Orthogonal decomposition-based transient flow field solving reduced-order modeling method

Abstract

The invention discloses a transient flow field solving reduced-order modeling method based on orthogonal decomposition, and belongs to the technical field of flow field calculation. Firstly, CFD simulation calculation of a transient flow field is carried out, and a flow field simulation data set is constructed; and preprocessing the flow field simulation data set to generate a transient flow field data set for reduced-order modeling. According to the transient flow field data set, an orthogonal substrate is obtained based on an orthogonal decomposition method; normalizing the orthogonal substrate in a two-norm form; projecting the transient flow field data set to a space formed by the space substrate to obtain a projection coefficient; and recombining the projection coefficient, and solving a time base and a parameter coefficient based on an orthogonal decomposition method. And constructing a training model to train a mapping relationship between the input parameters and the base parameter coefficients. And finally, superposing the parameter coefficient, the time base and the space base of the to-be-solved flow field to obtain the distribution condition of the to-be-solved flow field in a certain time range. The method has the stability and the high efficiency of reduced-order modeling calculation, and the transient flow field can be rapidly solved.

Description

Technical Field

[0001] The invention belongs to the technical field of flow field calculation, and in particular relates to a transient flow field solution reduction modeling method based on orthogonal decomposition. Background Art

[0002] In the field of fluid mechanics, solving transient flow fields is an important and challenging topic. Transient flow fields refer to fluid flows that change over time. They are widely present in nature and engineering applications, such as turbulence, aerodynamics, and combustion processes. Accurately simulating and predicting the behavior of transient flow fields is of great significance for understanding complex flow phenomena, optimizing engineering design, and improving system performance. However, the traditional full-order model (FOM) usually has extremely high computational costs because it needs to calculate every spatial and temporal point in the flow field, and it is difficult to meet the real-time requirements in practical applications.

[0003] Transient flow fields occupy a central position in fluid mechanics because many real flow phenomena have significant time dependence. For example, turbulence is widely present in nature and industrial applications, including atmospheric turbulence, ocean currents, and pipeline flow. The transient characteristics of flow fields make their prediction and control extremely difficult.

[0004] Traditional full-order models provide high-precision flow descriptions by performing detailed numerical calculations at every spatial and temporal point in the flow field. However, this approach usually involves millions or even hundreds of millions of computing nodes, and the number of variables that need to be solved at each node is also very large, such as velocity, pressure, temperature, etc. In order to capture the transient characteristics of the flow field, numerical simulations need to be calculated using very small time steps, which further increases the amount of calculations. Calculations with high dimensions and high temporal resolution require a lot of computing resources, including processor time and storage space. This may be difficult to achieve in practical applications, especially for situations where real-time simulation and prediction are required.

[0005] In order to overcome the limitations of traditional full-order models, the present invention has developed a transient flow field solution reduced-order modeling method based on orthogonal decomposition, which achieves fast and accurate flow field solution by reducing the computational degrees of freedom and the amount of calculation. The core idea is to extract the main modes of the flow field through a data-driven method and construct a low-dimensional basis containing the main dynamic behaviors. These bases can be obtained through orthogonal decomposition technology and used to project the original data so that it can be approximated and reconstructed in a low-dimensional space. In this way, the main features of the flow field are effectively captured, the computational degrees of freedom are reduced, and an accurate description of the flow behavior is maintained. Summary of the invention

[0006] The purpose of the present invention is to overcome the defects of the prior art and provide a transient flow field solution reduced-order modeling method based on orthogonal decomposition.

[0007] In order to realize the reduced-order model method for solving transient flow fields, the present invention adopts the following technical solutions:

[0008] A transient flow field solution reduction modeling method based on orthogonal decomposition includes the following steps:

[0009] Step 1: Determine the parameter domain and parameter samples, perform CFD simulation calculations of the transient flow field, and construct the flow field simulation data set U'.

[0010] Step 2: Preprocess the flow field simulation data set U', including data interpolation, cleaning, and denoising, to generate a transient flow field data set U that can be used for reduced-order modeling.

