A theoretical and experimental study on the separation method of the incident sound field based on a small-scale vector sensor is proposed in this study, with the aim of resolving the problem of separation and acquisition of an incident sound field under the interference of near-field sound scattering from a cylindrical shell in water. The method of identifying and separating sound waves obtained under plane wave conditions is extended to complex sound-field conditions. Simulation and experimental results show that the vector separation method can greatly reduce the sound pressure amplitude and the phase deviation of the incident sound field, which is affected by near-field scattering from the cylindrical surface. The separation accuracy is related to the deviation angle and the distance from the target surface. The maximum deviation of the pressure amplitude is less than 1 dB, and the phase deviation is less than 3°. This method can effectively suppress the near-field scattering of the cylindrical shell and improve the separation accuracy of the incident sound field. The research results have reference value for a range of practical engineering applications.
The cylindrical shell structure is the most common form of an underwater sports platform. Due to the influence of scattering near the shell surface, the incident acoustic signal received by a sensor on the shell surface in the sound field will display severe distortion. Incident sound field separation is used to study the suppression of near-field scattering on the surface of the shell and accurately obtain the amplitude and phase information of the incident sound field. Active acoustic feature control [
At present, the near-field acoustic holography (NAH) method is mainly used to examine the distribution of the sound field and perform the separation of the incident sound field on the surface of the cylindrical shell [
Acoustic vector sensors can simultaneously obtain a scalar sound pressure and a three-dimensional particle velocity. The combined processing of scalar and vector components has advantages over individual processing. Based on the underwater acoustic buoy in the form of a hollow ball, the distortion of the sound field caused by diffraction on the surface of the underwater acoustic device carrier was studied [
The acoustic field on the surface of a cylindrical shell is the superposition of the far-field incident wave and the surface near-field scattered wave. Based on the distribution of the surface acoustic field of the cylinder, this study proposes a method to separate the incident sound field by combining the processing of the sound pressure and the particle velocity. The obtained sound wave identification and the separation theory are extended to complex sound-field conditions, with the important characteristic of retaining the amplitude and phase information of the sound field. The relationships between the sound-field distribution on the surface of the cylinder and the separation error of the incident sound field with the deviation angle as well as distance are analyzed theoretically and numerically. The separation method of the incident sound field is verified using an actual cylindrical shell model sea test, and the measured separation error is given.
The acoustic field calculation of the near-field of the underwater target mainly uses the classical Rayleigh normal series solution and numerical solution. The normal series solution can be used to obtain the accurate sound-field solutions of several targets with regular geometric shapes. This can deeply reflect the physical mechanisms affecting the sound field and is a test benchmark for other numerical calculation methods. There is no strict analytical solution for the scattered sound field of a finite-length cylindrical shell. Nevertheless, the main source of near-field scattering of the shell is adjacent to the local surface. Therefore, when the wavelength of the sound wave is much smaller than the length of the cylindrical shell and the research object is far away from the end face of a cylindrical shell, the analytical solution of an infinitely long cylinder can be used to analyze the near-field and sound-field distribution law of a finite-length cylindrical shell.
As shown in Figure
Model of the surface acoustic field of an infinitely long rigid cylinder. (a) Three-dimensional. (b) Two-dimensional.
The derivatives of the Bessel function and the Hankel function of the first kind are obtained by the recursive formula.
By deriving the potential function corresponding to equation (
The total field of the target surface acoustic pressure and incoming wave velocity is
Considering the physical model geometry parameters and experimental verification frequency in practical applications, the cylinder radius is taken as 0.45 m, and the analysis frequency is selected as 4 kHz. The sum of the normal series of finite orders will produce a certain error depending on the number of terms used. However, it is generally considered best practice to take the highest number of terms as
For the distribution of the scattering sound field and total sound field of the cylinder (
Distribution of the sound field near the cylinder surface for a wave incident from the left. (a) Scattered sound field. (b) Total sound field.
Since the sensor is generally installed near the surface of the cylinder, the positions of 0.2 m, 0.3 m, and 0.4 m on the surface of the cylinder are selected, and the quantitative change of the sound field is observed, as shown in Figure
Azimuth characteristics of the near-field sound field at typical distances. (a) Scattered sound field. (b) Total sound field.
We focus on the sound-field distribution on the side of the incident sound field of the cylinder. From the distribution of sound pressure and phase with distance, we can clearly observe and understand the change and superposition of the three sound fields (incident
Distribution characteristics of the sound-field pressure after the cylindrical surface with distance (
According to the distribution of the incident and backscattered sound fields around the cylinder surface, the coordinate system shown in Figure
Sketch of receiving points near the cylinder surface.
