Internal sound field bounded uncertainty analysis method based on physical information neural network

Abstract

The invention discloses an in-structure sound field bounded uncertainty analysis method based on a physical information neural network. The method comprises the following steps: establishing a physical information loss function and establishing a physical information driven neural network; obtaining an input uncertain parameter value range of the internal sound field, obtaining a plurality of parameter levels, and training a sound pressure prediction model under the parameter levels; acquiring sound pressure of a sample point and establishing a data set; establishing a data driving residual error based on the data set, establishing an overall loss function by using the data driving residual error and a physical information loss function, and training a parameter-containing physical information driving neural network to obtain a parameter-containing internal sound field sound pressure prediction model; and establishing an interval model, and obtaining an internal sound field sound pressure uncertainty distribution range by using a global search algorithm and the parameter-containing internal sound field sound pressure prediction model. The method can solve the problem of prediction of the sound field in the structure containing uncertain parameters, and can effectively improve the calculation efficiency on the premise of ensuring that the calculation precision meets the engineering requirements.

Description

Technical Field

[0001] The invention belongs to the field of aerospace, and in particular relates to a bounded uncertainty analysis method of an acoustic field within a structure based on a physical information neural network. Background Art

[0002] As the main structure of aircraft, space stations, submarines, cars, high-speed trains, etc., the acoustic response inside the cavity structure is of great significance in many fields and plays a guiding role in structural design. For example, in the field of civil aircraft, high-speed trains, cars and other means of transportation, accurate calculation of acoustic response helps optimize the design, thereby reducing the maximum sound pressure inside the cavity, thereby greatly improving the comfort of passengers.

[0003] In actual engineering, due to manufacturing process defects, differences in measurement methods, and fluctuations in the service environment, the material properties, boundary conditions, external loads, etc. of the cavity structure are inevitably affected by various uncertain factors during service, which makes its internal sound field response also show certain uncertainty. In order to deal with the problem of uncertainty analysis, it is necessary to consider parameters when modeling and combine them with corresponding uncertainty propagation algorithms for analysis. For complex models in various engineering structures, it is impossible to directly obtain analytical solutions, and it is necessary to use numerical calculation methods such as finite element method, finite difference method and boundary element method to achieve parameter-containing modeling.

[0004] However, the parametric modeling of the interior sound field based on the above method has the following problems: First, the traditional parametric modeling method often relies on the idea of ​​interpolation, so high-order derivatives usually do not exist or are discontinuous, and many uncertainty propagation algorithms such as the interval perturbation method cannot be implemented because they require high-order derivatives about parameters. Secondly, the parametric modeling method needs to calculate multiple models separately, and its accuracy is related to the number of non-parametric models trained, so it is difficult to balance the calculation accuracy and efficiency. Summary of the invention

[0005] In view of the above problems, the present invention provides a bounded uncertainty analysis method for the sound field inside a structure based on a physical information neural network to solve the problem of predicting the sound field inside a structure with uncertain parameters, thereby improving the calculation efficiency while ensuring that the calculation accuracy meets engineering requirements.

[0006] An embodiment of the present invention provides a method for analyzing bounded uncertainty of an acoustic field in a structure based on a physical information neural network, which includes:

[0007] Step 1: obtaining a plurality of boundary points and internal points on the boundary surface of the internal sound field and in the geometric domain, respectively calculating the boundary condition residuals and the control equation residuals corresponding to the boundary points and the internal points, establishing a physical information loss function based on the boundary condition residuals and the control equation residuals, and establishing a physical information driven neural network using the physical information loss function;

[0008] Step 2: obtaining a value range of an input uncertain parameter of the interior sound field, obtaining a plurality of parameter levels within the value range, and training the physical information driven neural network at each parameter level in turn based on an adaptive moment estimation algorithm and a second-order quasi-Newton algorithm to obtain a plurality of interior sound field sound pressure prediction models;

