Sound pressure field reconstruction method and system and readable storage medium

Abstract

The invention relates to a sound pressure field reconstruction method and system and a readable storage medium. The sound pressure field reconstruction method comprises the following steps: S1, acquiring low-resolution sound pressure field data to form a first data set; s2, integrating the physical information neural network into a Bayesian neural network to obtain a Bayesian physical information neural network; s3, acquiring a second data set through the physical information neural network; s4, training the Bayesian physical information neural network by using the first data set and the second data set; and S5, sampling the Bayesian physical information neural network parameters through a Monte Carlo-Markov chain technology, and reconstructing a sound pressure field. A high-resolution sound pressure field is reconstructed from low-resolution sound pressure field data with a certain error, and the uncertainty of a reconstruction result can be synchronously obtained.

Description

Technical Field

[0001] The technical field of the present invention relates to a sound pressure field reconstruction method, system and readable storage medium. Background Art

[0002] Currently, various existing CFD numerical simulation methods cannot well integrate various types of fidelity data (such as data obtained from experiments, or low-precision and low-resolution flow field data obtained from numerical simulations). In engineering applications, there are also many inverse problems to be solved, that is, in the case where the boundary conditions and various parameters of the flow field are unknown, how to obtain accurate model parameters and flow field reconstruction through partial measurement data. Moreover, the quality of the CFD grid has a relatively large impact on the results, and the grid division itself is also very time-consuming in the calculation.

[0003] Physics Informed Neural Network (PINN for short) is an application method of machine learning in the traditional numerical field, especially for solving various problems related to partial differential equations (PDEs), including equation solving, parameter inversion, model discovery, control and optimization, etc. The principle of PINN is to approximate the solution of PDEs by training a neural network to minimize the loss function. The so-called loss function terms include the residual terms of the initial conditions and boundary conditions, as well as the PDE residual at selected points in the region. After training is completed, inference can be performed to obtain the physical field function values at space-time points.

[0004] Compared with traditional CFD solvers, PINN is superior in integrating data (observations) and physical knowledge (the governing equations describing the physical phenomenon). That is, when the spatio-temporal scattered measurement data is relatively sufficient, it is used to solve problems such as CFD-related parameter estimation, flow field reconstruction, and surrogate model construction. The advantage of PINN lies in that this method or idea can make up for the weaknesses of pure data-driven in the field of scientific machine learning. If the numerical format of the traditional CFD solver is considered as pure physics knowledge-driven, then PINN or more generally the machine learning embedded with physical knowledge is a fusion method of data-driven and knowledge-driven. The neural network embedded with physical knowledge is not a pure "knowledge-driven" method that is the opposite of the data-driven method, but exists as a bridge between the data method and the traditional knowledge-driven equation, that is, a method jointly driven by "knowledge" and "data".

[0005] A more straightforward example is to reconstruct the full flow field from velocity observation values. In experimental studies in disciplines such as aerodynamics, optical devices can be used to measure multiple scattered-point velocities through Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV) methods. However, the scattered-point velocities do not meet the requirements, and a high-resolution velocity field is essential for visualization and subsequent analysis. A very natural idea is to achieve "super-resolution" from scattered points to a high-resolution flow field through something similar to image interpolation, but the results obtained in this way may "not conform to physical laws". As a PINN method that incorporates physical knowledge, it is possible to reconstruct a high-resolution overall velocity field from this sparse velocity information. That is, by minimizing the loss term of the NS equation, the velocity field and pressure field are obtained simultaneously, making the results conform to "physical laws". Summary of the Invention

[0006] An object of the present invention is to provide a method for reconstructing an acoustic pressure field.

[0007] Another object of the present invention is to provide a readable storage medium.

[0008] Still another object of the present invention is to provide an acoustic pressure field reconstruction system.

[0009] An acoustic pressure field reconstruction method according to one aspect of the present invention includes: S1. Obtaining low-resolution acoustic pressure field data to form a first data set D u ; S2. Incorporating a physics-informed neural network into a Bayesian neural network to obtain a Bayesian physics-informed neural network; S3. Obtaining a second data set through the physics-informed neural network; S4. Training the Bayesian physics-informed neural network using the first data set and the second data set; S5. Sampling the parameters of the Bayesian physics-informed neural network through the Monte Carlo-Markov chain technique to reconstruct the acoustic pressure field.

