CN116090526A - Structural vibration noise inversion method based on embedded physical information neural network - Google Patents

Structural vibration noise inversion method based on embedded physical information neural network Download PDF

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CN116090526A
CN116090526A CN202310069902.XA CN202310069902A CN116090526A CN 116090526 A CN116090526 A CN 116090526A CN 202310069902 A CN202310069902 A CN 202310069902A CN 116090526 A CN116090526 A CN 116090526A
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宋晓东
周华伦
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Abstract

The invention discloses a structural vibration noise inversion method based on an embedded physical information neural network, which comprises the following steps: firstly, collecting vibration noise according to noise distribution conditions generated by structural vibration to obtain the distribution conditions of the vibration noise in space; describing the propagation of the vibration noise by using a physical control equation of the sound wave of the linear sound source according to the propagation characteristics of the structural vibration noise, and obtaining a partial differential equation expression form of the structural vibration by combining initial conditions and boundary conditions; approximating a true solution of a partial differential equation through a neural network, constructing a loss function through an automatic differential technology, and establishing a neural network embedded with physical information; training the neural network by taking the vibration noise of the actually measured structure as training data, optimizing network parameters, reducing loss function values, inverting the sound field distribution situation by using the neural network, and obtaining the distribution situation of the whole sound field through the actually measured data.

