CN112882039A - Array sparse method - Google Patents

Array sparse method Download PDF

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CN112882039A
CN112882039A CN202110031812.2A CN202110031812A CN112882039A CN 112882039 A CN112882039 A CN 112882039A CN 202110031812 A CN202110031812 A CN 202110031812A CN 112882039 A CN112882039 A CN 112882039A
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array element
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CN112882039B (en
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张晗
郑剑锋
白碧超
王峰
沈立峰
林振源
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Institute of Acoustics CAS
China Agricultural University
Changzhou University
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China Agricultural University
Changzhou University
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    • G—PHYSICS
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Abstract

The application discloses an array sparse method, which comprises the steps of collecting array data by using a full-focusing algorithm and acquiring all excitation receiving combinations; and calculating a directional diagram of the array by utilizing a binary particle swarm algorithm based on the array data and the excitation receiving combination, and thinning the array. According to the method, the layout of each element in the array is optimized through a binary particle swarm algorithm, so that the sparse array has better imaging quality than a reference full array, and the efficiency of full-matrix capture or a total focusing method can be improved.

Description

Array sparse method
Technical Field
The invention relates to the technical field of ultrasonic detection, in particular to an array sparse method.
Background
The basic idea of the ultrasonic phased array technology is derived from the radar electromagnetic wave phased array technology, and the phased array radar is formed by a large number of sub antenna arrays which are arranged according to a certain rule or shape combination, and forms flexible and variable focusing radar beams in a certain space-time range by controlling the amplitude and the phase of electromagnetic beams transmitted by each sub antenna array. The ultrasonic phased array is a transducer array consisting of a plurality of piezoelectric transducer elements, and can realize the phase control of ultrasonic waves.
Currently, the Total Focusing Method (TFM) in the related art uses full array acquisition, which means that a single array element excites all array elements for reception, and each array element is triggered in turn until all combinations of excitation and reception are used to obtain complete detection information. In the post-processing stage, focusing imaging of any position in the examination region is achieved by flexibly delaying the setting and reconstructing the various phased beams.
However, in the course of implementing the present invention, the inventors found that at least the following problems exist in the related art: the aperture of a transducer array of the high-resolution ultrasonic phased array detection system is large, the distance between elements is smaller than half of the wavelength, meanwhile, the number of required array elements is large, the hardware cost is high, the total focusing method is too time-consuming to calculate, and the high-resolution ultrasonic phased array detection system has limitations.
Disclosure of Invention
In view of the above-mentioned drawbacks or deficiencies in the related art, it is desirable to provide an array thinning method capable of thinning an array to a suitable level without degrading sound field characteristics, so that an optimized sparse array has better performance than a reference full array, while improving processing efficiency.
The application provides an array sparse method, which comprises the following steps:
collecting array data by using a full-focusing algorithm, and acquiring all excitation receiving combinations;
and calculating a directional diagram of the array by utilizing a binary particle swarm algorithm based on the array data and the excitation receiving combination, and thinning the array.
Optionally, in some embodiments of the present application, the binary particle swarm algorithm is solved by the following steps, including:
calculating a fitness value corresponding to each particle according to the speed and the position of each particle;
calculating the local optimal value of each particle and the global optimal value of the whole population according to the fitness value;
and according to the global optimal value, carrying out speed updating and position updating on the particles.
Optionally, in some embodiments of the present application, the position update of the particle is calculated by:
Figure BDA0002892646700000021
wherein, S (v)jk(t)) represents the probability of the state update in the kth iteration for the kth dimension of the jth particle.
Optionally, in some embodiments of the present application, the full focus algorithm includes:
the full matrix acquisition model is used for exciting a single array element, receiving all the array elements simultaneously, and sequentially carrying out the steps until all the excited receiving combinations are obtained;
the two-dimensional full-focusing imaging geometric model is characterized in that a one-dimensional linear array probe is arranged on the surface of a two-dimensional isotropic uniform medium, a point defect is located in the medium, and an imaging region is located below the array.
Optionally, in some embodiments of the present application, the sound pressure of the single array element is calculated by the following formula:
Figure BDA0002892646700000022
wherein r represents the distance between the imaging point and the array element, k represents the wave number, theta represents the direction angle, omega represents the angular frequency, and a represents the width of the array element.
