Denoising method and device for three-dimensional high-order discontinuous galerkin data in shock analysis
By eliminating Gibbs noise in 3D high-order discontinuous Galerkin data using a 3D graph attention network model, the problem of insufficient computational stability in 3D shock wave analysis is solved, and a highly efficient denoising effect is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
- Filing Date
- 2026-03-16
- Publication Date
- 2026-06-19
AI Technical Summary
Existing shock wave analysis methods are ineffective at eliminating Gibbs noise in three-dimensional high-order discontinuous Galerkin data, resulting in insufficient computational stability.
A three-dimensional graph attention network model is adopted. By constructing three-dimensional graph structure data, the relationship weights between nodes are dynamically learned using the graph attention mechanism. Combined with the three-dimensional square wave and Fourier series expansion methods, an intelligent denoising model is trained to eliminate Gibbs noise.
It improves the stability of the shock wave analysis process, is applicable to different three-dimensional flow field scenarios, achieves efficient denoising of three-dimensional high-order discontinuous Galerkin data, and enhances the stability and adaptability of the calculation.
Smart Images
Figure CN122243795A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of shock wave capture and analysis technology in fluid mechanics research, and in particular to a method and apparatus for denoising three-dimensional high-order discontinuous Galerkin data in shock wave analysis. Background Technology
[0002] In the research of fluid mechanics-related applications, shock wave capture analysis is an important research branch, especially in addressing the problem of how numerical oscillations near shock waves affect computational accuracy and stability.
[0003] Currently, commonly used methods for addressing numerical oscillations near shock waves include limiters, weighted essentially oscillatory reconstruction, and artificial viscosity. While these traditional methods effectively suppress numerical oscillations near shock waves, they still have limitations in terms of accuracy preservation, computational efficiency, and adaptability. For example, the first method, limiters, may excessively suppress solution fluctuations in smooth regions, leading to a decrease in global accuracy, and is sensitive to parameter selection. The second method, weighted essentially oscillatory reconstruction, maintains high-order accuracy but requires pre-judgment of correction units and has high computational costs. The third method, artificial viscosity, suppresses non-physical oscillations near shock waves by adding a dissipation correction term to the governing equations; however, artificial viscosity introduces additional dissipation, and the viscosity coefficient depends on empirical parameter adjustments, which can lead to excessive dissipation or residual oscillations if chosen improperly. Traditional shock wave capture methods are computationally expensive and rely on empirical parameters. With the continuous development of artificial intelligence technology, researchers have begun to explore using machine learning methods to eliminate the Gibbs phenomenon in higher-order discontinuous Galerkin methods. Preliminary attempts have been made to use artificial intelligence methods in two dimensions, proposing denoising methods based on graph convolutional filters and zero-shot learning, achieving denoising of two-dimensional high-order discontinuous Galerkin methods. For example, our research team conducted relevant research several years ago and published some of the research results (patent application number: 202311193875.3). The scheme designed in this work uses sawtooth waves and their Fourier series expansion in two dimensions, and uses them as the core means to carry out the subsequent analysis process.
[0004] However, in subsequent research, our team also discovered some problems, such as: the constructed two-dimensional dataset's Fourier series had a monotonous pattern, and the denoising results still retained some Gibbs noise; moreover, the research mainly focused on two-dimensional high-order discontinuous Galerkin denoising, while practical engineering applications include three-dimensional high-order discontinuous Galerkin flow fields, and the working conditions of high-order discontinuous Galerkin flow field scenarios in different dimensions differ significantly. The previously designed scheme for two-dimensional scenarios cannot be directly applied to the denoising of three-dimensional high-order discontinuous Galerkin data.
[0005] Therefore, how to eliminate Gibbs noise in three-dimensional calculations during shock wave capture analysis, thereby improving the stability of the analysis process, has become a topic that needs further research. Summary of the Invention
[0006] The embodiments of the present invention provide a method and apparatus for denoising three-dimensional high-order discontinuous Galerkin data in shock wave analysis, which can eliminate Gibbs noise in three-dimensional calculations during shock wave capture analysis, thereby improving the stability of the analysis process.
