CN114722690B - Acoustic super-surface sound field rapid prediction method based on variable reliability neural network - Google Patents

Acoustic super-surface sound field rapid prediction method based on variable reliability neural network Download PDF

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CN114722690B
CN114722690B CN202210643830.0A CN202210643830A CN114722690B CN 114722690 B CN114722690 B CN 114722690B CN 202210643830 A CN202210643830 A CN 202210643830A CN 114722690 B CN114722690 B CN 114722690B
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sound field
neural network
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distribution data
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CN114722690A (en
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周奇
吴金红
林泉
胡杰翔
刘华坪
黄旭丰
金朋
王胜一
毛义军
郑建国
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Huazhong University of Science and Technology
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    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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Abstract

The invention provides a variable reliability neural network-based rapid prediction method for an acoustic super-surface sound field, which comprises the following steps: acquiring geometric characteristics, design variables and variation ranges of the acoustic super-surface to be predicted and sound field information to be predicted; establishing a first precision finite element model and a second precision finite element model of the acoustic super surface according to the design variable of the acoustic super surface to be predicted; adopting a Latin hypercube sampling method, a first precision sample point and a second precision sample point; obtaining sound field distribution data of each first precision sample point and each second precision sample point through batch simulation of a finite element model, preprocessing the sound field distribution data, and expanding the sound field distribution data of the first precision sample points by using the sound field distribution data of the second precision sample points to obtain a training data set; and constructing a variable reliability neural network model, and training the variable reliability neural network model according to the training data set.

Description

Acoustic super-surface sound field rapid prediction method based on variable reliability neural network
Technical Field
The invention relates to the technical field of acoustic super-surface design, in particular to a method for quickly predicting an acoustic super-surface sound field based on a variable reliability neural network.
Background
The acoustic super-surface is a two-dimensional metamaterial technology, and can regulate and control the reflection angle and the refraction angle of incident waves by introducing phase mutation at different phase interfaces, so that the functions of noise suppression, sound stealth, sound focusing and the like are realized. Therefore, in order to realize a specific function, the physical parameters of the acoustic super-surface must be designed to construct a specific phase jump. This requires the manual evaluation of the distribution information of the scattered sound field under different physical parameter distributions. The traditional acoustic super-surface design method needs to call a high-performance numerical model, and time-consuming simulation usually causes delay of the whole design period. With the development of artificial intelligence technology, the neural network has been proved to be capable of effectively replacing a finite element simulation model, realizing the rapid prediction of sound field distribution and having higher precision.
However, the training effect of the neural network depends on the number and quality of data sets to a great extent, and the existing acoustic super-surface sound field prediction model based on the neural network needs to perform a large number of experiments or simulation to construct the same precision data set, and still needs to consume a large amount of time; meanwhile, in the super-surface design process, data with different accuracies exist, wherein the acquisition time and the calculation cost of high-accuracy data are high, and low-accuracy data are relatively easy to obtain. The generalization capability of the model trained by only adopting a small amount of high-precision data is poor, and the precision of the model trained by only adopting a large amount of low-precision data is low. Therefore, how to effectively utilize data with different precisions to reduce the overhead of neural network model construction and quickly predict the acoustic super-surface sound field is one of the key factors for improving the super-surface design efficiency.
Disclosure of Invention
In view of the above, the invention provides a variable reliability neural network-based acoustic super-surface sound field rapid prediction method which combines different precision data, reduces the overhead of neural network model construction, and is a method for rapidly predicting acoustic super-surface sound fields.
The technical scheme of the invention is realized as follows: the invention provides a variable-reliability neural network-based rapid prediction method for an acoustic super-surface sound field, which comprises the following steps of:
s1: acquiring geometric characteristics, design variables and variation ranges of the acoustic super-surface to be predicted and sound field information to be predicted; the geometrical characteristic of the acoustic super-surface is a structure with a thickness direction smaller than the wavelength of incident sound waves, which is equally divided into
Figure 707882DEST_PATH_IMAGE001
Units, each unit having different density and elastic modulus property values; the design variable is cell density
Figure 359443DEST_PATH_IMAGE002
And modulus of elasticity of unit
Figure 935918DEST_PATH_IMAGE003
Number of design variables
Figure 737652DEST_PATH_IMAGE004
(ii) a The sound field information to be predicted is sound pressure values of sampling points uniformly distributed around the super surface;
s2: establishing a finite element model of the acoustic super surface according to the design variable of the acoustic super surface to be predicted, and further establishing a first precision finite element model and a second precision finite element model of the acoustic super surface;
s3: acquiring a first precision sample point corresponding to the first precision finite element model and a second precision sample point corresponding to the second precision finite element model by adopting a Latin hypercube sampling method;
s4: acquiring sound field distribution data of each first precision sample point and each second precision sample point through finite element model batch simulation, preprocessing the data, and expanding the sound field distribution data of the first precision sample points by using the sound field distribution data of the second precision sample points to acquire a training data set;
s5: constructing a variable reliability neural network model, and training the variable reliability neural network model according to a training data set; the variable reliability neural network model learns the linear or nonlinear relation between the sound field distribution data of the first precision sample points and the sound field distribution data of the second precision sample points, the sound field distribution data of the second precision sample points provide trend information, and the predicted value is corrected by the sound field distribution data of the first precision sample points to fuse the sound field distribution data of the sample points with different precisions, so that the prediction precision of the neural network model is improved;
s6: and rapidly predicting the acoustic super-surface sound field by using the trained variable reliability neural network model.
