CN111342908A - Beam focusing sound field processing method and device and electronic equipment - Google Patents
Beam focusing sound field processing method and device and electronic equipment Download PDFInfo
- Publication number
- CN111342908A CN111342908A CN202010095039.1A CN202010095039A CN111342908A CN 111342908 A CN111342908 A CN 111342908A CN 202010095039 A CN202010095039 A CN 202010095039A CN 111342908 A CN111342908 A CN 111342908A
- Authority
- CN
- China
- Prior art keywords
- sound field
- sound
- information
- data
- propagation
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Images
Classifications
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B11/00—Transmission systems employing sonic, ultrasonic or infrasonic waves
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04R—LOUDSPEAKERS, MICROPHONES, GRAMOPHONE PICK-UPS OR LIKE ACOUSTIC ELECTROMECHANICAL TRANSDUCERS; DEAF-AID SETS; PUBLIC ADDRESS SYSTEMS
- H04R3/00—Circuits for transducers, loudspeakers or microphones
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04S—STEREOPHONIC SYSTEMS
- H04S7/00—Indicating arrangements; Control arrangements, e.g. balance control
- H04S7/30—Control circuits for electronic adaptation of the sound field
Landscapes
- Engineering & Computer Science (AREA)
- Signal Processing (AREA)
- Physics & Mathematics (AREA)
- Acoustics & Sound (AREA)
- Computer Networks & Wireless Communication (AREA)
- Circuit For Audible Band Transducer (AREA)
Abstract
The application provides a method and a device for processing a beam-focusing sound field and electronic equipment, wherein the method comprises the following steps: acquiring geometric data of a beam bunching mechanism and sound field data generated by a sound source; dividing a propagation path of the sound field data according to the geometric data of the beam bunching mechanism and the propagation characteristic information of the sound wave; and calculating sound field distribution information of the sound field data according to the division result of the propagation path to generate a nonlinear sound field model.
Description
Technical Field
The application relates to the field of underwater strong sound sources, in particular to a method and a device for processing a bunching sound field and electronic equipment.
Background
An Underwater Plasma Sound Source (UPSS) is a novel high-power Underwater strong Sound Source, is widely applied to the fields of ocean exploration, external shock wave lithotripsy, pipeline blockage removal and the like at present, and particularly has wide application prospects in the fields of Underwater acoustic countermeasure, Underwater ultra-remote secret communication, rapid and accurate Underwater target detection and the like. The acoustic pulse wave generated by the UPSS has weak or no directivity, cannot reach a desired intensity in a specified area without processing, and has a limited propagation distance. Currently, for single UPSS, the use of curved surface reflection technology to achieve directional radiation of acoustic pulse waves is considered to be the most effective solution to this problem.
However, the sound pulse wave is influenced by a series of complex 'nonlinear factors' in the reflection bunching process, so that accurate modeling of the UPSS bunching sound field is helpful for revealing bunching and propagation rules of the high-power sound pulse wave, enriching the directional radiation theory, and meanwhile, the sound source can be optimized, loss caused by nonlinearity is compensated in advance, the bunching effect is improved, and the sound intensity of the designated area is further improved.
At present, most of the modeling researches on the curved surface reflection bunching sound field are based on the smaller-power ESWL (external Shock Wave Lithotripsy) as the background, and the main problems exist: the influence of nonlinear factors and sound source parameters on the sound field is not fully considered; the theoretical waveform is usually adopted as the initial excitation waveform, and the error is large; many studies have considered the reflector as a rigid wall, ignoring the structural coupling dynamics of the reflector. In addition, at present, the analysis of the high-power UPSS bunched sound field mainly takes experimental research such as a high-speed photography method, a schlieren method, a distributed hydrophone array method and the like, but due to the influence of factors such as complex system assembly, shielding effect, small observation window and the like, the omnibearing measurement is difficult, and meanwhile, the experimental research period is long and the cost is high, so that the research of a nonlinear modeling method of the UPSS bunched sound field is urgently needed.
Disclosure of Invention
An embodiment of the present application provides a method and an apparatus for processing a beamforming sound field, and an electronic device, so as to solve the problems in the prior art.
In a first aspect, an embodiment provides a beamforming sound field processing method, including: acquiring geometric data of a beam bunching mechanism and sound field data generated by a sound source; dividing a propagation path of the sound field data according to the geometric data of the beam bunching mechanism and the propagation characteristic information of the sound wave; and calculating sound field distribution information of the sound field data according to the division result of the propagation path to generate a nonlinear sound field model.
In an alternative embodiment, dividing the propagation path of the sound field data according to the geometric data of the beamforming mechanism and the propagation characteristic information of the sound wave includes: acquiring reflection first focus information and reflection second focus information after coupling reflection at a sound source; and dividing the propagation path of the sound field data into a near sound source region, a beam-bunching region and a beam-bunching region according to the reflected first focus information and the reflected second focus information.
In an alternative embodiment, the generating a nonlinear sound field model by calculating sound field distribution information of the sound field data according to the division result of the propagation path includes: acquiring propagation medium parameters of sound field data; and analyzing the sound field distribution information of the sound field data in the near sound source area according to the propagation medium parameters to generate a near sound source area nonlinear sound field model.
In an alternative embodiment, the generating a nonlinear sound field model by calculating sound field distribution information of the sound field data according to the division result of the propagation path includes: acquiring pulse wave parameter information at the opening end face of a reflector of a sound source and a sound path difference caused by the reflector, and acquiring propagation medium parameters of sound field data; analyzing secondary sound field information generated by the reflector according to the pulse wave parameter information and the sound path difference; and analyzing the sound field distribution information of the sound field data in the beam-focusing area according to the secondary sound field information and the propagation medium parameters to generate a beam-focusing area nonlinear sound field model.
In an alternative embodiment, the generating a nonlinear sound field model by calculating sound field distribution information of the sound field data according to the division result of the propagation path includes: acquiring propagation medium parameters of a sound source; analyzing the medium distribution information of the sound field data in the near sound source area and the bunching area according to the propagation medium parameters; generating a calculation area according to the media division information; generating a sound field distribution diagram according to the calculation region; and analyzing the sound field distribution information of the sound field data in the near sound source area and the bunching area according to the sound field distribution diagram to generate a near sound source-bunching area nonlinear sound field model.