Optionally, in some embodiments of the present application, the paths of the excitation array element and the reception array element to the scattering point are calculated by:
Figure BDA0002892646700000023
Figure BDA0002892646700000024
wherein (x)i0) denotes an excitation array element, (x)j0) denotes a receiving array element, P (x)n,zm) The scattering point is indicated.
Optionally, in some embodiments of the present application, array element xiExcited, reflected by focusing point P and then formed by array element xjThe received acoustic propagation delay is calculated by:
Figure BDA0002892646700000031
wherein, tijpRepresenting the acoustic propagation delay and c the medium speed of sound.
Optionally, in some embodiments of the present application, the pixel value of any imaging point is calculated by:
Figure BDA0002892646700000032
wherein, I (x)n,zm) Representing pixel values, c representing the speed of sound of an acoustic wave in a medium, hijThe signal envelope of an echo signal received by the ith array element is shown when the ith array element is excited, and N is the number of the array elements.
Optionally, in some embodiments of the present application, the synthetic sound pressure in the sparse array is calculated by:
Figure BDA0002892646700000033
wherein, giRepresenting binary coefficients, gi1 indicates that the ith array element is in an active state, giA value of 0 indicates that the ith array element is in a quiescent state.
Optionally, in some embodiments of the present application, the directivity function of the acoustic beam in the sparse array is calculated by:
Figure BDA0002892646700000034
wherein, thetamIndicating the steering angle of the array.
In summary, the embodiment of the present application provides an array sparse method, which includes acquiring array data by using a full focus algorithm, acquiring all excitation receiving combinations, calculating a directional diagram of an array by using a binary particle swarm algorithm based on the array data and the excitation receiving combinations, and sparse the array. According to the embodiment of the application, the layout of each element in the array is optimized through a binary particle swarm algorithm, so that the sparse array has better imaging quality than a reference full array, and the efficiency of full-matrix capture or a total focusing method can be improved.
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Other features, objects and advantages of the present application will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, made with reference to the accompanying drawings in which:
fig. 1 is a schematic flowchart of an array sparse method according to an embodiment of the present disclosure;
FIG. 2 is a schematic diagram of a full array of 64 elements according to an embodiment of the present disclosure;
FIG. 3 is a directional diagram of the fully-optimized sparse array of FIG. 2 according to an embodiment of the present disclosure;
FIG. 4 is a graph illustrating iterative fitness value comparison between a genetic algorithm and a particle swarm algorithm provided in an embodiment of the present application;
FIG. 5 is a directional diagram of a full array of 51 elements provided by an embodiment of the present application;
fig. 6 is a TFM image using different arrays of point scattering provided by an embodiment of the present application;
FIG. 7 is an image of three point scatterings using different arrays according to an embodiment of the present application;
fig. 8 is a schematic diagram of a simulated imaging intensity distribution in a lateral direction compared with the whole array according to the embodiment of the present application.
Detailed Description
In order to make the technical solutions of the present application better understood, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
The terms "first," "second," "third," "fourth," and the like in the description and in the claims of the present application and in the drawings described above, if any, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the application described are capable of operation in sequences other than those illustrated or otherwise described herein.
Moreover, the terms "comprises," "comprising," and any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or modules is not necessarily limited to those steps or modules explicitly listed, but may include other steps or modules not expressly listed or inherent to such process, method, article, or apparatus.
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
For ease of understanding and explanation, the array thinning method provided by the embodiments of the present application is explained in detail below with reference to fig. 1 to 8.
Please refer to fig. 1, which is a flowchart illustrating an array sparse method according to an embodiment of the present application, the method including the following steps:
s101, collecting array data by using a full focusing algorithm, and acquiring all excitation receiving combinations.
Optionally, the full-focus algorithm in the embodiment of the present application includes a full-matrix acquisition model and a two-dimensional full-focus imaging geometric model. Specifically, the full-matrix acquisition model is used for exciting a single array element, all the array elements receive simultaneously, and the steps are sequentially carried out until all the excitation receiving combinations are obtained; a one-dimensional linear array probe in a two-dimensional full-focusing imaging geometric model is arranged on the surface of a two-dimensional isotropic uniform medium, a point defect is positioned in the medium, and an imaging area is positioned below the array. For example, in two-dimensional coordinate system xoz, the x-axis is along the array direction and parallel to the media surface, the z-axis is perpendicular to the media surface and pointing into the media, and the array is aligned on the x-axis.
