Fluidized bed flow field reconstruction method, system, equipment and medium based on limited measuring points

Abstract

The invention discloses a fluidized bed flow field reconstruction method, system and device based on limited measuring points and a medium. The method comprises the steps that fluidized bed internal flow field data obtained through CFD simulation is divided into a training set and a verification set; extracting a main POD mode of the physical field data from the training set and a mode coefficient of the corresponding POD mode; decomposing the POD modal matrix through QR, determining the position of a measuring point, and obtaining a measuring point signal at each moment; inputting the training set into a multi-layer perceptron model for training, and inputting a measuring point signal in the verification set at the current moment into a prediction model to obtain a predicted POD modal coefficient; carrying out linear superposition on the predicted POD modal coefficient and the main POD modal, and reconstructing an instantaneous physical field in combination with a time-mean value of physical field data; the system, the equipment and the medium are used for realizing the method. According to the reconstruction method, the multiple physical fields in the fluidized bed can be obtained in real time, and the measurement efficiency is improved on the premise that the reconstruction precision is guaranteed.

Description

Technical Field

[0001] The present invention belongs to the technical field of fluidized bed flow field reconstruction, and particularly relates to a fluidized bed flow field reconstruction method, system, device and medium based on finite measurement points. Background Art

[0002] Gas-solid fluidized bed reactors are widely used in the process industries of clean and efficient utilization of coal, petroleum and biomass. The real-time reconstruction and advanced prediction of the mesoscale structure (solid holdup field) and other physical fields inside the fluidized bed are of great significance for the real-time dynamic optimization of fluidized bed reactors, and the monitoring of abnormal conditions such as hot spots and flow dead zones. However, the current experimental and numerical simulation technology levels are not sufficient to support the real-time acquisition of multiple physical fields inside the fluidized bed, and the number of sensors that can be installed in the fluidized bed is limited. Only the measured point signals at some positions in the fluidized bed can be obtained by installing sensors. The existing related work mainly focuses on constructing a reduced-order model of the flow field, and there are currently problems that the reduced-order model cannot correspond to the internal state of the real fluidized bed and the long-term prediction error grows infinitely.

[0003] From the research progress at home and abroad, the fluidized bed flow field reconstruction technology based on measured point signals is still blank. Some related research appears in the field of turbulent flow reconstruction. Willcox K et al. (Willcox K. Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition[J]. Computers & Fluids, 2006, 35(2): 208-226.) used the Gappy POD method to reconstruct the turbulent flow field, but the number of measured points used is large, and it is impossible to accurately reconstruct the flow field based on a small number of measured points, and it cannot be directly used for the flow field reconstruction of more complex gas-solid fluidized beds. Summary of the Invention

[0004] In order to overcome the above-mentioned shortcomings in the prior art, the purpose of the present invention is to provide a fluidized bed flow field reconstruction method, system, device and medium based on finite measurement points. By analyzing the flow field inside the fluidized bed device, its main modes are obtained, and the spatial positions where the main physical information that can reflect the change of the mode coefficients are determined through OR mode decomposition. These positions are the optimal measurement point positions under the finite number of measurement points. The multi-layer perceptron model is optimized by the measured point signals at the optimal measurement point positions to accurately predict the POD mode coefficients, and then the entire physical field is restored through the predicted POD mode coefficients, thereby realizing the function of restoring the spatial physical field distribution inside the entire fluidized bed device with a finite number of measurement points and reducing the number of sensor arrangements; the reconstruction method of the present invention can not only obtain the information of multiple physical fields inside the fluidized bed in real time, but also has high reconstruction accuracy of the physical field.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A fluidized bed flow field reconstruction method based on limited measurement points includes the following steps:

[0007] Step 1: Obtain flow field data in the fluidized bed for a period of time based on CFD simulation, and divide the flow field data into a training set and a validation set;

[0008] Step 2: Extract the time-averaged value of the physical field data from the training set, perform intrinsic orthogonal decomposition (POD) on the physical field data after removing the time-averaged value, and extract r POD modes Φ j (x) is used as the main POD mode to form the POD mode matrix Φ and calculate the modal coefficients α of the r POD modes j (t i );