[0010] In one or more embodiments of the acoustic pressure field reconstruction method, in step S1, the first data set D u is obtained by measuring through instruments and / or solving using a CFD numerical solver in an experiment.

[0011] In one or more embodiments of the acoustic pressure field reconstruction method, in step S2, through the automatic differentiation mechanism of the physics-informed neural network, the acoustic propagation wave equation in partial differential form, the acoustic field boundary conditions, and the acoustic field initial conditions are incorporated into the Bayesian neural network in the form of a likelihood function with a Gaussian distribution.

[0012] In one or more embodiments of the sound pressure field reconstruction method, in the step S2, the likelihood function is

[0013]

[0014] The Bayesian physics-informed neural network is a posterior joint probability distribution function:

[0015]

[0016] where θ is a multi-dimensional vector, D = (D u ∪ D f ∪ D b ).

[0017] In one or more embodiments of the sound pressure field reconstruction method, in the step S3, the second data set is obtained by randomly sampling from the domain of the acoustic wave propagation equation N and the acoustic field boundary condition and acoustic field initial condition B equations. The second data set includes D f and D b ; where f = Nx(u; θ) and b = Bx(u; θ).

[0018] In one or more embodiments of the sound pressure field reconstruction method, in the step S4, the parameters θ of the Bayesian physics-informed neural network are corrected and improved by the first data set D u and the second data set.

[0019] In one or more embodiments of the sound pressure field reconstruction method, in the step S5, the Monte Carlo-Markov chain technique is used to sample the parameters θ in the Bayesian physics-informed neural network to obtain M sets of sampled parameter values For any input x, M posterior sampling results can be obtained The mean of the M posterior sampling results is used as the predicted value u(x) of the Bayesian physics-informed neural network for sound pressure field reconstruction.

[0020] In one or more embodiments of the sound pressure field reconstruction method, the mean square error value of the M posterior sampling results is used as the uncertainty of the predicted value u(x) and the uncertainty of the sound pressure field reconstruction.

[0021] According to another aspect of the present invention, a readable storage medium stores a computer program, which when executed by a processor implements the sound pressure field reconstruction method described in any one of the above.

[0022] A sound pressure field reconstruction system according to another aspect of the present invention includes a data processing module, and the data processing module includes: a computer-readable storage medium for storing instructions executable by a processor; and a processor for executing the instructions to implement the sound pressure field reconstruction method described in any one of the above.

[0023] The technical solution of this application integrates a physics-informed neural network into a Bayesian neural network, corrects and improves the parameters of the fused Bayesian physics-informed neural network, and performs sampling through the Monte Carlo-Markov chain technique to achieve high-resolution sound pressure field reconstruction, and can simultaneously obtain the uncertainty of the reconstruction result, thereby accelerating and improving the design work related to aeroengine noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The above and other features, properties, and advantages of the present invention will become more apparent from the following description in conjunction with the drawings and embodiments, in which the same reference numerals always represent the same features. It should be noted that these drawings are only examples and are not drawn according to the condition of equal scale, and should not be used to limit the actual scope of protection required by the present invention, where:

[0025] Figure 1 It is a flowchart of a sound pressure field reconstruction method for an embodiment.

[0026] Figure 2 It is a schematic diagram of the principle of a Bayesian physics-informed neural network for an embodiment.

[0027] Figure 3 It is a schematic diagram of the structure of a sound pressure field reconstruction system for an embodiment.

[0028] Reference Numerals:

[0029] 100 - Sound pressure field reconstruction method;

[0030] 1 - Data processing module;

[0031] 101 - Computer-readable storage medium;

[0032] 102 - Processor. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0033] Now, reference will be made in detail to the various embodiments of the present invention, and examples of these embodiments are shown in the drawings and described as follows. Although the present invention will be described in conjunction with the exemplary embodiments, it should be understood that this specification is not intended to limit the present invention to those exemplary embodiments. On the contrary, the present invention is intended to cover not only these exemplary embodiments, but also various alternative forms, modified forms, equivalent forms, and other embodiments that can be included within the spirit and scope of the present invention as defined by the appended claims.

