CN116306248A - Lithium battery temperature field prediction method based on space-time nonlinear error compensation model - Google Patents
Lithium battery temperature field prediction method based on space-time nonlinear error compensation model Download PDFInfo
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Abstract
The invention relates to the technical field of lithium ion battery optimization, in particular to a lithium battery temperature field prediction method based on a space-time nonlinear error compensation model. The invention adopts a spectrum method to deduce a space basis function, establishes a lithium battery temperature field prediction model in a mode that an embedded extreme learning machine approaches electrochemical heat production, has the advantages of simple calculation, short time, low time cost and the like compared with a pure mechanism modeling method, and simultaneously adopts a nuclear principal component analysis algorithm to obtain a global space basis function of lithium battery temperature field prediction error distribution based on the spectrum method, does not need priori knowledge, and is convenient for establishing the model; the invention builds a space-time nonlinear error compensation model based on a kernel principal component analysis algorithm and an extreme learning machine model, and performs nonlinear error compensation on an original principal prediction model in a time domain and a space domain, so that the method has higher prediction precision and effectiveness compared with the prior art.
Description
Technical Field
The invention relates to the technical field of lithium ion battery optimization, in particular to a lithium battery temperature field prediction method based on a space-time nonlinear error compensation model.
Background
The lithium ion battery has the advantages of higher unitary voltage, higher energy density, short utilization period of renewable resources, long cycle life, no pollution and the like, and the advantages make the lithium ion battery the first choice of energy storage element manufacturers. However, the problem of safety of lithium batteries is always a very serious concern, and since the sensitivity of lithium batteries to temperature changes is very strong, too high a temperature may directly cause the combustion, explosion and other consequences of lithium batteries in the process of charging and discharging, and too low a temperature may also directly cause the reduction of the practical usable energy and power density of lithium batteries.
Therefore, an accurate lithium battery temperature model is established in the manufacturing, using and optimizing processes of the lithium battery, so that the control, diagnosis and heat supply management of the battery can be more conveniently performed, and the method has an important effect on acquiring the temperature field distribution inside the lithium battery in real time.
In the current thermal model research of lithium ion batteries, the pure mechanism theory is complex and difficult to realize. When the distributed parameter system model is completely unknown, a modeling method based on a space-time separation framework is adopted, so that the method is an efficient modeling thought. In the related technology, under the space-time separation framework, a method based on data driving such as KL is adopted to obtain a thermal model space basis function under the conditions of priori knowledge and completely unknown thermal process, however, the method often cannot obtain the best effect when the system has strong nonlinearity; on the other hand, spectroscopy is widely used to obtain analytical models under known process knowledge, based on Spatial Basis Function (SBF) expansion, dominant modes can be captured to produce low-order approximations of the full-order PDE system. However, the nonlinear errors in the time dimension, namely the time domain and the space domain, are not compensated in the current research, so that the actual lithium battery temperature prediction is still not accurate enough, and an optimization space exists.
Disclosure of Invention
The invention aims to solve the technical problem that in the prior art, errors exist in the prediction of the lithium battery temperature field due to nonlinear errors in the time domain and the space domain.
In order to solve the technical problems, an embodiment of the present invention provides a lithium battery temperature field prediction method based on a space-time nonlinear error compensation model, the lithium battery temperature field prediction method includes the following steps:
s1, establishing a lithium battery temperature field prediction model based on a spectrum method and a first extreme learning machine model for data driving;
s2, establishing a space-time nonlinear error compensation model based on a kernel principal component analysis algorithm and a second limit learning machine model;
s3, embedding the space-time nonlinear error compensation model into the lithium battery temperature field prediction model to obtain a space-time nonlinear error compensation lithium battery temperature field prediction model;
and S4, training the space-time nonlinear error compensation lithium battery temperature field prediction model, and predicting the lithium battery temperature field by using the trained space-time nonlinear error compensation lithium battery temperature field prediction model to output a prediction result.
Still further, step S1 comprises the sub-steps of:
s11, expressing a lithium battery temperature field distribution parameter system as a partial differential equation T (x, y, T), and carrying out non-uniform separation on the partial differential equation to obtain a main function V (x, y, T) and an auxiliary function w (x, y, T), wherein the main function V (x, y, T) and the auxiliary function w (x, y, T) are thermal process parameters;
S12, decoupling the main function by using a time-space separation strategy to obtain a space basis function
And a time coefficient a (t);
s13, deducing the space basis function based on the spectrum method to obtain a second main function;
s14, based on the first extreme learning machine model, establishing a data driving time sequence model related to the time coefficient and the current and the voltage in the lithium battery temperature field distribution parameter system, outputting the data driving time sequence model to obtain a second time coefficient, integrating the second main function and the second time coefficient through a time-space reconstruction strategy, and outputting to obtain the lithium battery temperature field prediction model
The lithium battery temperature field prediction model +.>
The method meets the following conditions:
where k is the spatial domain time.
Further, the step S14 further includes the steps of:
and reducing the main function according to a Galerkin algorithm.
Still further, step S2 comprises the sub-steps of:
s21, predicting model of lithium battery temperature field
Decoupling by using the space-time separation strategy to obtain a space nonlinear compensation base function delta phi (x, y) and a time nonlinear compensation coefficient e (t);
s22, performing a space nonlinear compensation basis function on the space basis function based on the kernel principal component analysis algorithm to obtain a second space nonlinear compensation basis function;
S23, establishing a time sequence prediction model of the extreme learning machine about the time nonlinear compensation coefficient and the current and the voltage in the lithium battery temperature field distribution parameter system based on the second extreme learning machine model, outputting the data driving time sequence model to obtain the second time nonlinear compensation coefficient, synthesizing the second time nonlinear compensation coefficient and the second space nonlinear compensation basis function through a space-time reconstruction strategy, and outputting to obtain the space-time nonlinear error compensation model
Further, in step S23, the second temporal nonlinear compensation coefficient is a predicted value of the temporal nonlinear compensation coefficient at time t+1.