[0007] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions:
[0008] Firstly, a denoising method is provided for three-dimensional high-order discontinuous Galerkin data in shock wave analysis. The method is used in a computing system consisting of a server and a client. The three-dimensional flow field data to be denoised uploaded by the client includes three-dimensional noisy flow field physical quantities; these noisy flow field physical quantities include: flow field density. Density multiplied by velocity in the x-direction Density multiplied by velocity in the y-direction Density multiplied by velocity in the z-direction Density multiplied by energy ;
[0009] S1. The server generates three-dimensional graph structure data of the flow field based on the three-dimensional flow field data to be denoised; specifically, the three-dimensional flow field data to be denoised uploaded by the client also includes the three-dimensional mesh information of the flow field, including the number of mesh nodes and the adjacency relationship between mesh nodes.
[0010] The 3D graph structure data specifically includes: a feature matrix X0 generated based on the physical quantities of the 3D noisy flow field after calculating the noisy flow field using the 3D high-order discontinuous Galerkin method, and an adjacency matrix A0 generated based on the 3D mesh information of the flow field. X0 and A0 constitute the 3D noisy real flow field graph structure data that needs to be denoised using a trained 3D intelligent denoising model. For example, in the 3D flow field denoising module, the density of the flow field... Density multiplied by velocity in the x-direction Density multiplied by velocity in the y-direction Density multiplied by velocity in the z-direction Density multiplied by energy Denoising is performed on multiple feature matrices to establish a feature matrix X0 that includes the density of the flow field in the feature matrix. The velocity in the x-direction multiplied by the density of the characteristic matrix The velocity in the y-direction multiplied by the density of the characteristic matrix The velocity in the z-direction multiplied by the density of the characteristic matrix Energy multiplied by the density of the characteristic matrix .
[0011] S2. Establish a 3D training sample library using 3D graph structure data;
[0012] S3. Train a 3D graph attention network model; In this embodiment, the graph attention model is used for 3D denoising. The graph attention network dynamically learns the relationship weights between nodes in the graph through an attention mechanism, providing flexible and powerful modeling capabilities for 3D data denoising tasks. Specifically, a graph structure can be constructed based on the constructed 3D dataset, and the graph attention model is used for denoising. First, the attention coefficient e is calculated for each node pair. ,in, This indicates a tensor splicing operation. and Represents a node and nodes Features and weights in the current layer and mapping These are the learnable parameters of a neural network, and their mappings. This is used to map features onto the real number domain. To make the attention coefficients easier to compare across different nodes, the attention coefficients are normalized, resulting in the attention coefficients. : σ() represents the activation function, which uses the LeakyReLU activation function. The loss function during training is: ,in, It is the true value of the constructed three-dimensional square wave. This is the predicted value of a three-dimensional square wave output by a neural network, where D represents the sample set size of the sample data. The three-dimensional graph attention-based intelligent denoising model is implemented in a computer language, and the results are stored on a server after training for denoising of three-dimensional noisy flow field physical quantities.
[0013] S4. Gibbs noise removal is performed on the physical quantities of the noisy three-dimensional flow field using the trained three-dimensional graph attention network model. The graph structure data (feature matrix X0 and adjacency matrix A0) of the noisy three-dimensional flow field physical quantities are used as the input features of the three-dimensional graph attention network model, and the output results are returned to the client.
[0014] Specifically, S2 includes: acquiring the original three-dimensional square wave and its Fourier series expansion, and constructing a new three-dimensional square wave; using the original three-dimensional square wave to simulate clean three-dimensional data, and using the Fourier series expansion of the original three-dimensional square wave and the new three-dimensional square wave to simulate noisy three-dimensional data; and using the clean three-dimensional square wave and the noisy three-dimensional square wave to form input-output data training sample pairs, and storing them in a three-dimensional training sample library.
