CN114722690A - 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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CN114722690A
CN114722690A CN202210643830.0A CN202210643830A CN114722690A CN 114722690 A CN114722690 A CN 114722690A CN 202210643830 A CN202210643830 A CN 202210643830A CN 114722690 A CN114722690 A CN 114722690A
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CN114722690B (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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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; 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; 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 by introducing phase mutation at different phase interfaces, the reflection angle and the refraction angle of incident waves can be regulated, 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 method for quickly predicting an acoustic super-surface sound field based on a variable reliability neural network, 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 60635DEST_PATH_IMAGE001
Units, each unit having different density and elastic modulus property values; the design variable is cell density
Figure 384300DEST_PATH_IMAGE002
And modulus of elasticity of unit
Figure 429616DEST_PATH_IMAGE003
Number of design variables
Figure 231350DEST_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 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;
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 576881DEST_PATH_IMAGE005
(ii) a Wherein the content of the first and second substances,
Figure 664923DEST_PATH_IMAGE006
the first precision true value of the variable reliability neural network model is obtained;
Figure 72901DEST_PATH_IMAGE007
second precision true value for variable reliability neural network model；
Figure 537381DEST_PATH_IMAGE008
For a given input;
Figure 737418DEST_PATH_IMAGE009
a linear sub-network of the variable credibility neural network model is used for learning a linear relation between sound field distribution data of the second precision sample point and sound field distribution data of the first precision sample point based on given input and an output result of the second precision real value;
Figure 871727DEST_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 891636DEST_PATH_IMAGE011
and
Figure 894227DEST_PATH_IMAGE012
the weights of the output result of the linear sub-network and the output result of the non-linear sub-network,
Figure 683191DEST_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 516631DEST_PATH_IMAGE014
Linear sub-network
Figure 23835DEST_PATH_IMAGE015
And a non-linear sub-network
Figure 564538DEST_PATH_IMAGE016
(ii) a The process of constructing the variable reliability neural network comprises the following steps:
s501: given an input
Figure 348954DEST_PATH_IMAGE008
Given an input of length
Figure 949700DEST_PATH_IMAGE017
The vector of (a);
s502: constructing a second precision prediction part
Figure 944201DEST_PATH_IMAGE014
The number of input neurons is
Figure 288594DEST_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 193097DEST_PATH_IMAGE018
；
S503: will give a given input
Figure 230323DEST_PATH_IMAGE008
And the prediction result of the second precision output of the variable reliability neural network model
Figure 446540DEST_PATH_IMAGE018
Spliced into a new input
Figure 469991DEST_PATH_IMAGE019
；
S504: building a Linear sub-network
Figure 88054DEST_PATH_IMAGE015
Part of the network, without adding nonlinear activation functions, extracts new inputs through the fully-connected, convolutional and pooling layers
Figure 561761DEST_PATH_IMAGE019
Characterizing and outputting linear subnetwork prediction results
Figure 140641DEST_PATH_IMAGE020
；
S505: constructing a non-linear sub-network portion
Figure 826837DEST_PATH_IMAGE016
The partial network adds a non-linear activation function to extract new inputs through the full link, convolutional and pooling layers
Figure 564986DEST_PATH_IMAGE019
Characterizing and outputting a non-linear sub-network prediction result
Figure 944015DEST_PATH_IMAGE021
；
S506: prediction result of first precision output of variable reliability neural network
Figure 10191DEST_PATH_IMAGE022
Is composed of
Figure 765657DEST_PATH_IMAGE023
；
Figure 92734DEST_PATH_IMAGE011
And
Figure 518030DEST_PATH_IMAGE012
are respectively linear sub-networks
Figure 196136DEST_PATH_IMAGE015
And a non-linear sub-network
Figure 489714DEST_PATH_IMAGE016
The weight of (a) is calculated,
Figure 936876DEST_PATH_IMAGE024
。
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 obtaining of the first precision sample point corresponding to the first precision finite element model and the second precision sample point corresponding to the second precision finite element model by the latin hypercube sampling method are based on the number of the design variables
Figure 533073DEST_PATH_IMAGE025
