CN117034747B - Modeling method and prediction method of energy storage lithium ion battery temperature field prediction model based on OLPP and RVFLNN - Google Patents
Modeling method and prediction method of energy storage lithium ion battery temperature field prediction model based on OLPP and RVFLNN Download PDFInfo
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Abstract
The invention provides a modeling method of an energy storage lithium ion battery temperature field prediction model based on OLPP and RVFLNN, which comprises the following steps: step one, establishing a temperature model of a battery temperature space-time variable and a first time coefficient a (t) by utilizing OLPP, and acquiring a space basis function of the temperature space-time variable according to detected battery temperature data; constructing a low-order time sequence model based on the RVFLNN, and training the low-order time sequence model by adopting the first time coefficient a (t) obtained in the step one to obtain a second time coefficientStep three, the second time coefficient obtained in the step two is processedAnd (3) replacing the first time coefficient a (t) in the temperature model in the first step, and reconstructing the temperature model to obtain a battery temperature prediction model.
Description
Technical Field
The invention relates to the field of modeling of thermal process temperature fields of lithium ion batteries, in particular to a modeling method and a prediction method of an energy storage lithium ion battery temperature field prediction model based on orthogonal local retention projection and a random vector function link neural network.
Background
In recent years, modeling methods based on space-time separation are widely applied to lithium battery temperature prediction. The method firstly learns a space basis function through a dimension reduction method, and converts a temperature variable into a time coefficient. The calonan-Lowe (KL) method is the most commonly used dimension reduction method, but the KL method is a linear method, and the internal local relation of battery temperature data is ignored, so that the spatial basis function and the time coefficient obtained through learning may not retain complete space-time distribution information. To solve this problem, some scholars introduce Local Linear Embedding (LLE) and local manifold dimension reduction methods based on laplace feature mapping (LE) and the like into a space-time modeling framework. However, LLE and LE cannot provide clear space functions, so there is a limitation that after obtaining time coefficients by a dimension reduction method, a modeling method based on space-time separation can use a traditional machine learning method, such as a space-time extreme learning machine, a space-time least square support vector machine, and the like, to build a time sequence model for revealing the functional relation between lithium battery input and time coefficients. However, the hidden layer output of the space-time extreme learning machine is easy to generate a problem of a 'disease state matrix', so that the precision loss in the inversion process is large. The space-time least square support vector machine has low learning speed, is easy to be interfered by human and has poor calculation expandability, and finally, after a time sequence model is obtained, the original battery temperature distribution can be reconstructed through space-time synthesis based on a space-time separation modeling method.
Disclosure of Invention
The invention mainly aims to provide a modeling method of an energy storage lithium ion battery temperature field prediction model based on OLPP and RVFLNN, which solves the problems that a data conversion function cannot be provided before and after dimension reduction of a local manifold dimension reduction method and a time sequence model lacks consideration of data timeliness in the traditional space-time modeling method.
In order to achieve the above purpose, the invention adopts the following technical scheme: an energy storage lithium ion battery temperature field prediction model modeling method based on OLPP and RVFLNN specifically comprises the following steps:
step one, establishing a temperature model of a battery temperature space-time variable and a first time coefficient a (t) by utilizing OLPP, and acquiring a space basis function of the temperature space-time variable according to detected battery temperature data;
constructing a low-order time sequence model based on the RVFLNN, and training the low-order time sequence model by adopting the first time coefficient a (t) obtained in the step one to obtain a second time coefficient
Step three, the second time coefficient obtained in the step two is processedAnd (3) replacing the first time coefficient a (t) in the temperature model in the first step, and reconstructing the temperature model to obtain a battery temperature prediction model.
Preferably, the first step specifically includes the following steps:
step 11, separating the battery temperature T (x, y, z, T) into orthogonal space basis functions with model order N by using OLPPFirst time coefficient a i (t)：
Step 12, OLPP obtains the i-th orthogonal basis function by solving the following optimization function
Wherein, X= [ T (: 1), T (: 2), …, T (: L) 0 )]For the temperature data matrix, T (: T) = [ T (x) 1 ,y 1 ,z 1 ,t),...，T(x n ,y n ,z n ,t)] T ；The first i-1 space basis function matrixes; d is diagonal element +>Is a diagonal matrix of (a); s is S ij Is the ith row and jth column element of the similarity matrix S; l=d-S is a laplace matrix;
step 13, calculating a space basis function
Step 14, combining the unit orthogonality properties of the space basis functions of the formula (1) to obtain a first time coefficient a i (t)：
Preferably, the similarity matrix is calculated using the following formula:
if T (: i) -T (: j) is < theta, then T (: i) is considered to be close to T (: j), and the threshold value theta can be set by the user according to actual conditions.
