Sparse optimization method based on cross-shaped three-dimensional imaging sonar array

Abstract

The present invention a sparse optimization method based on cross-shaped three-dimensional imaging sonar array, comprising the following steps: first, constructing a beam pattern simultaneously applicable to a near field and a far field based on a cross-shaped array; then, constructing an energy function required by sparse optimization according to the beam pattern; then, introducing an array element position disturbance into a simulated annealing algorithm to increase the degree of freedom of the sparse process and increase the sparse rate of the sparse array, and using the simulated annealing algorithm to sparse optimization of the energy function; finally, after optimization, a sparse optimization cross-shaped array is obtained. The present invention ensures that the three-dimensional imaging sonar system has the desired performance at any distance, and greatly reduces the hardware complexity of the system. It provides an effective method to achieve high performance and ultra-low complexity 3D imaging sonar system.

Claims

1. A sparse optimization method based on cross-shaped three-dimensional imaging sonar array, comprising the following steps: constructing a beam pattern BP(W,u,v,,f.sub.j) simultaneously applicable to a near field and a far field based on a cross-shaped array, the beam pattern BP(W,u,v,,f.sub.j) being: $\mathrm{BP}\left(W,u,v,,f_j\right)=.Math.\underset{n=0}{\overset{N-1}{.Math.}}{}_n.Math.\exp \left[-j\frac{2f_j}{c}{y}_n.Math.v+\frac{y_n^2}{2}\right].Math..Math.\underset{m=1}{\overset{M}{.Math.}}{}_m\exp \left[-j\frac{2f_j}{c}{x}_m.Math.u+\frac{x_m^2}{2}\right].Math.$ wherein, W is a weight coefficient of the array, including a weight coefficient .sub.n of a vertical transmitting array and a weight coefficient .sub.m of a horizontal receiving array; f.sub.j is a transmitting frequency of a vertical beam in j direction; x.sub.m is a position of the m-th element of the horizontal receiving array; y.sub.n is a position of the nth element of the vertical transmitting array; c is a speed at which sound waves propagate in water;
=1/r1/r.sub.0; r is a target distance; r.sub.0 is a beam focusing distance;
u=sin .sub.asin .sub.a;
v=sin .sub.esin .sub.e; .sub.a is a horizontal beam-arrival direction; .sub.a is a horizontal beam-focusing direction; .sub.e is a vertical beam-arrival direction; .sub.e is a vertical beam-focusing direction; when =0, BP is a far field beam pattern; when 0, BP is a near field beam pattern; constructing an energy function E(W,A) required by sparse optimization according to the beam pattern BP(W,u,v,,f.sub.j), the energy function E(W,A) being: $E\left(W,A\right)={k_1\left({}_{\min }^{\max }\left(\underset{\left(u,v\right)}{.Math.}\left(\frac{BP\left(W,,u,v,f_j\right)}{B{P}_{MAX}}-b_d\right)\right)d\right)}^2+k_2{A}^2+{k_3\left(R_o-R_d\right)}^2$ wherein, k.sub.1, k.sub.2 and k.sub.3 are the weight coefficients of the corresponding items; b.sub.d is the desired beam pattern sidelobe peak; R.sub.d is the ratio of the maximum weight coefficient to the minimum weight coefficient in the weight coefficient matrix W; Ro is the ratio of the desired maximum weight coefficient to the minimum weight coefficient; the value range of u and v corresponds to the part of the sidelobe beam whose intensity is greater than b.sub.d; .sub.min and .sub.max represent the minimum and maximum values of S, respectively; introducing an array element position disturbance into a simulated annealing algorithm, and using the simulated annealing algorithm to sparse optimization of the energy function E(W,A); and after optimization, obtaining a sparse optimization cross-shaped array.

2. The sparse optimization method based on cross-shaped three-dimensional imaging sonar array according to claim 1, wherein, the introduction of an array element position disturbance into the simulated annealing algorithm comprises: when the selected array element weight coefficient is not 0, that is, the selected array is in the on state, caching (.sub.temp) the array element weight coefficient and the current array element position p.sub.xy=(x.sub.m, y.sub.n); closing the array element, updating the array element weight coefficient matrix W and the number of array elements A, and calculating the energy function; when the energy function decreases, accepting the state and selecting the next random array element; and when the energy function increases, turning on the array element again, and the weight coefficient adds a random disturbance within a certain range, and a disturbance is added to the original position p.sub.xy of the array element at the same time.

