Cavitation flow field reconstruction method based on sparse perception and unsupervised learning method

Abstract

The invention provides a cavitation flow field reconstruction method based on sparse perception and an unsupervised learning method, and the method comprises the steps: firstly, carrying out the numerical simulation of cavitation flow around a specific type of hydrofoil, considering the unique characteristics of a cavitation flow velocity field, executing the intrinsic orthogonal decomposition, and representing the intrinsic orthogonal decomposition as a representation form of the superposition of an average velocity field and a pulsation velocity field; a fluid velocity field modal library is constructed on the basis; and then an unsupervised clustering algorithm and sparse data sampling are executed to extract data samples, and fluid velocity field reconstruction is completed by using the velocity field modal library and a small number of data samples. Through verification and comparison of reconstruction effects under different sparse sampling strategies, high-fidelity reconstruction of a complex cavitation flow structure can be finally realized, and compared with the prior art, accuracy and robustness are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of cavitation flow field modeling and analysis technology, specifically involving a cavitation flow field reconstruction method based on sparse sensing and unsupervised learning. Background Technology

[0002] Cavitation flow, a typical complex flow phenomenon involving multiple physics coupling, is widely present in high-speed flow environments of equipment such as turbines, propellers, and hydraulic valves. It is highly correlated with the hydraulic mechanical performance, noise, and structural damage of these devices, necessitating in-depth research into its internal evolution mechanisms. Currently, most studies on cavitation flow in this field rely on numerical simulations, which suffer from significant deviations between modeling and boundary condition settings and the actual physical processes. Furthermore, the highly transient nature of cavitation flow and limitations imposed by experimental environments and conditions result in fragmented and sparse sensor data used in numerical simulations, hindering the reconstruction and in-depth understanding of the flow field structure. While some recent flow field reconstruction techniques based on sparse sensing and data-driven approaches can relatively reduce dependence on the number of sensors and measurement costs, they primarily focus on fluid around the flow and jet external fields, rarely applicable to cavitation flow problems with complex internal structures, strong unsteady characteristics, and multi-scale turbulent features. Therefore, improving the modeling and analysis methods for cavitation flow using sparse data to enhance the perception and reconstruction of complex flow structures is a pressing technical problem that needs to be addressed in this field. Summary of the Invention

[0003] In view of this, and to address the technical problems existing in this field, the present invention provides a method for reconstructing cavitation flow field based on sparse sensing and unsupervised learning, specifically including the following steps:

[0004] Step 1: Construct a three-dimensional numerical simulation model of the cavitation flow around a specific type of hydrofoil, and use the model to carry out numerical simulation of cavitation flow under preset working conditions and boundary conditions to obtain simulation data of unsteady velocity field corresponding to the complete working conditions.

[0005] Step 2: Perform dimensionless preprocessing on the unsteady velocity field simulation data obtained in Step 1 to eliminate the interference of scale differences on subsequent mode decomposition processing; establish the matrix of the entire velocity field based on the computational domain, and represent the velocity field as a superposition of the average velocity field and the fluctuating velocity field; perform intrinsic orthogonal decomposition (POD) on the fluctuating velocity field part, and represent it as the sum of several coherent intrinsic modes multiplied by their corresponding time coefficients, and establish the corresponding velocity field mode library;

[0006] Step 3: Using the unsteady velocity field simulation data obtained in Step 1, execute an unsupervised clustering algorithm to divide the velocity field region into multiple clusters; extract the clusters corresponding to different hole development stages, including attached holes, jet development, and hole detachment, and select sparse sampling points in each cluster to extract the corresponding velocity sample data, and construct a sample matrix based on this.

[0007] Step 4: Reconstruct the fluctuating velocity field using the velocity field mode library from Step 2 and the sample matrix from Step 3, and then obtain the fluid velocity field reconstruction result of the cavitation flow around the hydrofoil.

[0008] Step 5: Compare and analyze the error between the velocity field reconstruction results obtained by using different sparse sampling point selection strategies and the original velocity field obtained by simulation in Step 1. Evaluate the reconstruction accuracy and robustness of different strategies and verify and determine the final high-fidelity reconstruction scheme.

[0009] Furthermore, in step one, a three-dimensional numerical simulation model of the fluid cavitation flow around the Clark-Y hydrofoil is constructed, and a velocity inlet and a pressure outlet are set as boundary conditions, as well as a no-slip solid wall condition, for the computational domain.

