A method and system for solving oblique detonation flow field based on deep neural network

Abstract

The application discloses a method and system for solving oblique detonation flow field based on a deep neural network. The method comprises the following steps: establishing a flow field database; constructing a DeepM&Mnet framework for solving the oblique detonation flow field; training two DeepONets pre-training networks based on the flow field database, respectively, to obtain a network that minimizes a second loss function as a trained first pre-training network and a trained second pre-training network; and obtaining the oblique detonation flow field through inverse solving and / or forward solving based on known flow field data and the DeepM&Mnet framework. The application pre-trains the oblique detonation flow field data of various working conditions by using DeepONets, and then solves the oblique detonation flow field by using DeepM&Mnet containing physical constraints, so that the oblique detonation flow field can be solved based on a small amount of data in the case of insufficient boundary information.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of oblique detonation flow, and particularly relates to an oblique detonation flow field solving method and system based on deep neural network. BACKGROUND

[0002] The oblique detonation engine is a future hypersonic propulsion technology based on the high heat release rate and high thermal cycle efficiency of oblique detonation wave. The oblique detonation flow field and combustion mechanism of the combustion chamber are crucial to the development of the oblique detonation engine. Oblique detonation is a supersonic flow and combustion phenomenon involving complex wave structure and chemical reaction. The computational fluid dynamics (CFD) method is an important design means for engine aerodynamic design, but the traditional CFD method can only solve the flow field in the forward direction, i.e. the complete initial flow field, boundary conditions and other information are known. In actual engineering problems, there are often some unknown boundary conditions and some local information of the known flow field. For example, the designer can give the information of the injected fuel, but the fuel flowing in the supersonic airflow is very complex, and the fuel information reaching the combustion chamber is often unknown, so there are unknown information in the boundary conditions of the combustion chamber calculation domain. For another example, in the test, the speed, temperature, density, concentration and other information of the local region of the combustion chamber can be measured, and it is very difficult for the traditional CFD method to obtain a flow field result consistent with the test data for the supersonic multi-scale flow and combustion problem with chemical reaction such as oblique detonation. Therefore, how to obtain the oblique detonation flow field under the condition of insufficient boundary information and make full use of the local known information of the flow field to improve the accuracy of the flow field solving is a problem to be solved. SUMMARY

[0003] To solve the above problems, the present application provides an oblique detonation flow field solving method and system based on deep neural network, which pre-trains the oblique detonation flow field data of multiple working conditions by DeepONets, and then solves by DeepM&Mnet containing physical constraints, so as to solve the oblique detonation flow field based on a small amount of data under the condition of insufficient boundary information.

[0004] In one aspect, an oblique detonation flow field solving method based on deep neural network comprises:

[0005] establishing a flow field database;

[0006] constructing a DeepM&Mnet framework for solving the oblique detonation flow field; the DeepM&Mnet framework comprises a deep neural network, two DeepONets pre-training networks and a first loss function;

[0007] Based on the flow field database, two DeepONets pre-trained networks are trained respectively to obtain networks that minimize the second loss function, as the trained first pre-trained network DeepONet1 and the trained second pre-trained network DeepONet2;

[0008] Based on known flow field data, a deep neural network, a trained first pre-trained network DeepONet1 and a trained second pre-trained network DeepONet2, the oblique detonation flow field is obtained by inverse solution and / or forward solution.

[0009] Preferably, the establishing of the flow field database specifically includes:

[0010] Determine oblique detonation boundary conditions and required operating conditions;

[0011] Calculate the incoming flow parameters and obtain the incoming flow conditions in the flow field area;

[0012] Use CFD software to solve the oblique detonation flow field under various required working conditions and incoming flow conditions, and obtain the solved oblique detonation flow field data;

[0013] A flow field database is established based on multiple oblique detonation flow field data.

[0014] Preferably, the input and output of the two DeepONets are opposite. The first pre-trained network DeepONet1 takes the known data speed and temperature as input and the density of each component and the mass generation rate per unit volume as output; the second pre-trained network DeepONet2 takes the known data density of each component and the mass generation rate per unit volume as input and the speed and temperature as output.

