Time-domain Integration Research Articles

Application of the hybrid integration displacement algorithm based on CEEMDAN and wavelet threshold denoising in vibration screening equipment

Abstract Vibration screening equipment has an extensive application profile in material screening, in which the displacement parameters can reveal the motion state of the material and affect the screening efficiency. These displacement parameters can be obtained by integrating the acceleration signal of the equipment. In this paper, to prevent the noise in the acceleration signal from further amplifying its negative effects on the subsequent integration, the acceleration signal is preprocessed by the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and wavelet threshold denoising. Besides, a hybrid integration displacement algorithm is utilized to mitigate the influence of integration errors. The consistent results between simulation and platform experiments demonstrate that CEEMDAN in combination with wavelet threshold denoising can effectively remove noise while retaining the main frequency signal. In addition, the displacement signal obtained by the hybrid integration algorithm proposed in this paper is closer to the original displacement signal. Compared with the 2nd time-domain integration, the 2nd frequency-domain integration, and the empirical mode decomposition (EMD) integration methods, the integration method proposed in this paper achieves a smaller peak error, mean absolute error (MAE), and root mean square error (RMSE). The experimental results corroborate the superiority of this method in the application of vibration screening equipment.

Research on the mechanism and measures of riding comfort deterioration in a low floor tram

With the global widespread preference for low-floor trams, the expectation for tram riding comfort has been increasingly heightened. This paper identifies an abnormal riding comfort problem (ARCP, characterized by an excessive and W-shaped distribution of riding comfort) during dynamic field tests on a low-floor tram. To address ARCP, a multi-body dynamics model of the tram was constructed and validated its accuracy through dynamic field tests. By integrating track irregularities and wheel-rail contact analysis, the riding comfort index was assessed and reproduced the ARCP phenomenon. Linearization and time-domain integration studies were conducted on the mechanisms and measures to resolve the ARCP. The research findings reveal that the primary cause of the deterioration in the mean comfort index is the large amplitude of the track irregularity and the low equivalent conicity of the wheel-rail contact relationship. The main reason for the W-shaped distribution of riding comfort is the weaker inter-vehicle constraints and the lack of lateral energy-absorbing devices. Finally, optimization measures were proposed, including reducing the lateral stiffness of the second suspension, altering the carbody structural parameters, and modifying the inter-vehicle connection devices. This research enriches the study of tram dynamic performance and offers insights that may contribute to the resolution of ARCP.

Nonlinear metamaterial enabled aeroelastic vibration reduction of a supersonic cantilever wing plate

The violent vibration of supersonic wings threatens aircraft safety. This paper proposes the strongly nonlinear acoustic metamaterial (NAM) method to mitigate aeroelastic vibration in supersonic wing plates. We employ the cantilever plate to simulate the practical behavior of a wing. An aeroelastic vibration model of the NAM cantilever plate is established based on the mode superposition method and a modified third-order piston theory. The aerodynamic properties are systematically studied using both the timedomain integration and frequency-domain harmonic balance methods. While presenting the flutter and post-flutter behaviors of the NAM wing, we emphasize more on the pre-flutter broadband vibration that is prevalent in aircraft. The results show that the NAM method can reduce the low-frequency and broadband pre-flutter steady vibration by 50%–90%, while the post-flutter vibration is reduced by over 95%, and the critical flutter velocity is also slightly delayed. As clarified, the significant reduction arises from the bandgap, chaotic band, and nonlinear resonances of the NAM plate. The reduction effect is robust across a broad range of parameters, with optimal performance achieved with only 10% attached mass. This work offers a novel approach for reducing aeroelastic vibration in aircraft, and it expands the study of nonlinear acoustic/elastic metamaterials.

Quasinormal modes of the Mannheim–Kazanas black holes

Abstract A spherically symmetric black hole solution in the conformal Weyl gravity was found by Mannheim and Kazanas in 1988. While the quasinormal modes (QNMs) of these black holes have been considered in a few works, here we complement these studies by considering in detail the regime of vanishing cosmological constant and negative values of the Weyl parameter for which we find quasinormal frequencies for scalar, Dirac and electromagnetic perturbations with the time-domain integration and WKB methods. In particular, we derive the compact and remarkably accurate analytic formula for the frequencies in the form of expansion in terms of the inverse multipole number. Comparison with the time-domain integration shows that the 6th order WKB method with the Padé approximants is quite accurate, unless the black hole is in the near extreme state.