[0009] Step 3: POD modal matrix Φ composed of row vectors T Perform QR decomposition to obtain a column permutation matrix C; extract the first p rows of the column permutation matrix C to obtain an optimized measurement matrix M; determine the measurement point position based on the optimized measurement matrix M, and obtain the measurement point signal at each moment;

[0010] Step 4: Input the training set into the multi-layer perceptron model for training to obtain the prediction model of the POD modal coefficient; input the measurement point signal at the current moment in the validation set into the prediction model of the POD modal coefficient for feature extraction, and map the measurement point signal feature at the current moment to the modal coefficient α of the main POD mode j (t i ), and obtain the predicted POD modal coefficients;

[0011] Step 5: Compare the predicted POD modal coefficients with the corresponding main POD mode Φ in step 2 j (x) is linearly superimposed to obtain the pulsation value of the predicted physical field data, and combined with the time-averaged value of the physical field data extracted in step 2 to reconstruct the instantaneous physical field.

[0012] In step 1, a snapshot of the flow field data is sampled to obtain flow field data in the form of a D×N×M matrix, where D is the number of physical fields, N is the number of grids, and M is the number of snapshots; the physical field is one or more of the three directional components of solid content, gas phase pressure, and gas phase velocity and solid phase velocity.

[0013] The specific process of step 2 is as follows:

[0014] Step 2.1: Arrange the corresponding physical field data in the training set into a matrix Q(x,t i), where \(i = 1, 2, \cdots, M\), the dimension of matrix \(Q\) is \([N, M]\), where \(N\) is the number of grids and \(M\) is the number of snapshots; extract the time-averaged value of the physical field data The formula is as follows:

[0015]

[0016] Step 2.2: Remove the time-averaged value from the physical field data and calculate the pulsation value \(Q'(x, t)\) of the physical field data i ), the formula is as follows:

[0017]

[0018] Step 2.3: Perform proper orthogonal decomposition (POD) on the pulsation value \(Q'(x, t)\) of the physical field data i ) through singular value decomposition (SVD) to obtain all POD modes. The formula is as follows:

[0019]

[0020] where \(U = [u_1, u_2, \cdots, u r \) and \(V = [v_1, v_2, \cdots, v r \) are both orthogonal matrices. Each column of \(V\) is related to the time series of the modal coefficients of the physical field data; each column of \(U\) represents a POD mode of the physical field pulsation value \(Q'(x, t)\) i ), that is, \(\varPhi j (x)\). These column vectors form the POD mode matrix \(\varPhi\); \(\alpha j (t i ) represents the \(j\)-th POD mode coefficient; matrix \(\varLambda\) represents a diagonal matrix with diagonal elements being the singular values \(s i arranged from largest to smallest;

[0021] Step 2.4: Extract \(r\) POD modes \(\varPhi j (x)\) from all POD modes and calculate the modal coefficients \(\alpha j (t i );

[0022] Specifically: Sort the energy contributions of all POD modes from largest to smallest, and extract all the POD modes before the \(r\)-th POD mode \(\varPhi j (x)\) corresponding to the cumulative energy of 80% - 99% as the main POD modes;

[0023] The expression of the said energy contribution is where \(s i 2 is the \(j\)-th POD mode \(\varPhi j(x), where N is the number of grids and M is the number of snapshots.

[0024] In step 2.4, the j-th POD mode Φ j (x) and the modal coefficient α j (t i ) are calculated as follows: Project the fluctuating value Q′(x, t i ) of the physical field data onto the j-th POD mode Φ j (x), i.e., α j (t i ) = Φ j T (x)Q′(x, t i ).

[0025] In step 3, the first p rows of the column permutation matrix C are determined according to the extracted number of modes r, i.e., p = r.

[0026] In step 4, the multi-layer perceptron model consists of four layers. The first layer is the input layer for inputting the measurement point signals; the second layer is the first hidden layer for extracting the features of the measurement point signals; the third layer is the second hidden layer for mapping the features of the measurement point signals to the modal coefficients α j (t i ) of the main POD modes; the fourth layer is the output layer for outputting the POD modal coefficients α j (t i ).