Alternatively, the sound pressure of an individual array element is calculated by:
Figure BDA0002892646700000051
wherein r represents the distance between the imaging point and the array element, k represents the wave number, theta represents the direction angle, omega represents the angular frequency, and a represents the width of the array element.
Optionally, the paths of the excitation array element and the reception array element to the scattering point are calculated by:
Figure BDA0002892646700000052
Figure BDA0002892646700000053
wherein (x)i0) denotes an excitation array element, (x)j0) denotes a receiving array element, P (x)n,zm) The scattering point is indicated.
Optionally, array element xiExcited, reflected by focusing point P and then formed by array element xjThe received acoustic propagation delay is calculated by:
Figure BDA0002892646700000054
wherein, tijpRepresenting the acoustic propagation delay and c the medium speed of sound.
Alternatively, the pixel value of an arbitrary imaging point is calculated by the following equation:
Figure BDA0002892646700000061
wherein, I (x)n,zm) Representing pixel values, c representing the speed of sound of an acoustic wave in a medium, hijThe signal envelope of an echo signal received by the ith array element is shown when the ith array element is excited, and N is the number of the array elements.
Alternatively, the synthetic sound pressure in the sparse array is calculated by:
Figure BDA0002892646700000062
wherein, giRepresenting binary coefficients, gi1 indicates that the ith array element is in an active state, giA value of 0 indicates that the ith array element is in a quiescent state.
Optionally, the acoustic beam directivity function in the sparse array is calculated by:
Figure BDA0002892646700000063
wherein, thetamIndicating the steering angle of the array, e.g. theta, heremIs set to 0.
And S102, calculating a directional diagram of the array by using a binary particle swarm algorithm based on the array data and the excitation receiving combination, and sparsely arraying.
Optionally, in a solving process of a Binary Particle Swarm Optimization (BPSO), a fitness value corresponding to each Particle is calculated according to a speed and a position of each Particle; then, according to the fitness value, calculating a local optimal value of each particle and a global optimal value of the whole population; and further, according to the global optimal value, carrying out speed updating and position updating on the particles. In the embodiments of the present application, the determination is made by a predetermined condition, and if T is T ═ TmaxThen the global optimum is ended and output. Otherwise, repeating the steps and returning to the particle speed updating and the position updating.
For example, the fitness value of a particle is calculated by:
Fit＝ψ1*MSL+ψ2*MLW (8)
wherein psi1And psi2Is a coefficient value selected according to different optimization targets, msl (maximum Sidelobe levels) represents the maximum Sidelobe level, mlw (maximum Lobe width) represents the maximum beam width. It should be noted that ψ is a characteristic of the main lobe and the side lobe, which is to be considered1And psi2Are set to 1.
For another example, the velocity update of the particle is calculated by:
vjk(t+1)＝w(t)vjk(t)+c1R1k(t)[Yp-Yjk(t)]+c2R2k(t)[YG-Yjk(t)]
(9)
wherein, c1And c2Represents an acceleration factor, such as 2; v. ofjk(t) and Yjk(t) respectively representing the position and velocity of the kth dimension of the jth particle in the tth iteration;R1k(t) and R2k(t) represents a uniformly distributed random number between 0 and 1.
Figure BDA0002892646700000071
It should be noted that in order to control the overall search behavior of the particle, the particle velocity is limited to a bounded range. The embodiment of the application introduces a positive integer vmaxSo as to satisfy vjk(t)。
Figure BDA0002892646700000072
Wherein R is3k(t) represents a random number between 0 and 1, rmuRepresenting the probability of operating on the kth dimension of the jth particle.
As another example, the position update of the particle is calculated by:
Figure BDA0002892646700000073
wherein, S (v)jk(t)) represents the probability of the state update in the kth iteration for the kth dimension of the jth particle.