[0034] Meanwhile, this application uses specific terms to describe the embodiments of this application. For example, "one embodiment" and / or "an embodiment" mean a certain feature, structure, or characteristic related to at least one embodiment of this application. Therefore, it should be emphasized and noted that "an embodiment" or "one embodiment" mentioned twice or more at different positions in this specification does not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of this application can be appropriately combined.

[0035] Flowcharts are used in this application to illustrate the operations performed by the systems according to the embodiments of this application. It should be understood that the operations before or below do not necessarily need to be precisely executed in sequence. Other operations can also be added to these processes, or one or several steps of operations can be removed from these processes.

[0036] Although the physics-informed neural network can reconstruct the overall velocity field of the resolution from sparse velocity information, the highly non-convex and non-linear nature of PINN will cause many difficulties in actual training, such as gradient explosion, gradient disappearance, and inability to obtain the global optimal solution. In the problems of PDE parameter inversion and flow field reconstruction, when there is noise in a small amount of sample data, it will lead to a large PINN solution error or even the training cannot converge, resulting in the failure of the solution. At the same time, it is also impossible to measure the uncertainty of the final PINN model (Uncertainty Quantification).

[0037] Based on the above considerations, after in-depth research, the inventors designed a method for reconstructing the acoustic pressure field. By integrating the physics-informed neural network into the Bayesian neural network, the parameters of the fused Bayesian physics-informed neural network are corrected and improved, and sampling is performed through the Monte Carlo-Markov chain technique to achieve the reconstruction of the high-resolution acoustic pressure field, and the uncertainty of the reconstruction result can be obtained synchronously, so as to accelerate and improve the design work related to aero-engine noise.

[0038] Explanation of related terms is as follows:

[0039] "Acoustic pressure field reconstruction" refers to reconstructing a high-resolution acoustic pressure field from a coarse-grained or low-resolution acoustic pressure field.

[0040] "Physics-informed neural network" (PINN) refers to a neural network that integrates physical information. Through the automatic differentiation mechanism of the neural network, control equations, boundary conditions, initial conditions, etc. containing physical knowledge are incorporated into the neural network in the form of a loss function, and the physical laws of the problem to be solved are learned by minimizing the loss function during training and learning.

[0041] The "Bayesian neural network" (BNN) refers to a special type of neural network. The parameters of the model are not fixed but random variables that follow a specific probability distribution. During prediction, the parameters are sampled to obtain multiple prediction values and then averaged, so it is convenient to evaluate the uncertainty of the prediction values.

[0042] Reference Figure 1 As shown, in one embodiment, the specific steps of the acoustic pressure field reconstruction method 100 may include:

[0043] S1. Obtain low-resolution acoustic pressure field data to form the first dataset D u ;

[0044] Specifically, the acquisition method of the first dataset D u includes measuring through instruments and / or solving using a CFD numerical solver during the experiment. The CFD numerical solver is a CFD numerical solver with fewer grids, low precision, and low resolution. The number of grids is controlled within tens of thousands, and the precision and resolution are controlled within a relative error of 10 -1 within. Here and afterwards, u refers to the acoustic field pressure.

[0045] S2. Incorporate the physics-informed neural network into the Bayesian neural network to obtain the Bayesian physics-informed neural network;

[0046] Specifically, through the automatic differentiation mechanism of the physics-informed neural network, the partial differential form of the acoustic wave propagation equation, the acoustic field boundary conditions, and the acoustic field initial conditions are incorporated into the Bayesian neural network in the form of a likelihood function with a Gaussian distribution, so that the Bayesian neural network can learn the physical laws of the problem to be solved. The parameters of the Bayesian neural network are not fixed variables but a series of random variables. In this application, a Gaussian (normal) distribution is used for initialization, which is also called the prior distribution of the parameters.