In the range of (1), the Latin hypercube sampling method is adopted to generate the strain in the design variable range
Figure 698475DEST_PATH_IMAGE026
Second precision sample points generated from
Figure 530165DEST_PATH_IMAGE026
Randomly selecting from the second precision sample points
Figure 969849DEST_PATH_IMAGE027
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 is obtained through batch simulation of the finite element model, the data is preprocessed, and the sound field distribution data of the second-precision sample points is used to distribute the sound field of the first-precision sample pointsData expansion to obtain training data set, wherein the finite element model of the acoustic super surface is divided into
Figure 861582DEST_PATH_IMAGE028
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 solid 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 514280DEST_PATH_IMAGE026
An
Figure 25027DEST_PATH_IMAGE028
A second-precision data set composed of second-precision sample point sound field distribution data of dimensions, an
Figure 181202DEST_PATH_IMAGE027
An
Figure 650360DEST_PATH_IMAGE028
Dimensional first-precision sample point sound field distribution data; 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, in step S5, the training of the variable reliability neural network model further includes setting a loss function of the variable reliability neural network model training; loss function in variable reliability neural network model training
Figure 524776DEST_PATH_IMAGE029
Comprises the following steps:
Figure 963847DEST_PATH_IMAGE030
(ii) a Wherein
Figure 381053DEST_PATH_IMAGE031
A second precision prediction result of the ith given input of the variable reliability neural network model;
Figure 614588DEST_PATH_IMAGE032
a first precision prediction result of the ith given input of the variable reliability neural network model;
Figure 241879DEST_PATH_IMAGE006
the first precision true value of the variable reliability neural network model is obtained;
Figure 94428DEST_PATH_IMAGE007
the second precision true value is a variable credibility neural network model;
Figure 225195DEST_PATH_IMAGE033
is the second order norm error sign;
Figure 629632DEST_PATH_IMAGE034
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 478639DEST_PATH_IMAGE035
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 134880DEST_PATH_IMAGE036
；
Figure 385732DEST_PATH_IMAGE037
for the first precision data set from the second precisionThe weights of the sound field distribution data at the sample points,
Figure 961070DEST_PATH_IMAGE038
weights in the first precision data set derived from the own first precision sample point sound field distribution data,
Figure 172740DEST_PATH_IMAGE038
and
Figure 491726DEST_PATH_IMAGE037
for distinguishing the source of sample point sound field distribution data in the first precision data set,
Figure 862664DEST_PATH_IMAGE039
。
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, the neural network model with high precision can be built at low data cost, and the advantage of fast prediction of the neural network is utilized to realize fast prediction of the distribution of the acoustic super-surface sound field with different physical parameters, so that the super-surface design efficiency is improved.
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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 description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings 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 fig. 1-3, the invention provides a method for rapidly predicting an acoustic super-surface sound field based on a variable reliability neural network, comprising 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 a thickness direction smaller than the wavelength of incident sound waves, which is equally divided into
Figure 484269DEST_PATH_IMAGE001
Units, each unit having different density and elastic modulus property values; what is needed isThe design variable being cell density
Figure 42290DEST_PATH_IMAGE002
And modulus of elasticity of unit
Figure 164967DEST_PATH_IMAGE040
Number of design variables
Figure 124832DEST_PATH_IMAGE041
(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;
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 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 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 937847DEST_PATH_IMAGE025
In the range of (1), a Latin hypercube sampling method is adoptedGeneration within a range of variables
Figure 514322DEST_PATH_IMAGE026
Second precision sample points generated from
Figure 175110DEST_PATH_IMAGE026
Randomly selecting from the second precision sample points
Figure 864849DEST_PATH_IMAGE027
One as a first precision sample point. 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, where the design variable of this scheme has two dimensions of a unit density and a unit elastic modulus.