[0009] Step 3: using Latin hypercube sampling to obtain sample points in the geometric domain, and using the corresponding internal sound field sound pressure prediction model to obtain the sound pressure of the sample points at each parameter level, merging all the parameter levels and the sample point coordinates into parameter-containing independent variables, and using the parameter-containing independent variables and the sound pressure to form a data set;

[0010] Step 4: Calculate the data-driven residual on the data set, repeat step 1 to calculate the control equation residual and the boundary condition residual, use the three residuals to establish an overall loss function, use the overall loss function to establish a parameter-containing physical information driven neural network, and use an adaptive moment estimation algorithm and a second-order quasi-Newton algorithm to train the parameter-containing physical information driven neural network to obtain a parameter-containing internal sound field sound pressure prediction model;

[0011] Step 5: Establish an interval model based on the value range, use the global search algorithm and the parameter-containing internal sound field sound pressure prediction model to establish an optimization target, and solve the optimization target to obtain the uncertain sound pressure distribution range of the internal sound field under the interval model.

[0012] In some possible embodiments, the data set is generated by the physical information neural network at the multiple parameter levels.

[0013] In some possible embodiments, the control equation residual, the boundary condition residual and the data-driven residual based on the data set jointly establish the total loss function.

[0014] The bounded uncertainty analysis method of the interior sound field based on the physical information neural network provided by the embodiment of the present invention has at least the following advantages:

[0015] (1) The analysis method in the embodiment of the present invention utilizes physical information at different parameter levels to drive the neural network to generate a data set, and jointly trains the parameter-containing physical information driven neural network by controlling the residuals of the equations, the residuals of the boundary conditions, and the data-driven residuals based on the data set. Compared with the neural network trained only based on the residuals of the control equations and the residuals of the boundary conditions, the training speed and training accuracy are significantly improved, thereby improving the accuracy of subsequent uncertainty analysis.

[0016] (2) The analysis method in the embodiment of the present invention can provide any-order derivatives of the sound pressure field with respect to any parameter or any spatial coordinate, making the selection of uncertain propagation algorithms more diverse.

[0017] (3) The analysis method in the embodiment of the present invention does not require a large number of proxy models under different parameters for interpolation. It only needs to train a small number of physical information driven neural network models and parameter-containing physical information driven neural network models under different parameter levels to obtain a high-precision parameter-containing proxy model, thereby improving computational efficiency.

[0018] (4) The analysis method in the embodiment of the present invention adopts a neural network model driven by physical information, which has strong interpretability, simple principles, and strong generalization ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is a flow chart of a bounded uncertainty analysis method for an interior sound field based on a physical information neural network in an embodiment of the present invention;

[0020] Figure 2 It is a flowchart of the bounded uncertainty analysis method of the interior sound field based on the physical information neural network in the embodiment of the present invention;

[0021] Figure 3 Schematic diagram of a rectangular cavity model corresponding to the internal sound field in an embodiment of the present invention. DETAILED DESCRIPTION

[0022] In order to make the above-mentioned purposes, features and advantages of the embodiments of the present invention more understandable, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0023] refer to Figure 1 and Figure 2 The embodiment of the present invention provides a bounded uncertainty analysis method for the sound field in a structure based on a physical information neural network, comprising the following steps:

[0024] Step 1: Obtain multiple boundary points and internal points on the boundary surface of the internal sound field and in the geometric domain, respectively, calculate the boundary condition residuals and control equation residuals corresponding to the boundary points and the internal points, establish a physical information loss function based on the boundary condition residuals and the control equation residuals, and use the physical information loss function to establish a physical information driven neural network.

[0025] The sound pressure in the internal sound field satisfies the following set of partial differential equations:

[0026]

[0027] Where Ω is the geometric domain of the internal sound field, They represent the boundaries that satisfy the Dirichlet boundary condition (the first type of boundary condition), the Newman boundary condition (the second type of boundary condition) and the Robin boundary condition (the third type of boundary condition), k is the wave number in the medium, ρ is the air density, ω is the excitation angular frequency, and p bc is the sound pressure distribution on the boundary satisfying the Dirichlet boundary condition, v n To satisfy the Newman boundary condition, the external normal velocity distribution on the boundary is n Distribution of acoustic admittance coefficient on the boundary to satisfy the Robin boundary condition.

