A structural vibration and noise inversion method based on an embedded physical information neural network

Abstract

The application discloses a structure vibration noise inversion method based on an embedded physical information neural network, and specifically comprises the following steps: firstly, collecting vibration noise according to the noise distribution generated by structure vibration to obtain the distribution of vibration noise in space; secondly, using a physical control equation of a line sound source sound wave to describe the propagation of vibration noise according to the propagation characteristics of structure vibration noise, and combining initial conditions and boundary conditions to obtain the partial differential equation expression form of structure vibration; thirdly, approximating the real solution of the partial differential equation through a neural network, constructing a loss function through automatic differentiation technology, and establishing a neural network embedded with physical information; fourthly, training the neural network by taking the measured structure vibration noise as training data, optimizing network parameters, reducing the loss function value, and using the neural network to invert the sound field distribution; and finally, obtaining the distribution of the entire sound field through the measured data.

Description

TECHNICAL FIELD

[0001] The application 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

[0002] Sound is ubiquitous in our life, it is a direct way of conveying information and the main way of communication between people. Because of the existence of sound, we can feel the environment around us and make corresponding reactions. With the development of society, the causes of sound are gradually complex, and the influence on the surrounding environment gradually enters the field of vision of people, becoming a part of people's attention, and the harm caused by noise becomes the focus of people's research. As one of the four noises, traffic noise is increasingly developed in urban traffic, and high-speed railways and rail transit are developing rapidly today, and the harm caused by traffic noise is increasingly prominent. Since the structural vibration causing traffic noise belongs to low-frequency vibration, its propagation distance is far, and the harm to the human body and buildings cannot be ignored.

[0003] Reducing structural vibration noise and its impact on the surrounding environment has attracted the attention of relevant departments and experts and scholars, but the traditional method is often limited by the unknown sound field parameters, the setting conditions that do not match the actual situation, the complex structure composition and other factors, and the acoustic calculation accuracy is limited, it is difficult to accurately reflect the actual situation of vibration noise; and when using the traditional method to calculate the acoustic inversion problem, it is difficult, often needs to establish a complex acoustic calculation model, the calculation cost is large, the effect is poor, and it is urgent to develop a high-precision acoustic calculation method, combined with the physical knowledge in the generation and propagation process of vibration noise, to improve the existing problems, and provide strong technical support for reducing the impact of structural vibration noise.

[0004] In recent years, with the development of big data and the popularity of high-performance computing devices, neural networks have become a new tool in various research fields. Traditional neural networks are purely data-driven, ignoring the physical control laws behind the data. In the traditional field of acoustic calculation, there are a large number of physical models, such as point sound source sound wave model, line sound source sound wave model, and spherical sound source sound wave model. If these prior knowledge is fully utilized, the neural network can automatically satisfy the physical constraints during training, which can improve the acoustic calculation effect and make more full use of data. Consider using a neural network embedded with physical information for acoustic calculation. SUMMARY

[0005] Technical problem: A structural vibration noise inversion numerical model based on an embedded physical information neural network is proposed to quickly and accurately calculate the sound field distribution through the neural network according to the existing data, and realize the inversion of vibration noise.

[0006] Technical solution: In order to solve the above problems, the present application provides a structure vibration noise inversion method based on embedded physical information neural network, comprising the following steps:

[0007] (1) According to the noise distribution of structure vibration, the vibration noise is collected, the contents to be collected include the measurement point position, the measurement time and the sound pressure data of the measurement point, the training data of the neural network is constructed according to the measured data, the measurement point time and position coordinates are the training data features, and the sound pressure is the training data label;

[0008] (2) According to the propagation characteristics of the noise generated by the structure vibration, the measurement data is used, the noise generated by the vibration structure is regarded as a linear sound source sound wave to obtain the corresponding sound wave equation; the partial differential equation expression form of the noise generated by the structure vibration is obtained by combining the sound wave equation and the initial condition and the boundary condition; for the vibration noise problem, the data in the sampling space should satisfy the partial differential equation, and the data on the boundary of the sampling space should satisfy the initial condition and the boundary condition;

[0009] (3) Establish a neural network, construct a neural network loss function, and calculate the differential of the forward propagation result of the neural network by automatic differentiation technology , the partial differential equation residual error and the initial condition and boundary condition error are calculated, and the loss function of the neural network is constructed, the behavior of the neural network in the training process is constrained by the loss function, and the embedded physical information neural network is obtained;

[0010] (4) The data in step (1) is used to train the neural network with embedded physical information, and the Adams optimization method is used to optimize the neural network training parameters 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 step (2) is within the preset range, after the training is completed, the corresponding sound pressure value can be obtained by inputting the time and coordinates, and the vibration noise of the structure measured in step (1) is inverted.

