Robust Boundary Research Articles

On the thermodynamic boundary conditions of a solidifying mushy layer with outflow

AbstractThe free-boundary problem between a liquid region and a mushy layer (a reactive porous medium) must respect both thermodynamic and fluid dynamical considerations. We develop a steady two-dimensional forced-flow configuration to investigate the thermodynamic condition of marginal equilibrium that applies to a solidifying mushy layer with outflow and requires that streamlines are tangent to isotherms at the interface. We show that a ‘two-domain’ approach in which the mushy layer and liquid region are distinct domains is consistent with marginal equilibrium by extending the Stokes equations in a narrow transition region within the mushy layer. We show that the tangential fluid velocity changes rapidly in the transition region to satisfy marginal equilibrium. In convecting mushy layers with liquid channels, a buoyancy gradient can drive this tangential flow. We use asymptotic analysis in the limit of small Darcy number to derive a regime diagram for the existence of steady solutions. Thus we show that marginal equilibrium is a robust boundary condition and can be used without precise knowledge of the fluid flow near the interface.

Optimization analysis of Duffing oscillator with fractional derivatives

The improved version of the constrained optimization harmonic balance method is presented to solve the Duffing oscillator with two kinds of fractional order derivative terms. The analytical gradients of the objective function and nonlinear quality constraints with respect to optimization variables are formulated and the sensitivity information of the Fourier coefficients can also obtained. A new stability analysis method based on the analytical formulation of the nonlinear equality constraints is presented for the nonlinear system with fractional order derivatives. Furthermore, the robust stability boundary of periodic solution can be determined by the interval eigenvalue problem. In addition, the sensitivity information mixed with the interval analysis method is used to quantify the response bounds of periodic solution. Numerical examples show that the proposed approach is valid and effective for analyzing fractional derivative nonlinear system in the presence of uncertainties. It is illustrated that the bifurcation solution in the fractional nonlinear systems may not be sensitive to the variation of the influence parameters.

A co-evolving frontier between land and water: dilemmas of flexibility versus robustness in flood risk management

Floods cause enormous damage on land and thus question the boundary between land and water in an extreme way. As floods increase in frequency and intensity, flood risk management must change from a resistance-based approach to a resilience approach. Whereas land uses require robust boundaries between land and water, the changing water system demands more flexible boundaries. This contribution discusses this tension from a theoretical perspective of resilience and co-evolution, using a socio-ecological systems approach. This offers a new perspective on the co-evolving frontier between land and water.

Robust boundary tracking for reachable sets of nonlinear differential inclusions

The Euler scheme is, to date, the most important numerical method for ordinary differential inclusions because the use of the available higher-order methods is prohibited by their enormous complexity after spatial discretization. Therefore, it makes sense to reassess the Euler scheme and optimize its performance. In the present paper, a considerable reduction of the computational cost is achieved by setting up a numerical method that computes the boundaries instead of the complete reachable sets of the fully discretized Euler scheme from lower-dimensional data only. Rigorous proofs for the propriety of this method are given, and numerical examples illustrate the gain of computational efficiency as well as the robustness of the scheme against changes in the topology of the reachable sets.

Basic oxygen furnace steelmaking end-point prediction based on computer vision and general regression neural network

End-point prediction is one of the most difficult problems in basic oxygen furnace (BOF) steelmaking process. To address this problem, some researchers have proposed some methods based on flame image processing and pattern classification. Because of the dynamically changing flame and real-time needs during the blowing process, there are still some issues that need to be solved. We propose a novel method based on accurate and fast multi flame features extraction and general regression neural network (GRNN). Firstly, flame images were acquired, and then the background of each image was removed via color similarity determination algorithm; secondly, color, texture, and boundary features were extracted; the fast and robust boundary and texture features were extracted by using the proposed methods, and these features were tested for their validity to the end-point prediction via comparing them with some other similar methods; finally, the prediction model was built using multi-features and GRNN. The experimental results demonstrated that it is accurate and fast to use the proposed method to the BOF end-point predict.

Did Adria rotate relative to Africa?

