Simulation Of Wave Propagation Research Articles

Conflation of modal strain energy, spectral finite element, and machine learning techniques for damage detection in multi-span steel girder bridges with variable sections

A new approach is proposed to detect micro and small damages in multi-span bridges constructed with variable sections by combining modal strain energy and spectral finite element through the use of machine learning techniques. The traditional finite element methods are inefficient in detecting and estimating structures' micro-damages. Therefore, wave propagation-based methods must be applied. Micro-damages can be modeled through the spectral finite element method, widely adopted in wave propagation simulation. Among the frequency-based methods used in damage identification, the modal strain energy is more sensitive, especially in complicated structures. However, this method is difficult to apply to steel girders with variable sections and different support conditions. By combining the modal strain energy and the spectral finite element and applying the support vector regression method, the location and severity of damage in steel girders could be accurately identified to overcome the difficulties of detection in complicated elements. To improve the ability of the support vector regression method, in the damage severity estimation, it was combined with feature selection. To evaluate the proposed method's ability, first, an element of the beam- type, with the characteristics of a spectral finite element, is defined in the OpenSees software. To assess the accuracy of the defined element in detecting micro-damages, a tested numerical model was adopted to measure the accuracy of the provided element. Next, to detect small damages, the model of the steel girder bridge with the defined element was prepared, and the modal properties of the structure were extracted. Due to the change in cross-section along each girder, the modified modal strain energy-based damage index (β) equation was used in the subject model. By applying the damages of different severities in steel girders in single and multiple damage scenarios, the modified damage index β was calculated. With the damage indexes calculated in the different scenarios and applying the machine learning method, the severity of damage was estimated. The obtained results indicate that this proposed method is accurate and satisfactory for detecting and estimating micro and small damages with high accuracy in bridges with variable section girders.

A hybrid PML formulation for the 2D three-field dynamic poroelastic equations

Simulation of wave propagation in poroelastic half-spaces presents a common challenge in fields like geomechanics and biomechanics, requiring Absorbing Boundary Conditions (ABCs) at the semi-infinite space boundaries. Perfectly Matched Layers (PML) are a popular choice due to their excellent wave absorption properties. However, PML implementation can lead to problems with unknown stresses or strains, time convolutions, or PDE systems with Auxiliary Differential Equations (ADEs), which increases computational complexity and resource consumption.This article introduces a novel hybrid PML formulation for arbitrary poroelastic domains. Instead of using ADEs, this formulation utilizes time-history variables to reduce the number of unknowns and mathematical operations. The modification of the PDEs to account for the PML is limited to the PML domain only, resulting in smaller matrices while maintaining the governing equations in the interior domain and preserving the temporal structure of the problem. The hybrid approach introduces three scalar variables localized within the PML domain.The proposed formulation was tested in three numerical experiments in geophysics using realistic parameters for soft sites with free surfaces. The results were compared with numerical solutions from extended domains and simpler ABCs, such as paraxial approximation, demonstrating the accuracy, efficiency, and precision of the proposed method. The article also discusses the applicability of the method to complex media and its extension to the Multiaxial PML formulation.The codes used for the simulations are available for download from https://github.com/hmella/POROUS-HYBRID-PML.

Simulation of flexural-gravity wave propagation for elastic plates in shallow water using an energy-stable finite difference method with weakly enforced boundary and interface conditions

We introduce an energy stable, high-order-accurate finite difference approximation of the dynamic, pure bending Kirchhoff plate equations for complex geometries and spatially variable properties. We utilize the summation-by-parts (SBP) framework to discretize the biharmonic operator with variable coefficients, with attention given to free and clamped boundary conditions and corner conditions. Energy conservation is established by combining SBP boundary closures with weak enforcement of the boundary and interface conditions using a penalty (simultaneous approximation term, SAT) technique. Then we couple the plate equations to the shallow water equations to study flexural-gravity wave propagation, and prove that the semi-discrete system of equations is self-adjoint. We demonstrate the stability and accuracy properties of the method on curvilinear multiblock grids using the method of manufactured solutions. The method, which we provide in an open-source code, is then used to model ocean wave interactions with the Thwaites Glacier and Pine Island Ice Shelf in the Amundsen Sea off the coast of West Antarctica.