[0011] As a preferred embodiment of the present application, in step (1), a microphone matrix is arranged in a predetermined area of the structure to collect the noise generated by the structure vibration, and the collected data should include time, position and sound pressure.

[0012] As a preferred embodiment of the present application, in step (2), the propagation of the noise generated by the structure conforms to the physical control equation, the propagation of the structure vibration noise is regarded as a linear sound source sound wave, and is described in the form of partial differential equation.

[0013] As a preferred embodiment of the present application, in step (2), the corresponding partial differential equation of the linear sound source sound wave is as follows:

[0014]

[0015] Wherein, x is the position coordinate of the measuring point, t is the measuring time, u(x, t) is the sound pressure under the condition of coordinate x and time t, c0 is the sound velocity, and Ω is the internal region of the sampling space.

[0016] The solution u(x, t) of the sound wave equation is the sound pressure value generated by the vibration of the structure, and the above partial differential equation is taken as the vibration noise control equation of the structure, that is, the physical control equation; and the following expression is obtained according to the initial condition and the boundary condition of the structure:

[0017] B[u(x, t), x, t] = 0

[0018] Wherein, B[u(x, t), x, t] is an expression function of the initial condition and the boundary condition of the vibrating structure, is the coordinate value and time value of the i-th data in the internal region Ω of the sampling space.

[0019] As a preferred embodiment of the present application, in step (3), the loss function of the neural network is constructed as follows:

[0020] The residual error of the partial differential equation of the line sound source sound wave is:

[0021]

[0022] The initial condition and boundary condition error is:

[0023]

[0024] The loss function of the neural network is obtained according to the above residual error and error:

[0025]

[0026] Wherein, is the neural network calculation result of the data under the condition of coordinate x and time t, x i , t i is the coordinate value and time value of the i-th data in the internal region Ω of the sampling space, x j , t j is the coordinate value and time value of the j-th data in the boundary region of the sampling space , N f is the total number of data in the internal region Ω of the sampling space, N b is the total number of data in the boundary region of the sampling space .

[0027] Beneficial effects: compared with the prior art, the technical scheme of the present application has the following beneficial technical effects:

[0028] The application is based on a neural network embedded with physical information, combines measured data of structural vibration noise and propagation characteristics of vibration noise generated by a structure, utilizes physical characteristics thereof, and uses a neural network to fit a sound field distribution by using observation data, and belongs to an acoustic inversion method. Compared with a traditional acoustic calculation method and an acoustic inversion calculation method, the number of microphone array arrangements and material costs are saved, and the distribution of a sound field can be obtained by using fewer measuring points. When analyzing a problem, grid division is not needed, and problems such as distortion of a calculation result caused by rough grid division or high calculation complexity and low calculation efficiency caused by fine grid division are avoided. When a neural network is used for prediction, physical information of vibration noise is considered, prior knowledge of a problem is fully utilized, observation data is more fully utilized, and the operation efficiency of the neural network and the accuracy of a calculation result can be effectively improved, and an overfitting phenomenon is avoided. The method can be used to improve the calculation efficiency of a structural vibration noise prediction problem and improve the accuracy of vibration noise inversion, and provides a new idea for inversion of structural vibration noise. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 A structural vibration noise inversion method based on a neural network embedded with physical information.

[0030] Figure 2 A neural network structure diagram embedded with physical information.

[0031] Figure 3 A comparison between a prediction result of a neural network for vibration sound pressure and an actual distribution of vibration sound pressure and an error cloud map of the prediction result and the actual distribution, wherein, Fig. (a) is a prediction result of the neural network, Fig. (b) is an actual distribution, and Fig. (c) is an error

[0032] Figure 4 A loss function value change diagram in a neural network training process. DETAILED DESCRIPTION

[0033] The technical solutions of the application will be further described below in combination with the drawings and examples.

[0034] In the embodiment, a specific flowchart of the structural vibration noise inversion method based on the neural network embedded with physical information is as shown in Figure 1

[0035] ​Firstly, according to the noise distribution of structural vibration, the vibration noise is collected to obtain the distribution of vibration noise in space; according to the propagation characteristics of structural vibration noise, the physical control equation of linear sound source sound wave is used to describe the propagation of vibration noise, and the partial differential equation expression form of structural vibration is obtained combined with the initial and boundary conditions; the neural network is used to approximate the true solution of the partial differential equation, the loss function is constructed through automatic differentiation technology, and the neural network embedded with physical information is established; the measured structural vibration noise is used as training data to train the neural network, optimize the network parameters, reduce the loss function value, use the neural network to inverse the sound field distribution, and obtain the distribution of the whole sound field through the measured data. The method can be used to improve the calculation of unknown parameters in the structural vibration noise prediction problem, improve the accuracy of vibration noise inversion, and provide a new idea for the inversion of structural vibration noise.