On the basis of the above technical solution, preferably, the true value mathematical expression form of the variable reliability neural network model is:
Figure 286445DEST_PATH_IMAGE005
(ii) a Wherein the content of the first and second substances,
Figure 905645DEST_PATH_IMAGE006
the first precision true value of the variable reliability neural network model is obtained;
Figure 907099DEST_PATH_IMAGE007
the second precision true value is a variable credibility neural network model;
Figure 778103DEST_PATH_IMAGE008
for a given input;
Figure 181403DEST_PATH_IMAGE009
a linear sub-network of the variable reliability neural network model is used for learning a linear relation between the sound field distribution data of the second precision sample point and the sound field distribution data of the first precision sample point based on given input and an output result of the second precision true value;
Figure 971504DEST_PATH_IMAGE010
a nonlinear sub-network of the variable reliability neural network model is used for learning a nonlinear relation between the sound field distribution data of the second precision sample point and the sound field distribution data of the first precision sample point based on given input and an output result of the second precision true value;
Figure 132358DEST_PATH_IMAGE011
and
Figure 603791DEST_PATH_IMAGE012
the weights of the output result of the linear sub-network and the output result of the non-linear sub-network,
Figure 923914DEST_PATH_IMAGE013
；
in the step S5, a variable reliability neural network model is constructed, wherein the variable reliability neural network model comprises three parts, namely a second precision prediction part
Figure 88179DEST_PATH_IMAGE014
Linear sub-network
Figure 500444DEST_PATH_IMAGE015
And a non-linear sub-network
Figure 509988DEST_PATH_IMAGE016
(ii) a The process of constructing the variable reliability neural network comprises the following steps:
s501: given an input
Figure 684617DEST_PATH_IMAGE008
Given an input of length
Figure 691887DEST_PATH_IMAGE017
The vector of (a);
s502: constructing a second precision prediction part
Figure 951968DEST_PATH_IMAGE014
The number of input neurons is
Figure 765203DEST_PATH_IMAGE017
Extracting input features and outputting a predicted sound field through a full connection layer, a convolution layer and a pooling layer to obtain a second-precision output prediction result of the variable reliability neural network model
Figure 935284DEST_PATH_IMAGE018
；
S503: will give a given input
Figure 441352DEST_PATH_IMAGE008
And the prediction result of the second precision output of the variable reliability neural network model
Figure 188728DEST_PATH_IMAGE018
Spliced into a new input
Figure 805654DEST_PATH_IMAGE019
；
S504: building linear sub-networks
Figure 830242DEST_PATH_IMAGE015
Part of the network, without adding nonlinear activation functions, extracts new inputs through the fully-connected, convolutional and pooling layers
Figure 303949DEST_PATH_IMAGE019
Characterizing and outputting linear subnetwork prediction results
Figure 476304DEST_PATH_IMAGE020
；
S505: constructing a non-linear sub-network portion
Figure 70490DEST_PATH_IMAGE016
The partial network adds a non-linear activation function to extract new inputs through the full link, convolutional and pooling layers
Figure 277480DEST_PATH_IMAGE019
Is characterized in that the method comprises the following steps of,and outputting the non-linear sub-network prediction result
Figure 187667DEST_PATH_IMAGE021
；
S506: prediction result of first precision output of variable reliability neural network
Figure 847319DEST_PATH_IMAGE022
Is composed of
Figure 478151DEST_PATH_IMAGE023
；
Figure 336386DEST_PATH_IMAGE011
And
Figure 355157DEST_PATH_IMAGE012
are respectively linear sub-networks
Figure 439788DEST_PATH_IMAGE015
And a non-linear sub-network
Figure 202208DEST_PATH_IMAGE016
The weight of (a) is calculated,
Figure 180528DEST_PATH_IMAGE013
。
preferably, the nonlinear activation function is a relu function or a tanh function.
Preferably, in step S2, a finite element model of the acoustic super-surface is established according to the design variables of the acoustic super-surface to be predicted, and a first precision finite element model and a second precision finite element model of the acoustic super-surface are further established, specifically: placing the acoustic super surface on the upper surface of a rectangular flat plate, wherein the acoustic super surface is provided with a rectangular boundary; firstly, establishing a finite element model of an acoustic super surface and a rectangular flat plate, and meshing the finite element model by adopting a triangular non-structural mesh; further carrying out encryption processing on the mesh of the region where the acoustic super surface is located, and meeting the condition of consistent convergence of the mesh to obtain a first precision finite element model of the acoustic super surface; and the second precision finite element model of the acoustic super surface is obtained by amplifying the mesh size of the non-acoustic super surface area of the finite element model on the basis of the first precision finite element model of the acoustic super surface and keeping the mesh size of the acoustic super surface area unchanged.
Preferably, in step S3, the latin hypercube sampling method is adopted to obtain the first precision sample points corresponding to the first precision finite element model and the second precision sample points corresponding to the second precision finite element model, where the number of the design variables is
Figure 776726DEST_PATH_IMAGE024
In the range of (1), the Latin hypercube sampling method is adopted to generate the strain in the design variable range
Figure 410969DEST_PATH_IMAGE025
Second precision sample points generated from
Figure 773818DEST_PATH_IMAGE025
Randomly selecting from the second precision sample points
Figure 809907DEST_PATH_IMAGE026
One as a first precision sample point.
