Time Reversal Method Research Articles

Thermal holographic patterns for ultrasound hyperthermia

Holograms can shape wavefronts to produce arbitrary acoustic images. In this work, we experimentally demonstrate how acoustic holograms can produce controlled thermal patterns in absorbing media at ultrasonic frequencies. Magnetic resonance imaging (MRI)-compatible holographic ultrasound lenses were designed by time-reversal methods and manufactured using 3D-printing. Several thermal holographic patterns were measured using MRI thermometry and a thermographic camera in gelatin-milk phantoms and in an ex vivo liver tissue. The results show that acoustic holograms enable spatially controlled heating in arbitrary regions. Increasing the temperature using low-cost and MRI-compatible holographic transducers might be of great interest for many biomedical applications, such as ultrasound hyperthermia, where the control of specific thermal patterns is needed.

Partial discharge localization in power transformers using acoustic time reversal

The localization of partial discharges (PD) is important to monitor the conditioning of high voltage insulator materials. One of the key components in power grids is the high power transformer. Localization of PDs in these pieces of equipment can increase the reliability of power networks. One of the most commonly used methods to localize PDs is the time difference of arrival (TDoA) technique. Recently, time reversal (TR) techniques in the electromagnetic regime have been proposed to localize PD sources with a lower number of needed sensors compared to the TDoA technique. Contrary to TDoA, TR-based techniques do not need line-of-sight wave propagation from PD sources to the sensor(s). In this study, we extend the TR technique to localize PD sources in the acoustic regime for three-dimensional structures. Similar to the electromagnetic TR methods, a typical time reversal process includes three steps: 1) record the acoustic fields caused by a PD source using at least one sensor, 2) time reverse and back inject into the medium the recorded acoustic signal(s), 3) use a proper criterion to obtain the focusing point associated with the location of the PD source. The acoustic TR technique presented in this paper uses only one sensor. Numerical simulations are used to evaluate the performance of the acoustic TR technique for three-dimensional power transformer models. To do this, an open source MATLAB toolbox is used to solve the acoustic wave equation. The numerical results show that the TR technique can accurately localize the PD sources in three-dimensional power transformer models. Our analysis shows that the presence of windings inside the transformer tank does not degrade the efficiency of the acoustic TR technique.

An experiment on reconstruction and analyses of in-situ measured freak waves

Freak waves are destructive to marine and offshore structures, but their generation mechanisms are still unclear. To explore the possible generation mechanism of freak waves, some in-situ measured waves are reconstructed in a wave flume at model scale. To generate high-quality target waves, a modified time reversal (TR) method including a correction step is proposed. Five scaled in-situ measured waves, containing three freak waves and two non-freak waves, are reconstructed successfully.As reconstructed waves provide good agreement with the scaled in-situ measured waves, their formation mechanisms are analyzed by applying various dispersion relations. The results show the key contributions of the dispersive focusing in the freak wave formation. Then, to explore the nonlinear interactions of the quadratic order of these reconstructed waves, the wavelet-based bicoherence and its total bicoherence are presented, and large surface elevations are found to be related to high total bicoherences, indicating inescapable effects of wave-wave interactions in the wave formation. Furthermore, a phase coincidence level F is proposed to evaluate the phase coincidence level of these reconstructed waves. The results show that a low F (high phase focus level) means a high wave height, while a high wave height does not always exhibit a low F.

PS interferometric imaging condition for microseismic source elastic time-reversal imaging

SUMMARYThe time-reversal imaging method utilizes the wave equation to back-propagate recorded seismic data and a proper imaging condition to locate a passive seismic source. For an explosive source, the reconstructed wavefield is focused at the seismic source location and origin time. Although the elastic time-reversal wavefield for a moment tensor source may not exhibit a maximum at the true location at the origin time, it does exhibit a quasi-symmetrical spatial distribution around the source location that represents the radiation pattern of the moment tensor source. We propose the use of an interferometric imaging condition to solve the radiation pattern problem, which is combined with elastic PS cross-correlation imaging condition (referred to as the PS interferometric cross-correlation imaging condition) to locate a moment tensor source using elastic time-reversal imaging method. 2-D and 3-D numerical tests demonstrate that our proposed method can identify the moment tensor source location in complex velocity models with a high noise level. In tests of the sensitivity of the method to the accuracy of the velocity model, we find that the method can still get focused images under about 10–25 per cent random perturbations in P- and S-wave velocities, but only under about 5 per cent correlated perturbation of global P- and S-wave velocities with a potential bias in the location.

