Time Reversal Process Research Articles

Best reconstruction frequency for time-reversal process of Lamb waves and its determination from a single measurement

This article presents a theoretical framework for the concept of the best reconstruction frequency (BRF) of Lamb waves in elastic plates and its significance in the context of structural health monitoring (SHM). The time-reversal process (TRP) of Lamb waves has been widely explored for baseline-free damage detection in thin-walled structures. Previous studies have indicated that the accuracy of damage detection can be significantly improved by exciting Lamb waves at a frequency where the time-reversibility in the undamaged state is maximum within a desired frequency range. This frequency, termed the BRF, has been determined phenomenologically in prior research but lacked a rigorous theoretical foundation. In this study, the BRF is derived as the frequency at which the amplitude dispersion of the main mode of the reconstructed signal after the TRP is minimized. Accordingly, a method is put forth to determine this frequency from a single measurement using a broadband excitation eliminating the need to compute the similarity between the reconstructed and input waveforms at different excitation frequencies. The developed theory is validated with experiments conducted on an aluminium plate with Lamb waves generated and sensed by surface-bonded piezoelectric patch transducers. Notably, the study establishes that the BRF is a system property specific to a given transducer-plate-adhesive system and is independent of the distance between transducers. This characteristic makes it suitable for identifying damage locations when employing multiple sensing paths. The findings constitute an important milestone in understanding the TRP of Lamb waves and developing robust SHM technologies based on it.

Amplitude Dispersion Compensation in Time-Reversed Lamb Waves for Enhanced Sensitivity in Damage Detection

In Lamb wave-based baseline-free damage detection employing the time-reversal method (TRM), the damage index (DI) is computed from the similarity between the main mode of the reconstructed signal obtained after the time-reversal process (TRP) and the input signal, both normalized. However, a perfect similarity with a zero DI value cannot be achieved for undamaged structures due to the amplitude dispersion of Lamb waves, which is not compensated in the TRP. Thus, a nonzero DI does not necessarily indicate the presence of damage. Even worse is the fact that the similarity and, therefore, the DI for the pristine structure depend on the probing frequency, making it difficult to estimate a unique threshold value of DI for damage identification. The imperfect reconstruction also significantly reduces the relative sensitivity of the DI to the presence of damage. In this article, we propose a method to compensate the amplitude dispersion in the main mode of the reconstructed signal for undamaged metallic plates to achieve a zero threshold of DI. First, the transfer function of the main mode of the reconstructed signal for an undamaged path (the path with the least DI for a network of sensing paths) is obtained by exciting the actuator with a broadband excitation and extracting the S0 and A0 modes from the forward response measured at the sensor. To compensate the amplitude dispersion in the TRP-generated main mode, the transfer function of the recorded signal of a path is divided by the transfer function of the main mode obtained for the undamaged path. A comprehensive numerical study shows that the DI computed with the compensated reconstructed signal has much higher sensitivity to damage than that without applying the proposed compensation at all frequencies, providing the flexibility to choose the probing frequency according to the desired damage size to be detected.

A new methodology of non-destructive testing in a set of two parallel immersed plates using time reversal process and leaky Lamb waves

Ultrasound has been identified as a suitable method for inspecting complex structures (such as nuclear reactors), as it can propagate through both liquids and steel elements to be inspected. Leaky Lamb waves have been extensively researched to detect damages in plate-shaped structures, which are waves that reemit bulk waves towards the surrounding fluid. An imaging method based on the time reversal of Lamb waves has been applied in preliminary work to detect the edge of a single immersed plate and a machined notch. In this study, the frequency-domain topological energy method is applied to a set of two parallel immersed plates to succeed in accurately localizing defects represented by the edges of the plates. Firstly, the behaviour of leaky Lamb waves is briefly addressed. A 2D-STFT (two-dimensional Short Time Fourier Transform) is then used to separate the different Lamb modes, which is a powerful tool for tracking the modes involved in the propagation over time. The Fast Topological Imaging Method (FTIM), which allows for faster computations with less data storage, is applied to the case of Lamb waves in a set of parallel plates. Lamb modes can be identified then selected to improve the analysis of the obtained images. An original methodology is proposed based on spots (maxima) analysis for interpreting the results of this topological energy and identifying the edges of the two plates. This process could be applied, in the same manner, to other scattering defects in ultrasound non-destructive testing of plates.

