Effects of time-reversing array deformation in an ocean wave guide

Acoustic time reversal is a promising technique for spatial and temporal focusing of sound in unknown environments. Acoustic time reversal can be implemented with an array of transducers that listens to a remote sound source and then transmits a time-reversed version of what was heard. In a noisy environment, the performance of such a time-reversing array (TRA) will be degraded because the array will receive and transmit noise, and the intended signal may be masked by ambient noise at the retrofocus location. This article presents formal results for the signal-to-noise ratio at the intended focus (SNRf) for TRAs that receive and send finite-duration broadband signals in noisy environments. When the noise is homogeneous and uncorrelated, and a broadcast power limitation sets the TRA's electronic amplification, the formal results can be simplified to an algebraic formula that includes the characteristics of the signal, the remote source, the TRA, and the noisy environment. Here, SNRf is found to be proportional to the product of the signal bandwidth and the duration of the signal pulse after propagation through the environment. Using parabolic-equation propagation simulations, the formal results for SNRf are illustrated for a shallow water environment at source-array ranges of 1 to 40 km and bandwidths from several tens of Hz to more than 500 Hz for a signal center frequency of 500 Hz. Shallow-water TRA noise rejection is predicted to be superior to that possible in free space because TRAs successfully exploit multipath-propagation.

Among structural health monitoring techniques, Lamb waves is frequently used as diagnostic tools to detect damage in plate-like structures. Lamb waves usually excited by piezoelectric transducers essentially involve exciting the structure with high frequency guided-waves and processing the difference in structural response with respect to a baseline signal for the pristine condition to detect damage. As a kind of baseline free method, time reversal (TR) method applied to ultrasonic detection and focusing with arrays of transducers has been proposed. The decomposition of the time reversal operator (DORT) method is a selective detection and focusing technique using an array of transmit-receive transducers. Unlike body waves, the propagation of Lamb waves is complicated due to their dispersive and multimode characteristics. So Lamb wave is hard to locate different scatterers on the plate using DORT method because of the asymmetry of the time reversal transfer matrix. In this paper, a proposed approach based on the DORT method is developed to distinguish and locate two simulated damages on the aluminum plate using Lamb wave through finite element simulation on the commercial finite element code ANSYS platform. The behavior of reflected waves is analyzed by studying the eigenvalues and eigenvectors of the time reversal transfer matrix, showing that the number of significant eigenvalues is not exactly the number of damage targets and two significant eigenvalues correspond to one target. This method, which uses PZT array and operates under multi-modes pulse-echo mode, can estimate the position of the damaged zone in 2D image by numerically backpropagating selective eigenvector using the S0 and/or A0 Lamb wave propagation analytical solution.

A series of time reversal (phase conjugation) experiments was performed in shallow water including a range-dependent slope environment. Time reversal arrays implemented with center frequencies of 445 and 3500 Hz achieved sharp focal regions up to ranges of 30 and 13 km, respectively, in 110–130 m shallow water. Analysis with an image method indicates that the focal size approaches the diffraction limit of an array for given waveguide conditions, i.e., waveguide geometries and attenuation. The measured focal size has implications for the maximum achievable resolution of matched field processing, which is a computational implementation of the phase conjugation process. [Work supported by ONR.]

The DORT method (Decomposition de l'Operateur de Retournement Temporel) applies to ultrasonic detection and focusing with arrays of transducers. It is a signal analysis method based on the invariance of ultrasonic propagation under time reversal. It requires the measurement of the inter element impulse responses of the the propagating medium for all pair of elements in the array. A hermitian matrix called the time reversal operator is deduced from these responses and diagonalized. The eigenvectors are then used to perform selective focusing. This method is applied here to phase aberration correction. Experiments with weakly and strongly aberrating medium are shown.

Time reversal acoustic (TRA) focusing allows concentration of elastic energy at a location in the soil being investigated to detect landmines. The TRA process is conducted by broadcasting a wide bandwidth signal and recording the surface vibration by a Laser Doppler Vibrometer (LDV). The system impulse response from speaker to the LDV output can then be computed by cross correlating the original and recorded signals for each channel. Each transducer re-radiates the time reversal impulse response. This provides efficient focusing of the seismic wave in both space and time, thus enhancing the nonlinear effects associated with soil and landmine vibrations. Using orthogonal initial signals the suggested TRA procedure can be implemented simultaneously with multiple transmitters to increase the scanning speed. The nonlinear effects were investigated using a phase inversion method where the TRA signal is broadcast a second time with an opposite sign and the two received signals are added in post processing. The summed signal contains mainly the results of nonlinear wave interaction and tends to cancel the linear response. Small scale land mine detection experiments were conducted using a laser Doppler vibrometer and an array of speakers in the frequency band 50-500Hz. They demonstrate that the TRA system provides high concentration of elastic wave energy in the tested area. The measurements of spectral density of the TRA focused signal reveal increased spectral density in the vicinity of mine resonance frequencies. The nonlinear TRA phase inversion method shows higher contrast between mine and no mine than the linear TRA method.