[0015] Preferably, the second loss function is expressed as follows:

[0016]

[0017] MSE represents the second loss function; W represents the predicted variable, W j and They represent labeled data and predicted data respectively, and N represents the number of training data.

[0018] Preferably, when solving the inverse problem, the first loss function is expressed as follows:

[0019]

[0020] in, is the constraint of known data points, is the constraint of two DeepONets, is the constraint of the fluid control equation;

[0021] Constraints on known data points and the constraints of two DeepONets They are represented as follows:

[0022]

[0023] Where V represents any flow field output parameter; V(x j ,y j ) represents the output of the neural network; V data (x j ,y j ) represents a known data point; V ′ (x j ,y j ) represents the output of DeepONets; N d Indicates the number of known data; o Indicates the number of points used for DeepONets evaluation;

[0024] Fluid control equation constraints as follows:

[0025]

[0026] The items are:

[0027] U=[ρ1…ρ n ρuρv] T

[0028] F=[ρ1u…ρ n uρu 2 +Pρuv(e+p)u] T

[0029] G=[ρ1v…ρ n vρuvρv 2 +P(e+P)v] T

[0030]

[0031] Where ρ represents density; u represents velocity along the x-axis; v represents velocity along the y-axis; represents pressure; represents the number of components; ρ i represents the density of each component; represents the mass generation rate per unit volume; represents total energy; h represents specific enthalpy, h i Obtained from the thermodynamic data for each species; w i represents the molar mass of the gas, T represents the gas temperature; R0 is the universal gas constant.

[0032] Preferably, during forward solution, the first loss function is expressed as follows:

[0033]

[0034] wherein, is the constraint of two DeepONets, is the constraint of fluid governing equations;

[0035] constraint of two DeepONets is represented as follows:

[0036]

[0037] wherein, V represents any kind of flow field output parameter; V(x j ,y j ) represents the output of neural network; V ′ (x j ,y j ) represents the output of DeepONets; o represents the number of points for DeepONets evaluation;

[0038] constraint of fluid governing equations is as follows:

[0039]

[0040] wherein each term is respectively:

[0041] U = [ρ1…ρ n ρuρv] T

[0042] F = [ρ1u…ρ n uρu 2 + Pρuv(e + p)u] T

[0043] G = [ρ1v…ρ n vρuvρv 2 + P(e + P)v] T

[0044]

[0045] wherein, ρ represents density; u represents velocity along x-axis direction; v represents velocity along y-axis direction; P represents pressure; n represents component number; ρ i represents each component density; represents unit volume mass generation rate; represents total energy; h represents specific enthalpy, h i is obtained from the thermodynamic data of each species; w i represents gas molar mass, T represents gas temperature; R0 is universal gas constant.

[0046] In another aspect, a deep neural network-based oblique detonation flow field solving system comprises:

[0047] A database establishing module is configured to establish a flow field database.

[0048] A neural network constructing module is configured to construct a DeepM&Mnet framework for solving an oblique detonation flow field, wherein the DeepM&Mnet framework comprises a deep neural network, two DeepONets pre-training networks and a first loss function.

[0049] A training module is configured to train the two DeepONets pre-training networks based on the flow field database, respectively, to obtain a network that minimizes a second loss function as a trained first pre-training network DeepONet1 and a trained second pre-training network DeepONet2.

[0050] An oblique detonation flow field solving module is configured to obtain an oblique detonation flow field through inverse solving and / or forward solving based on known flow field data, the deep neural network, the trained first pre-training network DeepONet1 and the trained second pre-training network DeepONet2.

[0051] Compared with the prior art, the present application has the following beneficial effects:

[0052] The deep neural network-based oblique detonation flow field solving method and system of the present application can capture and learn flow field information by using the method of neural network to add physical control equation constraints based on local test point data, and reconstruct the density field, velocity field and pressure field related to oblique detonation. Compared with the existing forward CFD calculation, the present application can well solve the inverse problem and accurately reconstruct the oblique detonation flow field based on a small amount of test data under the condition of insufficient boundary information. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 The flow chart of the deep neural network-based oblique detonation flow field solving method of the embodiment of the present application is shown in the figure.