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;
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 218470DEST_PATH_IMAGE028
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 each first-precision sample point at each grid point through batch simulation carried by finite element analysis software, and representing the sound field distribution data of each preprocessed sample point as：
Figure 751082DEST_PATH_IMAGE042
Each element in the sound field distribution data corresponds to a sound pressure value of each grid point. Can be obtained together
Figure 215561DEST_PATH_IMAGE026
An
Figure 759806DEST_PATH_IMAGE028
A second-precision data set composed of second-precision sample point sound field distribution data of dimensions, an
Figure 549908DEST_PATH_IMAGE027
An
Figure 569816DEST_PATH_IMAGE028
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 may be referred to 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 may 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 447774DEST_PATH_IMAGE043
Linear sub-network
Figure 236738DEST_PATH_IMAGE044
And a non-linear sub-network
Figure 197741DEST_PATH_IMAGE045
(ii) a The specific process for constructing the variable reliability neural network comprises the following steps:
s501: given an input
Figure 314733DEST_PATH_IMAGE008
Given an input of length
Figure 121015DEST_PATH_IMAGE046
The vector of (a); each given input
Figure 30065DEST_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 themselves 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 771756DEST_PATH_IMAGE043
The number of input neurons is
Figure 766257DEST_PATH_IMAGE046
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 110650DEST_PATH_IMAGE018
；
S503: will give a given input
Figure 874207DEST_PATH_IMAGE008
And the prediction result of the second precision output of the variable reliability neural network model
Figure 786799DEST_PATH_IMAGE018
Spliced into a new input
Figure 268596DEST_PATH_IMAGE047
；
S504: building a Linear sub-network
Figure 416681DEST_PATH_IMAGE044
Part of the network, without adding nonlinear activation functions, extracts new inputs through the fully-connected, convolutional and pooling layers
Figure 910110DEST_PATH_IMAGE047
Characterizing and outputting linear subnetwork prediction results
Figure 118238DEST_PATH_IMAGE009
；
S505: constructing a non-linear sub-network portion
Figure 821751DEST_PATH_IMAGE045
The partial network adds a non-linear activation function to extract new inputs through the full link, convolutional and pooling layers
Figure 507948DEST_PATH_IMAGE047
Characterizing and outputting a non-linear sub-network prediction result
Figure 384112DEST_PATH_IMAGE021
；
S506: prediction result of first precision output of variable reliability neural network
Figure 497562DEST_PATH_IMAGE022
Is composed of
Figure 688372DEST_PATH_IMAGE048
；
Figure 53625DEST_PATH_IMAGE049
And
Figure 646280DEST_PATH_IMAGE050
respectively linear sub-network
Figure 196211DEST_PATH_IMAGE044
And a non-linear sub-network
Figure 874317DEST_PATH_IMAGE045
The weight of (a) is calculated,
Figure 43261DEST_PATH_IMAGE051
。
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 real value mathematical expression form of the variable reliability neural network model is as follows:
Figure 490423DEST_PATH_IMAGE052
(ii) a Wherein the content of the first and second substances,
Figure 211254DEST_PATH_IMAGE006
the first precision true value of the variable reliability neural network model is obtained;
Figure 252022DEST_PATH_IMAGE007
second-precision true for variable-reliability neural network modelReal value;
Figure 83712DEST_PATH_IMAGE008
for a given input;
Figure 385380DEST_PATH_IMAGE009
a linear sub-network of the variable credibility neural network model is used for learning a linear relation between sound field distribution data of the second precision sample point and sound field distribution data of the first precision sample point based on given input and an output result of the second precision real value;
Figure 418059DEST_PATH_IMAGE010
a non-linear sub-network, which is a varying-confidence neural network model, is used to learn a non-linear 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 structure of S506, and 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 as known from the formula of S506 and the above formula
Figure 70757DEST_PATH_IMAGE022
First precision true value of variable reliability neural network model
Figure 440558DEST_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 862312DEST_PATH_IMAGE029