Acceleration of Tensor Interpolation-Based Radio Map Estimation

The radio map of wireless communications should be surveyed in advance when installing base stations to efficiently utilize radio waves. Generally, this is calculated using radio wave propagation simulation. Because the simulation is time-consuming, a tensor-rank minimization-based interpolation method has been proposed as fast method. However, this method interpolates the radio map using an iterative algorithm. The number of iterations required for further acceleration should be reduced; therefore, we propose a tensor interpolation using rank minimization that considers the characteristics of radio wave propagation. Furthermore, we proved that the proposed method could interpolate with fewer iterations than the existing method.

SHYTCWAVES: A STOP-MOTION HYBRID TC-INDUCED WAVES METAMODEL

Waves produced by tropical cyclones (TCs) can be estimated using numerical models and non-stationary simulations forced with vortex-type time-varying wind fields. However, dynamical simulations are time and computationally demanding at regional-scale domains since high temporal resolutions are required to correctly simulate wave propagation. Early warning systems, as well as risk induced assessments, would benefit from fast and accurate estimates of the wave climate induced by close-to-real tracks geometry. For this reason, the objective of the proposed methodology is to obtain a tool capable of estimating the spatial and temporal variability of directional wave spectra produced by TCs at regional scale in deep waters using a hybrid approach, and statistical techniques, to reduce CPU time effort. SHyTCWaves is a metamodel that provides estimates of the directional wave spectra produced by TCs, which can be used as boundary conditions for local-scale models at nearshore coastal areas, in addition to providing faster than dynamically simulated TC forecast predictions.

Numerical Simulation of Pressure Wave Propagation and Its Effect on Damage to the Reactor Cavity under TNT Detonation for Steam Explosion

In a severe accident, molten corium may penetrate the reactor pressure vessel and enter the cooling water in the reactor cavity, and then a steam explosion may occur. Steam explosions can initiate pressure waves and threaten the structural integrity of the reactor cavity. To investigate the propagation characteristics of the pressure waves, including the propagation pattern, attenuation, and amplification under TNT detonation, a coupled numerical approach combined with arbitrary Lagrangian–Eulerian and fluid–structure interaction methods are utilized. The peak pressures of the incident and reflected shock waves decrease rapidly with increasing distance from the charge center, whereas the reflected pressure in the reactor cavity can be between 1.30 and 1.67 times the incident pressure. Then, structural analysis is performed to evaluate the damages to the concrete, liner plate, and reinforcements. From the numerical results, localized and superficial concrete damages are observed in the reactor cavity and the basemat; however, the risk of damage to the concrete, resulting in the collapse of these components is very low. The risk of damage to the liner plate and reinforcements is also very low since the maximum strain values are much lower than the failure criteria. Finally, the structural integrity of the reactor cavity will be maintained during the TNT detonation for the steam explosion.

Solving ordinary and partial differential equations using an analog computing system based on ultrasonic metasurfaces

Wave-based analog computing has recently emerged as a promising computing paradigm due to its potential for high computational efficiency and minimal crosstalk. Although low-frequency acoustic analog computing systems exist, their bulky size makes it difficult to integrate them into chips that are compatible with complementary metal-oxide semiconductors (CMOS). This research paper addresses this issue by introducing a compact analog computing system (ACS) that leverages the interactions between ultrasonic waves and metasurfaces to solve ordinary and partial differential equations. The results of our wave propagation simulations, conducted using MATLAB, demonstrate the high accuracy of the ACS in solving such differential equations. Our proposed device has the potential to enhance the prospects of wave-based analog computing systems as the supercomputers of tomorrow.