[0047] The likelihood function is

[0048]

[0049] The Bayesian physics-informed neural network is the posterior joint probability distribution function:

[0050]

[0051] where θ is a multi-dimensional vector, D = (D u ∪D f ∪D b ).

[0052] S3. Obtain the second dataset through the physics-informed neural network;

[0053] Specifically, the second data set is obtained by random sampling from the definition domain of the sound propagation wave equation N and the sound field boundary condition and the sound field initial condition B equation. The second data set includes D f and D b ; Among them, f=Nx(u; θ), b=Bx(u; θ).

[0054] S4. Training a Bayesian physical information neural network using the first data set and the second data set;

[0055] Specifically, Figure 2 The schematic diagram of the Bayesian physical information neural network principle shown in the figure, the first data set D u The second data set is used as training data to correct and improve the parameter θ of the Bayesian physical information neural network. Since the Bayesian neural network does not require traditional neural network training, that is, the Bayesian physical information neural network only needs to solve the posterior joint probability density of the neural network parameters according to the training data values.

[0056] S5. Sampling the parameters of the Bayesian physical information neural network through the Monte Carlo-Markov chain to reconstruct the acoustic pressure field;

[0057] Specifically, the parameter θ in the Bayesian physical information neural network is sampled by using the Monte Carlo-Markov chain (MCMC) technique to obtain M groups of sampled parameter values: For any input x, M posterior sampling results can be obtained The mean of the M posterior sampling results is used as the predicted value u(x) of the Bayesian physical information neural network to reconstruct the acoustic pressure field. The mean square error of the M posterior sampling results can be used as the uncertainty of the predicted value u(x) and the uncertainty of the acoustic pressure field reconstruction. Due to the characteristics of BNN, not only can the uncertainty of the results be obtained, but also because of its non-overfitting characteristics, more accurate prediction values ​​can be obtained when there is noise in the data.

[0058] In this way, a high-resolution sound pressure field can be reconstructed from low-resolution sound pressure field data with certain errors, and the uncertainty of the results can be obtained simultaneously, thereby accelerating and improving the design work related to aircraft engine noise.

[0059] Although the above method is illustrated and described as a series of actions for simplicity of explanation, it should be understood and appreciated that these steps are not limited by the order of the actions, because according to one or more embodiments, some actions may occur in a different order and / or concurrently with other actions from those illustrated and described herein or not illustrated and described herein but understandable to those skilled in the art.

[0060] The present invention also relates to a readable storage medium, on which a computer program is stored, and the program is executed by a processor to implement the sound pressure field reconstruction method introduced in the above embodiments.

[0061] As Figure 3 shown, the present invention also relates to a sound pressure field reconstruction system 10, including a data processing module 1, and the data processing module 1 includes a computer-readable storage medium 101 and a processor 102. The computer-readable storage medium 101 is used to store instructions executable by the processor 102; the processor 102 is used to execute the instructions to implement the sound pressure field reconstruction method introduced in the above embodiments.

[0062] It can be understood that the data processing module 1 in the previous embodiments may include one or more hardware processors 102, such as a system on a chip (SOC), a microcontroller, a microprocessor (such as an MCU chip or a 51 single-chip microcomputer), a reduced instruction set computer (RISC), an application-specific integrated circuit (ASIC), an application-specific instruction integrated processor (ASIP), a central processing unit (CPU), a graphics processing unit (GPU), a physics processing unit (PPU), a microcontroller unit, a digital signal processor (DSP), a field programmable gate array (FPGA), an advanced RISC machine (ARM), a programmable logic device (PLD), a combination of one or more of any circuits or processors capable of executing one or more functions. For example, in an aircraft, the processor 11 is integrated into a Full Authority Digital Engine Control (FADEC). And, the processor 11 of the data processing module 1 may be integrated with the processor of the data acquisition module, that is, a processor uniformly controls data acquisition, the output of the acquired coordinate data, input to the data processing system, data processing, and the output of measurement result data. Or the two may also exist separately and independently. One processor controls data acquisition and the output of the acquired coordinate data, and another processor controls the reception of the coordinate data, data processing, and the output of measurement result data. The two processors are electrically connected.