In an alternative embodiment, the generating a nonlinear sound field model by calculating sound field distribution information of the sound field data according to the division result of the propagation path includes: acquiring the sound channel characteristic information of a propagation medium of sound field data; generating propagation attenuation distribution information of sound field data in a converged area according to the acoustic channel characteristic information and the temperature gradient distribution calculation model; and analyzing the sound field distribution information of the sound field data in the converged area according to the propagation attenuation distribution information and the sound field distribution information of the sound field data in the converged area, and generating a converged beam area nonlinear sound field model.
In a second aspect, an embodiment provides a beamforming sound field processing apparatus, including: the data acquisition module is used for acquiring geometric data of the beam bunching mechanism and sound field data generated by a light source; the data processing module is used for dividing the propagation path of the sound field data according to the geometric data of the beam bunching mechanism and the propagation characteristic information of the sound waves; and the data calculation module is used for calculating sound field distribution information of the sound field data according to the division result of the propagation path and generating a nonlinear sound field model.
In an alternative embodiment, the region dividing module is configured to: acquiring reflection first focus information and reflection second focus information after coupling reflection at a sound source; and dividing the propagation path of the sound field data into a near sound source region, a beam-bunching region and a beam-bunching region according to the reflected first focus information and the reflected second focus information.
In an alternative embodiment, the data calculation module is configured to: acquiring propagation medium parameters of sound field data; and analyzing the sound field distribution information of the sound field data in the near sound source area according to the propagation medium parameters to generate a near sound source area nonlinear sound field model.
In an alternative embodiment, the data calculation module is further configured to: acquiring pulse wave parameter information at the opening end face of a reflector of a sound source and a sound path difference caused by the reflector, and acquiring propagation medium parameters of sound field data; analyzing secondary sound field information generated by the reflector according to the pulse wave parameter information and the sound path difference; and analyzing the sound field distribution information of the sound field data in the beam-focusing area according to the secondary sound field information and the propagation medium parameters to generate a beam-focusing area nonlinear sound field model.
In an alternative embodiment, the data calculation module is further configured to: acquiring propagation medium parameters of a sound source; analyzing the medium distribution information of the sound field data in the near sound source area and the bunching area according to the propagation medium parameters; generating a calculation area according to the media division information; generating a sound field distribution diagram according to the calculation region; and analyzing the sound field distribution information of the sound field data in the near sound source area and the bunching area according to the sound field distribution diagram to generate a near sound source-bunching area nonlinear sound field model.
In an alternative embodiment, the data calculation module is further configured to: acquiring the sound channel characteristic information of a propagation medium of sound field data; generating propagation attenuation distribution information of sound field data in a converged area according to the acoustic channel characteristic information and the temperature gradient distribution calculation model; and analyzing the sound field distribution information of the sound field data in the converged area according to the propagation attenuation distribution information and the sound field distribution information of the sound field data in the converged area, and generating a converged beam area nonlinear sound field model.
In a third aspect, an embodiment provides an electronic device, including: a memory for storing a computer program; a processor for performing the method of any of the preceding embodiments.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments of the present application will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and that those skilled in the art can also obtain other related drawings based on the drawings without inventive efforts.
Fig. 1 is an electronic device according to an embodiment of the present disclosure;
fig. 2 is a schematic scene of interaction between a terminal and a server according to an embodiment of the present application;
fig. 3 is a schematic structural diagram of a beam focusing mechanism for a beam focusing acoustic field according to an embodiment of the present application;
fig. 4 is a schematic flowchart of a beamforming sound field processing method according to an embodiment of the present application;
fig. 5 is a schematic diagram illustrating a division of a beam focusing sound field area according to an embodiment of the present application;
fig. 6 is a schematic flow chart of another beamforming sound field processing method according to an embodiment of the present application;
fig. 7 is a schematic flowchart of another beamforming sound field processing method according to an embodiment of the present application;
fig. 8 is a schematic structural diagram of a beamforming sound field processing apparatus according to an embodiment of the present application.
Icon: the system comprises an electronic device 1, a bus 10, a processor 11, a memory 12, a terminal 200, a server 100, a beam-focusing mechanism 300, a near sound source area 501, a beam-focusing area 502, a post-beam-focusing area 503, a beam-focusing sound field processing device 800, a data acquisition module 801, an area division module 802 and a data calculation module 803.
Detailed Description
The technical solutions in the embodiments of the present application will be described below with reference to the drawings in the embodiments of the present application.
As shown in fig. 1, the present embodiment provides an electronic apparatus 1 including: at least one processor 11 and a memory 12, one processor being exemplified in fig. 1. The processor 11 and the memory 12 are connected by a bus 10, and the memory 12 stores instructions executable by the processor 11 and the instructions are executed by the processor 11.
In one embodiment, the electronic device 1 may be a server 100. The server 100 obtains the geometric data of the beamforming mechanism 300 and the sound field data generated by the sound source at the terminal 200 through the communication network, divides the propagation path of the sound field data according to the geometric data of the beamforming mechanism 300 and the propagation characteristic information of the sound wave, calculates the sound field distribution information of the sound field data according to the division result of the propagation path, and generates the nonlinear sound field model describing the beamforming sound field according to the sound field distribution information.
In an embodiment, the electronic device 1 may be a terminal 200. The terminal 200 acquires the geometric data of the beam focusing mechanism 300 and the sound field data generated by the sound source, divides the propagation path of the sound field data according to the geometric data of the beam focusing mechanism 300 and the propagation characteristic information of the sound wave, calculates the sound field distribution information of the sound field data according to the division result of the propagation path, and generates a nonlinear sound field model for describing the beam focusing sound field according to the sound field distribution information.
