Time-domain Method Research Articles

Continuous Wave Ultrasound Testing Techniques

Currently, the primary method employed for ultrasound inspection is based on sending and detecting ultrasound pulses. Typically, pulse-based methods are essentially time-domain back-reflection methods, and the time-of-flight is the main measured parameter. Recently, continuous-wave methods have been developed in the radar and the fiber-optics fields, which demonstrate significantly better spatial resolution, higher signal-to-noise ratio, and ability to detect reflecting objects at very short distances. It is proposed to use the same approach to develop continuous-wave ultrasound inspection systems. The two main differences between the proposed continuous-wave ultrasonic testing and the classical pulsed ultrasound inspection method are: (i) in the continuous-wave ultrasonic testing method, the transmitted and received signals overlap in the time domain, while in the pulsed ultrasound inspection method the transmitted and received signals are separated in the time; and (ii) in the pulsed ultrasound inspection method the most important parameter is the time delay between the transmitted and received signals, while in the continuous-wave ultrasonic testing method the most informative parameters are the frequency and phase changes in the received signal in respect to modulated transmitted signal. This allows for additional flexibility in the continuous-wave ultrasonic measurements, through control of the frequency modulation. Also, the continuous-wave ultrasonic method potentially offers improved detection range and resolution; improved signal-to-noise ratio due to better energy efficiency and easier filtering; and reduced requirements on the voltage applied to the transducer, which in turn allows the use of simplified low-cost electronics. The theoretical basis of several continuous-wave ultrasound inspection technique is explained, and their advantages and limitations are discussed. Implementation of several prototype continuous-wave ultrasound testing systems is presented. Examples of the use of the systems for non-destructive testing are described.

A Novel Proposal of an Electro-Optical Sensor to Measure Various Levels of an Electric Field Using Pockels Effect Photonic Crystals

Electro-optic sensors based on the Pockels effect are key components for optical instrumentation due to their speed and accuracy. In this work, we propose a new electro-optic platform using two-dimensional photonic crystals of gallium arsenide and barium titanate (GaAs-BTO). This structure allows for the measurement of various electric field levels, from 0 kV/mm to 50 kV/mm, with a very high sensitivity and a compact size. The opto-geometric parameters of this sensor were chosen, optimized, and analyzed numerically using the Plane Wave Expansion (PWE) and Finite-Difference Time-Domain (FDTD) methods.

Nonlinear Loads Modelling and Harmonics Analysis: A Review

Abstract: In modern life, the applications of nonlinear loads are increasing, especially electronic loads, such as computers, monitors, and battery chargers. Moreover, the usage of semiconductors has increased in modern lighting systems, such as LED lamps and dimmers which are used to control the lighting level. Nonlinear loads may also be in the form of variable speed drive or arc furnace loads. Due to the spread of nonlinear loads, large amounts of harmonics are generated. To study the harmonics of nonlinear loads, it is essential to represent nonlinear loads by their equivalent models in the simulation programs. This paper presents a comprehensive review of modeling methods of nonlinear loads, including time domain methods, frequency domain methods, and state space methods. Equivalent circuits are presented for different types of nonlinear loads, including static loads, dynamic loads and arc furnace loads. The paper also presents the harmonic analysis performed by the Fourier transform of different types of nonlinear loads, including harmonic percentage and its angle. This paper is considered as a comprehensive reference for researchers and engineers to model nonlinear loads and is useful in power system planning for connecting nonlinear loads where mixing nonlinear loads of similar harmonic profiles causes worse situations. Moreover, knowing the nonlinear load profile will help in the suitable mixing of linear loads to achieve lower harmonics levels.

Convergence and accuracy of FDTD modelling for periodic plasmonic systems

Despite the widespread use of the finite-difference time-domain (FDTD) method for modeling plasmonic systems, there is a lack of detailed convergence and accuracy studies for periodic nanoparticle systems in which both particle radius and interparticle distance are critical parameters. Using an in-house parallelized 3D-FDTD code for which we implemented interface field averaging, convergence and accuracy were evaluated for various spherical particle radii, inter-distances, and radius-to-mesh size ratios. We found that Interface Field Averaging (IFA) FDTD improved accuracy and convergence with respect to per-component (Per-C) meshing. In the worst case of this study, the convergence error decreased from 4.9% to 2.6% only by using IFA. Accuracy was verified by benchmarking our simulation results with COMSOL Multiphysics software. Furthermore, we notice that there exists no general rule for choosing the mesh size. Careful convergence testing should therefore be carried out systematically.