Preferably, in step S4, the sound field distribution data of each first-precision sample point and each second-precision sample point are obtained through batch simulation of finite element models, the data are preprocessed, the sound field distribution data of the first-precision sample points are expanded by using the sound field distribution data of the second-precision sample points, a training data set is obtained, and the finite element model of the acoustic super-surface is divided into two parts
Figure 341120DEST_PATH_IMAGE027
The sound pressure value of each grid point is obtained through interpolation, and the sound pressure value of the point of the grid on the super surface or the entity is set to be 0; obtaining the sound pressure value of each second precision sample point or the first precision sample point at each grid point through self batch simulation of finite element analysis software, and obtaining the sound pressure values
Figure 462660DEST_PATH_IMAGE025
An
Figure 629199DEST_PATH_IMAGE027
A second-precision data set composed of second-precision sample point sound field distribution data of dimensions, and
Figure 926319DEST_PATH_IMAGE026
an
Figure 457795DEST_PATH_IMAGE027
First-precision sample point sound field distribution data of a dimension; if the sound field distribution data of the first-precision sample points is less than the sound field distribution data of the second-precision sample points, expanding the missing part in the sound field distribution data of the first-precision sample points by using the sound field distribution data of the second-precision sample points at the corresponding positions until the number of the sound field distribution data of the first-precision sample points is equal to that of the sound field distribution data of the second-precision sample points, and obtaining a first-precision data set; the second precision data set and the first precision data set constitute a training data set.
Preferably, the training of the variable reliability neural network model in step S5 further includes setting a loss function of the variable reliability neural network model training; loss function in variable reliability neural network model training
Figure 863368DEST_PATH_IMAGE028
Comprises the following steps:
Figure 771281DEST_PATH_IMAGE029
(ii) a Wherein
Figure 454066DEST_PATH_IMAGE030
A second precision prediction result of the ith given input of the variable reliability neural network model;
Figure 156443DEST_PATH_IMAGE031
first precision for given input of ith time of variable reliability neural network modelPredicting the result;
Figure 49313DEST_PATH_IMAGE006
the first precision true value of the variable reliability neural network model is obtained;
Figure 495338DEST_PATH_IMAGE007
the second precision true value is a variable credibility neural network model;
Figure 767050DEST_PATH_IMAGE032
is the second order norm error sign;
Figure 702645DEST_PATH_IMAGE033
the second precision loss is second-order norm error of the difference between a second precision predicted value and a second precision true value of the variable reliability neural network model;
Figure 20494DEST_PATH_IMAGE034
the first precision loss is second-order norm error of the difference between a first precision predicted value and a first precision true value of the variable reliability neural network model; gamma and 1-gamma are weights for the second loss of precision and the first loss of precision respectively,
Figure 443779DEST_PATH_IMAGE035
；
Figure 960211DEST_PATH_IMAGE036
for the weights in the first precision data set derived from the second precision sample point sound field distribution data,
Figure 4390DEST_PATH_IMAGE037
the weights in the first precision data set derived from the sound field distribution data of the own first precision sample point,
Figure 747218DEST_PATH_IMAGE037
and
Figure 535045DEST_PATH_IMAGE036
for distinguishing data of first precisionThe concentrated sample point sound field distribution data source,
Figure 171563DEST_PATH_IMAGE038
。
compared with the prior art, the acoustic super-surface sound field rapid prediction method based on the variable reliability neural network has the following beneficial effects:
(1) according to the scheme, the characteristics of the second precision data can be extracted through the second precision sub-network part, the linear and nonlinear relations between the high second precision data are respectively learned through the two linear and nonlinear sub-network parts, so that the prediction precision of the neural network model is improved by effectively utilizing the data with different precisions, the output weighted sum of the two sub-networks is the first precision prediction result, the requirement on the first precision data can be reduced, and the data set construction cost is reduced;
(2) according to the scheme, a neural network model with high precision can be constructed at low data cost, and the rapid prediction of the acoustic super-surface sound field distribution with different physical parameters is realized by utilizing the advantage of rapid prediction of the neural network, so that the super-surface design efficiency is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the prior art descriptions will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a flow chart of a variable confidence neural network-based method for rapidly predicting an acoustic super-surface sound field according to the present invention;
FIG. 2 is a schematic diagram of an acoustic super-surface model of the acoustic super-surface sound field rapid prediction method based on the variable confidence neural network;
FIG. 3 is a schematic diagram of finite element meshing of a first precision model and a second precision model of the acoustic super-surface sound field rapid prediction method based on the variable reliability neural network;
FIG. 4 is a schematic diagram of a predicted scattering sound field of the acoustic super-surface sound field rapid prediction method based on the variable reliability neural network;
FIG. 5 is a structural diagram of a variable reliability neural network model of the acoustic super-surface sound field rapid prediction method based on the variable reliability neural network.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
As shown in FIGS. 1-3, the invention provides a method for rapidly predicting an acoustic super-surface sound field based on a variable reliability neural network, which comprises the following steps:
s1: acquiring geometric characteristics, design variables and variation ranges of the acoustic super-surface to be predicted and sound field information to be predicted; the geometrical characteristic of the acoustic super-surface is a structure with the thickness direction smaller than the wavelength of incident sound waves, which is divided into
Figure 386644DEST_PATH_IMAGE001
Units, each unit having different density and elastic modulus property values; the design variable is cell density
Figure 351189DEST_PATH_IMAGE002
And modulus of elasticity of unit
Figure 739445DEST_PATH_IMAGE039
Number of design variables
Figure 168152DEST_PATH_IMAGE040
(ii) a The information of the sound field to be predicted is acquired by uniformly distributing the information around the super surfaceThe sound pressure value of the sampling point;
s2: establishing a finite element model of the acoustic super surface according to the design variable of the acoustic super surface to be predicted, and further establishing a first precision finite element model and a second precision finite element model of the acoustic super surface;
the specific content of the step is as follows: placing the acoustic super surface on the upper surface of a rectangular flat plate, wherein the acoustic super surface is provided with a rectangular boundary; firstly, establishing a finite element model of an acoustic super surface and a rectangular flat plate, and meshing the finite element model by adopting a triangular non-structural mesh; further encrypting the grids of the region where the acoustic super surface is located, and meeting the grid consistency convergence condition to obtain a first precision finite element model of the acoustic super surface; and the second precision finite element model of the acoustic super surface is obtained by amplifying the grid size of the non-acoustic super surface region of the finite element model by a certain factor on the basis of the first precision finite element model of the acoustic super surface, wherein the grid size of the non-acoustic super surface region of the finite element model is kept unchanged, and the amplification factor is a positive real number. It can be seen that the first precision finite element model is more precise than the second precision finite element model.