[0027] In step 5, the expression of the reconstructed instantaneous physical field is:

[0028]

[0029] where, represents the predicted POD modal coefficient, Φ j (x) represents the corresponding main POD mode in the training set, represents the time average value of the physical field extracted from the training set.

[0030] The present invention also provides a fluidized bed flow field reconstruction system based on limited measurement points, including:

[0031] Acquisition module: Obtain the flow field data in the fluidized bed for a period of time according to CFD simulation, and divide the flow field data into a training set and a validation set;

[0032] Extraction module: Extract the time average value of the physical field data from the training set, perform proper orthogonal decomposition POD on the physical field data after removing the time average value, extract r POD modes Φ j (x) as the main POD modes, form the POD mode matrix Φ, and calculate the modal coefficients α of the r POD modesj (t i );

[0033] Decomposition module: Perform QR decomposition on the POD modal matrix Φ composed of row vectors to obtain the column permutation matrix C; Extract the first p rows of the column permutation matrix C to obtain the optimized measurement matrix M; Determine the measuring point positions according to the optimized measurement matrix M and obtain the measuring point signals at each moment; T Perform QR decomposition on the POD modal matrix Φ composed of row vectors to obtain the column permutation matrix C; Extract the first p rows of the column permutation matrix C to obtain the optimized measurement matrix M; Determine the measuring point positions according to the optimized measurement matrix M and obtain the measuring point signals at each moment;

[0034] Model training module: Input the training set into the multi-layer perceptron model for training to obtain the prediction model of the POD modal coefficients; Input the measuring point signal at the current moment in the validation set into the prediction model of the POD modal coefficients for feature extraction, and map the feature of the measuring point signal at the current moment to the modal coefficients α of the main POD modes j (t i ) to obtain the predicted POD modal coefficients;

[0035] Reconstruction module: Linearly superimpose the predicted POD modal coefficients and the corresponding main POD modes Φ j (x) to obtain the pulsation value of the predicted physical field data, and combine it with the time average value of the extracted physical field data to reconstruct the instantaneous physical field.

[0036] The present invention also provides a fluidized bed flow field reconstruction device based on limited measuring points, including:

[0037] Memory: Used to store the computer program of the above-mentioned fluidized bed flow field reconstruction method based on limited measuring points, which is a computer-readable device;

[0038] Processor: Used to implement the above-mentioned fluidized bed flow field reconstruction method based on limited measuring points when executing the computer program.

[0039] The present invention also provides a computer-readable storage medium, the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it can implement the above-mentioned fluidized bed flow field reconstruction method based on limited measuring points.

[0040] Compared with the prior art, the beneficial effects of the present invention are:

[0041] 1. The present invention uses a multi-layer perceptron model to extract the features of the measuring point signals and complete the mapping of the features of the measuring point signals to the modal coefficients of the main POD modes, and has lower reconstruction error compared with the traditional Gappy POD reconstruction method.

[0042] 2. Through QR modal decomposition and a multi-layer perceptron model, the present invention can jointly reconstruct the internal physical field information of the entire fluidized bed device using the signals at a small number of measurement point positions, having the ability to reconstruct the information of the entire field from local and limited measurement point information, and improving the measurement efficiency.

[0043] 3. The present invention performs singular value decomposition (SVD) on the flow field in the fluidized bed to achieve proper orthogonal decomposition (POD), obtains its main POD modes, and determines the spatial positions where the main physical information reflecting the change of the modal coefficients is located through OR modal decomposition. These positions are the optimal measurement point positions under a limited number of measurement points. Measuring at these positions can obtain more flow field information, which is equivalent to reducing the number of sensors to achieve the same measurement accuracy.

[0044] In summary, compared with the prior art, the fluidized bed flow field reconstruction method based on limited measurement points proposed by the present invention, through QR modal decomposition and a multi-layer perceptron model, can not only obtain multiple physical fields in the fluidized bed in real time, but also has a reconstruction response speed of less than 10 ms in actual measurement, which can meet the signal real-time reconstruction in most application scenarios. Compared with traditional CFD calculations, it greatly improves the reconstruction efficiency of the overall physical field. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flow chart of the fluidized bed flow field reconstruction method based on limited measurement points of the present invention.