[0015] In this process, graph-structured data is represented using feature matrices and adjacency matrices. In the original 3D square wave, N points are taken in each of the x, y, and z directions to form an N×N×N structure, generating a feature matrix X. For example, the 3D square wave takes N points in each of the x, y, and z directions to form N×N×N data. The Fourier series expansion of the 3D square wave, and the new 3D square wave form similarly, also take N points in each of the x, y, and z directions to form N×N×N data. An adjacency matrix A is generated based on the proximity of each point to its surrounding spatial locations. Finally, the graph-structured data is composed of matrix X and matrix A.
[0016] A three-dimensional training data sample library is established using the graph structure data. The constructed three-dimensional square wave and Fourier series expansion and the new three-dimensional square wave are combined to form input-output data sample pairs, and the input-output data samples are stored as sample data in the three-dimensional training data sample library.
[0017] In this embodiment, the original three-dimensional square wave is A represents amplitude, T represents period, and x represents the value of the independent variable on the three-dimensional x-axis; the Fourier series expansion of the original three-dimensional square wave is expressed as: , where n represents the accumulation parameter; in the preferred scheme, n takes the value [10, 50], thereby achieving the optimal actual calculation effect.
[0018] The new form of three-dimensional square wave is represented as follows: ,in, This represents a newly constructed noisy square wave. Represents the original three-dimensional square wave. Represents a square wave in the Fourier series expansion. This represents an array of random numbers that follow a normal distribution. In practical applications, the constructed new square wave pattern exhibits intense fluctuations at discontinuities, with the fluctuations decreasing in size and eventually leveling out with increasing distance from the discontinuity. This ensures that the oscillation distribution of the deformed square wave matches the oscillation characteristics of the real flow field, thereby improving the adaptability of the training dataset to real-world application scenarios. Specifically, intelligent denoising models are trained on datasets containing both the new square wave pattern and those containing it. The denoising results are then compared in real flow fields, revealing that training with the new square wave pattern yields better denoising performance than training without it.
[0019] In a preferred embodiment, the 3D graph attention network model includes a total of 12 graph attention layers, comprising 6 deconvolutional layers and 6 convolutional layers. In these 12 graph attention layers, the first layer is the input layer, the twelfth layer is the output layer, and the second to eleventh layers are hidden layers. The attention coefficients are used to define the hidden layers. As convolutional kernels for graph attention layers, the hidden output dimensions are 8, 16, 32, 64, 128, 256, 128, 64, 32, 16, 8, and 1, respectively.
[0020] Secondly, a denoising device for three-dimensional high-order discontinuous Galerkin data in shock wave analysis is provided, comprising: a data receiving module for receiving three-dimensional flow field data to be denoised, including three-dimensional noisy flow field physical quantities, uploaded by a client; a three-dimensional flow field graph structure construction module for generating three-dimensional graph structure data of the flow field based on the three-dimensional flow field data to be denoised; a three-dimensional training data construction module for establishing a three-dimensional training sample library using the three-dimensional graph structure data; a three-dimensional denoising model training module for training a three-dimensional graph attention network model; and a three-dimensional flow field denoising module for denoising the three-dimensional noisy flow field physical quantities, including the flow field density, using the trained three-dimensional graph attention network model. Density multiplied by velocity in the x-direction Density multiplied by velocity in the y-direction Density multiplied by velocity in the z-direction Density multiplied by energy Gibbs noise removal is performed, where the graph structure data of the noisy 3D flow field physical quantities is used as the input features of the 3D graph attention network model; the data sending module is used to send the denoised 3D flow field data to the client.