A method to efficiently and rapidly approximate the vectorial fields generated by large area metasurfaces

In order to calculate the electromagnetic fields that are produced after light passes through a metasurface, simulation methods such as the Finite-Difference Time-Domain method are often employed. While these provide a good approximation to the fields, the level of detail at which the volume of space that the light is propagating in needs to be modelled and the time for which simulations need to run, mean that as the area of the metasurface is increased these simulations rapidly become unwieldy. In this paper we show how the result of a FDTD simulation of a unit cell can be used to generate a good approximation of the vectorial field that large area metasurfaces will generate, but using a fraction of the computational resources. This approach can provide an intermediate design step, allowing potentially interesting designs to be rapidly identified or discarded.

Assessing heart rate fragmentation to predict atrial fibrillation in the general population aged 65

Abstract Rationale Screening the general population aged 65 for atrial fibrillation (AF) has been proposed as a preventive measure against potential complications. The dysfunction of the autonomic nervous system (ANS) plays an important role in atrial fibrillation (AF). Short-term HRV is conceptually attributed to physiologic vagal tone modulation. But recent data suggest that a component of short-term HRV, called heart rate fragmentation (HRF), is related to ANS breakdown and may be a predictor of AF occurrence. Metrics derived from heart rate variability (HRV) that depict heart rate fragmentation (HRF) have been suggested to reflect autonomic nervous system (ANS) dysfunction. Objectives To assess the predictive capacity of HRF markers for AF occurrence over an 18-year follow-up in individuals aged 65 at the study’s inspection and to develop a predictive score for AF onset. Methods A cohort study was designed to prospectively assess the predictive value of ANS activity level among general population regarding cardiovascular events and mortality. 1011 subjects aged 65 were enrolled in the study from September 2000 to December 2002. The study population had no history of AF and a low cardiovascular risk. A median follow-up of 17.8 years was managed. HRV data were acquired by 24-h Holter electrcardiogram (ECG) monitoring at baseline and assessed by frequency domain and time domain methods. Heart rate fragmentation using the percentage of inflection points (PIP) and alpha 1-index (using fractal evaluation of NN intervals) were then calculated. The study outcome was the development of AF during follow-up, defined as a standard 12-lead ECG recording or Holter recording with ≥ 30 s of AF. Results AF was diagnosed in 123 patients during the 18-year follow-up, representing a cumulative incidence of 13.4%. Using multivariate analysis, the occurrence of AF was independently predicted by the male gender (HR=1.74, 95%CI:1.16-2.63, p<0.01), a heart rate below 70bpm (HR=1.85, 95%CI:1.18-2.90, p<0.01), an increased percentage of NN intervals that differ by more than 50 ms from the previous interval (pnn50) (HR=1.69, 95%CI:1.06-2.70, p=0.03), an increased percentage of inflection points (HR=2.80, 95%CI:1.66-4.72,p<0.01), and a reduced alpha 1 index (HR=1.61, 95%CI:1.03-2.53, p=0.04). Given these results, a predictive score was built up based on the 4 independent predictors, ranging from 0 to 6 (Graphical Abstract). The high-risk group, defined as having a PROOF-AF score of 4 or higher, exhibited a 3.3-fold higher risk of developing AF (Figure). The PROOF-AF score demonstrated superior predictive performance compared to other available risk scores for incident AF such as CHARGE-AF score, C2HEST score, FHS score, and JMC score. Conclusion HRF parameters, included in the PROOF-AF score, may be used to identify individuals aged 65 without pre-existing health conditions who are at high-risk of developing AF and assist population screening.Graphical abstractFigure

Arrayed electro-optic modulators for novel WDM multiplexing

In this paper, a novel silicon-on-chip integrated 4 × 1 wavelength division multiplexing (WDM) multiplexer has been developed. This is the first time that the multiplexer design incorporates arrayed electro-optical modulators with crosstalk cancellation. The design utilizes two types of electro-optic modulators in each channel. The first modulator, based on 1D-PhCNBC, extracts the desired wavelengths from the WDM spectrum. The second modulator, based on coupled hybrid plasmonics, acts as a switch to eliminate crosstalk of the desired optic wavelength signal at the multiplexer output. By combining the advantages of electro-optical modulators and crosstalk cancellation techniques, we anticipate that our proposed design contributes to the advancement of WDM multiplexing technology and facilitates the implementation of efficient and compact optical communication systems. Additionally, this synergy enables enhanced performance, reduced signal interference, and improved signal quality, leading to more reliable and high-speed data transmission in optical networks. The functionality of the device is theoretically simulated using 3D-FDTD (Finite-Difference Time-Domain) method.