[0028] The sound pressure of the internal sound field is fitted using a neural network. Since the input coordinates are only the spatial coordinates x, y, z, and the output coordinates are only the real and imaginary parts of the sound pressure, a neural network structure with 3 inputs and 2 outputs is constructed, which is expressed as:

[0029]

[0030] Where x = (x, y, z) T is the input coordinate, Act() is the activation function, z i is the intermediate variable of the i-th hidden layer, p=[p real ,p img ] T is the sound pressure vector, p real ,p img Represent the real and imaginary parts of the sound pressure respectively. i ,b i is the weight matrix and bias vector from the i-1th layer to the ith layer, which is the object of neural network optimization. The mapping function of the above neural network structure is written as p=NN(x,y,z).

[0031] Latin hypercube sampling is used to extract N pixels in the geometric domain of the internal sound field and on the boundary surface of the internal sound field. Domain Internal points x Domain With N Boundary Boundary collocation points x Boundary , where the internal and boundary collocation points satisfy:

[0032]

[0033] Based on the above internal and boundary points, the residuals of the control equations and boundary conditions of the neural network are calculated:

[0034]

[0035] where p i pre The neural network predicts the sound pressure value for the i-th internal collocation point, The neural network predicts the sound pressure value for the jth boundary point, x j is the spatial coordinate of the jth boundary point, v n,j is the external normal velocity at the jth boundary point, A n,j is the acoustic admittance coefficient at the jth boundary point, e PDE With e BC are the control equation residuals and boundary condition residuals, respectively.

[0036] Based on the residuals of the control equation and the residuals of the boundary conditions, a certain weight (W PDE With W BC ) and then get the physical information loss function Loss phy :

[0037] Loss phy =W PDE e PDE +W BC e BC ;

[0038] Based on the above physical information loss function and neural network structure, a physical information driven neural network is finally established.

[0039] In a possible example, a rectangular cavity structure is used as a typical internal sound field, and its geometric model is as follows: Figure 3 As shown. In this geometric model, the rectangular cavity size is: length L z 2m, width L x 1m, height L y To simulate the acoustic pressure generated by the free vibration of the thin plate at an angular frequency ω in the rectangular cavity, the free vibration approximates the modal vibration at z = 0 in the boundary, and its normal velocity distribution is approximately expressed as:

[0040]

[0041] Other boundaries (z≠0) are hard boundary conditions, and their normal velocity is expressed as:

[0042] v n (x,y)=0(z≠0);

[0043] Combining the relationship between acoustic velocity boundary conditions and sound pressure and the Helmholtz equation, the sound pressure in the internal sound field satisfies the following set of equations:

[0044]

[0045] Where Ω is the geometric domain of the rectangular cavity, is the boundary surface of the rectangular cavity, and its specific expression is:

[0046] Ω={(x,y,z)|0≤x≤1,0≤y≤1,0≤z≤2};

[0047]

[0048] For the above-mentioned internal sound field, a neural network is used to fit its sound pressure distribution. Specifically, a neural network structure with an input dimension of 3, an output dimension of 1, a hidden layer width of 64, a hidden layer depth of 3, and an activation function of the sin function is used for fitting. The three input dimensions are the x, y, and z coordinates of the sound pressure point to be calculated, and since the excitation is a pure imaginary number, the output is the imaginary part of the sound pressure at that point. The input-output mapping relationship is:

[0049]

[0050] Where x = (x, y, z) T is the input coordinate, z i is the intermediate variable of the i-th hidden layer. i ,b i is the weight matrix and bias vector from the i-1th layer to the ith layer, which is the hyperparameter to be optimized in the neural network. The mapping function of the above neural network structure is written as p=NN(x,y,z).