Further, in step S4, the step of training the space-time nonlinear error compensation lithium battery temperature field prediction model includes the following substeps:
s41, defining the number of hidden layers of the first extreme learning machine model and the second extreme learning machine as l respectively 1 、l 2 The output weights are respectively beta 1 、β 2 The activation function is G;
s42, training the first extreme learning machine model and determining l 1 、β 1 ；
S43, training the second limit learning machine model and determining l 2 、β 2 ；
S44, based on the number of hidden layers of the first extreme learning machine model and the second extreme learning machine and the output weight, adding the outputs of the lithium battery temperature field prediction model and the space-time nonlinear error compensation model to obtain a predicted value T (x, y, T) of the space-time nonlinear error compensation lithium battery temperature field prediction model.
Still further, step S42 includes the sub-steps of:
s421, determining the number l of hidden layers of the first extreme learning machine model 1 And randomly go throughInitializing all connection weights and thresholds of the hidden layers of the first extreme learning machine model;
s422, selecting a time coefficient parameter set from an initial training set obtained by the lithium battery temperature field distribution parameter system as a training sample and a test sample, comparing training effects, and outputting a weight beta according to the training results 1 Updating;
s423, re-dividing the training sample and the test sample, and adjusting the number of hidden layers 1 And iterating to step S421 for training until the output of the first extreme learning machine model meets the preset iteration requirement.
Still further, step S43 includes the sub-steps of:
S431, determining the number l of hidden layers of the second extreme learning machine model 2 Randomly initializing all connection weights and thresholds of the hidden layer of the second limit learning machine model;
s432, selecting a time coefficient parameter set from an initial training set obtained by the lithium battery temperature field distribution parameter system as a training sample and a test sample, comparing training effects, and outputting a weight beta according to the training results 2 Updating;
s433, re-dividing the training samples and the test samples, and adjusting the number of hidden layers 2 And iterating to step S431 for training until the output of the second extreme learning machine model meets the preset iteration requirement.
The beneficial technical effects achieved by the invention include:
1. the spatial basis function is deduced by adopting a spectrum method, and a lithium battery temperature field prediction model is established by approaching an electrochemical heat generation mode through an embedded Extreme Learning Machine (ELM), so that the method has the advantages of simple calculation, short time, low time cost and the like compared with a pure mechanism modeling method;
2. a kernel principal component analysis algorithm (KPCA) is adopted to obtain a global space basis function of lithium battery temperature field prediction error distribution based on a spectrum method, priori knowledge is not needed, and the model is convenient to build;
3. The method has the advantages that a space-time nonlinear error compensation model based on a kernel principal component analysis algorithm and an extreme learning machine model is constructed, nonlinear error compensation is carried out on an original principal prediction model in a time domain and a space domain, and compared with the prior art, the method has higher prediction precision and effectiveness.
Drawings
Fig. 1 is a schematic flow chart of steps of a lithium battery temperature field prediction method based on a space-time nonlinear error compensation model according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a lithium battery temperature field prediction model constructed in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of a first extreme learning machine according to an embodiment of the present invention;
fig. 4 is a schematic diagram of a neural network structure of an extreme learning machine according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a constructed spatio-temporal nonlinear error compensation model according to an embodiment of the present invention
FIG. 6 is a logic schematic diagram of a lithium battery temperature field prediction model based on space-time nonlinear error compensation according to an embodiment of the present invention;
fig. 7 is a schematic diagram of a lithium iron phosphate battery cell according to an embodiment of the present invention;
FIG. 8 is a numbering and distribution diagram of a battery sensor provided by an embodiment of the present invention;
FIG. 9 is a schematic of the basis functions of a spectral method-ELM neural observer algorithm;
FIG. 10 is a schematic diagram of a comparison of temperatures predicted by the spectral method-ELM neural observer algorithm with real temperatures;
FIG. 11 is a TNAE and SNAE schematic of a spectral method-ELM neural observer algorithm;
FIG. 12 is a schematic diagram showing the comparison of temperature predicted by a spectra-ELM time nonlinear error compensation algorithm with true temperature;
FIG. 13 is a TNAE and SNAE schematic of a spectra-ELM time nonlinear error compensation algorithm;
FIG. 14 is a schematic diagram of a basis function of a prediction model of a temperature field of a lithium battery with space-time nonlinear error compensation according to an embodiment of the present invention;
FIG. 15 is a schematic diagram of a comparison of predicted temperature and actual temperature of a lithium battery temperature field prediction model with spatiotemporal nonlinear error compensation provided by an embodiment of the present invention;
fig. 16 is a schematic diagram of a TNAE and SNAE of a lithium battery temperature field prediction model with spatiotemporal nonlinear error compensation provided by an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Referring to fig. 1, fig. 1 is a schematic flow chart of steps of a lithium battery temperature field prediction method based on a space-time nonlinear error compensation model according to an embodiment of the present invention, where the lithium battery temperature field prediction method includes the following steps:
s1, establishing a lithium battery temperature field prediction model based on a spectrum method and a first extreme learning machine model for data driving.
For convenience of explanation, the embodiment of the present invention describes the derivation process of the model involved in each step. In particular, in step S1, since the internal temperature distribution of the lithium ion battery is described by a set of partial differential equations, which belong to a distribution parameter system, it is theoretically an infinite dimensional system, and therefore, some methods are required to simplify and reduce the dimensions of the model. In the embodiment of the invention, a space-time variable is decomposed into a series of space basis functions capable of containing most space information and corresponding time coefficients by adopting an optimized spectrum method, then the time coefficients are used as the output of a model, and referring to fig. 2, fig. 2 is a logic schematic diagram of a lithium battery temperature field prediction model constructed in the embodiment of the invention.