Exemplarily, please refer to fig. 2 and fig. 3, which are a directional diagram of a full array of 64 elements and a directional diagram of an optimized sparse array provided by an embodiment of the present application, respectively. In the embodiment of the application, the initial population size is 50, the iteration number is 200, and r ismuIs 0.2.
It can be seen from figure 2 that in the pattern of the full array of 64 elements there is a large side lobe around the main lobe, with MSL and MLW at-13.2455 dB and 2.1557 deg. respectively. And as can be seen from fig. 3, in the optimized sparse array, the sidelobe suppression effect is obvious, and the MSL is-19.0035 dB, and the MLW of-6 dB is 2.4620 °. In contrast, MSL was reduced by 5.758dB, but MLW was slightly widened.
Alternatively, please refer to fig. 4, which is an iterative fitness value comparison graph of Genetic Algorithm (GA) and particle swarm optimization in the embodiment of the present application, and the graph includes a convergence curve of the fitness values of the GA and the BPSO optimization process. It should be noted that, as can be seen from fig. 4, the minimum fitness value obtained by using the BPSO is significantly lower than that of the GA, the minimum fitness value of the BPSO is 1.59 lower than that of the GA, the BPSO converges faster, and the optimization effect is better. Therefore, the embodiment of the present application is feasible to use the BPSO as an optimization method of the one-dimensional sparse array. Further, from the convergence curve of BPSO, it can be seen that the final fitness value is reduced to approximately-16.8617 compared to the reference full array, which is the sum of the MSL of the optimized sparse array and the MLW of-6 dB. The optimized sparse array layout is as follows: "01011100011001101111111111111111111101011111111101101011", the number of array elements is reduced by 13, which will greatly improve the efficiency of Full Matrix Capture (FMC) or Total Focusing (TFM).
For example, please refer to fig. 5, which is a directional diagram of a full array of 51 elements according to an embodiment of the present application. For comparison, the present embodiments plot a full-array pattern with the same number of elements as the optimized sparse array, with the array parameters shown in table 1.
TABLE 1 complete array parameters
Width of cell 0.53mm
Pitch of cells 0.63mm
Center frequency 5MHz
Speed of sound 6300m/s
Bandwidth (-6dB) 50％
Note that MSL in fig. 5 is almost unchanged, but MLW is significantly increased, compared to the full array of 64 elements. The MSL of the full array containing 51 elements and the MLW of-6 dB were measured to be-13.2476 dB and 2.7064 degrees, respectively. As the number of elements in the entire array decreases, the MLW increases 0.5507 °. This is readily understandable, since reducing the number of array elements will inevitably lead to reducing the size of the effective aperture of the entire array transducer, but an optimized sparse array based on the entire array is obtained by minimizing the fitness value, which guarantees the size of the effective aperture, so the imaging resolution is hardly affected.
Alternatively, please refer to fig. 6 and fig. 7, which are an image of a TFM using different arrays of point scattering and an image of three point scattering using different arrays in the embodiment of the present application, respectively. In order to verify the TFM effect of the optimized sparse array, the embodiment of the present application performs simulation by MATLAB to compare the three arrays. It should be noted that the Point Spread Function (PSF) is the response of the imaging algorithm to a single ideal scattering point. In a linear acoustic field, the imaging result of any defect can be regarded as a convolution process of the defect and the actual scattering function of the PSF. Therefore, the embodiments of the present application use the PSF to characterize the spatial imaging characteristics of the TFM algorithm.
Wherein, the complete array parameters are shown in table 1, and the array element distribution of the sparse array is determined according to the optimization result of the directional diagram. The output of each element is a five period gaussian window tone burst centered at 5MHz with a-6 dB bandwidth of 50%. Fig. 6 (a), (b) and (c) show the results of scaling in dB, respectively, to show punctate scattering at (0, 20 λ) after generating a pixel based on the FMC signal, with an imaging region of 30mm × 40 mm.
As can be seen from fig. 6 (a), (b) and (c), in the imaging region of the full array of 64 elements and the full array of 51 elements, there are "ear" shaped regions on both sides of the ideal point elliptical region, which are generated by the beam sidelobe scanning. Wherein the size of the point defect of the 51-element full array is larger than that of the point defect of the 64-element full array. It should be noted that the artifacts of the optimized sparse array imaging almost disappear, the single point defect is clearer, the size of the point defect is close to that of a 64-element full array, and the imaging effect of the three arrays is consistent with the theoretical analysis of the corresponding directional pattern composite beam.