Preferably, the step 13 specifically includes the following steps:
step 131, defining a matrix K i-1 The method comprises the following steps:
step 132, calculating 1 st spatial basis function
Pair matrix (XDX) T ) -1 XLX T Performing feature decomposition and taking the feature vector with the minimum feature value as the 1 st space basis function
Step 133, calculating the ith spatial basis function
Step 1331, define matrix M i The method comprises the following steps:
wherein I is an identity matrix;
step 1332, pair matrix M i Performing feature decomposition, and taking the feature vector with the minimum feature value as the ith space basis function
Step 134, connectingIncorporating phi i I.e. +.>i＝i+1；
Step 135, repeat step 15 until i=n.
Preferably, in step two, the training data set is assumed to beWherein z (t) = [ a (t-1, i (t-1), E (t-1)] T A (t) = [ a ] as input of timing model 1 (t),...,a N (t)] T The second step is a time coefficient vector, and specifically includes the following steps:
step 21, constructing an enhanced node using Z (t), assuming that the matrix form of the input data is represented as z= [ Z (1) T ,z(2) T ,…,z(L 0 ) T ] T The matrix form of the output data is expressed as a= [ a (1), z (2), …, a (L 0 )]Then, the enhanced node matrix H of RVFLNN may be calculated using the following equation:
wherein G (-) is an activation function, w i And b i (i=1, …, p) is the randomly generated enhancement node weight and bias, respectively, and p is the number of enhancement nodes;
in step 22, RVFLNN combines the input data and the enhancement nodes to generate a series matrix d= [ Z, H ], where the output of RVFLNN may be expressed as:
A＝Dβ，(8)
wherein β is the output weight;
step 23, calculating beta;
step 24: will randomly generate w i And b i (i=1, …, p) and β are substituted into equation (8) when new inputOn arrival, RVFLNN predicted firstTwo time coefficients->Expressed as:
wherein,for new input-based->The resulting series matrix.
Preferably, step 23 specifically includes the steps of:
step 231, calculating β by:
where λ is the regularization constant;
step 24, solving the formula (10) to obtain a solution of β:
wherein the method comprises the steps ofIs the pseudo-inverse of matrix D.
Preferably, the step three is embodied as using the obtained time sequence model to distribute the original temperature at any time tThe reconstruction is as follows:
the invention also provides an energy storage lithium ion battery temperature field prediction method based on orthogonal local retention projection and a random vector function link neural network, which comprises the following steps:
step one, obtaining current I (t) and voltage E (t) of a lithium battery at a moment t;
step two, calculating an enhancement node of the RVFLNN:
wherein G (-) is an activation function, w i And b i (i=1, …, p) is the randomly generated enhancement node weight and bias, respectively, p is the number of enhancement nodes,
step three,
Step four,
Wherein, beta is the output weight;
step five,
Phi is an orthogonal spatial basis function;
a (t-1) in the second step isPredicted values at a previous time.
Compared with the prior art, the invention has the following beneficial effects:
OLPP not only reserves local manifold information among data, but also can provide clear space function definition, and can convert the surface temperature of a battery at any moment into a time coefficient;
the enhanced node weight and bias of the RVFLNN are randomly generated, so that the RVFLNN has a faster learning speed than the traditional space-time least square support vector machine; furthermore, the presence of regularization constants enables RVFLNN to overcome the "sick matrix" problem of spatiotemporal extreme learning machines.
Drawings
FIG. 1 is a schematic diagram of modeling of the present invention;
FIG. 2 is a diagram showing a distribution of sensors in an experimental example;
FIG. 3 is a graph of the current detected in a lithium battery;
FIG. 4 is a graph of the voltage detected in a lithium battery;
FIG. 5 is a graph of predicted battery temperature profiles using a predictive model modeled in the present invention.