Still further, step S1 comprises the sub-steps of:
s11, expressing a lithium battery temperature field distribution parameter system as a partial differential equation T (x, y, T), and carrying out non-uniform separation on the partial differential equation to obtain a main function V (x, y, T) and an auxiliary function w (x, y, T), wherein the main function V (x, y, T) and the auxiliary function w (x, y, T) are thermal process parameters.
Specifically, according to the law of heat transfer, a general mathematical description of an industrial thermal process can be expressed by the following nonlinear PDE:
can be converted into:
wherein:
S＝(s 1 ,s 2 ,s 3 ,s 4 )，u＝(d z u 1 ,u 2 ,u 3 ,u 4 ) T 。
because the spectroscopy requires homogeneous boundary conditions, the present invention designs the helper functions w (x, y, t) to do non-homogeneous interference. After non-uniform separation, it can be described as:
T(x,y,t)＝V(x,y,t)+w(x,y,t) (3)；
wherein: w is a non-uniform term, which is derived to be constant, and the magnitude of the value is ambient temperature.
S12, decoupling the main function by using a time-space separation strategy to obtain a space basis function
And a time coefficient a (t).
The model described by the nonlinear partial differential equation is space-time coupled and cannot be directly used for on-line prediction and control. A common method is a space-time separation method, in which a space-time variable T (ST) is decoupled into a set of spaces
And corresponding time coefficient->
Usually, is->
The most dominant dynamics of DPS are obtained for the first n orders of (a). V (S, t) is therefore:
s13, deducing the space basis function based on the spectrum method to obtain a second main function.
The operators in equation (4) are uniform due to boundary conditions
Analytically derived as equation (6), learning the unit orthogonals BFs using a spectral method, the final derived form of which is:
wherein, xi in formula (6) x Not equal to 0 and ζ y Not equal to 0 is a constant coefficient related to lithium battery parameters. The eigenvalue lambda = - (lambda) x,i +λ y,j ) Rearranged by order of magnitude.
Representing a new sequence of characteristic values,/->
Is a corresponding feature function.
Wherein, the liquid crystal display device comprises a liquid crystal display device,
for operator->
The following equation holds:
for constant coefficient xi x And xi y Since the orthogonal eigenfunctions of the operators satisfy the following conditions:
considering normalization, assuming i=j, the inner product M of two identical eigenfunctions n The calculation can be performed as follows:
thus, the undetermined coefficient ζ x And xi y Can be designated as the following value such that equation (10) holds:
further, the step S14 further includes the steps of:
and reducing the main function according to a Galerkin algorithm. Although the boundary conditions of V (x, y, t) dependent PDE have been homogenized by non-uniformity separation, this model, which is still infinite in dimension, is not feasible in practical implementations. In order to build a Reduced Order Time Model (ROTM), a Galerkin (Galerkin) algorithm, one of the weighted residuals, is used for model reduction. In (4)Approximate V N The residual error of (2) is:
according to the Galerkin algorithm, the inner product of the residual and the weight function should be zero:
by replacing equations, (8) and (9) to equation (13), the following timing model RTOM can be obtained:
For practical applications, the derived ROTM may be in euler forward differential-discrete fashion, and the mathematical structure of the final time coefficient may be described as:
a(k)＝(a 1 ,a 2 ,...,a N ) T
A＝E N +ΔtA 0 ,B＝Δtk 2 B 0 ,C＝C 0 ，D＝ΔtD 0
wherein:
D 0 ＝(d 1 ,d 2 ,…，d N ) T ,
in the formula (15), Δt=1 is a sampling interval, E N Is an N-dimensional identity matrix, x r And y r Representing the specified position of m measurements, r=1, 2, …, m, W e (W, W, … W) T ，u＝(d z u 1 ,u 2 ,u 3 ,u 4 ) T 。
S14, based on the first extreme learning machine model, establishing a data driving time sequence model related to the time coefficient and the current and the voltage in the lithium battery temperature field distribution parameter system, outputting the data driving time sequence model to obtain a second time coefficient, integrating the second main function and the second time coefficient through a time-space reconstruction strategy, and outputting to obtain the lithium battery temperature field prediction model
The lithium battery temperature field prediction model +.>
The method meets the following conditions:
where k is the spatial domain time.
Electrochemical heat generation is the key to modeling the thermal process of the battery. Such heat generation may be analytically captured based on an equivalent circuit model or a first principle model. However, the heat generation derived from the equivalent circuit model may lack sufficient accuracy due to the simplishment. The first principle model with reliable accuracy is computationally complex, while requiring accurate parameters. In an embodiment of the invention, a common machine learning algorithm Extreme Learning Machine (ELM) is used to estimate u 1 The data-driven machine learning method using the measurement data is simple and self-adaptive, and can better approximate electrochemistryHeat generation u 1 The first extreme learning machine model is shown in FIG. 3, which better fits the spatio-temporal dynamics of the DPS.
Because of the global precision of the spectrum method, the estimated temperature of the k-order time steps of any point in the whole space domain can be rebuilt through T/S synthesis, and finally, the established space-time prediction model of the lithium battery temperature field based on the spectrum method and the data drive of the extreme learning machine is shown as a formula (16).
S2, establishing a space-time nonlinear error compensation model based on a kernel principal component analysis algorithm and a second extreme learning machine model.
