Time Reversal Process Research Articles

Notes about the macroscopic fluctuating theory

The macroscopic fluctuating theory developed during the last 30 years is applied to generic systems described by continuum fields ϕ(x, t) that evolve by a Langevin equation that locally either conserves or does not conserve the field. This paper aims to review well-known basic concepts and results from a pedagogical point of view by following a general framework in a practical and self-consistent way. From the probability of a path, we study the general properties of the system’s stationary state. In particular, we focus on the study of the quasipotential that defines the stationary distribution at the small noise limit. To discriminate between equilibrium and non-equilibrium stationary states, the system’s adjoint dynamics are defined as the system’s time-reversal Markov process. The equilibrium is then defined as the unique stationary state that is dynamically time-reversible, and therefore its adjoint dynamics are equal to those of the original one. This property is confronted with the macroscopic reversibility that occurs when the most probable path to create a fluctuation from the stationary state is equal to the time-reversed path that relaxes it. The lack of this symmetry implies a nonequilibrium stationary state; however, the converse is not true. Finally, we extensively study the two-body correlations at the stationary state. We derive some generic properties at various situations, including a discussion about the equivalence of ensembles in nonequilibrium systems.

An experimental validation of partial discharge localization using electromagnetic time reversal

The localization of partial discharge (PD) sources is of importance for the monitoring and maintenance of power transformers. Time difference of arrival (TDoA) based methods are widely adopted in the literature for the localization of PDs. Recently, time reversal (TR) was suggested as an efficient means to locate PD sources. As opposed to TDoA, which needs at least 4 sensors, TR is able to locate PD sources in power transformers with only one sensor. Moreover, it needs neither line-of-sight wave propagation from the PD sources to the sensor nor time synchronization. In this study, we present for the first time an experimental demonstration of the ability of the TR process to locate PD sources. A typical TR process includes three steps: (1) recording the PD-emitted field by a sensor, (2) time reversing and back injecting the signal into the medium, (3) using a proper criterion to obtain the focusing point which corresponds to the location of the PD source. In this work, we present a laboratory setup in which steps one and two are performed experimentally, both in the frequency and in the time domain. The obtained peak electric field value is used as a criterion in the third step. It is found that the accuracy of the proposed method is better than 2.5 cm in a transformer tank model with dimensions 73 × 73 × 103 cm3. The effects of the presence of scatterers such as transformer windings are also investigated experimentally and found not to affect the location accuracy of the method.

Scatterer identification in a 2D geophysical medium using an augmented computational time reversal method

AbstractThe problem of identifying an obstacle (scatterer) in the form of a cavity in a 2D geophysical medium is considered. This is posed as an inverse wave problem, where the location of the cavity is sought based on measurements of the elastic waves recorded by sensors located at certain points in the domain. The sensor measurements are noisy, and are generated synthetically as a first step. The inverse problem is solved by seeking the minimum of a specially designed cost functional, based on a computational time reversal (TR) procedure, where waves are radiated back in time from the sensors. The cost functional is defined to measure, for each scatterer candidate in the search space, the quality of the refocusing of the backward‐propagating waves on the given wave source at the end of the TR process. While the basic idea has appeared in previous publications, here it is applied to a 2D heterogeneous geophysical model (albeit a relatively simple one), and is enhanced by using several auxiliary techniques. These include (a) an “augmentation” technique, which is used to strengthen the coherent information (and thus to weaken the noncoherent information) by solving an elliptic problem at each time step; (b) experimentation with both instantaneous (impact) sources and time‐harmonic sources of finite duration; (c) combining the identification results of several sources and several source wavelengths to enhance identification; (d) reducing the size of the search space by a special “zooming in” technique; and (e) defining a performance index to assess the method's success and to provide a measure of confidence in the identification result in each specific case. Several numerical experiments are presented that demonstrate the performance of the proposed schemes. The sensitivity of the identification process to various parameters of the scatterer, the measurements, and the medium is investigated.