S3: acquiring a first precision sample point corresponding to the first precision finite element model and a second precision sample point corresponding to the second precision finite element model by adopting a Latin hypercube sampling method;
the specific process is as follows: number of variables in design
Figure 491817DEST_PATH_IMAGE024
In the range of (1), the Latin hypercube sampling method is adopted to generate the strain in the design variable range
Figure 271554DEST_PATH_IMAGE025
Second precision sample points generated from
Figure 197922DEST_PATH_IMAGE025
Randomly selecting from the second precision sample points
Figure 917354DEST_PATH_IMAGE026
As a first precisionSample points. The latin hypercube sampling method is a method for sampling efficiently from the distribution interval of variables, and for those skilled in the art, the latin hypercube sampling method is common knowledge and will not be described herein. In this scheme, the number of the first precision sample points or the second precision sample points may be generally determined according to the dimension of a design variable, and the design variable of this scheme has two dimensions of unit density and unit elastic modulus.
S4: obtaining sound field distribution data of each first precision sample point and each second precision sample point through batch simulation of a finite element model, preprocessing the sound field distribution data, and expanding the sound field distribution data of the first precision sample points by using the sound field distribution data of the second precision sample points to obtain a training data set;
the specific content is as follows: according to the scheme, finite element analysis software COMSOL can be adopted for carrying out finite element simulation, and data are generated through batch simulation of an automatic program, so that the sound pressure value of each grid endpoint in each sample point is obtained. The data preprocessing process comprises the following steps: partitioning a finite element model of an acoustic metasurface into
Figure 739817DEST_PATH_IMAGE027
The sound pressure value of each grid point of the grid matrix is obtained through interpolation, and the sound pressure value of the point of the grid on the super surface or the entity is set to be 0; obtaining the sound pressure value of each second-precision sample point or the first-precision sample point at each grid point through batch simulation carried by finite element analysis software, wherein the sound field distribution data of each preprocessed sample point is represented as:
Figure 803587DEST_PATH_IMAGE041
each element in the sound field distribution data corresponds to a sound pressure value of each grid point. Can be obtained together
Figure 736908DEST_PATH_IMAGE025
An
Figure 812312DEST_PATH_IMAGE027
A second-precision data set composed of second-precision sample point sound field distribution data of dimensions, an
Figure 805676DEST_PATH_IMAGE026
An
Figure 356743DEST_PATH_IMAGE027
First-precision sample point sound field distribution data of a dimension; if the sound field distribution data of the first-precision sample points is less than the sound field distribution data of the second-precision sample points, expanding the missing part in the sound field distribution data of the first-precision sample points by using the sound field distribution data of the second-precision sample points at the corresponding positions until the number of the sound field distribution data of the first-precision sample points is equal to that of the sound field distribution data of the second-precision sample points, and obtaining a first-precision data set; the second precision data set and the first precision data set constitute a training data set.
The part of the first-precision sample point sound field distribution data expanded by the second-precision sample point sound field distribution data can be called as 'pseudo first-precision' data, and in order to distinguish actual sources of the sample point sound field distribution data in the first-precision data set, weights can be further added to the own first-precision sound field data and the first-precision sound field expanded from the second-precision sound field data respectively.