Detailed Description
The following description is presented to enable one of ordinary skill in the art to make and use the invention. The preferred embodiments in the following description are by way of example only and other obvious variations will occur to those skilled in the art.
Example 1
An energy storage lithium ion battery temperature field prediction model modeling method based on orthogonal local hold projection (OLPP) and Random Vector Function Link Neural Network (RVFLNN) specifically comprises the following steps:
step one, acquiring a Space Basis Function (SBFs) of a temperature space-time variable by utilizing an orthogonal local preserving projection algorithm (OLPP), converting battery temperature data into a time coefficient, wherein the OLPP is a manifold learning method capable of preserving local features before and after data dimension reduction;
step two, constructing a low-order time sequence model based on a Random Vector Function Link Neural Network (RVFLNN) so as to reflect the time dynamics of temperature distribution;
and thirdly, performing inner product calculation on the time variable obtained by the time sequence model prediction and the space basis function, and reconstructing a temperature variable.
For the step one, it is assumed that the battery temperature dataset is { T (x i ,y i ,z i ,t),|i＝1,...,n；t＝1,2,...,L 0 X, y, z are three-dimensional coordinates in space, n is the number of sensors, t is time, L 0 For the total time length, it can be understood that L0 times of temperature data are collected, and L0 times of data are used for the total time lengthModel build, when modeling is complete, L0 is no longer needed.
The first step specifically comprises the following steps:
step 11, separating the battery temperature T (x, y, z, T) into orthogonal space basis functions with model order N by using OLPPTime coefficient a i (t)：
Step 12, OLPP obtains the i-th orthogonal basis function by solving the following optimization function
Wherein, X= [ T (: 1), T (: 2), …, T (: L) 0 )]For the temperature data matrix, T (: T) = [ T (x) 1 ,y 1 ,z 1 ,t),...,T(x n ,y n ,z n ,t)] T ；The first i-1 space basis function matrixes; d is diagonal element +>Is a diagonal matrix of (a); s is S ij Is the ith row and jth column element of the similarity matrix S; l=d-S is a laplace matrix; the similarity matrix is calculated using the following formula:
if T (: i) -T (: j) is less than theta, then considering that T (: i) is close to T (: j), and the threshold value theta can be set by a user according to actual conditions;
step 13, defining a matrix K i-1 The method comprises the following steps:
step 14, calculating the 1 st spatial basis function
Pair matrix (XDX) T ) -1 XLX T Performing feature decomposition and taking the feature vector with the minimum feature value as the 1 st space basis function
Step 15, calculating the ith space basis function
Step 151, defining a matrix M i The method comprises the following steps:
wherein I is an identity matrix;
step 152, matrix M i Performing feature decomposition, and taking the feature vector with the minimum feature value as the ith space basis function
Step 16, willIncorporating phi i I.e. +.>i＝i+1；
Step 17, repeating step 15 until i=n;
in step 18, the spatial basis functions learned by the above process are orthogonal, but in order to accurately reconstruct the space-time variables, the spatial basis functions also need to be unitized. Based on spaceThe unit orthogonality property of the basis function, in combination with equation (1), can be calculated from the time coefficient a i (t)：
From equation (6), it can be known that the battery surface temperature T (x, y, z, T) at any time can calculate the time coefficient vector a (T) = [ a ] by the obtained spatial basis function 1 (t),…,a N (t)] T 。
For the second step, the RVFLNN is used for constructing a low-order time sequence model, and the mapping relation between the current I (t), the voltage E (t) and the time coefficient a (t) is revealed. Assume the training dataset isWherein z (t) = [ a (t-1), I (t-1), E (t-1)] T A (t) = [ a ] as input of timing model 1 (t),...,a N (t)] T Is a temporal coefficient vector. The second step specifically comprises the following steps:
step 21, constructing an enhanced node by using z (t): let the matrix form of the input data be represented as z= [ Z (1) T ,z(2) T ,…,z(L 0 ) T ] T The matrix form of the output data is expressed as a= [ a (1), z (2), …, a (L 0 )]Where a is calculated by equation (6), then the enhanced node matrix H of RVFLNN may be calculated using the following equation:
wherein G (-) is an activation function, w i And b i (i=1, …, p) is the randomly generated enhancement node weight and bias, respectively, and p is the number of enhancement nodes;
in step 22, RVFLNN combines the input data and the enhancement nodes to generate a series matrix d= [ Z, H ], where the output of RVFLNN may be expressed as:
A＝Dβ，(8)
wherein β is the output weight;
step 23, calculating beta by the following formula:
where λ is the regularization constant;
step 24, solving the formula (9) to obtain a solution of beta:
wherein the method comprises the steps ofIs the pseudo-inverse of matrix D;
step 25: using randomly generated w i And b i (i=1, …, p) and β obtained by the formula (10) are substituted into the formula (8), when new inputWhen arriving, RVFLNN predicted time coefficient +.>Can be expressed as:
wherein,for a (t) predicted by equation (11), representing the same variable, only to distinguish a (t) of the modeling stage from a (t) in the final model obtained by modeling, where D (t), z (t) are also, H is a matrix form of H (t), t=1, …, L 0 ，H＝[h(1),…,h(L 0 )]. It should be noted that H is used for modeling, and when modeling is completed, only the corresponding time H (t) needs to be calculated in actual prediction.