Efficient Parallel FDTD Method Based on Non-Uniform Conformal Mesh

The finite-difference time-domain (FDTD) method is a versatile electromagnetic simulation technique, widely used for solving various broadband problems. However, when dealing with complex structures and large dimensions, especially when applying perfectly matched layer (PML) absorbing boundaries, tremendous computational burdens will occur. To reduce the computational time and memory, this paper presents a Message Passing Interface (MPI) parallel scheme based on non-uniform conformal FDTD, which is suitable for convolutional perfectly matched layer (CPML) absorbing boundaries, and adopts a domain decomposition approach, dividing the entire computational domain into several subdomains. More importantly, only one magnetic field exchange is required during the iterations, and the electric field update is divided into internal and external parts, facilitating the synchronous communication of magnetic fields between adjacent subdomains and internal electric field updates. Finally, unmanned helicopters, helical antennas, 100-period folded waveguides, and 16 × 16 phased array antennas are designed to verify the accuracy and efficiency of the algorithm. Moreover, we conducted parallel tests on a supercomputing platform, showing its satisfactory reduction in computational time and excellent parallel efficiency.

Silicon-based ultra-broadband mid-IR and LWIR near-perfect metamaterial absorber

Ultra-broadband metamaterial absorbers (UBMAs) that are compatible with CMOS technology for use in the mid-infrared and long-wave infrared regions are crucial for a variety of applications, including radiative cooling, thermal photovoltaic, and thermal imaging. In this regard, we propose, in this work, a design of an UBMA based on the heavily doped silicon (D-Si) and silicon carbide (SiC). The 3D finite-difference time-domain method is used, mainly, to numerically calculate the optical characteristics of the proposed UBMA. The absorber, which is made up of a periodic array of symmetrical multilayered square rings of D-Si and SiC, achieves high absorption with an average absorption of 95% over a wavelength range of 2.5–22 µm. This broad range of wavelength absorption is attained, encompassing the mid-, long-wave, and partial far-infrared regions. In addition to the materials' inherent absorption, the stimulation of magnetic polaritons, surface plasmon polaritons, localized surface plasmon resonance, and cavity resonance are responsible for the nearly perfect broadband absorption. Under normal incidence, the proposed UBMA is polarization-independent due to the symmetrical design of the absorber. Furthermore, the impact of the incidence angle on the absorption of transverse electric and transverse magnetic waves is examined.

Composite Electromagnetic Scattering Characteristics of Actual Terrain and Moving Rockets

This research involved studying the characteristics of composite electromagnetic scattering from a rocket moving above actual terrain using the finite-difference time-domain method. The angular distribution curve of the composite scattering coefficient was obtained, and the influences of factors such as the angle of incidence, the frequency of the incident electromagnetic wave, the content of moisture in soil, the dielectric constant of the rocket-shell material, the height of the rocket, and the undulation of the terrain on the composite scattering coefficient were investigated. Results show that the composite scattering coefficient oscillates with the scattering angle and increases in the direction of mirror reflection. It also decreases with increasing angle of incidence, frequency of the incident wave, and altitude of the rocket, while it increases with increasing soil moisture and dielectric constant of the rocket-shell materials. Although the influence of different terrain undulations on the composite scattering coefficient is noticeable, it follows no fixed pattern.

Surface-Enhanced Raman Spectroscopy Sensor Integrated with Ag@ZIF-8@Au Core-Shell-Shell Nanowire Membrane for Enrichment, Ultrasensitive Detection, and Inactivation of Bacteria in the Environment.