[0054] Figure 2 The overall flow chart of the deep neural network-based oblique detonation flow field solving method of the embodiment of the present application is shown in the figure.

[0055] Figure 3 The typical oblique detonation flow field characteristic diagram of the embodiment of the present application is shown in the figure.

[0056] Figure 4 The DeepM&Mnet framework principle diagram of the embodiment of the present application is shown in the figure.

[0057] Figure 5A structural schematic diagram of DeepONets of an embodiment of the present application;

[0058] Figure 6 A forward solving schematic diagram of DeepM&Mnet of an embodiment of the present application;

[0059] Figure 7 A structural block diagram of a deep neural network-based oblique detonation flow field solving system of an embodiment of the present application. DETAILED DESCRIPTION

[0060] The present application will be further described below in conjunction with the drawings and embodiments.

[0061] Referring to Figure 1 and Figure 2 , the present application is a deep neural network-based oblique detonation flow field solving method, comprising:

[0062] S101, establishing a flow field database;

[0063] S102, constructing a DeepM&Mnet framework for oblique detonation flow field solving; the DeepM&Mnet framework comprises a deep neural network, two DeepONets pre-training networks and a first loss function;

[0064] S103, based on the flow field database, training the two DeepONets pre-training networks respectively to obtain a network that minimizes a second loss function as a trained first pre-training network DeepONet1 and a trained second pre-training network DeepONet2;

[0065] S104, based on known flow field data, a deep neural network, the trained first pre-training network DeepONet1 and the trained second pre-training network DeepONet2, obtaining an oblique detonation flow field through inverse solving and / or forward solving. In this embodiment, the known flow field data includes certain boundary data and initial data (including velocity, temperature, density, etc.) of the flow field, and density gradient data of the overall flow field, etc.

[0066] The forward solving is to use a deep neural network to solve partial differential equations to obtain a flow field based on known boundary condition data and initial data of a flow field; the inverse solving is to use a deep neural network to predict the entire field of all states of interest based on only some data related to density, velocity or pressure. The embodiment is not limited according to different data and purposes.

[0067] S101, establishing a flow field database, specifically as follows.

[0068] The main concern of the oblique detonation engine is the region near the initiation in the combustion chamber, referring toFigure 3 A typical oblique detonation flow field is shown, including an oblique shock wave before detonation, a detonation initiation zone, and a complex wave structure composed of a series of compression waves and oblique detonation waves after detonation initiation. The flow field is a local region extracted from the aircraft combustion chamber. In order to study the flow in the oblique detonation engine, the geometry of the aircraft forebody and the inlet system needs to be considered to determine the appropriate oblique detonation wave inflow conditions. For example, the gas passes through two wedge surfaces and then enters the combustion chamber. Theoretical calculations of the inflow parameters are combined with oblique shock wave theory and standard atmospheric parameters to obtain the inflow conditions of the flow field region.

[0069] Further, the CFD software is used to solve the oblique detonation flow field under each working condition, and the solved oblique detonation flow field data is obtained. According to the needs of the deep neural network program, the data is post-processed, and a flow field database is established to provide sufficient data for the pre-training of the deep neural network.

[0070] The S102 constructs a DeepM&Mnet framework for solving the oblique detonation flow field, as follows.

[0071] The DeepM&Mnet framework includes a deep neural network, two DeepONets pre-training networks, and three loss functions. The principle is described in Figure 4 . First, a deep neural network is established, taking the flow field coordinates x and y as input, and the velocity, temperature, and component density, mass generation rate per unit volume (i is the component index, H2, O2, etc.) and other information as output.