For step three, using the obtained timing model, the raw temperature fraction at any time tClothCan be reconstructed as:
the formula (12) can be understood that a (t) is obtained by predicting the voltage and the current of the lithium battery, and the corresponding temperatures at different positions on the lithium battery at different moments are predicted according to the a (t) obtained by prediction.
Example two
The embodiment is a method for predicting the temperature of a lithium battery by using a model obtained by the modeling method of the embodiment: the method specifically comprises the following steps:
step one, obtaining current I (t) and voltage E (t) of a lithium battery at a moment t;
step two, calculating an enhancement node of the RVFLNN:
wherein G (-) is an activation function, w i And b i (i=1, …, p) is the randomly generated enhancement node weight and bias, respectively, p is the number of enhancement nodes,the initial value of a (t) is determined by the formula (6), and the initial values of I and E are determined by samples acquired during modeling, that is, the initial values are given to the values after modeling is completed;
step three,
Step four,
Wherein, beta is the output weight;
step five,
Phi is the orthogonal spatial basis function.
A (t-1) in the second step isPredicted values at a previous time. Beta and phi are parameters of the predictive model, and after the model is determined, the values of beta and phi are also determined.
Experimental example
In soft package of Li (NiCoMn) O 2 Thermal history experiments on ternary lithium batteries (LIBs) exemplify embodiments of the invention and to verify the performance and effectiveness of the invention. The standard capacity and rated voltage of the test battery were 32Ah and 3.7V, respectively, and the charge cut-off voltage and discharge cut-off voltage thereof were 4.2V and 2.75V, respectively.
As shown in fig. 2, a total of 30 thermocouple sensors (S1-S30) were uniformly distributed on the surface of the lithium battery (5 rows and 6 columns) to collect spatiotemporal temperature data. In the experiment, the cell was placed in a hot chamber, maintaining the ambient temperature at 25 ℃. Then, a 2A constant current discharge mode was used to excite the battery thermal process. Fig. 3 and 4 show the current and the resulting voltage. Fig. 5 shows the predicted temperature distribution at 500 seconds of the present patent.