[0021] This invention provides a method and apparatus for denoising three-dimensional high-order discontinuous Galerkin data in shock wave analysis. The server receives three-dimensional flow field data to be denoised from the client. This data includes three-dimensional noisy flow field physical quantities and flow field mesh information. Based on the topological connections of the three-dimensional spatial mesh, the three-dimensional flow field data is formed into a three-dimensional graph structure. A three-dimensional dataset is constructed by taking points in three-dimensional space using three-dimensional square waves, three-dimensional square waves with Fourier series expansions, and new-form three-dimensional square waves. A three-dimensional graph attention mechanism intelligent denoising model is trained. The trained three-dimensional graph attention model is used to denoise the three-dimensional noisy flow field data, eliminating three-dimensional Gibbs noise and ensuring stable three-dimensional computation. Compared to existing solutions that use sawtooth waves and their Fourier series expansions for two-dimensional flow field data, this embodiment improves the processing of three-dimensional flow field data by designing square waves and their Fourier series expansions and incorporating new-form three-dimensional square waves to form a graph structure by taking points in three-dimensional space. Then, a graph attention model is trained to eliminate numerical oscillations near the shock wave. The trained 3D denoising model is embedded into the numerical calculation of the shock wave capture analysis process, eliminating Gibbs noise in the 3D calculation and improving the stability of the analysis process. Attached Figure Description
[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0023] Figure 1 This is a schematic diagram of the system architecture provided in an embodiment of the present invention;
[0024] Figure 2 A flowchart of the method provided in an embodiment of the present invention;
[0025] Figure 3 A schematic diagram of a three-dimensional graph attention-based intelligent denoising model provided in an embodiment of the present invention;
[0026] Figure 4 This is a schematic diagram of the framework of the three-dimensional intelligent denoising method implemented in this invention;
[0027] Figure 5 This is a schematic diagram of the device structure provided in an embodiment of the present invention. Detailed Implementation
[0028] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Embodiments of the present invention will be described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in the specification of the present invention means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or couplings. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items. It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the meaning consistent with their meaning in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.
[0029] The hardware of this computing system was all purchased from the open market; it consists of existing hardware, and the system is built upon this hardware. Figure 1 The diagram illustrates a server-client computing system architecture. For example, in practical applications, the research team upgraded the CPU and added memory to the previously built computing system, thereby improving its computing power. This was used in the computing system design of this embodiment for further research and design.
[0030] like Figure 2 As shown, it includes:
[0031] Step 1: The server receives client data sent by the client. The client data includes: three-dimensional noisy flow field physical quantities and flow field mesh information. The three-dimensional noisy flow field physical quantities include density. Density multiplied by velocity in the x-direction Density multiplied by velocity in the y-direction Density multiplied by velocity in the z-direction Density multiplied by energy These are the five physical quantities of the three-dimensional flow field.
[0032] Step 2: Connect the physical quantities of the three-dimensional flow field to be denoised into a graph structure according to the topological connection of the mesh.
[0033] Step 3: Based on the three-dimensional square wave, the Fourier unfolded three-dimensional square wave, and the new morphology of the three-dimensional square wave, take points in the three-dimensional space to form graph structure data, and construct sample pairs to store in the three-dimensional training data sample library.
[0034] Step 4: Train a 3D graph attention intelligent model based on the 3D training data sample library. The structure of the 3D graph attention intelligent denoising model is as follows: Figure 3 The method described above is used to eliminate noise in the calculation of flow fields using the three-dimensional high-order discontinuous Galerkin numerical scheme.
[0035] Step 5: Use a 3D graph attention-based intelligent denoising model to denoise the 3D noisy flow field, such as... Figure 4 The method for intelligent denoising of the three-dimensional high-order discontinuous Galerkin numerical scheme is shown, and clean three-dimensional flow field data is returned to the client.
[0036] The method flow of this embodiment can be applied to, for example, Figure 1 In the scenario architecture shown, the client provides 3D noisy flow field physical quantities and flow field mesh information; the server uses the information provided by the client to complete the construction of the 3D flow field map structure; 3D training data is constructed using 3D square waves, 3D square waves with Fourier expansion, and new 3D square waves and stored in the 3D training data sample library; then, a 3D graph attention intelligent denoising model is trained; finally, the server uses the trained denoising model to perform Gibbs noise removal based on the 3D flow field physical quantities to be denoised provided by the client, and returns the clean 3D flow field data to the client.
[0037] In this embodiment, step 2 includes:
[0038] The server generates graph structure data based on the physical quantities of the three-dimensional noisy flow field and the flow field mesh information. Specifically, it generates a feature matrix X0 based on the physical quantities of the three-dimensional noisy flow field and an adjacency matrix A0 based on the flow field mesh information.
