest neighbors

Building a data subset X_l(the total number of nearest neighbors is not a fixed value, but a fraction (set to 10%) of the total number of observations); (6) with X_lUsing x as a training target_nTaking all corresponding incomplete observation features as input vectors, and training an ELM model; (7) training the ELM model twice to obtain the final ELMMI model, and estimating X_nAnd the complete observation is obtained

Adding complete subset X_completeIn (1).

ELM-based multiple interpolation algorithm (elmi):

inputting:

X_m×nas an incomplete data set

Parameter set for ELM model

Defining:

c^mismissing features being an observation

c^obsObservable features being an observed value

d^misFor incomplete observation

d^obsAs a complete observation

X is the total observation dataset

X_completeComplete subset of X

X_uncomIs a non-complete subset of X

X_estmationSet of estimates as complete observations

For some two observed values x_nAnd x_mSimilarity between them

Wherein GRC is a gray correlation coefficient and is expressed as GRC (x)_nj,x_mj)＝0.5/(|x_nj-x_mj|+0.5)

1. Decomposition of X into X_completeAnd X_uncom

2. Mixing X_uncomBy c^misThe data sets are represented and arranged from small to large

3. Normalization of X_completeAnd X_uncom

Within the p data sets, satisfying p ═ 1:1:5, the following steps are performed:

when n satisfies the formula

Proceed to step 4 to step 12

4. Using the parameter X_completeRewritten as x_nTraining the ELM model

In the formula, H is a hidden node matrix,

to output the weight matrix, the weight matrix is output,

is an observable in a complete subset

5. Using a model function f_ELMPrediction of X_uncomIs incompletely observed value x_n，x_n∈X_uncom

Rewriting a complete observation expression as

When m satisfies

Step 6 and step 7 were performed

6. Calculating weight coefficient gamma

γ＝(2β-1)/10

In the formula, β is a parameter coefficient.

7. Equation of computational similarity

M value cycle ends

8. According to the parameter X_completeWriting an equation lambda in descending order

9. When the equation value lambda is maximum, selecting one observation value to satisfy

10. ELM model training using the following equation

11. Using f_ELMEstimating missing value x_n∈X_uncomIs of the formula

Rewriting a complete observation expression as

12. Will be provided with

Instead of parameter set X_completeMiddle vector

n value cycle ends

13. Set of return estimates X_estimation(a)＝X_complete

And finishing the p value cycle.

And step 3: and (4) designing a prediction module algorithm. The invention introduces one-step advanced prediction and designs a multi-step advanced prediction algorithm as a component module of the lithium battery residual life prediction method. An extreme learning machine is designed based on ELM, and aims to complete the short-term and long-term residual life prediction tasks.

Step 3-1: and (5) verifying the extreme learning machine design. The invention designs a nucleation extreme learning machine KELM based on ELM, and the algorithm utilizes a kernel matrix of an ELM model and meets Mercer conditions, such as formula (5):

Ψ_KELM＝HH^T:f_KELM(x_i,x_j)＝h(x_i)·h(x_j) (5)

the output function of the KELM model is reconstructed as:

in the formula, Y and f_KELM(. the) respectively represents the identification matrix and the kernel function, m observed values are selected, and the formula is as follows:

the KELM model is trained using a variety of kernel functions that must satisfy the Mercer condition. The present invention trains a KELM model using wavelet functions (WAV) and Radial Basis Functions (RBF). The formulas for establishing the wavelet function and the RBF function are respectively as follows:

wherein tau, upsilon, zeta and xi are model parameters in the algorithm training process respectively.

Step 3-2: and designing a multi-step advanced prediction algorithm. Multi-step advanced prediction (MSP) is suitable for estimating the long-term remaining life of a lithium battery, and the method is divided into three categories: iterative, DirRec and direct. The invention designs a new model of multi-step advanced prediction based on a multiple interpolation technology and a DirRec method, and the model can generate a new prediction model after each calculation step.

The main characteristics are as follows: and calculating a new predicted value in the training subset, and discarding the last observation value, namely keeping the same number of the observation values of the training subset in each iterative calculation process. The new predicted value formula for estimating the L lithium battery capacities is as follows:

in the formula (f)_lFor the prediction model of L-order prediction step length, the estimation precision can be improved by carrying out cyclic training on the model by using the new prediction value.

