A Research On Positioning Characteristics And Reliability Analysis Of Two-Dimensional Underwater Acoustic Topological Insulators

Underwater acoustic positioning is the most important and reliable technology for the positioning and tracking of objectives in deep seas.However,realizing a directional and robust acoustic propagation which immunizes against surrounding noise,interference signals and various defects is still a challenge.Two-dimensional acoustic topological insulators,which has significantly revolutionized our scientific cognition of classical wave characteristics,provides an excellent platform for the control of the directional and robust acoustic beams.The topological edge states of the two-dimensional acoustic system can suppress backscattering well.In the case of defects such as the bending,disorder and other defects of their own structure,the propagation of the sound is still very robust,and sound waves can be transmitted almost lossless along the topological interface.Recently,topological acoustic transports of the acoustic topological insulators have provided people with a new way of sound wave manipulation,which provides an effective theoretical basis for the underwater acoustic positioning of acoustic topological insulators.In this paper,we designed an two-dimensional underwater acoustic topological insulators positioning system,studied the robust edge propagation caused by valley Hall polarization,and the directional transmission and reception characteristics of acoustic waves along the topological interface.Based on these properties,we discussed the positioning method of the target.Considering the complexity of the marine environment,it will adversely affect the underwater positioning of acoustic topological insulators.At the end of the paper,we analyzed the sensitivity and reliability of the positioning accuracy of the two-dimensional underwater acoustic topological insulators positioning system.The paper includes the following main research contents:(1)We designed a two-dimensional underwater acoustic topological insulators.When the rotational angle of the scatterer is?=n?/3(n=0,±1,±2...),the two-fold Dirac cones can be generated at the Brillouin zone corners due to the perfect match of the mirror symmetries between the lattice and the acoustic topological insulators.However,when the rotational angle is??n?/3(n=0,±1,±2...),the Dirac conical dispersion protected by the mirror symmetry will be lifted,resulting in an omnidirectional band gap and producing valley states at the K and K'points,because of the reduction of the point group symmetry,from the C_3vsymmetry to the C₃symmetry.we constructed an effective Hamiltonian in the vicinity of the K(K')valley,based on the k·p perturbation method.We Calculated the valley Chern numbers at different rotation angles by integrating the Berry curvature near the valley at the K(K')valley,thus revealing the cause of the valley Hall phase transition.We analyzed the relationship between the bandgap width and the rotation angle,designed the AB-type(The acoustic topological insulators has an upper domain rotation angle of?=–30^o and a lower domain rotation angle of?=30^o)and BA-type(The acoustic topological insulators has an upper domain rotation angle of?=30^o and a lower domain rotation angle of?=–30^o)super configuration with zigzag interface of opposite valley Hall phase,and discussed the topological boundary states of the AB-type(BA-type)supercell.(2)We discussed the localization mechanism of two-dimensional underwater acoustic topological insulators.We designed straight and zigzag two-dimensional acoustic topological waveguides,which fully demonstrates that the topological edge states have better anti-reflection characteristics.By comparing the transmission rates of three types of topology interface,including defect-free,cavity and disorder,we proved that the sound of the underwater acoustic topological insulators has good robustness to various defects.It is calculated that the sound wave will radiate along the direction of refraction angle of-68.38°(8.38°)at the exit port,the half-power beam width of the directional sound beam is 15.58°(17.72°),and the main beam efficiency is as high as 95%.It reflects that the directional sound beam generated by the two-dimensional topological insulator has better directivity and stronger anti-interference ability.We demonstrated that the HPBW of the main lobe can be reduced to below 7°and the BE can be increased to 98%by dividing the large sonic crystal into smaller one,or changing the sonic crystal spacing.We studied the directional response of the two-dimensional underwater acoustic topological insulators,that is,it can only respond to the sound waves from the sound source in a specific direction.Therefore,when two acoustic topological insulators are arranged in a two-dimensional space,passive positioning of underwater sound sources can be achieved,when three acoustic topological insulators are arranged in a space,one of which is used as a directional radiation sound source,then the active underwater target can be achieved positioning.(3)We analyzed the sensitivity and reliability of the positioning system of two-dimensional underwater acoustic topological insulators.We plotted the main sensitivity index,cross-sensitivity index,and total sensitivity index for sound speed and test frequency.We analyzed that in the obtained measurement data,choosing a smaller sound and a larger acoustic velocity and the test frequency has little effect on the change of positioning angle,and the acoustic velocity is the main influencing factor.Through the reliability analysis of positioning accuracy,it is found that when the positioning error is±2°,the failure probability is 0,the reliability index is greater than1,thus positioning accuracy is reliable.In this paper,we constructed a theoretical framework for the wave characteristics of a two-dimensional underwater acoustic topological insulators.Based on the characteristics of underwater acoustic topological directional propagation and directional response,we introduce the method of positioning underwater targets in detail,and analyze the sensitivity and reliability of the positioning accuracy of the underwater positioning system of acoustic topological insulators.Therefore,the research work in this paper provides new theoretical guidance and technical means to improve the ability of traditional acoustic equipment to resist structural defects and achieve efficient positioning of equipment such as submarines and underwater robots in complex marine environments.