A method and system for spatiotemporal modeling of lithium battery temperature field

Abstract

The present invention discloses a method and system for spatiotemporal modeling of a lithium battery temperature field. First, the spatiotemporal temperature data is non-uniformly separated to obtain the ambient temperature and the heat generation temperature, then the heat generation temperature is separated in time and space, and the spatial basis function and its corresponding low-order time coefficient are obtained by the spectral method; then the width learning network is used to construct a timing model and train it to obtain a trained timing model based on the width learning network; the low-order time coefficient, input current, and working voltage are input into the timing model to obtain a predicted low-order time coefficient, the low-order time coefficient and the spatial basis function are reconstructed in time and space to obtain the predicted heat generation temperature, and finally the heat generation temperature and the ambient temperature are non-uniformly synthesized to obtain the predicted spatiotemporal temperature data. The present invention can fully reflect the uneven distribution of temperature, and has a small amount of calculation, a fast speed, and can effectively obtain global spatial information.

Description

Technical Field

[0001] The present invention relates to the technical field of lithium battery temperature field testing, and in particular to a lithium battery temperature field spatiotemporal modeling method and system. Background Art

[0002] Since the 20th century, with the advent and commercialization of lithium batteries, lithium batteries have been widely used in electric vehicles, 3C electronic products, mobile energy storage systems and other fields due to their better discharge performance and recyclability. The performance of lithium batteries is closely related to temperature. Therefore, effective temperature prediction is crucial to the performance and safety of lithium batteries. However, due to the characteristics of spatiotemporal coupling and strong nonlinearity of the temperature field of lithium batteries, it is very difficult to model.

[0003] The earliest thermal model was a centralized pure thermal model proposed by Bernardi. This model uses entropy increase reactions and internal resistance to establish a simplified heat generation model from the perspective of energy conservation. Manuel et al. developed an electrothermal model of a single lithium-ion battery in the Simulink-Simscape environment. The model is divided into two parts: electrical and thermal models, which are then coupled. The heat generated by the battery is estimated using the lumped heat source method. Chiew et al. established a three-dimensional electrochemical-thermal coupling model of a commercial 26,650LiFePO4 battery to study the thermal characteristics of the battery. The proposed numerical method includes a pseudo-two-dimensional electrochemical model and a three-dimensional thermal lumped model. The thermal characteristics of the battery were studied during the discharge process at a range of temperatures and discharge rates. However, the lumped thermal model cannot fully reflect the uneven distribution of temperature in the actual battery.

[0004] An et al. established a one-dimensional electrochemical thermocouple model to simulate several constant current discharge processes of single-cell and multi-cell batteries under different physical conditions. The temperature distribution in the battery was studied based on a multi-unit one-dimensional model. KIM et al. established a two-dimensional thermal model based on the one-dimensional model, taking into account the inhomogeneity of temperature in space. By analyzing the distribution changes of various physical parameters on a certain cross section, more accurate calculation results can be obtained. Xu et al. established a three-dimensional thermal model, no longer considering only the temperature conduction of a certain cross section, but conducting it inside the entire battery body or even between battery bodies, and the results are closer to the actual situation. However, the above method uses the finite element method (FEM) and the finite difference method (FDM). Although the finite element method (FEM) and the finite difference method (FDM) are widely used, their computational cost for solving is very high, and they do not fully consider the time-space coupled thermodynamics. Therefore, it is not suitable to use the above method to calculate the temperature of lithium batteries during the actual use of lithium batteries.

[0005] Kurhunen-Loeve (KL) decomposition is an effective method to extract spatial dynamics from measurement data, but it requires covering the entire area with as many sensors as possible, which is difficult to do in practice.

[0006] Therefore, the current prediction and analysis of the temperature field of lithium batteries has the following problems: 1. The lumped thermal model cannot fully reflect the uneven temperature distribution in the actual battery; 2. The finite element method and finite difference method are too computationally intensive and inefficient; 3. The traditional data-driven model requires as many sensors as possible to cover the entire area, but full coverage is impossible in actual applications, and spatial information is prone to incompleteness. Summary of the invention

[0007] Therefore, the present invention proposes a lithium battery temperature field spatiotemporal modeling method and system, which can solve the problem of incomplete spatial information collected in the actual operation of lithium batteries, nonlinear and temperature field prediction with spatiotemporal coupling characteristics. The present invention can fully reflect the uneven distribution of temperature, with small calculation amount, fast speed, and can effectively obtain global spatial information.

[0008] The technical solution of the present invention is as follows:

[0009] A method for spatiotemporal modeling of a lithium battery temperature field comprises the following steps:

[0010] S1. Perform non-uniform separation on the temporal and spatial distribution temperature data of the lithium battery to obtain the ambient temperature and the heat generation temperature;

[0011] S2. Separate the heat generation temperature in time and space according to the principle of time and space separation, and obtain the space basis function through the spectrum method, and obtain the corresponding low-order time coefficient according to the space basis function;

[0012] S3. Use the width learning network to build a timing model, use the obtained low-order time coefficient, input current, and working voltage as the input of the model, train the model, and calculate the connection weight according to the ridge regression method to update the model. When the set weight value is reached, stop updating and obtain a trained timing model based on the width learning network;

[0013] S4. Input the obtained low-order time coefficient, input current and working voltage into the trained timing model to obtain the predicted low-order time coefficient. Then, the predicted low-order time coefficient and the spatial basis function obtained in step S2 are reconstructed in time and space to obtain the predicted heat generation temperature. Then, the predicted heat generation temperature is non-uniformly synthesized with the ambient temperature in step S1 to finally obtain the predicted time-space distribution temperature data.