[0063] The steps of the methods described in connection with the embodiments disclosed herein can be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. The software module may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such that the processor can read from, and write to, the storage medium. In an alternative, the storage medium may be integrated into the processor. The processor and the storage medium may reside in an ASIC. The ASIC may reside in a user terminal. In an alternative, the processor and the storage medium may reside as discrete components in a user terminal.

[0064] In one or more exemplary embodiments, the described functionality may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software as a computer program product, the functions may be stored on or transmitted via a computer-readable medium as one or more instructions or code. The computer-readable medium includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage medium may be any available medium that can be accessed by a computer. By way of example and not limitation, such computer-readable medium can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. Any electrical connection is properly termed a computer-readable medium. For example, if the software is transmitted from a web site, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of medium. As used herein, disk and disc include compact disc

[0065] (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk, and Blu-ray disc, where disk generally reproduces data magnetically, while disc reproduces data optically with lasers. Combinations of the above should also be included within the scope of computer-readable medium.

[0066] Although the present invention is disclosed above in preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, any modifications, equivalent changes, and decorations made to the above embodiments based on the technical essence of the present invention without departing from the technical solution of the present invention all fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for reconstructing a sound pressure field, characterized in that, it includes: S1. Obtain the sound pressure field data with low resolution to form the first data set D u ; S2. Incorporate a physics-informed neural network into a Bayesian neural network to obtain a Bayesian physics-informed neural network; S3. Obtain a second data set through the physics-informed neural network; S4. Use the first data set and the second data set to train the Bayesian physics-informed neural network; S5. Sample the parameters of the Bayesian physics-informed neural network through the Monte Carlo-Markov chain technique to reconstruct the sound pressure field.

2. The method for reconstructing a sound pressure field according to claim 1, characterized in that, In the step S1, the first data set D u is obtained by instrument measurement during the experiment and / or by using a CFD numerical solver to solve.

3. The method for reconstructing a sound pressure field according to claim 2, characterized in that, In the step S2, through the automatic differentiation mechanism of the physics-informed neural network, the sound propagation wave equation in partial differential form, the sound field boundary conditions, and the sound field initial conditions are incorporated into the Bayesian neural network in the form of a likelihood function with a Gaussian distribution.

4. The method for reconstructing a sound pressure field according to claim 3, characterized in that, In the step S2, the likelihood function is The Bayesian physics-informed neural network is a posterior joint probability distribution function: where θ is a multi-dimensional vector, D = (D u ∪ D f ∪ D b ).

5. The method for reconstructing a sound pressure field according to claim 4, characterized in that, In the step S3, the second data set is obtained by randomly sampling from the domain of the acoustic wave propagation equation N and the acoustic field boundary conditions and the acoustic field initial conditions B equation, and the second data set includes D f and D b ; where f = Nx(u; θ) and b = Bx(u; θ).

6. The method for reconstructing a sound pressure field according to claim 5, characterized in that, In the step S4, the parameters θ of the Bayesian physics-informed neural network are corrected and improved through the first data set D u and the second data set.

7. The method for reconstructing a sound pressure field according to claim 6, characterized in that, In the step S5, the parameters θ in the Bayesian physics-informed neural network are sampled by the Monte Carlo-Markov chain technique to obtain M sets of sampled parameter values. For any input x, M posterior sampling results can be obtained. The mean value of the M posterior sampling results is used as the predicted value u(x) of the Bayesian physics-informed neural network for acoustic pressure field reconstruction.

8. The method for reconstructing a sound pressure field according to claim 7, characterized in that, The mean square error value of the M posterior sampling results is used as the uncertainty of the predicted value u(x) and the uncertainty of the sound pressure field reconstruction.

9. A readable storage medium, on which a computer program is stored, characterized in that, When the program is executed by a processor, it implements the method for reconstructing a sound pressure field according to any one of claims 1-8.

10. A sound pressure field reconstruction system, characterized in that, it includes a data processing module, and the data processing module includes: A computer-readable storage medium for storing instructions executable by a processor; A processor for executing the instructions to implement the method for reconstructing a sound pressure field according to any one of claims 1 to 8.

Images