The kernel principal component analysis algorithm (KPCA) is a method for introducing kernel skills into principal component analysis, the processing capacity of a kernel function on nonlinear data is utilized, the conversion from an input space to a characteristic space is realized through nonlinear mapping phi, original linear inseparable data is changed into linear inseparable data, and then the data is processed according to the idea of PCA processing the linear inseparable data.
The principle is as follows: for M samples x of input space k (k＝1,...,M)，x k ∈R N Make the following
Its autocorrelation matrix is:
for the general PCA method, i.e. by solving the characteristic equation:
Cν＝λν (18)；
obtaining a characteristic value with the largest contribution rate and a characteristic vector corresponding to the characteristic value, introducing a nonlinear characteristic mapping function phi, and enabling sample points x1, x2 in an input space to be converted into sample points in the characteristic space
And assuming that:
the autocorrelation matrix in feature space F is:
autocorrelation matrix of pair (20)
Calculating the characteristic value and the characteristic vector, and obtaining the following formula:
all eigenvectors satisfying equation (21) for λ+.0 are eigenvectors
In the space of the collection generation. There are two useful information available at this time:
first, an equivalent equation of formula (20) can be obtained:
second, there is a corresponding set of coefficients, which can be written as:
substitution of the formula (20) and the formula (23) into the formula (22) can be obtained:
where k=1,..m.
To solve equation (24), for the right side of its equation, an n×n matrix K is defined:
two matrices are defined:
the n×n K matrix is an introduced kernel matrix that is computable by substituting data in the original space into a kernel function.
N x N vector α, where the j-th element is the parameter α j 。
Thus, formula (24) may be written as follows:
since the equation (26) has a kernel matrix K at both ends, the problem of obtaining the characteristic value of the above equation can be changed to:
Order the
The eigenvalues representing the kernel matrix K, namely:
wherein the method comprises the steps of
Representing a correlation matrix->
Whereby the following standard form can be changed to the j-th eigenvalue of the formula (27):
Kα＝λα (29)；
to obtain a feature vector per unit length, it is normalized, and according to (23) and (29), α needs to be processed as follows:
where p is the number of non-zero eigenvalues in the kernel matrix.
As can be seen from equation (19), assuming that the data in the feature space is centered, this is not the case in practice, and the following processing is required to obtain a core matrix of normalized data:
wherein, the liquid crystal display device comprises a liquid crystal display device,
defining a cumulative contribution rate:
wherein lambda is i The method is characterized in that the characteristic values corresponding to the kernel matrix are used for representing the quantity of the contained information by the size of the characteristic values, the ratio of the sum of the first n characteristic values to the sum of all characteristic values represents the ratio of the information contained in the whole characteristic space in the first n characteristic vectors, and when the calculated accumulated contribution rate meets the requirement, the information of the whole characteristic vector space can be represented by the first n characteristic components. Wherein the first n components of the feature vector, also called principal components of the feature vector, are typically selected from E i >0.99999。
The extreme learning machine (Extreme Learning Machine, ELM) is a novel intelligent data learning method, the essence of the ELM is still a single hidden layer feedforward neural network, and the extreme learning machine is characterized in that the initial input layer weight and bias are randomly selected and then do not need to be updated, the whole network training can be completed only by allowing the value obtained after the input data is input into the network to update the output layer weight through a matrix, and the calculation cost is greatly reduced, and the neural network structure of the extreme learning machine is shown as a figure 4.
The ELM training process is mainly divided into two phases: the first stage, the hidden layer parameters are initialized randomly, then some nonlinear mapping is used as an activation function, the input data is mapped to a first stage, the hidden layer parameters are initialized randomly, then some nonlinear mapping is used as an activation function, and the input data is mapped to a new feature space (ELM feature space). In short, the weights and deviations on ELM hidden layer nodes are randomly generated. The random feature mapping stage is different from many existing learning algorithms, such as SVM using kernel functions for feature mapping, using a boltzmann-restriction machine (RBM) in deep neural networks, automatic encoder, automatic decoder for feature learning, the nonlinear mapping function in ELM can be any nonlinear piecewise continuous function. In ELM, hidden layer node parameters are randomly generated from any continuous probability distribution, rather than being determined through training, resulting in significant efficiency advantages over conventional BP neural networks.
Through the first stage, w, b have been randomly generated to determine, from which the hidden layer output H can be calculated according to a formula. In the second stage of ELM learning, only the weights β of the output layer need be solved. In order to obtain the weight beta with good effect on the training sample set, the minimum training error needs to be ensured, and the minimum square difference between the output of the network and the sample label T can be used as the evaluation training error, so that the solution with the minimum objective function is the optimal solution. Namely, solving a weight beta connecting the hidden layer and the output layer by a method of minimizing an approximate square error, wherein an objective function is as follows:
min||Hβ-T||| 2 ,β∈R L×m (33)；
Where H is the output matrix of the hidden layer and T is the target matrix of the training data:
the optimal solution of equation (17) can be derived from knowledge of the line generation and matrix theory as:
wherein, the liquid crystal display device comprises a liquid crystal display device,
is Moore-Penrose generalized inverse of matrix H.
Because the lithium ion battery temperature field distribution parameter system has strong nonlinearity and uncertainty, the physical model is difficult to be made very precisely by learning only by a spectrum method, and a space-time nonlinearity error delta T exists. Therefore, a corresponding compensation model is needed to improve the accuracy of the original model. The embodiment of the invention starts from the dimension of the space domain and the time domain, and performs error compensation on the space-time nonlinear error delta T of the original model by establishing a space-time nonlinear error compensation model. Referring to fig. 5, fig. 5 is a logic schematic diagram of a space-time nonlinear error compensation model constructed according to an embodiment of the invention. Still further, step S2 comprises the sub-steps of:
s21, predicting model of lithium battery temperature field
And decoupling by using the space-time separation strategy to obtain a space nonlinear compensation base function delta phi (x, y) and a time nonlinear compensation coefficient e (t).