: The overall long-term goal for this project is to develop engineering tools that are useful to the Navy as it operates in uncertain, partially known, or unknown ocean environments. During the last year, this project has focused on further determining the utility of a fully-passive propagation-physics-based technique for blind deconvolution of array-recorded sounds from a remote source with emphasis on determining how sparse-array measurements might be used for this task. The long term goals of this project are: i) to determine the effectiveness of synthetic time reversal (STR) for the purposes of blind deconvolution in noisy unknown ocean sound channels, ii) to effectively apply STR to marine mammal sounds recorded in the ocean with vertical and/or horizontal arrays, and iii) to utilize the STR-estimated signals and ocean-sound-channel impulse responses to classify, localize, and/or track individual marine mammals (or other sound sources) of interest. Since early 2009 this project has focused on developing an acoustic-ray-based version of synthetic time reversal (STR), a fully-passive technique for recovering the original signal and the source-to-arrayelement impulse responses for a remote unknown sound source in an unknown underwater waveguide [1-4]. The specific objectives are to: a) determine STR performance as a function of the signal-tonoise, array size, and array element number using acoustic propagation simulations, b) verify these findings with simple airborne- or water-borne acoustic laboratory experiments involving multiple receivers and multiple ray paths, c) obtain and process underwater array recordings of remote-butcooperative sound sources, and d) obtain and process marine mammal vocalizations for the purposes of marine mammal localization, tracking, and identification. This research effort extends the prior modebased version of STR [1] to higher frequencies, smaller receiving arrays, sparse receiving arrays, and sound channels with modal dispersion

In the bioelectronic medicine field, vagus nerve stimulation (VNS) is a promising technique that is expected to treat numerous inflammatory conditions, in addition to the currently FDA approved treatment for epilepsy, depression and obesity [1]. However, current VNS techniques are still limited in the spatial resolution that they can achieve, which limits its therapeutic effect and induces side effects such as coughing, headache and throat pain. In our prior work, we presented a curved ultrasound (US) transducer array with a diameter of 2 mm and with 112 miniature US transducer elements, small enough to be wrapped around the vagus nerve for precise ultrasound nerve stimulation [2]. Due to the curved alignment of the US transducers with 48 of the elements simultaneously excited, the emitted US was naturally focused at the center of the curvature. Building on this work, we employ a beam steering technique to move the focal spot to arbitrary locations within the focal plane of the transducer array. The beam steering was controlled through an in-house built US driver system and was visualized using a pulsed laser schlieren system. The propagation of the US pulse in water was imaged and recorded. This method was found to be a rapid and effective means of visualizing the US propagation.

Structural health monitoring of buried pipelines is an important application for aging infrastructures. Ultrasonic guided wave inspection is an attractive tool, due to the long propagation of guided waves in the wall of a hollow cylinder. However, guided waves present a unique environment with heavily multi-modal signal propagation and complex dispersion (frequency-dependent propagation speeds). In order to alleviate these challenges, conventional techniques rely on high-voltage excitation with complex transducer arrays, but these systems are not conducive to a monitoring solution. Instead, they require periodic excavation and testing. In prior work, we have shown that Time Reversal allows for reliable detection with relatively simple antenna arrays that can be operated in low-power. This paper focuses on localization of these defects. We utilize a beamforming approach that makes use of theoretical dispersion curves to generate fault images. We show through simulations that Time Reversal Beamforming achieves high-resolution localization of a fault in the presence of strong dispersion and heavily multi-modal propagation.

When waves propagate through a complex medium like the turbulent atmosphere the wave field becomes incoherent and the wave intensity forms a complex speckle pattern. In this paper we study a speckle memory effect in the frequency domain and some of its consequences. This effect means that certain properties of the speckle pattern produced by wave transmission through a randomly scattering medium is preserved when shifting the frequency of the illumination. The speckle memory effect is characterized via a detailed novel analysis of the fourth-order moment of the random paraxial Green’s function at four different frequencies. We arrive at a precise characterization of the frequency memory effect and what governs the strength of the memory. As an application we quantify the statistical stability of time-reversal wave refocusing through a randomly scattering medium in the paraxial or beam regime. Time reversal refers to the situation when a transmitted wave field is recorded on a time-reversal mirror then time reversed and sent back into the complex medium. The re-emitted wave field then refocuses at the original source point. We compute the mean of the refocused wave and identify a novel quantitative description of its variance in terms of the radius of the time-reversal mirror, the size of its elements, the source bandwidth, and the statistics of the random medium fluctuations.