[0014] The present invention first eliminates the interference of non-uniform boundary conditions through non-uniform separation, and then performs time-space separation based on the spectral method. During time-space separation (T / S), the complex characteristics of space can be well represented by designing appropriate spatial basis functions. Then, a width learning network is used to capture the time nonlinearity of the corresponding low-order time coefficients, and a time series model is constructed. The low-order time coefficients predicted by the model and the spatial basis functions are reconstructed, and non-uniform synthesis is performed after reconstruction to finally obtain the predicted time-space distribution temperature data.

[0015] Furthermore, in step S1, the temporal and spatial distribution temperature data of the lithium battery is non-uniformly separated to obtain the ambient temperature and the heat generation temperature in the following process:

[0016] Since the thermal process of lithium-ion batteries is an infinite-dimensional distributed parameter system, first, the 3D system is reduced to a 2D model. Since the thickness of the battery used is small, the temperature change in the Z direction can be ignored. According to the heat conduction law of lithium-ion batteries, the thermal process is expressed in the following form:

[0017]

[0018] Where T(x,y,t) represents the temporal and spatial distribution temperature of the battery, where x∈[0,x 0 ] and y∈[0,y 0 ] is the spatial coordinate, t represents time, x 0 ,y 0 are the length and width of the battery respectively; ρ is the battery density; C p is the specific heat capacity; is the thermal conductivity; Q(x,y,t) represents the heat source;

[0019] The heat source Q(x,y,t) is corrected as follows:

[0020]

[0021] The parameter p(x) represents the local heating effect; I represents the current; E oc represents the open circuit potential; V represents the operating voltage; is a constant;

[0022] Therefore, formula (1) can be rewritten as:

[0023]

[0024] in

[0025] Considering the convection heat transfer at the boundary, it is expressed as:

[0026]

[0027] where h c is the convective heat transfer coefficient; T a is the ambient temperature;

[0028] Because the spectral method requires the boundary conditions to be uniform, an auxiliary function f(x,y,t) is designed to separate the non-uniform interference and satisfy the following formula:

[0029] T(x,y,t)=G(x,y,t)+f(x,y,t) (5)

[0030] Combining the boundary condition formula (4), it can be deduced that the auxiliary function f(x, y, t) is exactly equal to the ambient temperature T a :

[0031] f(x,y,t)=T a (6)

[0032] Therefore, according to formula (5), the heat generation temperature G(x, y, t) is obtained;

[0033] G(x,y,t)=T(x,y,t)-T a (7)

[0034] According to equation (5) and equation (2), equation (3) is converted into the following function related to the heat generation temperature G(x, y, t):

[0035]

[0036] The parameter p(x) represents the local heating effect.

[0037] Further, in step S2, the process of obtaining the spatial basis function and the corresponding low-order time coefficient is as follows:

[0038] According to the T / S separation method, G(x,y,t) is decomposed into orthogonal coupling series:

[0039]

[0040] Where a i (t) represents the i-th component of the time variable; φ i (x,y) represents the i-th component of the spatial basis function;

[0041] In practical applications, formula (9) is usually expressed as a finite N-dimensional form:

[0042]

[0043] After the non-uniform separation, the boundary conditions are uniform, so according to the spectral method, the operator The characteristic function of is used as the spatial basis function φ(x,y), which is derived as follows:

[0044]

[0045] Where:

[0046]

[0047] where θ x ≠0 and θ y ≠0 is a constant coefficient; λ x ,λ y represents the eigenvalue;

[0048] And the following transcendental equation is derived. The process of solving the eigenvalue by bisection method is as follows;

[0049]

[0050] in a is x or y, that is, λ a is x or y , l 0 For x 0 or 0 ;

[0051] ν=hl 0 , z 0 is the thickness of the battery;

[0052] Eigenvalue λ i,j =-(λ x,i +λ y,j ) are rearranged by order of magnitude and then expressed as a new Sequence, λ x,i Represents λ x The i-th component of y,j Represents λ y The jth component of , in addition, φ is the corresponding characteristic function;

[0053]

[0054] in express The i-th component of ; express The jth component of

[0055] For the operator The following equation holds:

[0056]

[0057] As an orthogonal eigenfunction, φ(x,y) is used as a spatial basis function. To simplify the derivation process, the constant coefficient θ in equation (12) can be x and θ y Specifying φ(x,y) as further normalized, for a set of desired orthogonal eigenfunctions, the following conditions should be satisfied:

[0058]

[0059] Among them, φ i (x,y) and φ j (x,y) represents the value of φ(x,y) in the i-th row and j-th column respectively;

[0060] Considering normalization, assuming i=j, the inner product M is calculated n :

[0061]

[0062] Among them, θ x,i Represents θ x The i-th component of y,j Represents θ y The jth component of

[0063] Therefore, the coefficient θ x and θ y It is specified as the following expression (18) so that formula (17) holds true:

[0064]

[0065] After obtaining the spatial basis function, the corresponding low-order time coefficient a(t)={a 1 (t),...,a n (t)}, where a i (t) is specifically expressed as follows:

[0066] a i (t)=<φ i (x,y),G(x,y,t)>,i=1,...,n (19)

[0067] By constructing a timing model to model the low-order time coefficients, adding the input signal u(t) = {u 1 ,...,u m}, that is, the low-order time coefficient a(t) is expressed as:

[0068] a(t)=Ψ(a(t-1),...,a(tn a ),u(t-1),...,u(tn b))+χ(t) (20)

[0069] where n a and n b is the maximum output and input lag, Ψ(·) represents the nonlinear function related to the time dynamics; χ(t) is the residual. Many machine learning networks can be used to learn Ψ(·), but width learning is more suitable due to its excellent performance.