[0010] Furthermore, in step two, the following processing procedures are specifically performed on the simulation data after the dimensionless preprocessing:

[0011] First, select a suitable plane from the computational domain and establish a matrix U(x,t) that contains the entire velocity field:

[0012]

[0013] In the formula, The average velocity field can be expressed as the superposition of the velocity fields at the following m time points:

[0014]

[0015] In the formula, u(x,t) i ) is the t-th i Instantaneous velocity field at any given moment;

[0016] U'(x,t) is the fluctuating velocity field, which can be expressed as the superposition of the fluctuating velocity fields at the following n time points:

[0017] U'(x,t)=[u'(x,t1),u'(x,t2),...,u'(x,t n )]

[0018] In the formula, u'(x,t) n ) is the t-th n Constant-time pulsating flow velocity field;

[0019] Performing eigenorthogonal decomposition on the fluctuating velocity field at different times yields the following form: the eigenmodes are multiplied by their corresponding time coefficients and then summed.

[0020]

[0021] In the formula, a j (t i () represents the time coefficient. Let M be the feature vector corresponding to each mode, and M be the number of coherent modes;

[0022] Finally, the instantaneous velocity field at each moment can be expressed in the following form:

[0023]

[0024] In the formula, N is the number of main coherent modes selected for reconstructing the velocity field.

[0025] Furthermore, the unsupervised clustering process in step three specifically includes:

[0026] First, randomly initialize k cluster centers, then perform the following iterations:

[0027] Calculate the Euclidean distance between each data point and different cluster centers, and assign each data point to the nearest cluster center; simultaneously update the corresponding cluster centers for each cluster based on the mean of all data points within the cluster, i.e.:

[0028]

[0029] In the formula, C i N is the cluster center of the updated i-th cluster. i x represents the number of data points in the i-th cluster. j Let j be the coordinates of data point j in the i-th cluster;

[0030] Set the following metrics for iterations:

[0031]

[0032] In the formula, ||x j -c i || represents x j With c i The Euclidean distance is used to minimize this metric until convergence ends the iteration. The resulting clusters are then used for subsequent sparse sampling and sample data extraction.

[0033] Furthermore, in step four, the pulsating velocity field is reconstructed using the velocity field mode library and the extracted sample matrix as follows:

[0034]

[0035] In the formula, P∈R r×n The sample matrix contains r samples at specified locations within the complete flow field. For the time coefficient to be determined, the following error function is calculated by approximating the solution using the least squares method:

[0036]

[0037] In the formula, ζ represents modal support;

[0038] To minimize the error, in the formula Taking the partial derivative and setting it equal to 0, we obtain the following relationship:

[0039]

[0040] Wherein, the matrix elements satisfy After solving, an approximate velocity flow field can be obtained.

[0041] The cavitation flow field reconstruction method based on sparse sensing and unsupervised learning provided by the present invention first performs numerical simulation on the cavitation flow around a specific type of hydrofoil. Considering the unique characteristics of the cavitation flow velocity field, intrinsic orthogonal decomposition is performed, representing it as a superposition of the average velocity field and the fluctuating velocity field. Based on this, a fluid velocity field mode library is constructed. Then, an unsupervised clustering algorithm and sparse data sampling are used to extract data samples, and the fluid velocity field is reconstructed using the velocity field mode library and a small number of data samples. Through verification and comparison of the reconstruction effect under different sparse sampling strategies, high-fidelity reconstruction of complex cavitation flow structures can be achieved, significantly improving accuracy and robustness compared to existing technologies. Attached Figure Description

[0042] Figure 1 A flowchart of the method provided by the present invention;

[0043] Figure 2 This is a schematic diagram illustrating the principle framework of each step in the method provided by the present invention;

[0044] Figure 3 This is a schematic diagram of the three-dimensional hydrofoil numerical model and computational domain setting based on the present invention;

[0045] Figure 4 A schematic diagram of the segmented regions corresponding to different stages of cavitation flow;

[0046] Figure 5 A schematic diagram comparing the reconstruction errors of the present invention and traditional methods. Detailed Implementation

[0047] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] The cavitation flow field reconstruction method based on sparse sensing and unsupervised learning provided by this invention, such as... Figure 1 and 2 As shown, the specific steps include:

[0049] Step 1: Construct a three-dimensional numerical simulation model of cavitation flow around a specific type of hydrofoil, and use this model to conduct numerical simulations of cavitation flow under preset operating conditions and boundary conditions to obtain unsteady velocity field simulation data corresponding to the complete operating conditions. This data will serve as the basis for subsequent velocity field mode extraction and offline training and verification of unsupervised clustering algorithms;

[0050] Step 2: Perform dimensionless preprocessing on the unsteady velocity field simulation data obtained in Step 1 to eliminate the interference of scale differences on subsequent mode decomposition processing; establish the matrix of the entire velocity field based on the computational domain, and represent the velocity field as a superposition of the average velocity field and the fluctuating velocity field; perform intrinsic orthogonal decomposition (POD) on the fluctuating velocity field part, and represent it as the sum of several coherent intrinsic modes multiplied by their corresponding time coefficients, and establish a corresponding velocity field mode library, thereby realizing the dimensionality reduction of the velocity field simulation data;