S22, performing space nonlinear compensation base functions on the space base functions based on the kernel principal component analysis algorithm to obtain second space nonlinear compensation base functions.
S23, establishing a time sequence prediction model of the extreme learning machine about the time nonlinear compensation coefficient and the current and the voltage in the lithium battery temperature field distribution parameter system based on the second extreme learning machine model, outputting the data driving time sequence model to obtain a second time nonlinear compensation coefficient, and supplementing the second time nonlinear compensation coefficient and the second space nonlinear through a space-time reconstruction strategySynthesizing the compensation basis functions and outputting to obtain the space-time nonlinear error compensation model
According to the structure of fig. 5, the implementation of the compensation model constructed in the embodiment of the invention firstly performs space-time separation on the prediction error temperature of the original model to obtain a time nonlinear error time coefficient, and the space basis function used in the separation process is still obtained by deduction through a KPCA principal component analysis method, namely the learning process of the space basis function is the space nonlinear error compensation process of the model; then building ELM time sequence prediction model, using current voltage I (t), U (t) and error time coefficient e (t) of previous moment as time sequence model input so as to obtain time coefficient prediction value of next moment time nonlinear error
Finally, carrying out space-time reconstruction with the space basis function to obtain a prediction compensation value of nonlinear error ++ >
And S3, embedding the space-time nonlinear error compensation model into the lithium battery temperature field prediction model to obtain a space-time nonlinear error compensation lithium battery temperature field prediction model.
The step is to embed the time nonlinear error compensation model constructed in the step S2 into the main prediction model frame in the step S1, so as to obtain a lithium battery temperature field prediction model based on space-time nonlinear error compensation. A specific implementation framework is shown in fig. 6.
In the embodiment of the invention, for the collected prediction error temperature data delta T (x, y, T), a KPCA method is adopted to learn a space basis function, and the method mainly comprises the following steps:
1. by combining the equation (25) and the equation (31) based on the spatial-temporal distribution data of the error temperature of the input space, a core matrix centering correction matrix can be obtained
2. Using Jacobi iteration, a correction kernel matrix is found according to equation (27)
Eigenvalue lambda of 1 ′,...,λ′ N And feature vector alpha' 1 ，...，α′ N ；
3. The obtained feature vector alpha 'is paired according to the formula (26)' 1 ，...，α′ N Normalizing if a feature vector alpha of unit orthogonalization is required to be obtained 1 ，...，α N Schmitt orthogonalization of the feature vectors is also required;
4. rearranging the corresponding feature vectors according to the sequence of the feature values from large to small;
5. Selecting a proper accumulated contribution rate E as a basis for determining the number of the space basis functions, and sequentially calculating the accumulated contribution rates E of the first n principal components 1 ,...,E n When E n >E, selecting the first N eigenvectors as principal components;
6. substituting the principal component obtained in the fifth step into the following formula (36) by snapshot, obtaining a corresponding spatial basis function, and then converting the discrete error distribution spatial basis function into a spatially continuous basis function by cubic spline interpolation
And S4, training the space-time nonlinear error compensation lithium battery temperature field prediction model, and predicting the lithium battery temperature field by using the trained space-time nonlinear error compensation lithium battery temperature field prediction model to output a prediction result.
Further, in step S4, the step of training the space-time nonlinear error compensation lithium battery temperature field prediction model includes the following substeps:
s41, defining the number of hidden layers of the first extreme learning machine model and the second extreme learning machine as l respectively 1 、l 2 The output weights are respectively beta 1 、β 2 The activation function is G.
S42, training the first extreme learning machine model and determining l 1 、β 1 。
Still further, step S42 includes the sub-steps of:
S421, determining the number l of hidden layers of the first extreme learning machine model 1 Randomly initializing all connection weights and thresholds of the hidden layers of the first extreme learning machine model;
s422, selecting a time coefficient parameter set from an initial training set obtained by the lithium battery temperature field distribution parameter system as a training sample and a test sample, comparing training effects, and outputting a weight beta according to the training results 1 Updating;
s423, re-dividing the training sample and the test sample, and adjusting the number of hidden layers 1 And iterating to step S421 for training until the output of the first extreme learning machine model meets the preset iteration requirement.
S43, training the second limit learning machine model and determining l 2 、β 2 。
Still further, step S43 includes the sub-steps of:
s431, determining the number l of hidden layers of the second extreme learning machine model 2 Randomly initializing all connection weights and thresholds of the hidden layer of the second limit learning machine model;
s432, selecting a time coefficient parameter set from an initial training set obtained by the lithium battery temperature field distribution parameter system as a training sample and a test sample, comparing training effects, and outputting a weight beta according to the training results 2 Updating;
s433, the training sample and the training sampleThe test sample is repartitioned and the number of hidden layers is adjusted 2 And iterating to step S431 for training until the output of the second extreme learning machine model meets the preset iteration requirement.
S44, based on the number of hidden layers of the first extreme learning machine model and the second extreme learning machine and the output weight, adding the outputs of the lithium battery temperature field prediction model and the space-time nonlinear error compensation model to obtain a predicted value T (x, y, T) of the space-time nonlinear error compensation lithium battery temperature field prediction model.
