Frequency-domain Wave Research Articles

Nondestructive evaluation of microstructure and mechanical property of post-processing annealed selective laser melted 316L stainless steel by laser ultrasonics

By using the laser ultrasonics nondestructive technology, combined with the microstructure and mechanical property of post-processing annealed selective laser melted 316L stainless steel characterized by scanning electron microscopy (SEM), electron backscattering diffraction (EBSD), and mechanical property testing, selective laser melted 316L stainless steel after post-processing annealing was evaluated. The results show that the frequency domain attenuation coefficient of ultrasonic waves is positively correlated with the average grain size; the time domain attenuation coefficient of ultrasonic waves is negatively correlated with the low angle boundary content. The tensile strength has a good correlation with the time domain attenuation coefficient and wave speed, the correlation coefficients R2 are 0.95 and 0.89 respectively; the yield strength correlates with the time domain attenuation coefficient, the correlation coefficient R2 is 0.76; the elongation has a good correlation with the frequency domain attenuation coefficient and wave speed, the correlation coefficient R2 is 0.90 and 0.86 respectively.

Efficient numerical simulation method for nonlinear guided wave in frequency domain

Abstract Nonlinear ultrasonic guided wave has attracted increasing attention for its ultra-sensitive to detect the incipient damages in service material by analyzing the amplitude of second harmonic wave. However, the mainstream method of simulating the second harmonic generation (SHG) in nonlinear material is using finite element method with time-domain solver, which is extremely time-consuming and can hardly simulate the huge and complex structures. In this paper, we propose a flexible finite element method based on frequency solver to simulate the SHG. The primary wave field, the second harmonic wave field and the static component field are separately set. This method is realized in Comsol Multiphysics software, the case of the SHG in plate indicates that the calculation efficiency has been significantly improved in compare with the time domain solver, whereas the results of time-domain solver and frequency domain solver have good agreement with each other. This method can be easily applied in the SHG analysis in huge and complex structures. Moreover, the primary wave field, the second harmonic wave field and the static component field can be respectively presented in the post-processing to help provide more information about physical insight of SHG.

Self-adaptive numerical dispersion suppressed method for shallow seismic simulation

Near-surface in seismic exploration generally refers to the low deceleration zone and a section of stratum below it, which can be described in geophysical language as “low velocity”, “low Q”, and “Free surface”, etc. Due to the presence of low-velocity layers in near-surface, shallow seismic simulation is plagued by numerical dispersion. Numerical dispersion affects the accuracy of seismic wave simulation, especially severe in shallow areas containing low-velocity layers. To improve the simulated quality, denser grids or higher-order difference schemes are used, but both of which would seriously reduce computational efficiency, especially for frequency-domain numerical modeling. Differentiation is replaced by difference in wave field simulation, which would inevitably result in numerical errors. These numerical errors are manifested as the difference between the phase velocity of the discretized wave field and the medium velocity. The waves with different wavenumber components have different phase velocities, and the larger the wavenumber, the more that its phase velocity lags the group velocity. Based on this theoretical analysis, a regularization factor is added to the frequency-domain acoustic wave equation to correct the phase velocity of high wavenumber components. According to the Von Neumann stability requirements, a regularization factor that adaptively changes with simulation parameters is derived. Compared to the fixed regularization factor, adaptive regularization factor can better match the velocity field and protect the effective wave field to the maximum extent while suppressing numerical dispersion. The improved acoustic wave equation can effectively suppress numerical dispersion without increasing the number of grids. Different numerical models demonstrate the effectiveness and efficiency of the improved acoustic equation with the adaptive regularization factor for suppressing numerical dispersion.

Theoretical modeling and dynamic analysis of designable grillages for repairing material surface defect

Designing structural grillages is an innovative solution to repair material surface defects. The grillages have advantages as lightweight and directionally enhanced, but their stability and stress concentration under dynamic loads may pose significant risks. Three analytical models of grillages above a semicircular defect are constructed. The analytical solution of the frequency-domain wave field around the semicircular defect under SH wave incidence is solved. The complex variable function method is introduced to simplify the wave field expression. The accuracy is verified by comparing it with classic examples. Applying the Modified Time-Frequency Transform to obtain the time-domain wave field. Based on the Multipoint Transient Input Method (MTIM), the transient surface displacement response of the grillage above the defect is derived, mainly discussing the superposition behavior of input waves in the grillage. MTIM is based on the analytical solution of local time-domain wave field and takes the time histories of the surface characteristic points as the wave input. It has been validated as an effective method for studying the dynamic response of structures. The numerical results show that grillage form, incident angle, and wave velocity ratio are important factors affecting the structural responses of grillage above the defect. This research aims to reveal the propagation characteristics of waves in grillages in filling material defects, providing theoretical guidance for the design and application of grillages in this field.