[0070] Furthermore, in step S3, the process of using the width learning network to construct the time series model is as follows:

[0071] Width learning is modified from RVFLNN and is not directly enhanced by the input node. The width learning network first maps the input into a set of mapping features.

[0072] First, assume that the input data set X = a(t-1),...,a(tn a ),u(t-1),,...,u(tn b ) is projected into the mapping feature Z through formula (20) i , then q groups of mapping features form a matrix Z q ≡[Z 1 ,…Z q ];

[0073]

[0074] Among them, W ei and β ei are randomly generated weights and biases, represents the activation function;

[0075] In order to increase the nonlinear factors of the network, enhanced nodes are introduced. The bth group of enhanced nodes H b By the mapping matrix Z q According to formula (22), we can calculate:

[0076]

[0077] Among them, W hb and β hb is the bth weight and bias randomly generated from the mapped feature layer to the enhanced node layer, represents the activation function; the matrix of the first b groups of enhanced nodes is represented by H b ≡[H 1 ,…,H b ];

[0078] Therefore, the output matrix Y = a(t) is further organized as:

[0079]

[0080] Where W m is the connection weight of the width structure, which is approximately calculated by the ridge regression method:

[0081]

[0082] In the formula, σ represents further constraints on weights; E represents the identity matrix;

[0083] Get the connection weight W m Then update the model, when W m When the set value is reached, the update is stopped, and the trained time series model based on the width learning network is obtained.

[0084] Further, in step S4, the process of obtaining the predicted spatiotemporal temperature distribution data is as follows:

[0085] After obtaining the spatial basis function φ(x, y) and the time series model, the input current I, the operating voltage V and the low-order time coefficient a(t-1)={a 1 (t-1),...,a N (t-1)} as input, and the low-order time coefficient at time t is obtained through the time series model Then Reconstruct the space-time with φ(x,y) to get the predicted heat generation temperature Then With ambient temperature T a Perform non-uniform synthesis and finally obtain the predicted spatiotemporal distribution temperature data

[0086] Right now, and The expression formula is as follows:

[0087]

[0088] Furthermore, three indicators, RMSE, SNAE, and TNAE, are introduced as error measurement criteria;

[0089]

[0090] Where S is the number of sensors; L is the number of snapshots; x i ,y i represents the spatial coordinates of the i-th sensor.

[0091] Furthermore, in step S1, temperature monitoring is performed by using a plurality of temperature sensors evenly distributed on the surface of the lithium battery at intervals to obtain a plurality of temporal and spatial distribution temperature data of the lithium battery.

[0092] The present invention also provides a lithium battery temperature field spatiotemporal modeling system, comprising a processor, and a non-uniform separation module, a spatiotemporal separation module, a model building module, and a reconstruction output module connected to the processor in communication;

[0093] The non-uniform separation module performs non-uniform separation on the time-space distribution temperature data of the lithium battery to obtain the ambient temperature and the heat generation temperature, and uploads the ambient temperature and the heat generation temperature to the processor, and the processor sends the heat generation temperature to the time-space separation module;

[0094] The time-space separation module performs time-space separation on the heat generation temperature according to the time-space separation principle, obtains the space basis function through the spectrum method, obtains the corresponding low-order time coefficient according to the space basis function, and transmits the space basis function and the low-order time coefficient to the processor, and the processor transmits the low-order time coefficient to the model building module;

[0095] The model building module uses a width learning network to build a timing model, uses the obtained low-order time coefficient, input current, and operating voltage as inputs of the model, trains the model, and calculates the connection weights according to the ridge regression method to update the model. When the set weight value is reached, the update is stopped to obtain a trained timing model based on the width learning network, and the timing model is transmitted to the processor;

[0096] The reconstruction output module reads the timing model, ambient temperature, spatial basis function and low-order time coefficient in the processor, and then inputs the obtained low-order time coefficient, input current and operating voltage into the trained timing model to obtain the predicted low-order time coefficient, and then performs spatiotemporal reconstruction on the predicted low-order time coefficient and the spatial basis function to obtain the predicted heat generation temperature, and then performs non-uniform synthesis on the predicted heat generation temperature and the ambient temperature, and finally obtains the predicted spatiotemporal distribution temperature data, and outputs the predicted spatiotemporal distribution temperature data to the processor.

[0097] Furthermore, the processor is communicatively connected to an acquisition module, and the acquisition module is connected to a plurality of temperature sensors, and the plurality of temperature sensors are evenly spaced and distributed on the surface of the lithium battery for temperature monitoring to obtain a plurality of spatiotemporal distribution temperature data of the lithium battery, and the plurality of spatiotemporal distribution temperature data are transmitted to the acquisition module, which is then transmitted to the processor, and the processor transmits the plurality of spatiotemporal distribution temperature data to the non-uniform separation module.

[0098] By evenly arranging a certain number of temperature sensors on the surface of the lithium battery for collection, it is possible to use a small number of sensors to collect data at different global locations, and then through time-space separation and spectral methods, the spatial basis function with global information can be obtained, which can well reflect the time-space characteristics.

[0099] Furthermore, the processor is communicatively connected to a display, and the processor outputs the predicted spatiotemporal distribution temperature data to the display for display.

[0100] The results are output to a display screen so that operators can better compare them with the original data to better analyze the prediction effect of the method of the present invention.