Extreme ultraviolet broadband imaging spectrometer using dispersion-matched zone plates.

We present simultaneous 1D imaging and broadband spectroscopy of a laser-produced plasma (LPP) source of extreme ultraviolet light, using a tapered zone plate that is matched to the dispersion of a transmission grating. We describe the design and fabrication of the zone plates in the 5-80 nm wavelength regime with designed spatial resolution of ∼10 µm and spectral resolution of ∼0.8 nm. Subsequently, we benchmark the imaging spectrometer with a solid tin target LPP. Plane wave propagation simulations qualitatively match the experimental results and confirm the device performance.

Time-lapse global inversion for surface-waves: A differential approach using a linear approximation of the Rayleigh wave phase velocity

Surface-wave methods have a wide range of possible applications in the monitoring of near-surface media. In classical monitoring methods, data measured at different times are inverted separately and independently, and the difference in the inversion results reflects the temporal changes in the medium. However, the results obtained in this way can be affected by the reproducibility of experimental measurements, measurement and inversion uncertainties, etc. In this study, we introduce Differential Inversion in surface-wave methods, which uses the difference between measured data as inversion input data, instead of the measured data themselves. More precisely, a linear approximation of Rayleigh wave phase velocity associated with its sensitivity kernel is used to relate the data difference with the model variations. This differential inversion approach is firstly tested with numerical data generated in a series of two-layer models in order to estimate the limitations of the linear approximation with a global inversion approach. It is shown that when the shear-wave velocity variation is more than 5%, the linear assumption is no longer relevant. With respect to the 5% of variation, we apply the differential inversion approach on laboratory data, obtained from three reduced-scale epoxy-resin two-layer models. The results show the feasibility of the differential inversion to estimate the shear-wave velocity differences between epoxy-resin models. The short calculation time is one of its advantages. However, a good estimation on the baseline is required in order to calculate the sensitivity kernel. Finally, the robustness of the proposed approach is verified by numerical data, using the Spectral Element Method to simulate wave propagation in the presence of an under-surface cavity.

Instantaneous Physics‐Based Ground Motion Maps Using Reduced‐Order Modeling

AbstractPhysics‐based simulations of earthquake ground motion are useful to complement recorded ground motions. However, the computational expense of performing numerical simulations hinders their applicability to tasks that require real‐time solutions or ensembles of solutions for different earthquake sources. To enable rapid physics‐based solutions, we present a reduced‐order modeling approach based on interpolated proper orthogonal decomposition (POD) to predict peak ground velocities (PGVs). As a demonstrator, we consider PGVs from regional 3D wave propagation simulations at the location of the 2008 MW 5.4 Chino Hills earthquake using double‐couple sources with varying depth and focal mechanisms. These simulations resolve frequencies ≤1.0 Hz and include topography, viscoelastic attenuation, and S‐wave speeds ≥500 m/s. We evaluate the accuracy of the interpolated POD reduced‐order model (ROM) as a function of the approximation method. Comparing the radial basis function (RBF), multilayer perceptron neural network, random forest, and k‐nearest neighbor, we find that the RBF interpolation gives the lowest error (≈0.1 cm/s) when tested against an independent data set. We also find that evaluating the ROM is 107–108 times faster than the wave propagation simulations. We use the ROM to generate PGV maps for 1 million different focal mechanisms, in which we identify potentially damaging ground motions and quantify correlations between focal mechanism, depth, and accuracy of the predicted PGV. Our results demonstrate that the ROM can rapidly and accurately approximate the PGV from wave propagation simulations with variable source properties, topography, and complex subsurface structure.