Description

Structural vibration noise inversion method based on embedded physical information neural network
Technical Field
The invention belongs to the field of noise inversion, and particularly relates to a structural vibration noise inversion method based on an embedded physical information neural network.
Background
Sound is ubiquitous in our lives, and is a direct way of conveying information, and is also the primary way of inter-person communication. Because of the presence of sound, we can feel the surrounding of the person and react accordingly. With the development of society, the cause of sound generation is gradually complicated, the influence on the surrounding environment gradually gets into the field of view of people, and the harm caused by noise becomes a part of attention, and the important direction of research of people is also. As traffic noise, which is one of four major noises, the hazard generated by the traffic noise is increasingly highlighted today when urban traffic is increasingly developed and high-speed railways and rail traffic are rapidly developed. Because the structural vibration generating traffic noise belongs to low-frequency vibration, the propagation distance is long, and the damage to human bodies and buildings is not negligible.
The method has the advantages that structural vibration noise is reduced, influence on the surrounding environment is reduced, high importance is brought to related departments and expert scholars, but the traditional method is limited in acoustic calculation accuracy due to factors such as unknown sound field parameters, incapability of fitting set conditions and actual structures, complex structural composition and the like, and the actual situation of the vibration noise is difficult to accurately reflect; the difficulty is high when the acoustic inversion problem is calculated by using the traditional method, a complex acoustic calculation model is often required to be established, the calculation cost is high, the effect is poor, a high-precision acoustic calculation method is required to be developed, the problems of the existing method are improved by combining the generation of vibration noise and physical knowledge in the propagation process, and a powerful technical support is provided for reducing the influence of the structural vibration noise.
In recent years, with the development of large data and the popularization of high-performance computing devices, neural networks have become new tools in various research fields. The traditional neural network is driven by pure data, and ignores the physical control rule behind the data. In the traditional acoustic computing field, a large number of physical models such as a point sound source sound wave model, a line sound source sound wave model, a ball sound source sound wave model and the like already exist, and if the priori knowledge is fully utilized, the neural network automatically meets physical constraint in the training process, so that the acoustic computing effect can be improved, and the data utilization is more complete. Acoustic calculations are considered using neural networks embedded with physical information.
Disclosure of Invention
Technical problems: the structural vibration noise inversion numerical model based on the embedded physical information neural network is provided, so that the sound field distribution is calculated through the neural network rapidly and accurately according to the existing data, and inversion of the vibration noise is realized.
The technical scheme is as follows: in order to solve the problems, the invention provides a structural vibration noise inversion method based on an embedded physical information neural network, which comprises the following steps:
(1) Collecting vibration noise according to noise distribution conditions generated by structural vibration, wherein the content to be collected comprises measuring point positions, measuring time and measuring point sound pressure data, training data of the neural network are constructed according to the measured data, the measuring point time and the position coordinates are training data characteristics, and the sound pressure is a training data label;
(2) According to the propagation characteristics of noise generated by structural vibration, using measurement data, regarding the noise generated by a vibration structure as a linear sound source sound wave to obtain a corresponding sound wave equation; the partial differential equation expression form of noise generated by structural vibration is obtained by combining the acoustic wave equation, the initial condition and the boundary condition, and for the vibration noise problem, the data in the sampling space should meet the partial differential equation, and the data in the boundary of the sampling space should meet the initial condition and the boundary condition;
(3) Establishing a neural network, constructing a neural network loss function, and transmitting results to the neural network forward direction through an automatic differentiation technology
Figure BDA0004064367190000021
Performing differential calculation to obtain partial differential equation residual error, initial condition and boundary condition error, constructing a loss function of the neural network, and restricting the behavior of the neural network in the training process through the loss function to obtain the embedded physical information neural network;
(4) Training the neural network embedded with the physical information by using the data in the step (1), optimizing the training parameters of the neural network by using an Adams optimization method in the training process, so that the error between the output of the neural network and the true solution of the partial differential equation constructed in the step (2) is within a preset range, and after the training is completed, inputting time and coordinates to obtain corresponding sound pressure values, thereby realizing inversion of the vibration noise of the structure measured in the step (1).
Preferably, in the step (1), the microphone matrix is arranged in a preset area of the structure to collect noise generated by the structural vibration, and the collected data includes time, position and sound pressure.
As a preferred aspect of the present invention, in the step (2), the noise generated by the structure propagates while conforming to a physical control equation, and the propagation of the structural vibration noise is regarded as a linear sound source sound wave and described in the form of a partial differential equation.
Preferably, in the step (2), a partial differential equation of the sound wave of the corresponding linear sound source is obtained as follows:
Figure BDA0004064367190000022