[0101] Compared with the prior art, the present invention has the following beneficial effects:

[0102] 1) In view of the problem that the lumped thermal model cannot fully reflect the spatial distribution unevenness of the battery thermal process, the present invention first performs non-uniform separation and then uses the idea of ​​time and space separation to process the data, which can well reflect the spatial distribution unevenness;

[0103] 2) In view of the problem of incomplete spatial information in traditional data-driven models, the present invention uses time-space separation and obtains spatial basis functions and their corresponding low-order time coefficients through spectral methods, which can comprehensively obtain spatial information and well reflect the time-space characteristics;

[0104] 3) In order to solve the problem of large amount of calculation in finite element method and finite difference method, the present invention adopts width learning network to process data information quickly, effectively reduce the amount of calculation, improve calculation efficiency, and due to the excellent performance of width learning, it can handle time nonlinearity well. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1 It is a flow chart of the spatiotemporal modeling method of the lithium battery temperature field of the present invention;

[0106] Figure 2 is a schematic diagram of a lithium battery temperature field spatiotemporal modeling system of the present invention;

[0107] Figure 3 This is a schematic diagram of the arrangement of temperature sensors on the surface of lithium batteries;

[0108] Figure 4 is a performance diagram of sensor L3 in Example 3;

[0109] Figure 5 is a performance diagram of sensor L8 in Example 3;

[0110] Figure 6 It is a performance diagram of sensor L13 in Example 3. DETAILED DESCRIPTION

[0111] The drawings are only for illustrative purposes and cannot be construed as limiting the present invention. To better illustrate the present embodiment, some parts of the drawings may be omitted, enlarged, or reduced, and do not represent the size of the actual product. For those skilled in the art, it is understandable that some well-known structures and their descriptions may be omitted in the drawings. The positional relationships described in the drawings are only for illustrative purposes and cannot be construed as limiting the present invention.

[0112] Embodiment 1:

[0113] like Figure 1 As shown, a method for spatiotemporal modeling of a lithium battery temperature field comprises the following steps:

[0114] S1. Perform non-uniform separation on the temporal and spatial distribution temperature data of the lithium battery to obtain the ambient temperature and the heat generation temperature;

[0115] S2. Separate the heat generation temperature in time and space according to the principle of time and space separation, and obtain the space basis function through the spectrum method, and obtain the corresponding low-order time coefficient according to the space basis function;

[0116] S3. Use the width learning network to build a timing model, use the obtained low-order time coefficient, input current, and working voltage as the input of the model, train the model, and calculate the connection weight according to the ridge regression method to update the model. When the set weight value is reached, stop updating and obtain a trained timing model based on the width learning network;

[0117] S4. Input the obtained low-order time coefficient, input current and working voltage into the trained timing model to obtain the predicted low-order time coefficient. Then, the predicted low-order time coefficient and the spatial basis function obtained in step S2 are reconstructed in time and space to obtain the predicted heat generation temperature. Then, the predicted heat generation temperature is non-uniformly synthesized with the ambient temperature in step S1 to finally obtain the predicted time-space distribution temperature data.

[0118] The present invention first eliminates the interference of non-uniform boundary conditions through non-uniform separation, and then performs time-space separation based on the spectral method. During time-space separation (T / S), the complex characteristics of space can be well represented by designing appropriate spatial basis functions. Then, a width learning network is used to capture the time nonlinearity of the corresponding low-order time coefficients, and a time series model is constructed. The low-order time coefficients predicted by the model and the spatial basis functions are reconstructed, and non-uniform synthesis is performed after reconstruction to finally obtain the predicted time-space distribution temperature data.

[0119] In this embodiment, in step S1, the temporal and spatial distribution temperature data of the lithium battery is non-uniformly separated to obtain the ambient temperature and the heat generation temperature in the following process:

[0120] Since the thermal process of lithium-ion batteries is an infinite-dimensional distributed parameter system, first, the 3D system is reduced to a 2D model. Since the thickness of the battery used is small, the temperature change in the Z direction can be ignored. According to the heat conduction law of lithium-ion batteries, the thermal process is expressed in the following form:

[0121]

[0122] Where T(x,y,t) represents the temporal and spatial distribution temperature of the battery, where x∈[0,x 0 ] and y∈[0,y 0 ] is the spatial coordinate, t represents time, x 0 ,y 0 are the length and width of the battery respectively; ρ is the battery density; C p is the specific heat capacity; is the thermal conductivity; Q(x,y,t) represents the heat source;

[0123] The heat source Q(x,y,t) is corrected as follows:

[0124]

[0125] The parameter p(x) represents the local heating effect; I represents the current; E oc represents the open circuit potential; V represents the operating voltage; is a constant;

[0126] Therefore, formula (1) can be rewritten as:

[0127]

[0128] in

[0129] Considering the convection heat transfer at the boundary, it is expressed as:

[0130]

[0131] where h c is the convective heat transfer coefficient; T a is the ambient temperature;

[0132] Because the spectral method requires the boundary conditions to be uniform, an auxiliary function f(x,y,t) is designed to separate the non-uniform interference and satisfy the following formula:

[0133] T(x,y,t)=G(x,y,t)+f(x,y,t) (5)

[0134] Combining the boundary condition formula (4), it can be deduced that the auxiliary function f(x, y, t) is exactly equal to the ambient temperature T a :

[0135] f(x,y,t)=T a (6)

[0136] Therefore, according to formula (5), the heat generation temperature G(x, y, t) is obtained;

[0137] G(x,y,t)=T(x,y,t)-T a (7)

[0138] According to equation (5) and equation (2), equation (3) is converted into the following function related to the heat generation temperature G(x, y, t):

[0139]

[0140] The parameter p(x) represents the local heating effect.