Simulation of wave propagation in austenitic stainless steel welds with solidification structure predicted by Cellular Automaton method

Austenitic stainless steel is widely used in nuclear power plants (NPPs) and a variety of occurrences of stress corrosion cracking (SCC) near its weld have been reported among NPPs. Ultrasonic testing is a critical technique for the detection and depth sizing of SCCs. However, such welds' anisotropic and heterogeneous properties cause difficulties in ultrasonic testing when ultrasonic waves propagate through welds. Deeply understanding the characteristics of ultrasonic waves with wave propagation simulation is effective to improve the accuracy of ultrasonic testing. To this end, it is necessary to take crystal orientation and grain boundary into account simultaneously in the numerical model. In this study, a model was developed so that the Cellular Automaton (CA) method can simulate the solidification structure from multilayer and multipass welding process, then the solidification structure of a 7-layer and 7-pass weld of austenitic stainless steel was predicted based on welding conditions. Finally, the finite element method was used to compute wave propagation in austenitic stainless steel weld with the solidification structure predicted. Numerical results of wave propagation in austenitic stainless steel weld were compared to those obtained by experiment.

Comparison of grain structure models for wave propagation analysis in centrifugally cast stainless steel

Centrifugally cast stainless steel (CASS) is widely used in primary coolant piping of pressurized water reactor plants because of its high corrosion resistance and high strength. An in-service inspection based on ultrasonic testing (UT) has to be conducted for weld joints of primary coolant piping on the basis of JSME Rules on Fitness-forService for Nuclear Power Plants. However, it is difficult to detect and size flaws in CASS components with high accuracy because of the following reasons: Ultrasonic waves are scattered and attenuated due to coarse grains, and anisotropic and heterogeneous properties in CASS lead to ultrasonic beam skewing. Numerical simulations are useful and reasonable ways for better understanding the ultrasonic wave propagation behavior in CASS. To effectively achieve this, the simulation model should include a three-dimensional (3D) grain structure. In this study, we modeled three kinds of the solidification grain structures of centrifugally CASS. One is obtained by using a cellular automaton method, another consists of many hexagonal columns with the same dimensions, and the other is transversely isotropic material. Then these structures were fed into an explicit finite element model for simulating wave propagation and the simulated results were compared with those measured by a laser Doppler vibrometer. Through the comparison, we investigated the applicability of these three kinds of solidification grain structure models to simulation for wave propagation.

Simulation of Wave Propagation Using Finite Differences in Oil Exploration

This paper presents a numerical solution for the 2D acoustic wave equation, considering heterogeneous media. It has been developed through a software in Fortran 90 that uses a second-order finite difference approximation. This program generates a set of patterns to detect the presence of oil in the subsurface. The algorithm is based on a geological domain where the sources (shots) and receivers are located. Each process takes care of a subset of sources and returns to the primary method patterns and seismograms corresponding to its group of sources. In the end, an image of the resulting seismogram is shown along the analyzed geologic profile. Stability and convergence tests were performed to ensure the reliability of the results. These tests were performed using a geological profile 100,000 m long and 17,400 m deep, divided into strata. For the execution of the software, a cluster of 16 processors was used as a computational platform.

Sea Surface Roughness Determination from Grazing Angle GPS Ocean Observations and Scatterometry Simulations

Measurements of grazing angle GNSS-R ocean reflections combined with meteorological troposphere data are used for retrieval of ocean wave heights and surface roughness parameters. The observational results are compared to multiphase screen simulations for the same atmosphere conditions. The retrieved data from observations and simulations give equal results within the error bounds of the methods. The obtained ocean mean wave-heights are almost proportional to the square of the wind speed when applying a first-order approximation model to the high-wave-number part of the measured GNSS-R power spectra. The spectral variances from the measurements link directly to the ocean surface roughness, which is also verified by the performed multiple phase-screen wave propagation simulations. Thus, grazing angle GNSS-R techniques are an efficient method for determining the ocean state and the conditions in the boundary layer of the troposphere.