3. The sparse optimization method based on cross-shaped three-dimensional imaging sonar array according to claim 2, wherein, in last step, the formula for adding disturbance is: $\left(x_m,y_n\right)=\{\begin{array}{cc}{p}_{\mathrm{xy}}+\left(\mathrm{unifrnd}\left(-0.1{}_{\min },0.1{}_{\min }\right),0\right),& \mathrm{if}\mathrm{receiving}\mathrm{array}\\ p_{\mathrm{xy}}+\left(\mathrm{unifrnd}\left(-0.1{}_{\min },0.1{}_{\min }\right)\right),& \mathrm{if}\mathrm{transmitting}\mathrm{array}\end{array}$ wherein, unifrnd(0.1.sub.min, 0.1.sub.min) is a function of the software MATLAB, which means that a random number is generated in the interval (0.1.sub.min, 0.1.sub.min).

4. The sparse optimization method based on cross-shaped three-dimensional imaging sonar array according to claim 1, wherein, the calculation formula of .sub.min and .sub.max is: ${}_{\min }=-\frac{2{}_{\min }}{D^2}{}_{\max }=\frac{2{}_{\min }}{D^2}$ wherein, .sub.min is the wavelength corresponding to the highest frequency among all emitted sound waves; D is the array aperture.

5. The sparse optimization method based on cross-shaped three-dimensional imaging sonar array according to claim 1, wherein, the transmitting frequency of the vertical beam in j direction is 205 kHz300 kHz, and the step is 5 kHz, j=1, 2, . . . , 20.

6. The sparse optimization method based on cross-shaped three-dimensional imaging sonar array according to claim 1, wherein, setting k.sub.1=10000, k.sub.2=20000, k.sub.3=1, b.sub.d=22 dB.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings may be obtained from these drawings without creative work.

(2) FIG. 1 is a flowchart of the array sparse optimization process of the present invention;

(3) FIG. 2 is a schematic diagram of dividing the far field and near field focusing intervals of the present invention;

(4) FIG. 3 is a schematic diagram of array disturbance in the sparse optimization process of the present invention;

(5) FIG. 4 is a schematic diagram of the sparse cross-shaped array of the present invention;

(6) FIG. 5 is a near field beam pattern of the obtained cross-shaped array of the present invention;

(7) FIG. 6 is a far field beam pattern of the obtained cross-shaped array of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

(8) In order to make the objectives, technical solutions, and advantages of the present invention clearer, the following further describes the present invention in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, and do not limit the protection scope of the present invention.

(9) In this embodiment, the initial array is a 100-element vertical transmitting array and a 100-element horizontal receiving array. The transducers are evenly distributed in a rectangular plane at half-wavelength spacing. The horizontal spacing and vertical spacing of the transducers are equal. The transmitting frequency f.sub.j is 205 kHz-300 kHz, and the step is 5 kHz, and the sound velocity is c=1500 m/s.

(10) As shown in FIG. 1, the sparse optimization method based on cross-shaped three-dimensional imaging sonar array provided by this embodiment comprises the following steps: S101, based on the multi-frequency transmission algorithm and the cross-shaped array, a beam pattern BP(W,u,v,,f.sub.j) simultaneously applicable to a near field and afar field is provided, the beam pattern BP(W,u,v,,f.sub.j) is:

(11) $\mathrm{BP}\left(W,u,v,,f_j\right)=.Math.\underset{n=0}{\overset{N-1}{.Math.}}{}_n.Math.\exp \left[-j\frac{2f_j}{c}{y}_n.Math.v+\frac{y_n^2}{2}\right].Math..Math.\underset{m=1}{\overset{M}{.Math.}}{}_m\exp \left[-j\frac{2f_j}{c}{x}_m.Math.u+\frac{x_m^2}{2}\right].Math.$ wherein, W is the weight coefficient of the array, including a weight coefficient .sub.n of the vertical transmitting array and a weight coefficient .sub.m of the horizontal receiving array; f.sub.j is the transmitting frequency 205 kHz-300 kHz in the vertical beam j direction, and the step is 5 kHz, j=1, 2, . . . , 20; x.sub.m is the position of the m-th element of the horizontal receiving array, x.sub.m=m.sub.min/2, m=1, 2, . . . , 100; .sub.min is the wavelength corresponding to the highest frequency among all emitted sound waves. y.sub.n is the position of the n-th element of the vertical transmitting array, y.sub.n=n.sub.min/2, n=1, 2, . . . , 100; c is the speed at which sound waves propagate in water 1500 m/s;
=1/r1/r.sub.0; r is the target distance, detecting a target within 50 meters; r.sub.0 is the beam focusing distance, the focusing range is 50 meters;
u=sin .sub.asin .sub.a, the value range u[0,1];
v=sin .sub.esin .sub.e, the value range v[0,1]; .sub.a is the horizontal beam arrival direction, the viewing angle range is 60; .sub.a is the horizontal beam focusing direction, the viewing angle range is 60; .sub.e is the vertical beam arrival direction, the viewing angle range is 60; .sub.e is the vertical beam focusing direction, the viewing angle range is 60; S102, an energy function E(W,A) required by sparse optimization according to the beam pattern BP(W,u,v,,f.sub.j) is constructed.