wherein x is the position coordinate of the measuring point, t is the measuring time, u (x, t) is the sound pressure under the conditions of the coordinate x and the time t, c 0 Sound velocity, Ω is the sampling space interior region;
the solution u (x, t) of the acoustic wave equation is the sound pressure value generated by the vibration of the structure, and the partial differential equation is used as a vibration noise control equation of the structure, namely a physical control equation; and the following expression is obtained according to the initial condition and the boundary condition of the structure:
B[u(x,t),x,t]＝0
Figure BDA0004064367190000023
wherein B [ u (x, t), x, t]The function is expressed for the initial conditions and boundary conditions of the vibrating structure,
Figure BDA0004064367190000035
is a sampling spatial boundary region.
As a preferred aspect of the present invention, in the step (3), a loss function of the neural network is constructed as follows:
the residual error of the partial differential equation of the sound wave of the line sound source is:
Figure BDA0004064367190000031
the initial conditions and boundary condition errors are:
Figure BDA0004064367190000032
the loss function of the neural network obtained according to the residual error and the error is as follows:
Figure BDA0004064367190000033
in the method, in the process of the invention,
Figure BDA0004064367190000034
calculation result of neural network for data under the condition of coordinates x and time t, x i 、t i For sampling the coordinate value and time value, x of the ith data in the space internal region omega j 、t j For sampling spatial boundary region +.>
Figure BDA0004064367190000036
Coordinate value and time value of jth data of (a), N f For sampling the total number of data in the space inner region Ω, N b For sampling spatial boundary region +.>
Figure BDA0004064367190000037
Is a data total number of (a).
The beneficial effects are that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
the invention relates to a neural network based on embedded physical information, which combines measured data of structural vibration noise and propagation characteristics of the vibration noise generated by the structure, utilizes the physical characteristics of the structural vibration noise to fit sound field distribution by utilizing observation data through the neural network, and belongs to an acoustic inversion method. Compared with the traditional acoustic calculation method and acoustic inversion calculation method, the number of microphone array arrangements and material resource cost are saved, and the distribution situation of the sound field can be obtained through fewer measuring points. When analyzing the problems, grid division is not needed, and the problems of high calculation complexity and low calculation efficiency caused by calculation result distortion due to coarse grid division or too fine grid division are avoided. When the neural network predicts, the physical information of vibration noise is considered, the priori knowledge of the problem is fully utilized, the observed data is fully utilized, the operation efficiency of the neural network and the accuracy of the calculation result can be effectively improved, and the phenomenon of overfitting is avoided. The method can be used for improving the calculation efficiency of the structural vibration noise prediction problem, improving the accuracy of vibration noise inversion and providing a new thought for inversion of structural vibration noise.
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Fig. 1 is a flow chart of a structural vibration noise inversion method based on an embedded physical information neural network.
Fig. 2 is a diagram of a neural network with embedded physical information.
FIG. 3 is a graph of the result of predicting vibration sound pressure by a neural network versus the actual distribution of vibration sound pressure and the error cloud of the result of predicting vibration sound pressure versus the actual distribution, wherein graph (a) is the result of predicting the neural network, graph (b) is the actual distribution, and graph (c) is the error
Figure BDA0004064367190000041
Fig. 4 is a graph of the change in the loss function value during neural network training.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings and examples.
In this embodiment, a specific flowchart of a structural vibration noise inversion method based on an embedded physical information neural network is shown in fig. 1.
Firstly, collecting vibration noise according to noise distribution conditions generated by structural vibration to obtain the distribution conditions of the vibration noise in space; describing the propagation of the vibration noise by using a physical control equation of the sound wave of the linear sound source according to the propagation characteristics of the structural vibration noise, and obtaining a partial differential equation expression form of the structural vibration by combining a primary value condition; approximating a true solution of a partial differential equation through a neural network, constructing a loss function through an automatic differential technology, and establishing a neural network embedded with physical information; training the neural network by taking the vibration noise of the actually measured structure as training data, optimizing network parameters, reducing loss function values, inverting the sound field distribution situation by using the neural network, and obtaining the distribution situation of the whole sound field through the actually measured data. The method can be used for improving the calculation of unknown parameters in the problem of predicting the structural vibration noise, improving the accuracy of inversion of the vibration noise and providing a new thought for inversion of the structural vibration noise.
The specific process of inverting the structural noise by the method of the invention is given below by taking inversion of the structural vibration noise of converting the structural model into the linear sound source sound wave as an example.
(1) Vibration noise sound field acquisition
Vibration noise analysis of an actual structure can be simplified by dividing the structure into subsystems to tie the problem. According to the sound field calculation results of all the subsystems and integrating all the subsystems, the sound field distribution condition of the whole structure can be obtained, which is a common simplified idea when acoustic calculation is carried out on complex bridge structures, building structures and the like. The noise distribution problem generated by independent structural vibration is considered in the embodiment, noise generated by the structural vibration is collected in 1s at different positions of the distance structure, and the data are divided into sampling space internal data and sampling space boundary data according to the position characteristics and time characteristics of the data collection. The number of each type of data acquisition is equal and is 350.