[0039] In this embodiment, step 3 includes:
[0040] The server uses three-dimensional square waves to simulate clean three-dimensional data, and uses three-dimensional square waves with Fourier series expansion and new forms of three-dimensional square waves to simulate noisy three-dimensional data, generating graph structure data and forming input-output data sample pairs. The input-output data samples are then stored as three-dimensional sample data in the three-dimensional training data sample library.
[0041] Wherein, the square wave takes one period as The square wave in the Fourier series expansion is , It is the amplitude. The new square wave, characterized by periodicity, exhibits intense fluctuations at discontinuities, which decrease with increasing distance from the discontinuity, eventually becoming flat. This data sample ensures that the oscillation distribution of the deformed square wave matches the oscillation characteristics of the real flow field, thereby improving the adaptability of the training dataset to practical application scenarios. Its construction expression is: , This represents a newly constructed noisy square wave. Represents the original square wave. Represents a square wave in the Fourier series expansion. This indicates the generation of a random number array that follows a normal distribution (Gaussian distribution).
[0042] The process of generating graph structure data from the three-dimensional square wave, the three-dimensional square wave with Fourier series expansion, and the new three-dimensional square wave includes: taking N points in the three-dimensional training data according to the three-dimensional space, i.e., the x-direction, y-direction, and z-direction respectively, to form N×N×N data, generating a feature matrix X, generating an adjacency matrix A according to the proximity of each point to its surrounding spatial position, and forming graph structure data through matrix X and matrix A.
[0043] In this embodiment, in step 4, the constructed 3D graph attention intelligent denoising model is as follows: Figure 3 As shown, it includes:
[0044] A 12-layer graph attention network, comprising 6 deconvolutional layers and 6 convolutional layers. The graph attention layer is used by the network to learn and extract structural features of the 3D flow field.
[0045] Specifically, the 3D graph attention intelligent denoising model consists of 12 graph attention layers, performing a total of 12 convolution operations. The convolution kernel of each graph attention layer is... , The attention coefficients are represented by the implicit output dimensions of 8, 16, 32, 64, 128, 256, 128, 64, 32, 16, 8, and 1, respectively; the graph attention layer convolutional kernels are... The methods for obtaining this include: first, calculating the similarity coefficient between neighboring nodes and itself. : , Let i represent the neighboring nodes of the current node i, where the weights are... and mapping It is learned through training a single-layer feedforward neural network, and the mapping is obtained. Used to map features onto the real number field. This indicates the merging of tensors. and Represents a node and nodes Features in the current layer, then through similarity coefficients Calculate the attention coefficient : Normalization is achieved through softmax, and the activation function is... Use LeakyReLU.
[0046] The graph attention layer utilizes attention coefficients through an aggregation function. As a method of node aggregation, to update the characteristics of lower-level nodes: ,in, This represents the number of layers in the neural network. It represents the features of all nodes in the graph attention layer. These are the weights of the l-th layer, i.e., the parameters that the network needs to learn. It is the feature of the j-th neighbor node in the l-th layer. This represents the activation function.
[0047] The LeakyReLU activation function is:
[0048]
[0049] In this embodiment, the loss function for training the 3D graph attention intelligent denoising model is: ,in, It is the true value of the constructed three-dimensional square wave. It is the predicted value of the three-dimensional square wave output by the neural network. This refers to the size of the sample set. The 3D graph attention intelligent denoising model is implemented using a computer language, and the results are stored on the server for later use after the model is trained.
[0050] In this embodiment, step 5 includes:
[0051] The three-dimensional noisy flow field physical quantities and the flow field mesh information are used to generate graph structure data, which is then used as input features for a three-dimensional graph attention intelligent denoising model. The three-dimensional graph attention intelligent denoising model outputs clean three-dimensional flow field physical quantities, such as... Figure 4 The diagram shows the framework of the three-dimensional intelligent denoising method. Finally, the denoised three-dimensional flow field data will be returned to the client.
[0052] This embodiment also provides an intelligent denoising device for a three-dimensional high-order discontinuous Galerkin numerical format. Specifically, the denoising device can run on a laboratory server, such as... Figure 5 As shown, the three-dimensional noise reduction device includes:
[0053] The data receiving module is used to receive the three-dimensional flow field physical quantities to be denoised sent by the client. The three-dimensional flow field data to be denoised includes: three-dimensional noisy flow field physical quantities and flow field mesh information.