As shown in fig. 2, which is an interaction schematic scenario of the server 100 and the terminal 200 in an embodiment of the present application, the terminal 200 may be a data acquisition device, and the server 100 may be a data processing server or a data storage server. The terminal 200 acquires geometric data of the beam focusing mechanism 300 and sound field data generated by a sound source, because the beam focusing mechanism 300 determines reflection efficiency, directivity and other related radiant energy of the acoustic pulse wave in the actual use process, the influence of nonlinear factors on the sound field analysis in a spatial domain is considered, the propagation path of the pulse wave in the sound field is further divided, and sound field distribution information is calculated for the divided regions respectively to obtain a final nonlinear sound field model. When the used bunching mechanism or the environment of the water area where the bunching mechanism is located changes, the parameters are input into the terminal 200 or the server 100, so that the time for generating the bunching sound field in a simulation mode can be shortened, the accuracy of the simulated bunching sound field is improved, and the bunching effect of the bunching mechanism 300 is detected.
In an embodiment, the communication network connection mode may be a wireless connection communication mode or a wired connection communication mode, and the wireless connection communication mode may be a wireless network transmission mode using a protocol IEEE802.11 a/b/c/n/g/ac for wireless communication (Wi-Fi), a wireless network transmission mode or a radio frequency transmission mode using a bluetooth device or a transmission device with a bluetooth protocol function, a Mobile network communication technology using a Global system for Mobile Communications (GSM), Code Division Multiple Access (CDMA), Wideband Code Division Multiple Access (WCDMA), time division synchronous code division multiple access (TD-SCDMA), Orthogonal Frequency Division Multiplexing (OFDM), and the like for communication.
The wired connection may be a manner of using a transmission line having a communication function such as an optical fiber, a network cable, or an electric wire, or another form having a capability equivalent to that of an optical fiber, a network cable, or an electric wire to transmit a data signal for communication purposes.
Please refer to fig. 3, which is a focusing sound field focusing mechanism 300 according to this embodiment, and the mechanism may be used in the electronic device shown in fig. 1 to implement the process of acquiring the geometric data of the focusing mechanism 300 and the sound field data generated by the sound source in the interactive scene shown in fig. 2, dividing the propagation path of the sound field data according to the geometric data of the focusing mechanism 300 and the propagation characteristic information of the sound wave, and calculating the sound field distribution information of the sound field data according to the division result of the propagation path. The beaming acoustic field beaming mechanism 300 may use a rotating ellipsoidal reflector or a rotating parabolic reflector as the reflective beaming mechanism for the UPSS directed radiation.
In one embodiment, the focusing mechanism 300 is a rotating ellipsoidal reflector, where a is the major semi-axis of the ellipsoid, b is the minor semi-axis, c is the half-focal length, h is the concave depth of the ellipsoidal reflector, and r is the opening radius; f1 is the first focus of reflection, F2 is the second focus of reflection, F1, F2 line is the sound axis of ellipsoid bowl. The radius of the opening of the reflector is 21.5cm, the depth of the concave surface is 16cm, the center of a sound source of the UPSS is 8cm, the UPSS adopts arc discharge, and the discharge electrode adopts an integrated structure and is vertically inserted into the hole at the bottom of the reflector.
Please refer to fig. 4, which is a beamforming sound field processing method provided in this embodiment, and the method may be executed by the electronic device 1 shown in fig. 1, and may be applied to the interactive scene shown in fig. 2 to implement a process of acquiring geometric data of the beamforming mechanism 300 and sound field data generated by the sound source, dividing a propagation path of the sound field data according to the geometric data of the beamforming mechanism 300 and propagation characteristic information of the sound wave, and calculating sound field distribution information of the sound field data according to a division result of the propagation path to obtain a nonlinear sound field model. The method comprises the following steps:
step 401: geometric data of the beamforming mechanism 300 and sound field data generated by the source are acquired.
In this step, there are many factors that influence the UPSS on the reflector of the beamforming mechanism 300, and since there are many nonlinear factors such as the structural coupling dynamics response of the reflector, diffraction, medium absorption, and acoustic pulse wave distortion when processing the beamforming sound field, it is necessary to perform segmented modeling and independent processing on various nonlinear factors, so that the beamforming sound field generated after the UPSS is described and reflected by the beamforming mechanism 300 is more accurate, and the defects of the beamforming mechanism 300 are more conveniently reflected.
Step 402: the propagation path of the sound field data is divided according to the geometric data of the beamforming mechanism 300 and the propagation characteristic information of the sound wave.
In this step, because the sound propagation process is influenced by different conditions, differences of mechanisms are generated according to nonlinear effects, and the influence effect of nonlinear factors of different sound field regions on the sound field is differentially divided into bunching sound field regions.
Step 403: and calculating sound field distribution information of the sound field data according to the division result of the propagation path to generate a nonlinear sound field model.
In this step, sound field distribution information is calculated respectively according to the division results of the sound field on the propagation path thereof, and corresponding nonlinear sound field models are generated respectively according to each divided region.
In one embodiment, as shown in fig. 5, the focusing sound field is divided into three parts, namely a near sound source region 501, a focusing region 502 and a post-focusing region 503, according to the geometric structure of the curved-surface reflection focusing mechanism 300.
The near-sound source region 501 is defined as a region from the first focus of the reflection of the ellipsoid rotating reflector to the propagation of the sound pulse wave to the inner surface of the reflector to the end face of the opening of the reflector.
The bunching region 502 is defined as the region of the reflected bunching region 502 where the acoustic pulse waves are coupled and reflected by the reflector to form a secondary wave source, and the inner surface of the reflector is to the second reflective focus of the ellipsoidal reflector.
The beam focusing region 503 is defined as a region where the acoustic pulse wave is focused and then attenuated to a small-amplitude acoustic pulse wave.
The beaming sound field corresponds to the near sound source area 501, the beaming area 502 and the beaming area 503, and the nonlinear effects have obvious differences, so that different areas are modeled in a segmented manner, and the problems of incomplete nonlinear factor consideration, large theoretical excitation waveform calculation error and difficult description of the beaming sound field in the practical application of the beaming mechanism 300 are solved.
