Time Reversal Method Research Articles

On the Accuracy of Correlation Estimator Based Fault Location Methods in Transmission Lines via Polynomial Chaos and Regression Analysis

The electromagnetic time reversal (EMTR) method has recently shown a novel advantage in locating faults along transmission lines. Under the ideal condition for EMTR, the key parameters in the transmission line between the direct and reversed phases are assumed to be identical. Thus, the fault position can be pinpointed via the cross-correlation matching theory. However, due to natural and geographical causes, the parameters vary along the line; therefore, accurately obtaining the parameters is difficult. In this article, we first investigate the impact of uncertain parameters on the performance of EMTR-based fault location methods. It has been observed that the performance is insensitive to the variation of the parameters in the lossless case of transmission lines. But in the case of the overhead line above the lossy ground, a significant error in fault location is witnessed. So, under parameter uncertainty, a novel approach to finding the confidence fault interval is proposed, based on utilizing the polynomial chaos and regression analysis. A simulation case with uncertain parameters for different scenarios is presented to validate the performance of the proposed approach.

A Novel Pipeline Corrosion Monitoring Method Based on Piezoelectric Active Sensing and CNN.

In this study, a piezoelectric active sensing-based time reversal method was investigated for monitoring pipeline internal corrosion. An effective method that combines wavelet packet energy with a Convolutional Neural Network (CNN) was proposed to identify the internal corrosion status of pipelines. Two lead zirconate titanate (PZT) patches were pasted on the outer surface of the pipeline as actuators and sensors to generate and receive ultrasonic signals propagating through the inner wall of the pipeline. Then, the time reversal technique was employed to reverse the received response signal in the time domain, and then to retransmit it as an excitation signal to obtain the focused signal. Afterward, the wavelet packet transform was used to decompose the focused signal, and the wavelet packet energy (WPE) with large components was extracted as the input of the CNN model to rapidly identify the corrosion degree inside the pipeline. The corrosion experiments were conducted to verify the correctness of the proposed method. The occurrence and development of corrosion in pipelines were generated by electrochemical corrosion, and nine different depths of corrosion were imposed on the sample pipeline. The experimental results indicated that the classification accuracy exceeded 99.01%. Therefore, this method can quantitatively monitor the corrosion status of pipelines and can pinpoint the internal corrosion degree of pipelines promptly and accurately. The WPE-CNN model in combination with the proposed time reversal method has high application potential for monitoring pipeline internal corrosion.

Fiber Optic Impact Location System Based on a Tracking Tandem Low-Coherence Interferometer

This study proposes a method for detecting small-length fluctuations for fiber-optic sensors (FOS). The method is based on a tracking tandem low-coherence interferometer and enables the ability to compensate for temperature and deformation drifts in FOS. As a result, the constant high sensitivity of FOS over a wide frequency range is guaranteed. Sensitivity to the level of 2 nm in the frequency range of 200 kHz has been demonstrated. The operation of the circuit is demonstrated on the example of the 2D location of acoustic signals using a correlation algorithm for signal processing, known as the time reversal method. It is shown that this system enables us to determine the place of the impact on the sample under the test with an accuracy of about 2 cm using a single sensor.