Comprises the following steps:
Figure 800312DEST_PATH_IMAGE030
(ii) a Wherein
Figure 674727DEST_PATH_IMAGE031
A second precision prediction result of the given input at the ith time of the variable reliability neural network model;
Figure 379378DEST_PATH_IMAGE032
a first precision prediction result of the ith given input of the variable reliability neural network model;
Figure 531005DEST_PATH_IMAGE006
the first precision true value of the variable reliability neural network model is obtained;
Figure 764540DEST_PATH_IMAGE007
the second precision true value is a variable credibility neural network model;
Figure 391831DEST_PATH_IMAGE033
is the second order norm error sign;
Figure 978801DEST_PATH_IMAGE034
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 640727DEST_PATH_IMAGE035
the first precision loss is a 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 45163DEST_PATH_IMAGE036
；
Figure 766607DEST_PATH_IMAGE037
for the weights in the first precision data set derived from the second precision sample point sound field distribution data,
Figure 281902DEST_PATH_IMAGE038
the weights in the first precision data set derived from the sound field distribution data of the own first precision sample point,
Figure 798334DEST_PATH_IMAGE038
and
Figure 249038DEST_PATH_IMAGE037
for distinguishing the source of sample point sound field distribution data in the first precision data set,
Figure 585341DEST_PATH_IMAGE039
。
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.
In order to more fully and intuitively explain the technical scheme of the invention, as shown in fig. 2, the figure shows an embodiment applied to a super-surface scattering sound 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 boundary of the simulation area is the plane wave radiation condition, and the super-surface area is divided into 25 units equally, so that
Figure 904327DEST_PATH_IMAGE001
=25, number of design variables 50, density range 1/3-2 kg/m3(ii) a The elastic modulus ranges from 1/3X 2.25X 106—6×2.25×106N/m2. 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 features of second precision output through a convolution and down sampling layer, splicing the features with the input to form a new vector, inputting the new vector to two parallel sub-networks, wherein the two sub-networks have the same structure and are composed of convolution kernel up sampling layers, 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 9686DEST_PATH_IMAGE053
；
Figure 631292DEST_PATH_IMAGE054
；
Figure 189312DEST_PATH_IMAGE055
(ii) a Wherein
Figure 577568DEST_PATH_IMAGE056
The total number of test sample points;
Figure 412800DEST_PATH_IMAGE057
and
Figure 329940DEST_PATH_IMAGE058
respectively obtaining 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 640836DEST_PATH_IMAGE060
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 263241DEST_PATH_IMAGE001
Units, each unit having different density and elastic modulus property values; the design variable is cell density
Figure 773857DEST_PATH_IMAGE002
And modulus of elasticity of unit
Figure 288015DEST_PATH_IMAGE003
Number of design variables
Figure 417645DEST_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 super-surface sound field based on the variable reliability neural network as claimed in claim 1, wherein the variable reliability neural network model is constructed in step S5, the variable reliability neural network model comprises three parts, and the second precision prediction part
Figure 966438DEST_PATH_IMAGE005
Linear sub-network
Figure 133108DEST_PATH_IMAGE006
And a non-linear sub-network
Figure 134562DEST_PATH_IMAGE007
(ii) a The process of constructing the variable reliability neural network comprises the following steps:
s501: given an input
Figure 67883DEST_PATH_IMAGE008
Given an input of length
Figure 595816DEST_PATH_IMAGE009
The vector of (a);
s502: constructing a second precision prediction part
Figure 323601DEST_PATH_IMAGE005
The number of input neurons is
Figure 812351DEST_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 283784DEST_PATH_IMAGE010
；
S503: will give a given input
Figure 148447DEST_PATH_IMAGE008
And the prediction result output by the second precision of the variable credibility neural network model
Figure 312712DEST_PATH_IMAGE010
Spliced into a new input
Figure 288758DEST_PATH_IMAGE011
；
S504: building a Linear sub-network
Figure 422936DEST_PATH_IMAGE006
Part of the network, without adding nonlinear activation functions, extracts new inputs through the fully-connected, convolutional and pooling layers
