CN113297789B - Sound vortex beam splitter design method based on machine learning - Google Patents
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Abstract
The invention discloses a machine learning-based sound vortex beam splitter design method, which adopts an acoustic super-surface structure to construct a super-neural network, so that the purpose that sound vortex beams carrying positive and negative topological charges respectively reach two different positions on a preset receiving plane is realized, and the emergent positions of the sound vortex beams can be flexibly controlled through the setting of a neural network label. The vortex beam splitter constructed based on the principle of the invention has the important advantages of flat appearance, large degree of freedom, real-time response and the like, overcomes the problems that the traditional forward design can only design the small degree of freedom, the original order of the incident vortex can not be reserved after beam splitting and the like, and has important significance for the research of novel acoustic angular momentum devices and the application thereof in the fields of acoustic communication, detection and the like.
Description
Technical Field
The invention relates to the field of acoustics, in particular to a design method of an acoustic vortex beam splitter.
Background
At present, the sound vortex carrying the orbital angular momentum is widely focused, and has important application value in the fields of particle manipulation, acoustic communication and the like. The acoustic device capable of carrying out beam splitting control on the vortex acoustic beam according to the topological charge number plays a key role in the aspects of vortex field identification, information modulation/demodulation and the like.
Existing mechanisms generally rely on forward design theory, and are generally completed through operations such as unwinding, focusing and the like by utilizing orthogonality of vortexes with different topological charges. The biggest limitation of these mechanisms is that the outgoing sound beam cannot retain the topological charge number of the incident vortex at all and the degree of freedom of manipulation is limited. The inability to preserve the topological charge number means that the topological properties carried by the scrolls themselves vanish after passing through the device, and thus the split scrolls cannot be manipulated based on their topological properties, which is extremely detrimental to the processing of the split scrolls. If the split post-swirl is required to be treated in a specific application, the existing mechanism is completely incapable of meeting the technical requirements. The limited control freedom means that the traditional device cannot flexibly control vortex beam splitting, and the emergent position after vortex beam splitting is generally limited. Therefore, a new technology is needed to ensure that the order of the vortex is unchanged after beam splitting on the basis of flexible control of the beam splitting of the vortex, namely the topological property of the vortex is unchanged.
Disclosure of Invention
The invention aims to: aiming at the defects in the prior art, the invention aims to provide an acoustic vortex beam splitter design method based on machine learning, which solves the technical problems that the vortex cannot keep the topological charge number and the control freedom degree of the split vortex in the traditional design method, and has great significance for post-treatment of the split vortex.
The technical scheme is as follows: the invention discloses a machine learning-based sound vortex beam splitter design method, which comprises the following steps:
step 1: constructing training set and test set
The vortex with different positive and negative orders of different initial phase distributions is marked as X 0 Is a training set; randomly generating another set of positive and negative different order vortices of different initial phase distribution from the training set, denoted as T 0 Is a test set.
Step 2: building training tags and test tags
Generating a tag (i.e. sound field distribution on the receiving surface) according to vortex beam splitting requirements: the label setting rules corresponding to the positive and negative order vortexes are as follows: the amplitude of the beam splitting preset emergent position is set to be 1, the other positions are set to be 0, and the spiral phase corresponding to the order is set at the position where the amplitude is 1. For example, if it is desired to split the scrolls of positive and negative orders to the upper left corner and the lower right corner, respectively, the following is set: the labels corresponding to the positive-order vortex are 1 in the amplitude value of the upper left corner and 0 in the other places; the label corresponding to the negative order vortex is a lower right corner amplitude of 1, and the other amplitude is 0. And simultaneously, the spiral phase corresponding to the order is set at the position with the respective amplitude value of 1. Namely: the label corresponding to the positive-order vortex is that the main energy of the sound wave is concentrated at the left upper corner of the receiving surface, the label corresponding to the negative-order vortex is that the main energy of the sound wave is concentrated at the right lower corner of the receiving surface, and the spiral phase of the corresponding order is attached.
Step 3: writing out an acoustic propagation equation
The method is used for simulating the actual propagation condition of the sound wave in the device, and is a theoretical basis for training the neural network.