And 4, step 4: and training an ELMMI multiple interpolation algorithm model.

Step 4-1: the invention introduces a group of missing observation values in each period of the battery aging data set

Artificially creating incomplete dataset X'_uncom. And the missing observation values are randomly imported into different data set periods, and the import probability of the last period of the training sequence is highest.

Step 4-2: and selecting the data of the voltage/current and SOC of the front 40 percent of the single battery to carry out ELMMI model training. Vector X in complete subset_completeIs rewritten as

The model training formula is as follows:

in the formula, H is a hidden node matrix,

is the output weight matrix. Using a model function f_ELMMIPredicted X'_uncomIncomplete vector of

x_n∈X_completeAnd a random missing observation is imported. Selecting the first 40% sampling value to train the model, wherein the model training formula is as follows:

step 4-3: the complete observation vector is represented as

The model training result is shown in fig. 2, and the training model selects a nonlinear model and a linear model and compares the nonlinear model and the linear model with the true value of the target parameter. FIG. 2 shows that even if the first 40% of observed values are used for training, the calculation result of the ELMMI nonlinear model provided by the invention is closest to the true value, and meanwhile, the nonlinear interpolation algorithm model used in the residual life prediction process of the lithium battery has more advantagesThe model can generate an effective predictive model with a limited number of observations.

And 5: and (3) carrying out model training on a multi-step advanced prediction method. For an incomplete data set containing 15% missing observations, a multi-interpolation algorithm is applied to fill data in an input subset, and a multi-step lead predictor is applied to calculate an RMSE value by respectively combining 5 different interpolation algorithms, as shown in Table 1. The interpolation algorithms include ELMSI, ELMMI, kNNI, LWLA, and MCMC, and the multi-step look-ahead predictor includes regression methods (RF), on-line sequential learning machine ELM (OS-ELM), radial basis function-nucleated ELM (KELM-RBF), wavelet function-nucleated ELM (KELM-WAV), and traditional ELM. The incomplete data set selected for this experiment contains three lag inputs, and model training is performed using the first 60% observations. Table 1 illustrates: (1)5 interpolation algorithms are combined with different predictors, and the predicted RMSE average values are equivalent; (2) RMSE of the KELM-RBF predictor is larger than that of other advanced predictors and reaches 18 percent, and the average value of the OS-ELM predictor is minimum and does not exceed 8.9 percent; (3) the ELMSI is combined with the OS-ELM, the RMSE average value is minimum, and the prediction effect is best.

TABLE 1 RMSE mean value (x 10) of multi-step look-ahead method combined with 5 interpolation algorithms³)

Interpolation algorithm	RF	OS-ELM	KELM-RBF	KELM-WAV	ELM
						ELMSI	6.514	1.965	15.624	5.789	2.030
kNNI	6.216	2.385	15.046	5.649	2.423
						LWLA	7.558	3.465	18.912	6.889	3.504
ELMMI	8.726	7.587	12.815	7.982	7.630
						MCMC	9.795	8.883	12.705	9.158	8.628

Experimental result 1:

the results were calculated according to table 1, yielding fig. 3. FIG. 3 shows that ELMSI is combined with different multi-step advanced prediction methods, the prediction result is the same as the result of a single-point interpolation algorithm, and the KNNI interpolation algorithm is combined with an RF predictor and a KELM-RBF predictor to obtain the optimal prediction result. In summary, the invention proposes to combine the multi-interpolation algorithm elmi with different multi-step look ahead methods, construct the multi-step look ahead predictor based on the multi-interpolation algorithm, and can realize an accurate and stable estimation process.