Under the condition of plane wave incidence, the relationship between sound pressure and particle velocity is as follows:
Regardless of frequency, the wave impedance is
According to the mathematical expression linking the scalar sound pressure and the vibration speed, the linear weighted joint processing was used. That is,
The vibration velocity was multiplied by the impedance
Variation of the separation error of the sound pressure amplitude of the incident sound field with distance. (a) 0 degrees. (b) 30 degrees.
For the incident sound field, if
The sound field on the surface of a cylinder is the superposition of a far-field incident plane wave and a near-field scattered wave. The near-field scattered wave does not have the characteristics of a plane wave. The above equation (
As the propagations of the incident and backscattered sound fields are in opposite directions, the joint treatment of sound pressure and vibration velocity forms a unilateral directivity. The direction of the maximum pressure is very small (near
Using equation (
Separation results of the incident sound field on the surface of a cylinder. (a) Separated sound field. (b) Time-domain waveform. (c) Change in incident sound field at 0.75 m with azimuth.
The main scattered wave in the range of ±30° around the
Due to the attenuation of the scattering field, the sound pressure amplitude and phase separation error (deviation between the separation value and the theoretical value) of the incident sound field will decrease with the distance from the cylindrical surface. The calculation results for the amplitude and phase error at the deviation angles of two typical receiver points are shown in Figures
Variation of sound pressure phase separation error with distance in the incident sound field. (a) 0 degrees. (b) 30 degrees.
The phase separation error shows a similar trend. For the 30° azimuth deviation angle, the separation amplitude error is less than 5° after 0.3 m from the targeted surface as shown in Figure
In order to further verify the vector separation method of the incident sound field, a physical model of a single-layer cylindrical shell with a spherical cap on both sides and a finite length was examined by numerical and sea tests.
The near-field scattering of a finite-length axisymmetric cylindrical shell can be obtained by converting the weak form volume fraction in a three-dimensional space into the area fraction on a two-dimensional surface to obtain the scattered sound field [
The cylindrical shell model is shown in Figure
Model of a single-layer cylindrical shell.
Taking the geometric center of the cylindrical shell as the origin, the plane wave was incident along the negative
Similar to the calculation results of infinitely long columns, the total sound pressure amplitude scattered from the surface of the finite cylindrical shell fluctuates with distance, and the phase value varies relative to the incident sound field. As the distance from the cylinder increases, the amplitude and phase fluctuations decrease. At a distance of 0.6 m (
Distribution of sound pressure and phase with distance from the model. (a) Amplitude. (b) Phase.
Further analysis of the time-domain waveform and error of the incident sound field separation in the horizontal direction (
Variation of separation error of the incident sound field from the surface of the model. (a) Time-domain waveform. (b) Amplitude. (c) Phase.
Based on the numerical analysis, the single-layer cylindrical shell was used as the target to perform the incident sound field separation test. The layout of the offshore test system is shown in Figure
Seaborne layout of the incident sound field separation test.
In the test, in order to reduce the influence of other scatterings, the pulse width of the transmitted signal was reduced to 2 ms. Compared with the monitoring signal, affected by the near-field scattering of the target surface near the receiving point, the sound-field signal received by the test vector sensor is significantly superimposed.
Figure
Time-domain signal of the incident sound field separation test. (a) 0°. (b) 30°.
Amplitude error of the incident sound field separation test. (a) 0°. (b) 30°.
Phase error of the incident sound field separation test. (a) 0°. (b) 30°.
The results of the numerical and sea tests show that the combined treatment of sound pressure and vibration velocity can effectively suppress the scattering interference of the cylindrical target surface. High-precision information of the amplitude and phase of the sound pressure in the incident sound field was obtained by separation.
This paper presents a vector processing method for the separation of the incident sound field after scattering from the surface of a cylindrical shell and further analyzes the influence of the received sound between the double-layer cylinder and the scattering of the sensor itself. The theoretical analysis and experimental verification show that the linear combined processing of scalar sound pressure and vector vibration velocity can effectively suppress the scattered sound field from the cylindrical surface and, hence, separate and obtain high-precision incident sound field pressure amplitude and phase information. The separation effect in front of the cylinder (0° direction) is better compared to off-axis positions. As the distance from the cylindrical surface increases, the amplitude and phase separation deviation of the incident sound field gradually decreases. At a typical distance acceptable for practical applications, the amplitude deviation of the measured incident sound pressure is less than 1 dB, and the phase deviation is less than 3°. It has certain engineering application value in underwater acoustic measurement, navigation, and so on.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This project was funded by the Ship Fund Project (7131304).