[0141] In this embodiment, in step S2, the process of obtaining the spatial basis function and the corresponding low-order time coefficient is as follows:

[0142] According to the T / S separation method, G(x,y,t) is decomposed into orthogonal coupling series:

[0143]

[0144] Where a i (t) represents the i-th component of the time variable; φ i (x,y) represents the i-th component of the spatial basis function;

[0145] In practical applications, formula (9) is usually expressed as a finite N-dimensional form:

[0146]

[0147] After the non-uniform separation, the boundary conditions are uniform, so according to the spectral method, the operator The characteristic function of is used as the spatial basis function φ(x,y), which is derived as follows:

[0148]

[0149] Where:

[0150]

[0151] where θ x ≠0 and θ y ≠0 is a constant coefficient; λ x ,λ y represents the eigenvalue;

[0152] And the following transcendental equation is derived. The process of solving the eigenvalue by bisection method is as follows;

[0153]

[0154] in a is x or y, that is, λ a is x or y , l 0 For x 0 or 0 ;

[0155] ν=hl 0 , z 0 is the thickness of the battery;

[0156] Eigenvalue λ i,j =-(λ x,i +λ y,j ) are rearranged by order of magnitude and then expressed as a new Sequence, λ x,i Represents λ x The i-th component of y,j Represents λ y The jth component of , in addition, φ is the corresponding characteristic function;

[0157]

[0158] in express The i-th component of ; express The jth component of

[0159] For the operator The following equation holds:

[0160]

[0161] As an orthogonal eigenfunction, φ(x,y) is used as a spatial basis function. To simplify the derivation process, the constant coefficient θ in equation (12) can be x and θ y Specifying φ(x,y) as further normalized, for a set of desired orthogonal eigenfunctions, the following conditions should be satisfied:

[0162]

[0163] Among them, φ i (x,y) and φ j (x,y) represents the value of φ(x,y) in the i-th row and j-th column respectively;

[0164] Considering normalization, assuming i=j, the inner product M is calculatedn :

[0165]

[0166] Among them, θ x,i Represents θ x The i-th component of y,j Represents θ y The jth component of

[0167] Therefore, the coefficient θ x and θ y It is specified as the following expression (18) so that formula (17) holds true:

[0168]

[0169] After obtaining the spatial basis function, the corresponding low-order time coefficient a(t)={a 1 (t),...,a n (t)}, where a i (t) is specifically expressed as follows:

[0170] a i (t)=<φ i (x,y),G(x,y,t)>,i=1,...,n (19)

[0171] By constructing a timing model to model the low-order time coefficients, adding the input signal u(t) = {u 1 ,...,u m}, that is, the low-order time coefficient a(t) is expressed as:

[0172] a(t)=Ψ(a(t-1),...,a(tn a ),u(t-1),...,u(tn b ))+χ(t) (20)

[0173] where n a and n b is the maximum output and input lag, Ψ(·) represents the nonlinear function related to the time dynamics; χ(t) is the residual. Many machine learning networks can be used to learn Ψ(·), but width learning is more suitable due to its excellent performance.

[0174] In this embodiment, in step S3, the process of using the width learning network to construct the time series model is as follows:

[0175] Width learning is modified from RVFLNN and is not directly enhanced by the input node. The width learning network first maps the input into a set of mapping features.

[0176] First, assume that the input data set X = a(t-1),...,a(tn a ),u(t-1),,...,u(tn b ) is projected into the mapping feature Z through formula (20) i , then q groups of mapping features form a matrix Z q ≡[Z 1 ,…Z q ];

[0177]

[0178] Among them, W ei and β ei are randomly generated weights and biases, represents the activation function;

[0179] In order to increase the nonlinear factors of the network, enhanced nodes are introduced. The bth group of enhanced nodes H b By the mapping matrix Z q According to formula (22), we can calculate:

[0180]

[0181] Among them, W hb and β hb is the bth weight and bias randomly generated from the mapped feature layer to the enhanced node layer, represents the activation function; the matrix of the first b groups of enhanced nodes is represented by H b ≡[H 1 ,…,H b ];

[0182] Therefore, the output matrix Y = a(t) is further organized as:

[0183]

[0184] Where W m is the connection weight of the width structure, which is approximately calculated by the ridge regression method:

[0185]

[0186] In the formula, σ represents further constraints on weights; E represents the identity matrix;

[0187] Get the connection weight W m Then update the model, when W m When the set value is reached, the update is stopped, and the trained time series model based on the width learning network is obtained.

[0188] In this embodiment, in step S4, the process of obtaining the predicted spatiotemporal distribution temperature data is as follows:

[0189] After obtaining the spatial basis function φ(x, y) and the time series model, the input current I, the operating voltage V and the low-order time coefficient a(t-1)={a 1 (t-1),...,a N (t-1)} as input, and the low-order time coefficient at time t is obtained through the time series model Then Reconstruct the space-time with φ(x,y) to get the predicted heat generation temperature Then With ambient temperature T a Perform non-uniform synthesis and finally obtain the predicted spatiotemporal distribution temperature data

[0190] Right now, and The expression formula is as follows:

[0191]

[0192] In this embodiment, three indicators, RMSE, SNAE, and TNAE, can be introduced as error measurement criteria;

[0193]

[0194] Where S is the number of sensors; L is the number of snapshots; x i ,y i represents the spatial coordinates of the i-th sensor.

[0195] In this embodiment, in step S1, temperature monitoring is performed by using a plurality of temperature sensors evenly distributed on the surface of the lithium battery at intervals to obtain a plurality of temporal and spatial distribution temperature data of the lithium battery.