Timelike Compton Scattering with CLAS12 at Jefferson Lab

Generalized Parton Distributions (GPDs) describe the correlations between the longitudinal momentum and the transverse position of the partons inside the nucleon. They are nowadays the subject of an intense effort of research, in the perspective of understanding nucleon structure. GPDs have been studied mainly using Deeply Virtual Compton Scattering (DVCS, ep → e’p’γ). Here we highlight the measurement of the time-reversal conjugate process of DVCS, Timelike Compton Scattering (TCS) using data taken by CLAS12. The experimental measurement of the TCS angular asymmetry will provide new information on the real part of GPDs. This proceeding assesses the current status of the TCS analysis and presents preliminary results based on CLAS12 data.

Exploiting dynamic sparsity for time reversal underwater acoustic communication under rapidly time varying channels

Underwater acoustic (UWA) communication encounters significant difficulties posed by the simultaneous presence of multipath and time variations. It has been recognized that, under the assumption that channel keeps static within the processing windows, time reversal (TR) processing approach is capable of mitigating multipath via the spatial–temporal focusing. However, for a rapidly time-varying UWA channel, the replica channel impulse response in time reversal processor need to be updated frequently to avoid performance degradation, which leads to huge computational complexity and significant overhead. Consider that after time reversal processing the resulting time-reversed channel response exhibits much more slow time variations compared to the original channel impulse response, previously Kalman filtering has been adopted to track the time-reversed channel response to alleviate the requirement of frequent channel update. Under the framework of dynamic compressed sensing (DCS), in this paper the time-reversed channel is formulated as a sparse set consisting of constant and slowly time-varying supports to derive the Kalman Filtered Compressed Sensing (KF-CS) channel estimation algorithm for time reversal communication. Based on the receiver structure by coupling the KF-CS estimator driven time reversal processor with a single channel decision-feedback equalizer (TR-DCS-DFE), shallow water experimental results with field data are provided to demonstrate the effectiveness of the proposed algorithm, compared to the classic time reversal communication scheme.

Frequency-Domain Decision Feedback Equalization for Single-Carrier Transmissions in Fast Time-Varying Underwater Acoustic Channels

Frequency-domain equalization (FDE) is a computationally efficient method to recover underwater acoustic single-carrier transmissions in a multipath environment. The FDE receivers often operate in a block-by-block manner, assuming that the channel is time invariant during a block duration. This assumption implies that traditional block-based FDE receivers experience performance degradation in fast time-varying channel conditions, since the interfrequency interference (IFI) is often not considered. Here, we focus on the IFI cancelation (IFIC) in single-carrier transmissions. The IFI formulations are developed for a blockwise FDE receiver, where the time reversal (TR) processing is incorporated to alleviate the interblock interference. Based on the formulations, the IFI is estimated by the time-varying impulse responses, which are obtained from an adaptive basis expansion model. A soft two-step IFIC strategy is then employed to address the IFI. In the first step, the main IFI is removed by the time-varying TR processing and explicit IFI cancelation. The residual IFI is suppressed by the frequency-domain decision feedback equalization (FD-DFE) in the second step. To further enhance the communication performance, we develop a soft-symbol-based iterative receiver, referred to as IFIC-FD-DFE. The impulse responses, explicit IFI, and residual IFI are updated in an iterative fashion, based on the soft symbol estimates. The proposed receiver has been tested using the at-sea measurements collected at the Gulf of Mexico in August 2017. Communication packets at four ranges at the carrier frequency of 160 kHz with a symbol rate of 32 kHz have been decoded. The effectiveness of the IFIC-FD-DFE receiver has been demonstrated via comparisons with several FDE schemes in the current literature.

An Experimental Study of Passive Time Reversal Process for Underwater Acoustic Communication in Shallow Waters of the Bay of Bengal

An Experimental Study of Passive Time Reversal Process for Underwater Acoustic Communication in Shallow Waters of the Bay of Bengal

An Iterative Deconvolution-Time Reversal Method with Noise Reduction, a High Resolution and Sidelobe Suppression for Active Sonar in Shallow Water Environments