Low-frequency acoustic source localization based on the cross-spectral time reversal method corrected in wavenumber domain

Near-filed acoustic holography can break the half wavelength limit by reversing the propagation matrix and achieve high-resolution for low-frequency source localization, but it will encounter the ill-posed problem. The subwavelength focusing also can be obtained by correcting the wavenumber spectrum of monopole time-reversed field into that of dipole time-reversed field through near field measurement, which can avoid the ill-posed problem. To further improve the identification accuracy of low-frequency sources in the strong noise environment, a cross-spectrum time reversal method corrected in wavenumber domain is proposed (CS-TR). First, a cross-spectrum time reversal function based on pressure measurement on a plane in the near field is constructed to obtain the initial time-reversed result. Then, the cross-spectrum time-reversed field is transformed into wavenumber domain, and the filter term that contains evanescent waves is corrected to make the result contains more evanescent waves which can improve the localization resolution of low-frequency sources. The essence of the cross-spectrum of the focusing result is to calculate the cross-correlation of signals from all directions, which can not only increase the content of evanescent waves during the correction process in wavenumber domain, but also can highlight the energy difference between signal and noise, making the localization capability significantly improved for low-frequency sources. Numerical simulation and experimental results show that the CS-TR method can significantly improve the spatial resolution at low frequencies. Multiple acoustic sources at 100 Hz were effectively identified when the signal-to-noise ratio (SNR) was 0 dB, and the spatial resolution reached 1/34 wavelength.

A finite-element based implementation of time-reversal and phase-conjugation acoustic source localization techniques in COMSOL multiphysics

In this work, we develop a general working procedure for a finite-element (FE) based implementation of time-reversal (TR) and phase-conjugation (PC) acoustic source localization techniques in COMSOL multiphysics commercial package using its in-built acoustics modules. To this end, a detailed step-by-step algorithm of the forward propagation is presented which includes creation of the computational domain and absorbing boundaries, defining acoustic source(s), meshing, solving, i.e., carrying out a time- or frequency-domain simulation followed by extracting data at virtual microphone array (nodes). The same procedure is used for implementing the TR simulations and frequency-domain PC except that source(s) inside the domain are now deactivated, and time-reversed or phase-conjugated data is enforced at the array nodes, followed by computation of the source map. The test-case of an idealized monopole in a 2D free-space is first considered whereby it is shown that both FE-based TR and PC methods deliver identical results which are in an excellent agreement with a finite-difference time-domain (FDTD) solver results, thereby validating the procedure. Next, the problem of localizing an idealized source in the presence of multiple scatterers and reflections which resemble an urban environment is considered. The COMSOL algorithms are shown to produce satisfactory results which demonstrate the efficiency of commercial FE solvers in handling complex geometries which otherwise tend to become tedious using the traditional FDTD solvers.

Moving Target Detection Based on Time Reversal in a Multipath Environment

Time reversal can resolve multipath problems and increase the detection probability, but the detection performance decreases when the target is moving. Because of the change in the channel response due to target motion, the focusing effect of a time-reversal-transmitted signal is reduced. In this article, a novel method based on time reversal, which detects a moving target embedded in a multipath environment with channel variation, is proposed. We establish conventional and time-reversal signal models of a moving target in an indoor diffuse multipath environment and derive likelihood ratio tests under these two conditions. The channel parameters and the changes due to target motion are obtained by echo estimation and are exploited as useful information by the detectors. The channel changes are taken into account in the time-reversal detector to improve its robustness. The time-reversal detector proposed in this article possesses the constant-false-alarm-rate property with respect to the unknown background noise. Although Monte Carlo simulation analysis has illustrated the superior performance of both conventional and time-reversal detectors and proved that both methods can improve the detection probability by exploiting the multipath effect, the time-reversal method outperforms the conventional method due to the spatial and temporal focusing effect on the channel.