(2) Partial differential equation form expression of structural vibration noise
According to the propagation characteristics of noise generated by structural vibration, a physical control equation, namely a partial differential equation, is adopted to describe the problem when the structure vibrates, the actual propagation situation is considered in the example, the vibration structure is considered as a linear sound source, and the generated sound wave is considered as a plane wave in the observation distance, namely the propagation problem of the plane wave in space. Plane waves can be considered as waves that do not attenuate with distance as they propagate in space. According to the propagation rule of the plane wave, the boundary condition and the initial condition of the structure, the problem is simplified to obtain the following physical control equation:
Figure BDA0004064367190000051
in the above formula, the first formula is a partial differential equation of sound wave of a linear sound source, and the sound velocity c 0 =10; the second formula is a boundary condition, and the third and fourth formulas are initial conditions; the inner region of the sampling space is Ω= (0, 1) × (0, 1)]The sampling space boundary region is
Figure BDA0004064367190000057
For convenience of calculation, the second, third and fourth formulas in the above formulas are written as:
B[u(x,t),x,t]＝0
Figure BDA0004064367190000056
and the distribution condition of the noise in the sampling space can be obtained by analyzing and solving the control equation of the noise generated by the structural vibration.
(3) Neural network embedded with physical information
In order to solve the above physical equation, a neural network is defined for approximating the true solution u (x, t) of the acoustic equation, a modified forward propagation neural network is selected as a bottom network, compared with the traditional forward propagation network, the modified forward propagation network performs Fourier feature transformation on data before the input data is transmitted into a hidden layer, then performs forward propagation on the data, regularizes the loss of each part in order to ensure that the different error component values of the loss function are relatively close, adds weight coefficients, avoids generating 'spectral deviation' in the prediction process of the neural network, thereby improving the prediction result of the neural network, and recording the result obtained by forward propagation of the data as
Figure BDA0004064367190000052
Its residual resulting from the partial differential equation is defined as:
Figure BDA0004064367190000053
due to the initial condition u (x, 0) =sin (pi x) +sin (2pi x),
Figure BDA0004064367190000054
The error resulting from the boundary condition u (0, t) =u (1, t) =0 is defined as:
Figure BDA0004064367190000055
from the data measured in (1), the data contained in Ω is noted as
Figure BDA0004064367190000061
Figure BDA0004064367190000068
All data contained in the list are recorded as +.>
Figure BDA0004064367190000062
N f 、N b Omega, & gt>
Figure BDA0004064367190000069
The total number of data contained in the data stream. Because the prediction result of the neural network has deviation from the actual value, the residual error generated on the partial differential equation when the neural network calculates the data in the sampling space and the error generated on the initial condition and the boundary condition when the data of the boundary of the sampling space are calculated can be calculated through an automatic differential technology. By calculating two values, the loss function of the neural network is defined as:
Figure BDA0004064367190000063
Figure BDA0004064367190000064
the partial differential equation residual part in the loss function can ensure that the calculation result of each forward propagation of the neural network automatically meets the constraint of the acoustic wave equation by calculating the partial differential equation residual part; />
Figure BDA0004064367190000065
In order to lose the initial condition and boundary condition error part in the function, the calculation result of each forward propagation of the neural network can be ensured to meet the initial condition and boundary condition met by the training data by calculating the term.
By adding regularization coefficients to each component of the loss function, the order of magnitude of each component of the loss function in the training process can be ensured to be close, loss function value components with larger difference are avoided, and the convergence of the loss function of the neural network in the training process is ensured. Fig. 2 is a block diagram of an improved forward propagation network and a block diagram of a neural network embedded with physical information.
(4) Training neural networks to invert sound field distribution
Training the neural network by using training data, setting the neural network to have three hidden layers, wherein the number of neurons in each layer is 150, selecting an Adam optimization algorithm in the training process, setting the learning rate to be 0.001, setting the training round to 40000 times, and respectively recording the change condition of each component of the loss function. By training the neural network, the sound pressure value of each point in the time-space domain can be predicted, so that the sound field distribution of the whole sampling space is inverted through measurement data. FIG. 3 is a graph showing the comparison between the result of the neural network predicting vibration sound pressure and the actual distribution of vibration sound pressure and the error cloud of the result of the neural network predicting sound pressure and the actual distribution of sound pressure, wherein the graph (a) is the result of the neural network predicting sound pressure of each point in the time-space domain after training
Figure BDA0004064367190000066
Graph (b) shows the actual distribution of sound pressure u (x, t), and graph (c) shows the error between the neural network prediction result and the actual distribution of sound pressure +.>
Figure BDA0004064367190000067
Fig. 4 shows the change of the loss function during training.
The foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which are intended to be comprehended within the scope of the present invention.