Matched filtering is widely used in active sonar because of its simplicity and ease of implementation. However, the resolution performance generally depends on the transmitted waveform. Moreover, its detection performance is limited by the high-level sidelobes and seriously degraded in a shallow water environment due to time spread induced by multipath propagation. This paper proposed a method named iterative deconvolution-time reversal (ID-TR), on which the energy of the cross-ambiguity function is modeled, as a convolution of the energy of the auto-ambiguity function of the transmitted signal with the generalized target reflectivity density. Similarly, the generalized target reflectivity density is a convolution of the spread function of channel with the reflectivity density of target as well. The ambiguity caused by the transmitted signal and the spread function of channel are removed by Richardson-Lucy iterative deconvolution and the time reversal processing, respectively. Moreover, this is a special case of the Richardson-Lucy algorithm that the blur function is one-dimensional and time-invariant. Therefore, the iteration deconvolution is actually implemented by the iterative temporal time reversal processing. Due to the iterative time reversal method can focus more and more energy on the strongest target with the iterative number increasing and then the peak-signal power increases, the simulated result shows that the noise reduction can achieve 250 dB in the “ideal” free field environment and 100 dB in a strong multipaths waveguide environment if a 1-ms linear frequency modulation with a 4-kHz frequency bandwidth is transmitted and the number of iteration is 10. Moreover, the range resolution is approximately a delta function. The results of the experiment in a tank show that the noise level is suppressed by more than 70 dB and the reverberation level is suppressed by 3 dB in the case of a single target and the iteration number being 8.

Investigation of a channel tracking based time reversal processing for underwater acoustic communication

This paper presents an investigation of a channel tracking based passive time reversal (PTR) communication method for mobile single-input/multiple-output communications in rapidly time-varying underwater acoustic channel. To investigate its performance in the non-stationary channels, the method is applied to a synthetic dataset generated by the underwater acoustic moving source model using normal mode method. The transmitted signal is modulated by the single-carrier modulation scheme using the carrier frequency of 20 kHz and bandwidth of 4, 8, and 12 kHz. From the comparisons with conventional PTR approach, the following advantages were found: (1) the quality of the equalization result hardly degrades even if the sound source moving speed increased, (2) suboptimal diversity combining is performed in the sense of the energy utilization of the multipath, (3) the dependence on the bandwidth is relatively small, and a significant performance improvement is seen especially for narrowband signals.

Guided ultrasonic wavefield cross-correlation with a curved array for high-resolution plate inspection

Abstract We present in this work an ultrasonic imaging technique based on wavefield cross-correlation that has potential for high-resolution inspecting of plates and plate-like structures. A curved transmit/receive array setup is used for acquiring wide-aperture waveform data beneficial for applying the presented imaging condition. An additional dispersion analysis using waveform data received by a linear array allows one to reveal the excited guided wave modes and possibly determine the shear wave velocity as an input parameter in the 3D wavefield simulation. Using synthetic but realistic data generated by realistic 3D simulations, we demonstrate the invariance of the time reversal process and the capability of the presented imaging approach for ultrasonic testing based on Lamb waves. In addition to the ability to localise and size multiple defects simultaneously, this imaging approach does not require baseline data and involves only minimal waveform data pre-processing.

Simple stochastic simulation of time irreversible and reversible processes

ABSTRACTAs time irreversibility of streamflow is marked for time scales up to several days, while common stochastic generation methods are good only for time-symmetric processes, the need for new methods to handle irreversibility, particularly in flood simulations, has been recently highlighted. From an investigation of the historical evolution of existing stochastic generation methods, which is a useful step before proposing new methods, the strengths and weaknesses of current approaches are located. Following this investigation, a generic solution to the stochastic generation problem is proposed. This is an analytical exact method based on an asymmetric moving-average scheme, capable of handling time irreversibility in addition to preserving the second-order stochastic structure, as well as higher-order marginal statistics, of a process. The method is studied theoretically in its general setting, as well as in its most interesting special cases, and is successfully applied to streamflow generation at an hourly scale.