[0011] Step 3: According to the transient flow field data set U, the eigenvector Γ and eigenvalue λ are obtained based on the orthogonal decomposition method: [Γ, λ] = eig(U T U), we further obtain the orthogonal basis Ω: Ω=UΓ.

[0012] Step 4: Normalize the orthogonal basis Ω by column in the form of bi-norm to obtain the normalized ROM space basis for:

[0013] Step 5: Transform the transient flow field dataset U to the spatial basis Projection is done in the space Φ of Zhang Cheng, and the projection coefficient A is obtained: A = Φ T U.

[0014] Step 6: Reorganize the projection coefficients, let The ROM reduction is further performed on M, and the time basis V and parameter coefficient L of the reorganized projection coefficient M are obtained based on the orthogonal decomposition method.

[0015] Step 7: Construct a training model to train the mapping relationship between the input parameter α and the parameter coefficient L to obtain the parameter coefficient L of the flow field to be solved * .

[0016] Step 8: Set the predicted parameter coefficient L * And the time basis V and space basis obtained based on the orthogonal analysis method By superposition, the distribution of the flow field to be solved within a certain time range can be obtained.

[0017] Preferably, in step one, the reduced-order model needs to first construct a flow field simulation data set, and the work of establishing a geometric model, defining material properties, setting boundary conditions, multi-physics field coupling, meshing, setting a solver, simulation calculation, etc. in the flow field simulation needs to be completed first in this step.

[0018] Preferably, in the step 2, necessary preprocessing is performed on the flow field simulation data set U', including data cleaning, denoising, etc., to ensure the accuracy and consistency of the transient flow field data set U.

[0019] Preferably, in step three, the ROM order reduction method is integrated, and orthogonal decomposition is used to perform linear algebraic operations on the transient flow field data set U to extract main features from the data set and construct an orthogonal basis.

[0020] Among them: ROM is the abbreviation of Reduced-Order Model, which is translated into reduced-order model in Chinese. Orthogonal decomposition methods are often used in reduced-order models, including eigenvalue decomposition (Eigenvalue Decomposition) or singular value decomposition (Singular Value Decomposition, SVD) to extract orthogonal bases. Orthogonal decomposition technology is used many times in the reduced-order model method for transient flow field solution. For example, the ROM reduced-order method in step 3 is eigenvalue decomposition, and its output form is [Γ,λ]=eig(U T U), step six obtains the time basis V and parameter coefficient L of the reorganized projection coefficient M based on the orthogonal decomposition method.

[0021] Preferably, in step 4, after obtaining the base, a normalized new ROM base is established, and this set of bases is represented in the form of a vector as The length of the normalized basis vector is 1, which avoids the loss of precision in numerical calculations caused by the amplitude of the basis vector being too large or too small, and improves the stability and reliability of the calculation process.

[0022] Preferably, in step 5, the transient flow field data set U is projected into the space Φ formed by the spatial basis to obtain the projection coefficient A. The projection coefficient A reflects the main mode and dynamic behavior of the transient flow field data in the low-dimensional basis space, and can identify the most important features and modes in the flow field, which is convenient for further analysis and processing.

[0023] Preferably, in step 6, an orthogonal decomposition method is integrated to extract the time basis and the corresponding coefficients through the orthogonal decomposition technology. The orthogonal decomposition of M is in the form of: M = V*L*V T , extract the main time basis V of the data, and solve the corresponding projection coefficient L, also known as the pst coefficient. Orthogonal decomposition reduces the dimensionality of high-dimensional data sets to low-dimensional subspaces, retaining the main features and reducing the amount of data. This can greatly simplify the analysis and calculation of complex systems.

[0024] Preferably, in step seven, a machine learning algorithm is used to train a regression model so that it can predict the projection coefficient L according to the input parameter α, and the relationship between the input parameter and the projection coefficient is established by training the model.

[0025] Among them: According to the characteristics of the data type in this method, the machine learning algorithm selects the linear regression algorithm. This method has more advantages in predicting continuous values ​​and can be used to construct a training model between the input parameter α and the parameter coefficient L to obtain the mapping relationship between the two.