Abstract. The first and foremost boundary condition for kinematic reconstructions of the Mediterranean region is the relative motion between Africa and Eurasia, constrained through reconstructions of the Atlantic Ocean. The Adria continental block is in a downgoing plate position relative to the strongly curved central Mediterranean subduction-related orogens, and forms the foreland of the Apennines, Alps, Dinarides, and Albanides–Hellenides. It is connected to the African plate through the Ionian Basin, likely with Lower Mesozoic oceanic lithosphere. If the relative motion of Adria versus Africa is known, its position relative to Eurasia can be constrained through a plate circuit, thus allowing robust boundary conditions for the reconstruction of the complex kinematic history of the Mediterranean region. Based on kinematic reconstructions for the Neogene motion of Adria versus Africa, as interpreted from the Alps and from Ionian Basin and its surrounding areas, it has been suggested that Adria underwent counterclockwise (ccw) vertical axis rotations ranging from ~ 0 to 20°. Here, we provide six new paleomagnetic poles from Adria, derived from the Lower Cretaceous to Upper Miocene carbonatic units of the Apulian peninsula (southern Italy). These, in combination with published poles from the Po Plain (Italy), the Istrian peninsula (Croatia), and the Gargano promontory (Italy), document a post-Eocene 9.8 ± 9.5° counterclockwise vertical axis rotation of Adria. Our results do not show evidence of significant Africa–Adria rotation between the Early Cretaceous and Eocene. Models based on reconstructions of the Alps, invoking 17° ccw rotation, and based on the Ionian Basin, invoking 2° ccw rotation, are both permitted within the documented rotation range, yet are mutually exclusive. This apparent enigma could possibly be solved only if one or more of the following conditions are satisfied: (i) Neogene shortening in the western Alps has been significantly underestimated (by as much as 150 km); (ii) Neogene extension in the Ionian Basin has been significantly underestimated (by as much as 420 km); and/or (iii) a major sinistral strike-slip zone has decoupled northern and southern Adria in Neogene time. Here we present five alternative reconstructions of Adria at 20 Ma, highlighting the kinematic uncertainties, and satisfying the inferred rotation pattern from this study and/or from previously proposed kinematic reconstructions.

Methods and advances in the study of aeroelasticity with uncertainties

Uncertainties denote the operators which describe data error, numerical error and model error in the mathematical methods. The study of aeroelasticity with uncertainty embedded in the subsystems, such as the uncertainty in the modeling of structures and aerodynamics, has been a hot topic in the last decades. In this paper, advances of the analysis and design in aeroelasticity with uncertainty are summarized in detail. According to the non-probabilistic or probabilistic uncertainty, the developments of theories, methods and experiments with application to both robust and probabilistic aeroelasticity analysis are presented, respectively. In addition, the advances in aeroelastic design considering either probabilistic or non-probabilistic uncertainties are introduced along with aeroelastic analysis. This review focuses on the robust aeroelasticity study based on the structured singular value method, namely the μ method. It covers the numerical calculation algorithm of the structured singular value, uncertainty model construction, robust aeroelastic stability analysis algorithms, uncertainty level verification, and robust flutter boundary prediction in the flight test, etc. The key results and conclusions are explored. Finally, several promising problems on aeroelasticity with uncertainty are proposed for future investigation.

Robust river boundaries extraction of dammed lakes in mountain areas after Wenchuan Earthquake from high resolution SAR images combining local connectivity and ACM

River boundaries extraction from SAR imagery is valuable for flood monitoring and damage assessment. Several rivers, parts of which include dammed lakes caused by landslides and rock avalanches triggered by the 2008 Wenchuan Earthquake, were taken as a case study for robust extraction. In this paper, a novel state-of-the-art approach for automated river boundaries extraction using high resolution synthetic aperture radar (SAR) intensity imagery is presented. The key of our approach lies in the combined usage of local connectivity feature of the river and a region-based active contours model (ACM) in a variational level set framework to differentiate between river and the background. First, sub-patched intensity thresholding segmentation is applied to SAR imagery. Pixels with intensities below the threshold are selected as potential river pixels while the others are potential background pixels. Second, potential river pixels are divided into several connected regions, considering that the river is a big connected region, only relatively bigger regions with similar contrast value are retained as the regions of interest (ROI) while others are noise due to pixel-level decision approach in the first step or shadows due to mountains terrain. Third, the ROI and their contours are regarded as local region and the initial contours to refine the river boundaries, which are used to reduce the scene complexity of ACM and its sensitivity to initial situation, respectively. A novel ACM driven by local image fitting (LIF) energy is presented and used for river boundaries extraction for the first time, which is not only robust against inhomogeneity widely spread in SAR imagery but also can work with efficiency without the need of re-initialization during iteration compared to traditional ACM. The proposed approach was tested on numerous high resolution airborne SAR images containing connected rivers or dammed lakes obtained by Chinese domestic radar system after Wenchuan Earthquake. For the overall dataset, the average commission error, omission error and root mean squared error were 6.5%, 3.3%, and 0.51, respectively. The average computational time for 4000 by 4000 image size was 21min using a PC-based MATLAB platform. Our experimental results demonstrate that the proposed approach is robust and effective.