[0046] Figure 2 is a schematic diagram of a simulated fluidized bed and the corresponding time-averaged solid holdup field contour map, where Figure 2 (a) is a schematic diagram of the simulated fluidized bed, Figure 2 (b) is the time-averaged solid holdup field contour map.

[0047] Figure 3 is the POD energy spectrum of the solid holdup field.

[0048] Figure 4 is the comparison between the reconstructed contour map and the real contour map of the instantaneous solid holdup field when retaining different numbers of modes at 10 s, where Figure 4 (a) is the reconstructed contour map of the first 16 modes, Figure 4 (b) is the reconstructed contour map of the first 24 modes, Figure 4 (c) is the reconstructed contour map of the first 95 modes, Figure 4 (d) is the real contour map.

[0049] Figure 5 is the comparison between the reconstructed contour map of the instantaneous solid holdup field by the reconstruction method of the present invention and the traditional GappyPOD method and the real contour map, where Figure 5 (a) is the reconstructed contour map using the traditional GappyPOD method, Figure 5(b) is the reconstructed cloud map using the reconstruction method of the present invention, Figure 5 (c) is the real cloud map. Detailed implementation manners

[0050] The technical solution of the present invention will be further introduced below in conjunction with the accompanying drawings and embodiments.

[0051] As Figure 1 shown, a fluidized bed flow field reconstruction method based on limited measurement points includes the following steps:

[0052] Step 1: Perform computational fluid dynamics (CFD) simulation on the simulated fluidized bed to obtain high-fidelity flow field data in the fluidized bed for a period of time, sample snapshots of the flow field data at a certain time interval, and obtain flow field data in the form of a D×N×M matrix, where D is the number of physical fields, N is the number of grids, the 2D or 3D grids are flattened into 1D, and M is the number of snapshots; then divide the flow field data into a training set and a validation set according to the number of snapshots M; the physical fields include one or more of solid volume fraction, gas phase pressure, and three direction components of gas phase velocity and solid phase velocity;

[0053] In this embodiment, the physical field is the solid volume fraction field φ s ;

[0054] Step 2: Extract the time average value of the physical field data from the training set, perform proper orthogonal decomposition (POD) on the physical field data after removing the time average value, and extract r POD modes Φ j (x) as the main POD modes to form a POD mode matrix Φ, and obtain the mode coefficients α j (t i );

[0055] Step 2.1: Arrange the corresponding physical field data in the training set into a matrix Q(x,t i ) with each moment as a column vector, i = 1, 2,..., M, the dimension of the matrix Q is [N, M], where N is the number of grids and M is the number of snapshots; extract the time average value of the physical field data The formula is as follows:

[0056]

[0057] Figure 2 (a) is a schematic diagram of the simulated fluidized bed model, and the blue area is the initial particle bed layer; Figure 2 (b) is the time-averaged solid volume fraction field cloud map extracted from the training set data, indicating the spatial distribution information of the solid volume fraction φ s Before performing POD, the mean value needs to be removed from each snapshot in the training set.

[0058] Step 2.2: Remove the time-average value from the physical field data and calculate the pulsation value Q′(x,t i ), and the formula is as follows:

[0059]

[0060] Step 2.3: Perform singular value decomposition (SVD) on the pulsation value Q′(x,t i ) to achieve POD and obtain all POD modes. The formula is as follows:

[0061]

[0062] where U = [u1, u2,..., u r and V = [v1, v2,..., v r are both orthogonal matrices. Each column of V is related to the modal coefficient time series of the physical field data; each column of U represents a POD mode of the physical field pulsation value Q′(x,t i ), that is, Φ j (x). These column vectors form the POD mode matrix Φ; α j (t i ) represents the modal coefficient of the j-th POD mode; the matrix Λ represents a diagonal matrix with diagonal elements being the singular values s i arranged from large to small.