[0036] The following will take the structural model into a linear sound source sound wave as an example to give the specific process of the method for inverting structural noise.

[0037] (1) Vibration noise sound field collection

[0038] The vibration noise analysis of the actual structure can be simplified by dividing the structure into subsystems. According to the sound field calculation results of each subsystem and the integration of each subsystem, the sound field distribution of the whole structure can be obtained, which is a common simplification idea when calculating the sound field of complex bridge structures, building structures and the like. This example considers the noise distribution problem caused by the vibration of a single structure. The noise caused by the vibration of the structure is collected at different positions from the structure within 1s, and the data is divided into internal sampling space data and boundary sampling space data according to the position characteristics and time characteristics of the data collection. The number of each type of data collection is equal, and each type of data collection is 350.

[0039] (2) Partial differential equation expression of structural vibration noise

[0040] According to the propagation characteristics of the noise generated by the structural vibration, the physical control equation of the structural vibration, i.e. the partial differential equation, is used to describe the problem, and the vibration structure is considered as a linear sound source in this example. The sound wave generated by the linear sound source is considered as a plane wave within the observation distance, i.e. the propagation problem of the plane wave in space. When the plane wave propagates in space, it can be regarded as a wave that does not attenuate with distance. According to the propagation law of the plane wave and the boundary conditions and initial conditions of the structure, the physical control equation is simplified as follows:

[0041]

[0042] In the above formula, the first formula is the partial differential equation of the linear sound source sound wave, the sound speed c0=10; the second formula is the boundary condition, and the third and fourth formulas are the initial conditions; the internal region of the sampling space is Ω=(0, 1)×(0, 1], and the boundary region of the sampling space is For convenience of calculation, the second, third and fourth formulas in the above formula are denoted as:

[0043] B[u(x, t), x, t]=0

[0044] By analyzing and solving the control equation of the noise generated by the above structure vibration, the distribution of the noise in the sampling space can be obtained.

[0045] (3) Neural network embedded with physical information

[0046] In order to solve the above physical equation, a neural network is first defined to approximate the true solution u(x, t) of the sound wave equation, and an improved forward propagation neural network is selected as the underlying network. Compared with the traditional forward propagation network, the improved forward propagation network first performs Fourier feature transformation on the input data before transmitting the data to the hidden layer, and then performs forward propagation on the data. In order to ensure that the different error components of the loss function are relatively close, the weights of each part of the loss are regularized, and the “spectral bias” of the neural network in the prediction process is avoided, thereby improving the prediction result of the neural network. The result obtained by the data after forward propagation is denoted as The residual error caused by the partial differential equation is defined as:

[0047]

[0048] The error caused by the initial condition u(x, 0)=sin(πx)+sin(2πx), and the boundary condition u(0, t)=u(1, t)=0 is defined as:

[0049]

[0050] The data contained in Ω measured from (1) is denoted as All the data contained in Ω are denoted as N f , N b are the total number of data contained in Ω, respectively. Since there is a deviation between the prediction result of the neural network and the actual value, through automatic differentiation technology, the residual error generated by the neural network in the calculation of the data in the sampling space on the partial differential equation and the error generated by the neural network in the calculation of the data on the boundary of the sampling space on the initial condition and the boundary condition can be calculated. By calculating the two values, the loss function of the neural network is defined as:

[0051]

[0052] For the partial differential equation residual part in the loss function, by calculating this term, it can be ensured that the calculation result of each forward propagation of the neural network automatically satisfies the constraint of the acoustic wave equation; For the initial condition and boundary condition error part in the loss function, by calculating this term, it can be ensured that the calculation result of each forward propagation of the neural network satisfies the initial condition and boundary condition satisfied by the training data.

[0053] By adding regularization coefficients to each component of the loss function, it can be ensured that the orders of magnitude of each component of the loss function during the training process are close, avoiding the generation of loss function value components with large differences, and ensuring the convergence of the loss function of the neural network during the training process. Figure 2 The structural diagram of the improved forward propagation network and the structural diagram of the neural network embedded with physical information.