According to Huygens principle, sound propagation can be seen as the radiation of a series of secondary sound sourcesWherein l is the layer number, i is the unit number of the first layer, ii is the unit number of the first-1 layer, lambda is the wavelength, x, y is the abscissa of the unit +.>d is the interlayer distance, and the interlayer spacing is generally 1 to 3 wavelengths. The radiation sound pressure of each unit of each layer is equal to the sum of the radiation sound pressure of each unit of the previous layer reaching the position. Thus, the association between the latter layer and the former layer can be written as: />Wherein->For each layer of input values, +.>Representing weights +.>Representing bias, all three being matrices, l being the number of layer sequences, ">Representing dot product. Here->Phi is the additional phase value of each layer of supersurface, < >>j 2 = -1, where w is the transmission matrix of acoustic diffraction, t is the transmission coefficient of the super surface, when the super surface adjusts only the phase but not the amplitude +.>
Step 4: construction of a superneural network
With an M-layer super-surface M x n super-surface super-neural network, the first super-surface layer corresponds to the input layer of the conventional neural network, the last super-surface layer corresponds to the output layer of the conventional neural network, and the middle (M-2) layer corresponds to the hidden layer of the conventional neural network. Wherein m is the number of units of each layer of neural network, m is the number of transverse units of the super surface, and n is the number of longitudinal units of the super surface.
Step 5: setting a loss function loss
The value of the loss function is used to measure the gap between the actual situation and the optimal situation after training.
The following formula is shown:
wherein:
k is a coefficient for balancing the contribution of two factors of phase and amplitude in the whole function, N is the number of units,
i.e. m x n.
p＝0.001·ones(N)
Wherein label is a label, output is a sound field distribution matrix of an output plane in an iterative process, ons represents a matrix with each element being 1, and Im and Re represent respectively taking an imaginary part and a real part of a complex number. Here loss can be divided into two parts, the former part acting mainly on the amplitude of the sound field and the latter part acting mainly on the phase of the sound field.
Step 6: the phase of each layer of super neural network is initialized, and each primitive of each layer of super surface randomly generates the phase.
Step 7: the iterative optimization code is written, the optimization target is set to minimize the loss function loss, and the workload of the step can be greatly reduced by utilizing the existing deep learning framework, such as iteration by utilizing Python software and Tensorflow deep learning framework.
Step 8: and after a plurality of iterations, outputting the phase value of the super surface of each layer.
Step 9: verifying trained superneural networks with test sets
And inputting the test set, and evaluating the sound field of the output plane. If the sound field distribution meets the requirement, no iteration is continued; if the sound field distribution still does not meet the requirement, the coefficient k and the training times are adjusted to continue iteration until the requirement is met.
Step 10: parameters of the supersurfaces of the layers are determined.
The technical difficulties of the invention are as follows: (1) The loss function loss itself comprises two parts, namely amplitude and phase, so that the duty cycle of the two parts needs to be adjusted by a coefficient k, and as a variable, k needs to be found by different attempts to find a figure of merit; (2) When the number of the vortex topology charges is large, the number of the training units is too large, so that high requirements on calculation resources are met.
The principle of the invention: after the sound wave passes through a plurality of layers of transmission type ultrasonic surfaces, a corresponding diffraction sound field exists. By adjusting the additional phase and transmission coefficients of the various layers of the supersurface, a distinct diffraction sound field can be generated. The desired sound field can be generated by adjusting the phase. The invention utilizes the gradient descent algorithm of the neural network to construct the acoustic superneural network by using the transmission coefficient of the adjustable element and the acoustic supersurface with additional phase. The transmission coefficient of the super surface is equivalent to the weight of the traditional neural network, and the additional phase is equivalent to the bias of the traditional neural network. Setting the desired sound field distribution in the output plane can be achieved by iterating the phase and transmission coefficients multiple times.
The beneficial effects are that: the invention adopts an acoustic super-surface structure to construct a super-neural network, realizes the purpose that the sound vortex beams carrying positive and negative topological charges respectively reach two different positions on a preset receiving plane, and the emergent positions of the sound vortex beams can be flexibly controlled through the arrangement of the neural network labels.
The sound vortex beam splitter mainly comprises a plurality of layers of super surfaces, each layer of super surface can execute the calculation function of a single-layer neural network, and the combination can realize the function of reserving the original topological charge numbers of the vortex with different orders after beam splitting.