[0063] Step 2.4: Extract r POD modes Φ j (x) from all POD modes as the main POD modes and calculate the modal coefficients α j (t i );

[0064] Specifically: Sort the energy contributions of all POD modes from large to small, and extract all POD modes before the r-th POD mode Φ j (x) corresponding to 80%-99% of the cumulative energy as the main POD modes; the expression of the energy contribution is where s i 2 is the energy of the j-th POD mode Φ j (x), N is the number of grids, and M is the number of snapshots.

[0065] The calculation of the modal coefficient α j (t i ) of the j-th POD mode is specifically: Project the pulsation value Q′(x,t i ) of the physical field data onto the j-th POD mode Φ j (x), that is, α j (ti )=Φ j T (x)Q′(x,t i ).

[0066] like Figure 3 As shown, the energy contribution (orange) and cumulative energy contribution (green) of all POD modes. In this embodiment, 83% of the cumulative energy is retained, that is, the intersection of the dotted lines in the figure corresponds to the 16th POD mode, so the first 16 POD modes are taken as the main POD modes.

[0067] Step 3: POD modal matrix Φ composed of row vectors T Perform column pivot orthogonal triangular (QR) decomposition to obtain a column permutation matrix C. Extract the first p rows of the column permutation matrix C. Determine the number of measurement points p based on the extracted modal number r, i.e., p = r, to obtain the optimized measurement matrix M, thereby quickly optimizing the measurement points. Determine the grid positions corresponding to positions where the row vectors of the optimized measurement matrix M are not 0 as the measurement point positions, and obtain the measurement point signals at each moment based on the measurement point positions, thereby reducing the reconstruction error of the physical field.

[0068] The formula for the pivot orthogonal triangular (QR) decomposition is as follows:

[0069] Φ T C T =QR

[0070] Where Φ represents an n×r matrix consisting of r POD modes, n is the number of grids N; C represents the matrix used to replace Φ T where Q is an orthogonal matrix and R is an upper triangular matrix.

[0071] Step 4: Input the training set into the multi-layer perceptron model (MLP) for training to obtain the prediction model of the POD modal coefficient; input the measurement point signal at the current moment in the validation set into the prediction model of the POD modal coefficient for feature extraction, and map the measurement point signal feature at the current moment to the modal coefficient α of the main POD mode j (t i ), and obtain the predicted POD modal coefficients.

[0072] The multi-layer perceptron model (MLP) consists of four layers. The first layer is the input layer, which is used to input the optimized measurement point signal; the second layer is the first hidden layer, which is used to extract the measurement point signal features; the third layer is the second hidden layer, which maps the measurement point signal features to the modal coefficient α of the main POD mode extracted from the training set through the ReLU activation function. j (t i ); The fourth layer is the output layer, which is used to output the POD modal coefficient α j (ti ); Each layer is composed of multiple neurons. The number of neurons in the input layer is determined by the number of measurement points p, and the number of neurons in the two hidden layers and the output layer is determined by the reconstruction error of the validation set Each neuron is connected to the neurons in the previous and next layers to form a fully connected neural network.

[0073] The reconstruction error The calculation formula is as follows:

[0074]

[0075] Among them, x i and denote the real and reconstructed physical fields at the i-th moment, respectively, ||·||2 denotes the 2-norm of the vector, and M denotes the number of snapshots in the validation set.

[0076] In this embodiment, the number of neurons in the input layer is 16, and the number of neurons in the two hidden layers and the output layer is 48.

[0077] Before training the multi-layer perceptron (MLP) model, both the input layer data and the output layer data are subjected to maximum and minimum normalization, and the trainable parameters of the fully connected neural network are achieved by reducing the mean square error (MSE) of the training set data.

[0078] Step 5: Based on the predicted POD modal coefficients, the main POD mode Φ corresponding to step 2 j (x) performing linear superposition to obtain the pulsation value of the predicted physical field data, and combining it with the time-averaged value of the physical field data extracted in step 2 to reconstruct the instantaneous physical field;

[0079] The reconstructed instantaneous physical field is shown The expression is:

[0080]

[0081] in, represents the predicted POD modal coefficient, represents the time-averaged value of the physical field extracted from the training set.