S5: constructing a variable reliability neural network model, and training the variable reliability neural network model according to a training data set; the variable reliability neural network model learns the linear or nonlinear relation between the sound field distribution data of the first precision sample points and the sound field distribution data of the second precision sample points, the sound field distribution data of the second precision sample points provide trend information, and the predicted value is corrected by using the sound field distribution data of the first precision sample points to fuse the sound field distribution data of the sample points with different precisions, so that the prediction precision of the neural network model is improved;
the variable-reliability neural network model comprises three parts, namely a second precision prediction part
Figure 828175DEST_PATH_IMAGE042
Linear sub-network
Figure 758085DEST_PATH_IMAGE043
And a non-linear sub-network
Figure 984667DEST_PATH_IMAGE044
(ii) a The specific process for constructing the variable reliability neural network comprises the following steps:
s501: given an input
Figure 695134DEST_PATH_IMAGE008
Given an input of length
Figure 907941DEST_PATH_IMAGE045
The vector of (a); each given input
Figure 285833DEST_PATH_IMAGE008
There are corresponding second precision sample points and first precision sample points; of course, the first-precision sample points here include both the first-precision sample points corresponding to the sound field distribution data of a part of the first-precision sample points and the second-precision sample points corresponding to the "pseudo first-precision" data expanded from the second-precision sound field data;
s502: constructing a second precision prediction part
Figure 417737DEST_PATH_IMAGE042
The number of input neurons is
Figure 881079DEST_PATH_IMAGE045
Extracting input features and outputting a predicted sound field through a full connection layer, a convolution layer and a pooling layer to obtain a second-precision output prediction result of the variable reliability neural network model
Figure 957681DEST_PATH_IMAGE018
；
S503: will give a given input
Figure 986817DEST_PATH_IMAGE008
And the prediction result of the second precision output of the variable reliability neural network model
Figure 227305DEST_PATH_IMAGE018
Spliced into a new input
Figure 115627DEST_PATH_IMAGE046
；
S504: building a Linear sub-network
Figure 732553DEST_PATH_IMAGE043
Part of the network, without adding nonlinear activation functions, extracts new inputs through the fully-connected, convolutional and pooling layers
Figure 881775DEST_PATH_IMAGE046
Characterizing and outputting linear subnetwork prediction results
Figure 558744DEST_PATH_IMAGE009
；
S505: constructing a non-linear sub-network portion
Figure 668782DEST_PATH_IMAGE044
The partial network adds a non-linear activation function to extract new inputs through the full link, convolutional and pooling layers
Figure 823820DEST_PATH_IMAGE046
Characterizing and outputting a non-linear sub-network prediction result
Figure 93127DEST_PATH_IMAGE021
；
S506: prediction result of first precision output of variable reliability neural network
Figure 347522DEST_PATH_IMAGE022
Is composed of
Figure 7174DEST_PATH_IMAGE023
；
Figure 28219DEST_PATH_IMAGE011
And
Figure 89716DEST_PATH_IMAGE047
are respectively linear sub-networks
Figure 544706DEST_PATH_IMAGE043
And a non-linear sub-network
Figure 691654DEST_PATH_IMAGE044
The weight of (a) is calculated,
Figure 250811DEST_PATH_IMAGE013
。
fully-connected layers, convolutional layers, pooling layers, and nonlinear activation functions are all terms commonly used in the art. The nonlinear activation function in the above step may be a relu function or a tanh function.
The true value mathematical expression form of the variable reliability neural network model is as follows:
Figure 166814DEST_PATH_IMAGE048
(ii) a Wherein the content of the first and second substances,
Figure 28591DEST_PATH_IMAGE006
the first precision true value of the variable reliability neural network model is obtained;
Figure 725152DEST_PATH_IMAGE007
the second precision true value is a variable credibility neural network model;
Figure 25683DEST_PATH_IMAGE008
for a given input;
Figure 733876DEST_PATH_IMAGE009
a linear sub-network of the variable reliability neural network model is used for learning a linear relation between the sound field distribution data of the second precision sample point and the sound field distribution data of the first precision sample point based on given input and an output result of the second precision true value;
Figure 94450DEST_PATH_IMAGE010
the nonlinear sub-network, which is a varying confidence neural network model, is used to learn the nonlinear relationship between the second-precision sample point sound field distribution data and the first-precision sample point sound field distribution data based on given inputs and output results of the second-precision true values. The formula is similar to the formula of S506 in structure, and as can be seen from the formula of S506 and the above formula, the process of training the variable reliability neural network model is the prediction result output by the first precision of the variable reliability neural network
Figure 278307DEST_PATH_IMAGE022
First precision true value of direction-variable credibility neural network model
Figure 116950DEST_PATH_IMAGE006
The process of successive approximation.
In a preferred embodiment of the present invention, when training the reliability-varying neural network, the reliability-varying neural network has both the first precision output and the second precision output, so that the loss of both the first precision output and the second precision output needs to be considered. Loss function in order variable credibility neural network model training
Figure 945229DEST_PATH_IMAGE028
Comprises the following steps:
Figure 273442DEST_PATH_IMAGE029
(ii) a Wherein
Figure 616698DEST_PATH_IMAGE030
A second precision prediction result of the ith given input of the variable reliability neural network model;
Figure 963759DEST_PATH_IMAGE031
a first precision prediction result of the ith given input of the variable reliability neural network model;
Figure 708862DEST_PATH_IMAGE006
the first precision true value of the variable reliability neural network model is obtained;
Figure 473555DEST_PATH_IMAGE007
the second precision true value is a variable credibility neural network model;
Figure 304108DEST_PATH_IMAGE032
is the second order norm error sign;
Figure 422237DEST_PATH_IMAGE033
the second precision loss is second-order norm error of the difference between a second precision predicted value and a second precision true value of the variable reliability neural network model;
Figure 84162DEST_PATH_IMAGE034
the first precision loss is second-order norm error of the difference between a first precision predicted value and a first precision true value of the variable reliability neural network model; gamma and 1-gamma are weights for the second loss of precision and the first loss of precision respectively,
Figure 957440DEST_PATH_IMAGE035
；
Figure 212972DEST_PATH_IMAGE036
for the weights in the first precision data set derived from the second precision sample point sound field distribution data,
Figure 993846DEST_PATH_IMAGE037
the weights in the first precision data set derived from the sound field distribution data of the own first precision sample point,
Figure 713541DEST_PATH_IMAGE037
and
Figure 429824DEST_PATH_IMAGE036
for distinguishing the source of sample point sound field distribution data in the first precision data set,
Figure 297286DEST_PATH_IMAGE038
。
s6: and rapidly predicting the acoustic super-surface sound field by using the trained variable reliability neural network model.
By utilizing the constructed variable reliability neural network, a corresponding predicted sound field can be obtained as long as given input in any design variable range is given, so that the rapid prediction of the super-surface sound field is realized.
For a more complete and intuitive description of the technical solution of the present invention, fig. 2 shows an embodiment applied to a super-surface scattering acoustic field. As can be seen from FIG. 2, the incident sound wave is vertically downward incident along the vertical direction, the background medium is water, the simulation area boundary is the plane wave radiation condition, and the super-surface area is equally divided into 25 units, so that
Figure 85113DEST_PATH_IMAGE001
=25, number of design variables 50, density range 1/3-2 kg/m 3 (ii) a The elastic modulus ranges from 1/3X 2.25X 10 6 —6×2.25×10 6 N/m 2 . The acoustic super-surface is located on the upper surface of the baffle.