Time-Reversal Source Reconstruction With Electromagnetic Kurtosis

The time-reversal (TR) technique has been developed to solve inverse problems and to reconstruct sources. However, much work on the topic so far has not considered the determination of source excitation time instants, which is a crucial step toward practical applications of the TR method. In this article, we introduce the concept of kurtosis into the TR process to reconstruct not only spatial locations but also excitation time instants of the sources. Our method paves the way for extensions and applications of the TR method to real-world problems such as identifying radiation sources of different time in various environments. Numerical examples are presented to demonstrate the effectiveness of the proposed concept and method.

Using Lamb wave TDTE method to realize ultrasonic array super-resolution imaging of multiple asymmetric defects

Lamb waves are characterized by frequency dispersion and mode conversion. The imaging results obtained with traditional ultrasonic array imaging methods suffer from artifacts, reducing the imaging accuracy. In addition, traditional methods are subjected to the Rayleigh criterion and cannot image multiple defects with spacing smaller than the resolution threshold of ultrasound array imaging. In this paper, an ultrasonic Lamb wave inverse scattering topological imaging method based on time-domain topological energy (TDTE) was proposed. In this method, the topological progressive process of the inverse scattering topological imaging method was transformed into solving the direct and the adjoint sound fields. Then, by inverting the time of the adjoint sound field, the direct and the adjoint sound field can focus adaptively at the defect, which overcomes the influence of Lamb wave mode conversion and dispersion on the imaging results, and improves the imaging accuracy and resolution. Finally, the direct and the adjoint sound field are fused, and the TDTE value was taken as the pixel value of imaging. Accordingly, the limitation of the Rayleigh criterion was broken; the resolution of imaging was improved; the multi asymmetric defect imaging with the interval was realized less than the resolution threshold of the ultrasonic array imaging. The experimental results show that the TDTE method for multiple asymmetric defects can achieve super-resolution than the total focus method (TFM) and time-reversal (TR) method and can accurately distinguish the asymmetric defects when the defect spacing is smaller than the resolution threshold of the ultrasonic array imaging.

Locating Ships Using Time Reversal and Matrix Pencil Method by Their Underwater Acoustic Signals.

This paper presents a technique, based on the matrix pencil method (MPM), for the compression of underwater acoustic signals produced by boat engines. The compressed signal, represented by its complex resonance expansion, is intended to be sent over a low-bit-rate wireless communication channel. We demonstrate that the method can provide data compression greater than 60%, ensuring a correlation greater than 93% between the reconstructed and the original signal, at a sampling frequency of 2.2 kHz. Once the signal was reconstituted, a localization process was carried out with the time reversal method (TR) using information from four different sensors in a simulation environment. This process sought to achieve the identification of the position of the ship using only passive sensors, considering two different sensor arrangements.

Generation of transversely oriented optical polarization Möbius strips.

We report a time-reversal method based on the Richards-Wolf vectorial diffraction theory to generate a prescribed polarization topology on a defined trajectory within areas of relatively high intensity. An example is given to generate transversely oriented optical Möbius strips that wander around an axis perpendicular to the beam propagation direction. A number of sets of dipole antennae are purposefully positioned on a defined trajectory in the y = 0 plane and the radiation fields are collected by one high-NA objective lens. By sending the complex conjugate of the radiation fields in a time-reversed manner, the focal fields are calculated and the optical polarization topology on the trajectory can be tailored to form prescribed Möbius strips. The ability to control optical polarization topologies may find applications in nanofabrication, quantum communication, and light-matter interaction.

Feasibility study of 3D time-reversal reconstruction of proton-induced acoustic signals for dose verification in the head and the liver: A simulation study.