The vortex beam splitter constructed based on the principle of the invention has the important advantages of flat appearance, large degree of freedom, real-time response and the like, overcomes the problems that the traditional forward design can only design the small degree of freedom, the original order of the incident vortex can not be reserved after beam splitting and the like, and has important significance for the research of novel acoustic angular momentum devices and the application thereof in the fields of acoustic communication, detection and the like.
Drawings
Fig. 1 is a schematic flow diagram of the principles of the present invention.
Fig. 2 is a schematic diagram of the operation of the present invention.
FIG. 3 is a graph of the results of the operation of example 1; FIG. (a) shows the phase distribution on the receiving plane after +1 order vortex beam splitting; graph (b) shows the amplitude distribution on the receiving plane after +1 order vortex beam splitting; FIG. (c) shows the phase distribution on the receiving plane after-1 order vortex beam splitting; graph (d) shows the amplitude distribution on the receiving plane after-1 order vortex beam splitting.
FIG. 4 is a graph of the results of the operation of example 2; FIG. (a) shows the phase distribution on the receiving plane after +3 order vortex beam splitting; graph (b) shows the amplitude distribution on the receiving plane after +3-order vortex beam splitting; FIG. (c) shows the phase distribution on the receiving plane after-3-order vortex beam splitting; graph (d) shows the amplitude distribution on the receiving plane after-3 rd order vortex beam splitting.
FIG. 5 is a graph of the results of the operation of example 3; FIG. (a) shows the phase distribution on the receiving plane after +1 order vortex beam splitting; graph (b) shows the amplitude distribution on the receiving plane after +1 order vortex beam splitting; FIG. (c) shows the phase distribution on the receiving plane after-1 order vortex beam splitting; graph (d) shows the amplitude distribution on the receiving plane after-1 order vortex beam splitting.
Detailed Description
The present invention will be described in further detail with reference to examples.
FIG. 1 is a schematic flow chart of the invention, wherein the vortexes with different positive and negative orders of different initial phase distributions are used as a training set, and the vortexes with different positive and negative orders of different initial phase distributions of the training set are randomly generated to be used as a test set; constructing a training label and a test label according to vortex beam splitting requirements; constructing an ultra-neural network model according to an acoustic propagation equation; setting a loss function loss; initializing the phase of each layer of super neural network; writing an iteration optimization code for iteration; verifying the effect by using the test set; parameters of the supersurfaces of the layers are determined.
The invention discloses a machine learning-based sound vortex beam splitter design method, which comprises the following steps of:
step 1: generating training sets and test sets
The vortex with different positive and negative orders of different initial phase distributions is marked as X 0 Is a training set; randomly generating another set of positive and negative different order vortices of different initial phase distribution from the training set, denoted as T 0 Is a test set.
Step 2: generating training tags and test tags
And generating a label according to the vortex beam splitting requirement. The label with positive order is the main sound wave energy concentrated at the left upper corner of the receiving surface, the label with negative order is the sound wave main energy concentrated at the right lower corner of the receiving surface, and the spiral phase with corresponding order is attached.
Step 3: writing out an acoustic propagation equation
According to Huygens principle, sound propagation can be seen as the radiation of a series of secondary sound sourcesWherein l is the layer number, i is the unit number of the first layer, ii is the unit number of the first-1 layer, lambda is the wavelength, x, y is the abscissa of the unit +.>d is the interlayer distance, and the interlayer spacing is generally 1 to 3 wavelengths. The radiation sound pressure of each unit of each layer is equal to the sum of the radiation sound pressure of each unit of the previous layer reaching the position. Thus, the association between the latter layer and the former layer can be written as: />Wherein->For each layer of input values, +.>Representing weights +.>Indicating bias, l is the number of layer sequences, +.>Representing dot product. Here->Phi is the additional phase value of each layer of supersurface, < >>Where w is the transmission matrix of acoustic diffraction, t is the transmission coefficient of the supersurface, when the supersurface adjusts only the phase but not the amplitude,
step 4: constructing a super neural network:
with an M-layer super-surface M x n super-surface super-neural network, the first super-surface layer corresponds to the input layer of the conventional neural network, the last super-surface layer corresponds to the output layer of the conventional neural network, and the middle (M-2) layer corresponds to the hidden layer of the conventional neural network.
