Cross-flow flat plate type SOFC single cell surface temperature field prediction method based on tensor CP decomposition

Abstract

The invention discloses a cross-flow flat plate type SOFC single cell surface temperature field prediction method based on tensor CP decomposition, and the method comprises the steps: carrying out the space-time separation of the two-dimensional temperature field tensor of the surface of an SOFC single cell through employing a tensor CP decomposition technology, building a low-dimensional time sequence model of a nominal system, predicting the future low-dimensional feature value, and finally, carrying out the prediction of the temperature field of the surface of the SOFC single cell. Future information of the surface temperature field of the SOFC single cell is predicted in a spatio-temporal data reconstruction mode. According to the method, under the condition that the model prediction precision is guaranteed, the complexity of the prediction model is greatly reduced, the model calculation efficiency is improved, and the problems that a traditional finite element analysis method is long in consumed time and not suitable for online application are solved. The method is particularly suitable for the two-dimensional temperature field modeling problem of the surface of the cross-flow flat plate type SOFC single cell, the temperature field modeling method can better adapt to the modeling and online operation problems of a computing resource limited system, and the application prospect is very wide.

Description

Technical Field

[0001] The present invention belongs to the technical field of solid oxide fuel cell (SOFC) thermal management, and relates to a method for predicting the surface temperature field of a SOFC, and specifically to a method for predicting the surface temperature field of a cross-flow flat-plate SOFC single cell based on tensor CP decomposition. Background Art

[0002] Solid Oxide Fuel Cell (SOFC) is a high-efficiency energy conversion device that is not limited by the Carnot cycle and has the advantage of high-efficiency energy conversion. In recent years, it has become a research hotspot in the field of fuel cell applications. However, some technical challenges currently make it difficult for SOFC to be applied on a large scale. Fuel cell thermal management is one of the important challenges. The operating temperature of SOFC is generally between 600 and 1000°C. The internal temperature of batteries of different types and structures may be unevenly distributed under working conditions. Rapid local temperature changes will cause uneven distribution of thermal stress on the electrode and electrolyte materials. Excessive local thermal stress will cause the internal materials of the battery to rupture, which will cause the battery to fail completely. Therefore, controlling the temperature and thermal stress distribution of the fuel cell, improving the stability and durability of the fuel cell, and thus improving its overall efficiency and service life are key tasks in current SOFC research.

[0003] An important prerequisite for implementing thermal management technology is to establish an effective mathematical model of the battery temperature field. However, since the working process of SOFC involves the coupling of multiple physical fields such as electrochemistry, heat transfer and fluid transport, it is an impossible task to construct an accurate mathematical model of the temperature field. At present, the cost of actual SOFC system construction and experiments is high. Researchers usually use finite element analysis to numerically analyze the thermal-electrical-current coupling process during the working process of SOFC, and use the results obtained in the design of SOFC system. However, the solution process that relies entirely on finite element analysis requires a lot of computing power resources, and it is impossible to quickly obtain the dynamic distribution information of SOFC physical quantities in a short time. This type of method is not suitable for the needs of rapid response of online tasks. Therefore, it is particularly urgent to develop a new mathematical model of SOFC system that is both efficient and accurate.

[0004] At present, there are data-driven research methods, such as principal component analysis, KL decomposition, and independent component analysis, which simplify the SOFC thermal system into a one-dimensional system for processing and apply it to the single-channel SOFC temperature field modeling problem. However, the above research methods cannot solve the problem of surface temperature field modeling of a single cell of a cross-flow flat-plate SOFC with two-dimensional spatial temperature characteristics. Summary of the invention

[0005] Aiming at the problem of modeling the surface temperature field of a cross-flow flat-plate SOFC single cell, the present invention provides a method for predicting the surface temperature field of a cross-flow flat-plate SOFC single cell based on tensor CP decomposition. The method uses tensor CP decomposition technology to reduce the dimension of the two-dimensional surface temperature field data of a cross-flow flat-plate SOFC single cell (abbreviated as SOFC single cell), and then respectively establishes a low-dimensional time series model of the nominal system to predict the future low-dimensional eigenvalues, and then predicts the future information of the battery surface temperature field by reconstructing the spatiotemporal data. The method proposed by the present invention greatly reduces the complexity of the prediction model and improves the model calculation efficiency while ensuring the model prediction accuracy, solving the problem that the traditional finite element analysis method is time-consuming and not suitable for online application.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] A method for predicting the surface temperature field of a cross-flow flat-plate SOFC single cell based on tensor CP decomposition comprises the following steps:

[0008] Step (1) sufficient temperature sensors are arranged on the surface of the SOFC single cell to collect the cell surface temperature information when the SOFC single cell works normally under a given operating environment and gas input flow rate conditions over a period of time, and the obtained two-dimensional temperature field data of the cell surface are preprocessed and sorted into a tensor form to obtain a two-dimensional temperature field tensor of the SOFC single cell surface;

[0009] Step (2) selects the initial rank of the tensor CP decomposition as 1, uses the tensor CP decomposition to the two-dimensional temperature field tensor of the SOFC single cell surface obtained in step (1), and determines whether the inverse transformation result of the tensor CP decomposition and the reconstruction error of the original data meet the accuracy requirements. If not, discard the decomposition result and increase the rank of the tensor decomposition. Repeat the above judgment until the reconstruction error meets the preset accuracy, extract two spatial modal factor matrices as two spatial characteristic matrices of the original high-order data, and extract the time modal factor matrix as the low-order time characteristic matrix;

[0010] Step (3) constructing a low-order time characteristic prediction model based on a recurrent neural network (RNN), wherein the prediction model consists of two recurrent network layers and one fully connected layer, wherein: the recurrent network layer predicts the input sequence, and a PReLU activation function is connected after each recurrent network layer to further improve the expression ability of the model; the fully connected layer performs weighted summation on the output of the recurrent network layer, converts the features predicted by the recurrent network layer into the final prediction result, and finally further improves the nonlinear approximation ability of the model through the activation function;

[0011] Step (4) Given a sequence of external input variables, the low-order time characteristic matrix obtained by tensor CP decomposition and the RNN-based low-order time characteristic prediction model are used to predict the low-order time characteristic matrix at future moments, and then the two spatial characteristic matrices are combined for dimensionality increase and reconstruction to obtain the high-order temperature field prediction value at future moments.

[0012] Compared with the prior art, the present invention has the following advantages:

[0013] 1. The present invention utilizes spatial invariance and uses tensor CP decomposition to project high-dimensional temperature field spatiotemporal data into low-dimensional feature space, avoiding the high computational burden of direct modeling of high-dimensional spatiotemporal data. The algorithm proposed in the present invention fully considers the spatiotemporal distribution relationship of the two-dimensional temperature field on the battery surface. While retaining the same order, it has less precision loss and higher accuracy than traditional dimensionality reduction algorithms.

[0014] 2. The tensor CP decomposition adopted in the present invention is a linear dimension reduction algorithm with high execution efficiency and short operation time. It solves the problem of long time consumption of traditional finite element analysis method and is particularly suitable for online modeling problems.

[0015] 3. The present invention adopts a time series prediction algorithm based on RNN, which can effectively capture feature dependencies through a hidden state mechanism and show good anti-interference when dealing with noise that may exist in the time series. Specifically, RNN can capture long-term dependencies in sequence data, the PReLU activation function used can handle nonlinear problems in negative areas, and by adjusting the value of the learnable parameter a, the gradient vanishing problem can be reduced to a certain extent.

[0016] 4. The present invention is particularly suitable for the problem of two-dimensional temperature field modeling on the surface of a cross-flow flat-plate SOFC single cell. Both theoretical analysis and experimental results have proved that the method proposed in the present invention is a high-precision and high-efficiency temperature field modeling method, which can better adapt to the modeling and online operation problems of systems with limited computing resources and has a very broad application prospect. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is the vector form and matrix factor diagram of the third-order tensor CP decomposition;

[0018] Figure 2 is the structure diagram of the superdiagonal tensor Λ;

[0019] Figure 3 Compute graph for RNN module unit;

[0020] Figure 4 The structure diagram of the neural network for time series prediction established;

[0021] Figure 5Schematic diagram of the cross-flow flat-plate SOFC structure;

[0022] Figure 6 is the oxidant flow rate v(t);

[0023] Figure 7 Slice and visualize the original tensor along the time dimension;

[0024] Figure 8 Reconstruct error slice visualization for tensor CP decomposition;

[0025] Fig. 9 Visualize the factor matrix for temporal modal decomposition;

[0026] Fig.10 This is the time mode prediction result diagram;

[0027] Fig.11 Visualize the modeling error slices. DETAILED DESCRIPTION

[0028] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0029] The present invention provides a cross-flow flat-plate SOFC single cell surface temperature field prediction method based on tensor CP decomposition. First, the two-dimensional temperature field tensor of the SOFC single cell surface is separated in time and space by using the tensor CP decomposition technology. Then, a low-dimensional time series model of the nominal system is established to predict the future low-dimensional eigenvalues. Finally, the future information of the SOFC single cell surface temperature field is predicted by reconstructing the spatiotemporal data. Specifically, the following steps are included:

[0030] Step (1) sufficient temperature sensors are arranged on the surface of the SOFC cell to collect the cell surface temperature information when the SOFC cell is working normally under a given operating environment and gas input flow rate over a period of time, and the obtained two-dimensional temperature field data of the cell surface are preprocessed and sorted into a tensor form to obtain the two-dimensional temperature field tensor of the SOFC cell surface. The specific steps are as follows:

[0031] Step (11) assumes that there are enough temperature sensors arranged on the surface of the SOFC cell. Without loss of generality, m×n temperature sensors are evenly arranged on the x-axis and y-axis, where m is the number of temperature sensors per row on the x-axis, n is the number of temperature sensors per column on the y-axis, and the total number of time steps in the test process is k. Given the oxidant flow rate at the t-th moment is v(t), the spatiotemporal data set of the two-dimensional temperature field on the surface of the SOFC cell collected at k time steps is T temp (x,y,t).

[0032] Step (12) collects the two-dimensional temperature field spatiotemporal data set T of the SOFC single cell surface temp (x, y, t) to obtain the two-dimensional temperature field tensor of the SOFC single cell surface. The preprocessing process mainly includes the following three steps:

[0033] First, the collected data are checked for missing values, and if any are found, they are filled with the mean of the temperature matrix at the current moment.

[0034] Secondly, check whether there are outliers in the tensor elements. Since the temperature field has a hysteresis characteristic, the temperature point data between adjacent moments and adjacent positions will not change suddenly. Therefore, if the data contains noise data greater than 3 times the standard deviation, it will be replaced with the mean of the temperature matrix at the current moment.

[0035] Finally, in order to make the tensor CP decomposition process and the prediction model The back propagation process is more stable, and the data needs to be normalized to the maximum and minimum values ​​so that the original data range is scaled between 0 and 1 to obtain the two-dimensional temperature field tensor of the SOFC single cell surface. The maximum-minimum normalization formula can be expressed as:

[0036]

[0037] Among them, max(T temp ) and min(T temp ) represent the temperature field spatiotemporal dataset T temp The maximum and minimum values ​​in (x,y,t).

[0038] Step (2) selects the initial rank of tensor CP decomposition as 1, uses tensor CP decomposition on the two-dimensional temperature field tensor of the SOFC single cell surface obtained in step (1), and determines whether the inverse transformation result of tensor CP decomposition and the reconstruction error of the original data meet the accuracy requirements. If not, discard the decomposition result and increase the rank of tensor decomposition. Repeat the above judgment until the reconstruction error meets the preset accuracy, extract two spatial modal factor matrices as two spatial characteristic matrices of the original high-order data, and extract the time modal factor matrix as the low-order time characteristic matrix. The specific steps are as follows:

[0039] Step (21) performs a tensor CP decomposition of the two-dimensional temperature field tensor Z (x, y, t) on the surface of the SOFC single cell with an initial rank of 1 to obtain two spatial modal decomposition factor matrices and a time modal decomposition factor matrix;

[0040] Step (22) determines whether the inverse transformation result of the tensor CP decomposition and the reconstruction error of the original data meet the accuracy requirements of the system; if not, discard the decomposition result, increase the rank of the tensor CP decomposition, repeat the above steps of tensor CP decomposition until the reconstruction error meets the accuracy requirements, and obtain the final rank r;

[0041] Step (23) extracts the spatial modal factor matrix as the spatial characteristic matrix of the original high-order data, and the temporal modal factor matrix as the low-order temporal characteristic matrix.

[0042] The vector form and factor matrix form of the third-order tensor CP decomposition are shown in the figure below: Figure 1 As shown, the tensor CP decomposition of the third-order tensor Z(x,y,t) can be described as:

[0043]

[0044] In the formula, the tensor It represents the approximate tensor obtained by decomposing and reconstructing the original tensor Z(x, y, t) through tensor CP. The Λ form is a superdiagonal tensor, which is characterized by non-zero diagonal elements and all other elements are 0, such as Figure 2 As shown. λ represents the diagonal element value of the superdiagonal tensor, and its meaning represents the degree of correlation between different decomposition factor matrices. and They represent the decomposition factor matrices of the original tensor Z(x, y, t) in three modes. The decomposition factor matrix can be specifically represented by the corresponding vectors of the three dimensions as X = [x 1 ,x 2 ,...,x r ],Y=[y 1 ,y 2 ,...,y r ],T=[t 1 ,t 2 ,...,t r ], and the decomposition factor matrix is ​​usually orthogonal and can be regarded as the principal component along the corresponding mode. Where x is the column vector of the X modal factor matrix. In formula (2) Represents the outer product, also known as the vector product or cross product, which is a binary operation that combines two vectors in three-dimensional space into a higher-dimensional tensor. The element representation of the tensor outer product as follows:

[0045]

[0046] Step (3) constructs a low-order time characteristic prediction model based on a recurrent neural network (RNN), wherein the prediction model consists of two recurrent network layers and one fully connected layer, wherein: the recurrent network layer predicts the input sequence, and a PReLU activation function is connected after each recurrent network layer to further improve the expression ability of the model; the fully connected layer performs weighted summation on the output of the recurrent network layer, converts the features predicted by the recurrent network layer into the final prediction results, and finally the activation function is used to further improve the nonlinear approximation ability of the model.

[0047] Step (4) Given a sequence of external input variables, the low-order time characteristic matrix obtained by tensor CP decomposition and the RNN-based low-order time characteristic prediction model are used to predict the low-order time characteristic matrix at future moments, and then the two spatial characteristic matrices are combined for dimensionality increase and reconstruction to obtain the high-order temperature field prediction value at future moments.

[0048] In the present invention, the process of predictive modeling is to construct a lookback window of size w at each sampling time k, and construct a prediction model for the data set based on the true value of the time component from the kth time to the previous kw times and the external factors of the system. Iterative update is performed. The purpose is to enable the model to obtain a single-step predicted temperature field prediction tensor based on the system input and the current state of the controlled object.

[0049] Assume that the observation value of the time modal factor matrix T(t,r) at point (p,γ) is t γ (p). Where γ represents the γth component in the T(t,r) matrix, and p represents the pth time step, then 1≤p≤k and 1≤γ≤r t The prediction process considers the oxidant flow v(t) of the SOFC cell and the low-order time characteristic matrix component t r (t) constitutes the following external input sequence data set samples

[0050] U(t)=[t r (t)...t r (tw); v(t)...v(tw)] T (4)

[0051] Where w is the size of the lookback window. Establish a time series prediction data set, let w<p<k, then the feature window constructed at time p is U(p)=[t γ (p)...t γ (pw); v(p)...v(pw)] T Through the prediction model The modeling results in the following functional relationship:

[0052]

[0053] In the formula, It is a set of time series prediction models based on RNN training, representing the use of time characteristic matrix component t γ Combined with the first w historical observations in the external input variable sequence, we get U(p), and use U(p) to predict the predicted value of the time characteristic matrix component at the next moment. All r t Quantity Aggregate and merge into a predicted low-order time matrix What you get Expands to the following form:

[0054]

[0055] Finally, the high-order temperature field prediction tensor at the future moment is obtained by inverse transformation of tensor CP. It is expressed as:

[0056]

[0057] For the prediction tensor Perform inverse normalization to obtain high-order temperature field data on the original feature space The predicted value at the future time p+1. Inverse normalization formula:

[0058]

[0059] In the present invention, the spatiotemporal modeling process can be described as:

[0060] 1. Tensor CP decomposition and time-space separation:

[0061] In this step, the tensor CP decomposition can be written in the following matrix form:

[0062]

[0063] In the formula, Z (n) represents the matrixization of the tensor Z in the nth mode. The matrixization of a tensor is also called tensor expansion or tensor flattening, which is the process of expanding a high-order tensor into a matrix along a certain mode. For example, Z (1) The first modulus expansion of Z keeps the first dimension of the tensor as the row index of the matrix, and the second and third dimensions form the column matrix of the matrix. The resulting matrix The “⊙” operation represents the Khatri-Rao product. In equation (9), for a matrix T=[t 1 ,t 2 ...,t r] and the y×r matrix Y=[y 1 ,y 2 ...,y r The Khatri-Rao product of ] is a matrix of shape ty×rr, as shown in formula (10):

[0064]

[0065] The core task of tensor CP decomposition is to solve the optimal factor matrices X, Y, and T, so that the Frobenius norm between the original tensor and the decomposition model is as small as possible. Therefore, the process of solving the decomposition factor can be written as an optimization problem:

[0066]

[0067] Among them, ||·|| represents the Frobenius norm of the tensor error, that is, the sum of all elements and then the square root:

[0068]

[0069] In the above formula, tensor E is the reconstruction tensor The error representation obtained by subtracting the original tensor Z, (E) αβγ is the element representation of the tensor E.