[0196] The present invention can fully reflect the uneven distribution of temperature, has a small amount of calculation, a high speed, and can effectively obtain global spatial information.

[0197] Embodiment 2:

[0198] like Figure 2 As shown, this embodiment also provides a lithium battery temperature field spatiotemporal modeling system, including a processor, and a non-uniform separation module, a spatiotemporal separation module, a model building module, and a reconstruction output module connected to the processor in communication;

[0199] The non-uniform separation module performs non-uniform separation on the time-space distribution temperature data of the lithium battery to obtain the ambient temperature and the heat generation temperature, and uploads the ambient temperature and the heat generation temperature to the processor, and the processor sends the heat generation temperature to the time-space separation module;

[0200] The time-space separation module performs time-space separation on the heat generation temperature according to the time-space separation principle, obtains the space basis function through the spectrum method, obtains the corresponding low-order time coefficient according to the space basis function, and transmits the space basis function and the low-order time coefficient to the processor, and the processor transmits the low-order time coefficient to the model building module;

[0201] The model building module uses a width learning network to build a timing model, uses the obtained low-order time coefficient, input current, and operating voltage as inputs of the model, trains the model, and calculates the connection weights according to the ridge regression method to update the model. When the set weight value is reached, the update is stopped to obtain a trained timing model based on the width learning network, and the timing model is transmitted to the processor;

[0202] The reconstruction output module reads the timing model, ambient temperature, spatial basis function and low-order time coefficient in the processor, and then inputs the obtained low-order time coefficient, input current and operating voltage into the trained timing model to obtain the predicted low-order time coefficient, and then performs spatiotemporal reconstruction on the predicted low-order time coefficient and the spatial basis function to obtain the predicted heat generation temperature, and then performs non-uniform synthesis on the predicted heat generation temperature and the ambient temperature, and finally obtains the predicted spatiotemporal distribution temperature data, and outputs the predicted spatiotemporal distribution temperature data to the processor.

[0203] In this embodiment, the processor is communicatively connected to an acquisition module, and the acquisition module is connected to a plurality of temperature sensors. The plurality of temperature sensors are evenly spaced and distributed on the surface of the lithium battery for temperature monitoring to obtain a plurality of spatiotemporal distribution temperature data of the lithium battery, and the plurality of spatiotemporal distribution temperature data are transmitted to the acquisition module, which is then transmitted to the processor, and the processor transmits the plurality of spatiotemporal distribution temperature data to the non-uniform separation module.

[0204] This embodiment collects data by evenly arranging a certain number of temperature sensors on the surface of the lithium battery, so as to use a small number of sensors to collect data at different global locations, and then obtains spatial basis functions with global information through time-space separation and spectral methods, which can well reflect the time-space characteristics.

[0205] In this embodiment, the processor is communicatively connected to a display, and the processor outputs the predicted spatiotemporal temperature distribution data to the display for display. Outputting the results to the display screen allows operators to better compare with the original data to better analyze the prediction effect of the method of the present invention.

[0206] The system in this embodiment can be integrated on a microcomputer, and external common accessories such as a casing and a heat sink can be added outside the microcomputer to form a device, which can be configured according to actual application scenarios.

[0207] Embodiment 3:

[0208] LiFePO 4 Taking the thermal process of a battery as an example, the battery parameters are shown in Table I, and the spatiotemporal modeling method of the lithium battery temperature field in Example 1 is implemented as an example. Figure 3 As shown, 20 temperature sensors are evenly distributed on the surface of the lithium battery, and the input current and the generated working voltage are used as the input signal of the system u(t)=[I(t),U(t)], where I(t) is the input current and U(t) is the working voltage.

[0209] Table I

[0210]

[0211] This embodiment uses 1370s of data since discharge, with a sample interval of Δt=1s, a total of 1370 groups, each group containing 20 spatiotemporal temperature distribution data collected by the temperature sensor. Figure 3 In the embodiment, the first 1000 sets of data of the black shadow sensors (i.e., L1, L5, L7, L9, L12, L14, L16, and L20) are selected to obtain the spatial basis functions according to the spatiotemporal modeling method in Example 1, and are used for training the timing model, and the last 370 sets of data of the remaining temperature sensors are used for the performance test of the timing model.

[0212] The steps of implementing the lithium battery temperature field spatiotemporal modeling method in Example 1 are as follows:

[0213] 1. Perform non-uniform separation according to equations (5) to (7) to obtain the heat generation temperature;

[0214] Second, the heat generation temperature is separated in time and space according to the principle of time and space separation, and the spatial basis function and the corresponding low-order time coefficient are obtained respectively;

[0215] 1) Obtain the spatial basis function according to the spectral method;

[0216] 1. According to the battery size parameters, in [0,x 0 ] and [0,y 0] uniformly select s points between ], and use formula (13) to obtain the eigenvalue λ x and λ y ;

[0217] 2. The obtained eigenvalue is calculated according to the formula λ i,j =-(λ x,i +λ y,j ) After calculation, sort by size;

[0218] 3. According to the specific coordinate information of the sensor, the formula (12) is used to calculate and Then the spatial basis function φ(x,y) is obtained by equation (11);

[0219] 2) The low-order time coefficient a(t) is obtained from formula (20);

[0220] 3. Use the width learning network to build a timing model: Take the low-order time coefficient a(t) and the input current and working voltage as the timing model input, train the model, and calculate the connection weight W from formula (24): m , when W m When the set value is reached, the update stops, and the trained time series model based on the width learning network is obtained;

[0221] 4. Perform space-time reconstruction: obtain the predicted time coefficient Then, the time-space reconstruction is performed according to formula (25) to obtain the predicted heat generation temperature Then, non-uniform synthesis is performed through equation (26) to obtain the predicted spatiotemporal distribution temperature data:

[0222] This embodiment selects three sensors L3, L8, and L11 for performance comparison. The results are as follows: Figure 4-Figure 6 shown.