Please refer to fig. 6, which is a beamforming sound field processing method provided in this embodiment, and the method may be executed by the electronic device 1 shown in fig. 1, and may be applied to the interactive scene shown in fig. 2 to implement a process of acquiring geometric data of the beamforming mechanism 300 and sound field data generated by the sound source, dividing a propagation path of the sound field data according to the geometric data of the beamforming mechanism 300 and propagation characteristic information of the sound wave, and calculating sound field distribution information of the sound field data according to a division result of the propagation path to obtain a nonlinear sound field model. The method comprises the following steps:
step 601: geometric data of the beamforming mechanism 300 and sound field data generated by the source are acquired. Please refer to the description of step 401 in the above embodiment.
Step 602: and acquiring the first reflected focus information and the second reflected focus information after coupling reflection at the sound source.
In this step, the reflected first focus information and the reflected second focus information after coupling reflection at the sound source are acquired for dividing the calculation region.
Step 603: the propagation path of the sound field data is divided into a near sound source region 501, a beam-bunching region 502, and a post-bunching region 503 according to the reflected first focus information and the reflected second focus information.
In this step, the near-acoustic source region 501 is defined as a region from the reflected first focus of the ellipsoidal rotating reflector to the inner surface to the end surface of the opening of the reflector where the acoustic pulse wave propagates, based on the reflected first focus information and the reflected second focus information after coupling and reflection. The bunching region 502 is defined as the region of the reflected bunching region 502 where the acoustic pulse waves are coupled and reflected by the reflector to form a secondary wave source, and the inner surface of the reflector is to the second reflective focus of the ellipsoidal reflector. The beam focusing region 503 is defined as a region where the acoustic pulse wave is focused and then attenuated to a small-amplitude acoustic pulse wave.
Step 604: propagation medium parameters of the sound field data are acquired.
In this step, the propagation medium may be a fluid, and the propagation medium parameter may be a reynolds number Re, a dimensionless number that may be used to characterize the fluid flow. In the near-sound source region 501, the amplitude of the sound pulse wave is large, and the nonlinear effect is remarkable, so that the sound pulse wave basically follows the spherical expansion law.
Step 605: according to the propagation medium parameters, the sound field distribution information of the sound field data in the near sound source area 501 is analyzed, and a near sound source area nonlinear sound field model is generated.
In this step, the acoustic pulse wave generated by UPSS can be calculated according to the free sound field when it does not reach the reflector surface, and when the acoustic Reynolds number Re > 1, the nonlinear effect is significant, and the absorption attenuation can be ignored because of the short propagation distance.
In an embodiment, the propagation model equation of the near-sound source region 501 may be accurately described by using a KZK equation, the KZK equation is shown in formula (1) in a cylindrical coordinate system, three terms on the right side of the KZK equation respectively represent a diffraction term, an absorption term and a nonlinear term, when the sound field of the near-sound source region 501 is regarded as a free sound field, the diffraction term and the absorption term may be omitted, and at this time, the KZK equation may be simplified into a Burgers equation under a spherical expansion condition to be solved, as shown in formula (2).
Wherein p is sound pressure, z axial coordinate is sound wave propagation direction, r is radial coordinate, t ═ t-z/c0Is a delay time, c0In order to be the speed of sound,
is the acoustic dissipation ratio in a hot viscous fluid, η 'is the volume viscosity coefficient, η' is the shear viscosity coefficient, kappa is the heat transfer coefficient, cv、cpRespectively constant volume and constant pressure specific heat capacity, β is nonlinear coefficient
ρ0Is the liquid ambient density.
Step 606: acquiring pulse wave parameter information at the opening end face of a reflector of a sound source and a sound path difference caused by the reflector, and acquiring propagation medium parameters of sound field data.
In this step, pulse wave parameter information at the opening end face of the reflection housing is acquired, and the pulse wave parameter information may include pulse wave shape, peak pressure, acoustic pulse width, acoustic pulse wave energy, and the like.
In one embodiment, when the acoustic pulse wave reaches the reflector, the acoustic wave reflected by the reflector after the acoustic pulse wave reaches the reflector is regarded as a secondary wave source in consideration of the structural coupling dynamic response of the reflector, that is, the reflector is in elastic deformation under the impact action of the high-intensity acoustic pulse wave.
In one embodiment, the sound pulse wave pressure sensor is used for measuring pulse wave parameter information, and the sound field distribution on the opening end surface of the reflecting cover is radially symmetrical, so that the measuring points can be uniformly distributed at the intersection point of the opening end surface and the sound axis and at the edge of the opening end surface.
Step 607: and analyzing the secondary sound field information generated by the reflector according to the pulse wave parameter information and the sound path difference.
In the step, the acoustic pulse wave parameter information measured at the intersection point of the opening end face and the acoustic axis is used as input data, and the initial sound source function of the secondary wave source is solved by using the reverse KZK equation to obtain the pulse wave waveform of the equivalent pulse sound source.
Because the sound pulse wave generates time delay due to the sound path difference when reaching the inner surface of the reflector, the sound field on the inner surface of the reflector is not uniformly distributed and has directivity, the sound pressure amplitude at the center of the sound axis is large, and the sound pressure amplitude at the edge end face of the reflector is small, so that the phase difference needs to be introduced into the initial sound source function.
In one embodiment, the phase difference is caused by the difference of acoustic paths of the acoustic pulse waves reflected and propagated to the end face of the opening through the reflector.
In an embodiment, the established equivalent pulse sound source model may be modified by using the acoustic pulse wave parameter information acquired at other measurement points.
Step 608: and analyzing the sound field distribution information of the sound field data in the beam-focusing area 502 according to the secondary sound field information and the propagation medium parameters to generate a beam-focusing area nonlinear sound field model.
In this step, the pulse waveform of the equivalent pulse sound source is used as an initial excitation waveform for solving the KZK equation, so as to complete the calculation of the sound field distribution in the beam focusing region 502.