[0054] The 3D flow field graph structure construction module is used to generate graph structure data from the 3D flow field data to be denoised;
[0055] The 3D training data construction module is used to store sample pairs composed of graph-structured 3D square waves and Fourier series expansions, as well as new morphological 3D square waves, into the 3D training data sample library.
[0056] The 3D denoising model training module uses constructed 3D training data to perform graph attention mechanism modeling and train a 3D intelligent denoising model.
[0057] The 3D flow field denoising module is used to denoise noisy 3D flow field graph structure data using a trained 3D graph attention denoising model, resulting in clean 3D flow field data.
[0058] The data transmission module is used to send the denoised 3D flow field data to the client.
[0059] The advantages of this invention are: it achieves intelligent denoising of the three-dimensional high-order discontinuous Galerkin numerical scheme; after the three-dimensional graph attention denoising model is trained, it is applicable to any three-dimensional graph structure data, without the need to retrain the model, only the denoising model needs to be called to achieve denoising of the three-dimensional flow field data; the model can output clean three-dimensional flow field data when inputting noisy three-dimensional data, and has good generalization performance.
[0060] This invention provides an intelligent denoising method and apparatus for three-dimensional high-order discontinuous Galerkin numerical schemes, applicable to numerical calculations of three-dimensional high-order discontinuous Galerkin flow fields with different three-dimensional examples, orders, and computational grids. Specifically, it performs numerical simulations of three-dimensional hypersonic cylinder flow, three-dimensional front step flow, and three-dimensional hemispherical flow for different high-order discontinuous Galerkin orders and computational grid densities. During the calculation process, a constructed three-dimensional graph attention intelligent denoising model is embedded to eliminate numerical oscillations near the shock wave. First, the noisy three-dimensional flow field data is constructed into a graph structure. Then, the trained three-dimensional graph attention denoising model is used to denoise the physical quantities of the noisy three-dimensional flow field. Finally, noise is eliminated, ensuring the stable execution of three-dimensional numerical calculations of high-order discontinuous Galerkin.
[0061] This invention provides an intelligent denoising method and apparatus for a three-dimensional high-order discontinuous Galerkin numerical scheme. Using noisy three-dimensional flow field physical quantities and mesh information provided by the client, a three-dimensional flow field graph structure is constructed on the server side. A training data sample library is built using three-dimensional square waves, three-dimensional square waves with Fourier series expansion, and novel three-dimensional square waves. Then, graph attention mechanism modeling is performed to train a three-dimensional intelligent denoising model. The trained denoising model is used to denoise the noisy three-dimensional flow field physical quantities, and finally, clean three-dimensional flow field data is returned to the client. The three-dimensional intelligent denoising model involved in this solution exhibits good generalization performance. After training, the model can be embedded into three-dimensional high-order discontinuous Galerkin calculations to suppress numerical oscillations near shock waves in three-dimensional flow fields with different meshes, orders, and types.
[0062] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on its differences from other embodiments. In particular, the device embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The above descriptions are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A denoising method for three-dimensional high-order discontinuous Galerkin data in shock wave analysis, the method being used in a computing system consisting of a server and a client, characterized in that... The three-dimensional flow field data to be denoised uploaded by the client includes three-dimensional noisy flow field physical quantities; the three-dimensional noisy flow field physical quantities include: flow field density, density multiplied by velocity in the x-direction, density multiplied by velocity in the y-direction, density multiplied by velocity in the z-direction, and density multiplied by energy; S1. The server generates three-dimensional graph structure data of the flow field based on the three-dimensional flow field data to be denoised; S2. Establish a three-dimensional training sample library using the three-dimensional graph structure data; S3. Train a 3D graph attention network model; S4. Gibbs noise removal is performed on the three-dimensional noisy flow field physical quantities using the trained three-dimensional graph attention network model. The graph structure data of the noisy three-dimensional flow field physical quantities is used as the input features of the three-dimensional graph attention network model, and the output results are returned to the client.