[0051] In the geometric domain of the internal sound field, 6750 internal collocation points are extracted by Latin hypercube sampling; on the boundary surface of the internal sound field, 2250 boundary collocation points are extracted by Latin hypercube sampling, where the internal collocation points and the boundary collocation points satisfy:

[0052]

[0053] Calculate the residuals of the control equations and boundary conditions of the neural network fitting sound pressure at the internal and boundary points, that is:

[0054]

[0055] After optimization, take W PDE =1, W BC is 100, and the physical information loss function expression is:

[0056] Loss phy =e PDE +100e BC ;

[0057] Combining the above physical information loss function with the neural network structure, a physical information driven neural network is established.

[0058] Step 2: Obtain the value range of the input uncertain parameters of the internal sound field, obtain multiple parameter levels within the value range, and train the physical information driven neural network at each parameter level in turn based on the adaptive moment estimation algorithm and the second-order quasi-Newton algorithm to obtain multiple internal sound field sound pressure prediction models.

[0059] For bounded uncertainty problems, the value range of the input uncertain parameters is quantified within a certain range Ω θ In this range, Ω θ Use Latin hypercube sampling or uniform sampling to obtain N θ parameter levels, thus obtaining the parameter set:

[0060]

[0061] Take the values ​​of each parameter in the set Q in turn, use the adaptive moment estimation algorithm and the second-order quasi-Newton algorithm to train the physical information driven neural network at the corresponding parameter levels in turn, and obtain the sound pressure prediction model of the internal sound field at different parameter levels, which are recorded as

[0062] In a possible example, the speed of sound is about 343m / s at standard atmospheric pressure of 20°C. Due to fluctuations in temperature and pressure, the speed of sound may fluctuate within a certain range. Similarly, the angular frequency ω of the plate vibration will also fluctuate within a certain range, and the speed of sound and the angular frequency form input uncertain parameters. The range of the speed of sound and the angular frequency is:

[0063]

[0064] In order to realize the normalization of the neural network input, the uncertain parameters are normalized. Considering that the upper and lower bounds of the sound speed and angular frequency are known, min-max normalization is used, that is:

[0065]

[0066] Within the above range of values, two parameter levels are extracted to train the physical information driven neural network. Specifically, uniform sampling is adopted to obtain four groups of parameter levels, each group of parameter levels includes two corresponding parameter levels c0 and ω, and the absolute values ​​corresponding to the four groups of parameter levels and the relative values ​​after normalization are shown in Table 1.

[0067] Table 1 Four groups of parameter levels

[0068]

[0069] For the above four groups of parameter levels, physical information driven neural networks under corresponding parameter levels are established in turn, and the physical information driven neural networks are trained using adaptive moment estimation algorithm and second-order quasi-Newton algorithm respectively. Specifically, the adaptive moment estimation algorithm is used for 6000 training times at learning rates of 0.01 and 0.001, and then the second-order quasi-Newton algorithm is used for 6000 training times. After the above training, the prediction models of the sound pressure of the internal sound field under the four groups of parameter levels are obtained, which are recorded as NN1(x, y, z),…,NN4(x, y, z) in turn.

[0070] Step 3: Use Latin hypercube sampling to obtain sample points in the geometric domain, and use the corresponding internal sound field sound pressure prediction model to obtain the sound pressure of the sample points at each parameter level in turn, merge all parameter levels and sample point coordinates into parameter-containing independent variables, and use the parameter-containing independent variables and sound pressure to form a data set.