In one embodiment, the parameters of the reflector and the parameters of the equivalent pulse sound source are set, initial conditions and boundary conditions are set, the K-th step diffraction term is calculated in the spatial axis direction, the calculation result of the K-th step diffraction term is used as data input for calculating the absorption term in the K + 1-th step, and the calculation result of the absorption term in the K + 1-th step is used as data input for calculating the nonlinear term in the K + 2-th step.
In an embodiment, the calculation step length of three adjacent terms of the KZK equation may include a diffraction term, an absorption term, and a nonlinear term, and in order to ensure convergence of numerical solution, the calculation step length in the spatial axis direction should be small enough to ensure that the calculation error does not affect the numerical result during the sharing solution. Therefore, whether the spatial axis direction reaches the calculation boundary can be judged according to the set boundary condition, and if the spatial axis direction does not reach the calculation boundary, the calculation is continued.
The sound field of the beam-bunching area 502 is affected by various factors such as diffraction, absorption, nonlinearity and the like, the KZK equation contains independent diffraction terms, absorption terms and nonlinear terms, the three terms cannot affect each other in principle, and as long as the space step length in the propagation direction is small enough, the three terms can be processed respectively without affecting the numerical simulation result.
Step 609: acoustic channel characteristic information of a propagation medium of the sound field data is acquired.
In this step, the propagation medium may be a fluid, and the acoustic channel characteristic information may include environmental noise information and multipath information.
In the beam-bunching back region 503, since the acoustic pulse wave generated after being converged by reflection is affected by propagation losses such as spreading loss, absorption loss, boundary loss, and scattering loss when propagating in the underwater acoustic channel, the waveform of the acoustic pulse wave may be broadened in the propagation process, the waveform may be aliased in the time domain, severe distortion may be generated, and frequency information of the acoustic pulse wave may be selectively faded due to multipath effect.
Step 610: and generating propagation attenuation distribution information of the sound field data in the beaming region 503 according to the acoustic channel characteristic information and the temperature gradient distribution calculation model.
In this step, the temperature gradient distribution calculation model is used to obtain environmental information propagated by the acoustic pulse wave, and propagation attenuation distribution information can be obtained according to the obtained environmental information in combination with the acoustic channel characteristic information. The propagation attenuation distribution information is used to indicate the degree of propagation attenuation of the acoustic pulse wave in the current environment.
In an embodiment, when the acoustic pulse wave propagation model is established for an actual water area, characteristics of an underwater acoustic channel of the water area, including environmental noise information and multipath effect information, are measured, and a Bellhop acoustic propagation model is used according to the environmental noise information to calculate and obtain an acoustic propagation attenuation distribution diagram according to temperature gradient distribution, so that an attenuation coefficient and multipath time delay information of the actual water area underwater acoustic channel are obtained.
Step 611: analyzing the sound field distribution information of the sound field data in the beaming area 503 according to the propagation attenuation distribution information and the sound field distribution information of the sound field data in the beaming area 502, and generating a beaming area nonlinear sound field model.
In this step, the propagation attenuation distribution information and the acoustic field distribution information can be used to obtain the time domain waveforms of the acoustic pulse waves at different distances, and the propagation attenuation model of the acoustic pulse waves in the beam convergence region 503 in the underwater acoustic channel is obtained by combining the factors such as the expansion loss, the absorption loss, the boundary loss, the scattering loss and the like.
In one embodiment, the acoustic pulse wave propagation attenuation model is as follows:
TL＝20lg r+α(f)r+g(r)(dB)(3)
where TL denotes attenuation loss of propagation of the acoustic pulse wave, r denotes a radial direction, α (f) denotes an absorption coefficient depending on frequency, and g (r) denotes a boundary reflection loss.
Please refer to fig. 7, which is a beamforming sound field processing method provided in this embodiment, and the method may be executed by the electronic device 1 shown in fig. 1, and may be applied to the interactive scene shown in fig. 2 to implement a process of acquiring geometric data of the beamforming mechanism 300 and sound field data generated by the sound source, dividing a propagation path of the sound field data according to the geometric data of the beamforming mechanism 300 and propagation characteristic information of the sound wave, and calculating sound field distribution information of the sound field data according to a division result of the propagation path.
The method comprises the following steps:
step 701: geometric data of the beamforming mechanism 300 and sound field data generated by the source are acquired. Please refer to the description of step 401 in the above embodiment.
Step 702: and acquiring the first reflected focus information and the second reflected focus information after coupling reflection at the sound source. Please refer to the description of step 602 in the above embodiments.
Step 703: the propagation path of the sound field data is divided into a near sound source region 501, a beam-bunching region 502, and a post-bunching region 503 according to the reflected first focus information and the reflected second focus information. Please refer to the description of step 603 in the above embodiments.
Step 704: and acquiring the propagation medium parameters of the sound source.
In this step, the propagation medium may be water, and the propagation medium parameters may include state parameters for describing the water, such as a flux, a density, a resistance to change of speed, and the like.
Step 705: according to the propagation medium parameters, the medium distribution information of the sound field data in the near sound source area 501 and the bunching area 502 is analyzed.
In this step, distribution information of the propagation medium in the near-sound-source region 501 and the bunching region 502 is acquired based on the propagation medium parameters.
In an embodiment, since the KZK equation is a wave equation under a parabolic approximation, the numerical calculation result can accurately describe only the sound field distribution in the near-acoustic-axis region, and a Computational Fluid Dynamics (CFD) method is used to build a sound field model to obtain the acoustic pulse wave forming process and the curved surface reflection bunching process of the near-acoustic source region 501 and the bunching region 502.
In one embodiment, a Navier-Stokes equation in a compressible unsteady conservation mode is used as a basic control equation of a bunching sound field, and a viscosity effect in the Navier-Stokes equation is neglected to obtain a conservation-type Euler equation, wherein the Navier-Stokes equation is as follows:
in the formula (I), the compound is shown in the specification,
for a conservative variable, also called a solution vector,
in order to be a flux,
is the source item.
For the case in the three-dimensional state:
where ρ is the density, p is the sound pressure, u, V are the particle velocities in the x and y directions, respectively, E is the energy, V is the resistance to change velocity, and V is perpendicular to the surface element dS.