(12) As shown in FIG. 2, the entire observation scene is divided into two parts, the near field and the far field; when =0, BP(W,u,v,,f.sub.j) is a far field beam pattern; when 0, BP(W,u,v,,f.sub.j) is a near field beam pattern.

(13) The near field is composed of multiple focus intervals, and each focus interval selects a beam focus distance r.sub.0, then the boundaries of the focus interval are r.sub.0 and r.sub.0+, that is, the Depth of Field (DOF) is [r.sub.0,r.sub.0+]. r.sub.0 corresponds to .sub.max, r.sub.0+ corresponds to .sub.min.

(14) In the depth of field, the main lobe attenuation is less than 3 dB. An energy function E(W,A) required by sparse optimization according to the beam pattern is constructed, the energy function E(W,A) is:

(15) $E\left(W,A\right)={k_1\left({}_{\min }^{\max }\left(\underset{\left(u,v\right)}{.Math.}\left(\frac{BP\left(W,,u,v,f_j\right)}{B{P}_{MAX}}-b_d\right)\right)d\right)}^2+k_2{A}^2+{k_3\left(R_o-R_d\right)}^2$ wherein, k.sub.1, k.sub.2 and k.sub.3 are the weight coefficients of the corresponding items, setting k.sub.1=10000, k.sub.2=20000, k.sub.3=1; b.sub.d is the desired beam pattern sidelobe peak, b.sub.d is 22 dB; Ro is the ratio of the maximum weight coefficient to the minimum weight coefficient in the weight coefficient matrix W; R.sub.d is the ratio of the desired maximum weight coefficient to the minimum weight coefficient, R.sub.d is 3; the value range of u and v corresponds to the part of the sidelobe beam whose intensity is greater than b.sub.d; .sub.min and .sub.max represent the minimum and maximum values of respectively; the calculation formula of .sub.min and .sub.max is:

(16) ${}_{\min }=-\frac{2{}_{\min }}{D^2}{}_{\max }=\frac{2{}_{\min }}{D^2}$ wherein, .sub.min is the wavelength corresponding to the highest frequency among all emitted sound waves, .sub.min is 2.5 mm; D is the array aperture, D is 25 cm. S103, introducing an array element position disturbance into a simulated annealing algorithm, and using the simulated annealing algorithm to sparse optimization of the energy function E(W,A).

(17) An array element position disturbance is introduced into the simulated annealing algorithm to increase the degree of freedom of the sparse process and increase the sparse rate of the sparse array. As shown in FIG. 3, the distance between the array elements is d.sub.i(i=1, 2, . . . 100), and the array elements deviate from their original positions due to position disturbances. The horizontal and vertical deviation distances are x and y respectively. Specifically, the formula for adding disturbance is: a. if the selected array element weight coefficient is not 0, that is, the selected array is in the on state, the array element weight coefficient and the current array element position p.sub.xy=(x.sub.m, y.sub.n) are cached (.sub.temp). b. closing the array element, updating the array element weight coefficient matrix W and the number of array elements A, and calculating the energy function. c. when the energy function decreases, accepting the state and selecting the next random array element. d. when the energy function increases, turning on the array element again, and the weight coefficient adds a random disturbance within a certain range, and a disturbance is added to the original position p.sub.xy of the array element at the same time. the formula for adding disturbance is:

(18) $\left(x_m,y_n\right)=\{\begin{array}{cc}{p}_{\mathrm{xy}}+\left(\mathrm{unifrnd}\left(-0.1{}_{\min },0.1{}_{\min }\right),0\right),& \mathrm{if}\mathrm{receiving}\mathrm{array}\\ p_{\mathrm{xy}}+\left(\mathrm{unifrnd}\left(-0.1{}_{\min },0.1{}_{\min }\right)\right),& \mathrm{if}\mathrm{transmitting}\mathrm{array}\end{array}$ wherein, unifrnd(0.1.sub.min, 0.1.sub.min) is a function of the software MATLAB, which means that a random number is generated in the interval (0.1.sub.min, 0.1.sub.min). S104, after S103 optimization, a sparse optimization cross-shaped array can be obtained, the number of array elements is 120, and the weight coefficient is between 0.5 and 1.5, as shown in FIG. 4. In addition, the beam pattern of the obtained array in the near field is shown in FIG. 5, and the sidelobe is suppressed at 22 dB; the beam pattern in the far field is shown in FIG. 6, and the sidelobe is also suppressed at 22 dB.

(19) A cross-shaped array that satisfies the three-dimensional imaging sonar system with desired performance at any distance can be constructed by using the sparse optimization method of the cross-shaped three-dimensional imaging sonar array provided by this embodiment.

(20) The specific implementations described above describe the technical solutions and beneficial effects of the present invention in detail. It should be understood that the above descriptions are only the most preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, additions, and equivalent replacements within the scope shall be included in the protection scope of the present invention.