[0026] Preferably, in step eight, the predicted parameter coefficient L * And the time basis V and space basis obtained based on the orthogonal analysis method Combination can predict the future flow field state distribution and realize the complete process from input parameters to predicting transient flow field distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 This is a model architecture diagram of the present invention;

[0028] Figure 2 is a flow chart of the present invention;

[0029] Figure 3 It is a schematic diagram of the effect of an embodiment of the present invention;

[0030] Figure 4 It is a schematic diagram of the effect of an embodiment of the present invention. DETAILED DESCRIPTION

[0031] The following is a further description of a specific implementation of a transient flow field solution reduction modeling method based on orthogonal decomposition of the present invention in conjunction with an embodiment. The transient flow field solution reduction modeling method based on orthogonal decomposition of the present invention is not limited to the description of the following embodiment.

[0032] Embodiment 1:

[0033] A transient flow field solution reduced-order modeling method based on orthogonal decomposition, such as Figure 1 , 2 , 3, including the following steps:

[0034] Step 1: According to the cylinder flow model, determine the input parameters - velocity, parameter sample n sensor 8 samples and 16 samples are selected respectively. CFD simulation calculation of transient flow field is carried out to construct flow field simulation data set U'. The flow state of different flow field moments in the data set is as follows: Figure 3 As shown in the cloud images a, b, c, and d on the left.

[0035] Step 2: Preprocess the flow field simulation data set U', including data interpolation, cleaning, and denoising, to generate a transient flow field data set U that can be used for reduced-order modeling.

[0036] Step 3: According to the transient flow field data set U, the eigenvector Γ and eigenvalue λ are obtained based on the orthogonal decomposition method: [Γ, λ] = eig(U T U), we further obtain the orthogonal basis Ω: Ω=UΓ.

[0037] Step 4: Normalize the orthogonal basis Ω by column in the form of bi-norm to obtain the normalized ROM space basis for:

[0038] Step 5: Transform the transient flow field dataset U to the spatial basis Projection is done in the space Φ of Zhang Cheng, and the projection coefficient A is obtained: A = Φ T U.

[0039] Step 6: Reorganize the projection coefficients,

[0040] The ROM reduction is further performed on M, and the time basis V and parameter coefficient L of the reorganized projection coefficient M are obtained based on the orthogonal decomposition method.

[0041] Step 7: Construct a training model to train the mapping relationship between the input parameter α and the parameter coefficient L to obtain the parameter coefficient L of the flow field to be solved * .

[0042] Step 8: Set the predicted parameter coefficient L * And the time basis V and space basis obtained based on the orthogonal analysis method By superposition, we can obtain the distribution of the flow field to be solved within a certain time range.

[0043] Furthermore, in step 1, based on the two-dimensional transient cylindrical flow wake, the flow field with Reynolds number Re=100 is reconstructed to solve the incompressible Navier-Stokes equations. It is necessary to complete the following tasks in CFD numerical simulation: establishing a geometric model, defining material properties, setting boundary conditions, multi-physics field coupling, meshing, setting solvers, simulation calculations, etc. After the solution is completed, the flow field solutions at different times of the data set are obtained. 8 samples and 16 samples are respectively extracted from the flow field solutions at different times to form the simulation data set U'.

[0044] Furthermore, in step 2, the flow field simulation data set U' is interpolated, cleaned, and denoised through preprocessing operations to generate 8-sample and 16-sample transient flow field data sets U that can be used for reduced-order modeling. The preprocessing step reduces the spikes and outliers in the data, ensures the stability of the numerical calculation process, and avoids instability or abnormal behavior during the reduced-order process.

[0045] Furthermore, in step 3, an orthogonal basis is obtained according to the eigenvalue decomposition of the simulation data set, which specifically includes: performing eigenvalue decomposition on the 8-sample and 16-sample transient flow field data set U to obtain the eigenvector Γ and eigenvalue λ: [Γ, λ] = eig(U T U), and further calculate the orthogonal basis Ω: Ω = UΓ. This process converts the original data into a new orthogonal basis, which not only reduces the dimension of the data, but also retains the main features of the data, ensuring that important information is not lost while compressing the data. By calculating the orthogonal basis Ω, a new data form can be obtained. The calculation of eigenvalues ​​and eigenvectors also provides the essential characteristics of the data, which can better understand the dynamic behavior of the flow field.