[0072] In reverse solving, the loss function (first loss function) of the DeepM&Mnet framework is represented as follows:

[0073]

[0074] where, is the constraint of the known data points, is the constraint of the two DeepONets, is the constraint of the fluid control equation;

[0075] The constraints of the known data points and the two DeepONets are represented as follows:

[0076]

[0077] where V represents any flow field output parameter; V(x j ,y j ) represents the output of the neural network; V data (x j, y j ) represents known data points; V ′ (x j , y j ) represents the output of DeepONets; N d represents the number of known data; o represents the number of points used for DeepONets evaluation;

[0078] Fluid control equation constraints As follows:

[0079]

[0080] Wherein each term is respectively:

[0081] U = [ρ1…ρ n ρuρv] T

[0082] F = [ρ1u…ρ n uρu 2 + Pρuv(e + p)u] T

[0083] G = [ρ1v…ρ n vρuvρv 2 + P(e + P)v] T

[0084]

[0085] Wherein, ρ represents the density; u represents the velocity along the x-axis direction; v represents the velocity along the y-axis direction; P represents the pressure; represents; ρ i represents; represents the total energy; h represents the specific enthalpy, h i Obtained from the thermodynamic data of each species; w i represents the molar mass of the gas, T represents the gas temperature; R0 is the universal gas constant.

[0086] In this embodiment, 0 is called the universal gas (ideal gas) constant, which does not change with the molecular weight of the gas, and is 8.314 J / (mol·K).

[0087] When solving forward, the loss function (first loss function) of the DeepM&Mnet framework is represented as follows:

[0088]

[0089] And The specific implementation of is the same as that of reverse solving.

[0090] Further, each DeepONets pre-training network consists of two sub-networks: a branch network for the input field and a trunk network for the output field position. The trunk network of DeepONets takes the coordinate (x, y) as input, and outputs the coordinate (x, y) as output. The branch network takes the coordinate function [φ(x1, y1), …, φ(xm, ym)] of m discrete values as input, and outputs the coordinate (b1, b2, …, b m) as output. The output vectors of the trunk network and the branch network obtain the final output through the dot product (see FIG. 1). G(φ)(x, y) represents this function that can only be represented by some discrete points, which are called sampling points. As an example, the number of points of the DeepONets branch network can be set to 75, and the number of points of the trunk network can be set to 48. Here, the logarithm of the original data is used for all densities, and the original data is used for the velocity and temperature. It should be noted that this is only to represent the processing of the training data on the density, velocity, and temperature. m m T p T p p Figure 5

[0091] In DeepM&Mnet, the input and output of the two DeepONets (the first pre-training network DeepONet1 and the second pre-training network DeepONet2) are opposite, that is, DeepONet1 takes the velocity and temperature as input, and generates the density of each component and the mass generation rate per unit volume as output; DeepONet2 takes the density of each component and the mass generation rate per unit volume as input, and generates the velocity and temperature as output.

[0092] In this embodiment, the first pre-training network DeepONet1 and the second pre-training network DeepONet2 are pre-trained, that is, all data are known, and are not formal prediction. When the known data are the velocity and temperature, the DeepONet1 network is used to obtain the density of each component and the mass generation rate per unit volume, and when the known data are the density of each component and the mass generation rate per unit volume, the DeepONet2 network is used to obtain the velocity and temperature. The weights and biases of the two networks are different according to the training data, the DeepONet1 network learns the data to predict the density of each component and the mass generation rate per unit volume through learning of the velocity and temperature; and the DeepONet2 network is the opposite. The amount of training data and the number of network layers are different between the networks, and the use of the DeepONet network makes the training effect better.

[0093] ​​​​​​​​​In this embodiment, the parameters of the deep neural network are as follows: the hidden layer of the neural network is 6x50; the activation function is tanh; the learning rate is 5x10 -4 ; the period is 300000 times, once refers to a round of training.

[0094] By continuously reducing the first loss function value, the prediction result of the neural network can be constrained.

[0095] The S103 trains two DeepONets pre-training networks, specifically as follows.

[0096] Using the database established by S101, DeepONet1 and DeepONet2 are trained respectively. The loss function is as follows:

[0097]

[0098] Wherein, V represents the predicted variable, V j and respectively represent the labeled data and the predicted data, and N represents the number of training data. In this embodiment, the parameters of DeepONet1 and DeepONet2 networks are as follows: the hidden layer of the neural network is 6x40; the activation function is tanh; the learning rate is 8x10 -4 ; the period is 20000.

[0099] Through the training of the oblique detonation flow field database, the trained DeepONet1 and DeepONet2 are obtained.