Black holes in Starobinsky-Bel-Robinson Gravity and the breakdown of quasinormal modes/null geodesics correspondence

We show that perturbations of a scalar field in the background of the spherically symmetric black hole obtained with the Starobinsky-Bel-Robinson Gravity are unstable unless the dimensionless coupling β describing the compactification of M-theory is small enough. In the sector of stability quasinormal spectrum show peculiar behavior both in the frequency and time domains: the ringing consists of two stages where two different modes dominate. The WKB method does not reproduce part of the spectrum including the fundamental mode, which is responsible for the first stage of the ringing. As a result, the correspondence between the high frequency quasinormal modes and characteristics of the null geodesics reproduces only one branch of the eikonal spectrum. The frequencies are obtained with the help of three methods (Frobenius, WKB and time-domain integration) with excellent agreement among them.

Late time decay of scalar and Dirac fields around an asymptotically de Sitter black hole in the Euler–Heisenberg electrodynamics

We compute the quasinormal modes of massive scalar and Dirac fields within the framework of asymptotically de Sitter black holes in Euler–Heisenberg non-linear electrodynamics. We pay particular attention to the regime μM/mP2≫1,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu M/m_{P}^2 \\gg 1,$$\\end{document} where μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu $$\\end{document} and M denote the masses of the field and the black hole, respectively, and mP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_{P}$$\\end{document} represents the Planck mass, covering a range from primordial to large astrophysical black holes. Through time-domain integration, we demonstrate that, contrary to the asymptotically flat case, the quasinormal modes also dictate the asymptotic decay of fields. Employing the 6th order WKB formula, we derive a precise analytic approximation for quasinormal modes in the regime μM/mP2≫1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu M/m_{P}^2 \\gg 1$$\\end{document} without resorting to expansion in terms of the inverse multipole number. This analytic expression takes on a concise form in the limit of linear electrodynamics, represented by the Reissner–Nordström black holes. Our numerical analysis indicates the stability of the fields under consideration against linear perturbations.

A Time-Domain Wavenumber Integration Model for Underwater Acoustics Based on the High-Order Finite Difference Method

Simulating the acoustic field excited by pulse sound sources holds significant practical value in computational ocean acoustics. Two primary methods exist for modeling underwater acoustic propagation in the time domain: the Fourier synthesis technique based on frequency decomposition and the time-domain underwater acoustic propagation model (TD-UAPM). TD-UAPMs solve the wave equation in the time domain without requiring frequency decomposition, providing a more intuitive explanation of the physical process of sound energy propagation over time. However, time-stepping numerical methods can accumulate numerical errors, making it crucial to improve the algorithm’s accuracy for TD-UAPMs. Herein, the time-domain wavenumber integration model SPARC was improved by replacing the second-order finite element method (FEM) with the high-order accuracy finite difference method (FDM). Furthermore, the matched interface and boundary (MIB) method was used to process the seabed more accurately. The improved model was validated using three classic underwater acoustic benchmarks. By comparing the acoustic solutions obtained using the FDM and the FEM, it is evident that the improved model requires fewer grid points while maintaining the same level of accuracy, leading to lower computational costs and faster processing compared to the original model.

A time-domain integration method with equivalent complex damping model based on viscoelastic material constitutive relation

The complex damping model is only applied in frequency-domain. Based on the constitutive relation of viscoelastic materials, a vibration equation is equivalent to the constitutive relation of complex damping theory and the frequency response function satisfying the causality constraint. Compared with the existing equivalent complex damping model, the proposed equivalent damping model can consider more natural frequencies. The calculation formulas of Gauss precise integral method and improvement constant average acceleration method are derived. By the equivalent complex damping, the seismic time-history response of the typical example could carry on the numerical calculation. Compared with the Gauss precise integral calculation results of complex damping vibration equation, some conclusions can be analyzed. The proposed two methods could avoid divergent phenomenon in the time-domain numerical solution of complex damping vibration equation. The time-domain integral method of equivalent complex damping theory is stable and convergent. The Gauss precise integral method has strong equivalence and big computational complexity. The improvement constant average acceleration method has weak equivalence and small computational complexity.