[0070] For equation (11), mathematically, it is an optimization problem of the objective function, and the decomposition factor matrix can be solved by the alternating least squares algorithm. The main idea of ​​the alternating least squares algorithm is to fix other variables to solve a single variable. X can be solved by fixing matrices Y and T; then fixing X and Y to solve T; then fixing X and T to solve Y. Repeat the above process until the convergence condition is met.

[0071] According to the tensor CP decomposition after tensor matrixization, the above minimization problem can be rewritten as:

[0072] in,

[0073] The optimal solution to the above minimization problem is:

[0074]

[0075] In the formula, the superscript "-1" indicates the pseudo-inverse of the tensor, and the pseudo-inverse of the Khatri-Rao product can be transformed. Therefore, the optimal solution of the above formula can also be written as:

[0076]

[0077] Finally, the solution process of solving the decomposition factor matrix by the alternating least squares algorithm in the present invention can be specifically expressed as follows: First, input the temperature field tensor data The approximate tensor is then approximated before the algorithm is solved using the random matrix method. Then, the algorithm starts to solve the problem in a loop, and each loop updates the X, Y, and T matrices and recalculates the approximate tensor After each iteration, check the convergence conditions If the convergence condition is met, the algorithm will stop iterating immediately; otherwise, the algorithm will stop iterating when the number of iterations reaches the maximum number of iterations i. max The iteration stops when . Finally, the algorithm outputs the solved factorization matrices X, Y, and T and the final approximate tensor

[0078] 2. Low-order temporal characteristics prediction modeling

[0079] The present invention adopts the prediction model constructed Identify low-order representation models. In the tensor CP decomposition stage, the decomposition result contains a low-order time characteristic matrix t r is the rth column vector in the low-order time characteristic matrix T(t,r), and a lookback window of size w is constructed. r The predictive modeling process can be described as: combining the oxidant flow rate v(t) with the low-order time characteristic matrix component t r (t) Construct an external input sequence data set sample U(t), set the activation function f(·), and train to obtain a prediction model The prediction process expression is:

[0080]

[0081] Prediction Model It contains 2 recurrent network layers and 1 fully connected layer, where each recurrent network layer is followed by a PReLU activation function. By introducing a recurrent network layer, the past information can be implicitly embedded in the current state when processing the input of each time step, so as to better understand the meaning of the current input. By combining the PReLU activation function, the slope on the negative axis can be adaptively adjusted, so that the network can better capture the features in the data, thereby making the prediction model in the present invention have a stronger ability to solve nonlinear problems. The mathematical calculation formula of the PReLU activation function is as follows:

[0082]

[0083] Among them, parameter a is a learnable parameter.

[0084] The function of the fully connected layer is to reduce the feature dimension of the output data of the recurrent network layer. The recurrent network layer contains multiple hidden layers and the number of neurons in the hidden layer is large, which leads to a high feature dimension of the output data. Since the prediction task adopts a single-step prediction, a linear layer is needed to reduce the feature dimension to 1.

[0085] The calculation process of the recurrent network layer is as follows Figure 3 As shown, where h t-1 and x t Represents the hidden state of the previous moment and the input of the current moment. The hidden state h t-1 What is saved is the information of the previous time step t-1, x t is the input vector of the tth time step. The two vectors are first concatenated together to form a new vector as the input for subsequent calculations. The concatenated vector is fed into a nonlinear transformation node with a tanh activation function to output a new hidden state h t , this process can be described by the following formula:

[0086]

[0087] Where W hx is the weight matrix, b h is the bias term, Represents a vector concatenation operation. Among them, the tanh activation function can standardize the input data to the range of (1,-1), which helps to maintain numerical stability during model training. The expression of the tanh activation function is as follows:

[0088]

[0089] The new hidden state h at the current moment is calculated t After that, then by h t Participate in calculating the output o at the current moment t , and h t is retained as one of the inputs for the next moment. Among them, the output o at the current moment t It can be expressed as:

[0090] o t =W ho h t +b o (20)

[0091] Where W ho The weight matrix from hidden state to output, b o is the bias term of the output layer.

[0092] Since the time series prediction method used in the present invention is a single-step prediction of multiple input variables, the input features are n=1 (n depends on the number of external input variables considered in the prediction modeling), the number of features of the prediction module prediction output depends on the size of the hidden layer, and the output of the prediction model in the single-step prediction is a single value. Therefore, it is necessary to add a fully connected layer after the prediction module to reduce the features, so as to obtain the output of the single-step prediction and increase the prediction model. The nonlinear expression ability of the model is as follows: Figure 4 shown.