Channel processing-based time-reversal method for multi-target tunable focusing

Achieving tunable focus of electromagnetic field energy at multiple target points is a critical challenge in the wireless power transfer (WPT) domain. In order to solve this problem, some techniques such as optimal constrained power focusing (OCPF) and time reversal (TR) have been proposed. The former presents limited practical applicability while the latter is noteworthy for its adaptive spatiotemporal synchronous focusing characteristics. However, the time reversal mirror (TRM) method necessitates intricate pretesting and has highly complex systems. In this study, we introduce a novel channel processing method, named channel extraction, selection, weighting, and reconstruction (CESWR), to attain balanced power distribution for multiple users, featuring low complexity, high computability, and rapid convergence. Unlike the traditional TR approach, our proposed method, based on channel correlation considerations, filters the channel impulse response (CIR) for multiple targets, dividing them into distinct characteristic and similar components for each target. This method ensures focused generation at both receiving ends while facilitating high-precision regulation of the peak voltage of the received signal. Furthermore, this study implements a rigorous examination of the linearity intrinsic to the proposed method, explicating a singular correspondence between the tuning of theoretical weights and the resultant outcomes. In order to verify the efficacy of this method, we construct a single-input multiple-output time-reversal cavity (SIMO-TRC) system. Subsequent experiments conducted for both loosely and tightly correlated models, provide invaluable insights. Evidently, in the loosely correlated model, the CESWR method exhibits proficiency in attaining a peak voltage ratio (PVR) of nearly 1.00 at the two receivers, with a minuscule numerical discrepancy of merely <inline-formula><tex-math id="M1">\begin{document}$8 \times {10^{ - 6}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230547_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230547_M1.png"/></alternatives></inline-formula> mV. In stark contrast, under the tightly correlated model, the CESWR method demonstrates an enhanced ability to differentiate between two targets, thus offering a noticeable improvement over the classic single-target TR method.

A noise-based high-resolution time-reversal method for acoustic defect localization in water pipes.

Pressurized water supply pipeline systems (PWSPS) are quintessential to human development and sustenance, but suffer a multitude of unresolved defects (i.e., leaks, blockages, etc.) due to aging and inaccessibility. In this paper, the ubiquitous high-frequency background noise in PWSPS is harnessed to introduce a high-resolution, passive defect detection technique. The relation between the acoustic Green's and cross correlation functions for a pressurized water pipe is derived for the case of high frequency waves, i.e., acoustic wavelengths smaller than the pipe diameter. This relation is subsequently used to formulate a time-reversal technique for localizing anomalies such as small variations in pipe wall impedance and through-wall defects (i.e., leaks). It is shown that the derived relationship between the cross correlation and acoustic Green's functions enables very accurate defect detection and localization by measuring the background noise at two locations along a pipe. This is an important result given that (i) there is limited access to buried PWSPS to conduct high-frequency active defect detection, and (ii) traditional methods to actively probe pipes (e.g., valve maneuverer) are low-resolution (tens to hundreds of meters) and often result in pipe overloading and fatigue.

Partial discharge localization using time reversal: Application to gas insulated switchgear

• Single sensor partial discharge (PD) localization in gas insulated switchgear. • Localization of PD using electromagnetic the time reversal (EMTR) method. • Investigation of the effect of noise, PD length, location, and orientation. • Single sensor localization of multiple, simultaneous PD in gas insulated switchgear. Gas-insulated switchgear (GIS) are some of the most reliable and most expensive equipment that are nowadays used in power systems. Condition monitoring of the power system equipment can help operators detect defects like partial discharges (PDs) early, prevent severe damage to the insulation of the apparatus and the related costs. Different techniques such as time difference of arrival (TDoA) have already been implemented to localize PDs. The TDoA technique requires four synchronized sensors to find the 3D location, it does not yield accurate results in a realistic situation when having multiple PDs, noise, scattering or obstacles which mask the line of sight between the sensor(s) and the PD. To have a powerful and accurate technique that can localize single or multiple PDs in power transformers in the presence of noise, scattering, obstacles, etc., using a single sensor, the time reversal (TR) technique has recently been proposed in both the acoustic and electromagnetic regimes. In this paper, the electromagnetic time reversal (EMTR) technique is applied to localize PDs in GIS, which have a more complicated structure than a transformer. The performance of the method is demonstrated considering several realistic case studies involving two pipe-shape and T-shape parts of a GIS.