Integration Technology with Thin Films Co-Fabricated in Laminated Composite Structures for Defect Detection and Damage Monitoring.

Despite the well-established nature of non-destructive testing (NDT) technologies, autonomous monitoring systems are still in high demand. The solution lies in harnessing the potential of intelligent structures, particularly in industries like aeronautics. Substantial downtime occurs due to routine maintenance, leading to lost revenue when aircraft are grounded for inspection and repairs. This article explores an innovative approach using intelligent materials to enhance condition-based maintenance, ultimately cutting life-cycle costs. The study emphasizes a paradigm shift toward structural health monitoring (SHM), utilizing embedded sensors for real-time monitoring. Active thin film piezoelectric materials are proposed for their integration into composite structures. The work evaluates passive sensing through acoustic emission (AE) signals and active sensing using Lamb wave propagation, presenting amplitude-based and frequency domain approaches for damage detection. A comprehensive signal processing approach is presented, and the damage index and damage size correlation function are introduced to enable continuous monitoring due to their sensitivity to changes in material properties and defect severity. Additionally, finite element modeling and experimental validation are proposed to enhance their understanding and applicability. This research contributes to developing more efficient and cost-effective aircraft maintenance approaches through SHM, addressing the competitive demands of the aeronautic industry.

Practical Aspects of Physics-Informed Neural Networks Applied to Solve Frequency-Domain Acoustic Wave Forward Problem

Abstract Physics-informed neural networks (PINNs) have been used by researchers to solve partial differential equation (PDE)-constrained problems. We evaluate PINNs to solve for frequency-domain acoustic wavefields. PINNs can solely use PDEs to define the loss function for optimization without the need for labels. Partial derivatives of PDEs are calculated by mesh-free automatic differentiations. Thus, PINNs are free of numerical dispersion artifacts. It has been applied to the scattered acoustic wave equation, which relied on boundary conditions (BCs) provided by the background analytical wavefield. For a more direct implementation, we solve the nonscattered acoustic wave equation, avoiding limitations related to relying on the background homogeneous medium for BCs. Experiments support our following insights. Although solving time-domain wave equations using PINNs does not require absorbing boundary conditions (ABCs), ABCs are required to ensure a unique solution for PINNs that solve frequency-domain wave equations, because the single-frequency wavefield is not localized and contains wavefield information over the full domain. However, it is not trivial to include the ABC in the PINN implementation, so we develop an adaptive amplitude-scaled and phase-shifted sine activation function, which performs better than the previous implementations. Because there are only two outputs for the fully connected neural network (FCNN), we validate a linearly shrinking FCNN that can achieve a comparable and even better accuracy with a cheaper computational cost. However, there is a spectral bias problem, that is, PINNs learn low-frequency wavefields far more easily than higher frequencies, and the accuracy of higher frequency wavefields is often poor. Because the shapes of multifrequency wavefields are similar, we initialize the FCNN for higher frequency wavefields by that of the lower frequencies, partly mitigating the spectral bias problem. We further incorporate multiscale positional encoding to alleviate the spectral bias problem. We share our codes, data, and results via a public repository.

Modeling multisource multifrequency acoustic wavefields by a multiscale Fourier feature physics-informed neural network with adaptive activation functions

Recently, the physics-informed neural network (PINN) was adopted to solve partial differential equation (PDE)-based forward and inverse problems. Compared to numerical differentiation, a PINN calculates derivatives by mesh-free automatic differentiation without dispersion artifacts. The Fourier feature PINN was applied to solve the frequency-domain acoustic wave equation to model multifrequency scattered wavefields. Although solving for scattered wavefields avoids the source singularity problem, it has drawbacks (e.g., requiring an analytic formula for computing the background wavefield, which only exists for the wave equation for simple models). We evaluated an approach for modeling multisource multifrequency acoustic wavefields using a multiscale Fourier feature mapping (MFFM) PINN with adaptive activations, directly solving for full wavefields instead of scattered wavefields and naturally avoiding the drawbacks of solving the scattered wave equation. For the MFFM, we explored the determination of the maximum and number of Fourier scales. Our inputs to the MFFM were only the spatial coordinates of the subsurface model; this result is lower than that of previous work (improving the efficiency of the PINN while maintaining its accuracy). Because the activation function is extremely important for a PINN, we use an existing technique and adapt it to a new architecture and develop an adaptive amplitude-scaled and phase-shifted sine activation function, which performs the best among the studied activation functions. Experiments show that the MFFM, adaptive activation, an appropriate learning rate, a linearly shrinking NN, and transfer learning greatly improve the convergence rate, accuracy, and efficiency of the PINN for simulating multisource multifrequency wavefields, laying the foundation for applying a PINN to wave equation-based inversion and imaging. We shared our codes, data, and results via a public repository.