[0046] Furthermore, in step 4, the orthogonal basis Ω is normalized by column in the form of bi-norm to obtain the normalized ROM space basis This step helps to reduce the impact of mutation data in the 8-sample and 16-sample transient flow field datasets U, ensuring that different data contribute to the model in a balanced manner, thereby improving numerical stability.

[0047] Furthermore, in step 5, the transient flow field data set U of 8 samples and 16 samples is transformed to the spatial basis Projection is performed on the Zhang Cheng space Φ to obtain the projection coefficient A. This step projects the high-dimensional data into the low-dimensional space, which is equivalent to compressing the data, which not only reduces the storage requirements but also improves the efficiency in data transmission and processing.

[0048] Furthermore, in step six, the time basis V and parameter coefficient L of the reorganized projection coefficient M are obtained based on the orthogonal decomposition method, and the reorganized data is more suitable for training the machine learning model.

[0049] Furthermore, in step seven, after obtaining the normalized ROM space basis, a training model is constructed, and a linear regression method is used to establish a function mapping between the input parameters and the parameter coefficients extracted from the flow field data.

[0050] Furthermore, in step eight, the predicted parameter coefficient L * And the time basis V and space basis obtained based on the orthogonal analysis method The combination can predict the future flow field state distribution. Figure 3 The prediction results of 8-sample data sets and 16-sample data sets are shown. Through the transient flow field parameterized reduced-order model method used in the present invention, the prediction error is successfully reduced to less than 5% after 5000 iterations. When more samples are selected, the calculated results are more accurate. The predicted flow field solution shown in the upper right corner can fully analyze the shedding state of different vortices.

[0051] The reduced-order model method can efficiently reconstruct complex flow field distributions without the need for direct numerical simulations, which are computationally expensive. This data-driven approach improves computational efficiency and can provide high-precision flow field predictions in a relatively short period of time, making it suitable for practical application scenarios such as real-time monitoring and prediction.

[0052] Embodiment 2:

[0053] A transient flow field solution reduced-order modeling method based on orthogonal decomposition, such as Figure 1 , 2 , as shown in 4, comprising the following steps:

[0054] Step 1: Collect ocean current data based on satellite and ship observations and determine the input parameters - ocean current speed, parameter sample n sensor 70 samples and 100 samples were selected respectively. Transient flow field CFD simulation calculation was performed to construct the flow field simulation data set U'. The flow states of the ocean currents at different data points in the data set are as follows: Figure 4 Indicated by the yellow dot.

[0055] Step 2: Preprocess the flow field simulation data set U', including data interpolation, cleaning, and denoising, to generate a transient flow field data set U that can be used for reduced-order modeling.

[0056] Step 3: According to the transient flow field data set U, the eigenvector Γ and eigenvalue λ are obtained based on the orthogonal decomposition method: [Γ, λ] = eig(U T U), we further obtain the orthogonal basis Ω: Ω=UΓ.

[0057] Step 4: Normalize the orthogonal basis Ω by column in the form of bi-norm to obtain the normalized ROM space basis for:

[0058] Step 5: Transform the transient flow field dataset U to the spatial basis Projection is done in the space Φ of Zhang Cheng, and the projection coefficient A is obtained: A = Φ T U.

[0059] Step 6: Reorganize the projection coefficients, let The ROM reduction is further performed on M, and the time basis V and parameter coefficient L of the reorganized projection coefficient M are obtained based on the orthogonal decomposition method.

[0060] Step 7: Construct a training model to train the mapping relationship between the input parameter α and the parameter coefficient L to obtain the parameter coefficient L of the flow field to be solved * .

[0061] Step 8: Set the predicted parameter coefficient L * And the time basis V and space basis obtained based on the orthogonal analysis method By superposition, we can obtain the distribution of the flow field to be solved within a certain time range.