The embodiment of the invention provides the following comparative examples according to the lithium battery temperature field prediction method based on the space-time nonlinear error compensation model:
comparative example one
Firstly, for a lithium battery temperature field prediction model using a spectrum method-ELM, the embodiment of the invention and the prior art are verified by using lithium iron phosphate battery cells as shown in fig. 7, when the discharge rate is higher, the temperature uniformity of the battery is poorer, and the nonlinearity of the space data is stronger, so that a larger discharge rate should be selected. The data of the embodiment of the invention are obtained based on a com sol lithium battery electrochemical-thermal coupling model, and discharge is carried out at a discharge rate of 5C under the excitation of a random input signal. The battery cathode is set to be grounded, the discharge cut-off voltage is set to be 2.3V, the output temperature recording interval time is 1s, 1370 groups of data are obtained in total, each group of data comprises temperature values of 20 points, the first 1100 groups of data are used as model training samples, and the last 270 groups of data are used as test samples for verifying model effects. The ELM neural network model inputs signals to select the current and terminal voltage of the lithium battery during discharging, and the output signals are predicted time coefficients. The simulation platform includes compilation of simulation programs all implemented in the context of matlab 2018 b.
Fig. 8 is a number and distribution diagram of battery sensors, with a spacing of 2.5cm in the x-axis in the lateral direction and 6cm in the y-axis in the longitudinal direction, for a total of 20, and detailed parameters of the battery are shown in table 1.
Table 1 battery detailed parameter table
Firstly, carrying out dimension reduction on the obtained 1370 group of lithium battery temperature distribution data by adopting a space basis function deduced by a spectrum method to obtain the space basis function meeting the requirement. When the cumulative contribution rate is selected 0.9999995, 3 spatial basis functions are obtained, that is, the order of the spatial basis functions is 3. The specific case is shown in fig. 9.
And secondly, after the space basis function is obtained, the corresponding low-order time coefficient can be obtained by projecting the space-time data onto the space basis function according to the formula (5). The 1370 set of temperature spatiotemporal data can obtain 1370 set of time coefficients, the first 1100 sets are used as training samples of the model, and the last 270 sets are used as test samples for verifying the effect of the model. After grouping, selecting a certain ELM network structure, randomly initializing various parameters of the network, selecting a current signal I (t) and a terminal voltage U (t) when the lithium battery is discharged and a time coefficient a (t) at the current moment as inputs of a model, and training the model by taking electrochemical heat generation U (t) at the current moment as outputs. After training the model, inputting the input signals of the rear 270 groups into the model, and obtaining the low-order time coefficient of the next moment through the Galerkin method and the Euler forward difference formula (15) 
Then, according to the formula (13), the predicted low-order time coefficient and the space basis function obtained in the previous step are subjected to space reconstruction to obtain +.>
The temperature changes of the 3 groups of data representing three different positions are respectively selected from the 20 groups of data to be used as comparison.
To illustrate the spatial distribution as much as possible, the temperatures of the three sensors S2, S15, S18 distributed on the surface of the battery near the upper, middle and bottom are selected to test the model effect, and fig. 10 shows the comparison of the temperatures predicted by the spectrum method and ELM neural observer algorithm with the real temperatures, and the number of hidden neurons of the neural network is 55.
In addition, the embodiment of the invention directly uses the common error value
At the same time, RMSE, TNSE, RNSE indexes are also introduced as model error measurement standards. The expression method is as follows:
1. root Mean Square Error (RMSE):
where L is the time length and S is the number of sample points collected.
2. Time standard absolute error (TNAE):
3. spatial standard absolute error (SNAE):
the root mean square error of the temperature prediction based on the spectral and data-driven prediction model can be calculated as 0.0567 according to equation (20). TNAE and SNAE obtained from the formulas (21) and (22) are shown in FIG. 11. The time average of TNAE and SNAE in FIG. 11 were chosen as TNAE and SNAE for this model, respectively, so RMSE, TNAE, SNAE based on the spectral and data-driven predictive algorithm models were 0.0567, 0.1475, 0.0424, respectively. It can be seen that the model has a higher error difference in two positions than in other positions, one being at the bottom right corner furthest from the positive and negative lugs No. 16 and No. 20 sensors.
Comparative example two
Temperature field prediction model for spectra-ELM time nonlinear error compensation:
first, 1369 sets of temperature error data Δt (x, y, T) obtained by subtracting the 1369 sets of lithium battery temperature distribution data obtained by prediction in comparative example one from the real data are obtained, and the time points corresponding to these data are (2 s-1370 s). And then reducing the dimension of the space basis function deduced by adopting a spectrum method to obtain the space basis function meeting the requirement.
Secondly, according to the formula (5), the corresponding nonlinear error low-order time coefficient f (T) can be obtained by projecting error temperature space-time data deltaT (x, y, T) onto a space basis function. The 1369 set of temperature spatiotemporal data can obtain 1369 sets of time coefficients, and the front 1099 sets, namely the corresponding (2 s-1100 s) moments, are used as training samples of the model, and the rear 270 sets are also used as test samples for verifying the model effect. After grouping, selecting a certain ELM network structure, randomly initializing various parameters of the network, selecting a current signal I (t) and a terminal voltage U (t) when the lithium battery is discharged and a nonlinear error time coefficient f (t) at the current moment as inputs of a model, and taking an electrochemical heat generation f (t+1) at the next moment as outputs to train the model. After training the model, inputting the input signals of the rear 270 groups into the model, and obtaining the nonlinear error time coefficient at the next moment 
Then, according to the formula (13), the predicted low-order time coefficient and the space basis function obtained in the previous step are subjected to space reconstruction to obtain the predicted error temperature +.>
Finally, the predicted temperature data obtained by the predictive model in the last step +.>
And adding the compensation to obtain the final predicted temperature T (x, y, T).
Similarly, 3 sets of data s2, s15, s18, respectively, from the 20 sets of data, represent the temperature changes at three different locations, as shown in fig. 12. The time average of the maximum value and the SNAE in the TNAE in the graph was chosen as the TNAE and SNAE of the model, respectively, with values 0.0917, 0.0243, respectively. Wherein RMSE is 0.0337 as shown in fig. 13.