[0051] Step 3: Using the unsteady velocity field simulation data obtained in Step 1, perform an unsupervised clustering algorithm to divide the velocity field region into multiple clusters; extract, for example... Figure 4 The diagram shows clusters corresponding to different stages of cavity development, including attached cavities, jet development, and cavity detachment. Blocks 1 and 4 correspond to the attached cavity stage, blocks 5 and 7 to the jet development stage, and blocks 2, 3, 6, and 8 to the cavity detachment stage accompanied by complex vortex structures. Sparse sampling points are selected within each cluster to extract corresponding velocity sample data, and a sample matrix is ​​constructed based on this. In practice, various suitable sparse sampling strategies are selected to extract velocity sample data. This method allows the clustering results to better reflect the flow field characteristics and improves the efficiency of sparse sampling of velocity data.

[0052] Step 4: Reconstruct the fluctuating velocity field using the velocity field mode library from Step 2 and the sample matrix from Step 3, and then obtain the fluid velocity field reconstruction result of the cavitation flow around the hydrofoil.

[0053] Step 5: Compare and analyze the error between the velocity field reconstruction results obtained by using different sparse sampling point selection strategies and the original velocity field obtained by simulation in Step 1. Evaluate the reconstruction accuracy and robustness of different strategies and verify and determine the final high-fidelity reconstruction scheme.

[0054] In a preferred embodiment of the present invention, such as Figure 3 As shown, in step one, a three-dimensional numerical simulation model of the fluid cavitation flow around the Clark-Y hydrofoil is constructed, and a velocity inlet and a pressure outlet are set as boundary conditions, as well as a no-slip solid wall condition, for the computational domain.

[0055] In a preferred embodiment of the present invention, the following processing procedure is specifically performed on the simulation data after dimensionless preprocessing in step two:

[0056] First, select a suitable plane from the computational domain and establish a matrix U(x,t) that contains the entire velocity field:

[0057]

[0058] In the formula, The average velocity field can be expressed as the superposition of the velocity fields at the following m time points:

[0059]

[0060] In the formula, u(x,t) i ) is the t-th i Instantaneous velocity field at any given moment;

[0061] U'(x,t) is the fluctuating velocity field, which can be expressed as the superposition of the fluctuating velocity fields at the following n time points:

[0062] U'(x,t)=[u'(x,t1),u'(x,t2),...,u'(x,t n )]

[0063] In the formula, u'(x,t) n ) is the t-th n Constant-time pulsating flow velocity field;

[0064] Performing eigenorthogonal decomposition on the fluctuating velocity field at different times yields the following form: the eigenmodes are multiplied by their corresponding time coefficients and then summed.

[0065]

[0066] In the formula, a j (t i () represents the time coefficient. Let M be the feature vector corresponding to each mode, and M be the number of coherent modes;

[0067] The inner product between modes satisfies:

[0068]

[0069] The time coefficient is specifically defined as follows:

[0070]

[0071] Finally, the instantaneous velocity field at each moment can be expressed in the following form:

[0072]

[0073] In the formula, N is the number of main coherent modes selected for reconstructing the velocity field.

[0074] In a preferred embodiment of the present invention, the unsupervised clustering process in step three specifically includes:

[0075] First, randomly initialize k cluster centers, then perform the following iterations:

[0076] Calculate the Euclidean distance between each data point and different cluster centers, and assign each data point to the nearest cluster center; simultaneously update the corresponding cluster centers for each cluster based on the mean of all data points within the cluster, i.e.:

[0077]

[0078] In the formula, C i N is the cluster center of the updated i-th cluster. i x represents the number of data points in the i-th cluster. j Let j be the coordinates of data point j in the i-th cluster;

[0079] Set the following metrics for iterations:

[0080]

[0081] In the formula, ||x j -c i || represents x j With c i The iteration ends when the Euclidean distance is minimized, and the resulting clusters are used for subsequent sparse sampling and sample data extraction.

[0082] In a preferred embodiment of the present invention, in step four, the pulsating velocity field is reconstructed using the velocity field mode library and the extracted sample matrix as follows:

[0083]

[0084] In the formula, P∈Rr×n The sample matrix contains r samples at specified locations within the complete flow field. For the time coefficient to be determined, the following error function is calculated by approximating the solution using the least squares method:

[0085]

[0086] In the formula, ζ represents modal support;

[0087] To minimize the error, in the formula Taking the partial derivative and setting it equal to 0, we obtain the following relationship:

[0088]

[0089] Wherein, the matrix elements satisfy After solving, an approximate velocity flow field can be obtained.

[0090] For velocity field reconstruction results obtained using different sparse sampling strategies, the mean square error index between them and the original simulation data can be used for comparison and evaluation. Figure 5 The figure shows a comparison of the mean square error between the reconstruction based on unsupervised clustering of the present invention and traditional methods. It can be seen that the overall mean square error of the method of the present invention is significantly better than that of traditional methods, which fully meets the acceptable range for engineering and has good accuracy and applicability.