The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made therein without departing from the spirit and scope of the invention, which is defined by the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (7)
1. A modeling method of an energy storage lithium ion battery temperature field prediction model based on OLPP and RVFLNN specifically comprises the following steps:
step one, establishing a temperature model of a battery temperature space-time variable and a first time coefficient a (t) by utilizing OLPP, and acquiring a space basis function of the temperature space-time variable according to detected battery temperature data;
constructing a low-order time sequence model based on the RVFLNN, and training the low-order time sequence model by adopting the first time coefficient a (t) obtained in the step one to obtain a second time coefficient
Step three, the second time coefficient obtained in the step two is processedReplacing a first time coefficient a (t) in the temperature model in the first step, and reconstructing the temperature model to obtain a battery temperature prediction model;
the first step specifically comprises the following steps:
step 11, separating the battery temperature T (x, y, z, T) into orthogonal space basis functions with model order N by using OLPPFirst time coefficient a i (t)：
Wherein x, y and z are three-dimensional space coordinates, and t is time;
step 12, OLPP obtains the i-th orthogonal basis function by solving the following optimization function
Wherein, X= [ T (: 1), T (: 2), …, T (: L) 0 )]For the temperature data matrix, T (: T) = [ T (x) 1 ，y 1 ，z 1 ，t),…,T(x n ，y n ，z n ，t)] T ，L 0 N is the number of sensors for the total duration;the first i-1 space basis function matrixes; d is diagonal element +>Is a diagonal matrix of (a); s is S ij Is the ith row and jth column element of the similarity matrix S; l=d-S is a laplace matrix;
step 13, calculating a space basis function
Step 14, combining the unit orthogonality properties of the space basis functions of the formula (1) to obtain a first time coefficient a i (t)：
2. Modeling method in accordance with claim 1, characterized in that the similarity matrix is calculated using the following formula:
if T (: i) -T (: j) is < theta, then T (: i) is considered to be close to T (: j), and the threshold value theta can be set by the user according to actual conditions.
3. Modeling method in accordance with claim 2, characterized in that step 13 comprises in particular the steps of:
step 131, defining a matrix K i-1 The method comprises the following steps:
step 132, calculating 1 st spatial basis function
Pair matrix (XDX) T ) -1 XLX T Performing feature decomposition and taking the feature vector with the minimum feature value as the 1 st space basis function
Step 133, calculating the ith spatial basis function
Step 1331, define matrix M i The method comprises the following steps:
wherein I is an identity matrix;
step 1332, pair matrix M i Performing feature decomposition, and taking the feature vector with the minimum feature value as the ith space basis function
Step 134, connectingIncorporating phi i I.e. +.>i＝i+1；
Step 135, repeat step 131-step 134 until i=n.
4. A modeling method as claimed in claim 3 wherein in step two, the training data set is assumed to beWherein z (t) = [ a (t-1), I (t-1), E (t-1)] T A (t) = [ a ] as input of timing model 1 (t)，…，a N (t)] T For the time coefficient vector, I (t-1) is the current at the time t-1, E (t-1) is the voltage at the time t-1, and the second step specifically comprises the following steps:
step 21, constructing an enhanced node using Z (t), assuming that the matrix form of the input data is represented as z= [ Z (1) T ,z(2) T ,…,z(L 0 ) T ] T The matrix form of the output data is expressed as a= [ a (1), z (2), …, a (L 0 )]Then, the enhanced node matrix H of RVFLNN may be calculated using the following equation:
wherein G (-) is an activation function, w i And b i Respectively randomly generated weight and bias of the enhancement nodes, i= (1, …, p), wherein p is the number of the enhancement nodes;
in step 22, RVFLNN combines the input data and the enhancement nodes to generate a series matrix d= [ Z, H ], where the output of RVFLNN may be expressed as:
A＝Dβ， (8)
wherein β is the output weight;
step 23, calculating beta;
step 24: will randomly generate w i And b i And beta is substituted into formula (8) when new inputOn arrival, second time coefficient of RVFLNN prediction +.>Expressed as:
wherein,for new input-based->The obtained serial matrix, h (t) is the enhancement node of RVFLNN at the moment t.
5. Modeling method in accordance with claim 4, characterized in that step 23 comprises in particular the steps of:
step 231, calculating β by:
where λ is the regularization constant;
step 232, solving the formula (10) to obtain a solution of β as follows:
wherein the method comprises the steps ofIs the pseudo-inverse of matrix D.
6. The modeling method as defined in claim 5, wherein the third step is to use the obtained time series model to distribute the original temperature at any time tThe reconstruction is as follows:
phi is the orthogonal spatial basis function.
7. The prediction method of the energy storage lithium ion battery temperature field prediction model based on the OLPP and the RVFLNN comprises the following steps of:
step one, obtaining current I (t) and voltage E (t) of a lithium battery at a moment t;
step two, calculating an enhancement node of the RVFLNN:
wherein G (-) is an activation function, w i And b i The weight and bias of the enhancement nodes are generated randomly, p is the number of the enhancement nodes,
step three,
Step four,
Wherein, beta is the output weight;
step five,
Phi is an orthogonal spatial basis function;
a (t-1) in the second step isPredicted values at a previous time.
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