FIG. 3 is a left diagram of the finite element meshing schematic of the first precision model and the second precision model, which is a schematic diagram of the finite element meshing of the high precision model, i.e. the first precision model; the right diagram is a diagram of finite element meshing of a low-precision model, i.e., a second-precision model. Establishing a finite element model of the acoustic super surface, the baffle and the background; and carrying out mesh division on the finite element model by adopting a triangular non-structural mesh, wherein the maximum size of the mesh in the super-surface region is 0.02m, the maximum size of the mesh in other regions of the first precision model is 0.1m, and the maximum size of the mesh in other regions of the second precision model is 1.5 m.
In this embodiment, a latin hypercube sampling method is used to obtain 500 sampling points within the design variable range as second precision sample points, and from these 50 sampling points are randomly selected as first precision sample points.
As shown in fig. 4, which is a schematic diagram of a diffuse sound field to be predicted in an embodiment, a simulation region is divided into a regular grid of 48 × 64 dimensions, a diffuse sound pressure value at each point is obtained through interpolation, and for a point located in a solid region such as a super-surface and a baffle, a sound pressure value is set to 0, and 500 pieces of second precision data and 50 pieces of first precision data are generated through MATLAB program script batch simulation.
In this embodiment, the constructed variable reliability neural network model is composed of a full connection layer, a convolutional layer, an upsampling layer, and a pooling layer, and a relu activation function is used. Fig. 5 is a network structure diagram, and input design variable parameters are subjected to full connection, convolution and up-sampling layer feature extraction to obtain a 48 × 64 dimensional output matrix, which is a second precision output. Then extracting the characteristics of second precision output through a convolution and down-sampling layer, splicing the characteristics with the input to form a new vector, and inputting the new vector to two parallel sub-networks, wherein the two sub-networks have consistent structures and are composed of a convolution kernel up-sampling layer, and the upper molecular network has no nonlinear activation function and is used for learning the linear relation between high second precision data; the lower half of the sub-networks contain nonlinear activation functions for learning nonlinear relationships between high second precision data. The weighted sum of the outputs of the two sub-networks is the final first precision prediction result. The legend below fig. 5 represents the processing steps of vector dimension conversion, convolution, pooling, upsampling, or vector stitching, in that order.
It should be noted that the specific embodiment given in this specification is only illustrative and does not constitute the only limitation of the specific embodiment of the present invention, and for those skilled in the art, on the basis of the embodiment provided in the present invention, the above-mentioned fast prediction method for a super-surface scattering sound field based on a variable reliability neural network model is similarly adopted to realize fast prediction of different super-surface scattering sound field distributions.
In order to better show the advantages of the proposed acoustic super-surface sound field rapid prediction method based on the variable reliability neural network, the embodiment simultaneously adopts a transfer learning method with wide application, a multi-precision neural network based on a gaussian process, a single-precision neural network only adopting first precision data, and a single-precision neural network only adopting second precision data for comparison. The model structure of the comparative method is consistent with the second precision network portion of fig. 5. RMSE, MMAE and RE are used as evaluation criteria of global errors and local errors, and the calculation formula is as follows:
Figure 95532DEST_PATH_IMAGE049
；
Figure 310613DEST_PATH_IMAGE050
；
Figure 399792DEST_PATH_IMAGE051
(ii) a Wherein
Figure 991310DEST_PATH_IMAGE052
The total number of test sample points;
Figure 357701DEST_PATH_IMAGE053
and
Figure 540420DEST_PATH_IMAGE054
respectively representing a real scattering sound field and a predicted scattering sound field of the ith test sample point; the final comparison results are as follows.
Figure DEST_PATH_IMAGE056
As can be seen from the table, the super-surface sound field is predicted by the method, and compared with a conventional single-precision model, a transfer learning model, a Gaussian process neural network-based model and the like, the global precision and the local precision are improved to a certain extent.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (7)

1. The acoustic super-surface sound field rapid prediction method based on the variable reliability neural network is characterized by comprising the following steps of:
s1: acquiring geometric characteristics, design variables and variation ranges of the acoustic super-surface to be predicted and sound field information to be predicted; the geometrical characteristic of the acoustic super-surface is a structure with the thickness direction smaller than the wavelength of incident sound waves, which is divided into
Figure 730622DEST_PATH_IMAGE001
Units, each unit having different density and elastic modulus property values; the design variable is cell density
Figure 659264DEST_PATH_IMAGE002
And modulus of elasticity of unit
Figure 122607DEST_PATH_IMAGE003
Number of design variables
Figure 935842DEST_PATH_IMAGE004
(ii) a The sound field information to be predicted is sound pressure values of sampling points uniformly distributed around the super surface;
s2: establishing a finite element model of the acoustic super surface according to the design variable of the acoustic super surface to be predicted, and further establishing a first precision finite element model and a second precision finite element model of the acoustic super surface;
s3: acquiring a first precision sample point corresponding to the first precision finite element model and a second precision sample point corresponding to the second precision finite element model by adopting a Latin hypercube sampling method;
s4: acquiring sound field distribution data of each first precision sample point and each second precision sample point through finite element model batch simulation, preprocessing the data, and expanding the sound field distribution data of the first precision sample points by using the sound field distribution data of the second precision sample points to acquire a training data set;
s5: constructing a variable reliability neural network model, and training the variable reliability neural network model according to a training data set; the variable reliability neural network model learns the linear or nonlinear relation between the sound field distribution data of the first precision sample points and the sound field distribution data of the second precision sample points, the sound field distribution data of the second precision sample points provide trend information, and the predicted value is corrected by the sound field distribution data of the first precision sample points to fuse the sound field distribution data of the sample points with different precisions, so that the prediction precision of the neural network model is improved;
s6: and rapidly predicting the acoustic super-surface sound field by using the trained variable reliability neural network model.