Detection of Surface Breaking Cracks Filled With Solid Impurities Using a Baseline-Free NEWS-TR Method

The use of piezoceramic transducers for cracks identification via guided wave has attracted significant attention recently. Most studies assume that the medium in surface breaking cracks is only air. However, it is common that such cracks are filled with impurities (e.g. dust, grease) due to its exposure to the operational environment. The impurities may affect the propagation of the ultrasonic guided wave and hence it is of practical interest to develop detection methods for surface breaking cracks filled with impurities. This work investigates the possible effect of contact acoustic nonlinearity (CAN) on detecting surface breaking cracks filled with solid impurities. A baseline-free method is proposed to detect surface breaking cracks filled with solid impurities using the nonlinear elastic wave spectroscopy (NEWS) as a pre-treatment of time-reversal (TR). This method involves three key issues: selecting low-frequency swept signal modulated by Hanning window as an excitation signal, comparing the initial filtered response with the nonlinear time reversal response to determine the nonlinear feature related to such cracks, and determining the recommended low cut-off frequency to extract such nonlinear feature. The feasibility of the proposed method is experimentally and numerically verified using aluminum beams with surface breaking cracks. Results show that due to the existence of solid impurities, the crack interacts with low-frequency ultrasonic waves, which leads to nonlinear components in the response signal. It also indicates that after the time-reversal processing, the shifting of the maximum peak frequency from the second harmonic range to the third harmonic range can be used as a damage-sensitive nonlinear feature for detecting such cracks. The proposed method provides a promising way to identify surface breaking cracks filled with solid impurities without reference signal.

Fast Range and Motion Parameters Estimation for Maneuvering Targets Using Time-Reversal Process

For maneuvering targets, their motion during long observing time will deteriorate the integration results and degrade the performance of range and motion parameters estimation. To solve this problem, a computationally efficient method based on the time-reversal (TR) process and maximum likelihood (ML) principle, i.e., TR-MLE is proposed. The proposed method decouples the joint parameter estimation problem into two simpler problems, which not only increases the efficiency but also improves the estimation performance in low signal-noise-ratio. Furthermore, a fast method using Chirp-Z transform and Newton's method is developed for a more efficient implementation. The theoretical analysis of the noise properties after the TR process is carried out. Then, the corresponding Cramer–Rao lower bound that can evaluate the performance loss introduced by the TR process is discussed in detail. Simulated data and real data are used to assess the performance of the proposed method.

Damage Imaging in Mesoscale Concrete Modeling Based on the Ultrasonic Time-Reversal Technique

A novel method combining the time-reversal method (TRM) with wavelet analysis was proposed for damage imaging in mesoscale concrete modeling. The damage was imaged by the convergence of time-reversed wave signals after wavelet analysis. Through numerical study, three concrete models of different damage sizes were built with randomly distributed aggregate particles. The time-reversal process was simulated using the reverse damage-scattered ultrasonic wave signals as excitations recorded by the sensors. Then, the wavelet analysis was employed to extract certain frequency component, which can enhance detection precision and the signal-to-noise ratio. The damage imaging showed clearly the location of the defect. The results from experimental testing also demonstrated that this detection technique is an efficient and effective method for damage imaging in mesoscale concrete.

Experimental validation of time-reversal technique for defect detection in air-filled pipes using high frequency acoustic waves

Pipeline systems are extensively used for the transportation and distribution of the gas, water and petroleum products. The sustainability of the pipelines can be improved by utilizing the transient (acoustic)-based defect detection methods (TBDDM). In these methods, the probing pressure wave is generated in the pipe system, and the measured response is used to identify the defects. In this paper, experiments are performed on the acrylic pipe to study the acoustic wave propagation. The acrylic pipe is filled with air such that rigid pipe assumption is valid. Theoretical predictions applied with time reversal and match-field processing are validated with the experiments for the leak detection in a pipe system. The waveforms of Gaussian-modulated sine wave and Chirp are utilized as the transmitted signals in the frequency range of 1–15 kHz. The experimental results show that time-reversal technique is capable of accurate detection with a good resolution.

Time-reversal techniques for defect detection in pipe system using high frequency acoustic waves

Recent research has shown that transient (acoustic)-based defect detection methods (TBDDM) in water pipelines are a promising new approach that may help achieve more sustainable urban water supply systems (UWSS). These methods are based on the generation of a probing pressure wave in the pipe system, and the use of the measured response to identify defects. This paper develops an analytical solution for sound propagation in inviscid axisymmetric pipe system with sound source at the boundary. The solution is given for rigid and elastic pipe wall. This analytical model is used to apply time reversal and match-field processing to the detection of blockages and leaks in a single pipe system. The wave forms used at the source are Gaussian-modulated sine wave and Chirp with frequency ranging from 5 to 60 kHz. The results show accurate detection with resolution of the order of the probing wave length.