[0062] Furthermore, in step 1, sensors are randomly placed on the water surface, and the number of sensors during training is set to n sensor , using 70 and 200 sensors respectively, the flow field simulation data set is generated by CFD numerical simulation, which numerically solves the incompressible Navier-Stokes equations. In CFD numerical simulation, it is necessary to complete the following tasks: establishing a geometric model, defining material properties, setting boundary conditions, multi-physics field coupling, meshing, setting solvers, simulation calculations, etc. After the solution is completed, 70 and 200 sensor position points are extracted from the flow field solution, respectively, to form a simulation data set U' of 70 samples and 100 samples.

[0063] Furthermore, in step 2, the flow field simulation data set U' is interpolated, cleaned, and denoised through preprocessing operations to generate 70-sample and 100-sample transient flow field data sets U that can be used for reduced-order modeling. The spikes and outliers in the data are reduced to ensure the stability of the numerical calculation process and avoid instability or abnormal behavior during the reduced-order process.

[0064] Furthermore, in step 3, an orthogonal basis is obtained according to the eigenvalue decomposition of the transient flow field data set, specifically including: obtaining the eigenvector Γ and eigenvalue λ by eigenvalue decomposition of the 70-sample and 100-sample transient flow field data set U: [Γ, λ] = eig(U T U), and further calculate the orthogonal basis Ω: Ω = UΓ. This process converts the original data into a new orthogonal basis, which not only reduces the dimension of the data, but also retains the main features of the data, ensuring that important information is not lost while compressing the data. By calculating the orthogonal basis Ω, a new data form can be obtained. The calculation of eigenvalues ​​and eigenvectors also provides the essential characteristics of the data, which can better understand the dynamic behavior of the flow field.

[0065] Furthermore, in step 4, the orthogonal basis Ω is normalized by column in the form of bi-norm to obtain the normalized ROM space basis This step helps to eliminate the influence of mutation data in the 70-sample and 100-sample transient flow field data sets U, ensuring that different data contribute to the model in a balanced manner, thereby improving numerical stability.

[0066] Furthermore, in step 5, the transient flow field dataset U is transformed to the spatial basis Projection is performed on the Zhang Cheng space Φ to obtain the projection coefficient A. This step projects the high-dimensional data into the low-dimensional space, which is equivalent to compressing the data, which not only reduces the storage requirements but also improves the efficiency in data transmission and processing.

[0067] Furthermore, in step six, the time basis V and parameter coefficient L of the reorganized projection coefficient M are obtained based on the orthogonal decomposition method, and the reorganized data is more suitable for training the machine learning model.

[0068] Furthermore, in step seven, after obtaining the normalized ROM space basis, a training model is constructed by a linear regression method, and the trained model is used to establish a function mapping between input parameters and parameter coefficients extracted from flow field data.

[0069] Furthermore, in step eight, the flow field distribution in unknown situations is predicted by mapping new input parameters. Figure 4 The prediction results using 70 sample data sets and 100 sample data sets are shown. Through the transient flow field parameterization reduction model method proposed in this paper, it can be seen that when the number of samples reaches a sufficient level, the calculation results will tend to be stable.

[0070] The reduced-order model method can effectively reconstruct complex flow field distributions without the need for time-consuming direct numerical simulations. This reduced-order model method not only improves computational efficiency, but also provides high-precision flow field predictions in a relatively short period of time, performs well in processing large-scale data, and can meet the needs of rapid response.