2. The method for rapidly predicting the acoustic hypersurface sound field based on the variable credibility neural network as claimed in claim 1, wherein the step S5 is used for constructing the variable credibility neural network model, the variable credibility neural network model comprises three parts, and the second precision prediction part
Figure 168240DEST_PATH_IMAGE005
Linear sub-network
Figure 533362DEST_PATH_IMAGE006
And a non-linear sub-network
Figure 218422DEST_PATH_IMAGE007
(ii) a The process of constructing the variable reliability neural network comprises the following steps:
s501: given an input
Figure 835348DEST_PATH_IMAGE008
Given an input of length
Figure 46886DEST_PATH_IMAGE009
The vector of (a);
s502: constructing a second precision prediction part
Figure 458276DEST_PATH_IMAGE005
The number of input neurons is
Figure 630631DEST_PATH_IMAGE009
Extracting input features and outputting a predicted sound field through a full connection layer, a convolution layer and a pooling layer to obtain a second-precision output prediction result of the variable reliability neural network model
Figure 411768DEST_PATH_IMAGE010
；
S503: will give a given input
Figure 618758DEST_PATH_IMAGE008
And the prediction result output by the second precision of the variable credibility neural network model
Figure 466628DEST_PATH_IMAGE010
Spliced into a new input
Figure 126280DEST_PATH_IMAGE011
；
S504: building a Linear sub-network
Figure 209642DEST_PATH_IMAGE006
Part of the network, without adding nonlinear activation functions, extracts new inputs through the full connection layer, convolution layer and pooling layer
Figure 739981DEST_PATH_IMAGE011
Characteristically, linear sub-network prediction results are output
Figure 758752DEST_PATH_IMAGE012
；
S505: constructing a non-linear sub-network portion
Figure 30334DEST_PATH_IMAGE007
The partial network adds a non-linear activation function to extract new inputs through the full link, convolutional and pooling layers
Figure 527174DEST_PATH_IMAGE011
Characterizing and outputting a non-linear sub-network prediction result
Figure 443178DEST_PATH_IMAGE013
；
S506: prediction result of first precision output of variable reliability neural network
Figure 491905DEST_PATH_IMAGE014
Is composed of
Figure 126149DEST_PATH_IMAGE015
；
Figure 161101DEST_PATH_IMAGE016
And
Figure 656296DEST_PATH_IMAGE017
respectively linear sub-network
Figure 751291DEST_PATH_IMAGE006
And a non-linear sub-network
Figure 872831DEST_PATH_IMAGE007
The weight of (a) is calculated,
Figure 836108DEST_PATH_IMAGE018
。
3. the acoustic super-surface sound field rapid prediction method based on the variable confidence neural network as claimed in claim 2, wherein the nonlinear activation function is a relu function or a tanh function.
4. The acoustic super-surface sound field rapid prediction method based on the variable reliability neural network as claimed in any one of claims 1 to 3, wherein in step S2, a finite element model of the acoustic super-surface is established according to the design variables of the acoustic super-surface to be predicted, and further a first precision finite element model and a second precision finite element model of the acoustic super-surface are established, specifically: placing the acoustic super surface on the upper surface of a rectangular flat plate, wherein the acoustic super surface is provided with a rectangular boundary; firstly, establishing a finite element model of an acoustic super surface and a rectangular flat plate, and meshing the finite element model by adopting a triangular non-structural mesh; further carrying out encryption processing on the mesh of the region where the acoustic super surface is located, and meeting the condition of consistent convergence of the mesh to obtain a first precision finite element model of the acoustic super surface; and the second precision finite element model of the acoustic super surface is obtained by amplifying the mesh size of the non-acoustic super surface area of the finite element model on the basis of the first precision finite element model of the acoustic super surface and keeping the mesh size of the acoustic super surface area unchanged.
5. The method for rapidly predicting the acoustic super-surface sound field based on the variable reliability neural network as claimed in any one of claims 1 to 3, wherein the step S3 of obtaining the first precision sample points corresponding to the first precision finite element model and the second precision sample points corresponding to the second precision finite element model by the Latin hypercube sampling method is performed based on the number of the design variables
Figure 461124DEST_PATH_IMAGE019
In the range of (1), the Latin hypercube sampling method is adopted to generate the strain in the range of design variables
Figure 992600DEST_PATH_IMAGE020
Second precision sample points generated from
Figure 335856DEST_PATH_IMAGE020
Randomly selecting from the second precision sample points
Figure 368403DEST_PATH_IMAGE021
One as a first precision sample point.