Nearshore Observations and Modeling: Synergy for Coastal Flooding Prediction

Coastal inundation has recently started to require significant attention worldwide. The increasing frequency and intensity of extreme events (sea storms, tsunami waves) are highly stressing coastal environments by endangering a large number of residential areas, ecosystems, and tourist facilities, and also leading to potential environmental risks. Predicting such events and the generated coastal flooding is thus of paramount importance and can be accomplished by exploiting the potential of different tools. An example is the combination of remote sensors, like marine radars, with numerical models. Specifically, while instruments like X-band radars are able to precisely reconstruct both wave field and bathymetry up to some kilometers off the coast, wave-resolving Boussinesq-type models can reproduce the wave propagation in the nearshore area and the consequent coastal flooding. Hence, starting from baseline simulations of wave propagation and the conversion of water elevation results into radar images, the present work illustrates the reconstruction of coastal data (wave field and seabed depth) using a specifically suited data processing method, named the “Local Method”, and the use of such coastal data to run numerical simulations of coastal inundation in different scenarios. Such scenarios were built using two different European beaches, i.e., Senigallia (Italy) and Oostende (Belgium), and three different directional spreading values to evaluate the performances in cases of either long- or short-crested waves. Both baseline and inundation simulations were run using the FUNWAVE-TVD solver. The overall validation of the methodology, in terms of maximum inundation, shows its good performance, especially in cases of short-crested wind waves. Furthermore, the application on Oostende Beach demonstrates that the present methodology might work using only open-access tools, providing an easy investigation of coastal inundation and potential low-cost integration into early warning systems.

Assessment of the 1693 tsunami wave generation and propagation simulation based on multiple focal mechanism scenarios for recent disaster mitigation in eastern sicily, Italy

The 1693 tsunami was the most extensive earthquake-tsunami event in Sicily, submerging Catania, Augusta, and Syracuse. However, the earthquake rupture, water level, arrival time, and furthest inundation distance of the tsunami waves are not yet known. This study aims to investigate the tsunamigenic source, run-up height, furthest inundation distance, and arrival time of the 1693 tsunami waves on the east coast of Sicily. Moreover, the assessment of tsunami-prone zones was also conducted based on worst-case earthquake-tsunami scenarios. Numerical modeling was applied by proposing six offshore focal mechanism scenarios using the shallow water equation in Delft3D and Delft Dashboard. The input parameters include length, width, strike, dip, slip, rake, and depth of the earthquake rupture. Meanwhile, the tsunami wave propagation onshore utilized XBeach and ArcGIS, considering the maximum run-up height, surface roughness analyzed from land use maps, slope, river existence, and coastline from Digital Terrain Model (DTM) identification. The results indicate that the worst possible impact of the 1693 tsunami was generated by an earthquake with a magnitude of Mw 7.13. The maximum water level, furthest inundation distance, and arrival time achieved 7.7 m, 318 m, and 9 min after wave generation offshore, respectively. This simulation is consistent with the discovery of 1693 tsunami deposits at a distance of less than 400 m from the coastlines of Augusta and Syracuse, but it is above the estimated furthest inundation distance in previous studies, which only reached around 100 m–200 m from the eastern coastline of Sicily. The results of the study are reliable as they align with the 1697 historical document where seawater inundated San Filippo Square, Catania.

Non-uniform Rectilinear Grid in the Waveguide Modeling of the Vocal Tract

For many years, a digital waveguide model is being used for sound propagation in the modeling of the vocal tract with the structured and uniform mesh of scattering junctions connected by same delay lines. There are many varieties in the formation and layouts of the mesh grid called topologies. Current novel work has been dedicated to the mesh of two-dimensional digital waveguide models of sound propagation in the vocal tract with the structured and non-uniform rectilinear grid in orientation. In this work, there are two types of delay lines: one is called a smaller-delay line and other is called a larger-delay line. The larger-delay lines are the double of the smaller delay lines. The scheme of using the combination of both smaller- and larger-delay lines generates the non-uniform rectilinear two-dimensional waveguide mesh. The advantage of this approach is the ability to get a transfer function without fractional delay. This eliminates the need to get interpolation for the approximation of fractional delay and give efficient simulation for sound wave propagation in the two-dimensional waveguide modeling of the vocal tract. The simulation has been performed by considering the vowels /ɔ/, /a/, /i/ and /u/ in this work. By keeping the same sampling frequency, the standard two-dimensional waveguide model with uniform mesh is considered as our benchmark model. The results and efficiency of the proposed model have compared with our benchmark model.