2. The method of claim 1, wherein S2 include: Obtain the original three-dimensional square wave and its Fourier series expansion, and construct a new three-dimensional square wave. The original three-dimensional square wave is used to simulate clean three-dimensional data, and the Fourier series expansion result of the original three-dimensional square wave and the new three-dimensional square wave are used to simulate noisy three-dimensional data. Clean 3D square waves and noisy 3D square waves are used to form input-output data training sample pairs, which are then stored in the 3D training sample library.
3. The method according to claim 1, characterized in that, In the original three-dimensional square wave, N points are taken in the three-dimensional space, namely in the x, y, and z directions, to form an N×N×N structure and generate the feature matrix X. An adjacency matrix A is generated based on the proximity of each point to its surrounding spatial locations; then, the graph structure data is composed of matrix X and matrix A.
4. The method according to claim 3, characterized in that, The original three-dimensional square wave is A represents amplitude, T represents period, and x represents the value of the independent variable on the three-dimensional coordinate x-axis; The Fourier series expansion of the original three-dimensional square wave is expressed as follows: , where n represents the accumulated parameter; The new form of three-dimensional square wave is represented as follows: ,in, This represents a newly constructed noisy square wave. Represents the original three-dimensional square wave. Represents a square wave in the Fourier series expansion. This represents an array of random numbers that follow a normal distribution.
5. The method according to claim 1, characterized in that, The three-dimensional graph attention network model includes: a graph neural network model with a total of 12 graph attention layers, including 6 deconvolutional layers and 6 convolutional layers.
6. The method according to claim 5, characterized in that, In the 12 graph attention layers, the first graph attention layer is the input layer, the 12th graph attention layer is the output layer, and the second to 11th graph attention layers are hidden layers.
7. The method according to claim 5, characterized in that, Attention coefficient As convolutional kernels for graph attention layers, the hidden output dimensions are 8, 16, 32, 64, 128, 256, 128, 64, 32, 16, 8, and 1, respectively.
8. A denoising device for three-dimensional high-order discontinuous Galerkin data in shock wave analysis, characterized in that, include: The data receiving module is used to receive the three-dimensional flow field data to be denoised uploaded by the client, which includes the physical quantities of the three-dimensional noisy flow field. A three-dimensional flow field graph structure construction module is used to generate three-dimensional graph structure data of the flow field based on the three-dimensional flow field data to be denoised. A 3D training data construction module is used to establish a 3D training sample library using the 3D graph structure data; The 3D denoising model training module is used to train a 3D graph attention network model. The three-dimensional flow field denoising module is used to remove Gibbs noise from the three-dimensional noisy flow field physical quantities, including the flow field density, density multiplied by the velocity in the x-direction, density multiplied by the velocity in the y-direction, density multiplied by the velocity in the z-direction, and density multiplied by the energy, through a trained three-dimensional graph attention network model. The graph structure data of the noisy three-dimensional flow field physical quantities is used as the input features of the three-dimensional graph attention network model. The data transmission module is used to send the denoised 3D flow field data to the client.
9. The method according to claim 8, characterized in that, The three-dimensional flow field diagram structure construction module is specifically used to obtain the original three-dimensional square wave and the Fourier series expansion result of the original three-dimensional square wave, and construct a new three-dimensional square wave; use the original three-dimensional square wave to simulate clean three-dimensional data, and use the Fourier series expansion result of the original three-dimensional square wave and the new three-dimensional square wave to simulate noisy three-dimensional data. Clean 3D square waves and noisy 3D square waves are used to form input-output data training sample pairs, which are then stored in the 3D training sample library.
10. The method according to claim 8, characterized in that, The three-dimensional graph attention network model includes: a graph neural network model with a total of 12 graph attention layers, including 6 deconvolutional layers and 6 convolutional layers; In the 12 graph attention layers, the first graph attention layer is the input layer, the 12th graph attention layer is the output layer, and the second to 11th graph attention layers are hidden layers; with attention coefficients... As convolutional kernels for graph attention layers, the hidden output dimensions are 8, 16, 32, 64, 128, 256, 128, 64, 32, 16, 8, and 1, respectively.