Step 5: setting a loss function loss:
wherein:
k is a coefficient, N is the number of units, i.e. m x N
p＝0.001·ones(N)
Wherein label is a label, and output is a sound field distribution matrix of an output plane in an iterative process. Here loss can be divided into two parts, the former part acting mainly on the amplitude of the sound field and the latter part acting mainly on the phase of the sound field.
Step 6: the phase of each layer of super neural network is initialized, and each primitive of each layer of super surface randomly generates the phase.
Step 7: and iterating by using Python software and a Tensorflow deep learning framework, and setting an optimization target to minimize a loss function loss.
Step 8: and after a plurality of iterations, outputting the phase value of the super surface of each layer.
Step 9: verifying trained superneural networks with test sets
And inputting the test set, and evaluating the sound field of the output plane. If the sound field distribution meets the requirement, iteration is not continued, and if the sound field distribution still does not meet the requirement, the coefficient k and the training times are adjusted to continue iteration.
The beam amplitude distribution after splitting on the receiving surface generally has a relatively regular doughnut shape and has a helical phase that is dependent on the order.
Example 1:
in this embodiment, the ±1-order vortex beam splitting is taken as an example, and further illustrates that the beam splitting of the positive and negative order vortices is realized through an acoustic superneural network.
The super surface is divided into 4 layers, the number of units of each layer is 56 x 56, only phase modulation is used, and the super surface comprises the following steps:
step 1: and randomly generating sound source data sets with topological charge numbers of +1 and-1 in different initial phases, wherein the sound source data sets are randomly divided into two parts, one part is a training set and the other part is a test set.
Step 2: generating labels of receiving planes, wherein the labels are inscribed circles in areas where +1-order vortex energy is concentrated in the upper left corners 28 x 28, the inscribed circles in areas where-1-order vortex energy is concentrated in the lower right corners 28 x 28, meanwhile, setting the amplitude of the labels to be 1 in an energy concentrating area, the topological charge number of the phase is the same as that of the input vortex, and setting the phase and the amplitude of other areas to be 0.
Step 3: the training set is randomly divided into a plurality of groups, the groups are input into an acoustic superneural network, and the acoustic superneural network is simulated by a program and depends on Python software and Tensorflow deep learning frameworks. The framework has the function of automatically solving the gradient, and sets the optimization target as loss minimization. After setting the optimization target and the iteration times, the Tensorflow automatically calculates the gradient according to the iteration, thereby updating the additional phase value.
Step 4: after the iteration is generally carried out until the loss is stable, the sound field of the output plane is continuously iterated, so that the iteration times can be determined by observing the loss value. If the sound field still cannot meet the requirements after loss stabilization, the neural network can be optimized by adjusting the coefficient k, and the k value is usually 0.001-0.1.
Step 5: after the iteration is completed, additional phase values of the super-surface of each layer are output, and the structural parameters of the super-surface can be determined.
As shown in fig. 2, which is a schematic diagram of the working principle of the present invention, the super-surface part is a main part of the present invention, the super-surface is equal to the receiving plane area, the sound source emitting surface area (the number of the units is 28×28) is a quarter of the super-surface area, and the centers of the parts are on the same axis.
The vortex emitted by the sound source corresponds to the training set and the test set, and the sound field on the receiving surface corresponds to the tag.
The vortex emitted by the sound source presents +1st-order vortex after 4 layers of super surfaces are trained, and most of energy is concentrated in the upper left corner of the receiving plane. And the vortex with different initial phase distributions can basically keep the vortex shape and the topological charge number thereof.
Fig. 3 is a view showing the sound field of the receiving plane of embodiment 1, and fig. (a) shows the phase distribution on the receiving plane after +1-order vortex beam splitting; graph (b) shows the amplitude distribution on the receiving plane after +1 order vortex beam splitting; FIG. (c) shows the phase distribution on the receiving plane after-1 order vortex beam splitting; graph (d) shows the amplitude distribution on the receiving plane after-1 order vortex beam splitting. It can be seen that the +1 order vortex is mostly concentrated in the upper left black circle, the-1 order vortex is mostly concentrated in the lower right black circle, and the corresponding topological charge-related phase planes are respectively reserved.
Example 2:
this embodiment is substantially the same as embodiment 1 except that the embodiment employs a 3 rd order vortex beam splitting. This example serves to illustrate that the method of the present invention is applicable not only to a particular order of swirl, but to all orders of swirl.