The scaling and shift of morphogen gene expression boundary in a nonlinear reaction diffusion system.

The scaling and shift of the gene expression boundary in a developing embryo are two key problems with regard to morphogen gradient formation in developmental biology. In this study, a bigradient model was applied to a nonlinear reaction diffusion system (NRDS) to investigate the location of morphogen gene expression boundary. In contrast to the traditional synthesis-diffusion-degradation model, the introduction of NRDS in this study contributes to the precise gene expression boundary at arbitrary location along the anterior-posterior axis other than simply midembryo even when the linear characteristic lengths of two morphogens are equal. The scaling location depends on the ratio of two morphogen influxes (w) and concentrations (r) as well as the nonlinear reaction diffusion parameters (a, n). We also formulate a direct relationship between the shift in the gene expression boundary and the influx of morphogen and find that enhancing the morphogen influx is helpful to build up a robust gene expression boundary. By analyzing the robustness of the morphogen gene expression boundary and comparing with the relevant results in linear reaction diffusion system, we determine the precise range of the ratio of the two morphogen influxes with a lower shift in the morphogen gene expression boundary and increased system robustness.

Adaptive robust boundary control of shaft vibrations under perturbations with unknown upper bounds

SummaryThis paper presents robust and adaptive boundary control designs to stabilize the two‐dimensional vibration of hybrid shaft model. The hybrid shaft is mathematically represented by a set of partial differential equations, governing the shaft vibrations, coupled to ordinary differential equations, describing rigid body spinning and dynamic boundary conditions. The control objective is to stabilize the transverse vibrations of the perturbed shaft while regulating the spinning rate. To achieve this, the paper first establishes robust boundary control laws that fulfil the control objective in the presence of modeling uncertainties and external disturbances operating over the shaft domain and boundary. Lyapunov‐based analyses show that the proposed robust control exponentially stabilizes the shaft with vanishing distributive perturbations, while assuring ultimately bounded vibrations in the case of nonvanishing perturbations. Then, adaptive control philosophy is utilized to achieve redesigned robust controllers that only use online adaptation of control gains without acquiring the knowledge of bounds on perturbations, as well as dynamic parameters. An advantage of this design is avoiding an overconservative robust control law, which may induce poor stability and chattering in tackling system perturbations with unknown upper bounds. Simulations through finite element method illustrate the results. Copyright © 2014 John Wiley & Sons, Ltd.

Automatic Ki-67 Counting Using Robust Cell Detection and Online Dictionary Learning

Ki-67 proliferation index is a valid and important biomarker to gauge neuroendocrine tumor (NET) cell progression within the gastrointestinal tract and pancreas. Automatic Ki-67 assessment is very challenging due to complex variations of cell characteristics. In this paper, we propose an integrated learning-based framework for accurate automatic Ki-67 counting for NET. The main contributions of our method are: 1) A robust cell counting and boundary delineation algorithm that is designed to localize both tumor and nontumor cells. 2) A novel online sparse dictionary learning method to select a set of representative training samples. 3) An automated framework that is used to differentiate tumor from nontumor cells (such as lymphocytes) and immunopositive from immunonegative tumor cells for the assessment of Ki-67 proliferation index. The proposed method has been extensively tested using 46 NET cases. The performance is compared with pathologists' manual annotations. The automatic Ki-67 counting is quite accurate compared with pathologists' manual annotations. This is much more accurate than existing methods.

Enhanced Decoupled Active Contour Using Structural and Textural Variation Energy Functionals.