Numerical Simulation of Elastic Wave in Frequency Domain Based on Generalized Finite Difference Method With a Multiaxial Convolutional Perfectly Matched Layer Boundary

Numerical Simulation of Elastic Wave in Frequency Domain Based on Generalized Finite Difference Method With a Multiaxial Convolutional Perfectly Matched Layer Boundary

Transfer learning Fourier neural operator for solving parametric frequency-domain wave equations

Transfer learning Fourier neural operator for solving parametric frequency-domain wave equations

A 17-point composite average-derivative optimal method for high-accuracy frequency-domain scalar wave modeling

The frequency-domain finite-difference (FD) technique, especially the average-derivative method (ADM), is widely utilized in wavefield modeling. However, conventional low-order FD techniques are insufficient for high-accuracy demands. Applying high-order FD operator and optimizing their coefficients are effective measures for improving the accuracy of seismic modeling. However, these approaches suffer from the limitations of constant density media and approximant perfectly matched layer (PML). To address this issue, we have developed a composite-ADM 17-point scheme for a scalar-wave equation. This novel scheme is based on the composition of ADM discretizations with different grid intervals, which successfully removes the above limitations and achieves high accuracy. To suppress the numerical dispersion, we take the L∞ norm to construct the objective function, which we minimize using the Grey Wolf Optimizer (GWO) and Particle Swarm Optimization (PSO) algorithms. Numerical analysis indicates that the composite-ADM greatly reduces phase velocity error compared with the traditional-ADM, requiring only 2.44 grid points per wavelength within a 1% phase velocity error. Using numerical examples in homogeneous and complex models, we demonstrate the accuracy and versatility of the composite-ADM 17-point scheme in variable density media with exact PML. Furthermore, we extend this optimal scheme to the case of 2D viscous and 3D scalar-wave equations, making it a more practical and versatile solution.

A Dual Neural Network Approach to Topology Optimization for Thermal-Electromagnetic Device Design

Topology optimization for engineering problems often requires multiphysics (dual objective functions) and multi-timescale considerations to be coupled with manufacturing constraints across a range of target values. We present a dual neural network approach to topology optimization to optimize a 3-dimensional thermal-electromagnetic device (optical shutter) for maximum temperature rise across a range of extinction ratios while also considering manufacturing tolerances. One neural network performs the topology optimization, allocating material to each sub-pixel within a repeating unit cell. The size of each sub-pixel is selected with manufacturing considerations in mind. The other neural network is trained to predict performance of the device using extinction ratio and temperature rise over a given time period. Training data is generated using a finite element model for both the electromagnetic wave frequency domain and thermal time domain problems. Optimized designs across a range of targets are shown.

Robust fast direct integral equation solver for three-dimensional doubly periodic scattering problems with a large number of layers

Frequency-domain wave scattering problems that arise in acoustics and electromagnetism can be often described by the Helmholtz equation. This work presents a boundary integral equation method for the Helmholtz equation in 3-D multilayered media with many doubly periodic smooth layers. Compared with conventional quasi-periodic Green's function method, the new method is robust at all scattering parameters. A periodizing scheme is used to decompose the solution into near- and far-field contributions. The near-field contribution uses the free-space Green's function in an integral equation on the interface in the unit cell and its immediate eight neighbors; the far-field contribution uses proxy point sources that enclose the unit cell. A specialized high-order quadrature is developed to discretize the underlying surface integral operators to keep the number of unknowns per layer small. We achieve overall linear computational complexity in the number of layers by reducing the linear system into block tridiagonal form and then solving the system directly via block LU decomposition. The new solver is capable of handling a 100-interface structure with 961.3k unknowns to 10−5 accuracy in less than 2 hours on a desktop workstation.