Comparative example three
The lithium battery temperature field prediction model based on KPCA-ELM space-time nonlinear error compensation constructed according to the embodiment of the invention:
in the first step, the method of obtaining data is the same as that in comparative example two. The 1369 set of lithium battery temperature distribution data obtained by prediction in comparative example one was subtracted from the real data to obtain 1369 set of temperature error data Δt (x, y, T) corresponding to the time points (2 s-1370 s). And (3) reducing the dimension of the obtained 1369-group lithium battery temperature distribution data by adopting a space basis function deduced by KPCA to obtain the space basis function meeting the requirement. When the cumulative contribution rate is selected 0.9999995, 3 spatial basis functions are obtained, that is, the order of the spatial basis functions is 3. The distribution of the spatial basis functions can be obtained by cubic spline interpolation, as shown in fig. 14.
Secondly, according to the formula (5), the corresponding nonlinear error low-order time coefficient f (T) can be obtained by projecting error temperature space-time data deltaT (x, y, T) onto a space basis function. The 1369 set of temperature spatiotemporal data can obtain 1369 sets of time coefficients, and the front 1099 sets, namely the corresponding (2 s-1100 s) moments, are used as training samples of the model, and the rear 270 sets are also used as test samples for verifying the model effect. After grouping, selecting a certain ELM network structure, randomly initializing various parameters of the network, selecting a current signal I (t) and a terminal voltage U (t) when the lithium battery is discharged and a nonlinear error time coefficient e (t) at the current moment as inputs of a model, and training the model by taking the nonlinear error time coefficient e (t+1) at the next moment as outputs. After training the model, inputting the input signals of the rear 270 groups into the model, and obtaining the nonlinear error time coefficient at the next moment
Then, according to the formula (13), the predicted low-order time coefficient and the space basis function obtained in the previous step are subjected to space reconstruction to obtain the predicted error temperature +.>
Finally, the predicted temperature data obtained by the predictive model in the last step +.>
And adding the compensation to obtain the final predicted temperature T (x, y, T).
Similarly, 3 sets of data s2, s15, s18, respectively, are selected from the 20 sets of data to represent the temperature changes at three different locations for comparison, as shown in fig. 15.
And thirdly, verifying the compensation effect of the KPCA-ELM space-time nonlinear error compensation model. The temperature prediction data is compared with the space-time prediction data obtained by the method of only performing time nonlinear error in the first comparative example, and indexes such as Root Mean Square Error (RMSE), time standard absolute error (TNSE) and space standard absolute error (RNSE) are used as model error measurement standards by comparing the prediction conditions of 3 points at the same position. The conditions of the obtained prediction results of the two modeling methods are compared through the conditions.
The root mean square error of the temperature prediction based on the spectral and data-driven prediction model can be calculated as 0.0230 according to equation (20). The TNAE and SNAE obtained from formulas (21) and (22) are shown in FIG. 16, and the time average value of the maximum value and SNAE in TNAE in the graph is selected as TNAE and SNAE of the model, respectively, and the values are 0.0703 and 0.0182, respectively.
In order to verify the model effect constructed in the embodiment of the present invention, the compensation model prediction effects of the first, second and third comparative examples are compared, and the specific cases are shown in table 2.
Table 2 comparative example Compensation model prediction results comparison table
The result analysis of the table shows that the prediction effect after the time nonlinear compensation optimization of the spectral method data driving model is improved considerably compared with the prediction effect before the optimization. The RMSE value is reduced to 0.023, the tnae and the SANE values are respectively reduced by about 0.020 and about 0.006, and the rest error values except for 206 in the spatial standard absolute error diagram are relatively close and the whole is relatively gentle, which shows that the compensation of the spatial nonlinearity of the model is obvious, therefore, the results fully show that compared with the space-time nonlinearity error compensation optimization strategy used in the embodiment of the invention, the temperature field prediction model only carrying out the time nonlinearity error compensation has better effect.
The beneficial technical effects achieved by the invention include:
1. the spatial basis function is deduced by adopting a spectrum method, and a lithium battery temperature field prediction model is established by approaching an electrochemical heat generation mode through an embedded Extreme Learning Machine (ELM), so that the method has the advantages of simple calculation, short time, low time cost and the like compared with a pure mechanism modeling method;
2. a kernel principal component analysis algorithm (KPCA) is adopted to obtain a global space basis function of lithium battery temperature field prediction error distribution based on a spectrum method, priori knowledge is not needed, and the model is convenient to build;
3. The method has the advantages that a space-time nonlinear error compensation model based on a kernel principal component analysis algorithm and an extreme learning machine model is constructed, nonlinear error compensation is carried out on an original principal prediction model in a time domain and a space domain, and compared with the prior art, the method has higher prediction precision and effectiveness.
Those skilled in the art will appreciate that implementing all or part of the above-described methods in accordance with the embodiments may be accomplished by way of a computer program stored on a computer readable storage medium, which when executed may comprise the steps of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM) or the like.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
From the above description of the embodiments, it will be clear to those skilled in the art that the above-described embodiment method may be implemented by means of software plus a necessary general hardware platform, but of course may also be implemented by means of hardware, but in many cases the former is a preferred embodiment. Based on such understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art in the form of a software product stored in a storage medium (e.g. ROM/RAM, magnetic disk, optical disk) comprising instructions for causing a terminal (which may be a mobile phone, a computer, a server, an air conditioner, or a network device, etc.) to perform the method according to the embodiments of the present invention.
While the embodiments of the present invention have been illustrated and described in connection with the drawings, what is presently considered to be the most practical and preferred embodiments of the invention, it is to be understood that the invention is not limited to the disclosed embodiments, but on the contrary, is intended to cover various equivalent modifications and equivalent arrangements included within the spirit and scope of the appended claims.