Active contours are a popular approach for object segmentation that uses an energy minimizing spline to extract an object's boundary. Nonparametric approaches can be computationally complex, whereas parametric approaches can be impacted by parameter sensitivity. A decoupled active contour (DAC) overcomes these problems by decoupling the external and internal energies and optimizing them separately. However a drawback of this approach is its reliance on the edge gradient as the external energy. This can lead to poor convergence toward the object boundary in the presence of weak object and strong background edges. To overcome these issues with convergence, a novel approach is proposed that takes advantage of a sparse texture model, which explicitly considers texture for boundary detection. The approach then defines the external energy as a weighted combination of textural and structural variation maps and feeds it into a multifunctional hidden Markov model for more robust object boundary detection. The enhanced DAC (EDAC) is qualitatively and visually analyzed on two natural image data sets as well as Brodatz images. The results demonstrate that EDAC effectively combines texture and structural information to extract the object boundary without impact on computation time and a reliance on color.

Zonal detached eddy simulation (ZDES) of a spatially developing flat plate turbulent boundary layer over the Reynolds number range 3 150 ⩽ Reθ ⩽ 14 000

A Wall-Modeled Large Eddy Simulation (WMLES) of a spatially developing zero-pressure gradient smooth flat plate turbulent boundary layer is performed by means of the third mode of the Zonal Detached Eddy Simulation technique. The outer layer is resolved by a Large Eddy Simulation whereas the wall is modeled by a RANS simulation zone, with a RANS/LES interface prescribed at a fixed location. A revisited cost assessment of the Direct Numerical Simulation of high Reynolds numbers (Reθ ⩾ 10 000) wall-bounded flows emphasizes how moderate the cost of the WMLES approach is compared to methods resolving the near-wall dynamics. This makes possible the simulation over a wide Reynolds number range 3 150 ⩽ Reθ ⩽ 14 000, leaving quite enough space for very large scale motions to develop. For a better skin friction prediction, it is shown that the RANS/LES interface should be high enough in the boundary layer and at a location scaling in boundary layer thickness units (e.g., 0.1δ) rather than in wall units. Velocity spectra are compared to experimental data. The outer layer is well resolved, except near the RANS/LES interface where the very simple and robust passive boundary treatment might be improved by a more specific treatment. Besides, the inner RANS zone also contains large scale fluctuations down to the wall. It is shown that these fluctuations fit better to the experimental data for the same interface location that provides a better skin friction prediction. Numerical tests suggest that the observed very large scale motions may appear in an autonomous way, independently from the near-wall dynamics. It still has to be determined whether the observed structures have a physical or a numerical origin. In order to assess how the large scale motions contribute to skin friction, the Reynolds shear stress contribution is studied as suggested by the FIK identity [K. Fukagata, K. Iwamoto, and N. Kasagi, “Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows,” Phys. Fluids 14, L73 (2002)]. Scale decomposition is achieved thanks to the co-spectrum of the Reynolds shear stress in function of the length scale and of the wall distance. The contribution of the large scales to streamwise turbulence intensity and to the Reynolds shear stress is assessed. At the considered Reynolds numbers, the observed largest scales contribute significantly to the Reynolds shear stress in the outer layer but are almost inactive in the sense of Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, 1976)] closer to the wall. The modeled Cf amounts to only 11% of the total Cf: most of the skin friction is resolved by the present simulations rather than modeled. The large scales, defined by λx > δ, represent the largest contribution to the resolved Cf. It is surmised that there is a correlation between the large scale motions being closer to the experimental data and the better skin friction prediction enabled by a proper interface positioning.

A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains

We present a robust and accurate outflow boundary condition and an associated numerical algorithm for incompressible flow simulations on unbounded physical domains, aiming at maximizing the domain truncation without adversely affecting the flow physics. The proposed outflow boundary condition allows for the influx of kinetic energy into the domain through the outflow boundaries, and prevents un-controlled growth in the energy of the domain in such situations. The numerical algorithm for the outflow boundary condition is developed on top of a rotational velocity-correction type strategy to de-couple the pressure and velocity computations, and a special construction in the algorithmic formulation prevents the numerical locking at the outflow boundaries for time-dependent problems. Extensive numerical tests for flow problems with bounded and semi-bounded physical domains demonstrate that this outflow boundary condition and the numerical algorithm produce stable and accurate simulations on even severely truncated computational domains, where strong vortices may be present at or exit the outflow boundaries. The method developed herein has the potential to significantly expedite simulations of incompressible flows involving outflow or open boundaries, and to enable such simulations at Reynolds numbers significantly higher than the state of the art.