An efficient modelling technique for simulation of guided waves in delaminated composite and sandwich structures

The paper presents a higher order laminate model with sub-lamination capability for simulating wave propagation within delaminated composite and sandwich beams. Each sub-laminate adopts cubic and quadratic through-thickness variation for axial and transverse displacement, respectively. This is achieved by taking displacements at external surfaces, which are beneficial for connecting sub-laminates, used to model multilayered structures by stacking them in the thickness direction without additional treatment. The model has the flexibility to achieve the desired level of accuracy and computational efficiency by using a suitable sub-lamination scheme. The delamination can be inserted conveniently between two sub-laminates stacked one over the other. The effect of contact within delamination regions is also incorporated in this model to capture higher harmonics induced by a clapping mechanism produced during delamination closing. The model is implemented within a framework of spectral finite elements in the time-domain. The accuracy and computational efficiency of the model are thoroughly checked by solving numerical examples of wave propagation within intact/delaminated composite/sandwich beams. Detailed finite element (FE) models used to produce results for validation show that the proposed model can save more than 90% of computing time and memory compared to detailed FE modelling to achieve similar level accuracy. The model is finally utilised to investigate the influence of delamination sizes and location on the wave response of sandwich beams.

Numerical Study on the Dynamic Propagation Model of Cracks from Different Angles under the Effect of Circular Hole Explosion

A dynamic disturbance will induce cracks around the tunnel in tunnel blasting or shield construction. To investigate the overall stability of cracks with various angles during a fixed borehole (round hole explosion) blasting, models containing an individual crack with different angles were introduced for simulation research. The research set up a thin sheet model with a length of 350 mm and a width of 150 mm, with a 7 mm diameter hole and a pre-existing crack of 75 mm and 5 mm in the middle. The evolution of the stress wave propagation model and the crack propagation model were simulated using the AUTODYN software. And in this study, the theory of stress wave is used to creatively explain the dynamic load under the action of formation and reasons for the danger zone. The results indicate that pre-existing cracks from different angles will have an impact on the blast hole and the new cracks generated around itself. At 45–90°, pre-existing cracks will direct reflected stress waves to promote some cracks around the hole to have faster growth rates than others, and these special cracks with faster growths and longer lengths will more easily connect with the free surface or other cracks, resulting in overall instability. And these conditions are consistent with the prediction made by the stress wave propagation simulation study. The research results have certain guiding significance for the stability analysis and hazardous area prediction of tunnel blasting with existing cracks.

Machine learning simulation of one-dimensional deterministic water wave propagation

Deterministic phase-resolved prediction of the evolution of surface gravity waves in water is challenging due to their complex spatio-temporal dynamics. Physics-based methods of varying complexity are available, but the conflicting objectives of numerical efficiency and accuracy impede real-time wave prediction. Data-driven methods may be able to overcome this challenge by using training data generated by complex numerical methods. This work explores the potential of a machine learning (ML) approach based on a fully convolutional encoder–decoder architecture for the efficient and accurate prediction of water waves. The high-order spectral (HOS) method forms the foundation for the generation of the training data. The HOS method is applied for different, consecutive orders of nonlinearity starting from first order up to fourth order. The JONSWAP wave energy spectrum serves as the basis for modeling the one-dimensional irregular sea states. The overall objective of this work is to evaluate whether the complex non-linear physical processes can be identified and learned by the ML approach. The trained ML flow mapper is used to perform time integration of an initial sea state. The results indicate that the proposed ML approach is able to reproduce the distinctive physical processes of the different orders of nonlinearities. It is shown that the ML approach enables fast and accurate predictions of one-dimensional waves over a time horizon that spans multiple peak periods.