Since the Navier-Stokes equation is an underdetermined equation, in order to make the solution of the Navier-Stokes equation unique, the state equation of water is required to be introduced to form a closed equation set, and the state equation of water is as follows:
wherein γ is a specific heat ratio, and γ is 7.15.
Step 706: a calculation area is generated based on the media partition information.
In this step, the calculation region may be modeled with a finite, symmetric calculation region for computational convenience. The beam-focusing sound field in this embodiment is an axisymmetric structure, so the calculation area can be taken as a quarter sound field with the sound axis as the symmetric center to simplify the calculation, wherein the sound axis is the central symmetric axis of the ellipsoidal reflector in the sound relay direction.
In one embodiment, a two-dimensional axially symmetric region centered on the acoustic axis is also preferred.
Step 707: and generating a sound field distribution diagram according to the calculation region.
In the step, a physical calculation region of the bunching sound field is relatively simple, a single-connected-region structural grid can be adopted for calculation, the coupling between the reflector and the water medium is processed by a common node method, the divided initial grid is smoothed by an elliptic partial differential method, the density degree and the orthogonality degree of the grid are adjusted, the reasonable distribution of the grid in the calculation region is ensured, and the quality of the grid and the accuracy of a numerical calculation method are improved.
Step 708: according to the sound field distribution diagram, sound field distribution information of the sound field data in the near sound source area 501 and the bunching area 502 is analyzed, and a near sound source-bunching area nonlinear sound field model is generated.
In the step, discrete grid units are determined according to the sound field distribution diagram, the discrete grid units are used as control bodies, an approximate discrete equation approximating to a flow control equation is constructed, and the equation (3) is solved by adopting a finite volume method.
In one embodiment, since each grid cell is in a finite volume format, when the control volume is processed by a grid-centric approach, the finite volume format is called a grid-centric control volume. Since the flow field parameters are stored at the control volume center point, the present embodiment calculates the traffic flowing through the control volume boundary using a flux differential format based on an approximate Riemann solution.
In one embodiment, to prevent overshoot or over-expansion of the solution around the ping wave when flux differential format is used, a limiter is used. To prevent non-physical understanding, the flux differential format must also introduce entropy correction.
In one embodiment, a 1 or 2-level virtual control volume is disposed around the periphery of the computing area, and the value of the virtual control volume may be given according to boundary conditions. In the two-dimensional axisymmetric region described in this embodiment, the acoustic axis is set as a symmetric boundary, the boundaries of other water areas are set as absorption boundaries, and an acoustic-solid coupling boundary is formed between the reflection cover and the water medium.
In one embodiment, a multi-step longge-Kutta (change-Kutta) method with TVD (Terminal Velocity Dive) property is used to discretize the time of calculating the sound field, and a TVD type change-Kutta method with second or third order accuracy may be used.
In an embodiment, a Weighted substantially Non-oscillatory (WENO) format is used for improvement to realize the reconstruction of the symmetric WENO format, and the optimized symmetric WENO format is used for calculating the control equation (3).
Step 709: acoustic channel characteristic information of a propagation medium of the sound field data is acquired. Please refer to the description of step 609 in the above embodiments.
Step 710: and generating propagation attenuation distribution information of the sound field data in the beaming region 503 according to the acoustic channel characteristic information and the temperature gradient distribution calculation model. Please refer to the description of step 610 in the above embodiments.
Step 711: analyzing the sound field distribution information of the sound field data in the beaming area 503 according to the propagation attenuation distribution information and the sound field distribution information of the sound field data in the beaming area 502, and generating a beaming area nonlinear sound field model.
In this step, the waveform of the focused beam obtained in step 708 in the direction of the acoustic axis is used, the ambient noise is superimposed on the waveform, and the acoustic pulse wave time domain waveforms at different distances are calculated by using a Thorp empirical formula in combination with propagation attenuation information and multipath time delay information. For analyzing the sound field distribution information of the sound field data in the focused region 503, please refer to the description of step 611 in the above embodiment.
Please refer to fig. 8, which is a beamforming sound field processing apparatus 800 according to this embodiment, the apparatus 800 may be applied to the electronic device 1 shown in fig. 1, and may be applied to the interactive scene shown in fig. 2, so as to obtain geometric data of the beamforming mechanism 300 and sound field data generated by the sound source, divide a propagation path of the sound field data according to the geometric data of the beamforming mechanism 300 and propagation characteristic information of the sound wave, and calculate sound field distribution information of the sound field data according to a division result of the propagation path, so as to generate a nonlinear sound field model. The apparatus 800 comprises: a data acquisition module 801, an area division module 802, and a data calculation module 803. The specific principle relationship of each module is as follows:
and a data acquisition module 801, configured to acquire geometric data of the beamforming mechanism 300 and sound field data generated by the sound source. And a region dividing module 802, configured to divide a propagation path of the sound field data according to the geometric data of the beamforming mechanism 300 and the propagation characteristic information of the sound wave. A data calculating module 803, configured to calculate sound field distribution information of the sound field data according to the division result of the propagation path.
In one embodiment, the area division module 802 is configured to: and acquiring the first reflected focus information and the second reflected focus information after coupling reflection at the sound source. The propagation path of the sound field data is divided into a near sound source region 501, a beam-bunching region 502, and a post-bunching region 503 according to the reflected first focus information and the reflected second focus information.
In one embodiment, the data calculation module 803 is configured to: acquiring propagation medium parameters of sound field data; according to the propagation medium parameters, the sound field distribution information of the sound field data in the near sound source area 501 is analyzed, and a near sound source area nonlinear sound field model is generated.
In one embodiment, the data calculation module 803 is further configured to: acquiring pulse wave parameter information at the opening end face of a reflector of a sound source and a sound path difference caused by the reflector, and acquiring propagation medium parameters of sound field data. And analyzing the secondary sound field information generated by the reflector according to the pulse wave parameter information and the sound path difference. And analyzing the sound field distribution information of the sound field data in the beam-focusing area 502 according to the secondary sound field information and the propagation medium parameters to generate a beam-focusing area nonlinear sound field model.
