Time-domain Integration Research Articles

A Novel Acceleration-Based Approach for Monitoring the Long-Term Displacement of Bridge Cables

The cables of the long-span bridge are usually featured as ultra-low frequency, hence making the acceleration unable to accurately capture the information, e.g. damping ratios, for assessing the cable state assessment and mitigating the excessive structural vibration. The displacement was approved to be more sensitive to the low-frequency vibration than the acceleration. However, there is still a lack of effective method to accurately monitor the long-term displacements of bridge cables using reference-free methods. To address this issue, this paper develops a novel acceleration-based approach for monitoring the long-term displacements of the cables of long-span bridges. In the monitoring scheme, recursive least squares method is utilized to conduct baseline correction in the time domain integration of acceleration. An adaptive band-pass filtering method considering cable vibration characteristics is used to eliminate noise, thus avoiding the difficulty of selecting the cut-off frequency by experience in traditional methods. A numerical test of an analytical cable model and a field experiment of the hanger of a full-scale suspension bridge are applied to the applicability and robustness of the developed method. Result shows that adaptive band-pass filter considering the vibration characteristics is suitable for estimating the displacements of the cables. The estimated displacements using the developed method agree well with the background truth in both time and frequency domains.

Nonlinear Aeroelastic Characteristics of a Supersonic All-Movable Fin with Single or Multiple Freeplay Nonlinearities

Establishing the aeroelastic characteristic of all-movable fins with freeplay nonlinearities is one of the most common problems in the design of supersonic flight vehicles. In this context, this study provided novel points of view on the nonlinear aeroelastic characteristics of an all-movable fin with freeplay nonlinearities in its root. The unsteady aerodynamic model that was employed uses the second-order piston theory considering thickness effects. For a system with multiple freeplay nonlinearities, a discrete scanning method based on the describing function method was established to solve the limit-cycle oscillations (LCOs) and avoid the loss of solutions. Combining this with the time-domain integration method, the influences of the support stiffness at the root of the fin and the freeplay size ratio of the bending and torsional degrees of freedom on the dynamical response of the system were analyzed. The results demonstrate that systems with a single freeplay nonlinearity exhibit two completely different types of LCO, while systems with multiple freeplay nonlinearities exhibit complex dynamical behaviors such as LCO and quasi-periodic and chaotic motions. The path of a quasi-periodic torus breaking into chaos was observed. Furthermore, a harmonic initial condition for the time-domain integration is proposed; this can be used for a quick check of the frequency-domain calculation results.

Terahertz Metamaterial Biosensor With Double Resonant Frequencies for Specific Detection of Early-Stage Hepatocellular Carcinoma

A novel strategy for screening early hepatocellular carcinoma (HCC) using a terahertz (THz) metamaterials (MMs) biosensor modified with the antibody against alpha-fetoprotein (AFP) is proposed. The designed biosensor consists of split-resonant-rings (SRRs) with double resonant frequencies that are optimized using the finite integration time domain (FITD) method and manufactured by a surface micromachining process. The experimental results indicate that the HCC biomarker AFP could be accurately distinguished with a concentration as low as 0.1 ng/mL via analyzing the shifts of double resonant frequencies. Meanwhile, specific detection of AFP-antigen in solution and HCC serum has been achieved through the antigen-antibody specific binding. These results demonstrate the sensitivity and specificity of THz MMs biosensor for molecular detection of trace cancer biomarkers in biochemical sensing. Furthermore, the sensitivity of specific cancer biomarkers can be further improved by optimizing the MM structure and applying the double resonant frequencies. Therefore, this approach may own great potential for special identification of early cancer molecules.

Radiated Magnetic Field Research of Primary–Secondary Fusion MV Switch Subjected to Ultraserious Transient Current

With the extensive application of primary-secondary fusion Medium Voltage(MV) switch, the fault rate of acquisition circuit board of medium voltage switch increases obviously. The maintenance staff highly suspect that the electromagnetic compatibility of the MV switch has been damaged due to the short-range radiation interference. However, this kind of new switch is not equipped with electromagnetic field sensor to record the signal in real time. To solve this problem, firstly, electromagnetic interference signals under two kinds of ultra-serious current conditions (lightning current and inrush current) were found and obtained by originality test in this paper. Then, the finite integral time domain (FITD) method was introduced into the primary- secondary fusion switch, and the radiated magnetic fields of two kinds of transient currents are obtained. Finally, the radiated magnetic field near the secondary equipment were calculated and analyzed, and the research results have reference value for the resist of radiated magnetic field and the formulation of EMC standards of MV switch. The obtained radiated magnetic field can cause the sensitive equipment to malfunction.

Amplitude-dependent modal coefficients accounting for localized nonlinear losses in a time-domain integration of woodwind model

This article develops the design of a sound synthesis model of a woodwind instrument by modal decomposition of the input impedance, taking into account viscothermal losses as well as localized nonlinear losses at the end of the resonator. This formalism has already been applied by Diab et al. [Journal of Sound and Vibration 528 (2022) 116892] to the study of forced systems. It is now implemented for self-oscillating systems. The employed method extends the definition of the input impedance to the nonlinear domain by adding a dependance on the RMS acoustic velocity at a geometric discontinuity. The poles and residues resulting from the modal decomposition are fitted as a function of this velocity. Thus, the pressure-flow relation defined by the resonator is completed by new equations which account for the dependence with the velocity at the end of the tube. To assess the ability of the model to reproduce a real phenomenon, comparisons with the experimental results of Atig et al. [PhD thesis, Université du Maine (2004)] and Dalmont and Frappé [Journal of the Acoustical Society of America 122(2) (2007) 1173–1179] were carried out. Simulations show that the model reproduces these experimental results qualitatively and quantitatively.

Numerical Modelling of Dynamic Electromagnetic Problems Based on the Time-Domain Finite Integration Technique

Developing numerical methods to solve dynamic electromagnetic problems has broad application prospects. In computational electromagnetics, traditional numerical methods are commonly used to deal with static electromagnetic problems. However, they can hardly be applied in the modeling of time-varying materials and moving objects. So far, the studies on numerical methods that can efficiently solve dynamic electromagnetic problems are still very limited. In this paper, a numerical method called the time-domain finite integration technique (TDFIT) is extended to tackle this problem via the introduction of time-varying iterative coefficients. In order to validate the effectiveness of the proposed algorithm, three numerical examples are demonstrated, including two microstrip structures with a time-varying medium and a rapidly rotating structure. The numerical results reveal that the time-varying medium can induce a nonlinear spectrum shift, and the radar cross section (RCS) of a rapidly rotating structure is highly dependent on the rotating speed. The proposed algorithm opens a new avenue for the exploration of many intriguing phenomena in fundamental physics, including frequency conversion and magnetless nonreciprocity. Meanwhile, it can also lead to a wide range of promising practical applications, such as active electron devices, space-time metamaterials, and hypersonic vehicles.

Transient Response Sensitivity Analysis of Localized Nonlinear Structure Using Direct Differentiation Method

Based on the direct differentiation method, sensitivity analysis of transient responses with respect to local nonlinearity is developed in this paper. Solutions of nonlinear equations and time-domain integration are combined to compute the response sensitivities, which consist of three steps: firstly, the nonlinear differential equations of motion are solved using Newton–Raphson iteration to obtain the transient response; secondly, the algebraic equations of the sensitivity are obtained by differentiating the incremental equation of motion with respect to nonlinear coefficients; thirdly, the nonlinear transient response sensitivities are determined using the Newmark-β integration in the interested time range. Three validation studies, including a Duffing oscillator, a nonlinear multiple-degrees-of-freedom (MDOF) system, and a cantilever beam with local nonlinearity, are adopted to illustrate the application of the proposed method. The comparisons among the finite difference method (FDM), the Poincaré method (PCM), the Lindstedt–Poincaré method (LPM), and the proposed method are conducted. The key factors, such as the parameter perturbation step size, the secular term, and the time step, are discussed to verify the accuracy and efficiency. Results show that parameter perturbation selection in the FDM sensitivity analysis is related to the nonlinear features depending on the initial condition; the consistency of the transient response sensitivity can be improved based on the accurate nonlinear response when a small time step is adopted in the proposed method.

Quantum corrections to the quasinormal modes of the Schwarzschild black hole

Based on the minimum measurable momentum concepts associated with the quantum gravity effects acting on the large-scale dynamics of the universe, we study the quantum effect of the EUP on the Hawking evaporation of the black hole. The results show the quantum corrections may shorten the lifetime of the massive black hole. To verify the new EUP on the black hole stability, the scalar field and electromagnetic field are derived and the time evolution of the black hole is analyzed in terms of the time domain integration method, the quantum effect alters the oscillation and decay time of black hole. Furthermore, we use the WKB numerical approximation method to calculate the quasinormal mode frequencies and analyze the influence of the EUP parameter $$\alpha $$ on the scattering problem. This shows that the EUP significantly increases the area of the total absorption cross-section of the black hole.

Bistable enhanced passive absorber based on integration of nonlinear energy sink with acoustic black hole beam

The nonlinear energy sink (NES) has a broader frequency bandwidth than the linear tuned-mass-damper (TMD), making it more robust. However, the NES is only efficient in a narrow energy range. The mitigation property of NES may deteriorate when input energy is too small or large. To overcome this shortage, a novel NES named ABH-BNES is proposed in this paper, by combining a bistable nonlinear energy sink (BNES, which has negative linear stiffness, cubic nonlinear stiffness, and linear damping) and acoustic black hole (ABH) beam. The negative linear stiffness and cubic nonlinear stiffness elements can generate a large cross-well motion to improve the performance of vibration mitigation for low input energy. By replacing the attached mass in traditional NES as an ABH beam, multiple high-damping modes can be introduced into the vibration absorber. So that the performance of ABH-BNES is also enhanced for large input energy. First, the Gaussian Expansion Method and Modal Approach are employed to establish the dynamic model of a single-dof linear oscillator coupling with an ABH-BNES. Such a modeling approach is verified by comparing it with the models in the existing literature and established by the finite element method (FEM). The slow invariant flow (SIM) theory and time-domain integration are employed to analyze the novel NES's vibration mitigation mechanism. In addition, a multi-solution boundary related to the existence of targeted energy transfer is derived for optimizing the nonlinear absorber. Then, the energy method is used to verify the superiority of the novel NES by comparing it with TMD, NES, and the Linear ABH absorber. The results show that the ABH-BNES can behave with an excellent mitigation effect and an extensive energy bandwidth when the parameters are appropriately selected. Finally, an experiment is carried out to verify the new NES's superiority and the correctness of the theoretical model.

In-Body to On-Body Channel Characterization and Modeling Based on Heterogeneous Human Models at HBC-UWB Band

In this work, the in-body to on-body (IB2OB) channel characteristics of the ultrawideband (UWB) link from 10 to 50 MHz at the human body communication (HBC) band are studied for developing high-speed and large-capacity intrabody wireless communication systems. Incorporating the time-domain finite integration technique (FIT) with three types of anatomical human models (adult male, adult female, and teenager) and a simple geometric human model with homogeneous or multilayer biological tissues, the 10–50-MHz signal propagation characteristics are investigated, and a comprehensive path loss model is proposed based on typical in-body links of the heart, brain, and intestine to the on-body sensor nodes. The statistical results show that a linear regulation term related to the surface wave propagation should be added to construct a more accurate logarithmic-distance path loss model in the sense of least-mean-square error (LMSE), indicating that the surface wave propagation mechanism can describe the 10–50-MHz signal propagation more accurately. The shadow fading in decibel is normally distributed around the mean path loss with a standard deviation in the range of 7–9 dB. And the average group delay of the IB2OB channel fluctuates around 0–7 ns, illustrating that the channel can be approximated as a linear phase response. Moreover, the experimental verification is conducted with a tissue-equivalent liquid phantom and an adult man, demonstrating the validity of our proposed statistical path loss model. The key parameters for channel characterization in simulations and measurements are summarized to provide useful insights for HBC-UWB communication system design and performance analysis.

The high-order smooth interpolated reproducing kernel particle method for elastodynamics problems

Combining the interpolation reproducing kernel particle method (IRKPM) with the integral weak form of elastodynamics, we present a high-order smooth interpolated reproducing kernel particle method for an elastodynamics plane problem. The shape function of IRKPM not only has the interpolation property at any point but also has a high-order smoothness not lower than that of the kernel function. This new method overcomes the difficulties of most meshless methods in dealing with essential boundary conditions and ensures high numerical accuracy. For time domain integration, we use the classical Newmark average acceleration method. By numerical examples we demonstrate that the proposed method has the advantages of higher accuracy, smaller scale of solving problem, and direct application of boundary conditions.

Large deformation of sandwich wide panel

This work addresses the general nonlinear static and dynamic formulations of sandwich panels with compressible cores under large deformation, within the framework of Extended High-order Sandwich Panel Theory. The commonly-used assumption named large displacement with moderate rotation, is assessed. Within a total Lagrange manner, the weak form of the nonlinear equation of equilibrium is derived via the principle of virtual work and further linearized through the Newton-Raphson iteration. Both the static and dynamic governing equations are acquired with respect to the nodal degrees of freedom. Numerical techniques involving Newton-Raphson method for the static analysis, and Newmark-Beta method for the time domain integration are employed to get the solutions. The static and transient mechanical response of simply supported sandwich panels under static pressure and dynamic blast is conducted respectively. The closed linear solutions and finite element models are accomplished to validate. Conclusions are drawn that the deformation gradient, as well as the displacement and rotation, critically determines the structural stiffness and internal force, and their relationship is originally provided in this paper. The structural stiffness at large deformation is stronger than that at small deformation. The assumption of large displacement with moderate rotation is inadequate for sandwich structure in large deformation.

Transfer Functions of Bridge and Train: Case Study of the Yunjung Bridge in Honam High-Speed Railway System

We propose the inverse transfer function (TFinv) changing the ground motion amplitude recorded at the train to the free-field equivalent ground motion supposing that the train is on the bridge. This process is needed to estimate the free-field motions from the seismic records observed at the on-board accelerometer which is used for the on-board earthquake warning system. To estimate the TFinv, evaluation of two transfer functions is needed: a transfer function of the bridge (TFbridge), and the other transfer function of the train (TFtrain). For the estimation of the TFbridge, we simplified an example bridge (named Yunjung bridge) located in the Honam high-speed railway as SDOF models finding its natural frequency dependent on the girder type and span length. Then, using time-domain integration methods (Newmark and Duhamel), SDOF response and TFbridge is calculated. For the TFtrain, we modeled the rail base and train following the similitude law and performed the shaking table test with various earthquake ground motions, and evaluated the TFtrain empirically comparing the responses at the train and the rail base. Two models of TFinv based on the moment magnitude ranges of input ground motions are proposed.

Quasinormal modes of self-dual black holes in loop quantum gravity

We study the evolution of a test scalar field on the background geometry of a regular loop quantum black hole characterized by two loop quantum gravity correction parameters, namely, the polymeric function and the minimum area gap. The calculations of quasinormal frequencies in asymptotically flat spacetime are performed with the help of higher-order Wentzel-Kramers-Brillouin expansion and related Pad\'e approximants, the improved asymptotic iteration method, and time-domain integration. The effects of free parameters of the theory on the quasinormal modes are studied and deviations from those of the Schwarzschild black holes are investigated. We show that the loop quantum gravity correction parameters have opposite effects on the quasinormal frequencies and the loop quantum black holes are dynamically stable.

Small-signal stability analysis of implicit integration methods for power systems with delays

The paper focuses on the accuracy and stability of implicit numerical methods when utilized for the Time Domain Integration (TDI) of power systems with inclusion of time delays. In particular, a small-disturbance analysis technique is proposed to evaluate the numerical distortion that TDI methods induce to the dynamic modes of power systems modeled as Delay Differential Algebraic Equations (DDAEs). The case study illustrates the features of the proposed technique through simulations conducted using the IEEE 14-bus test system, and considering three examples of implicit integration methods, namely Backward Euler Method (BEM), Implicit Trapezoidal Method (ITM), and 2-stage Radau IIA.

An Explicit Time-Domain Finite-Element Boundary Integral Method for Analysis of Electromagnetic Scattering

A numerical scheme, which hybridizes the element-level dual-field time-domain finite-element domain decomposition method (ELDDM) and the time-domain boundary integral (TDBI) method to accurately and efficiently analyze open-region transient electromagnetic scattering problems, is proposed. Element-level decomposition decouples Maxwell equations on a discretization element from those on its neighboring elements using equivalent currents defined on their faces. For any element inside the computation domain, the equivalent currents are obtained from fields in the neighboring elements. For any element on the boundary of the computation domain, the equivalent currents are obtained using the fields generated by TDBI. To generate these fields, TDBI “radiates” equivalent currents on a Huygens surface enclosing the scatterer. This approach when combined with a leapfrog-type time updates results in a fully explicit numerical scheme that allows ELDDM and TDBI to use different time steps. Numerical results that demonstrate the applicability of the proposed method to concave and disconnected scatterers are presented.

Moving force identification of simply supported bridges through the integral time domain method

This paper presents a new form of inversion matrix, which aims to obtain more accurate moving force identification results from the responses of a simply supported bridge deck to vehicles passing over it. The load identification process of the modal superposition method discretizes the time-domain integral equation of the load response, obtains the load inversion matrix, and converts the load identification problem into a linear equation solving problem. The inversion matrix formation process of this traditional time domain method (TDM) can introduce the load compression error and the discretization error of the unit impulse response function, which affect the load solution. To reduce the source of error and maintain the stability of the solution, the discretized unit impulse response function is replaced by an integral form, thereby eliminating the discretization error. This method is called the integral time domain method (ITDM). A supported beam subjected to a single force and two forces is illustrated as a numerical example. Through numerical analysis, the effects of the two methods in single time-varying force identification are analyzed. Using two moving forces analysis, when noise is included, the influence of discretization error on the load solution is analyzed. Numerical results show that the discretization error has a greater impact on the load inversion using the acceleration response than the bending moment and displacement response inversion, and the ITDM should be used to avoid the interference of discrete error.

Theoretical and Experimental Study of the Torque Impact and Shaft Response during the Rapid Engaging Process of a Gas Turbine

Gas turbines produce torque impacts during the rapid engaging process, which could obviously affect the safety of the propulsion shafting. To analyze the impact load and the corresponding response of a shaft, a calculation method is proposed for the torque impact load, based on a propulsion shafting model and the motion characteristics of a synchro-self-shifting (SSS) clutch. In addition, the time-domain integration method was used to analyze the shaft response under an impact load. Finally, the engaging process was reproduced in an experimental plant, and the proposed method was verified with measured transient torque responses. The results show that an obvious torque impact is produced in the shafting under the action of the damping force when the SSS clutch meshes during the engaging process, with the torque response amplitude fluctuating within a certain range. Adjusting the engaging parameters of the working engine and the engaging engine can reduce the amplitude of the shaft response.

Fast Recognition Algorithm for Human Motion Posture Using Multimodal Bioinformation Fusion

To address the problems of low feature extraction accuracy, large bias of human motion pose recognition and posture recognition error, poor recognition effect, and low recognition rate of traditional human motion posture fast recognition algorithm, we propose a human motion posture fast recognition algorithm using multimodal bioinformation fusion. First, wavelet packet decomposition with sample entropy is used to extract the human motion posture hand features such as kurtosis, time domain feature skewness, and frequency domain feature electromyogram (EMG) integral value and time domain features such as mean, standard deviation, and interquartile distance of leg motion amplitude. Second, after normalizing the two features, the human hand and leg motion feature set is obtained, and finally the feature set is used to construct a human motion posture fast recognition model based on multimodal bioinformation fusion, and the feature set is input into the recognition model, which completes the fusion of human motion posture information by improving the typical correlation analysis method, and the fusion result is used as the input of the minimum distance classifier to achieve human motion posture fast recognition. The results show that the proposed algorithm has high accuracy of feature extraction, small bias of human motion posture recognition, the posture recognition error is -0.21∼0.02, the recognition rate is always above 95%, and the practical application effect is good.

Microseismic Time Delay Estimation Method Based on Continuous Wavelet.

The microseismic signal is easily affected by observation noise and the inaccurate estimation of traditional methods will seriously reduce the location accuracy of the microseismic event. Therefore, based on the continuous wavelet spectrum and the similarity coefficient, a fast and efficient microseismic time delay estimation method is proposed. Firstly, the original signals are denoised by continuous wavelet transform. Subsequently, the time-frequency transform of the original signal by continuous wavelet transform, time-frequency signal extraction is the process of band-pass filtering, which can further reduce the influence of noise interference on the time delay estimation. Finally, we calculated the similarity between the time-frequency signals via the time domain and frequency domain integration. The similarity function is based on correlation and proposed according to the time-frequency transformation provided by the phase spectrum to evaluate the similarity between two noisy signals. The time delay estimation is determined by searching for the similarity function peak. The experimental results show the precision and accuracy of the method over the cross-correlation method and generalized cross-correlation phase transformation method, especially when the signal-to-noise ratio is low. Therefore, a new time delay estimation method for non-stationary random signals is presented in this paper.