Virtual Source Technique Research Articles

Virtual source total focusing method for crack detection in complex curved structure

Accurate non-destructive testing and evaluation of cracks is important for the quality assurance and life-cycle management of key components in aerospace and energy industries. This paper presents a novel imaging method for cracks detection in complex curved structure , combining virtual source technique, multi-mode total focusing method and phase coherence imaging method. The virtual source on the sample surface is employed as the emitter and receiver for the ultrasonic array imaging. In this way, the calculation complexity of imaging algorithm due to beam path search can be reduced, and the detection sensitivity in the region of interest can be improved. In addition, the phase coherence factor is used to suppress the background noise and imaging artifacts, which significantly improves the quality of ultrasonic array imaging. A complex curved sample with variable thickness and non-developable surface was used to examine the effectiveness of the virtual source total focusing method. The signal-to-noise ratio of the crack defect is increased by more than 25 dB using the novel method compared with that of the conventional total focusing method, and the quantitative evaluation error of defect is less than 2.67%.

Improved inherent strain extraction algorithm based analytical surface modeling for Ti-6Al-4V and SS316L selective laser melting part

Selective laser melting (SLM) is one of the most popular metal additive manufacturing (AM) techniques relied on powder bed and has been widely used in numerous fields. Printing surface modeling is a critical step for product development and quality control of SLM parts as the surface profile has a great impact on the structure and functional performance of printed parts. However, it is still a challenge to predict the printing surface geometry of the SLM part accurately and quickly due to the complex physical processes and thermomechanical behaviors in SLM. To address this barrier, a comprehensive bottom-up modeling approach based on an improved inherent strain method (ISM) is proposed to estimate the surface fluctuation between designed and printed parts and further predict the printing surfaces of SLM parts. The improved inherent strain is extracted from multi-physics analytical calculation considering the thermal influences of in-plane scanning tracks, interlayer re-melting and interlayer strain accumulation. Specifically, temperature filed is obtained from the quasi-static heat analytical model integrating residual temperature involving the heat contribution of in-plane scanning tracks via virtual heat source technique. The interlayer strain accumulation and interlayer re-melting effects are embedded into the inherent strain terms through the layer-lever fluctuation superposition and re-melted depth parameter respectively. Strain compositions are solved through thermo-elastic Green function models and modified elastic-plastic McDowell analytical models, where temperature-dependent material properties are employed. The proposed method has been validated by experimental observations from the literature via two SLM parts using two distinct materials (Ti-6Al-4 V and SS316L).

Analysis of Spontaneous and Implicit Internal Self-Excitation in Aircraft Variable Frequency AC Power System Based on Dual-Stator Winding Induction Generator

The dual-stator winding induction generator (DWIG) is an alternative main generator in a variable frequency ac power system. So far, the existing studies have not covered the issue of DWIGs excitation controllability, which is a matter of importance for airworthiness. In this article, we develop an impedance-based modeling and analysis technique to investigate DWIGs excitation controllability. Two related topics are presented: the spontaneous self-excitation analysis in uncontrolled system and the implicit internal self-excitation pattern analysis in actively controlled system. In the topic about spontaneous self-excitation, a virtual impulse source technique is developed to derive the impedance-based method properly in the analysis for uncontrolled DWIG. In the second topic, the analysis performed in the presence of a closed-loop controller figures out the same underlying mechanism in both the plant's open-loop stability and the spontaneous self-excitation. The experimental results verify the proposed analysis and techniques that benefit the comprehensive understanding and practical application of DWIG-based power system.

Virtual source for the fractional-order Bessel–Gauss beams

First, the nonparaxial integral expression of fractional-order Bessel–Gauss (FBG) beams during propagation is rigorously derived by using the virtual source technique and the principle of independent transmission and superposition of light, together with Weber integral formula and Fourier–Bessel transform pair. Then, the analytic expression of the important axial optical field amplitude of FBG beams is obtained. Finally, the on-axis intensity and phase of FBG beams are calculated on the basis of the analytic expression. Calculated results quantitatively revealed some important intensity information regarding the near-field propagation characteristic of FBG beams.

Odd version Mathieu-Gaussian beam based on Green function

Like the theoretical pattern of non-diffracting Bessel beams, ideal non-diffracting Mathieu beams also carry infinite energy, but cannot be generated as a physically realizable entity. Mathieu-Gaussian beams can be experimentally generated by modulating ideal Mathieu beams with a Gaussian function, and thus they are a kind of pseudo-non-diffracting beams with finite energy and finite transverse extent. The research of Mathieu-Gaussian beam propagating characteristics in free space is of great significance. In order to analytically study the propagation of Mathieu-Gaussian beams, the Mathieu function is expanded into the superposition of a series of Bessel functions in polar coordinates based on the superposition principle of light waves. It means that the Mathieu-Gaussian beam can be converted into accumulation of the infinite terms of the Bessel beams with different orders. According to the properties of the Bessel function, the free-space propagation properties of Mathieu-Gaussian beams can be studied in the circular cylindrical coordinates. Thus, a group of virtual optical sources are introduced to generate the odd Mathieu-Gaussian beams of the first kind, i.e., (2n+2)th-order, which is a family of Mathieu-Gaussian beams. Using the virtual source technique and the Green function, we derive the rigorous integral formula for the odd Mathieu-Gaussian beams of the first kind. Taking for example the first three orders with non-paraxial corrections, the analytical solution of the on-axis field of odd Mathieu-Gaussian beams of the first kind is further obtained from the integral formula. The axial intensity distribution of the odd Mathieu-Gaussian beams of the first kind is numerically calculated by the integral formula. The simulation results show that the calculation results obtained with the paraxial theory and the rigorous integral expressions of non-paraxial Mathieu-Gaussian beams are obviously different when the propagation distance of the odd Mathieu-Gaussian beams of the first kind is small. The calculation results of the two methods are coming closer and closer with the increasing propagation distance. The results indicate that the correct results can be obtained with the paraxial theory when we study the propagation of Mathieu-Gaussian beams in the far-field, but the non-paraxial theory must be used to obtain correct results when we study the propagation of Mathieu-Gaussian beams in the near-field. Owing to the complexity of the non-paraxial theory, it is difficult to obtain the exact analytic solutions of Mathieu-Gaussian beams in the near-field with the classical diffraction theory. Based on the superposition principle of light waves, by introducing the virtual source technique and the Green function, the complex Mathieu-Gaussian function can be expanded into the superposition of a series of simple Bessel functions, and the axial intensity distributions of Mathieu-Gaussian beams in the far-field and the near-field can be studied well. It will also provide a feasible method to study other complex beams propagating in free space.

Dynamic Grid Power Routing Using Controllable Network Transformers (CNTs) With Decoupled Closed-Loop Controller

Increases in system loads and in levels of penetration of renewable energy, together with limited investment in transmission infrastructure, are fostering the need for a smarter and more dynamically controllable grid. Flexible ac transmission systems devices can be used to dynamically control the grid and more efficiently route power and thus mitigate these stresses, but such devices are either too complicated and expensive for implementation or incapable of independently controlling active and reactive powers. A controllable network transformer (CNT) has a fractionally rated direct ac/ac converter and was introduced as a simpler and more cost-effective solution to realize dynamic power control between two areas. The CNT utilizes the dual virtual quadrature source (DVQS) technique to change both the line voltage amplitude and phase angle, thus enabling a dynamic power control; however, the control variables defined in this technique have a cross-coupling effect between active and reactive powers. In this paper, the CNT operating ranges with and without considering line resistance are analyzed; then, a decoupled closed-loop controller is designed to achieve independent active and reactive power control based on a reference power control command. To address the possibility of power overshoot in a CNT with DVQS, a hybrid open-loop/closed-loop proportional–integral controller is also proposed. Simulations and experimental results are given to verify the controller design.

Numerically exact three-dimensional propagation

Solving propagation in a three-dimensional environment is one of the most challenging problems in computational physics. However, for cases where the environment possesses some kind of symmetry be it rotational or translational, the propagation problem can be simplified considerably. It can be shown that in problems where the environment is translationally invariant, the 3D wave equation can be Fourier transformed along the direction of translational symmetry to reduce it to a 2D equation for each spectral component. The 3D solution can be obtained by solving the 2D wave equation for each spectral component and performing the inverse Fourier transform. In this paper, we use the above technique to compute propagation in an ideal and a penetrable wedge. For the ideal wedge, the pressure-release boundary condition is applied to both boundaries and for the penetrable wedge, the pressure-release boundary condition is applied to the horizontal surface and the continuity of pressure and normal velocity is imposed on the sloped interface. To obtain a numerically exact solution, we use the virtual source technique to solve the 2D problem for each spectral component.

Combined surface and borehole seismic imaging in a hard rock terrain: A field test of seismic interferometry

Seismic images are inherently directionally biased by the source-receiver geometry. This directional bias is particularly problematic for seismic imaging in hard rock terrains where structural dips may have any orientation with respect to the surface. We tested a technique for partially mitigating directional bias by combining surface and borehole seismic data and evaluated the results of a first field test of the technique. In this technique, surface data acquired using standard 2D acquisition procedures were combined with borehole data derived from a walk-away vertical seismic profile (VSP). The VSP data were transformed into the borehole datum using seismic interferometry. The interferometry created virtual shot records comprising sources and receivers in the borehole. The virtual shot records were then processed, using standard common midpoint techniques, resulting in an image from the borehole datum. The combination of the surface and borehole data increased the range of illumination angles resulting in seismic images that included reflections from structures with a wider range of dips than is available to surface profiling alone. The field test demonstrated that the surface and borehole data provide complementary information, which is more than either data set alone can provide. The test also verified the robustness of the virtual source technique even when the original VSP data are highly contaminated by high-amplitude tube waves. These results demonstrated that the combined imaging approach has significant potential for application in the polydeformed hard rock domains often encountered in minerals exploration.

A high-fidelity model for mitigating underwater pile driving noise in a shallow ocean waveguide

Driving large piles into the seafloor, as is done when constructing off-shore wind farms, produces high level underwater noise that can have an adverse effect on local marine life. This talk reviews an investigation of methods to mitigate this pile driving noise. A numerical model was used to simulate the structural vibrations in the pile and its coupling to the acoustic field in surrounding air, water and sediment. The simulated acoustic field in the immediate vicinity of the pile was then coupled into an ocean waveguide propagation model using a virtual-source technique to match the boundary conditions. These numerical models were used to assess the relative contribution of the air-borne, water-borne, and sediment-borne acoustic radiation to the noise level in the water-column at ranges up to several hundred meters from the pile. Various noise mitigation methods were simulated and compared. It was determined that a dewatered cofferdam, which places a layer of air between the vibrating pile and the seawater, has the potential to reduce the far-field noise level by approximately 20 dB. A practical method for creating a dewatered cofferdam during construction is the subject of ongoing work.

The use of the virtual source technique in computing scattering from periodic ocean surfaces

In this paper the virtual source technique is used to compute scattering of a plane wave from a periodic ocean surface. The virtual source technique is a method of imposing boundary conditions using virtual sources, with initially unknown complex amplitudes. These amplitudes are then determined by applying the boundary conditions. The fields due to these virtual sources are given by the environment Green's function. In principle, satisfying boundary conditions on an infinite surface requires an infinite number of sources. In this paper, the periodic nature of the surface is employed to populate a single period of the surface with virtual sources and m surface periods are added to obtain scattering from the entire surface. The use of an accelerated sum formula makes it possible to obtain a convergent sum with relatively small number of terms (∼40). The accuracy of the technique is verified by comparing its results with those obtained using the integral equation technique.

Investigations of marine mammal exposure to sound scattered from the sea surface.

Scattering of sound from the rough sea surface results in variations in sound intensity. If the surface height variations are smooth, as they are during a swell, the surface can act as a concave mirror and amplify the sound intensity at its focal region. We have shown both analytically and using numerical modeling that the intensity at the focal region is a function of frequency: for a singly curved surface, the intensity at the focus varies linearly with frequency and for a doubly curved surface, this dependence is quadratic. Scattering of sound waves from a rough surface can also result in a reduction in intensity through dispersion. In this paper, we investigate the possible effects of exposure to sound scattered from the sea surface on marine mammals by computing the scintillation index as a function of range and depth for a variety of ocean environments, including those with surface ducts. We compute the scintillation index using a Monte Carlo technique, where for each surface height realization, we compute the scattered field in the waveguide exactly using the virtual source technique. We compute the Green’s functions needed in the virtual source technique using the Scooter propagation model.

Exact and approximate techniques for scattering from targets embedded in a layered medium.

To be able to accurately compute scattering from a target embedded in a layered medium (waveguide), the scattering and propagation problems must be solved as a single boundary value problem. This is accomplished by solving the wave equation in an environment that contains both the target and the waveguide and satisfying boundary conditions on the surface of the target and the boundaries of the waveguide. One way that this can be accomplished is by the use of the virtual source technique, which replaces the target with a collection of sources whose amplitudes are determined from the boundary conditions on the surface of the target. This method converts the problem of scattering from a target in a waveguide to a multisource propagation problem. In this paper, the virtual source technique is used to compute scattering from a target in a waveguide and various ways to speed up computation are examined. These include the use of various propagation models to propagate the field produced by the virtual sources to the receiver. Various solutions are compared and the advantages and disadvantages of each model are discussed.

Transient Response of an Orthotropic Cylindrical Shell to an Underwater Explosive Loading

The transient response of an elastic orthotropic cylindrical shell immersed in an acoustic fluid and subjected to a shock loading is investigated in this article. The Sanders thin shell theory is employed in the analysis and the governing equations of the motion for orthotropic cylindrical shell are derived by using Hamilton's principle. The type of loading is the exponentially decaying plane acoustic wave induced by underwater explosion. The reflected-afterflow virtual-source (RAVS) technique is used to simulate the fluid-structure interaction. The numerical analyses are performed to look into the influences of the shell radius and thickness upon the non-dimensional radial velocity, mid-surface strain, 0th mode radial displacement and 1st mode radial velocity of the shells.

Scattering from rotationally‐symmetric objects using only free space Green's functions

To compute scattering from an object, one has to solve the wave equation and impose the appropriate boundary conditions on the surface of the object. For objects for which the wave equation can be separated, like cylinders, spheres and spheroids, this problem can be solved analytically. For more general objects, methods like the finite element or boundary element techniques can be employed. The use of free space Green's functions offers another method for computation of scattering from a general‐shaped object. This method, which is known as the method of field superposition or the virtual source technique, can be used to impose the appropriate boundary conditions on the surface of the object by using free space Green's function with complex amplitudes. These amplitudes are determined from a matrix equation that results when boundary conditions are imposed. In this paper we apply this technique to compute scattering from rotationally symmetric objects. These objects can be homogeneous solids or shells, fil...

Propagation in an elastic wedge using the virtual source technique

In this paper the virtual source technique is used to model propagation of waves in a range-dependent ocean overlying an elastic bottom with arbitrarily-shaped ocean-bottom interface. The virtual source technique provides the means to impose boundary conditions on arbitrarily-shaped boundaries by replacing them by a collection of sources whose amplitudes are determined from the boundary conditions. The method is applied to propagation in an elastic Pekeris waveguide, an acoustic wedge and an elastic wedge. In the case of propagation in an elastic Pekeris waveguide, the results agree very well with those obtained from the wavenumber integral technique, as they do with the solution of the parabolic equation (PE) technique in the case of propagation in an acoustic wedge. The results for propagation in an elastic wedge qualitatively agree with those obtained from an elastic PE solution.

Propagation in an elastic wedge using the virtual source technique

The virtual source technique, which is based on the boundary integral method, provides the means to impose boundary conditions on arbitrarily shaped boundaries by replacing them by a collection of sources whose amplitudes are determined from the boundary conditions. In this paper the virtual source technique is used to model propagation of waves in a range-dependent ocean overlying an elastic bottom with arbitrarily shaped ocean-bottom interface. The method is applied to propagation in an elastic Pekeris waveguide, an acoustic wedge, and an elastic wedge. In the case of propagation in an elastic Pekeris waveguide, the results agree very well with those obtained from the wavenumber integral technique, as they do with the solution of the parabolic equation (PE) technique in the case of propagation in an acoustic wedge. The results for propagation in an elastic wedge qualitatively agree with those obtained from an elastic PE solution.

Modeling of glints due to surface curvature using the virtual source technique

The virtual source technique, also known as the method of superposition or the auxiliary source technique, has been widely used to model scattering from targets. In this technique the target is replaced by a collection of sources of unknown complex amplitudes. The source amplitudes are calculated by applying the appropriate boundary conditions at the surface of the target. In this paper, the virtual source technique is used to compute scattering from rough surfaces. For sound scattering from the rough ocean surface, this is done by solving the wave equation for a half‐space ocean overlaying a bottom and forcing the solution to satisfy the pressure‐release boundary condition at a desired surface. The method is applied to study the effect of focusing of energy (glints) due to reflection of sound from a gently sloping, but concave ocean surface for various ocean conditions. Additionally, the method is applied to the study of scattering of waves from an infinite periodic surface.

A Scalable Priority-Based Multi-Path Routing Protocol for Wireless Sensor Networks

In this paper, a scalable priority-based multi-path routing protocol (PRIMP) is proposed for wireless sensor networks to offer extended network lifetime and robust network fault tolerance, under the context of stringent energy constraint and vulnerability of sensors to dynamic environmental conditions. A novel interest dissemination strategy which invokes an on-demand virtual source technique is designed in PRIMP to minimize communication overheads and energy wastage. In routing, data traffic is distributed over multiple braided data paths simultaneously by a priority-based probabilistic approach at each hop to achieve the robustness against the unreliable transmission due to frequent node failures. Extensive simulations validate that PRIMP exhibits significantly better performance in energy conservation, load-balancing and data delivery than comparable schemes, while at the same time PRIMP achieves a nice scalability feature in terms of energy dissipation with various network sizes and network densities. Last but not least, PRIMP addresses the slow startup problem that is prevalent in data-centric routing schemes.

Development and Evaluation of the Offshore and Coastal Dispersion Model

The Offshore and Coastal Dispersion (OCD) model has been developed for the Minerals Management Service (MMS) to determine the impact of offshore and onshore emissions from point sources on the air quality of coastal regions. Constructed on the framework of the EPA guideline model MPTER, the OCD model incorporates overwater plume transport and dispersion as well as changes that occur as the plume crosses the shoreline. Hourly meteorological data are needed from both offshore and onshore locations, including wind direction and speed, mixing height, overwater air temperature and relative humidity, and the sea surface temperature. Observed turbulence intensities are preferred by the model but are not mandatory. Building downwash and plume rise are incorporated into the OCD model similar to their use in the Buoyant Line and Point Source (BLP) model. Partial plume penetration into elevated inversions is treated using Briggs’ model. Dispersion coefficients are proportional to turbulence intensities. A virtual source technique is used to change the rate of plume growth as the overwater plume intercepts the overland internal boundry layer. The continuous shoreline fumigation case is treated using an approach suggested by Deardorff and Willis. Calculation of plume reflection from elevated terrain follows the Rough Terrain Dispersion Model (RTDM). The OCD model and the modified EPA model used as an interim model for overwater applications by the MMS were tested with measurements from three offshore tracer experiments. The OCD model was shown to be a clear improvement over the EPA model and was officially approved by the MMS in March 1985.