Multi-scale seismic full waveform inversion in the frequency-domain with a multi-grid method

Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based on the optimal steep descent methods, we present an algorithm which combines the preconditioned bi-conjugated gradient stable method and the multi-grid method to compute the wave propagation and the gradient space. The multiple scale prosperity of the waveform inversion and the multi-grid method can overcome the inverse problems local minima defect and accelerate convergence. The local inhomogeneous three-hole model simulated results and the Marmousi model certify the algorithm effectiveness.

Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential

Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time （HB-AFT） do- main technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.

Application of pseudo-random frequency domain electromagnetic method in mining areas with strong interferences

Due to the strong electromagnetic interferences and human interference,traditional electromagnetic methods cannot obtain high quality resistivity data of mineral deposits in Chinese mines.The wide field electromagnetic method(WFEM),in which the pseudo-random signal is taken as the transmitter source,can extract high quality resistivity data in areas with sever interference by only measuring the electric field component.We use the WFEM to extract the resistivity information of the Dongguashan mine in southeast China.Compared with the audio magnetotelluric(AMT)method,and the controlled source audio-frequency magnetotelluric(CSAMT) method,the WFEM can obtain data with higher quality and simpler operations.The inversion results indicate that the WFEM can accurately identify the location of the main ore-body,which can be used for deep mine exploration in areas with strong interference.

Acoustic reflection well logging modeling using the frequency-domain finite-element method with a hybrid PML

In this paper, we propose a hybrid PML （H-PML） combining the normal absorption factor of convolutional PML （C-PML） with tangential absorption factor of Mutiaxial PML （M-PML）. The H-PML boundary conditions can better suppress the numerical instability in some extreme models, and the computational speed of finite-element method and the dynamic range are greatly increased using this HPML. We use the finite-element method with a hybrid PML to model the acoustic reflection of the interface when wireline and well logging while drilling （LWD）, in a formation with a reflector outside the borehole. The simulation results suggests that the PS- and SP- reflected waves arrive at the same time when the inclination between the well and the outer interface is zero, and the difference in arrival times increases with increasing dip angle. When there are fractures outside the well, the reflection signal is clearer in the subsequent reflection waves and may be used to identify the fractured zone. The difference between the dominant wavelength and the model scale shows that LWD reflection logging data are of higher resolution and quality than wireline acoustic reflection logging.

Modified slow-fast analysis method for slow-fast dynamical systems with two scales in frequency domain

A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term as a slow-varying parameter,a generalized autonomous fast subsystem can be defined,the equilibrium branches as well as the bifurcations of which can be employed to account for the mechanism of the bursting oscillations by combining the transformed phase portrait introduced.As an example,a typical periodically excited Hartley model is used to demonstrate the validness of the method,in which the exciting frequency is far less than the natural frequency.The equilibrium branches and their bifurcations of the fast subsystem with the variation of the slow-varying parameter are presented.Bursting oscillations for two typical cases are considered,which reveals that,fold bifurcation may cause the the trajectory to jump between different equilibrium branches,while Hopf bifurcation may cause the trajectory to oscillate around the stable limit cycle.

Comparison of delay compensation methods for real-time hybrid simulation using frequency-domain evaluation index

The delay compensation method plays an essential role in maintaining the stability and achieving accurate real-time hybrid simulation results. The effectiveness of various compensation methods in different test scenarios, however, needs to be quantitatively evaluated. In this study, four compensation methods （i.e., the polynomial extrapolation, the linear acceleration extrapolation, the inverse compensation and the adaptive inverse compensation） are selected and compared experimentally using a frequency evaluation index （FEI） method. The effectiveness of the FEI method is first verified through comparison with the discrete transfer fimction approach for compensation methods assuming constant delay. Incomparable advantage is further demonstrated for the FEI method when applied to adaptive compensation methods, where the discrete transfer function approach is difficult to implement. Both numerical simulation and laboratory tests with predefined displacements are conducted using sinusoidal signals and random signals as inputs. Findings from numerical simulation and experimental results demonstrate that the FEI method is an efficient and effective approach to compare the performance of different compensation methods, especially for those requiring adaptation of compensation parameters.