In one embodiment, the data calculation module 803 is further configured to: and acquiring the propagation medium parameters of the sound source. According to the propagation medium parameters, the medium distribution information of the sound field data in the near sound source area 501 and the bunching area 502 is analyzed. Generating a calculation area according to the media division information; and generating a sound field distribution diagram according to the calculation region. According to the sound field distribution diagram, sound field distribution information of the sound field data in the near sound source area 501 and the bunching area 502 is analyzed, and a near sound source-bunching area nonlinear sound field model is generated.
In one embodiment, the data calculation module 803 is further configured to: acoustic channel characteristic information of a propagation medium of the sound field data is acquired. And generating propagation attenuation distribution information of the sound field data in the beaming region 503 according to the acoustic channel characteristic information and the temperature gradient distribution calculation model. Analyzing the sound field distribution information of the sound field data in the beaming area 503 according to the propagation attenuation distribution information and the sound field distribution information of the sound field data in the beaming area 502, and generating a beaming area nonlinear sound field model.
Please refer to the description of the corresponding method portion of each module in the above embodiments.
By adopting the technical scheme provided by the embodiment, the following remarkable effects are achieved:
(1) various nonlinear factors such as coupling dynamic response, diffraction, medium absorption and acoustic pulse wave distortion of the reflector structure are comprehensively considered, the sectional modeling idea is adopted by utilizing the independence of various nonlinear factors, and the description of the high-power UPSS bunching sound field is more accurate.
(2) The equivalent pulse sound source model is established by adopting the measured data, so that errors caused by adopting a fixed theoretical waveform in the traditional method are effectively reduced, and a new idea is provided for solving the problem of sound field initialization.
(3) The method is favorable for further enriching the UPSS directional radiation theory and providing a new technical support for UPSS application research.
(4) The processing method provided by the embodiment has clear thought, and the sound field model is accurately described in a segmented manner and is easy to realize.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions when actually implemented, and for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection of devices or units through some communication interfaces, and may be in an electrical, mechanical or other form.
In addition, units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
Furthermore, the functional modules in the embodiments of the present application may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.
It should be noted that the functions, if implemented in the form of software functional modules and sold or used as independent products, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present application or portions thereof that substantially contribute to the prior art may be embodied in the form of a software product stored in a storage medium and including instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present application. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
In this document, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions.
The above description is only an example of the present application and is not intended to limit the scope of the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims (10)
1. A beamforming sound field processing method, comprising:
acquiring geometric data of a beam bunching mechanism and sound field data generated by a sound source;
dividing the propagation path of the sound field data according to the geometric data of the beam bunching mechanism and the propagation characteristic information of the sound wave;
and calculating sound field distribution information of the sound field data according to the division result of the propagation path to generate a nonlinear sound field model.
2. The method according to claim 1, wherein the dividing the propagation path of the sound field data according to the geometrical data of the beamforming mechanism and the propagation characteristic information of the sound wave comprises:
acquiring reflection first focus information and reflection second focus information after coupling reflection at the sound source;
and dividing the propagation path of the sound field data into a near sound source region, a beam bunching region and a beam bunching region according to the reflected first focus information and the reflected second focus information.
3. The method according to claim 2, wherein the calculating sound field distribution information of the sound field data according to the division result of the propagation path to generate a nonlinear sound field model comprises:
acquiring propagation medium parameters of the sound field data;
and analyzing the sound field distribution information of the sound field data in the near sound source area according to the propagation medium parameters to generate a near sound source area nonlinear sound field model.
4. The method according to claim 2, wherein the calculating sound field distribution information of the sound field data according to the division result of the propagation path to generate a nonlinear sound field model comprises:
acquiring pulse wave parameter information at the opening end face of a reflector of the sound source and a sound path difference caused by the reflector, and acquiring propagation medium parameters of the sound field data;
analyzing secondary sound field information generated by the reflector according to the pulse wave parameter information and the sound path difference;
and analyzing the sound field distribution information of the sound field data in the beam-focusing area according to the secondary sound field information and the propagation medium parameters to generate a beam-focusing area nonlinear sound field model.
5. The method according to claim 2, wherein the calculating sound field distribution information of the sound field data according to the division result of the propagation path to generate a nonlinear sound field model comprises:
acquiring the propagation medium parameters of the sound source;
analyzing the medium distribution information of the sound field data in the near sound source area and the bunching area according to the propagation medium parameters;
generating a calculation region according to the medium distribution information;
generating a sound field distribution diagram according to the calculation region;
and analyzing the sound field distribution information of the sound field data in the near sound source area and the bunching area according to the sound field distribution map to generate a near sound source-bunching area nonlinear sound field model.
6. The method according to claim 2, wherein the calculating sound field distribution information of the sound field data according to the division result of the propagation path to generate a nonlinear sound field model comprises:
acquiring the sound channel characteristic information of a propagation medium of the sound field data;
generating propagation attenuation distribution information of the sound field data in the beam convergence zone according to the acoustic channel characteristic information and the temperature gradient distribution calculation model;
and analyzing the sound field distribution information of the sound field data in the beam convergence zone according to the propagation attenuation distribution information and the sound field distribution information of the sound field data in the beam convergence zone, and generating a beam convergence zone nonlinear sound field model.
7. A beamforming sound field processing apparatus, comprising:
the data acquisition module is used for acquiring geometric data of the beam bunching mechanism and sound field data generated by a light source;
the region dividing module is used for dividing the propagation path of the sound field data according to the geometric data of the beam bunching mechanism and the propagation characteristic information of the sound wave;
and the data calculation module is used for calculating sound field distribution information of the sound field data according to the division result of the propagation path and generating a nonlinear sound field model.
8. The apparatus of claim 7, wherein the region partitioning module is configured to:
acquiring reflection first focus information and reflection second focus information after coupling reflection at the sound source;
and dividing the propagation path of the sound field data into a near sound source region, a beam bunching region and a beam bunching region according to the reflected first focus information and the reflected second focus information.