[0071] In the geometric domain Ω, Latin hypercube sampling is used to extract N s Sample points. Take the spatial coordinates of these sample points as input and substitute them into The sound pressure values ​​of these sample points at different parameter levels are obtained and regarded as the true value of the sound pressure at this point at this parameter level. Combine the spatial coordinates of the sample points with the corresponding parameters to obtain the parameter-containing independent variables:

[0072] X=(x,y,z,θ1,θ2,…,θ n ) T ;

[0073] Using the parameterized independent variables and the corresponding true value of the sound pressure, a s N θ Dataset of data:

[0074]

[0075] In a possible example, 500 sample points are extracted using Latin hypercube sampling in the geometric domain Ω of a rectangular cavity. The spatial coordinates of the 500 sample points are used as the input of the internal sound field sound pressure prediction model to obtain the values ​​of the sound pressure of the 500 sample points under four sets of parameter levels. The spatial coordinates of the sample points are combined with two parameters (angular frequency ω and sound speed c0) to obtain the parameter-containing independent variable X, which is expressed as:

[0076]

[0077] Using the parameterized independent variables and the corresponding sound pressure, a data set containing 2000 data items is formed, expressed as:

[0078]

[0079] Step 4: Calculate the data-driven residuals on the data set, repeat step 1 to calculate the control equation residuals and boundary condition residuals, use the three residuals to establish an overall loss function, use the overall loss function to establish a parameter-containing physical information driven neural network, and use the adaptive moment estimation algorithm and the second-order quasi-Newton algorithm to train the parameter-containing physical information driven neural network to obtain a parameter-containing internal sound field sound pressure prediction model.

[0080] In order to realize the modeling of the neural network driven by parameterized physical information, another neural network structure will be used to fit the sound pressure distribution under any parameter value and any spatial coordinate. Since the input coordinates have spatial coordinates x, y, z and parameter coordinates θ1, θ2, …, θ n , and the output coordinates only have the real and imaginary parts of the sound pressure, so a neural network structure with 3+n inputs and 2 outputs is constructed, expressed as:

[0081]

[0082] Where X=(x,y,z,θ1,θ2,…,θ n ) T is the input parameter-containing independent variable. The neural network mapping function is written as p=NN p (x,y,z,θ1,θ2,…,θ n ).

[0083] The dataset The parameterized independent variable in NN p (x,y,z,θ1,θ2,…,θ n ) input to obtain the predicted sound pressure Using the corresponding true value The data-driven residual is obtained, expressed as:

[0084]

[0085] The internal points and the boundary points are extracted in a similar manner as in step 1, where the internal points and the boundary points satisfy:

[0086]

[0087] Where Ω θ is the parameter independent variable space, and × represents the Cartesian product. Repeat the method in step 1 at these internal and boundary points to obtain the control equation residual and boundary condition residual. Based on the control equation residual, boundary condition residual and data-driven residual, calculate the overall loss function Loss, which is expressed as:

[0088] Loss = W PDE e PDE +W BC e BC +WData e Data ;

[0089] where e Data is the data-driven residual, W Data The residual weight is driven by data. Based on the overall loss function, a physical information driven neural network with parameters is constructed. The adaptive moment estimation algorithm and the second-order quasi-Newton algorithm are used to train the physical information driven neural network with parameters to obtain a sound pressure prediction model for the internal sound field with parameters.

[0090] In a possible example, in order to realize the modeling of the neural network driven by parameter-containing physical information, the neural network structure is used to fit the sound pressure distribution under any spatial coordinates under any parameter value. Specifically, a neural network structure with an input dimension of 5, an output dimension of 1, a hidden layer width of 64, a hidden layer depth of 3, and an activation function of the sin function is used for fitting. The five input dimensions are the x, y, and z coordinates of the sound pressure point to be calculated and the two parameter coordinates θ ω , The output is the sound pressure value, and its input-output mapping is expressed as:

[0091]

[0092] Where X is the input parameter-containing independent variable, and the neural network mapping function is recorded as NN p (x,y,z,θ1,θ2). The neural network NN p The inputs of (x, y, z, θ1, θ2) are set as the independent variables with parameters in the database in turn, and the predicted sound pressure value corresponding to the k-th independent variable with parameters is recorded as The sound pressure values ​​corresponding to the independent variables in the database can be approximately considered as the true values. The true value of the sound pressure corresponding to the kth independent variable is recorded as Based on this, the data-driven residual on the training set is obtained, which is expressed as:

[0093]

[0094] In the independent variable space, 20,000 internal collocation points and 6,000 boundary collocation points are extracted using Latin hypercube sampling, where the internal collocation points and boundary collocation points satisfy:

[0095]

[0096] Repeat step 1 to obtain the residual of the control equation and the residual of the boundary condition e PDE With e BC In order to make the residual of the control equation and the residual of the boundary condition only expressed as a function of the input and output of the neural network, the relationship between the wavelength k, the speed of sound c0 and the excitation angular frequency ω k = ω / c0 is substituted into the residual expression of the control equation, and the control equation and the boundary condition are rewritten as:

[0097]

[0098] Based on the control equation residual, boundary condition residual and data-driven residual, the overall loss function is obtained. Specifically, after hyperparameter optimization, the control equation residual, boundary condition residual and data-driven residual are taken as: W PDE =1,W BC =100,W Data =1, then: Loss = W PDE e PDE +W BC e BC +W Data e Data =e PDE +100e BC +e Data ;

[0099] Based on the above overall loss function and neural network structure NN p (x,y,z,θ1,θ2), establish a neural network driven by physical information.

[0100] For the above-mentioned parameter-containing physical information driven neural network, the adaptive moment estimation algorithm and the second-order quasi-Newton algorithm are used for training respectively. Specifically, the adaptive moment estimation algorithm is used for training 6000 times at learning rates of 0.01 and 0.001 respectively, and then the second-order quasi-Newton algorithm is used for training 18000 times. After the above training, the parameter-containing internal sound field sound pressure prediction model is obtained.

[0101] Step 5: Establish an interval model based on the value range, use the global search algorithm and the parameter-containing internal sound field sound pressure prediction model to establish the optimization target, and solve the optimization target to obtain the uncertain sound pressure distribution range of the internal sound field under the interval model.

[0102] Take the parameters θ in step 2 i The upper limit of the range With the lower bound θ i , and obtain the value range of each parameter Take the Cartesian product of each parameter value interval to obtain the interval model corresponding to the uncertain value range:

[0103]

[0104] Where × represents the Cartesian product. Taking the above interval model as input, the sound pressure prediction model of the internal sound field with parameters obtained in step 4 is used to analyze the uncertainty of the sound pressure at the fixed point in the geometric domain of the internal sound field. For the fixed point x0, y0, z0, the problem of calculating the upper and lower bounds of the uncertain sound pressure interval of the fixed point is transformed into the following two optimization problems:

[0105]

[0106] stAθ≤b;

[0107]

[0108] stAθ≤b;

[0109] in f are the upper and lower bounds of the uncertain sound pressure interval of the fixed point, respectively. The meanings of the matrix A and vector θ, b are as follows:

[0110]

[0111] The penalty function method is used to transform the linear constrained optimization problem of the nonlinear objective function into an unconstrained optimization problem:

[0112]

[0113] Where σ is a penalty factor, which is a sufficiently large number. The adaptive moment estimation algorithm is used to iterate multiple times in the parameter space. When the number of iterations is reached, the value at this time is considered to be the upper bound (lower bound) of the uncertain sound pressure.

[0114] In one possible example, the parameter variable θ normalized by min-max in step 2 is ω , The value range is:

[0115]

[0116] Since the excitation frequency has almost no correlation with the sound speed, the interval model is used to describe it, and the uncertainty interval is set as:

[0117]

[0118] where θ ω I =[0,1], Consider the uncertain response of the sound pressure at the center point (x0 = 0.5, y0 = 0.5, z0 = 1) to the parameters. According to the global search algorithm, the problem of calculating the upper and lower bounds of the uncertain sound pressure interval at this point is transformed into the following two optimization problems:

[0119]

[0120] stAθ≤b;

[0121]

[0122] stAθ≤b;

[0123] The matrix A and vector θ,b are:

[0124]

[0125] The penalty function method is used to transform the linear constrained optimization problem of the nonlinear objective function into an unconstrained optimization problem:

[0126]

[0127] The penalty factor σ is set to 100. After 100 iterations of the adaptive moment estimation algorithm, the upper and lower bounds of the response function are obtained:

[0128]

[0129] That is, the uncertain sound pressure interval at this point (x0=0.5, y0=0.5, z0=1) is [10.4860, 12.0004].