Ultrasonic guided wave imaging of pipelines based on physics embedded inversion neural network

Pipeline corrosion quantification plays a vital role in guaranteeing the safety of critical industrial structures and thus significant work has been carried out to address such an issue. Although quantitative imaging is crucial for non-destructive testing, research in guided wave pipeline testing has primarily centered on qualitative approaches. Here, we propose a deep neural network built upon physical model to reconstruct pipe wall thickness from ultrasonic guided wave (UGW) signals. The workflow of reconstruction contains three layers, where each layer consists of a fixed forward network and a residual inversion network. The forward model is represented by an agent convolutional neural network which would be embedded into the entire inversion network. The residuals between data from the forward model and real signals are then mapped into velocity profile differences through sub-inversion network. Numerical experiments were conducted to verify the inversion performance of the deep neural network using thickness maps obtained from guided wave frequency domain information. Results show that inversion images are capable to reveal the positions, shapes, and depths of corrosion with high resolution and precision, yielding an average inversion of 87.37% in the test set. In addition, by utilizing the periodicity of the pipeline, the inversion accuracy of eight pairs of transducers were improved from 67.7% to 89.43% with high-order helical guided wave. Compared with traditional high-precision inversion methods such as full waveform inversion, the proposed method achieved approximately 300 times faster inversion speed at the cost of some accuracy. The research demonstrates that real-time quantitative imaging of defects on pipes can be achieved accurately by physics embedded network. Furthermore, an experimental verification of the method was carried out through UGW pipeline testing, demonstrating its feasibility. The mean squared error of wall thickness reconstruction was 0.0070, achieving a high level of precision.

Multiscale model reduction of finite-difference frequency-domain wave modelling in acoustic media

SUMMARY Frequency-domain wave modelling can easily describe the visco-acoustic behaviour of wave propagation using frequency-dependent velocities. Conventional finite-difference (FD) modelling in the frequency domain is computationally prohibitive for solving the acoustic Helmholtz equation in complicated and large geological models. To reduce the computational cost of traditional FD Helmholtz solvers, we develop a multiscale FD frequency-domain method that uses multiscale basis functions to significantly reduce the dimension of system matrices associated with the Helmholtz equation. Due to the insufficient accuracy of the first-order multiscale basis functions in the case of strongly heterogeneous models, we introduce the multinode coarse-element scheme into the scalar Helmholtz equation, a scheme previously developed in the extended multiscale finite-element method for vector problems. This multinode scheme enables multiscale basis functions to capture accurate fine-scale medium property variations. We use one homogeneous model and two heterogeneous models to validate our multiscale method for accuracy and computational cost. Numerical results demonstrate that our new approach can significantly reduce the time and memory costs of acoustic wave modelling while maintaining accuracy, indicating the great potential of our multiscale method in large-scale modelling applications.

Finite-element modelling of seismoelectric and electroseismic waves in frequency domain: 2-D SHTE mode

SUMMARYWe propose a frequency-domain finite-element (FDFE) method to simulate the 2-D SHTE mode seismoelectric and electroseismic waves. By neglecting the secondary weak wavefield feedbacks, the SH and TE waves are solved, separately. In a finite plane region, propagations of both SH and TE waves can be described as the Helmholtz equation with boundary conditions, which is proved to be equivalent to the extremum of functional by conducting calculus of variation. The computation region is partitioned into structured rectangular elements with the bilinear interpolation. The proposed FDFE algorithm solves the wavefield in frequency domain and avoids adopting the quasi-static approximation. One advantage of the proposed algorithm is its ability to accurately simulate the seismoelectric and electroseismic responses generated from the free surface. We verify the proposed algorithm based on a layered model beneath a free surface by comparing the waveforms calculated using the FDFE algorithm with those calculated using analytically-based method. The proposed algorithm is applied in feasibility studies of interface seismoelectric and electroseismic responses in exploring the hydrocarbon reservoir and monitoring the time-lapse pollutant within a sand channel.

Stochastic wave spectra estimation (SWSE) based on response surface methodology considering uncertainty in transfer functions of a ship

In this paper, a new wave spectra estimation method is proposed in which the frequency domain wave estimation method (FDWE) is extended into a probabilistic analytical framework in order to estimate the encountered sea states involving uncertainty in transfer functions of a ship. The proposed method, named the Stochastic Wave Spectra Estimation (SWSE), makes use of an Hermite polynomial chaos expansion (PCE) to represent the uncertainty in the transfer functions and the response surfaces. The method involves a mathematical formulation where an extension of the deterministic FDWE concept to the space of random variables is made. The proposed method can accurately and easily estimate the encountered wave spectra based on ship response measurements accounting for uncertainty in the transfer functions. In this paper, numerical and experimental investigations of the proposed SWSE are made, where the uncertainties in the transfer functions of heave and pitch motions of a containership are taken into account. The validity of the SWSE is demonstrated by comparison to results of uncertainty analyses through the Monte-Carlo simulations (MCS).