A core-shell-shell sandwich material is developed with silver nanowires as the core, ZIF-8 as an inner shell, and gold nanoparticles as the outer shell, namely, Ag@ZIF-8@Au nanowires (AZA-NW). Then, the synthesized AZA-NW is transformed into a surface-enhanced Raman spectroscopy (SERS) sensor (named M-AZA) by the vacuum filtration method and used to enrich, detect, and inactivate traces of bacteria in the environment. The M-AZA sensor has three main functions: (1) trace bacteria are effectively enriched, with an enrichment efficiency of 91.4%; (2) ultrasensitive detection of trace bacteria is realized, with a minimum detectable concentration of 1 × 101 CFU/mL; (3) bacteria are effectively killed up to 92.4%. The shell thickness of ZIF-8 (5-75 nm) is controlled by adjusting the synthesis conditions. At an optimum shell thickness of 15 nm, the effect of gold nanoparticles and ZIF-8 shell on the sensor's stability, SERS activity, and antibacterial performance is investigated. The simulation of the SERS sensor using the finite difference time domain (FDTD) method is consistent with the experimental results, theoretically demonstrating the role of the gold nanoparticles and the ZIF-8 shell. The sensor also shows excellent stability, safety, and generalizability. The campus water sample is then tested on-site by the M-AZA SERS sensor, indicating its potential for practical applications.

Terahertz Nondestructive Measurement of Heat Radiation Performance of Thermal Barrier Coatings Based on Hybrid Artificial Neural Network

Effective control of the micro- and nanostructure of thermal barrier coatings is essential to enhance the thermal radiation performance of the coating, which helps to determine the remaining service life of the coating. This paper proposed a method to measure the radiation properties of thermal barrier coatings by terahertz nondestructive testing technique, using APS-prepared thermal barrier coatings as the object of study. Radiative properties were a comprehensive set of properties characterized by the diffuse reflectance, transmittance, and absorptance of the thermal barrier coating. The coating data in actual service were obtained by scanning electron microscopy and metallographic experiments, and the data were used as the simulation model critical value. The terahertz time-domain simulation data of coatings with different microstructural features were obtained using the finite-different time-domain (FDTD) method. In simulating the real test signals, white noise with a signal-to-noise ratio of 20 dB was added, and fast Fourier transform (FFT), short-time Fourier transform (STFT), and wavelet transform (WT) were used to reduce the noise and compare their noise reduction effects. Different machine learning methods were used to build the model, including support vector machine algorithm (SVM) and k-nearest neighbor algorithm (KNN). The principal component algorithm (PCA) was used to reduce the dimensionality of terahertz time-domain data, and the SVM algorithm and KNN algorithm were optimized using the particle swarm optimization algorithm (PSO) and the ant colony optimization algorithm (ACO), respectively, to improve the robustness of the system. The K-fold cross-validation method was used to construct the model to improve the adaptability of the model. It could be clearly seen that the novel hybrid PCA-ACO-SVM model had superior prediction performance. Finally, this work proposed a novel, convenient, nondestructive, online, safe and highly accurate method for measuring the radiation performance of thermal barrier coatings, which could be used for the judgment of the service life of thermal barrier coatings.

A hybrid room acoustic modeling approach combining image source, acoustic diffusion equation, and time-domain discontinuous Galerkin methods

In this paper a hybrid model is introduced that constructs a broadband room impulse response using a geometrical (image source method) and a statistical method (acoustic diffusion equation) for the high-frequency range, supported by a wave-based method (time-domain discontinuous Galerkin method) for the low-frequency range. A crucial element concerns the construction of the high-frequency impulse response where a transition from a predominantly specular (image source) to a predominantly diffuse sound-field (diffusion equation) is required. To achieve this transition an analytical envelope is introduced. A key factor is the room-averaged scattering coefficient which accounts for all scattering behavior of the room and determines the speed of transition from a specular to a non-specular sound-field. To evaluate its performance, the model is compared to a broadband wave-based solver for two reference scenarios. The hybrid model shows promising results in terms of reverberation time (T20), center time (Ts) and bass-ratio (BR). Aspects such as the used geometrical complexity, the ‘room-averaged’ scattering coefficients, and other model simplifications and assumptions are discussed.

Decoding imagined speech with delay differential analysis

Speech decoding from non-invasive EEG signals can achieve relatively high accuracy (70–80%) for strictly delimited classification tasks, but for more complex tasks non-invasive speech decoding typically yields a 20–50% classification accuracy. However, decoder generalization, or how well algorithms perform objectively across datasets, is complicated by the small size and heterogeneity of existing EEG datasets. Furthermore, the limited availability of open access code hampers a comparison between methods. This study explores the application of a novel non-linear method for signal processing, delay differential analysis (DDA), to speech decoding. We provide a systematic evaluation of its performance on two public imagined speech decoding datasets relative to all publicly available deep learning methods. The results support DDA as a compelling alternative or complementary approach to deep learning methods for speech decoding. DDA is a fast and efficient time-domain open-source method that fits data using only few strong features and does not require extensive preprocessing.