Time-Reversal Processing for Downlink-Limited Passive UHF RFID in Pulsed Wave Mode

This letter provides experimental evidence that, in a complex environment, a time-reversal processing of electromagnetic waves can increase the energy efficiency of the reader to tag communication and, hence, can increase the activation range of a passive ultrahigh frequency (UHF) radio frequency identification (RFID) system. A first experiment performed in a free-space environment shows that in addition to the classical continuous wave (CW) mode, a type AD222 passive UHF RFID tag can successfully operate in a pulsed wave (PW) mode using pulses with half-width 5 ns and period 35 ns. In a second experiment performed in a complex multipath environment, it is shown that the energy efficiency of the RFID system in the PW mode can be increased by applying a time-reversal (TR) processing strategy. Furthermore, it is shown that both PW and TR strategies involve less energy to activate the tag than the classical CW mode does. As a consequence, given a fixed amount of energy, TR processing can increase the activation range of the RFID system.

Time Reversal Based MAC for Multi-Hop Underwater Acoustic Networks

Constrained-energy underwater acoustic nodes are typically connected via a multi-hop underwater acoustic network (MHUAN) to cover a broad marine region. Recently, protocols for efficiently connecting such nodes have received considerable attention. In this paper, we show that the time reversal (TR) process plays an important role in the medium access control (MAC) because of its physical capability to exploit the multi-path energy from the richly scattering underwater environment, as well as to focus the signal energy in both spatial and temporal domains. In MHUANs, with severe multi-path propagation at the physical layer, the active TR process spatially focuses the signals to the location of the intended receiver; this significantly diminishes the interference among parallel links. We propose an active TR-based MAC protocol for MHUANs, with the aim of minimizing collision and maximizing channel utilization simultaneously. Furthermore, by considering the impact of the cross-correlation between different links on the TR-based medium access, we derive the threshold of the link cross-correlation to resolve collision caused by the high cross-correlation between realistic links. We perform simulations using the OPNET and BELLHOP environments, and show that the proposed TR-based MAC results in significantly improved throughput, decreased delay, and reduced data drop ratio in MHUANs.

Temporal Focusing Effects of Time-Reversal Frequency Diverse Array Antenna

Omnidirectional or the phased-array antenna is usually adopted in the time-reversal literature, but it cannot focus the power of the transmitted signals in both time- and space-domains. In this letter, we propose the hybridization of time reversal and frequency diverse array (FDA), which transmits the signal with a small frequency offset across the array to generate both angle- and range-dependent beampattern, for temporal focusing. The time-reversal FDA channel is modeled in multipath scenarios. For the given parameters with 12 transmit elements spaced by half-wavelength, carrier frequency 1 GHz, and frequency offset 1 kHz, the peak of time-reversal FDA focusing is 18.7% higher than that of a standard FDA. Both theoretic analysis and simulation results verify that, while maintaining FDA angular-time periodicity, the FDA range periodicity is eliminated and the energy is focused at the target position by the use of time-reversal processing.

Beam Steering of a Multi-Port Chassis Antenna Using the Least Squares Method and Theory of Characteristic Modes

This communication aims to obtain the maximum gain of a multi-port chassis antenna at the desired direction. The beam steering algorithm provides the weighting vector for the multi-port antenna to achieve the above goal. This communication uses the conventional least squares (LSs) method and the theory of characteristic modes (CMs) to find the efficient beam steering algorithm for a multiport chassis antenna. Owing to orthogonal properties of the CMs, the following two advantages emerge: 1) the algorithm provides a simple LS solution without computation of matrix inversion and 2) the physical meaning of this simple LS solution is equivalent to the narrowband time-reversal processing, i.e., phase conjugation processing. Consequently, the proposed algorithm makes it possible to efficiently control the radiation pattern of the multiport antenna in the desired direction with any kind of desired polarization. Validation was conducted by applying the proposed method to an insect-like drone model having three CMs.