TABLE 2 different MS predictors combine 5 interpolation algorithms to calculate the error value E of the end life_RUL(％)

Interpolation algorithm	RF	OS-ELM	KELM-RBF	KELM-WAV	ELM
						ELMSI	-23	-10.5	-12.5	-12.5	-11
kNNI	-23	-11	-12.5	-12.5	-12.5
						LWLA	-22	-11	-12.5	-12.5	-12.5
ELMMI	-24.4	-20.4	-20.4	-20.5	-21.0
						MCMC	-46.2	-50.4	-61.2	-46.4	-44.2

Experimental results 2:

the invention designs a multi-step advanced prediction method applied to a prediction module in an integral frame, and an error value (E) of the end life is calculated by using a DirRec method in MSP (mixed Signal processor) in an experiment_RUL) The results are shown in Table 2. When the multi-step look-ahead method is combined with the elmi interpolation algorithm, the calculation error of all multi-step look-ahead (MS) predictors is low. Table 2 illustrates: (1) the MCMC has the maximum overall error value which is more than 45 percent, and the error values of the ELMSI, the kNNI and the LWLA are equivalent and are not more than 23 percent; (2) the average error value of the predictor combining ELM and different interpolation technologies is minimum, the short-term and long-term remaining service life of the lithium battery can be well estimated, the establishment time of the predictor is short, and the estimation precision is high; (3) for the one-step look-ahead process, OS-ELM and ELMSI (ELMMI) are combined and comparedThe interpolation algorithm has better prediction performance; (4) obtaining the same error value of two coring functions of multi-step advanced prediction; (5) the performance of a prediction model established by the RF predictor is better, but the performance of the predictor is obviously reduced in one-step advanced prediction; (6) both the ELM predictor and the RF predictor require more calculation time and are not suitable for the online real-time working state of the lithium battery.

Effect of the Algorithm

The invention provides a method for predicting the residual life of a lithium iron phosphate battery under the condition of lacking an observed value, designs a single-point and multiple interpolation technology, introduces an advanced prediction algorithm, and provides a complete observation data set and a prediction module.

(1) The invention develops a predictor for battery current estimation based on an electro-dynamic learning machine (ELM) design, and performs simulation comparison with predictors such as a fuzzy neural Network (NFS), a data processing Grouping Method (GMDH) and a Random Forest (RF).

(2) The invention provides an ELM-based missing observation interpolation algorithm, namely single-point interpolation (ELMSI) and multiple interpolation (ELMMI).

(3) The invention constructs a multi-form prediction network based on ELM, and realizes short-term and long-term prediction calculation at the same time.

(4) The invention integrates the ELMSI and ELMMI interpolation algorithm and is used for the residual life prediction process of the lithium battery with a missing observation value.

(5) In the invention, random missing observation values are artificially introduced into a preprocessing module, and are classified for multiple times by using ELMMI, and simultaneously, the uncertainty and the confidence coefficient of a new algorithm are calculated.

FIG. 1 illustrates:

(1) the overall frame is divided into two modules: a left preprocessing module and a right prediction module;

(2) the total input of the prediction scheme is a lithium battery observation data set, and the output is a one-step advanced prediction/multi-step advanced prediction end life estimated value and RMSE;

(3) the preprocessing module comprises a single-point interpolation algorithm (ELMSI, kNNI and LWLA) and a multiple-interpolation algorithm (MCMC and ELMMI), and the observation data set is subjected to three processes of classification, normalization and interpolation to obtain a complete data set which is input into the prediction module;

(4) the prediction module comprises a one-step advanced prediction (NAR) and a multi-step advanced prediction (an iteration method, a DirDec method and a direct method), a complete data set obtained through an interpolation algorithm is used as an input value of the predictor, and the prediction method is used for estimating the residual life (RUL) and the RMSE average value of the lithium battery and comparing the values.

FIG. 2 illustrates:

(1) FIG. 2 is a graph showing the comparison result between the non-linear model, the linear model and the real value of the target parameter.

(2) FIG. 2 shows that: even if a small number of observations are used for training, the results obtained by the nonlinear prediction model are closer to the true values than the linear regression model.

(3) The results show that: the non-linear interpolation algorithm model is used in the lithium battery residual life prediction process to be more advantageous, and the model can generate an effective prediction model by using a limited number of observed values.

FIG. 3 illustrates:

(1) FIG. 3 shows the calculation of RMSE values using a multi-step look-ahead predictor in combination with 5 different interpolation algorithms.

(2) The incomplete data set selected in the experiment contains three lag inputs, the prediction model is trained by utilizing the first 60% of observed values, and the result shows that: the predicted result from the single point interpolation algorithm, when combined by OS-ELM and ELMSI, yields the lowest RMSE value.