In order to quantitatively evaluate the imaging performance of the array, the embodiment of the application introduces the signal-to-noise ratio and the imaging resolution of the array performance index. Wherein, the signal-to-noise ratio (SNR) is the ratio of the reflected signal power to the noise power imaging, and the embodiment of the application calculates the peak amplitude I of the defect positionmaxAverage amplitude A of non-defective area in background portion of imageaverageTo measure the signal-to-noise ratio of the image and convert the unit to decibels, i.e.
Figure BDA0002892646700000091
The imaging resolution includes a vertical resolution and a horizontal resolution. The vertical resolution is related to the center frequency and bandwidth of the transducer, and the horizontal resolution is primarily determined by the main lobe width of the transmitted beam. To quantitatively assess the imaging resolution of an array, the examples of the present application introduce an API, i.e., a calculation by the following formula
Figure BDA0002892646700000092
Wherein A is-6dBRepresenting the area of the-6 dB region of the main peak point drop.
Note that the smaller the API, the better the imaging resolution of the array. The API of (a), (b) and (c) in fig. 6 are 0.6160, 0.6595 and 0.7180, respectively, and the SNR is 39.9085dB, 39.9452dB and 39.9125dB, respectively, by calculation in the example of the present application. The optimized sparse array has higher confidence than the 51-element full arrayNoise ratio, and API value is smaller. In addition, in the whole simulation process, compared with a 64-element full array, the imaging time of the optimized sparse array is reduced by more than 20%, which means that the sparse array can improve the efficiency of ultrasonic detection. Although the API of the optimized sparse array is slightly increased compared to the reference full array, the errors are small, which ensures that the image resolution of the sparse array is close to the image resolution of the reference full array on the one hand, and on the other hand by modifying the coefficient ψ of the fitting function according to the actual situation1And psi2The performance of the optimized sparse array can be biased towards resolution.
In order to study the imaging performance of the three arrays on the short-distance scatterers, three point-like scatterers are established in the embodiment of the application, and the distance between the three point-like scatterers is 2 mm. That is, the scattering positions were (-1.59 λ, 20 λ), (0, 20 λ), and (1.59 λ, 20 λ), respectively, and the TFM results for the three arrays are shown in FIG. 7. As can be seen from fig. 7, the full array of 64 elements has the strongest side lobe energy near the main lobe and there are significant artifacts, while the elliptical image area at the point scatter of the full array of 51 elements is the largest, indicating the lowest lateral resolution in these three arrays. It should be noted that the optimized sparse array has good imaging quality for three scattered points, artifacts near the defect point are obviously reduced, and the scattered point contour is clearly visible. Some one-dimensional patterns extracted from fig. 7 are plotted in fig. 8, which are distributed in the lateral direction and intersect the main lobe peak points.
Optionally, please refer to fig. 8, which is a schematic diagram of the simulated imaging intensity distribution in the lateral direction compared to the whole array in the embodiment of the present application. Wherein, the curve (r) represents a full array of 64 elements, the curve (r) represents a full array of 51 elements, and the curve (r) represents an optimized sparse array. As can be seen from fig. 8, the peak center difference represents the pixel peak dip level in the x direction at the z-axis depth of two adjacent scatterers in the image, recorded as Δ a. In fig. 8, the horizontal widths of the three array main lobes are very close to each other, but the Δ a of the optimized sparse array is minimal, indicating that two adjacent scatterers can be better distinguished. Also, the sparse array has the lowest side beams of the three arrays, so there are fewer imaging artifacts and a higher signal-to-noise ratio.
It should be noted that in order to study the generality of the proposed method, the embodiments of the present application compute the imaging performance of several one-dimensional full arrays with different numbers of array elements, corresponding optimized sparse arrays, and full arrays with the same number of array elements as the optimized sparse arrays. Array parameters referring to Table 1, the processor identified by Intel (R) core (TM) i7-8750CPU @2.20GHz was used in the embodiment of the present application and the operating environment was MATLAB R2015b, the results are shown in Table 2.