Low-frequency sound source localization in enclosed space based on time reversal method

This study investigates sound source localization (SSL) in enclosed space at low frequencies. Reverberation and noise are important factors that affect localization result. Time reversal technology has the characteristics of compensating the multipath effect and adaptive focus, therefore, it can realize (SSL) in enclosed space. In order to improve the spatial resolution of localization, the recovery of the second transmitting signal received after time reversal is completed by the compressive sensing algorithm. We propose time reversal sparse Bayesian learning (TR-SBL) method to solve the problem of SSL. Firstly, time reversal focusing model of sound source propagation in the enclosed space is established. Then compressive sensing algorithm is performed on the second received signal, a sparse Bayesian framework is used to solve the localization problem. The time reversal method can overcome the reverberation interference in the enclosed space, and the compressive sensing algorithm can improve the spatial resolution. A series of simulations, which can be compared with the time reversal method and L1 norm method, are carried out to verify the localization performance of the proposed method, including simulations of sound sources with different frequencies, signal-to-noise ratios (SNRs), absorption coefficients, and positions. The algorithm is also evaluated in a reverberation chamber using sound sources with different frequencies. The numerical simulations and experimental results show that the proposed method achieves good localization performance in a low-SNR and reverberation environment, the spatial resolution is up to 0.1 m for a sound source with a frequency of 125 Hz.

Sub-wavelength focusing for low-frequency sound sources using an iterative time reversal method

Microphone array measurements processed with imaging algorithms are commonly performed to identify and quantify noise sources in machines, which is the premise of noise control. However, due to the limitations of the half-wavelength theory, beamforming and time reversal (TR) methods cannot effectively separate multiple low-frequency sources. Although near-field acoustic holography can overcome the diffraction limit, it will encounter an ill-posed problem. To avoid solving the inverse problem, iterative TR processing (iterative-TR) is proposed to obtain the sub-wavelength focusing and improve the spatial resolution at low frequency. The focusing result is corrected step by step with iteration implemented until it reaches the convergence threshold. The propagation matrix between microphones and focusing points is reconstructed by singular-value normalization to ensure the convergence of the iteration. Numerical simulation results show that the iterative-TR method is able to break through the diffraction limit below 1000 Hz within a measurement distance of 0.5 m and reach convergence within 105 iterations, which is less than 10 s. The experimental results indoors with significant reverberation show that iterative-TR has the ability to stably give the multiple source positions with 0.11 m spacing even at 100 Hz, that is, the spatial resolution reaches 1/31 wavelength. Detailed analysis shows that the overall performance of iterative-TR outperforms other methods capable of sub-wavelength focusing for signals below 1000 Hz. The identification of two loudspeakers in a car shows the practicality of the proposed method.

Fast inverse elastic scattering of multiple particles in three dimensions* *The first author was partially supported by the Funds for Creative Research Groups of NSFC (No. 11621101), NSFC Grants 11871427 and U21A20425.

Many applications require recovering the geometric information of multiple elastic particles based on the scattering information. In this paper, we consider the inverse time-harmonic elastic scattering of multiple rigid particles in three dimensions. We measure the far field information and apply the time reversal method to recover the unknown elastic particles. Two regimes are considered depending on the size and distance among particles. First, an asymptotic analysis for the imaging of small and distant particles is given based on the scattering property of a single particle, which can be used for selective focusing. Second, when particles are not small but well-separated, a fast algorithm, based on the combination of multiple scattering theory and fast multipole method, is proposed to efficiently simulate the forward multiple scattering problem and applied to the inverse elastic scattering. Numerical experiments demonstrate the proposed method can effectively recover the locations and shapes of multiple unknown particles.

A physically-informed deep-learning model using time-reversal for locating a source from sparse and highly noisy sensors data

We approximate the underwater acoustic wave problem for locating sources in that medium. We create a time dependent synthetic data-set of sensor recorded pressures, based on a small set of sensors placed in the domain, and perturb this data with high random multiplicative noise. We show that reference time-reversal based method struggles with high noise, and a naive deep-learning method also fails. We propose a method, based on physically-informed neural-networks and time-reversal, for approximating the source location even in the presence of high sensors noise.