Goal-oriented error estimation applied to direct solution of steady-state analysis with frequency-domain finite element method

Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It leads to the high quality locM error bounds in the problem of the direct-solution steady-state dynamic analysis with a frequency-domain finite element, which involves the enrichments with plural variable basis functions. The solution of the steady-state dynamic procedure calculates the harmonic response directly in terms of the physical degrees of freedom in the model, which uses the mass, damping, and stiffness matrices of the system. A three-dimensional finite element example is carried out to illustrate the computational procedures.

A Krylov Space-Based Finite Element Time Domain Method for Broadband Frequency Domain Solutions

A Krylov space based time domain method for wave propagation problems is introduced. The proposed method uses the Arnoldi algorithm to obtain broad-band frequency domain solutions. This method is especially advantageous in cases where slow convergence is observed when using traditional time domain methods. The efficiency of the method is examined in several test cases to show its fast convergence in such problems.

Acoustic viscoelastic modeling by frequency-domain boundary element method

Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element methods. Targeted at viscoelastic numerical modeling for multilayered media, the constant-Q acoustic wave equation is transformed into the corresponding wave integral representation with its Green＇s function accounting for viscoelastic coefficients. An efficient alternative for full-waveform solution to the integral equation is proposed in this article by extending conventional frequency-domain boundary element methods to viscoelastic media. The viscoelastic boundary element method enjoys a distinct characteristic of the explicit use of boundary continuity conditions of displacement and traction, leading to a semi-analytical solution with sufficient accuracy for simulating the viscoelastic effect across irregular interfaces. Numerical experiments to study the viscoelastic absorption of different Q values demonstrate the accuracy and applicability of the method.

Frequency-time Domain Shielding Effectiveness of Materials and Their Strong Electromagnetic Field Test

To describe the shielding ability of materials accurately and comprehensively,the frequency-domain and time-domain shielding effectiveness(SE) of material is investigated.The relevance between them was analyzed based on the minimum phase method,and the time-domain SE can be derived from frequency-domain SE.The SE of an energy selective surface(ESS) made of a novel material is investigated,and the relationship between SE and radiation field intensity are analyzed.The results show that not only material,but also the intensity of radiation electric field shows influence on SE in its frequency; for some materials,the dependence of SE on radiation electric field intensity needs to be considered.Therefore,it is necessary to research on the SE of shielding material in high-intensity electromagnetic environment.

Characteristic signal extracted from a continuous time signal on the aspect of frequency domain

Extracting characteristic signal from a continuous signal can effectively reduce the difficulty of analyzing the running states of a single-variable nonlinear system.Whether the extracted characteristic signal can accurately reflect the running states of the system is very important.In this paper, a method called automatic sampling method(ASM) for extracting characteristic signals is investigated.The complete definition is described, the effectiveness is proved theoretically, and the general formulas of the extracted characteristic signals are derived for the first time.Furthermore, typical Chua's circuit is used to accomplish a lot of experimental research on the aspect of frequency domain.The experimental results show that ASM is feasible and practical, and can automatically generate a characteristic signal with the change of the original signal.

Error Analysis in Frequency Domain for Linear Multipass Algorithms

Error analysis methods in frequency domain are developed in this paper for determining the characteristic root and transfer function errors when the linear multipass algorithms are used to solve linear differential equations. The relation between the local truncation error in time domain and the error in frequency domain is established, which is the basis for developing the error estimation methods. The error estimation methods for the digital simulation model constructed by using the Runge-Kutta algorithms and the linear multistep predictor-corrector algorithms are also given.

THE STUDY ON MEASURING TECHNIQUE OF PARTIAL DISCHARGE IN GAS INSULATED SWITCHGEAR USING ULTRA HIGH FREQUENCY METHOD WITH EXTERNAL SENSORS

Objective In order to find early latent faults and prevent catastrophic failures, diagnosis of insulation condition by measuring technique of partial discharge(PD) in gas insulated switchgear (GIS) is applied in this paper, which is one of the most basic ways for diagnosis of insulation condition. Methods Ultra high frequency(UHF) PD detection method by using internal sensors has been proved efficient, because it may avoid the disturbance of corona, but the sensor installation of this method will be limited by the structure and operation condition of GIS. There are some of electromagnetic (E-M) waves leak from the place of insulation spacer, therefore, the external sensors UHF measuring PD technique is applied, which isn't limited by the operation condition of GIS. Results This paper analyzes propagated electromagnetic (E-M) waves of partial discharge pulse excited by using the finite-difference time-domain (FDTD) method. The signal collected at the outer point is more complex than that of the inner point, and the signals' amplitude of outer is about half of the inner, because it propagates through spacer and insulation slot. Set up UHF PD measuring system. The typical PD in 252kV GIS bus bar was measured using PD detection UHF technique with external sensors. Finally, compare the results of UHF measuring technique using external sensors with the results of FDTD method simulation and the traditional IEC60270 method detection. Conclusion The results of experiment shows that the UHF technique can realize the diagnosis of insulation condition, the results of FDTD method simulation and the result UHF method detection can demonstrate each other, which gives references to further researches and application for UHF PD measuring technique.

Applying a Step Approach Method in Solving the Multi-Frequency Radiation From a Complex Obstacle

In this paper,a step approach method in the time domain is developed to calculate the radiated waves from an arbitrary obstacle pulsating with multiple frequencies.The computing scheme is based on the Boundary Integral Equation and derived in the time domain;thus,the time-harmonic Neumann boundary condition can be imposed.By the present method,the values of the initial conditions are set to zero,and the approach process is carried forward in a loop from the first time step to the last.At each time step,the radiated pressure on each element is updated.After several loops,the correct radiated pressures can be obtained.A sphere pulsating with a monopole frequency in an infinite acoustic domain is calculated first.This result is compared with the analytical solution,and both of them are in good agreement.Then,a complex-shaped radiator is taken as the studied case.The pulsating frequency of this case is multiple,and the waves propagate in half space.It is shown that the present method can treat multiple-frequency pulsation well,even when the radiator is a complex shape,and a robust convergence can be attained quickly.

Efficient solution of large-scale matrix of acoustic wave equations in 3D frequency domain

In 3D frequency domain seismic forward and inversion calculation,the huge amount of calculation and storage is one of the main factors that restrict the processing speed and calculation efficiency.The frequency domain finite-difference forward simulation algorithm based on the acoustic wave equation establishes a large bandwidth complex matrix according to the discretized acoustic wave equation,and then the frequency domain wave field value is obtained by solving the matrix equation.In this study,the predecessor's optimized five-point method is extended to a 3D seven-point finite-difference scheme,and then a perfectly matched layer absorbing boundary condition(PML)is added to establish the corresponding matrix equation.In order to solve the complex matrix,we transform it to the equivalent real number domain to expand the solvable range of the matrix,and establish two objective functions to transform the matrix solving problem into an optimization problem that can be solved using gradient methods,and then use conjugate gradient algorithm to solve the problem.Previous studies have shown that in the conjugate gradient algorithm,the product of the matrix and the vector is the main factor that affects the calculation efficiency.Therefore,this study proposes a method that transform bandwidth matrix and vector product problem into some equivalent vector and vector product algorithm,thereby reducing the amount of calculation and storage.

Hydroelasticity Analysis in Frequency Domain and Time Domain

Hydroelasticity has been introduced in ship seakeeping assessment for more than three decades, and it finally becomes an essential tool in marine industry for design of some types of ship. In the 35 years of evolution, hydroelasticity methods applied in industry of marine and offshore energy grown up from two dimensional to three dimensional and now has analysis models of linear model in frequency domain and nonlinear model in time domain. In this paper, we present the three dimensional hydroelasticity theory model in frequency domain and time domain, show the difference in the approach, and discuss their applications in wave-structure interaction.

基于改进TFDR法的核电站仪控电缆断裂缺陷检测

时频域反射(time-frequency domain reflectometry,TFDR)法具有成熟便捷、分辨率较高的特点,广泛应用于各类电缆的故障测距。为了有效判别和精确定位核电站仪控电缆绝缘屏蔽层断裂缺陷,文中通过介入热应力,提出一种改进TFDR法。对50 m多芯仪控电缆进行不同程度的断裂破损模拟,并使用传统TFDR法和改进TFDR法进行检测实验验证。检测结果显示,改进TFDR法对弱断裂缺陷的定位峰峰值为0.2,是传统TFDR法的2.5倍,且不同程度断裂缺陷下定位误差率均小于2.5%。可得出如下结论:相较于传统TFDR法,改进TFDR法使用热应力浮动方差曲线作为缺陷判别的依据,可显著提高对弱断裂缺陷的判别能力;改进TDFR法通过对原定位距离进行修正,进一步提高了对弱断裂破损的定位精准度,可实现对微弱缺陷的有效识别定位。

基于FDD法的模态参数连续自动识别及频率变异性分析

模态参数是分析桥梁运营状态变化的重要指标,可为桥梁状态评估提供数据基础。基于频域分解法(FDD)的模态参数连续自动识别方法,分析了模态参数与环境之间的关系。采用前、后向线性均值滤波方法对奇异值曲线进行滤波处理,剔除噪声干扰引起的虚假毛刺峰值;提出了Dvp指标,结合波峰波谷检测算法识别得到了真实模态参数对应的奇异值峰值;引入K-means聚类法实现了奇异值曲线真实峰值的自动选取。针对实际健康监测数据存储格式,设计了模态参数连续自动识别框架,并提出了融入模态参数的自动识别算法,实现了模态参数连续、自动识别。将所提出的方法运用于斜拉桥的实测数据中,通过连续自动识别得到一个月的模态参数,分析了环境对结构频率的影响程度。研究结果表明:所提出的基于FDD的模态参数自动识别方法能够实现模态参数的自动识别;所提出的融合自动识别算法的数据自动分析框架能够实现模态参数连续、自动识别,能解决桥梁健康监测数据的连续自动分析;桥梁结构频率受环境温度影响较大,随机环境因素所引起的结构频率随机性不可忽略。

Control of Virtual Synchronous Generator for Frequency Regulation Using a Coordinated Self-adaptive Method

Power inverter adopting virtual synchronous generator(VSG)control can provide inertia support for distributed generation systems.However,it cannot take into account the dynamic regulation characteristics of frequency.Thus,when the system encounters a sudden change in load or disturbance,the dynamic process of frequency regulation will be greatly influenced.In view of this issue,an improved VSG control strategy based on a coordinated self-adaptive(CSA)method is proposed.The time domain analysis method is used to study the influences of virtual inertia and damping parameter perturbation on the system steady and dynamic performances.Furthermore,in order to make the control strategy suitable for large load changes and suppress frequency variations beyond the limit,the secondary frequency modulation is introduced into the control loop.Through the coordinated adaptive control of virtual inertia,virtual damping and frequency modulation,the dynamic performance of vSG frequency regulation can be obviously improved.Simulation and experiment results have verified the effectiveness of the proposed CSA control strategy.

Finite difference time domain method forward simulation of complex geoelectricity ground penetrating radar model

The ground penetrating radar(GPR) forward simulation all aims at the singular and regular models, such as sandwich model, round cavity, square cavity, and so on, which are comparably simple. But as to the forward of curl interface underground or “v” figure complex model, it is difficult to realize. So it is important to forward the complex geoelectricity model. This paper takes two Maxwell’s vorticity equations as departure point, makes use of the principles of Yee’s space grid model theory and the basic principle finite difference time domain method, and deduces a GPR forward system of equation of two dimensional spaces. The Mur super absorbed boundary condition is adopted to solve the super strong reflection on the interceptive boundary when there is the forward simulation. And a self-made program is used to process forward simulation to two typical geoelectricity model.