[0130] In summary, in the bounded uncertainty analysis method of the internal sound field based on the physical information neural network provided in the embodiment of the present invention, a physical information loss function is constructed based on the geometric domain of the internal sound field and a physical information driven neural network is established, which can make full use of the physical information in the model and enhance the interpretability of the neural network prediction of sound pressure. Latin hypercube sampling is used to obtain the sound pressure data of the sample points and establish a data set, and a data-driven residual is constructed based on the data set. The overall loss function is constructed using the physical information loss function and the data-driven residual, which accelerates the convergence speed of the parameter-containing physical information neural network and improves the accuracy of sound pressure prediction. An interval model is established for the value range of the input uncertain parameters, and the interval perturbation method is used to obtain the uncertainty distribution range of the sound pressure in the internal sound field. The uncertainty distribution range of the sound pressure can be quickly obtained without iteration. The present invention can systematically solve the problem of predicting the internal sound field of a structure with uncertain parameters, and effectively improve the calculation efficiency while ensuring that the calculation accuracy meets the engineering requirements.

[0131] The various embodiments or implementation methods in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments, and the same or similar parts between the various embodiments can be referenced to each other.

[0132] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "illustrative embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials, or characteristics described in conjunction with the embodiments or examples are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0133] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A bounded uncertainty analysis method for the sound field inside a structure based on a physical information neural network, characterized in that: include: Step 1: obtaining a plurality of boundary points and internal points on the boundary surface of the internal sound field and in the geometric domain, respectively calculating the boundary condition residuals and the control equation residuals corresponding to the boundary points and the internal points, establishing a physical information loss function based on the boundary condition residuals and the control equation residuals, and establishing a physical information driven neural network using the physical information loss function; Step 2: obtaining a value range of an input uncertain parameter of the interior sound field, obtaining a plurality of parameter levels within the value range, and training the physical information driven neural network at each parameter level in turn based on an adaptive moment estimation algorithm and a second-order quasi-Newton algorithm to obtain a plurality of interior sound field sound pressure prediction models; Step 3: using Latin hypercube sampling to obtain sample points in the geometric domain, and using the corresponding internal sound field sound pressure prediction model to obtain the sound pressure of the sample points at each parameter level, merging all the parameter levels and the sample point coordinates into parameter-containing independent variables, and using the parameter-containing independent variables and the sound pressure to form a data set; Step 4: Calculate the data-driven residual on the data set, repeat step 1 to calculate the control equation residual and the boundary condition residual, use the three residuals to establish an overall loss function, use the overall loss function to establish a parameter-containing physical information driven neural network, and use an adaptive moment estimation algorithm and a second-order quasi-Newton algorithm to train the parameter-containing physical information driven neural network to obtain a parameter-containing internal sound field sound pressure prediction model; Step 5: Establish an interval model based on the value range, use the global search algorithm and the parameter-containing internal sound field sound pressure prediction model to establish an optimization target, and solve the optimization target to obtain the uncertain sound pressure distribution range of the internal sound field under the interval model.

2. The method for analyzing bounded uncertainty of interior sound field based on physical information neural network according to claim 1 is characterized in that: The data set is generated by the physical information neural network at the plurality of parameter levels.

3. The method for analyzing bounded uncertainty of interior sound field based on physical information neural network according to claim 1 is characterized in that: The control equation residuals, the boundary condition residuals and the data-driven residuals based on the data set jointly establish the total loss function.

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