[0082] Figure 4 The reconstructed cloud map and the real cloud map of the instantaneous solid content field with different modes retained at 10s show that the spatial distribution structure of the reconstructed cloud map with 16 modes retained is consistent with that of the reconstructed cloud map with 24 and 95 modes retained, as well as the real cloud map, indicating that the reconstruction method of the present invention can fully reflect the large-scale structure in the solid content flow field with fewer measurement points, reducing the number of sensors required to achieve the same measurement accuracy.

[0083] Figure 5 (a) is the cloud map of the instantaneous solid holdup field reconstructed by the traditional Gappy POD method, and the traditional Gappy POD method uses regular measurement points for reconstruction; Figure 5 (b) is the cloud map of the instantaneous solid holdup field reconstructed by the reconstruction method of the present invention, Figure 5 (c) is the true cloud map of the instantaneous solid holdup field; the small circles in the figure indicate the positions of the measurement points. Compared with the traditional Gappy POD method, the reconstructed cloud map of the instantaneous solid holdup field by the reconstruction method proposed by the present invention is more consistent with the true cloud map of the instantaneous solid holdup field under the condition of the same number of measurement points, with good reconstruction quality and small reconstruction error.

Claims

1. A fluidized bed flow field reconstruction method based on limited measuring points, characterized in that It includes the following steps: Step 1: Obtain the fluidized bed internal flow field data for a period of time according to CFD simulation, and divide the flow field data into a training set and a validation set; Step 2: Extract the time-averaged value of the physical field data from the training set, perform proper orthogonal decomposition (POD) on the physical field data after removing the time-averaged value, and extract r POD modes Φ j (x) as the main POD modes, form the POD mode matrix Φ, and calculate the modal coefficients α j (t i ); Step 3: Perform QR decomposition on the POD modal matrix Φ composed of row vectors T to obtain a column permutation matrix C; extract the first p rows of the column permutation matrix C to obtain an optimized measurement matrix M; determine the measuring point positions according to the optimized measurement matrix M, and acquire the measuring point signals at each moment; Step 4: Input the training set into the multi-layer perceptron model for training to obtain a prediction model for the POD modal coefficients; input the measured point signal at the current moment in the validation set into the prediction model for the POD modal coefficients for feature extraction, and map the feature of the measured point signal at the current moment to the modal coefficient α j (t i ) of the main POD modes to obtain the predicted POD modal coefficients; Step 5: Linearly superpose the predicted POD modal coefficients with the corresponding main POD modes Φ j (x) to obtain the pulsation value of the predicted physical field data, and combine it with the time-average value of the physical field data extracted in Step 2 to reconstruct the instantaneous physical field.

2. The fluidized bed flow field reconstruction method based on limited measurement points according to claim 1, wherein: In Step 1, sample snapshots of the flow field data to obtain the flow field data in the form of a D×N×M matrix, where D is the number of physical fields, N is the number of grids, and M is the number of snapshots; the physical field is one or more of the solid holdup, gas phase pressure, and the three direction components of the gas phase velocity and the solid phase velocity.

3. A fluidized bed flow field reconstruction method based on limited measuring points according to claim 1, characterized in that, The specific process of Step 2 is as follows: Step 2.1: Arrange the corresponding physical field data in the training set into a matrix Q(x,t i ) as column vectors for each moment, where i = 1, 2,..., M. The dimension of matrix Q is [N, M], where N is the number of grids and M is the number of snapshots; extract the time-averaged value of the physical field data The formula is as follows: Step 2.2: Remove the time-averaged value from the physical field data and calculate the pulsation value Q′(x, t i ), and the formula is as follows: Step 2.3: For the pulsation value Q′(x,t i ) of the physical field data, perform proper orthogonal decomposition (POD) by singular value decomposition (SVD) to obtain all POD modes. The formula is as follows: where \(U = [u_1, u_2, \cdots, u r \) and \(V = [v_1, v_2, \cdots, v r \) are both orthogonal matrices, each column of \(V\) is related to the modal coefficient time series of the physical field data; each column of \(U\) represents a POD mode of the physical field pulsation value \(Q'(x, t i ), that is, \(\varPhi j (x)\), and these column vectors form the POD mode matrix \(\varPhi\); \(\alpha j (t i )\) represents the \(j\)th POD mode coefficient; the matrix \(\varLambda\) represents a diagonal matrix with diagonal elements being the singular values \(s i \) arranged from large to small; Step 2.4: Extract r POD modes Φ j (x), and calculate the modal coefficients α j (t i ) of the r POD modes; Specifically: Sort the energy contributions of all POD modes from largest to smallest, and extract all the POD modes before the r-th POD mode Φ j (x) corresponding to the cumulative energy of 80%-99% as the main POD modes; The expression for the energy contribution is where s i 2 is the energy of the j-th POD mode Φ j (x), N is the number of grids, and M is the number of snapshots.