A simple and robust boundary treatment for the forced Korteweg–de Vries equation

In this paper, we propose a simple and robust numerical method for the forced Korteweg–de Vries (fKdV) equation which models free surface waves of an incompressible and inviscid fluid flow over a bump. The fKdV equation is defined in an infinite domain. However, to solve the equation numerically we must truncate the infinite domain to a bounded domain by introducing an artificial boundary and imposing boundary conditions there. Due to unsuitable artificial boundary conditions, most wave propagation problems have numerical difficulties (e.g., the truncated computational domain must be large enough or the numerical simulation must be terminated before the wave approaches the artificial boundary for the quality of the numerical solution). To solve this boundary problem, we develop an absorbing non-reflecting boundary treatment which uses outward wave velocity. The basic idea of the proposing algorithm is that we first calculate an outward wave velocity from the solutions at the previous and present time steps and then we obtain a solution at the next time step on the artificial boundary by moving the solution at the present time step with the velocity. And then we update solutions at the next time step inside the domain using the calculated solution on the artificial boundary. Numerical experiments with various initial conditions for the KdV and fKdV equations are presented to illustrate the accuracy and efficiency of our method.

Robust boundary detection and tracking of left ventricles on ultrasound images using active shape model and ant colony optimization.

Information regarding the motion, strain and synchronization are important for cardiac diagnosis and therapy. Extraction of such information from ultrasound images remains an open problem till today. In this paper, a novel method is proposed to extract the boundaries of left ventricles and track these boundaries in ultrasound image sequences. The initial detection of boundaries was performed by an active shape model scheme. Subsequent refinement of the boundaries was done by using local variance information of the images. The main objective of this paper is the formulation of a new boundary tracking algorithm using ant colony optimization technique. The experiments conducted on the simulated image sequences and the real cardiac ultrasound image sequences shows a positive and promising result.

Robust and Quality Boundary Constrained Tetrahedral Mesh Generation

AbstractA novel method for boundary constrained tetrahedral mesh generation is proposed based on Advancing Front Technique (AFT) and conforming Delaunay triangulation. Given a triangulated surface mesh, AFT is firstly applied to mesh several layers of elements adjacent to the boundary. The rest of the domain is then meshed by the conforming Delaunay triangulation. The non-conformal interface between two parts of meshes are adjusted. Mesh refinement and mesh optimization are then preformed to obtain a more reasonable-sized mesh with better quality. Robustness and quality of the proposed method is shown. Convergence proof of each stage as well as the whole algorithm is provided. Various numerical examples are included as well as the quality of the meshes.

A Robust Boundary Localization for Degraded Iris Images

Boundary localization is one of the key issues for reliable iris recognition system. For degraded iris images, some frequently-occurred cases such as dominant texture patterns, eyelashes or eyelids occlusions, low contrast between iris and sclera, and pupil deviation, will lead to inaccurate boundary localization. Specifically, if the intensive transition from iris to sclera is too smooth, outer boundary localization will be very difficult. To stress the problem, in this paper the boundary localization method is proposed in which nonlinear gray-level transformation is innovated in outer boundary localization process. The experimental results depict that our algorithm have improved the localization accuracy for degraded iris compared to the classical algorithms.

Shot Boundary Detection Algorithm Based on Multi-Feature Fusion

To establish a general and robust shot boundary detection algorithm, according to characteristics of lens conversion and the ideal of multiple video features fusion, a shot boundary detection algorithm is proposed based on YUV histogram, texture feature and edge orientation histogram in the paper. Besides, global and self-adaptive threshold are combined to use so as to control the process of shot boundary detection and enhance the accuracy of threshold selection. The experiment results show that the algorithm can effectively realize video shot boundary detection and strengthen the robustness of the detection.

Noise-induced rupture process: Phase boundary and scaling of waiting time distribution

A bundle of fibers has been considered here as a model for composite materials, where breaking of the fibers occur due to a combined influence of applied load (stress) and external noise. Through numerical simulation and a mean-field calculation we show that there exists a robust phase boundary between continuous (no waiting time) and intermittent fracturing regimes. In the intermittent regime, throughout the entire rupture process avalanches of different sizes are produced and there is a waiting time between two consecutive avalanches. The statistics of waiting times follows a Γ distribution and the avalanche distribution shows power-law scaling, similar to what has been observed in the case of earthquake events and bursts in fracture experiments. We propose a prediction scheme that can tell when the system is expected to reach the continuous fracturing point from the intermittent phase.