Time domain turbo equalization based on vector approximate message passing for multiple-input multiple-output underwater acoustic communications.

This paper proposes a high-performance receiver for underwater acoustic communications based on time reversal processing for multiple-input multiple-output (MIMO) systems. The receiver employs the vector approximate message passing (VAMP) algorithm as a soft equalizer in turbo equalization. By performing self-iteration between the inner soft slicer and the inner soft equalizer, the VAMP algorithm achieves near-optimal performance. Furthermore, an iterative channel-estimation-based soft successive interference cancellation method is incorporated to suppress co-channel interference in the MIMO system. Additionally, the introduction of passive time reversal technology can combine multiple channels into a single channel, which greatly reduces the computational complexity of the MIMO system, especially for large MIMO systems. The effectiveness of the proposed receiver is verified using experimental data collected in Songhua Lake, China in 2019. The results demonstrate that the proposed receiver significantly reduces the complexity of the traditional parallel-VAMP receiver without sacrificing performance and outperforms other receivers of the same type. Moreover, our experimental results also verify that the VAMP-turbo outperforms the generalized approximate message passing (GAMP)-turbo in terms of bit error rate and convergence performance.

Tree Roots GPR Detection Based on 3-D Time-Reversal Signal Processing

Tree Roots GPR Detection Based on 3-D Time-Reversal Signal Processing

A single-channel virtual receiving array using a time-reversal chaotic cavity.

Chaotic reverberation in a cavity, when coupled with time reversal acoustics, can be harnessed to build a perfect time-reversal mirror for transmitting and receiving highly focused sounds with a small number of transducers. In this article, a virtual receiving array, comprised of a single receiving transducer and a chaotic cavity, is developed based on time reversal processing of the reverberation inside the cavity. A prototype array, having 10 × 10 virtual receiving elements, is built and evaluated against a comparable physical array in terms of its localization and waveform reproduction capabilities. It turns out that the most crucial factor in the success of a virtual array is the ergodicity of its chaotic cavity, the exact mathematical expression for which is also derived. The virtual receiving array presented here may find some niche applications in reverberant environments, where a physical array turns out to be too costly or cumbersome to operate.

The irreversibility of relativistic time-dilation

The fluctuation relations, which characterize irreversible processes in nature, are among the most important results in non-equilibrium physics. In short, these relations say that it is exponentially unlikely for us to observe a time-reversed process and, thus, establish the thermodynamic arrow of time pointing from low to high entropy. On the other hand, fundamental physical theories are invariant under time-reversal symmetry. Although in Newtonian and quantum physics the emergence of irreversible processes, as well as fluctuation relations, is relatively well understood, many problems arise when relativity enters the game. In this work, by considering a specific class of spacetimes, we explore the question of how the time-dilation effect enters into the fluctuation relations. We conclude that a positive entropy production emerges as a consequence of both the special relativistic and the gravitational (enclosed in the equivalence principle) time-dilation effects.

Directional microwave heating based on time reversal quantified by information theory

Microwave heating has found extensive applications across diverse industries. However, achieving directional heating remains a significant challenge due to the complexities involved in controlling the electromagnetic field distribution. To address this issue, a novel directional heating method based on time reversal is proposed in this paper. A small signal source is placed at the heated medium to radiate electromagnetic waves. The information received by each receiving unit undergoes specialized processing before being transmitted back to the cavity. Consequently, the time reversal electromagnetic field of each receiving unit gathers at the heating material to achieve directional heating. Moreover, methods are being proposed to calculate the amount of information during time reversal using information theory. These approaches also aim to quantify the disparity in electromagnetic field distribution before and after the time reversal process. A comprehensive multi-physics model of microwave heating is established to simulate the directional heating process based on time reversal. An experimental system is also constructed to validate the proposed model, where the heating results are measured by an infrared thermal imager and a thermocouple. Finally, the effects of frequency, power and phase on the performance of directional microwave heating are analyzed.