Comparison of the FWI-Adjoint and Time Reversal Methods for the Identification of Elastic Scatterers

The paper falls into the category of computational methods for inverse scattering techniques for the identification of scatterers. We consider a linear elastodynamic problem and compare two popular methods for identifying a scatterer in the domain. Finite elements are employed with each of the two methods for spatial discretization. One method considered is Full Waveform Inversion using a gradient-based optimization and the adjoint method. In the adjoint procedure for calculating the gradient, we use the variant of discretizing the unknown parameters from the outset while all other variables remain continuous. Gradient optimization is performed in the examples using a quasi-Newton method. The other method compared is the computational Time Reversal technique, which is used in combination with an augmentation procedure to enhance performance. advantages and limitations of the two methods are outlined, and their performance is compared through an example from geophysics.

Optical vortex fields with an arbitrary orbital angular momentum orientation.

Optical vortex fields with a tilted phase singularity line are associated with a tilted orbital angular momentum (OAM). In this Letter, we propose a method to generate optical vortex fields with arbitrary OAM orientation based on the time-reversal method, vectorial diffraction theory, and a 4Pi optical configuration. The ability to control the 3D OAM orientation may find applications in optical tweezing, light-matter interaction, and spin-orbital coupling.

Interpretation of time reversal focal spots based on point-source homogenization

SUMMARYThe time reversal method is based on the backpropagation of seismic waveforms recorded at a set of receivers. When this set forms a closed surface and the elastic properties of the medium are correct, the seismic energy focuses at the source location, creating a focal spot. Such a spot is smooth in space, whereas the original wavefield usually shows a displacement discontinuity at the source. The goal of this paper is to discuss the link between the focal spot and the original source using the concept of homogenized point source. We show that the backpropagated wavefield is equivalent to the sum of two low-wavenumber fields resulting from the homogenization of the original point source. In other words, the homogenized point source is the equivalent force for producing the focal spot. In addition to the demonstration in the general 3-D heterogeneous case, we present some numerical examples in 2-D.

An efficient Lamb wave-based virtual refined time-reversal method for damage localization in plates using broadband measurements

This study proposes a modified virtual time-reversal (VTR) algorithm for baseline signal-free damage detection in plate-like structures. The physical actuation and sensing of Lamb waves are performed using a broadband Gaussian excitation instead of the conventional narrowband modulated tone burst excitations. The forward response and the reconstructed signal due to the time-reversal process for a narrowband input signal are then constructed virtually using the broadband transfer function. The method eliminates the possibility of numerical errors encountered in the conventional VTR method based on narrowband excitations. It is also more efficient than the traditional VTR algorithm because it can probe at multiple excitation frequencies using a single measurement for each sensing path. This modified VTR algorithm is employed in the recently developed refined time-reversal method (RTRM), which uses an extended signal length of the reconstructed signal for computing damage index (DI) and probes the structure at the best reconstruction frequency. The new method is termed the virtual refined time-reversal method (VRTRM). The DIs based on the VRTRM are used in the reconstruction algorithm for probabilistic inspection of defects to achieve baseline signal-free localization of damages. The efficacy of the proposed VRTRM for damage localization is experimentally verified with the established technique RTRM. Experiments are performed in an aluminium plate equipped with a network of surface-bonded piezoelectric patch transducers to illustrate the conventional VTR’s pitfalls and the modified VTR’s accuracy for a single mass damage scenario. The results show that the proposed VRTRM is as accurate as the established technique RTRM in estimating the reconstructed signals and localizing a block mass damage. Finally, the VRTRM is shown to localize in a dual damage scenario with excellent accuracy. In contrast, the conventional main mode-based VTR method fails to localize the damages with or without single-mode tuning.

Transversely oriented cylindrically polarized optical fields.