[0100] The S104 solves the oblique detonation flow field, specifically as follows.

[0101] Reverse solving (see Figure 4 ): the deep neural network of DeepM&Mnet is established, the x, y coordinates are input into DeepM&Mnet, and three loss functions are completely retained, that is, it contains and Based on the pre-trained DeepONet1 and DeepONet2, a small amount of known flow field data is used, without complete boundary conditions, and the reverse solving of the oblique detonation flow field can be realized by minimizing the loss function.

[0102] Forward solving (see Figure 6 ): the deep neural network of DeepM&Mnet is established, the x, y coordinates are input into DeepM&Mnet, and the loss function is only retained and Two loss functions, based on pre-trained DeepONet1, DeepONet2, by minimizing the loss function, can realize the forward solution of the oblique detonation flow field. If some data are known, the known data can be input into the deep neural network for training based on the forward solution, and the local known information in the flow field space is used to help improve the accuracy of the flow field solution and improve the solution accuracy.

[0103] Referring to Figure 7 As an implementation of the method shown in the above figures, the embodiment provides an embodiment of an oblique detonation flow field solving system based on a deep neural network, which corresponds to the method embodiment shown in Figure 1 The system can be applied to various electronic devices.

[0104] In another aspect, an oblique detonation flow field solving system based on a deep neural network includes:

[0105] The database establishment module 701 is configured to establish a flow field database.

[0106] The neural network construction module 702 is configured to construct a DeepM&Mnet framework for solving the oblique detonation flow field, wherein the DeepM&Mnet framework includes a deep neural network, two DeepONets pre-trained networks, and a first loss function.

[0107] The training module 703 is configured to train the two DeepONets pre-trained networks based on the flow field database to obtain a network that minimizes a second loss function as a trained first pre-trained network DeepONet1 and a trained second pre-trained network DeepONet2.

[0108] The oblique detonation flow field solving module 704 is configured to obtain the oblique detonation flow field by inverse solving and / or forward solving based on known flow field data, a deep neural network, the trained first pre-trained network DeepONet1, and the trained second pre-trained network DeepONet2.

[0109] A specific implementation of an oblique detonation flow field solving system based on a deep neural network is the same as an oblique detonation flow field solving method based on a deep neural network, and the embodiment will not be repeated.

[0110] The above embodiments are only for illustrating the technical concept and characteristics of the present application, and the purpose is to enable those skilled in the art to understand the content of the present application and implement it, and cannot limit the protection scope of the present application. Any equivalent changes or modifications made in accordance with the spirit and essence of the present application shall be covered within the protection scope of the present application.

Claims

1. A method for solving oblique detonation flow field based on deep neural network, characterized in that: include: Establish a flow field database; Construct the DeepM&Mnet framework for solving oblique detonation flow fields; The DeepM&Mnet framework includes a deep neural network, two DeepONets pre-trained networks and a first loss function; Based on the flow field database, two DeepONets pre-trained networks are trained respectively to obtain networks that minimize the second loss function, as the trained first pre-trained network DeepONet1 and the trained second pre-trained network DeepONet2; Based on known flow field data, a deep neural network, a trained first pre-trained network DeepONet1, and a trained second pre-trained network DeepONet2, an oblique detonation flow field is obtained by reverse solution and / or forward solution; When solving inversely, the first loss function is expressed as follows: in, is the constraint of known data points, is the constraint of two DeepONets, is the constraint of the fluid control equation; Constraints on known data points and the constraints of two DeepONets They are represented as follows: Where V represents any flow field output parameter; V(x j ,y j ) represents the output of the neural network; V data (x j ,y j ) represents a known data point; V ′ (x j ,y j ) represents the output of DeepONets; N d Indicates the number of known data; N o Indicates the number of points used for DeepONets evaluation; Fluid control equation constraints as follows: The items are: U=[ρ1…ρ n r u r v [e] T F=[ρ1u…ρ n u r u 2 +P ρuv(e+p)u] T G[ρ1v...ρ n v ρuv ρv 2 +P(e+P)v] T Where ρ represents density; u represents velocity along the x-axis; v represents velocity along the y-axis; P represents pressure; n represents the number of components; ρ i represents the density of each component; represents the mass generation rate per unit volume; e represents the total energy; h represents the specific enthalpy, h i Obtained from the thermodynamic data for each species; w i represents the molar mass of the gas, T represents the gas temperature; R0 is the universal gas constant.