Multiple-Input-Multiple-Output Filtered Multitone Time Reversal Acoustic Communications Using Direct Adaptation-Based Turbo Equalization.

This paper proposes using direct adaptation (DA)-based turbo equalization in multiple-input-multiple-output (MIMO) filtered multitone (FMT) time reversal (TR) acoustic communications to jointly suppress noise, residual co-channel interference (CCI) and intersymbol interference (ISI) after the TR process. Soft information-based adaptive decision feedback equalization (ADFE) adjusted according to the recursive expected least squares (RELS) algorithm, including interference cancellation and decoding, is used to construct the DA-based turbo equalization. In the proposed method, soft information is exchanged between soft symbols with soft decisions of decoding iteratively, and interference suppression is proceeded successively and iteratively until the performance is stable. The principle of the proposed method is analyzed, and based on the acoustic channel responses measured in a real experiment, the performance is assessed in relation to that of anther two methods. Compared with the MIMO-FMT TR underwater acoustic communication using interference suppression without error control coding (ECC), the proposed method performs better, benefitting from the ECC included in turbo equalization. Additionally, compared with the MIMO-FMT TR underwater acoustic communication using interference suppression based on hard decision equalization and decoding, the proposed method exhibits superior performance by exploiting soft information.

Numerical modeling of Mach-stem formation in high-amplitude time-reversal focusing.

In acoustics, time-reversal processing is commonly used to exploit multiple scatterings in reverberant environments to focus sound to a specific location. Recently, the nonlinear characteristics of time-reversal focusing at amplitudes as high as 200 dB have been reported [Patchett and Anderson, J. Acoust. Soc. Am. 151(6), 3603-3614 (2022)]. These studies were experimental in nature and suggested that converging waves nonlinearly interact in the focusing of waves, leading to nonlinear amplification. This study investigates the nonlinear interactions and subsequent characteristics from a model-based approach. Utilizing both finite difference and finite-element models, it is shown that nonlinear interactions between high-amplitude waves lead to free-space Mach-wave coalescence of the converging waves. The number of waves used in both models represents a small piece of the full aperture of converging waves experimentally. Limiting the number of waves limits the number of Mach-stem formations and reduces the nonlinear growth of the focus amplitudes when compared to experiment. However, limiting the number of waves allows the identification of individual Mach waves. Mach wave coalescence leading to Mach-stem formation appears to be the mechanism behind nonlinear amplification of peak focus amplitudes observed in high-amplitude time-reversal focusing.

Impact localization and force reconstruction for composite plates based on virtual time reversal processing with time-domain spectral finite element method

Composite structures are widely used in different industries as important load-carrying components due to their excellent performance. These structures are prone to be damaged under low-velocity impacts with invisible cracks. Hence, impact identification is a critical part of composite structural health monitoring. In this paper, an approach is developed, which is based on time-reversal (T-R) processing and time-domain spectral finite element method. The spatial and temporal focusing properties of T-R are utilized to locate the impact source and restore the impact force, respectively. Moreover, the impact energy is evaluated by establishing the function of impact force and kinetic energy at the impact moment. The proposed method is validated experimentally for different scenarios. The influences of the signal length and accuracy of the numerical model on the proposed method are discussed in detail. The results demonstrate that the proposed method can correctly locate the impact source in composite structures, and the identified impact force can reproduce the impact event efficiently. The impact localization is essentially independent of the effect of signal length while it is vulnerable to the mesh grid. Besides, the developed method has consistent results in the case of data perturbation of material properties in the numerical model, which shows its good robustness.