Claims (5)

1. The structural vibration noise inversion method based on the embedded physical information neural network is characterized by comprising the following steps of:
(1) Collecting vibration noise according to noise distribution conditions generated by structural vibration, wherein the content to be collected comprises measuring point positions, measuring time and measuring point sound pressure data, training data of the neural network are constructed according to the measured data, the measuring point time and the position coordinates are training data characteristics, and the sound pressure is a training data label;
(2) According to the propagation characteristics of noise generated by structural vibration, using measurement data, regarding the noise generated by a vibration structure as a linear sound source sound wave to obtain a corresponding sound wave equation; the partial differential equation expression form of noise generated by structural vibration is obtained by combining the acoustic wave equation, the initial condition and the boundary condition, and for the vibration noise problem, the data in the sampling space should meet the partial differential equation, and the data in the boundary of the sampling space should meet the initial condition and the boundary condition;
(3) Establishing a neural network, constructing a neural network loss function, and transmitting results to the neural network forward direction through an automatic differentiation technology
Figure FDA0004064367180000012
Performing differential calculation to obtain partial differential equation residual error, initial condition and boundary condition error, constructing a loss function of the neural network, and restricting the behavior of the neural network in the training process through the loss function to obtain the embedded physical information neural network;
(4) Training the neural network embedded with the physical information by using the data in the step (1), optimizing the training parameters of the neural network by using an Adams optimization method in the training process, so that the error between the output of the neural network and the true solution of the partial differential equation constructed in the step (2) is within a preset range, and after the training is completed, inputting time and coordinates to obtain corresponding sound pressure values, thereby realizing inversion of the vibration noise of the structure measured in the step (1).
2. The inversion method of structural vibration noise based on embedded physical information neural network according to claim 1, wherein in the step (1), the noise generated by the structural vibration is collected by arranging a microphone matrix in a preset area of the structure, and the collected data includes time, position and sound pressure.
3. The inversion method of structural vibration noise based on embedded physical information neural network according to claim 1, wherein in the step (2), the propagation of noise generated by the structure accords with a physical control equation, and the propagation of the structural vibration noise is regarded as a linear sound source sound wave and is described in the form of a partial differential equation.
4. A method for inverting structural vibration noise based on embedded physical information neural network according to claim 1 or 3, wherein in step (2), partial differential equations of corresponding line sound source sound waves are obtained as follows:
Figure FDA0004064367180000011
wherein x is the position coordinate of the measuring point, t is the measuring time, u (x, t) is the sound pressure under the conditions of the coordinate x and the time t, c 0 Sound velocity, Ω is the sampling space interior region;
the solution u (x, t) of the acoustic wave equation is the sound pressure value generated by the vibration of the structure, and the partial differential equation is used as a vibration noise control equation of the structure, namely a physical control equation; and the following expression is obtained according to the initial condition and the boundary condition of the structure:
B[u(x,t),x,t]＝0
Figure FDA0004064367180000021
wherein B [ u (x, t), x, t]The function is expressed for the initial conditions and boundary conditions of the vibrating structure,
Figure FDA0004064367180000022
is a sampling spatial boundary region.
5. The inversion method of structural vibration noise based on embedded physical information neural network according to claim 4, wherein in the step (3), a loss function of the neural network is constructed as follows:
the residual error of the partial differential equation of the sound wave of the line sound source is:
Figure FDA0004064367180000023
the initial conditions and boundary condition errors are:
Figure FDA0004064367180000024
the loss function of the neural network obtained according to the residual error and the error is as follows:
Figure FDA0004064367180000025
in the method, in the process of the invention,
Figure FDA0004064367180000026
calculation result of neural network for data under the condition of coordinates x and time t, x i 、t i For sampling the coordinate value and time value, x of the ith data in the space internal region omega j 、t j For sampling spatial boundary region +.>
Figure FDA0004064367180000027
Coordinate value and time value of jth data of (a), N f For sampling the total number of data in the space inner region Ω, N b For sampling spatial boundary region +.>
Figure FDA0004064367180000028
Is a data total number of (a). />
CN202310069902.XA 2023-02-07 2023-02-07 Structural vibration noise inversion method based on embedded physical information neural network Pending CN116090526A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116644658A (en) * 2023-05-11 2023-08-25 华中科技大学 Gas discharge temperature inversion method based on physical information neural network
CN117390348A (en) * 2023-12-08 2024-01-12 国网安徽省电力有限公司电力科学研究院 Method and system for capacity attenuation treatment of metallized film capacitor

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116644658A (en) * 2023-05-11 2023-08-25 华中科技大学 Gas discharge temperature inversion method based on physical information neural network
CN116644658B (en) * 2023-05-11 2024-03-15 华中科技大学 Gas discharge temperature inversion method based on physical information neural network
CN117390348A (en) * 2023-12-08 2024-01-12 国网安徽省电力有限公司电力科学研究院 Method and system for capacity attenuation treatment of metallized film capacitor
CN117390348B (en) * 2023-12-08 2024-04-02 国网安徽省电力有限公司电力科学研究院 Method and system for capacity attenuation treatment of metallized film capacitor

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