[0223] In this embodiment, the prediction error is measured and calculated using the three indicators of RMSE, SNAE, and TNAE according to formulas (27)-(29), and the calculation results of RMSE, SNAE, and TNAE are 0.1171, 0.0923, and 0.2851, respectively. It can be seen that the present invention has high accuracy and can effectively predict the temperature field of lithium batteries.

[0224] Obviously, the above embodiments of the present invention are only examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A method for spatiotemporal modeling of a lithium battery temperature field, characterized in that: The following steps are involved: S1. Perform non-uniform separation on the temporal and spatial distribution temperature data of the lithium battery to obtain the ambient temperature and the heat generation temperature; S2. Separate the heat generation temperature in time and space according to the principle of time and space separation, and obtain the space basis function through the spectrum method, and obtain the corresponding low-order time coefficient according to the space basis function; S3. Use the width learning network to build a timing model, use the obtained low-order time coefficient, input current, and working voltage as the input of the model, train the model, and calculate the connection weight according to the ridge regression method to update the model. When the set weight value is reached, stop updating and obtain a trained timing model based on the width learning network; S4. Input the obtained low-order time coefficient, input current and working voltage into the trained timing model to obtain the predicted low-order time coefficient. Then, the predicted low-order time coefficient and the spatial basis function obtained in step S2 are reconstructed in time and space to obtain the predicted heat generation temperature. Then, the predicted heat generation temperature is non-uniformly synthesized with the ambient temperature in step S1 to finally obtain the predicted time-space distribution temperature data.

2. A method for spatiotemporal modeling of a lithium battery temperature field according to claim 1, characterized in that: In step S1, the process of performing non-uniform separation on the temporal and spatial distribution temperature data of the lithium battery to obtain the ambient temperature and the heat generation temperature is as follows: Since the thermal process of lithium-ion batteries is an infinite-dimensional distributed parameter system, first, the 3D system is reduced to a 2D model, the temperature change in the Z direction is ignored, and according to the heat conduction law of lithium-ion batteries, the thermal process is expressed in the following form: Where T(x,y,t) represents the spatiotemporal distribution temperature of the battery, where x∈[0,x0] and y∈[0,y0] are spatial coordinates, t represents time, x0, y0 are the length and width of the battery respectively; ρ is the battery density; C p is the specific heat capacity; is the thermal conductivity; Q(x,y,t) represents the heat source; The heat source Q(x,y,t) is corrected as follows: The parameter p(x) represents the local heating effect; I represents the current; E oc represents the open circuit potential; V represents the operating voltage; is a constant; Therefore, formula (1) can be rewritten as: in Considering the convection heat transfer at the boundary, it is expressed as: where h c is the convective heat transfer coefficient; T a is the ambient temperature; Because the spectral method requires the boundary conditions to be uniform, an auxiliary function f(x,y,t) is designed to separate the non-uniform interference and satisfy the following formula: T(x,y,t)=G(x,y,t)+f(x,y,t) (5) Combining the boundary condition formula (4), it can be deduced that the auxiliary function f(x, y, t) is exactly equal to the ambient temperature T a : f(x,y,t)=T a (6) Therefore, according to formula (5), the heat generation temperature G(x, y, t) is obtained; G(x,y,t)=T(x,y,t)-T a (7) According to equation (5) and equation (2), equation (3) is converted into the following function related to the heat generation temperature G(x, y, t): The parameter p(x) represents the local heating effect.

3. A method for spatiotemporal modeling of a lithium battery temperature field according to claim 2, characterized in that: In step S2, the process of obtaining the spatial basis function and the corresponding low-order time coefficient is as follows: According to the T / S separation method, G(x,y,t) is decomposed into orthogonal coupling series: Where a i (t) represents the i-th component of the time variable; φ i (x, y) represents the i-th component of the spatial basis function; Formula (9) is expressed in a finite N-dimensional form: After the non-uniform separation, the boundary conditions are uniform, so according to the spectral method, the operator The characteristic function of is used as the spatial basis function φ(x,y), which is derived as follows: Where: where θ x ≠0 and θ y ≠0 is a constant coefficient; λ x ,λ y represents the eigenvalue; And the following transcendental equation is derived. The process of solving the eigenvalue by bisection method is as follows; in a is x or y, that is, λ a is x or y , l0 is x0 or y0; Eigenvalue λ i,j =-(λ x,i +λ y,j ) are rearranged by order of magnitude and then expressed as a new Sequence, λ x,i Represents λ x The i-th component of y,j Represents λ y The jth component of , in addition, φ is the corresponding characteristic function; in express The i-th component of ; express The jth component of For the operator The following equation holds: As an orthogonal eigenfunction, φ(x,y) is used as a spatial basis function. To simplify the derivation process, the constant coefficient θ in equation (12) is replaced by x and θ y Specifying φ(x,y) as further normalized, for a set of desired orthogonal eigenfunctions, the following conditions are satisfied: Among them, φ i (x,y) and φ j (x,y) represents the value of φ(x,y) in the i-th row and j-th column respectively; Considering normalization, assuming i=j, the inner product M is calculated n : Among them, θ x,i Represents θ x The i-th component of y,j Represents θ y The jth component of Therefore, the coefficient θ x and θ y It is specified as the following expression (18) so that formula (17) holds true: After obtaining the spatial basis function, the corresponding low-order time coefficient is obtained according to the above formula (9): a(t)={a1(t),…,a n (t)}, where a i (t) is specifically expressed as follows: a i (t)=<φ i (x,y),G(x,y,t)>,i=1,…,n (19) By constructing a time series model to model the low-order time coefficients, adding the input signal u(t) = {u1,...,u m }, that is, the low-order time coefficient a(t) is expressed as: a(t)=Ψ(a(t-1),...,a(t-n a ),u(t-1),...,u(t-n b ))+χ(t) (20) Where n a and n b are the maximum output and input hysteresis, Ψ(·) represents the nonlinear function related to the time dynamics; χ(t) is the residual.