4. A fluidized bed flow field reconstruction method based on limited measurement points according to claim 3, characterized in that, In step 2.4, the modal coefficient α j of the j-th POD mode Φ j (x) is calculated as follows: project the pulsation value Q′(x, t i ) of the physical field data onto the j-th POD mode Φ i (x), i.e., α j (t j ) = Φ i j T (x)Q′(x, t(x)Q′(x, t i ).

5. A fluidized bed flow field reconstruction method based on limited measurement points according to claim 1, characterized in that In Step 3, the first p rows of the column permutation matrix C are determined according to the extracted number of modes r, that is, p = r.

6. A fluidized bed flow field reconstruction method based on limited measurement points according to claim 1, characterized in that In step 4, the multi-layer perceptron model consists of four layers. The first layer is the input layer, which is used to input the optimized measured point signals. The second layer is the first hidden layer, which is used to extract the characteristics of the measured point signals. The third layer is the second hidden layer, which is used to map the characteristics of the measured point signals to the modal coefficient α j (t i ) of the main POD mode. The fourth layer is the output layer, which is used to output the POD modal coefficient α j (t i ).

7. A fluidized bed flow field reconstruction method based on limited measuring points according to claim 1, characterized in that In step 5, the reconstructed instantaneous physical field shown has the following expression: Among them, represents the predicted POD modal coefficient, and Φ j (x) represents the corresponding main POD mode in the training set, represents the time-averaged value of the physical field extracted from the training set.

8. A fluidized bed flow field reconstruction system based on limited measurement points, which is used to implement the method described in any one of claims 1-7, and is characterized in that, It includes: Acquisition module: Obtain the fluidized bed internal flow field data for a period of time according to CFD simulation, and divide the flow field data into a training set and a validation set; Extraction module: Extract the time-averaged value of the physical field data from the training set, perform proper orthogonal decomposition (POD) on the physical field data after removing the time-averaged value, and extract r POD modes Φ j (x) as the main POD modes to form the POD mode matrix Φ, and calculate the modal coefficients α j (t i ); Decomposition module: Perform QR decomposition on the POD modal matrix Φ composed of row vectors T to obtain a column permutation matrix C; extract the first p rows of the column permutation matrix C to obtain an optimized measurement matrix M; determine the measurement point positions according to the optimized measurement matrix M and acquire the measurement point signals at each moment; Model training module: Input the training set into a multi-layer perceptron model for training to obtain a prediction model of POD modal coefficients; Input the measured point signal at the current moment in the validation set into the prediction model of POD modal coefficients for feature extraction, and map the feature of the measured point signal at the current moment to the modal coefficient α j (t i ) of the main POD mode to obtain the predicted POD modal coefficients; Reconstruction module: linearly superimpose the predicted POD modal coefficients and the corresponding main POD modes Φ j (x) to obtain the pulsation value of the predicted physical field data, and combine it with the time average value of the extracted physical field data to reconstruct the instantaneous physical field.

9. A fluidized bed flow field reconstruction device based on limited measurement points, characterized in that It includes: Memory: Used to store the computer program of a fluidized bed flow field reconstruction method based on limited measurement points according to any one of claims 1-7, and is a computer-readable device; Processor: Used to implement a fluidized bed flow field reconstruction method based on limited measurement points according to any one of claims 1-7 when executing the computer program.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by the processor, it can implement a fluidized bed flow field reconstruction method based on limited measurement points according to any one of claims 1-7.

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