TABLE 2 Performance of different arrays
Figure BDA0002892646700000101
Figure BDA0002892646700000111
It should be noted that, for the descriptions of the same steps and the same contents in this embodiment as those in other embodiments, reference may be made to the descriptions in other embodiments, which are not described herein again.
The embodiment of the application provides an array sparse method, which comprises the steps of firstly utilizing a full-focusing algorithm to collect array data, acquiring all excitation receiving combinations, then utilizing a binary particle swarm algorithm to calculate a directional diagram of an array based on the array data and the excitation receiving combinations, and sparse the array. According to the embodiment of the application, the layout of each element in the array is optimized through a binary particle swarm algorithm, so that the sparse array has better imaging quality than a reference full array, and the efficiency of full-matrix capture or a total focusing method can be improved.
The above description is only a preferred embodiment of the application and is illustrative of the principles of the technology employed. It will be appreciated by a person skilled in the art that the scope of the invention as referred to in the present application is not limited to the embodiments with a specific combination of the above-mentioned features, but also covers other embodiments with any combination of the above-mentioned features or their equivalents without departing from the inventive concept. For example, the above features may be replaced with (but not limited to) features having similar functions disclosed in the present application.

Claims (10)

1. An array sparseness method, comprising:
collecting array data by using a full-focusing algorithm, and acquiring all excitation receiving combinations;
and calculating a directional diagram of the array by utilizing a binary particle swarm algorithm based on the array data and the excitation receiving combination, and thinning the array.
2. The array sparseness method of claim 1, wherein said binary particle swarm algorithm is solved by the steps comprising:
calculating a fitness value corresponding to each particle according to the speed and the position of each particle;
calculating the local optimal value of each particle and the global optimal value of the whole population according to the fitness value;
and according to the global optimal value, carrying out speed updating and position updating on the particles.
3. The array sparseness method of claim 2, wherein the particle location update is calculated by:
Figure FDA0002892646690000011
wherein, S (v)jk(t)) represents the probability of the state update in the kth iteration for the kth dimension of the jth particle.
4. The array sparseness method of claim 1, wherein said full focus algorithm comprises:
the full matrix acquisition model is used for exciting a single array element, receiving all the array elements simultaneously, and sequentially carrying out the steps until all the excited receiving combinations are obtained;
the two-dimensional full-focusing imaging geometric model is characterized in that a one-dimensional linear array probe is arranged on the surface of a two-dimensional isotropic uniform medium, a point defect is located in the medium, and an imaging region is located below the array.
5. The array sparseness method of claim 4, wherein the acoustic pressure of said single array element is calculated by:
Figure FDA0002892646690000012
wherein r represents the distance between the imaging point and the array element, k represents the wave number, theta represents the direction angle, omega represents the angular frequency, and a represents the width of the array element.
6. The array sparseness method of claim 4, wherein the path of the excitation array element and the reception array element to the scattering point is calculated by:
Figure FDA0002892646690000021
Figure FDA0002892646690000022
wherein (x)i0) denotes an excitation array element, (x)j0) denotes a receiving array element, P (x)n，zm) The scattering point is indicated.
7. The array sparseness method of claim 6, wherein array element xiExcited, reflected by focusing point P and then formed by array element xjThe received acoustic propagation delay is calculated by:
Figure FDA0002892646690000023
wherein, tijpRepresenting the acoustic propagation delay and c the medium speed of sound.
8. The array thinning method according to claim 7, wherein the pixel value of any imaging point is calculated by the following formula:
Figure FDA0002892646690000024
wherein, I (x)n，zm) Representing pixel values, c representing the speed of sound of an acoustic wave in a medium, hijThe signal envelope of an echo signal received by the ith array element is shown when the ith array element is excited, and N is the number of the array elements.
9. The array sparseness method of claim 5, wherein a synthetic acoustic pressure in the sparse array is calculated by:
Figure FDA0002892646690000025
wherein, giRepresenting binary coefficients, gi1 indicates that the ith array element is in an active state, giA value of 0 indicates that the ith array element is in a quiescent state.
10. The array sparseness method of claim 9, wherein the acoustic beam directivity function in the sparse array is calculated by:
Figure FDA0002892646690000026
wherein, thetamIndicating the steering angle of the array.
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