[0054] (4) Training the neural network to invert the acoustic field distribution

[0055] The neural network is trained using the training data, and the neural network is set to have three hidden layers, with 150 neurons in each layer. During the training process, the Adam optimization algorithm is selected as the optimization algorithm, and the learning rate is set to 0.001. The training is performed for 40,000 times, and the changes of each component of the loss function are recorded. By training the neural network, the sound pressure values of each point in the time-space domain can be predicted, and thus the acoustic field distribution of the entire sampling space can be inverted from the measurement data. Figure 3 The comparison between the prediction result of the neural network for the vibration sound pressure and the actual distribution of the vibration sound pressure, and the error cloud diagram of the prediction result of the neural network and the actual distribution of the sound pressure, wherein Fig. (a) is the prediction result of the neural network for the sound pressure of each point in the time-space domain after training Fig. (b) is the actual distribution of the sound pressure u(x, t), and Fig. (c) is the error between the prediction result of the neural network and the actual distribution of the sound pressure Figure 4 The changes of the loss function during the training process.

[0056] The above only describes the preferred embodiments of the present application, and it should be noted that for those skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, and these improvements and refinements should also be considered as the protection scope of the present application.

Claims

1. A structural vibration noise inversion method based on an embedded physical information neural network, characterized in that, Includes the following steps: (1) Based on the noise distribution generated by structural vibration, the vibration noise is collected. The content to be collected includes the measurement point location, measurement time and sound pressure data of the measurement point. The training data of the neural network is constructed based on the measured data. The measurement point time and location coordinates are the training data features, and the sound pressure is the training data label. (2) Based on the propagation characteristics of noise generated by structural vibration, the noise generated by the vibrating structure is regarded as a line sound source sound wave using measurement data to obtain the corresponding sound wave equation; combined with the sound wave equation and initial and boundary conditions, the partial differential equation expression of noise generated by structural vibration is obtained. For vibration noise problems, the data inside the sampling space should satisfy the partial differential equation, and the data at the boundary of the sampling space should satisfy the initial and boundary conditions. (3) Establish a neural network, construct the neural network loss function, and use automatic differentiation techniques to analyze the forward propagation results of the neural network. Differential calculations are performed to obtain the residuals of the partial differential equations and the errors of the initial and boundary conditions. The loss function of the neural network is then constructed based on this. The behavior of the neural network during the training process is constrained by the loss function, thereby obtaining the embedded physical information neural network. (4) Use the data in step (1) to train the neural network with embedded physical information. During the training process, the Adams optimization method is used to optimize the training parameters of the neural network so that the error between the output of the neural network and the true solution of the partial differential equation constructed in step (2) is within the preset range. After the training is completed, the corresponding sound pressure value can be obtained by inputting the time and coordinates, so as to realize the inversion of the vibration noise of the structure measured in step (1). In step (2), the partial differential equation of the corresponding line sound source sound wave is obtained as follows: In the formula, x is the position coordinate of the measuring point, t is the measurement time, u(x,t) is the sound pressure under the conditions of coordinate x and time t, c0 is the sound speed, and Ω is the internal region of the sampling space; The solution u(x,t) to the acoustic wave equation is the sound pressure value generated by the structural vibration. The above partial differential equation is used as the vibration noise control equation for the structure, i.e., the physical control equation. Based on the initial and boundary conditions of the structure, the following expression is obtained: In the formula, B[u(x,t),x,t] represents the initial and boundary conditions of the vibrating structure. This refers to the boundary region of the sampling space.

2. The structural vibration noise inversion method based on an embedded physical information neural network according to claim 1, characterized in that, In step (1), a microphone matrix is ​​arranged in a preset area of ​​the structure to collect the noise generated by the vibration of the structure. The collected data should include time, location and sound pressure.

3. The structural vibration noise inversion method based on an embedded physical information neural network according to claim 1, characterized in that, In step (2), the propagation of noise generated by the structure conforms to the physical control equation. The propagation of structural vibration noise is regarded as a line source sound wave and described in the form of partial differential equations.

4. The structural vibration noise inversion method based on an embedded physical information neural network according to claim 1, characterized in that, In step (3), the loss function for constructing the neural network is as follows: The residual of the partial differential equation for the sound wave from the line source is: The initial and boundary condition errors are: Based on the residuals and errors mentioned above, the loss function of the neural network is: In the formula, The neural network computation results for data under coordinates x and time t, where x i t i Let x be the coordinates and time value of the i-th data point within the sampling space region Ω. j t j Sampling space boundary region The coordinates and time value of the j-th data point, N f N represents the total number of data points within the sampling space region Ω. b Sampling space boundary region The total number of data in the dataset.

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