With the rapid development of urban rail transit and underground space development, the occurrence of excavation near existing tunnels is becoming more common. This excavation and unloading will inevitably cause soil deformation outside the pit and the tunnel buried therein. This paper presents an investigation into the entire excavation process and the deformation effects on the adjacent subway structure under complex construction environments, including soft soil foundations and adjacent subway intersections, based on measured data of pit construction. The horizontal and vertical displacements of deep soils in two pits were analyzed along with safety management measures to determine the horizontal displacement curve pattern and the lateral displacement development distribution law of deep soils. The analysis of subway deformation data shows that after excavation, the subway tunnel undergoes “lateral expansion” and “vertical compression” type deformation, accompanied by “in-pit” horizontal displacement and “settlement” vertical displacement. Furthermore, a correlation analysis reveals a clear linear relationship between pit deformation and subway structure deformation, which can be used as a prediction method for adjacent structure deformation. Finally, a comparative analysis of existing relevant influence zone models and tunnel deformation prediction formulas is carried out based on the monitoring. The results of this study have significant guiding implications for the excavation construction of soft soil foundations in the vicinity of subway crossings.

Time reversal acoustics is based on the time reversal symmetry of the acoustic fields. A detailed description of the acoustic field equation showing the time reversal symmetry property of S the solution is given. A geometric structure of a metamaterial for both an electromagnetic wave and acoustic wave is given. Then, the geometric structure of the metamaterial to implement time reversal acoustics is given. Time reversal acoustics has been successfully applied to non-destructive testing, medical ultrasound imaging, and underwater acoustics. The advantage of using metamaterial in time reversal acoustics is that it supports modes which radiate spatial information of the near field of a source efficiently in the far field.

To reduce time and cost of damage inspection, on-line impact monitoring of aircraft composite structures is needed. A digital monitor based on an array of piezoelectric transducers (PZTs) is developed to record the impact region of impacts on-line. It is small in size, lightweight and has low power consumption, but there are two problems with the impact alarm region localization method of the digital monitor at the current stage. The first one is that the accuracy rate of the impact alarm region localization is low, especially on complex composite structures. The second problem is that the area of impact alarm region is large when a large scale structure is monitored and the number of PZTs is limited which increases the time and cost of damage inspections. To solve the two problems, an impact alarm region imaging and localization method based on digital sequences and time reversal is proposed. In this method, the frequency band of impact response signals is estimated based on the digital sequences first. Then, characteristic signals of impact response signals are constructed by sinusoidal modulation signals. Finally, the phase synthesis time reversal impact imaging method is adopted to obtain the impact region image. Depending on the image, an error ellipse is generated to give out the final impact alarm region. A validation experiment is implemented on a complex composite wing box of a real aircraft. The validation results show that the accuracy rate of impact alarm region localization is approximately 100%. The area of impact alarm region can be reduced and the number of PZTs needed to cover the same impact monitoring region is reduced by more than a half.

This chapter contains sections titled: Introduction Theory of Time-Reversal Acoustics Application of TR to Medical Ultrasound Imaging Application of Time-Reversal Acoustics to Ultrasonic Nondestructive Testing Application of TRA to Landmine or Buried Object Detection Application of Time-Reversal Acoustics to Underwater Acoustics References

Time-reversal (TR) techniques have shown promising results for detection and localization of scatterers in multiple scattering environments. These techniques exploit the TR invariance of the wave equation. Most of TR applications require the analysis of the TR operator obtained from the MDM of a TR array. Eigenvalue decomposition of the TR operator forms the basis of techniques such as decomposition of the TR operator and TR multiple signal classification. In this letter, we have introduced a new approach that is based on the independent component analysis (ICA). The ICA takes advantage of the statistical independence of scattered signals from well-resolved scatterers and breaks the mixed received signal by each receiving antenna to independent components based on maximizing the non-Gaussianity of mixed signal components. Some preprocessing steps such as centering and whitening are also required. One advantage of the TR imaging based on ICA is that imaging and focusing can be achieved using only one transmitting antenna, which lowers the complexity of the implementation compared with other techniques.

This paper presents an interdisciplinary review of the correlation properties of random wavefields. We expose several important theoretical results of various fields, ranging from time reversal in acoustics to transport theory in condensed matter physics. Using numerical simulations, we introduce the correlation process in an intuitive manner. We establish a fruitful mapping between time reversal and correlation, which enables us to transpose many known results from acoustics to seismology. We show that the multiple-scattering formalism developed in condensed matter physics provides a rigorous basis to analyze the field correlations in disordered media. We discuss extensively the various factors controlling and affecting the retrieval of the Green's function of a complex medium from the correlation of either noise or coda. Acoustic imaging of complex samples in the laboratory and seismic tomography of geologic structures give a glimpse of the promising wide range of applications of the correlation method.