[0093] In the present invention, the definitions of the above parameters are shown in Table 1:

[0094] Table 1

[0095]

[0096]

[0097]

[0098] Example 1

[0099] This embodiment provides a prediction modeling method based on tensor CP decomposition and RNN structure, the method comprising the following steps:

[0100] Step (1) collects a two-dimensional temperature field data set of a cross-flow flat-plate SOFC single cell surface, preprocesses the data, and organizes the data into a tensor form to obtain a two-dimensional temperature field tensor of the cell surface.

[0101] Step (2) performs a tensor CP decomposition with an initial rank r of 1 on the two-dimensional temperature field tensor on the surface of a single cell of a cross-flow flat-plate SOFC to obtain a spatial modal decomposition factor matrix, a temporal modal factor matrix and a core superdiagonal tensor, and determines whether the inverse transformation result of the tensor CP decomposition and the reconstruction error of the original data meet the accuracy requirements of the system; if not, discard the decomposition result and increase the rank of the tensor decomposition, repeat the above steps until the reconstruction error meets the accuracy requirements, and extract two spatial modal factor matrices as the spatial characteristics of the high-order data, and the temporal modal factor matrix as the low-order temporal characteristics.

[0102] Step (3) uses the low-order time characteristic matrix obtained by tensor CP decomposition, given an external input variable sequence, to train the RNN-based prediction model, and then predict the low-order time characteristic matrix of the system in the future.

[0103] Step (4) reconstructs the predicted low-order time characteristic matrix, spatial modal factor matrix, and superdiagonal tensor by up-dimensionality to obtain a high-order predicted value of the two-dimensional temperature field on the surface of the SOFC single cell at a future time.

[0104] Example 2

[0105] In order to demonstrate the effectiveness of the modeling method based on tensor CP decomposition and RNN-based time series prediction in Example 1, this example takes a cross-flow flat-plate SOFC single cell as an example to study the temperature field modeling problem during its operation under different oxidant flow input conditions, illustrating that this method has the advantages of high efficiency and stability.

[0106] The test conditions are described as follows:

[0107] Consider a cross-flow flat-plate SOFC single cell with a size of 100.5 mm*100.5 mm and a structure as follows: Figure 5 As shown. Assume that 10×10 temperature probes are evenly arranged on the surface of the SOFC cell, the ambient temperature and initial operating temperature are 800℃, the sampling period is 1s, and the total experimental time is 3600s. Given that the anode input uses hydrogen as fuel, its input flow rate is 2m / s, and the cathode input uses oxygen as the oxidant, its input flow rate is v(t), as shown Figure 6 The experimental process was solved by finite element analysis to obtain the two-dimensional temperature field data T of the SOFC single cell surface. temp (x, y, t), which is preprocessed in the technical details and organized into third-order tensor data The result of slicing and visualizing the obtained tensor Z(x,y,t) along the time dimension is as follows: Figure 7 As shown in Figure 2, the reconstruction error of the given temperature field is required to be no greater than 3°C.

[0108] Result analysis:

[0109] First, the original tensor Z(x, y, t) is subjected to tensor CP decomposition, and the inspection reconstruction error method described in the present invention is used to determine the final rank r=4 of the tensor CP decomposition, and its maximum reconstruction error is 2.38°C, which meets the accuracy requirement. The reconstruction error slice obtained by inverse transformation and dimensionality increase after tensor CP decomposition is visualized, as shown in Figure 8 As shown. Subsequently, the tensor CP decomposition factor matrix T(t,r) in the time mode is as follows: Fig. 9 As shown in the figure, by analyzing the visualization results of the reconstruction error slices, although the tensor CP decomposition algorithm is a linear algorithm, its reconstruction accuracy can meet the expected requirements when processing the nonlinear distribution data of the two-dimensional temperature field on the surface of a single SOFC cell.

[0110] Then, the prediction model is established using the method described in the present invention. Then the time modal component t 1 ,t 2 ,t 3 and t 4 Combined to obtain the low-order time characteristic prediction matrix The results are as follows Fig.10 shown. Fig.10 The red dashed line represents the prediction result of the training set, the blue dotted line represents the prediction result of the test set, and the black solid line represents the true value. It can be clearly seen from the experimental results that the prediction model Not only does it perform well on the training data, it also shows good generalization ability on the test set, which shows that the prediction model The main features of the time series are effectively captured, and the dynamic changes of the time modal factor matrix are successfully learned.