In vivo range and dose verification based on proton-induced acoustics (protoacoustics) is potentially a useful tool for proton therapy. Built upon our previous study with two-dimensional reconstruction, the time reversal (TR) method was extended to three-dimensional (3D) and evaluated at two treatment sites (head and liver) through simulation, with the emphasis on a number of aspects such as increased spatial coverage, computational workload, and signal interference among slices. Two mono-energetic pencil beams were modeled in each site. The k-Wave toolbox was used to investigate the propagation and TR reconstruction of acoustic waves. The performance was quantitatively assessed based on mean square error (MSE) for dose verification and Bragg peak localization error (ΔBP ) for range verification, with regard to five parameters: number of sensors, sampling duration, sampling timestep, spill time, and noise level. The respective impacts of five parameters are examined. Under the optimum setting, the achievable ΔBP can be limited within 1 voxel (voxel size: 3×3×3mm3 ) and the achievable MSE can be limited below 0.02, for the head case (56sensors) and the liver case (204sensors), respectively. The feasibility of range and dose verification utilizing the 3D TR method is demonstrated, as the very first step. In spite of several challenges unique to the 3D case (spatial coverage, computational workload, and signal interference among slices, etc.), promising performance is found and can be further improved through optimizing the deployment of sensors. The proposed approach may find potential use in several applications: beam diagnostics, in vivo dosimetry, and treatment monitoring.

Ultrasonic Signal Transmission Performance in Bolted Connections of Wood Structures under Different Preloads

In industrial applications, bolt connections are simple and economical, contributing to their popularity for use in wood packing boxes. However, they can easily fail when subjected to a continuous vibrational load under usual working conditions such as transportation and hoisting. Based on an ultrasonic technique, nondestructive evaluation can be used to quickly detect large-scale structures, but the complex propagation properties in wood limit its application. To solve this problem, a time-reversal method was adopted to predict the residual preload on bolted connections by focusing on the signals collected by wood structures, which helps to assess the structures’ reliability. In this study, the residual preload of bolted connections in wood structures was predicted using the deep-learning method, LSTM, one-dimensional Resnet and Densenet, and tree classification models. It was confirmed that the use of the time-reversal method for ultrasonic detection focused on the signals transmitted in bolted connections of wood structures and deep-learning methods are a feasible way to predict an ultrasonic transmission model.

The Quasi-reversibility Method to Numerically Solve an Inverse Source Problem for Hyperbolic Equations

We propose a numerical method to solve an inverse source problem of computing the initial condition of hyperbolic equations from the measurements of Cauchy data. This problem arises in thermo- and photo-acoustic tomography in a bounded cavity, in which the reflection of the wave makes the widely-used approaches, such as the time reversal method, not applicable. In order to solve this inverse source problem, we approximate the solution to the hyperbolic equation by its Fourier series with respect to a special orthonormal basis of $$L^2$$ . Then, we derive a coupled system of elliptic equations for the corresponding Fourier coefficients. We solve it by the quasi-reversibility method. The desired initial condition follows. We rigorously prove the convergence of the quasi-reversibility method as the noise level tends to 0. Some numerical examples are provided. In addition, we numerically prove that the use of the special basic above is significant.

M-ary nonlinear sine chirp spread spectrum for underwater acoustic communication based on virtual time-reversal mirror method

Linear chirp spread spectrum technique is widely used in underwater acoustic communication because of their resilience to high multipath and Doppler shift. Linear frequency modulated signal requires a high spreading factor to nearly reach orthogonality between two pairs of signals. On the other hand, nonlinear chirp spread spectrum signals can provide orthogonality at a low spreading factor. As a result, it improves spectral efficiency and is more insensitive to Doppler spread than the linear counterpart. To achieve a higher data rate, we propose two variants (half cycle sine and full cycle sine) of the M-ary nonlinear sine chirp spread spectrum technique based on virtual time-reversal mirror (VTRM). The proposed scheme uses different frequency bands to transmit chirp, and VTRM is used to improve the bit error rate due to high multipath. Its superior Doppler sensitivity makes it suitable for underwater acoustic communication. Furthermore, the proposed method uses a simple, low-power bank of matched filters; thus, it reduces the overall system complexity. Simulations are performed in different underwater acoustic channels to verify the robustness of the proposed scheme.

A Numerical Study on Computational Time Reversal for Structural Health Monitoring

Structural health monitoring problems are studied numerically with the time reversal method (TR). The dynamic output of the structure is applied, time reversed, as an external loading and its propagation within the deformable medium is followed backwards in time. Unknown loading sources or damages can be discovered by means of this method, focused by the reversed signal. The method is theoretically justified by the time-reversibility of the wave equation. Damage identification problems relevant to structural health monitoring for truss and frame structures are studied here. Beam structures are used for the demonstration of the concept, by means of numerical experiments. The influence of the signal-to-noise ratio (SNR) on the results was investigated, since this quantity influences the applicability of the method in real-life cases. The method is promising, in view of the increasing availability of distributed intelligent sensors and actuators.