Multi Fano Resonance-based Plasmonic MIM Nanosensor for Label-Free Virus Detection

Plasmonics-based sensors have grown more popular in the biosensing sector because of their label-free detection feature, which not only makes the sensor easier to use but also eliminates the need for numerous antibodies, which is a requirement for enzyme-linked immunosorbent assays. In this paper, a plasmonic-based refractive index sensor is proposed consisting of a linear rectangular waveguide coupled with a semi-ring arc and a microring resonator on both sides separated by a coupling distance. The Finite Difference Time Domain method is used to study the transmittance characteristics of the sensor. The transmittance curve displays Quintuple Fano resonances, which show sensitivity of 1000, 1184, 1290, 1914, and 2372.1 nm/RIU at 1.037, 1.211, 1.323, 2.051, and 2.383 μm, respectively. Further investigation is carried out by varying structural and geometrical parameters, such as the microring resonator’s radius and the coupling distance between the semi-ring arc and the microring resonator, which may arise due to fabrication intricacies. The performance of the sensor is investigated using the Figure of Merit, Q factor, and Detection limit producing a value of 30.41 RIU−1, 30.2, and 0.0328, respectively. The proposed sensor is further examined for its potential use in the detection of HSV, influenza A, HIV, and M13 Bacteriophage viruses.

Enhancing mid-infrared surface phonon polariton modes: optimization of structural parameters in Nb-doped SrTiO3 with hole array structures for advanced infrared sensors

This study utilized the finite difference time domain method to investigate the mid infrared surface phonon polaritons and localized surface phonon resonances in undoped and niobium (Nb)-doped SrTiO3 (STO) with planar and holes array structures. Research has shown that Nb-doped STO operates in the Reststrahlen band of 8.06–18.48 µm, providing a wider spectral response than undoped STO (12.58–18.26 µm) and effectively covering the atmospheric window of long wave infrared. This indicates that the increase in virtual permittivity has the least impact on spectral broadening, indicating that the new infrared sensor technology has broad prospects. The optimization of structural parameters, including the period, filling factor, and depth of STO holes array, as well as the response to changes in incident light angle, is crucial for guiding the design of high-performance optoelectronic devices. In addition, this study explored the excitation of four resonant modes within a holes array and analyzed their relationship with array parameters to enhance the design of optoelectronic applications.

High-Q Multiband Narrowband Absorbers Based on Two-Dimensional Graphene Metamaterials

In this paper, an absorber with multi-band, tunable, high Q, and high sensitivity, based on terahertz periodic two-dimensional patterned graphene surface plasmon resonance (SPR), is proposed. The absorber consists of a bottom metal film separated by a periodically patterned graphene metamaterial structure and a SiO2 dielectric layer, where the patterned graphene layer is etched by “+” and “L” shapes and circles. It has simple structural features that can greatly simplify the fabrication process. We have analyzed the optical properties of a graphene surface plasmon perfect metamaterial absorber based on graphene in the terahertz region using the finite-difference method in time domain (FDTD). The results show that the absorber device exhibits three perfect absorption peaks in the terahertz bands of f1 = 1.55 THz, f2 = 4.19 THz, and f3 = 6.92 THz, with absorption rates as high as 98.70%, 99.63%, and 99.42%, respectively. By discussing the effects of parameters such as the geometrical dimensions of patterned graphene metamaterial structure “+” width W1, “L” width W2, circular width R, and the thickness of the dielectric layer on the absorption performance of absorber, as well as investigating the chemical potential and relaxation time of patterned-layer graphene material, it was found that the amplitude of the absorption peaks and the frequency of resonance of absorber devices can be dynamically adjusted. Finally, we simulated the spectra as the surrounding refractive index n varied to better evaluate the sensing performance of the structure, yielding structural sensitivities up to 382 GHz/RIU. Based on this study, we find that the results of our research will open new doors for the use of multi-band, tunable, polarization-independent metamaterial absorbers that are insensitive to large-angle oblique incidence.