Modeling free space Mach stem formation in high-amplitude focusing of sound using time reversal

In acoustics, time reversal processing may be used to focus sound to a selected spatial location. Recently, the nonlinear characteristics of time-reversalfocusing at amplitudes as high as 200 dB have been reported [Patchett and Anderson, J. Acoust. Soc. Am., 151(6), (2022)]. These studies were experimental in nature and suggested that converging waves nonlinearly interact in the focusing of waves, leading to surprising observations of nonlinear amplification. This study investigates the nonlinear interactions and subsequent characteristics from a model-based approach. Utilizing both the k-Wave© package for MATLAB©, and COMSOL Multiphysics©, it is shown that nonlinear interactions between high-amplitude waves leads to free-space Mach-wave coalescence of the converging waves. The number of waves used in both models represents a small piece of the full aperture of converging waves experimentally. Limiting the number of waves limits the number of Mach-stem formations and reduces the nonlinear growth of thefocus amplitudes when compared to experiment. However, limiting the number of waves allows the identification of individual Mach waves. Mach wave coalescence leading to Mach-stem formation appears to be the mechanism behind nonlinear amplification of peak focus amplitudes observed in high amplitude time reversal focusing.

A Score-Based Approach for Training Schrödinger Bridges for Data Modelling

A Schrödinger bridge is a stochastic process connecting two given probability distributions over time. It has been recently applied as an approach for generative data modelling. The computational training of such bridges requires the repeated estimation of the drift function for a time-reversed stochastic process using samples generated by the corresponding forward process. We introduce a modified score- function-based method for computing such reverse drifts, which can be efficiently implemented by a feed-forward neural network. We applied our approach to artificial datasets with increasing complexity. Finally, we evaluated its performance on genetic data, where Schrödinger bridges can be used to model the time evolution of single-cell RNA measurements.

Time reversal of long coda waves: Experiments in the nonlinear regime.

A problem that arises when the time-reversal process is applied in a nonlinear regime is related to the generation of harmonics: conventional piezoelectric transducers cannot work properly at the frequency of the second harmonic. Then, the time-reversed wave cannot be completely emitted. Few works provide a solution to this issue. Thus, we study the alternative of performing a cross correlation of the wavefield. In a linear regime, this procedure is an accurate method for estimating real time-reversal properties. To study both procedures in the nonlinear regime in detail, we measure the wavefield of a wave that (1) traverses a multiple scattering medium, composed by a random set of parallel copper rods and (2) propagates inside a reverberant cavity, consisting of an aluminum case immersed in water. Cross correlation yields a virtually focused wavefield, where the focal width at the frequency of the first, second, and third harmonics can be measured. We compare these values with those obtained in a real time-reversal experiment. Results suggest that both time-reversal procedures are equivalent. In addition, we discuss the possibility of amplitude estimation at the focal spot and the limits of this work based on a theoretical model.

Fluctuation Theorem for Information Thermodynamics of Quantum Correlated Systems.

We establish a fluctuation theorem for an open quantum bipartite system that explicitly manifests the role played by quantum correlation. Generally quantum correlations may substantially modify the universality of classical thermodynamic relations in composite systems. Our fluctuation theorem finds a non-equilibrium parameter of genuinely quantum nature that sheds light on the emerging quantum information thermodynamics. Specifically we show that the statistics of quantum correlation fluctuation obtained in a time-reversed process can provide a useful insight into addressing work and heat in the resulting thermodynamic evolution. We illustrate these quantum thermodynamic relations by two examples of quantum correlated systems.

High-resolution ultrasonic imaging technology for the damage of concrete structures based on total focusing method

Concrete has diverse internal acoustic interface, and the scattering of ultrasonic wave is serious and complicated. Based on total focusing method (TFM) imaging, this paper investigates the concrete inspection resolution optimization method. Firstly, the reinforced concrete model was simulated, using time reversal (TR) algorithm to process the signal, the defects and rebars signal amplitudes increased by 7.6 dB and 4.7 dB, respectively. Then in order to reduce the structural noise, the phase coherence imaging (PCI) algorithm was applied, resulting in a signal-to-noise ratio (SNR) improvement of about 22.2 dB on average. Finally, the imaging positions were corrected. In the experiment, to eliminate the influence of the probe ringing on the detection signal, digital filtering was introduced to restore the signal wave packet,and the image SNR was improved by 3.2 dB after TR processing and by 9.4 dB after PCI processing.