Figure 800828DEST_PATH_IMAGE011
Characterization and output of linear subnetwork prediction results
Figure 604836DEST_PATH_IMAGE012
；
S505: constructing a non-linear sub-network portion
Figure 943545DEST_PATH_IMAGE007
The partial network adds a non-linear activation function to extract new inputs through the full link, convolutional and pooling layers
Figure 756780DEST_PATH_IMAGE011
Characterizing and outputting a non-linear sub-network prediction result
Figure 989178DEST_PATH_IMAGE013
；
S506: prediction result of first precision output of variable reliability neural network
Figure 495246DEST_PATH_IMAGE014
Is composed of
Figure 304939DEST_PATH_IMAGE015
；
Figure 921865DEST_PATH_IMAGE017
And
Figure 743190DEST_PATH_IMAGE019
respectively linear sub-network
Figure 295526DEST_PATH_IMAGE006
And a non-linear sub-network
Figure 467881DEST_PATH_IMAGE007
The weight of (a) is calculated,
Figure 622919DEST_PATH_IMAGE020
。
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 hypersurface sound field based on the variable credibility neural network as claimed in any one of claims 1 to 3, wherein the step S3 adopts a Latin hypercube sampling method to obtain first precision sample points corresponding to the first precision finite element model and second precision sample points corresponding to the second precision finite element model according to the number of design variables
Figure 829909DEST_PATH_IMAGE021
In the range of (1), the Latin hypercube sampling method is adopted to generate the strain in the design variable range
Figure 802413DEST_PATH_IMAGE022
Second precision sample points generated from
Figure 196486DEST_PATH_IMAGE022
Randomly selecting from the second precision sample points
Figure 155214DEST_PATH_IMAGE023
One as a first precision sample point.
6. 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 5, wherein the step S4 is implemented by performing batch simulation on finite element models to obtain the sound field distribution data of each of the first precision sample points and the second precision sample points, 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 to obtain the training data set, and dividing the finite element models of the acoustic super-surface into the finite element models
Figure 826498DEST_PATH_IMAGE024
The regular grid matrix of (1) obtains the sound pressure value of each grid point 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 845270DEST_PATH_IMAGE022
An
Figure 992217DEST_PATH_IMAGE025
A second-precision data set composed of second-precision sample point sound field distribution data of dimensions, an
Figure 754637DEST_PATH_IMAGE023
An
Figure 529695DEST_PATH_IMAGE024
Dimensional first-precision sample point sound field distribution data; 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.
7. The method for rapidly predicting the acoustic hypersurface sound field based on the variable reliability neural network of claim 6, wherein the step S5 trains the variable reliability neural network model, and further comprises setting a loss function of the variable reliability neural network model; loss function in variable reliability neural network model training
Figure 453789DEST_PATH_IMAGE026
Comprises the following steps:
Figure 88032DEST_PATH_IMAGE027
(ii) a Wherein
Figure 995421DEST_PATH_IMAGE028
A second precision prediction result of the ith given input of the variable reliability neural network model;
Figure 31510DEST_PATH_IMAGE029
a first precision prediction result of the ith given input of the variable reliability neural network model;
Figure 985560DEST_PATH_IMAGE030
the first precision true value of the variable reliability neural network model is obtained;
Figure 107099DEST_PATH_IMAGE031
the second precision true value is a variable credibility neural network model;
Figure 211322DEST_PATH_IMAGE032
is the second order norm error sign;
Figure 446125DEST_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 977600DEST_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 320857DEST_PATH_IMAGE035
；
Figure 87825DEST_PATH_IMAGE036
for the weights in the first precision data set derived from the second precision sample point sound field distribution data,
Figure 832927DEST_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 535304DEST_PATH_IMAGE037
and
Figure 975643DEST_PATH_IMAGE036
for distinguishing the source of the sample point sound field distribution data in the first precision data set,
Figure 421668DEST_PATH_IMAGE038
。
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