Claims (8)
1. The lithium battery temperature field prediction method based on the space-time nonlinear error compensation model is characterized by comprising the following steps of:
s1, establishing a lithium battery temperature field prediction model based on a spectrum method and a first extreme learning machine model for data driving;
s2, establishing a space-time nonlinear error compensation model based on a kernel principal component analysis algorithm and a second limit learning machine model;
s3, embedding the space-time nonlinear error compensation model into the lithium battery temperature field prediction model to obtain a space-time nonlinear error compensation lithium battery temperature field prediction model;
and S4, training the space-time nonlinear error compensation lithium battery temperature field prediction model, and predicting the lithium battery temperature field by using the trained space-time nonlinear error compensation lithium battery temperature field prediction model to output a prediction result.
2. The method for predicting the temperature field of a lithium battery based on a space-time nonlinear error compensation model as set forth in claim 1, wherein the step S1 comprises the sub-steps of:
s11, expressing a lithium battery temperature field distribution parameter system as a partial differential equation T (x, y, T), and carrying out non-uniform separation on the partial differential equation to obtain a main function V (x, y, T) and an auxiliary function w (x, y, T), wherein the main function V (x, y, T) and the auxiliary function w (x, y, T) are thermal process parameters;
S12, decoupling the main function by using a time-space separation strategy to obtain a space basis function
And a time coefficient a (t);
s13, deducing the space basis function based on the spectrum method to obtain a second main function;
s14, based on the first extreme learning machine model, establishing a data driving time sequence model related to the time coefficient and the current and the voltage in the lithium battery temperature field distribution parameter system, outputting the data driving time sequence model to obtain a second time coefficient, integrating the second main function and the second time coefficient through a time-space reconstruction strategy, and outputting to obtain the lithium battery temperature field prediction model
The lithium battery temperature field prediction model +.>
The method meets the following conditions:
where k is the spatial domain time.
3. The method for predicting the temperature field of a lithium battery based on a space-time nonlinear error compensation model as set forth in claim 2, further comprising the step of, before step S14:
and reducing the main function according to a Galerkin algorithm.
4. The lithium battery temperature field prediction method based on a space-time nonlinear error compensation model according to claim 2, wherein the step S2 comprises the following sub-steps:
s21, predicting model of lithium battery temperature field 
Decoupling by using the space-time separation strategy to obtain a space nonlinear compensation base function delta phi (x, y) and a time nonlinear compensation coefficient e (t);
s22, performing a space nonlinear compensation basis function on the space basis function based on the kernel principal component analysis algorithm to obtain a second space nonlinear compensation basis function;
s23, establishing a time sequence prediction model of the extreme learning machine about the time nonlinear compensation coefficient and the current and the voltage in the lithium battery temperature field distribution parameter system based on the second extreme learning machine model, outputting the data driving time sequence model to obtain the second time nonlinear compensation coefficient, synthesizing the second time nonlinear compensation coefficient and the second space nonlinear compensation basis function through a space-time reconstruction strategy, and outputting to obtain the space-time nonlinear error compensation model
5. The method for predicting the temperature field of a lithium battery based on a space-time nonlinear error compensation model as set forth in claim 4, wherein in step S23, the second time nonlinear compensation coefficient is a predicted value of the time nonlinear compensation coefficient at time t+1.
6. The method for predicting the temperature field of a lithium battery based on a space-time nonlinear error compensation model as set forth in claim 4, wherein in step S4, the step of training the space-time nonlinear error compensation lithium battery temperature field prediction model comprises the sub-steps of:
S41, defining the number of hidden layers of the first extreme learning machine model and the second extreme learning machine as l respectively 1 、l 2 The output weights are respectively beta 1 、β 2 The activation function is G;
s42, training the first extreme learning machine model and determining l 1 、β 1 ；
S43, training the second limit learning machine model and determining l 2 、β 2 ；
S44, based on the number of hidden layers of the first extreme learning machine model and the second extreme learning machine and the output weight, adding the outputs of the lithium battery temperature field prediction model and the space-time nonlinear error compensation model to obtain a predicted value T (x, y, T) of the space-time nonlinear error compensation lithium battery temperature field prediction model.
7. The method for predicting the temperature field of a lithium battery based on a space-time nonlinear error compensation model as set forth in claim 6, wherein the step S42 comprises the substeps of:
s421, determining the number l of hidden layers of the first extreme learning machine model 1 Randomly initializing all connection weights and thresholds of the hidden layers of the first extreme learning machine model;
s422, from the aboveThe initial training set obtained by the lithium battery temperature field distribution parameter system selects a time coefficient parameter set as a training sample and a test sample, and compares training effects, and outputs weight beta according to the training results 1 Updating;
s423, re-dividing the training sample and the test sample, and adjusting the number of hidden layers 1 And iterating to step S421 for training until the output of the first extreme learning machine model meets the preset iteration requirement.
8. The method for predicting the temperature field of a lithium battery based on a space-time nonlinear error compensation model as set forth in claim 6, wherein the step S43 comprises the substeps of:
s431, determining the number l of hidden layers of the second extreme learning machine model 2 Randomly initializing all connection weights and thresholds of the hidden layer of the second limit learning machine model;
s432, selecting a time coefficient parameter set from an initial training set obtained by the lithium battery temperature field distribution parameter system as a training sample and a test sample, comparing training effects, and outputting a weight beta according to the training results 2 Updating;
s433, re-dividing the training samples and the test samples, and adjusting the number of hidden layers 2 And iterating to step S431 for training until the output of the second extreme learning machine model meets the preset iteration requirement.
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