6. The method as claimed in claim 5, wherein the step S4 includes obtaining sound field distribution data of each first precision sample point and each second precision sample point through finite element model batch simulation, preprocessing the sound field distribution data, expanding the sound field distribution data of the first precision sample points by using the sound field distribution data of the second precision sample points, and obtaining a training data set by dividing the finite element model of the acoustic super surface into finite element models
Figure 113506DEST_PATH_IMAGE022
The sound pressure value of each grid point is obtained through interpolation, and the sound pressure value of the point of the grid on the super surface or the entity is set to be 0; obtaining the sound pressure value of each second precision sample point or the first precision sample point at each grid point through self batch simulation of finite element analysis software, and obtaining the sound pressure values
Figure 550303DEST_PATH_IMAGE020
An
Figure 505490DEST_PATH_IMAGE023
A second-precision data set composed of second-precision sample point sound field distribution data of dimensions, and
Figure 951514DEST_PATH_IMAGE021
an
Figure 285544DEST_PATH_IMAGE022
First-precision sample point sound field distribution data of a dimension; if the sound field distribution data of the first-precision sample points is less than the sound field distribution data of the second-precision sample points, expanding the missing part in the sound field distribution data of the first-precision sample points by using the sound field distribution data of the second-precision sample points at the corresponding positions until the number of the sound field distribution data of the first-precision sample points is equal to that of the sound field distribution data of the second-precision sample points, and obtaining a first-precision data set; second precisionThe data set and the first precision data set constitute a training data set.
7. The method for rapidly predicting the acoustic super-surface sound field based on the variable reliability neural network as claimed in claim 6, wherein the step S5 trains the variable reliability neural network model, further comprising setting a loss function of the variable reliability neural network model training; loss function in variable reliability neural network model training
Figure 784921DEST_PATH_IMAGE024
Comprises the following steps:
Figure 102769DEST_PATH_IMAGE025
(ii) a Wherein
Figure 86906DEST_PATH_IMAGE026
A second precision prediction result of the ith given input of the variable reliability neural network model;
Figure 806600DEST_PATH_IMAGE027
a first precision prediction result of the ith given input of the variable reliability neural network model;
Figure 975413DEST_PATH_IMAGE028
the first precision true value of the variable reliability neural network model is obtained;
Figure 514979DEST_PATH_IMAGE029
the second precision true value is a variable credibility neural network model;
Figure 302807DEST_PATH_IMAGE030
is the second order norm error sign;
Figure 1641DEST_PATH_IMAGE031
for a second loss of precision, i.e. a second predicted value of precision for the varying-reliability neural network modelA second order norm error of a difference from the second precision true value;
Figure 216722DEST_PATH_IMAGE032
the first precision loss is second-order norm error of the difference between a first precision predicted value and a first precision true value of the variable reliability neural network model; gamma and 1-gamma are weights for the second loss of precision and the first loss of precision respectively,
Figure 243584DEST_PATH_IMAGE033
；
Figure 835102DEST_PATH_IMAGE034
weights derived from second precision sample point sound field distribution data in the first precision data set,
Figure 388443DEST_PATH_IMAGE035
the weights in the first precision data set derived from the sound field distribution data of the own first precision sample point,
Figure 508846DEST_PATH_IMAGE035
and
Figure 288583DEST_PATH_IMAGE034
for distinguishing the source of sample point sound field distribution data in the first precision data set,
Figure 41382DEST_PATH_IMAGE036
。
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112115639A (en) * 2020-09-03 2020-12-22 南京理工大学 Electromagnetic superstructure surface construction method under unit near-coupling condition based on deep learning
WO2020263358A1 (en) * 2019-06-24 2020-12-30 Nanyang Technological University Machine learning techniques for estimating mechanical properties of materials
CN112182938A (en) * 2020-10-13 2021-01-05 上海交通大学 Mesoscopic structural part mechanical property prediction method based on transfer learning-multi-fidelity modeling
CN113361025A (en) * 2021-04-28 2021-09-07 华东理工大学 Creep fatigue probability damage evaluation method based on machine learning
CN113627098A (en) * 2021-07-23 2021-11-09 北京理工大学 CFD model confirmation method and product design method
CN114357636A (en) * 2021-12-01 2022-04-15 中国船舶重工集团公司第七一九研究所 Ultra-thin ultra-low frequency underwater sound reflection super-surface design method

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US10873812B2 (en) * 2017-02-09 2020-12-22 The University Of Sussex Acoustic wave manipulation by means of a time delay array
EP3935470A4 (en) * 2019-03-08 2022-12-14 Schlumberger Technology Corporation System and method for supervised learning of permeability of earth formations
CN113177356B (en) * 2021-04-28 2021-10-15 北京航空航天大学 Target electromagnetic scattering characteristic rapid prediction method based on deep learning
CN113836657B (en) * 2021-09-14 2023-09-12 天津大学 Reflection type underwater sound super-surface design method for realizing underwater sound regulation and control

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2020263358A1 (en) * 2019-06-24 2020-12-30 Nanyang Technological University Machine learning techniques for estimating mechanical properties of materials
CN112115639A (en) * 2020-09-03 2020-12-22 南京理工大学 Electromagnetic superstructure surface construction method under unit near-coupling condition based on deep learning
CN112182938A (en) * 2020-10-13 2021-01-05 上海交通大学 Mesoscopic structural part mechanical property prediction method based on transfer learning-multi-fidelity modeling
CN113361025A (en) * 2021-04-28 2021-09-07 华东理工大学 Creep fatigue probability damage evaluation method based on machine learning
CN113627098A (en) * 2021-07-23 2021-11-09 北京理工大学 CFD model confirmation method and product design method
CN114357636A (en) * 2021-12-01 2022-04-15 中国船舶重工集团公司第七一九研究所 Ultra-thin ultra-low frequency underwater sound reflection super-surface design method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
Automated Recognition of Wood Damages using Artificial Neural Network;Zhao Dong ET AL;《2009 International Conference on Measuring Technology and Mechatronics Automation》;20091231;第1-3页 *
声学超表面抑制Mack第2模态机理与优化设计;赵瑞等;《气体物理》;20181130;第1-6页 *

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