(3) The different curves in fig. 3 reflect the RMSE average obtained by different interpolation algorithms.

(4) As can be seen from fig. 3, the elmi is combined with various predictors, the prediction result is the same as that of the single-point interpolation algorithm, and the KNNI interpolation algorithm is combined with the RF predictor and the KELM-RBF predictor to obtain the optimal prediction result.

(5) The invention provides a method for combining a multi-interpolation algorithm ELMMI with different multi-step advance prediction methods to construct a multi-step advance predictor based on the multi-interpolation algorithm, which can realize an accurate and stable estimation process.

Claims (2)

1. A method for predicting the residual life of a lithium battery under the condition of missing observed values is characterized by comprising the following steps:

step 1: designing a total framework of a lithium battery residual life prediction method under the condition of missing observation values; calculating and predicting based on an ELM (extreme learning machine); the preprocessing module designs single-point interpolation and multiple interpolation based on an ELM algorithm, and the prediction module designs a multi-step advanced prediction method based on the traditional ELM, the nucleation ELM and the online sequential ELM;

step 2: designing an algorithm of a preprocessing module; designing single-point interpolation and multiple interpolation algorithms based on the traditional ELM algorithm;

step 2-1: introducing an ELM algorithm of an extreme learning machine; giving a group of m observation values, and randomly distributing input weight and hidden layer deviation by using ELM; ELM analyzes and adjusts output weight, and the algorithm formula is as follows:

where α is the output weight, h_iFor non-linear feature mapping, w_iTo connect the ith hidden node to the input node, b_iA threshold value of the ith hidden node; minimizing prediction error H alpha-F Y in ELM model training period²And the output weight rated value alpha is calculated according to the following formula:

wherein the content of the first and second substances,

representing an output node x_jThe error vector of (a) is calculated,

for regularization parameters, F is a function F_ELMThe solution of (1); to solve the optimization problem, the following least-norm least-squares solution of the linear system is found:

Hα＝F (4)

the least squares solution is obtained from equation (4)α＝H^TF；H^TObtaining prior information by utilizing an orthogonal projection technology;

step 2-2: designing a single-point interpolation algorithm ELMSI: the observation data set is first divided into two distinct subsets, complete subset X_completeAnd incomplete subset X_uncomThen to the subset X_uncomAny observation vector x in (2)_nBy the use of X_completeTraining an ELM model by all complete observations in (1); finally, a target feature vector X is defined_nAnd estimating X by using the trained ELM model_nThe missing observation feature of (a);

step 2-3: design of an ELMMI (multiple interpolation algorithm): in the initial state, ELMMI divides the data set into two subsets, complete subset X_completeAnd incomplete subset X_uncom(ii) a By X_uncomEach observation vector x of_nThe loop creates p estimation sets and satisfies p e [1,5 ]]Generating a complete estimation data set with a matrix size of m multiplied by n for each estimation set; by using X_completeCircularly train the ELM model with x_nAll incomplete observation features in (1) are target vectors, the rest observation features are input vectors, and an incomplete subset X is estimated_uncomThe missing observation vector features in (1); computing recently input observations x using a similarity function λ_nAnd complete subset X_completeA similarity between each of the observations; interpolation algorithm searching complete subset X_completeSelecting the l nearest neighbors

Building a data subset X_l(ii) a With X_lUsing x as a training target_nTaking all corresponding incomplete observation features as input vectors, and training an ELM model; training the ELM model twice to obtain the final ELMMI model, and estimating X_nAnd the complete observation is obtained

Adding complete subset X_completePerforming the following steps;

and step 3: designing a prediction module algorithm; introducing one-step advanced prediction, and designing a multi-step advanced prediction algorithm as a component module of the lithium battery residual life prediction method; designing a nuclear limit learning machine based on the ELM;

step 3-1: designing a coring extreme learning machine; designing a nucleation extreme learning machine KELM based on the ELM, utilizing a kernel matrix of the ELM model, and meeting Mercer conditions, such as formula (5):