[0071] The above contents are further detailed descriptions of the present invention in combination with specific implementation methods, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A transient flow field solution reduction modeling method based on orthogonal decomposition, characterized in that: The following steps are involved: Step 1: Determine the parameter domain and parameter samples, perform CFD simulation calculations of the transient flow field, and construct the flow field simulation data set U'; Step 2: Preprocess the flow field simulation data set U', including data interpolation, cleaning, and denoising, to generate a transient flow field data set U for reduced-order modeling; Step 3: According to the transient flow field data set U, the eigenvector Γ and eigenvalue λ are obtained based on the orthogonal decomposition method: [Γ, λ] = eig(U T U), and further obtain the orthogonal basis Ω: Ω = UΓ; Step 4: Normalize the orthogonal basis Ω by column in the form of bi-norm to obtain the normalized ROM space basis for: Step 5: Transform the transient flow field dataset U to the spatial basis Projection is done in the space Φ of Zhang Cheng, and the projection coefficient A is obtained: A = Φ T U; Step 6: Reorganize the projection coefficients, let Further ROM reduction is performed on M, and the time basis V and parameter coefficient L of the reorganized projection coefficient M are obtained based on the orthogonal decomposition method; Step 7: Construct a training model to train the mapping relationship between the input parameter α and the parameter coefficient L to obtain the parameter coefficient L of the flow field to be solved * ; Step 8: Set the predicted parameter coefficient L * And the time basis V and space basis obtained based on the orthogonal analysis method By superposition, we can obtain the distribution of the flow field to be solved within a certain time range.

2. The method for solving a reduced-order model of a transient flow field based on orthogonal decomposition as claimed in claim 1, characterized in that: In the step one, the reduced-order model needs to first construct a flow field simulation data set. The establishment of a geometric model, definition of material properties, setting of boundary conditions, multi-physics field coupling, meshing, setting of solvers, and simulation calculations in the flow field simulation need to be completed first in step one.

3. The transient flow field solution reduced-order model method based on orthogonal decomposition as claimed in claim 1 is characterized in that In the step 2, the flow field simulation data set U' is preprocessed, including data cleaning and denoising, to ensure the accuracy and consistency of the transient flow field data set U.

4. The transient flow field solution reduced-order model method based on orthogonal decomposition as claimed in claim 1 is characterized in that In step 3, the ROM order reduction method is integrated and orthogonal decomposition is used to perform linear algebra operations on the transient flow field data set U to extract the main features from the data set and construct an orthogonal basis.

5. The method for solving a reduced-order model of a transient flow field based on orthogonal decomposition as claimed in claim 1, characterized in that: After the base is obtained in step 4, a new ROM base is established after normalization; this set of bases is represented by a vector as follows: The length of the normalized basis vector is 1, which avoids the loss of precision in numerical calculations caused by the amplitude of the basis vector being too large or too small.

6. The transient flow field solution reduced-order model method based on orthogonal decomposition as claimed in claim 1 is characterized in that The step 5 is to project the transient flow field data set U onto the space Φ formed by the spatial basis to obtain a projection coefficient A; The projection coefficient A reflects the main patterns and dynamic behaviors of transient flow field data in the low-dimensional basis space. As the most important features and patterns in identifying the flow field, it facilitates further analysis and processing.

7. The transient flow field solution reduced-order model method based on orthogonal decomposition as claimed in claim 1 is characterized in that In step 6, the orthogonal decomposition method is integrated to extract the time basis and the corresponding coefficients through the orthogonal decomposition technology; the orthogonal decomposition of M is in the form of: M = V*L*V T , extract the main time basis V of the data, and solve the corresponding projection coefficient L; orthogonal decomposition reduces the dimensionality of the high-dimensional data set to a low-dimensional subspace, retaining the main features and reducing the amount of data.

8. The transient flow field solution reduced-order model method based on orthogonal decomposition as claimed in claim 1 is characterized in that The step seven uses a machine learning algorithm to train a regression model so that it can predict the projection coefficient L according to the input parameter α, and the relationship between the input parameter and the projection coefficient is established by training the model. According to the characteristics of the data type, the machine learning algorithm selects the linear regression algorithm, constructs a training model between the input parameter α and the parameter coefficient L, and obtains the mapping relationship between the two.

9. The transient flow field solution reduced-order model method based on orthogonal decomposition as claimed in claim 1 is characterized in that The step eight will predict the parameter coefficient L * And the time basis V and space basis obtained based on the orthogonal analysis method Combination can predict the future flow field state distribution and realize the complete process from input parameters to predicting transient flow field distribution.

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