Ultra-high Q-factor quasi-BIC BaTiO3 metasurface for electro-optic modulation

Metasurfaces play a crucial role in trapping electromagnetic waves with specific wavelengths, serving as a significant platform for enhancing light–matter interactions. In all kinds of dynamic modulation metasurfaces, electro-optic modulation metasurfaces have attracted much attention due to its advantages of fast, stable and high efficiency. In order to respond to the extremely weak refractive index change of the electro-optical effect of the materials, the metasurfaces are required to support optical signals with high Q values. The quasi-bound state in the continuum (Q-BIC) is often used to enhance the light-field modulation capability of metasurfaces and to improve the modulation sensitivity of electro-optic modulators due to its ability to generate high Q-factor resonances. However, the design of an electro-optic modulation metasurface that facilitates the application of voltage and achieves modulation efficiency of nearly 100% is still in urgent need of development. In this study, single-crystal BTO metasurfaces are modeled using finite-difference time-domain method, and the structural symmetry is broken to introduce a Q-BIC resonance to generate a high Q-factor optical signal of 2.45 × 104 for high-depth electro-optic modulation. By simulating an applied electric field of 143 V/mm on the metasurface, a slight refractive index change of BTO of 8 × 10−4 was produced, leading to an electro-optical intensity modulation depth of 100%. Furthermore, the nanostructure of the metasurface was carefully designed to facilitate nano-fabrication and voltage application, and it is ideal for the development of low-power, CMOS-compatible, and miniaturized electro-optic modulation devices. Although the results of this study are based on simulations, they provide a crucial theoretical basis and guidance for the realization of efficient and realistic design of dynamic metasurfaces.

A linearly polarized light emission with a composite nanowire grating in whole white band

To obtain a highly linearly polarized light, a composite model consisting of white light emission, anti-reflection film, and metal-dielectric-metal nanowire grating was designed, analyzed, optimized, and fabricated. Based on the finite-difference time-domain method, the impacts of material, period, height, and incidence angle on the polarization performance of the composite model were discussed. The metal-dielectric-metal nanowire grating was fabricated on blue chip and fluorescent ceramics using nanoimprint technology. The employed materials of metal-dielectric-metal nanowire grating were aluminum and PMMA, with the period of 200 nm, wire width of 100 nm, and the height of metal and dielectric were 100 nm and 120 nm. Additionally, the anti-reflection film consisting of PMMA with the thickness of 45 nm was incorporated on fluorescent ceramics to enhance energy efficiency. Finally, through a series of test experiments, the composite model can be realized by the extinction ratio of 40 dB, while the transmittance of TM mode exceeds 50% at 450–750 nm. The theoretical analysis of this study is verified by experiments, and it has significant potential in the pursuit of high brightness, ultra-thin micro displays.

Comparison of time-domain and frequency-domain models for vibration prediction of a rail transit viaduct paved with floating slab track

Noise from rail transit viaducts often has a negative effect on surrounding buildings and nearby residents. To reduce the bridge vibration and radiated noise, floating slab tracks have been widely adopted in rail transit viaducts. To calculate the vibration of coupled track-bridge systems, both time-domain and frequency-domain methods can be applied although their relative performance is not very clear. This study aims to compare the two approaches and then provide some guidelines in choosing the appropriate method for predicting the vibration. The principle and methodology of the two calculation methods are firstly introduced, and the models for the train, floating slab track and bridge are developed using similar parameters. To further improve the efficiency and accuracy of the frequency-domain method, a half period method and a weighted average method are proposed to calculate the average responses of a certain point on the rail, floating slab and bridge to approximate the response during the pass-by. An indirect method is used to estimate the wheel–rail combined roughness from the measured rail acceleration when the train is running on the bridge, and compared with the direct measurement rail roughness. For the vibration of the bridge and floating slab, comparisons are made between results obtained from the time-domain and frequency-domain methods with different train speeds, and between results from experiment and simulation with different roughness. It is found that the wheel–rail contact forces and other structural responses from the two approaches show good consistency in the frequency region above 20 Hz. It is shown that a good approximation of the response during the pass-by can be obtained using the frequency-domain method by adopting the half period average or a simplified weighted average of two wheel position cases. When using the measured roughness and estimated roughness, the simulated vibration of the floating slab and bridge match well with the experimental results, and the indirect method can be used to modify direct measurement roughness in lower frequency regions. In the vibration prediction, the rail vibration or roughness, and other parameters in the vehicle–track–bridge system, should be measured accurately to ensure high reliability.