Ψ_KELM＝HH^T:f_KELM(x_i,x_j)＝h(x_i)·h(x_j) (5)

the output function of the KELM model is reconstructed as:

in the formula, Y and f_KELM(. the) respectively represents the identification matrix and the kernel function, m observed values are selected, and the formula is as follows:

training a KELM model by utilizing various kernel functions, wherein the functions meet the Mercer condition; training a KELM model by utilizing a wavelet function WAV and a radial basis function RBF, and establishing formulas of the wavelet function and the RBF respectively as follows:

wherein tau, upsilon, zeta and xi are model parameters in the algorithm training process respectively;

step 3-2: designing a multi-step advanced prediction algorithm; multi-step advanced prediction MSP is classified into three major categories: iterative, DirRec and direct; designing a new model of multi-step advanced prediction based on a multiple interpolation technology and a DirRec method, wherein the model generates a new prediction model after each calculation step;

calculating a new predicted value in the training subset, and discarding the last observation value, namely keeping the same number of observation values of the training subset in each iterative calculation process; the new predicted value formula for estimating the L lithium battery capacities is as follows:

in the formula (f)_lA prediction model for predicting step length of L order;

and 4, step 4: training an ELMMI multiple interpolation algorithm model;

step 4-1: introducing a set of missing observations in each cycle of a battery aging data set

Creating incomplete data set X_u'_ncom(ii) a The missing observation values are randomly imported into different data set periods, and the import probability of the last period of the training sequence is highest;

step 4-2: selecting the voltage/current and SOC (state of charge) data of 40-50% of the front of the single battery to carry out ELMMI model training; vector X in complete subset_completeIs rewritten as

The model training formula is as follows:

in the formula, H is a hidden node matrix,

is an output weight matrix; using a model function f_ELMMIPredicted X'_uncomIncomplete vector of

x_n∈X_completeAnd introducing random missing observation values; selecting the first 40-50% sampling value to train the model, wherein the model training formula is as follows:

step 4-3: the complete observation vector is represented as

The training model selects a nonlinear model and a linear model, and compares the nonlinear model and the linear model with the real value of the target parameter;

and 5: training a multi-step advanced prediction method model; and for an incomplete data set containing less than 20% of missing observed values, performing data filling on the input subset by using a multiple interpolation algorithm.

2. The method for predicting the remaining life of the lithium battery under the condition of missing observed values as claimed in claim 1, wherein in the step 2-3, the ELM-based multiple interpolation algorithm ELMMI further comprises the following steps:

inputting: x_m×nIs an incomplete data set, is a parameter set of an ELM model;

defining: c. C^misIs a missing feature of an observed value, c^obsObservable features being an observation, d^misFor incomplete observation, d^obsFor complete observations, X is the total observation dataset, X_completeIs a complete subset of X, X_uncomIs a non-complete subset of X, X_estmationFor the estimated set of full observations,

for some two observed values x_nAnd x_mThe similarity between them;

wherein GRC is a gray correlation coefficient and is expressed as GRC (x)_nj,x_mj)＝0.5/(|x_nj-x_mj||+0.5)；

1) Decomposition of X into X_completeAnd X_uncom；

2) Mixing X_uncomBy c^misThe data sets are represented and arranged from small to large;

3) normalization of X_completeAnd X_uncom；

Within the p data sets, satisfying p ═ 1:1:5, the following steps are performed:

when n satisfies the formula

Performing steps 4) to 12);

4) using the parameter X_completeRewritten as x_nTraining an ELM model;

in the formula, H is a hidden node matrix,

to output the weight matrix, the weight matrix is output,

is an observable in a complete subset;

5) using a model function f_ELMPrediction of X_uncomIs incompletely observed value x_n，x_n∈X_uncom

Rewriting a complete observation expression as

When m satisfies

Then, step 6) and step 7) are performed;

6) calculating a weight coefficient gamma:

γ＝(2β-1)/10

in the formula, beta is a parameter coefficient;

7) calculating a similarity equation:

the value M is taken out and circulated;

8) according to the parameter X_completeWriting an equation lambda in descending order;

9) when the equation value lambda is maximum, selecting one observation value to satisfy

10) The ELM model was trained using the following formula:

11) using f_ELMEstimating missing value x_n∈X_uncomIs of the formula

Rewriting a complete observation expression as

12) Will be provided with

Instead of parameter set X_completeA medium vector;

n value cycle is finished;

13) set of return estimates X_estimation(a)＝X_complete；

And finishing the p value cycle.

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