4. A method for spatiotemporal modeling of a lithium battery temperature field according to claim 3, characterized in that: In step S3, the process of using the width learning network to construct a time series model is as follows: First, assume that the input data set X = a(t-1),...,a(tn a ),u(t-1),,...,u(tn b ) is projected into the mapping feature Z through formula (20) i , then q groups of mapping features form a matrix Z q ≡[Z1,...Z q ]; Among them, W ei and β ei are randomly generated weights and biases, represents the activation function; In order to increase the nonlinear factors of the network, enhanced nodes are introduced. The bth group of enhanced nodes H b By the mapping matrix Z q According to formula (22), we can calculate: Among them, W hb and β hb is the bth weight and bias randomly generated from the mapped feature layer to the enhanced node layer, represents the activation function; the matrix of the first b groups of enhanced nodes is represented by H b ≡[H1,...,H b ]; Therefore, the output matrix Y = a(t) is further organized as: Where W m is the connection weight of the width structure, which is approximately calculated by the ridge regression method: In the formula, σ represents further constraints on weights; E represents the identity matrix; Get the connection weight W m Then update the model, when W m When the set value is reached, the update is stopped, and the trained time series model based on the width learning network is obtained.

5. A method for spatiotemporal modeling of a lithium battery temperature field according to claim 4, characterized in that: In step S4, the process of obtaining the predicted spatiotemporal temperature distribution data is as follows: After obtaining the spatial basis function φ(x,y) and the time series model, the input current I, the operating voltage V and the low-order time coefficient a(t-1)={a1(t-1),...,a N (t-1)} as input, and the low-order time coefficient at time t is obtained through the time series model Then Reconstruct the space-time with φ(x,y) to get the predicted heat generation temperature Then With ambient temperature T a Perform non-uniform synthesis and finally obtain the predicted spatiotemporal distribution temperature data Right now, and The expression formula is as follows:

6. A method for spatiotemporal modeling of a lithium battery temperature field according to claim 5, characterized in that: The three indicators of RMSE, SNAE and TNAE are introduced as error measurement criteria; Where S is the number of sensors; L is the number of snapshots; x i ,y i represents the spatial coordinates of the i-th sensor.

7. A method for spatiotemporal modeling of a lithium battery temperature field according to claim 1, characterized in that: In step S1, temperature monitoring is performed by using a plurality of temperature sensors evenly distributed on the surface of the lithium battery at intervals to obtain a plurality of temporal and spatial distribution temperature data of the lithium battery.

8. A lithium battery temperature field spatiotemporal modeling system, characterized in that: It includes a processor, and a non-uniform separation module, a time-space separation module, a model building module, and a reconstruction output module connected to the processor in communication; The non-uniform separation module performs non-uniform separation on the time-space distribution temperature data of the lithium battery to obtain the ambient temperature and the heat generation temperature, and uploads the ambient temperature and the heat generation temperature to the processor, and the processor sends the heat generation temperature to the time-space separation module; The time-space separation module performs time-space separation on the heat generation temperature according to the time-space separation principle, obtains the space basis function through the spectrum method, obtains the corresponding low-order time coefficient according to the space basis function, and transmits the space basis function and the low-order time coefficient to the processor, and the processor transmits the low-order time coefficient to the model building module; The model building module uses a width learning network to build a timing model, uses the obtained low-order time coefficient, input current, and operating voltage as inputs of the model, trains the model, and calculates the connection weights according to the ridge regression method to update the model. When the set weight value is reached, the update is stopped to obtain a trained timing model based on the width learning network, and the timing model is transmitted to the processor; The reconstruction output module reads the timing model, ambient temperature, spatial basis function and low-order time coefficient in the processor, and then inputs the obtained low-order time coefficient, input current and operating voltage into the trained timing model to obtain the predicted low-order time coefficient, and then performs spatiotemporal reconstruction on the predicted low-order time coefficient and the spatial basis function to obtain the predicted heat generation temperature, and then performs non-uniform synthesis on the predicted heat generation temperature and the ambient temperature, and finally obtains the predicted spatiotemporal distribution temperature data, and outputs the predicted spatiotemporal distribution temperature data to the processor.

9. A lithium battery temperature field spatiotemporal modeling system according to claim 8, characterized in that: The processor is communicatively connected to an acquisition module, and the acquisition module is connected to a plurality of temperature sensors. The plurality of temperature sensors are evenly spaced and distributed on the surface of the lithium battery for temperature monitoring to obtain a plurality of spatiotemporal distribution temperature data of the lithium battery, and the plurality of spatiotemporal distribution temperature data are transmitted to the acquisition module, which is then transmitted to the processor, and the processor transmits the plurality of spatiotemporal distribution temperature data to the non-uniform separation module.

10. A lithium battery temperature field spatiotemporal modeling system according to claim 8, characterized in that: The processor is communicatively connected to a display, and the processor outputs the predicted spatiotemporal distribution temperature data to the display for display.

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