2. The method for solving oblique detonation flow field based on deep neural network according to claim 1, characterized in that: The establishment of the flow field database specifically includes: Determine oblique detonation boundary conditions and required operating conditions; Calculate the incoming flow parameters and obtain the incoming flow conditions in the flow field area; Use CFD software to solve the oblique detonation flow field under various required working conditions and incoming flow conditions, and obtain the solved oblique detonation flow field data; A flow field database is established based on multiple oblique detonation flow field data.

3. The method for solving oblique detonation flow field based on deep neural network according to claim 1, characterized in that: The input and output of the two DeepONets are opposite. The first pre-trained network DeepONet1 takes the known data speed and temperature as input and outputs the density of each component and the mass generation rate per unit volume; The second pre-trained network DeepONet2 takes the known data of density of each component and mass generation rate per unit volume as input, and takes velocity and temperature as output.

4. The method for solving oblique detonation flow field based on deep neural network according to claim 1, characterized in that: The second loss function is expressed as follows: MSE represents the second loss function; W represents the predicted variable, W j and They represent labeled data and predicted data respectively, and N represents the number of training data.

5. The method for solving oblique detonation flow field based on deep neural network according to claim 1, characterized in that: When solving forward, the first loss function is expressed as follows: in, is the constraint of two DeepONets, is the constraint of the fluid control equation; Constraints of Two DeepONets It is expressed as follows: Where V represents any flow field output parameter; V(x j ,y j ) represents the output of the neural network; V ′ (x j ,y j ) represents the output of DeepONets; N o Indicates the number of points used for DeepONets evaluation; Fluid control equation constraints as follows: The items are: U=[ρ1…ρ n [ru pv e] T F=[ρ1u…ρ n u r u 2 +P ρuv(e+p)u] T G=[ρ1v…p n v ρuv ρv 2 +P(e+P)v] T 6. A deep neural network-based oblique detonation flow field solution system, characterized in that: include: Database establishment module, used to establish flow field database; A neural network building module for constructing a DeepM&Mnet framework for solving oblique detonation flow fields; the DeepM&Mnet framework includes a deep neural network, two DeepONets pre-trained networks, and a first loss function; A training module is used to train two DeepONets pre-trained networks based on the flow field database, respectively, to obtain a network that minimizes the second loss function as the trained first pre-trained network DeepONet1 and the trained second pre-trained network DeepONet2; An oblique detonation flow field solving module is used to obtain the oblique detonation flow field through inverse solution and / or forward solution based on known flow field data, a deep neural network, a trained first pre-trained network DeepONet1, and a trained second pre-trained network DeepONet2; When solving inversely, the first loss function is expressed as follows: in, is the constraint of known data points, is the constraint of two DeepONets, is the constraint of the fluid control equation; Constraints on known data points and the constraints of two DeepONets They are represented as follows: Where V represents any flow field output parameter; V(x j ,y j ) represents the output of the neural network; V data (x j ,y j ) represents a known data point; V ′ (x j ,y j ) represents the output of DeepONets; N d Indicates the number of known data; N o Indicates the number of points used for DeepONets evaluation; Fluid control equation constraints as follows: The items are: U=[ρ1…ρ n [ru pv e] t F=[ρ1u…ρ n u r u 2 +P ρuv(e+p)u] T G[ρ1v...ρ n v ρuv ρv 2 +P(e+P)v] T Where ρ represents density; u represents velocity along the x-axis; v represents velocity along the y-axis; P represents pressure; n represents the number of components; ρ i represents the density of each component; represents the mass generation rate per unit volume; e represents the total energy; h represents the specific enthalpy, h i Obtained from the thermodynamic data for each species; w i represents the molar mass of the gas, T represents the gas temperature; R0 is the universal gas constant.

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