Energy-band echoes: Time-reversed light emission from optically driven quasiparticle wave packets

The at-will control of quantum states is a primary goal of quantum science and technology. The celebrated Hahn echo exemplifies such quantum-state control based on a time-reversal process in a few-level system. Here, we propose a different echo phenomenon associated with the energy-band structure in quantum many-body systems. We show that the dynamics of quasiparticle wavepackets can be reversed by a driving electric-field pulse, yielding echoes with the time-reversed waveform of the optical excitation pulse when the quasiparticles recombine. The present echoes are observed not only in band insulators but also in correlated insulators, including a Mott insulator and a spontaneously-broken-symmetry charge-ordered insulator, in one- and higher-dimensional systems, irrespective of the integrability of the models. Analytical expressions reveal the conditions under which the echoes appear, and they also indicate that the frequency of the echo pulses reflects the dispersion relation for quasiparticles such as electron-hole pairs, doublon-holon pairs, and kink-antikink pairs. These findings provide a framework for all-optical momentum-resolved spectroscopy of the quasiparticles in quantum many-body systems.

Application of time-reversal in electromagnetic power synthesis under distributed motion platform

Space-time adaptive focusing is the most prominent feature of time-reversal electromagnetic waves. This paper studies the spatial power synthesis technology of distributed motion platforms based on time-reversal electromagnetic waves. Firstly, the spatial power synthesis process based on time-reversal on a distributed fixed platform is modeled. Then, the time-reversal signal processing process of a distributed array on the motion platform is deduced, and the feasibility of realizing precise power focusing is verified in theory. Finally, the factors affecting the power synthesis effect in the target area are analyzed. The simulation results indicate that the spatial power synthesis on the distributed motion platform based on the time-reversal can effectively balance between power focusing effect and computational complexity. Also, the proposed method has better efficiency than the existing techniques, and it has strong practicability and feasibility.

Reversible Markov decision processes and the Gaussian free field

A Markov decision problem is called reversible if the stationary controlled Markov chain is reversible under every stationary Markovian strategy. A natural application in which such problems arise is in the control of Metropolis–Hastings type dynamics. We characterize all discrete time reversible Markov decision processes with finite state and action spaces. We show that the policy iteration algorithm for finding an optimal policy can be significantly simplified in Markov decision problems of this type. We also highlight the relation between the finite time evolution of the accrual of reward and the Gaussian free field associated to the controlled Markov chain.

An enhanced GPR-based data processing approach for detecting subsurface utilities in urban distribution networks

Ground-penetrating radar (GPR) is a non-destructive technique that helps find subsurface utilities. In geophysical investigations, the availability of noise sources, and the complexity of utility networks mean that performing a routine field operation and processing may not reveal the wanted anomalies. Thus, we use data acquisition and processing strategy to detect every single hyperbolic event (which means a probable anomaly) more accurately. In this approach, we first acquire data in parallel lines that cross the predetermined utility line path, use pre-processing techniques (zero-time correction, dewowing, etc.), and then use compensated time reversal (CTR) processing technique. Moreover, we group detected events depending on how frequently they occur through all traverses, where repeated events are probably caused by a utility line. For a better understanding, we compared CTR outputs with conventional processing (using filtering and Kirchhoff migration). This approach was used in a field that comprises buried utilities, such as pipelines and cables. Data were acquired along 4 parallel traverses with a GPR MALA tool and an antenna frequency of 250 MHz. Results indicate that the CTR generates better resolution/higher signal-to-noise ratio, and precise utility location as confirmed by drillings.