Cylindrical vector (CV) beams have nonuniform polarization vector distribution with a singularity line directed along the optical axis. In this paper, we propose a method to synthesize transversely oriented cylindrically polarized optical fields in the focal region with a singularity line perpendicular to the optical axis. The scheme is based on the time-reversal method, the vectorial diffraction theory, and the 4Pi optical configuration. Both transversely oriented radially polarized and azimuthally polarized optical fields are demonstrated. The superposition of transverse cylindrically polarized optical fields leads to a peculiar distribution carrying controllable transverse spin angular momentum (SAM) and transverse orbital angular momentum (OAM) that may find applications in optical tweezing, light-matter interaction, and unidirectional beam propagation excitation.

Acoustophoresis in suspensions with local and time-discrete sound fields based on the time reversal technique

Abstract. In this paper, a new approach of three-dimensional acoustic particle manipulation (acoustophoresis) in closed and liquid-filled vessels based on the time reversal technique is discussed. Based on simulation studies, this work investigates the technical prerequisites to achieve appropriate acoustic radiation forces (ARFs) for the manipulation of small particles with the time reversal method by utilizing multiple reflections in a closed vessel. The time-discrete and localized acoustic pressure field required for this purpose is generated by a time reversal mirror composed of 24 piezoceramic transducers. The paper also gives an outlook on practical evaluation of the simulation results based on a demonstrator setup.

Research on damage monitoring of sandwich armor composite structure based on time reversal principle

Abstract With the wide application of lightweight armor composite, it is of great significance to monitor delamination damage in laminated materials. Ultrasonic testing often needs to be immersed in liquid for monitoring, which is inconvenient for large-size specimens and cannot be monitored in real time. In structural health monitoring, the corresponding relationship between damage and response signal characteristics (such as amplitude and energy) is established, which is greatly affected by various environmental factors (such as temperature and load). Due to the particularity of the multi-layer composite structure with large thickness, the problem of Lamb wave multi-mode and frequency dispersion affects the accuracy of damage monitoring, which brings great difficulty to the accuracy of damage monitoring. Four piezoelectric sensors were arranged on the surface of the 5 mm sandwich armor composite composed of alumina ceramic, T700 carbon fiber and TC4 titanium alloy. The signal-to-noise ratio of the obtained damage scattering signal was improved by time reversal method and Gabor wavelet transform. Monitoring and imaging of single damage and multiple damage on the reverse side of armor composite were studied. The experimental results show that the radial error of single damage location is 4.24 mm, and the radial error of multiple damage location is 5.39 mm.

A Spatial Multitarget Ultrasound Neuromodulation System Using High-Powered 2-D Array Transducer.

Transcranial focused ultrasound (tFUS) is increasingly used in experimental neuroscience due to its neuromodulatory effectiveness in animal studies. However, achieving multitarget tFUS in small animals is typically limited by transducer size, energy transfer efficiency, and brain volume. The objective of this work was to construct an ultrasound system for multitarget neuromodulation in small animals. First, a miniaturized high-powered 2-D array transducer was developed. The phase delay of each array element was calculated based on the multifocal time-reversal method, generating multiple foci simultaneously in a 3-D field. The effects of the axial focal length, interfocus spacing (lateral distance between the two focal centers), and the number of foci on the focal properties of the pressure field were examined through numerical simulations. In-vitro ultrasonic measurements and transcranial simulations on a rat skull were conducted. The minimum interfocus spacing separating two -6-dB foci and the peak full-width at half-maximum were positively correlated with axial focal length; the relative relationship between the interfocus spacing and pressure field properties was similar for each axial focal length. The maximum acoustic pressure and spatial average intensity at focus in deionized water were 2.21 MPa and 133 W/cm2, respectively. The simulated and experimental results were compared, demonstrating agreement in both peak position and focus shape. The ultrasound system can provide a neuroscientific platform for evaluating the feasibility of multitarget ultrasound stimulation treatment protocols, thus improving the understanding of functional neuroanatomy.

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.