[0111] Finally, combining the spatial decomposition factor matrices X, Y, the core diagonal tensor Λ and the low-order temporal feature prediction matrix After the inverse transformation of tensor CP decomposition, high-order tensor prediction data can be obtained

[0112] The above modeling process runs on a computer with an Intel i7-11800H CPU, DDR416 memory, and an Nvidia GeforceRTX 3070 graphics card. The training time of the model is approximately 430.85s, and the single-step running time of the model is approximately 2.49s.

[0113] The spatiotemporal error function ζ, root mean square error (RMSE) and maximum error rate (MER) are defined as:

[0114]

[0115] In this embodiment, the slice visualization result of the error tensor ζ(x, y, t) is as follows: Fig.11 As shown. By observing the result information in the figure, it can be seen that the maximum error is only 1.96℃. The maximum error rate MER reflects the performance of the model in the worst case, indicating that the model described in the present invention can control the error within a reasonable range. RMSE is one of the commonly used indicators for evaluating the accuracy of the prediction model. It measures the degree of deviation between the predicted value and the true value. RMSE = 0.723 indicates that the deviation of the model is small and the overall modeling accuracy is high.

[0116] Aiming at the problem of modeling the two-dimensional temperature field on the surface of a single cell of a cross-flow flat-plate SOFC, this embodiment avoids the process of establishing a highly coupled complex mathematical model and the long cost of model solving, solves the problem that the traditional finite element analysis method is time-consuming and not suitable for online application, and illustrates the advantages of the method of the present invention in terms of short calculation time and high model accuracy.

Claims

1. A method for predicting the surface temperature field of a cross-flow flat-plate SOFC single cell based on tensor CP decomposition, characterized in that The method comprises the following steps: Step (1) sufficient temperature sensors are arranged on the surface of the SOFC single cell to collect the cell surface temperature information when the SOFC single cell works normally under a given operating environment and gas input flow rate conditions over a period of time, and the obtained two-dimensional temperature field data of the cell surface are preprocessed and sorted into a tensor form to obtain a two-dimensional temperature field tensor of the SOFC single cell surface; Step (2) selects the initial rank of the tensor CP decomposition as 1, uses the tensor CP decomposition to the two-dimensional temperature field tensor of the SOFC single cell surface obtained in step (1), and determines whether the inverse transformation result of the tensor CP decomposition and the reconstruction error of the original data meet the accuracy requirements. If not, discard the decomposition result and increase the rank of the tensor decomposition. Repeat the above judgment until the reconstruction error meets the preset accuracy, extract two spatial modal factor matrices as two spatial characteristic matrices of the original high-order data, and extract the time modal factor matrix as the low-order time characteristic matrix; Step (3) constructing a low-order time characteristic prediction model based on RNN, wherein the prediction model consists of two recurrent network layers and one fully connected layer, wherein: the recurrent network layer predicts the input sequence, and a PReLU activation function is connected after each recurrent network layer to further improve the expression ability of the model; the fully connected layer performs weighted summation on the output of the recurrent network layer, converts the features predicted by the recurrent network layer into the final prediction result, and finally further improves the nonlinear approximation ability of the model through the activation function; Step (4) Given a sequence of external input variables, the low-order time characteristic matrix obtained by tensor CP decomposition and the RNN-based low-order time characteristic prediction model are used to predict the low-order time characteristic matrix at future moments, and then the two spatial characteristic matrices are combined for dimensionality increase and reconstruction to obtain the high-order temperature field prediction value at future moments.

2. The method for predicting the surface temperature field of a cross-flow flat-plate SOFC single cell based on tensor CP decomposition according to claim 1 is characterized in that The specific steps of step (1) are as follows: Step (11) assumes that sufficient temperature sensors are arranged on the surface of the SOFC cell, that is, m×n temperature sensors are evenly arranged on the x-axis and y-axis, where m is the number of temperature sensors in each row on the x-axis, n is the number of temperature sensors in each column on the y-axis, the total number of time steps in the test process is k, the oxidant flow rate at the t-th moment is v(t), and the spatiotemporal data set of the two-dimensional temperature field on the surface of the SOFC cell collected at k time steps is T temp (x,y,t); Step (12) collects the temperature field spatiotemporal data set T temp (x, y, t) to preprocess the data and obtain the two-dimensional temperature field tensor of the SOFC single cell surface. The specific steps are as follows: First, the collected data is checked for missing values, and if missing values ​​exist, they are filled with the mean value of the temperature matrix at the current moment; Secondly, check whether there are outliers in the tensor elements. If the data contains noise data greater than 3 times the standard deviation, replace it with the mean of the temperature matrix at the current moment; Finally, the data is normalized to the maximum and minimum values ​​so that the original data range is scaled between 0 and 1 to obtain the two-dimensional temperature field tensor of the SOFC single cell surface.