[0091] It should be understood that the sequence number of each step in the embodiments of the present invention does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0092] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for reconstructing cavitation flow field based on sparse sensing and unsupervised learning, characterized in that: Specifically, the following steps are included: Step 1: Construct a three-dimensional numerical simulation model of the cavitation flow around a specific type of hydrofoil, and use the model to carry out numerical simulation of cavitation flow under preset working conditions and boundary conditions to obtain simulation data of unsteady velocity field corresponding to the complete working conditions. Step 2: Perform dimensionless preprocessing on the unsteady velocity field simulation data obtained in Step 1 to eliminate the interference of scale differences on subsequent modal decomposition processing; The matrix of the entire velocity field is established based on the computational domain, and the velocity field is represented as a superposition of the average velocity field and the fluctuating velocity field. The eigenorthogonal decomposition is performed on the fluctuating velocity field part, and it is represented as the sum of several coherent eigenmodes multiplied by their corresponding time coefficients. A corresponding velocity field mode library is also established. Step 3: Using the unsteady velocity field simulation data obtained in Step 1, execute an unsupervised clustering algorithm to divide the velocity field region into multiple clusters; extract the clusters corresponding to different hole development stages, including attached holes, jet development, and hole detachment, and select sparse sampling points in each cluster to extract the corresponding velocity sample data, and construct a sample matrix based on this. Step 4: Reconstruct the fluctuating velocity field using the velocity field mode library from Step 2 and the sample matrix from Step 3, and then obtain the fluid velocity field reconstruction result of the cavitation flow around the hydrofoil. Step 5: Compare and analyze the error between the velocity field reconstruction results obtained by using different sparse sampling point selection strategies and the original velocity field obtained by simulation in Step 1. Evaluate the reconstruction accuracy and robustness of different strategies and verify and determine the final high-fidelity reconstruction scheme.

2. The method as described in claim 1, characterized in that: In step one, a three-dimensional numerical simulation model of the fluid cavitation flow around the Clark-Y hydrofoil is constructed, and a velocity inlet and a pressure outlet are set as boundary conditions, as well as a no-slip solid wall condition, for the computational domain.

3. The method as described in claim 1, characterized in that: In step two, the following processing procedures are specifically performed on the simulation data after the dimensionless preprocessing is completed: First, select a suitable plane from the computational domain and establish a matrix U(x,t) that contains the entire velocity field: In the formula, The average velocity field can be expressed as the superposition of the velocity fields at the following m time points: In the formula, u(x,t) i ) is the t-th i Instantaneous velocity field at any given moment; U'(x,t) is the fluctuating velocity field, which can be expressed as the superposition of the fluctuating velocity fields at the following n time points: U'(x,t)=[u'(x,t1),u'(x,t2),...,u'(x,t n )] In the formula, u'(x,t) n ) is the t-th n Constant-time pulsating flow velocity field; Performing eigenorthogonal decomposition on the fluctuating velocity field at different times yields the following form: the eigenmodes are multiplied by their corresponding time coefficients and then summed. In the formula, a j (t i () represents the time coefficient. Let M be the feature vector corresponding to each mode, and M be the number of coherent modes; Finally, the instantaneous velocity field at each moment can be expressed in the following form: In the formula, N is the number of main coherent modes selected for reconstructing the velocity field.

4. The method as described in claim 1, characterized in that: Step three, the unsupervised clustering process, specifically includes: First, randomly initialize k cluster centers, then perform the following iterations: Calculate the Euclidean distance between each data point and different cluster centers, and assign each data point to the nearest cluster center; simultaneously update the corresponding cluster centers for each cluster based on the mean of all data points within the cluster, i.e.: In the formula, C i N is the cluster center of the updated i-th cluster. i x represents the number of data points in the i-th cluster. j Let j be the coordinates of data point j in the i-th cluster; Set the following metrics for iterations: In the formula, ||x j -c i || represents x j With c i The iteration ends when the Euclidean distance is minimized, and the resulting clusters are used for subsequent sparse sampling and sample data extraction.

5. The method as described in claim 1, characterized in that: In step four, the pulsating velocity field is reconstructed using the velocity field mode library and the extracted sample matrix as follows: In the formula, P∈R r×n This is a sample matrix containing r samples at specified locations within the complete flow field; For the time coefficient to be determined, the following error function is calculated by approximating the solution using the least squares method: In the formula, This indicates modal support, where ζ is the error integral operator. and φ k For the time coefficients and feature vectors after sparse sampling; To minimize the error, in the formula Taking the partial derivative and setting it equal to 0, we obtain the following relationship: Wherein, the matrix elements satisfy After solving, an approximate velocity flow field can be obtained.

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