Data-driven modeling of Bay-Ocean wave spectra at bridge-tunnel crossing of Chesapeake Bay, USA

The Chesapeake Bay Bridge-Tunnel (CBBT) was designed in the early 1960s and first opened on April 15, 1964. It is a 28.3-km bridge-tunnel system that crosses the mouth of Chesapeake Bay. Because there is a lack of reliable long-term observations of surface waves near the Chesapeake Bay entrance, accurate forecasts and hindcasts of wave conditions are essential for maintaining and expanding the bridge-tunnel infrastructure. To estimate wave parameters and energy spectra near the CBBT, novel composite data-driven models were developed using the wind, water level, and offshore wave data as input. The developed models provide satisfactory predictions of both integral wave parameters and energy density spectra of sea and swell waves at the Chesapeake Bay entrance. The developed models can rapidly hindcast the wave characteristics and spectra during an extreme event (i.e., the Halloween storm in 1991). This paper provides a novel framework for developing surrogate models to predict wave spectra in the frequency domain and hindcast historical wave climate, which can be applied to other sea-crossing bridges and/or tunnel sites near bay entrances. The data-driven models, based on deep neural networks, allow for estimating waves without a high demand for computational resources, and thus serve as a useful tool for the characterization and simulation of the complex wave environment at the interface of estuary and ocean.

Analysis of various algorithms for optimizing the wave energy converters associated with a sloped wall-type breakwater

The optimal arrangement of multiple wave energy converters (WECs) is an important topic that can greatly affect the efficiency of ocean energy extraction. This study used various algorithms to optimize multiple heaving-buoy-type hemispherical WEC associated with a sloped wall-type breakwater. To this end, a calculation framework linking a three-dimensional frequency-domain numerical wave tank (FR-NWT) based on the Rankin panel method and an optimization algorithm was established. The fitness function for optimization was set to the power efficiency of WEC. The algorithms used were a genetic algorithm, simulated annealing algorithm, particle swarm optimization algorithm (PSO), and advanced PSO algorithm. Under irregular wave conditions, optimization of the spacing between each WEC, the distance between the WEC and the breakwater, the diameter and draft of the WEC, the bottom length and slope angle of the breakwater were performed. The results of the advanced PSO algorithm were consistent and did not converge to local maxima. The excellence of the advanced PSO algorithm in this study was demonstrated.

Design and Preparation of Flexible Graphene/Nonwoven Composites with Simultaneous Broadband Absorption and Stable Properties

As the world moves into the 21st century, the complex electromagnetic wave environment is receiving widespread attention due to its impact on human health, suggesting the critical importance of wearable absorbing materials. In this paper, graphene nonwoven (RGO/NW) composites were prepared by diffusely distributing graphene sheets in a polypropylene three-dimensional framework through Hummers' method. Moreover, based on the Jaumann structural material design concept, the RGO/NW composite was designed as a multilayer microwave absorber, with self-recovery capability. It achieves effective absorption (reflection loss of -10 dB) in the 2~18 GHz electromagnetic wave frequency domain, exhibiting a larger bandwidth than that reported in the literature for absorbers of equivalent thickness. In addition, the rationally designed three-layer sample has an electromagnetic wave absorption of over 97% (reflection loss of -15 dB) of the bandwidth over 14 GHz. In addition, due to the physical and chemical stability of graphene and the deformation recovery ability of nonwoven fabric, the absorber also shows good deformation recovery ability and stable absorption performance. This broadband absorption and extreme environmental adaptability make this flexible absorber promising for various applications, especially for personnel wearable devices.

Research on hydrodynamic performance calculation of buoy-chain-sprocket wave energy collection device

Buoy-chain-sprocket wave energy collection device is a new type of oscillating buoy wave energy collection device, which has a good application prospect. The calculation method of the hydrodynamic performance of wave energy device (e.g. the first-level average collection efficiency of wave energy) is the core scientific problem of wave energy device, and it is also the theoretical basis for the optimization and control of wave energy device prototype. In this paper, on basis of linear potential flow theory, after the velocity potentials are calculated with eigenfunction expansion method and matching asymptotic expansion method, the frequency-domain wave loads in the heave, surge and pitch directions of the floating body are obtained. And then the motion coordination relationship of the floating body of buoy-chain-sprocket wave energy collection device is used to establish time-domain hydrodynamic motion response equations of the floating body of the device based on the Cummins method. After these equations are solved via the fourth-order Runge-Kutta method, the first-level average collection efficiency of the wave energy device is acquired. In order to further improve the calculation accuracy, the frequency-domain wave-exciting force is calculated by using variable draft depth when the hydrodynamic response of buoy-chain-sprocket wave energy collection device is calculated in this paper. Finally, the reliability of the above calculation method for the hydrodynamic performance of buoy-chain-sprocket wave energy collection device is verified through physical model experiment.