3. The method for predicting the surface temperature field of a cross-flow flat-plate SOFC single cell based on tensor CP decomposition according to claim 1 is characterized in that The specific steps of step (2) are as follows: Step (21) performs a tensor CP decomposition with an initial rank of 1 on the obtained two-dimensional temperature field tensor Z (x, y, t) on the surface of the SOFC single cell to obtain two spatial modal decomposition factor matrices and one temporal modal decomposition factor matrix; Step (22) determines whether the inverse transformation result of the tensor CP decomposition and the reconstruction error of the original data meet the accuracy requirements of the system; if not, discard the decomposition result, increase the rank of the tensor CP decomposition, repeat the above steps of tensor CP decomposition until the reconstruction error meets the accuracy requirements, and obtain the final rank r; Step (23) extracts the spatial modal factor matrix as the spatial characteristic matrix of the original high-order data, and the temporal modal factor matrix as the low-order temporal characteristic matrix.

4. The method for predicting the surface temperature field of a cross-flow flat-plate SOFC single cell based on tensor CP decomposition according to claim 3 is characterized in that The tensor CP decomposition is described as: In the formula, represents the approximate tensor obtained by decomposing and reconstructing the quantity Z(x,y,t) through the tensor CP; Λ is the superdiagonal tensor; λ represents the diagonal element value of the superdiagonal tensor; and Respectively represent the decomposition factor matrices of Z(x,y,t) in three spatial modes; Represents the outer product.

5. The method for predicting the surface temperature field of a cross-flow flat-plate SOFC single cell based on tensor CP decomposition according to claim 1 is characterized in that The calculation process of the recurrent network layer is as follows: h t-1 and x t Represents the hidden state of the previous moment and the input of the current moment. The hidden state h t-1 What is saved is the information of the previous time step t-1, x t is the input vector of the tth time step. The two vectors are first concatenated together to form a new vector as the input for subsequent calculations. The concatenated vector is sent to a nonlinear transformation node with a tanh activation function to output a new hidden state h t , this process is described by the following formula: Where W hx is the weight matrix, b h is the bias term, Represents a vector concatenation operation; The new hidden state h at the current moment is calculated t Afterwards, by h t Participate in calculating the output o at the current moment t , and h t is retained and used as one of the inputs for the next moment.

6. The method for predicting the surface temperature field of a cross-flow flat-plate SOFC single cell based on tensor CP decomposition according to claim 5 is characterized in that Said o t It is expressed as: o t =W ho h t +b o Where W ho The weight matrix from hidden state to output, b o is the bias term of the output layer.

7. The method for predicting the surface temperature field of a cross-flow flat-plate SOFC single cell based on tensor CP decomposition according to claim 1 is characterized in that The specific steps of step (4) are as follows: Step (41) Assume that the observed value of the time modal factor matrix T(t,r) at point (p,γ) is t γ (p), where γ represents the γth component in the T(t,r) matrix and p represents the pth time step, then 1≤p≤k and 1≤γ≤r t ; Step (42) The prediction process considers the oxidant flow v(t) of the SOFC cell and the low-order time characteristic matrix component t r (t), constitutes the following external input sequence data set samples U(t)=[t r (t)...t r (t-w);v(t)...v(t-w)] T Among them, w is the size of the lookback window; Step (43) establishes a time series prediction data set, and sets w<p<k. Then the feature window constructed at time p is U(p)=[t γ (p)...t γ (pw); v(p)...v(pw)] T ; Step (44) obtains the following functional relationship by modeling the low-order time characteristic prediction model: In the formula, It is a low-order temporal feature prediction model based on RNN, which represents the use of temporal feature matrix component t γ Combined with the first w historical observations in the external input variable sequence, we get U(p), and use U(p) to predict the predicted value of the time characteristic matrix component at the next moment. Step (45) convert all r t Quantity Aggregate and merge into a predicted low-order time matrix What you get Expands to the following form: Step (46) obtains the high-order temperature field prediction tensor at the future moment by inverse transformation of tensor CP. It is expressed as: Step (47) Perform inverse normalization to obtain high-order temperature field data in the original feature space The predicted value at time p+1 in the future.

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