9. The apparatus of claim 8, wherein the data computation module is configured to:
acquiring propagation medium parameters of the sound field data;
and analyzing the sound field distribution information of the sound field data in the near sound source area according to the propagation medium parameters to generate a near sound source area nonlinear sound field model.
10. An electronic device, comprising:
a memory for storing a computer program;
a processor for performing the method of any one of claims 1-6.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010095039.1A CN111342908B (en) | 2020-02-18 | 2020-02-18 | Beam focusing sound field processing method and device and electronic equipment |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010095039.1A CN111342908B (en) | 2020-02-18 | 2020-02-18 | Beam focusing sound field processing method and device and electronic equipment |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111342908A true CN111342908A (en) | 2020-06-26 |
| CN111342908B CN111342908B (en) | 2021-09-10 |
Family
ID=71186017
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010095039.1A Active CN111342908B (en) | 2020-02-18 | 2020-02-18 | Beam focusing sound field processing method and device and electronic equipment |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111342908B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114264721A (en) * | 2021-11-26 | 2022-04-01 | 海鹰企业集团有限责任公司 | Novel sound velocity processing system |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101548896A (en) * | 2008-03-31 | 2009-10-07 | 株式会社东芝 | Ultrasound diagnosis apparatus |
| CN103164588A (en) * | 2013-04-15 | 2013-06-19 | 西北工业大学 | Method of designing high-power energy-gathered reflex housing |
| CN103170068A (en) * | 2013-04-15 | 2013-06-26 | 南京大学 | Quantitative determining method of nonlinear sound field of phased array |
| WO2013185844A1 (en) * | 2012-06-15 | 2013-12-19 | Sezer Nagihan | Passive communication system and method involving ultrasound signal patterns |
| CN103776524A (en) * | 2014-02-21 | 2014-05-07 | 南京大学 | System and method for measuring distribution of strong focused ultrasound nonlinearity sound fields |
| CN104063628A (en) * | 2014-07-15 | 2014-09-24 | 南京大学 | Method for calculating non-linear sound field of lens type high focused transducer |
-
2020
- 2020-02-18 CN CN202010095039.1A patent/CN111342908B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101548896A (en) * | 2008-03-31 | 2009-10-07 | 株式会社东芝 | Ultrasound diagnosis apparatus |
| WO2013185844A1 (en) * | 2012-06-15 | 2013-12-19 | Sezer Nagihan | Passive communication system and method involving ultrasound signal patterns |
| CN103164588A (en) * | 2013-04-15 | 2013-06-19 | 西北工业大学 | Method of designing high-power energy-gathered reflex housing |
| CN103170068A (en) * | 2013-04-15 | 2013-06-26 | 南京大学 | Quantitative determining method of nonlinear sound field of phased array |
| CN103776524A (en) * | 2014-02-21 | 2014-05-07 | 南京大学 | System and method for measuring distribution of strong focused ultrasound nonlinearity sound fields |
| CN104063628A (en) * | 2014-07-15 | 2014-09-24 | 南京大学 | Method for calculating non-linear sound field of lens type high focused transducer |
Non-Patent Citations (1)
| Title |
|---|
| 刘小龙，黄建国，张群飞: "水下等离子体声源的聚束特性研究", 《高压物理学报》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114264721A (en) * | 2021-11-26 | 2022-04-01 | 海鹰企业集团有限责任公司 | Novel sound velocity processing system |
| CN114264721B (en) * | 2021-11-26 | 2024-04-19 | 海鹰企业集团有限责任公司 | Novel sound velocity processing system |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111342908B (en) | 2021-09-10 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Zeng et al. | Evaluation of the angular spectrum approach for simulations of near-field pressures | |
| Treeby et al. | Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method | |
| Habets | Room impulse response generator | |
| Wise et al. | Representing arbitrary acoustic source and sensor distributions in Fourier collocation methods | |
| Averiyanov et al. | Nonlinear and diffraction effects in propagation of N-waves in randomly inhomogeneous moving media | |
| Zhang et al. | Transient nearfield acoustic holography based on an interpolated time-domain equivalent source method | |
| Molnar et al. | Estimating density, velocity, and pressure fields in supersonic flows using physics-informed BOS | |
| Wu et al. | A method to compute the radiated sound power based on mapped acoustic radiation modes | |
| Mehra et al. | Acoustic pulse propagation in an urban environment using a three-dimensional numerical simulation | |
| Yan et al. | Acoustic tomography system for online monitoring of temperature fields | |
| Zhong et al. | The near field, Westervelt far field, and inverse-law far field of the audio sound generated by parametric array loudspeakers | |
| CN111342908B (en) | Beam focusing sound field processing method and device and electronic equipment | |
| Yin et al. | Near-field imaging of obstacles with the factorization method: fluid–solid interaction | |
| Franco et al. | Acoustic beam modeling of ultrasonic transducers and arrays using the impulse response and the discrete representation methods | |
| Li et al. | A quasianalytical time domain solution for scattering from a homogeneous sphere | |
| Hargreaves et al. | A transient boundary element method model of Schroeder diffuser scattering using well mouth impedance | |
| Wu | Reconstructing transient acoustic radiation from an arbitrary object with a uniform surface velocity distribution | |
| Diaz et al. | High-performance multi-GPU solver for describing nonlinear acoustic waves in homogeneous thermoviscous media | |
| Ke et al. | Simulation of sound propagation over porous barriers of arbitrary shapes | |
| Brick et al. | Fast direct solution of 3-D scattering problems via nonuniform grid-based matrix compression | |
| Kelly et al. | An annular superposition integral for axisymmetric radiators | |
| Chernokozhin et al. | Scattering by thin shells in fluids: Fast solver and experimental validation | |
| D'Amico et al. | Reformulation of the Stochastic BEM to improve the computational efficiency in the prediction of the vibro-acoustic behaviour of structures with uncertainties | |
| Burnett | Radiation boundary conditions for the Helmholtz equation for ellipsoidal, prolate spheroidal, oblate spheroidal and spherical domain boundaries | |
| Dimant et al. | Lens mediated scattering of sound by sound with finite aperture beams |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |