Sparse Modal Decomposition Method Addressing Underdetermined Vortex-Induced Vibration Reconstruction Problem for Marine Risers

When investigating the vortex-induced vibration(VIV)of marine risers,extrapolating the dynamic response on the entire length based on limited sensor measurements is a crucial step in both laboratory experiments and fatigue monitoring of real risers.The problem is conventionally solved using the modal decomposition method,based on the principle that the response can be approximated by a weighted sum of limited vibration modes.However,the method is not valid when the problem is underdetermined,i.e.,the number of unknown mode weights is more than the number of known measurements.This study proposed a sparse modal decomposition method based on the compressed sensing theory and the Compressive Sampling Matching Pursuit(Co Sa MP)algorithm,exploiting the sparsity of VIV in the modal space.In the validation study based on high-order VIV experiment data,the proposed method successfully reconstructed the response using only seven acceleration measurements when the conventional methods failed.A primary advantage of the proposed method is that it offers a completely data-driven approach for the underdetermined VIV reconstruction problem,which is more favorable than existing model-dependent solutions for many practical applications such as riser structural health monitoring.

A rened analytical model for reconstruction problems in diuse reectance spectroscopy

A rened analytical model of spatially resolved diffuse reectance with small source-detector separations(SDSs)for the in vivo skin studies is proposed.Compared to the conventional model developed by Farrell et al.,it accounts for the limited acceptance angle of the detectorber.The rened model is validated in the wide range of optical parameters by Monte Carlo simulations of skin diffuse reectance at SDSs of units of mm.Cases of uniform dermis and two-layered epidermis-dermis structures are studied.Higher accuracy of the rened model compared to the conventional one is demonstrated in the separate,constraint-free reconstruction of absorption and reduced scattering spectra of uniform dermis from the Monte Carlo simulated data.In the case of epidermis-dermis geometry,the recovered values of reduced scattering in dermis are overestimated and the recovered values of absorption are underestimated for both analytical models.Presumably,in the presence of a thin mismatched topical layer,only the effective attenuation coe±cient of the bottom layer can be accurately recovered using a diffusion theorybased analytical model while separate reconstruction of absorption and reduced scattering fails due to the inapplicability of the method of images.These-ndings require implementation of more sophisticated models of light transfer in inhomogeneous media in the recovery algorithms.

Extension of sound field reconstruction based on element radiation superposition method in a sparsity framework

Nearfield acoustic holography(NAH)is a powerful tool for realizing source identification and sound field reconstruction.The wave superposition(WS)-based NAH is appropriate for the spatially extended sources and does not require the complex numerical integrals.Equivalent source method(ESM),as a classical WS approach,is widely used due to its simplicity and efficiency.In the ESM,a virtual source surface is introduced,on which the virtual point sources are taken as the assumed sources,and an optimal retreat distance needs to be considered.A newly proposed WS-based approach,the element radiation superposition method(ERSM),uses piston surface source as the assumed source with no need to choose a virtual source surface.To satisfy the application conditions of piston pressure formula,the sizes of pistons are assumed to be as small as possible,which results in a large number of pistons and sampling points.In this paper,transfer matrix modes(TMMs),which are composed of the singular vectors of the vibro-acoustic transfer matrix,are used as the sparse basis of piston normal velocities.Then,the compressive ERSM based on TMMs is proposed.Compared with the conventional ERSM,the proposed method maintains a good pressure reconstruction when the number of sampling points and pistons are both reduced.Besides,the proposed method is compared with the compressive ESM in a mathematical sense.Both simulations and experiments for a rectangular plate demonstrate the advantage of the proposed method over the existing methods.

Image reconstruction based on total-variation minimization and alternating direction method in linear scan computed tomography

Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation （TV） minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method （ADM） to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.

Variational regularization method of solving the Cauchy problem for Laplace's equation: Innovation of the Grad–Shafranov(GS) reconstruction

The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace＇s equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace＇s equation. Then, the ＇L-Curve＇ principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3.

Unhappy triad in limb reconstruction:Management by Ilizarov method

AIM To evaluate the results of the Ilizarov method in management of cases with bone loss, soft tissue loss and infection.METHODS Twenty eight patients with severe leg trauma complicated by bone loss, soft tissue loss and infection were managed by distraction osteogenesis in our institution. After radical debridement of all the infected and dead tissues the Ilizarov frame was applied, corticotomy was done and bone transport started. The wounds were left open to drain. Partial limb shortening was done in seven cases to reduce the size of both the skeletal and soft tissue defects. The average follow up period was 39 mo(range 27-56 mo). RESULTS The infection was eradicated in all cases. All the soft tissue defects healed during bone transport and plastic surgery was only required in 2 cases. Skeletal defects were treated in all cases. All patients required another surgery at the docking site to fashion the soft tissue and to cover the bone ends. The external fixation time ranged from 9 to 17 mo with an average of 13 mo. The complications included pin tract infection in 16 cases, wire breakage in 2 cases, unstable scar in 4 cases and chronic edema in 3 cases. According to the association for study and application of methods of Ilizarov score the bone results were excellent in 10, good in 16 and fair in 2 cases while the functional results were excellent in 8, good in 17 and fair in 3 cases. CONCLUSION Distraction osteogenesis is a good method that can treat the three problems of this triad simultaneously.

An efficient source wavefield reconstruction scheme using single boundary layer values for the spectral element method

In the adjoint-state method, the forward-propagated source wavefield and the backward-propagated receiver wavefield must be available simultaneously either for seismic imaging in migration or for gradient calculation in inversion. A feasible way to avoid the excessive storage demand is to reconstruct the source wavefield backward in time by storing the entire history of the wavefield in perfectly matched layers. In this paper, we make full use of the elementwise global property of the Laplace operator of the spectral element method (SEM) and propose an efficient source wavefield reconstruction method at the cost of storing the wavefield history only at single boundary layer nodes. Numerical experiments indicate that the accuracy of the proposed method is identical to that of the conventional method and is independent of the order of the Lagrange polynomials, the element type, and the temporal discretization method. In contrast, the memory-saving ratios of the conventional method versus our method is at least N when using either quadrilateral or hexahedron elements, respectively, where N is the order of the Lagrange polynomials used in the SEM. A higher memorysaving ratio is achieved with triangular elements versus quadrilaterals. The new method is applied to reverse time migration by considering the Marmousi model as a benchmark. Numerical results demonstrate that the method is able to provide the same result as the conventional method but with about 1/25 times lower storage demand. With the proposed wavefield reconstruction method, the storage demand is dramatically reduced;therefore, in-core memory storage is feasible even for large-scale three-dimensional adjoint inversion problems.

Reconstruction of electrical capacitance tomography images based on fast linearized alternating direction method of multipliers for two-phase flow system

Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction,a new ECT image reconstruction method based on fast linearized alternating direction method of multipliers(FLADMM)is proposed in this paper.On the basis of theoretical analysis of compressed sensing(CS),the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section.A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge.A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function.Simulation data and experimental results indicate that compared with other methods,the quality and speed of reconstructed images are markedly improved.Also,the dynamic experimental results indicate that the proposed algorithm can ful fill the real-time requirement of ECT systems in the application.

Nonlinear dynamic response and stability analysis of the stapes reconstruction in human middle ear

Stapes fracture causes hearing loss and instability in the middle ear hearing system(MEHS). The material used in the stapes reconstruction restores stapes, but the effects of the nonlinear material parameters on the stability of the MEHS are still unknown. To address this challenge, the nonlinear dynamic response and stability of the stapes reconstruction are investigated using a multi-degree-of-freedom mechanical model. The material parameters of the implant are tentatively determined by analyzing the natural frequencies of the undamped system. The dynamical properties of the MEHS are characterized under different external excitations. The approximate solution of the MEHS near the resonant frequency is derived through the multiple-time-scale method(MTSM). The results show that the nonlinear stiffness of the material has little influence on the MEHS in the healthy state, but it causes resonant phenomena between the ossicle and the implant in the pathological state.

Critical Approach to Methods of Glacier Reconstruction in High Asia and Discussion of the Probability of a Qinghai-Xizang (Tibetan) Inland Ice

This overview discusses old and new results as to the controversy on the past glacier extension in High Asia, which has been debated for 35 years now. This paper makes an attempt to come closer to a solution. H.v. Wissmann's interpretation (1959) of a small-scale glaciation contrasts with M. Kuhle's reconstruction (1974) of a large-scale glaciation with a 2.4 million km2 extended Qinghai-Xizang (Tibetan) inland glaciation and a Himalaya-Karakorum icestream network. Both opinions find support but also contradiction in the International and Chinese literature (Academia Sinica). The solution of this question is of supraregional importance because of the subtropical position of the concerned areas. In case of large albedo-intensive ice surfaces, a global cooling would be the energetical consequence and, furthermore, a breakdown of the summer monsoon. The current and interglacial heat-low above the very effective heating panel of the Qinghai-Xizang (Tibetan) Plateau exceeding 4000 m, which gives rise to this monsoon circulation, would be replaced by the cold-high of an inland ice. In addition, the plate-tectonically created Pleistocene history of the uplift of High Asia — should the occasion arise up to beyond the snowline (ELA) —would attain a paleoclimatically great, perhaps global importance. In case of a heavy superimposed ice load, the question would come up as to the glacio-isostatic interruption of this primary uplift. The production of the loesses sedimentated in NE-China and their very probable glacial genesis as well as an eustatic lowering of the sea-level by 5 to 7 m in the maximum case of glaciation are immediately tied up with the question of glaciation we want to discuss. Not the least, the problems of biotopes of the sanctuary-centres of flora and fauna, i.e., interglacial re-settlement, are also dependent on it. On the basis of this Quaternary- geomorphological-glaciological connection, future contributions are requested on the past glaciation, the current and glacial permafrost table and periglacial development, the history of uplift, and the development of Ice Age lakes and loess, but also on the development of vegetation and fauna in High Asia.

A new two-step variational model for multiplicative noise removal with applications to texture images

Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motivated by the TV-Stokes model,we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this paper.In the first step,we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field smoothing.Once the isophote directions are constructed,an image is restored to fit the constructed directions in the second step.The existence and uniqueness of the solution to the variational problems are proved.In these two steps,we use the gradient descent method and construct finite difference schemes to solve the problems.Especially,the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the calculation.Experimental results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well.

Preliminary analysis of reactivity reconstruction capability based on inverse kinetics method under different initial reactivity states

Online reactivity monitoring plays an important role in operation and safety analyses of fission reactor systems. The inverse kinetics method, which is based on a point kinetics model, is the most widely used method for reactivity reconstruction of critical water reactors. However, this method is seldom applied to the reactivity reconstruction of subcritical reactors. In this study, an inverse kinetics method was employed for the reactivity reconstruction of a lead-based reactor under different initial reactivity states(ρ_0= 0,-2786,-5486,-8367, and-12,371 pcm). The results showed that the deviation in the reactivity of the lead-based subcritical reactor was greater when ρ_0 became smaller. The reactivity reconstructed using the inverse kinetics method was globally underestimated. At a given reactivity perturbation, the relative and absolute errors increased with the decrease in the initial reactivity. At a given initial reactivity, with the increase in the reactivity perturbation, the absolute error increased, whereas the relative error remained the same.This deviation is due to the variation in the external neutron source, spatial-spectral effects, and sub-diffusive effects, which require further study.

New Method of Reconstruction from Nonparallel Stereo and Application to Surgical Navigator

A new method to reconstruct 3D scene points from nonparallel stereo is proposed. From a pair of conjugate images in an arbitrarily configured stereo system that has been calibrated, coordinates of 3D scene points can be computed directly using the method, bypassing the process of rectifying images or iterative solution involved in existing methods. Experiment results from both simulated data and real images validate the method. Practical application to surgical navigator shows that the method has advantages to improve efficiency and accuracy of 3D reconstruction from nonparallel stereo system in comparison with the conventional method that employs algorithm for standard parallel axes stereo geometry.

SPECTRAL/HP ELEMENT METHOD WITH HIERARCHICAL RECONSTRUCTION FOR SOLVING NONLINEAR HYPERBOLIC CONSERVATION LAWS

The hierarchical reconstruction （HR） [Liu, Shu, Tadmor and Zhang, SINUM ＇07] has been successfully applied to prevent oscillations in solutions computed by finite volume, Runge-Kutta discontinuous Galerkin, spectral volume schemes for solving hyperbolic conservation laws. In this paper, we demonstrate that HR can also be combined with spectral/hp element method for solving hyperbolic conservation laws. An orthogonal spectral basis written in terms of Jacobi polynomials is applied. High computational efficiency is obtained due to such matrix-free algorithm. The formulation is conservative, and essential nomoscillation is enforced by the HR limiter. We show that HR preserves the order of accuracy of the spectral/hp element method for smooth solution problems and generate essentially non-oscillatory solutions profiles for capturing discontinuous solutions without local characteristic decomposition. In addition, we introduce a postprocessing technique to improve HR for limiting high degree numerical solutions.

Computing methods for icosahedral and symmetry-mismatch reconstruction of viruses by cryo-electron microscopy

Three-dimensional(3 D)reconstruction of icosahedral viruses has played a crucial role in the development of cryoelectron microscopy single-particle reconstruction,with many cryo-electron microscopy techniques first established for structural studies of icosahedral viruses,owing to their high symmetry and large mass.This review summarizes the computational methods for icosahedral and symmetry-mismatch reconstruction of viruses,as well as the likely challenges and bottlenecks in virus reconstruction,such as symmetry mismatch reconstruction,contrast transformation function(CTF)correction,and particle distortion.

TRACKING AND RECONSTRUCTION METHODS FOR MOVING-INTERFACES

A simple,efficient and accurate high resolution method to tracking moving-interfaces-the characteristic integral-averaging finite volume method on unstructured meshes is proposed. And some numerical tests and evaluation of six main efficient methods for interface reconstruction are made. Through strict numerical simulation,their characters,advantages and shortcomings are compared,analyzed and commended in particular.

Reconstruction method of differentiated backprojection-projection onto convex sets in the interior problem and design of bone-nail model

This work focuses on the application of the reconstruction method of differentiated backprojection （DBP）-projection onto convex sets （POCS） in the interior problem.First,we present the definition of the interior problem and real truncated Hilbert transform,and then outline the implementation steps of DBP-POCS.After that,we introduce the middle-part known condition for region of interest （ROI） accurate reconstruction and the unique condition of the interior problem,and verify the uniqueness and stability of the interior problem accurate reconstruction through numerical experiments,and then compare the results for the interior problem in reconstruction images using filtered backprojection （FBP）.In addition,the authors also design the application models of ROI reconstruction and make an initial attempt to the application of DBP-POCS method in the interior problem.

Temperature Field Reconstruction in High-Temperature Gas by Using the Colored Background Oriented Schlieren Method

A 3D temperature field reconstruction method using the colored background oriented schlieren(CBOS)method is proposed to address image blurring due to the different refractive index of the multi-wavelength light and significant errors produced when the traditional background oriented schlieren(BOS)method is applied to high-temperature gas.First,the traditional method is employed to reconstruct the non-uniform 3D temperature field.Second,the CBOS method is applied to correct the distortion.Then,by analyzing the correlation coefficient among different color points of the colored background pattern,the non-uniform temperature field is reconstructed much more accurately.Finally,the experimental results are verified by applying the Runge-Kutta ray-tracing method and the thermocouple contact measurement method.The maximum average temperature error of the CBOS-reconstructed temperature field is 12.92°C,compared with the thermocouples.Therefore,an accurate three-dimensional reconstruction of the temperature field can be achieved by the proposed method effectively.

RECONSTRUCTION OF PART OF AN ACTUAL BLAST-WAVE FLOW FIELD TO AGREE WITH EXPERIMENTAL DATA BY USING NUMERICAL METHOD WITH HIGH IDENTIFICATION

In this paper, on the basis of experimental data of two kinds of chemical explosions, the piston-pushing model of spherical blast-waves and the second-order Godunov-type scheme of finite difference methods with high identification to discontinuity are used to the numerical reconstruction of part of an actual hemispherical blast-wave flow field by properly adjusting the moving bounary conditions of a piston. This method is simple and reliable. It is suitable to the evaluation of effects of the blast-wave flow field away from the explosion center.

FITTING CORRECTION METHOD OF RING ARTIFACTS FOR RECONSTRUCTING CONE-BEAM CT IMAGES

In high-resolution cone-beam computed tomography （CBCT） using the flat-panel detector, imperfect or defect detector elements cause ring artifacts due to the none-uniformity of their X-ray response. They often disturb the image quality. A dedicated fitting correction method for high-resolution micro-CT is presented. The method converts each elementary X-ray response curve to an average one, and eliminates response inconsistency among pixels. Other factors of the method are discussed, such as the correction factor variability by different sampling frames and nonlinear factors over the whole spectrum. Results show that the noise and artifacts are both reduced in reconstructed images