On the Application of Fractional Derivative Operator Theory to the Electromagnetic Modeling of Frequency Dispersive Media

Fractional derivative operators are finding applications in a wide variety of fields with their ability to better model certain phenomena exhibiting spatial and temporal nonlocality. One area in which these operators are applicable is in the field of electromagnetism, thereby modelling transient wave propagation in complex media. To apply fractional derivative operators to electromagnetic problems, the operator must adhere to certain principles, like the trigonometric functions invariance property. The Grünwald–Letnikov and Marchaud fractional derivative operators comply with these principles and therefore could be applied. The fractional derivative arises when modelling frequency-dispersive dielectric media. The time-domain convolution integral in the relation between the electric displacement and the polarisation density, containing an empirical extension of the Debye model, is approximated directly. A common approach is to recursively update the convolution integral by approximating the time series by a truncated sum of decaying exponentials, with the coefficients found through means of optimisation or fitting. The finite-difference time-domain schemes using this approach have shown to be more computationally efficient compared to other approaches using auxiliary differential equation methods.

A Hybrid Discrete-Finite Element method for continuous and discontinuous beam-like members including nonlinear geometric and material effects

This paper introduces a novel formulation, called Hybrid Discrete-Finite Element (HybriDFEM) method, for modelling one-directional continuous and discontinuous planar beam-like members, including nonlinear geometric and material effects. In this method, the structure is modelled as a series of distinct rigid blocks, connected to each other through contact pairs distributed along the interfaces. Each of those contact pairs are composed of two nonlinear multidirectional springs in series, which can represent either the deformation of the blocks themselves, or the deformation of their interface. Unlike the Applied Element Method, in which contact pairs are composed of one single spring, the current approach allows capturing phenomena such as sectional deformations or relative deformations between two blocks composed of different materials. This method shares similarities with the Discrete Element Methods in its ability to model contact interfaces between rigid or deformable units, but does not require a numerical time-domain integration scheme. More importantly, its formulation resembles that of the classical Finite Elements Method, allowing one to easily couple the latter with HybriDFEM. Following the presentation of its formulation, the method is benchmarked against analytical solutions selected from the literature, ranging from the linear-elastic response of a cantilever beam to the buckling and rocking response of continuous flexible columns, and rigid block stackings. One final example showcases the coupling of a HybriDFEM element with a linear beam finite element.

Test measurements of an ASIC for X-ray material discrimination by using on-chip time domain integration and a CdTe sensor

Using time-domain integration (TDI) and a two-dimensional sensor is beneficial for X-ray imaging of moving objects. Applying on-chip instead off-chip TDI decreases the required data throughput between an ASIC and the backend several times [1]. This, in turn, allows us to significantly simplify the ASIC itself as well as the backend.We present the results of test measurements of an ASIC dedicated for X-ray material discrimination by using on-chip TDI and a CdTe sensor.The main part of the ASIC is an 192 × 64 pixel matrix. The pixel size is 100 μm × 100 μm, so the chip size is approximately 6.7 mm × 2 cm. The chip is manufactured in a 130 nm CMOS technology with 8 metal layers. A single pixel analog front-end consists of a charge-sensitive amplifier, a shaper, and three discriminators followed by counters. The test was conducted with a 0.75 mm thick CdTe sensor.First, we show the results of the discriminator offset correction followed by the evaluation of the pixel analog front-end gain and noise conducted with single energy radiation. Next, the results of moving objects imaging are obtained by using an industrial X-ray machine for food inspection (continuous energy spectrum). This is carried out to present an example of the image and evaluate the image signal to noise ratio for different energy discriminator thresholds, sensor bias voltages, detector module temperatures and object speeds.

Analytic expressions for quasinormal modes of the Reissner–Nordström-like black holes

The Reissner–Nordström metric encompasses three distinct interpretations: first, as a charged static black hole in the Einstein–Maxwell theory; second, within the brane world model, where the charge is construed as a tidal parameter emanating from extra dimensions; and third, in the context of the Einstein-aether theory, wherein the charge is associated with the aether parameter. Considering these interpretations, we derive analytic expressions for the proper oscillation frequencies of black holes, known as quasinormal modes, for scalar, electromagnetic and Dirac perturbations. Employing the higher WKB technique and an expansion in terms of the inverse multipole number, our analytic formulas exhibit notable agreement with previously published numerical data and time-domain integration results. Additionally, we verify the correspondence between null geodesics and eikonal quasinormal modes for these cases.

The fermionic greybody factor and quasinormal modes of hairy black holes, as well as Hawking radiation’s power spectrum and sparsity

A hairy black hole (HBH) emerges due to matter surrounding the Schwarzschild metric when using the Extended Gravitational Decoupling (GD) approach. The fermionic greybody factors (GFs) and quasinormal modes (QNMs) as well as Hawking spectra and sparsity of HBH solutions are investigated. We consider massive and massless spin-1/2 fermions, along with massless spin-3/2 fermions. The equations of the effective potential for fermions with different spins are derived in HBH spacetime. Then, the rigorous bound method is used to calculate the fermionic spin-1/2 and spin-3/2 GFs. With the time domain integration method at our disposal, we illustrate the impact of additional parameters on the ringdown waveform of the massless fermionic spin-1/2 and spin-3/2 fields and, in turn, on their quasinormal modes. We then delve into investigating the Hawking spectra and sparsity of the radiation emitted by an HBH. Hairy parameters significantly affect the sparsity of Hawking radiation as well. We observe that the total power emitted by the BH increases both with α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and Q but decreases with l0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_{0}$$\\end{document}. Our study conclusively shows the significant impact of the additional parameters on important astrophysical phenomena such as quasinormal modes, Hawking spectra, and sparsity.

Simulation analysis of energy metering error of non-vehicle charger

This paper studies three methods of DC energy measurement for non-vehicle chargers, namely, the average value method, effective value method, and time domain integration method, introduces the definition of ripple, and analyzes the characteristics of constant voltage, constant current charging mode and pulse charging mode of electric vehicles, providing an algorithm basis for the establishment of DC energy metering error model and simulation analysis. This paper studies high-power DC energy measurement algorithms with ripple parameters, analyzes the error characteristics of various algorithms, summarizes the relevant laws, and provides a theoretical basis for the design of a high-precision DC metering module under the influence of ripple.

Uncertainty quantification and probabilistic reliability analysis for the self-excited vibration of a spline-shafting system

Floating involute splines are widely used in large-torque, high-speed aerospace power transmission systems. The spline rotor system may suffer from self-excited vibration due to poor lubrication. The unavoidable manufacturing tolerances, mounting errors, component deformation, and other factors make the self-excited vibration occurrence conditions have significant uncertainties. This paper provides new insights into the uncertainty quantification and reliability analysis of self-excited vibration of a spline-shafting system based on an advanced Kriging surrogate model. First, a rotor nonlinear dynamics model considering tooth surface friction is established. Then an effective Kriging surrogate model is developed to quantify the uncertainty propagation in nonlinear rotor dynamics considering the randomness of parameters such as friction coefficient, and load torque, which enables the rapid estimation of statistical information of the self-excited vibration response by the time-domain numerical integration method. The probability of instability and reliability of the system under multi-parameter uncertainty for the occurrence of self-excited vibration is also predicted. Finally, the validity of the proposed method is verified by Monte Carlo simulation. This contribution will further enrich the theory and applications of probabilistic statistical analysis and reliability assessment of complex rotating machinery.

Quasinormal ringing of regular Einstein-Yang-Mills black hole

In this letter, we study quasinormal modes of regular non-minimal Einstein-Yang-Mills (EYM) black holes. We mainly consider the scalar field perturbation and axial gravitational perturbation of the EYM black hole. The corresponding effective potential is derived by solving the field equations. The quasinormal ringing of EYM black hole under scalar field perturbation and axial gravitational perturbation is given through time domain integration. Our results show that the magnetic charge Q will reduce the damping rate of the gravitational waves generated by the EYM black hole after being disturbed.

A 3D time-domain solution for the bending of viscoelastic shells

This article presents a time domain analysis of viscoelastic doubly curved shallow shells employing 3D solution based on equilibrium equations. The constitutive equation is transformed into Laplace domain in order to avoid the time domain integration. The partial differential equations are solved for the mid-surface variables by applying the Navier Technique. The thickness equations are solved using the differential quadrature method (DQM). Lagrange interpolation polynomial are employed as basis functions. Each layer of the panel is discretized by the Chebyshev–Gauss–Lobatto grid distribution. The time-domain displacements are obtained by using the inverse Laplace transformation in an approximate numerical manner. The 3D solution is compared with references in the literature. Given the inclusion of comprehensive 3D time domain solutions, these results can be considered as a benchmark for reference.

Light-guiding-light-based temporal integration of broadband terahertz pulses in air

The next generation of all-optical computation platforms prefers the light-guiding-light (LGL) scheme inside a medium that envisions circuitry-free and rapidly reconfigurable systems powered by dynamic interactions between light beams. Currently, suitable LGL materials and corresponding mechanisms are in urgent need. In this work, we proposed ubiquitous air as a restorable LGL signal manipulation medium with transient air-plasma waveguide circuits. Briefly, by focusing femtosecond laser beams in free space, the created atmospheric plasma filament array via photoionization was able to guide terahertz (THz) pulses along its epsilon-near-zero zone with a 1/f-profile spectral response. Consequently, this achieved a time-domain integration of the THz pulse in broad bandwidth. When the pumping laser was sequentially turned off and on, this air-plasma multi-filament structure was erased and rebuilt within nano- and femto-seconds, respectively, allowing rapid and repeated rearrangements of the all-optical stage. Furthermore, this air-based LGL information processing approach is promising to pave the way toward all-optical calculations during free-space directional transmission of THz waves, in which way the delivered THz signal can be remotely controlled.

A 0.9-V 50-MS/s 67.3-dB-SNDR SAR-ISDM ADC With an Oscillator-Based Integrator

A two-step analog-to-digital converter (ADC), using a successive approximation register (SAR) ADC and a time-domain incremental Σmodulator (ISDM) for the coarse and fine conversion, is proposed for power-efficient data conversion. A high-gain gated-delay oscillator (GDO) with a time-domain integration technique is employed to achieve the first-order noise shaping in the fine ISDM conversion. The proposed ADC fabricated in a 40-nm CMOS technology achieves a peak SNDR of 67.3 dB, the Schreier figure of merit (FoMS) of 169.27 dB, and the Walden figure of merit (FoMW) of 16.76 fJ/conversion-step.

Characterization of water content and inspection of delamination in spruce, oak and meranti woods after pyrolysis processing using a new terahertz time-domain spectroscopy method

Wood has been widely used as a building and interior furniture decoration material due to its excellent insulation of heat and electricity, strong buffer effect on vibration, high strength, etc. Generally, wood materials should be processed by pyrolysis technique in order to improve corrosion resistance, flame retardancy, and dimensional stability. However, during pyrolysis, the main components of wood, such as cellulose, hemicellulose, and lignin, undergo chemical reactions causing the damage of the internal structure. With existing non-destructive evaluation methods, such as thermography and radiography, it is difficult to detect the degree of delamination within the wood due to its anisotropy physical properties and complex internal structure. In this work, a novel normalized time-domain integration method is proposed to detect the delamination of wood materials at different pyrolysis temperatures. The experimental results show the great robustness and detection efficiency of this method. Furthermore, numerical simulation and experiments are used to build the relationship between the terahertz time-domain signal and water content. Compared with spruce and oak, meranti is more resistant to pyrolysis and has higher structural stability.