FIG. 4 shows the +3 order vortex beam splitting of example 2, and FIG. (a) shows the phase distribution on the receiving plane after +3 order vortex beam splitting; graph (b) shows the amplitude distribution on the receiving plane after +3-order vortex beam splitting; FIG. (c) shows the phase distribution on the receiving plane after-3-order vortex beam splitting; graph (d) shows the amplitude distribution on the receiving plane after-3 rd order vortex beam splitting. It can be seen that the +3 order vortex is mostly concentrated in the upper left black circle, the-3 order vortex is mostly concentrated in the lower right black circle, and the corresponding topological charge-related phase planes are respectively reserved.
Example 3:
this embodiment is substantially the same as embodiment 1 except for the position of this embodiment after vortex beam splitting. The embodiment is mainly used for explaining the advantage of great control freedom of the method, and the vortex emergence position can be changed by changing the setting of the tag.
FIG. 5 shows the vortex beam splitting case of +3 order, (a) shows the phase distribution on the receiving plane after vortex beam splitting of +1 order; (b) The graph shows the amplitude distribution on the receiving plane after +1-order vortex beam splitting; (c) The diagram shows the phase distribution on the receiving plane after-1 order vortex beam splitting; (d) The graph shows the amplitude distribution on the receiving plane after-1 order vortex beam splitting. It can be seen that the vast majority of the energy of the +1 order vortex is concentrated in the left black circle, the vast majority of the energy of the-1 order vortex is concentrated in the right black circle, and the corresponding topological charge number-related phase surfaces are respectively reserved in the black circles.
Claims (4)
1. The method for designing the sound vortex beam splitter based on machine learning is characterized by comprising the following steps of:
(1) Constructing training set and testing set data with different initial phases and topological charge numbers and corresponding labels;
(2) Simulating actual propagation conditions of sound waves in the device according to the sound propagation equation: the relation between the back layer and the front layer of the super surface is as follows:wherein (1)>For each layer of input values, +.>Representing weights +.>Representing bias, l is the number of layers, and "o" represents dot product; />Phi is the additional phase value of each layer of supersurface, < >>Wherein w is the transmission matrix of acoustic diffraction, t is the transmission coefficient of the super surface, when the super surface adjusts only the phase but not the amplitude +.>
(3) Constructing an acoustic superneural network according to an acoustic propagation equation: constructing a super-surface super-neural network of M layers of super-surfaces M x n, wherein the first layer of super-surface corresponds to an input layer of a traditional neural network, the last layer of super-surface corresponds to an output layer of the traditional neural network, and the middle (M-2) layer corresponds to a hidden layer of the traditional neural network; wherein m is the number of units of each layer of neural network, m is the number of transverse units of the super surface, and n is the number of longitudinal units of the super surface;
(4) Setting a loss function, initializing an initial phase of each layer of neural network, performing iterative optimization, outputting relevant parameters of the super surface of each layer after the optimization is finished, and verifying a training result by using a test set; the loss function loss is:
p＝0.001·ones(N)
wherein k is a coefficient, N is the number of units, i.e. m is N, label is a label, output is a sound field distribution matrix of an output plane in an iterative process, ones represents a matrix with each element being 1, and Im and Re represent respectively taking an imaginary part and a real part from a complex number;
(5) Parameters of the supersurfaces of the layers are determined.
2. The machine learning based acoustic vortex beam splitter design method of claim 1 wherein: in the step (1), the positive and negative scrolls with different orders of different initial phase distributions are marked as X 0 Is a training set; randomly generating another set of positive and negative different order vortices of different initial phase distribution from the training set, denoted as T 0 Is a test set; generating a label according to vortex beam splitting requirements.
3. The machine learning based acoustic vortex beam splitter design method of claim 1 wherein: in the step (4), initializing the phase of each layer of super neural network, and randomly generating the phase of each primitive of each layer of super surface; setting an optimization target as loss function loss minimization, and outputting phase values of the super surfaces of each layer after a plurality of iterations; and verifying the trained superneural network by using the test set, inputting the test set, and evaluating the sound field of the output plane.
4. The machine learning based acoustic vortex beam splitter design method of claim 3 wherein: if the sound field distribution meets the requirement, no iteration is continued; if the sound field distribution still does not meet the requirement, the coefficient k and the training times are adjusted to continue iteration until the requirement is met.
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