Physical-virtual time reversing of nonlinear Lamb waves for fatigue crack detection and quantification

This article presents the investigation of a nonlinear Lamb wave time reversing technique for fatigue crack detection and quantification. A 2D analytical framework is initially presented, modeling Lamb wave generation, propagation, wave crack linear and nonlinear interaction, and reception. This study extends the Time Reversal (TR) techniques into the realm of nonlinear Lamb waves. Due to the structural transfer function variation between the forward and backward transmission process, the Virtual Time Reversal (VTR) algorithm reveals obvious deviation for predicting nonlinear Lamb waves, given that it replaces the backward TR procedure with the forward transfer function. However, this study demonstrates that the difference between the physical nonlinear TR method and the conventional VTR algorithm proves to be sensitive to detect and quantify fatigue cracks. Fatigue tests on a thin aluminum plate with a rivet hole are conducted to induce a fatigue crack. The experimental results further illuminate that the proposed physical-virtual nonlinear Lamb wave TR technique possesses remarkable sensitivity to the nucleation and growth of fatigue cracks. The paper finishes with discussion, concluding remarks, and suggestions for future work.

Broadband signal reconstruction for SHM: An experimental and numerical time reversal methodology

Structural Health Monitoring (SHM) aims to shift aircraft maintenance from a time-based to a condition-based approach. Within all the SHM techniques, Acoustic Emission (AE) allows for the monitoring of large areas by analyzing Lamb waves propagating in plate like structures. In this study, the authors proposed a Time Reversal (TR) methodology with the aim of reconstructing an original and unaltered signal from an AE event. Although the TR method has been applied in Narrow-Band (NwB) signal reconstruction, it fails when a Broad-Band (BdB) signal, such as a real AE event, is present. Therefore, a novel methodology based on the use of a Frequencies Compensation Transfer Function (FCTF), which is capable of reconstructing both NwB and real BdB signals, is presented. The study was carried out experimentally using several sensor layouts and materials with two different AE sources: (i) a Numerically Built Broadband (NBB) signal, (ii) a Pencil Lead Break (PLB). The results were validated numerically using Abaqus/CAETM with the implementation of absorbing boundaries to minimize edge reflections.

Time Reversal and Fractional Fourier Transform-Based Method for LFM Signal Detection in Underwater Multi-Path Channel

Fractional Fourier transform (FrFT) is a useful tool to detect linear frequency modulated (LFM) signal. However, the detection performance of the FrFT-based method will deteriorate drastically in underwater multi-path environment. This paper proposes a novel method based on time-reversal and fractional Fourier transform (TR-FrFT) to solve this problem. We make use of the focusing ability of time-reversal to mitigate the influence of multi-path, and then improve the detection performance of FrFT. Simulated results show that, compared to FrFT, the difference between peak value and maximum pseudo-peak value of the signal processed by TR-FrFT is improved by 8.75 dB. Lake experiments results indicate that, the difference between peak value and maximum pseudo-peak value of the signal processed by TR-FrFT is improved by 7.6 dB. The detection performance curves of FrFT and TR-FrFT detectors with simulated data and lake experiments data verify the effectiveness of proposed method.

Microseismic Source Location Estimation Using Reverse Double-Difference Time Imaging

To locate microseismic sources, the reverse double-difference time imaging method is proposed in this paper. The traditional time-reversal imaging method requires an accurate velocity model. To reduce the influence of the velocity model errors, this method uses the reverse travel time difference from adjacent receivers to each grid point of the velocity model and the arrival time difference of the microseismic event for imaging. We propose two imaging conditions for single source imaging and multi-source imaging to obtain high-resolution images of the sources. These imaging conditions are robust and can eliminate the error caused by outliers in the reverse double-difference time. The k-means clustering algorithm is used to optimize positioning results. Numerical experiments for source location estimation demonstrate that the reverse double-difference time imaging method is stable and reliable, and can locate multiple seismic sources with high-precision when the velocity model has errors. Some factors affecting the accuracy of source location estimation in the reverse double-difference time imaging are tested using 2D numerical experiments.