Circular-arc Model Research Articles

A novel dynamic parameter method (DPM) based on ANN for safety assessment of corroded pipelines

Corrosion in oil and gas pipelines is inevitable, which seriously affects the safety of pipelines. The safety assessment of corroded pipelines is a matter of urgency. To describe the damage behavior of pipelines, the Chen-Chu criterion was proposed. However, a key parameter in Chen-Chu criterion was determined empirically. In this paper, a novel dynamic parameter method (DPM) is proposed to determine the key parameter based on artificial neural network (ANN). The empirical parameter in Chen-Chu criterion is optimized by ANN and turns into dynamic one varying with input. The data for training in ANN is obtained by double circular arc (DCA) model. Compared to finite element method and previous prediction equations, the DPM are closer to the experimental data. Besides, by comparing with the experimental data, it is found that DPM is even more accurate than direct ANN method. It provides a new idea for the fusion of solution of traditional methods and data-driven methods.

Empirical Model for the Description of Weld Seam Geometry in Coaxial Laser Hot-Wire Deposition Welding Processes with Different Steel Wires

Claddings are used to protect areas of components that are exposed to particular chemical, physical or tribological stresses. The aim when developing a cladding process is to achieve a cladding with low waviness in order to reduce the amount of machining required. Computational models and FEA simulations can be used to determine process parameters for claddings with low rework including a prediction of the height and width of a single weld seam aswell as the development of welding strategies. In this paper empirical models describing the geometry of single weld seams on a substrate manufactured with a coaxial laser hot-wire cladding process are investigated for three steel wire materials and different welding parameters. The coordinates of surface points of the weld seams were detected using a laser scanning microscope and post-processed by a self-created script. In order to describe the cross sectional shape of the weld seams, the parameters of parabolic, cosinusiodal or circular arc model functions are derived from the surface data using a fitting algorithm. For the tested wire materials, an effect of the wire material on the shape of the weld seam was not observed. The investigations also show that regardless of the varied welding parameter set or wire material, a circular model function appears to be the most suitable model shape for describing the cross sectional weld seam geometry in coaxial laser metal deposition with hot-wire. The regression residua using a circular arc model function ranged from 18.9 upmum to 34.6 upmum, which indicates a good approximation.

Integrity assessment of the pipelines containing an isolated corrosion pit

Corrosion pits often appear in steel pipelines under saline or marine immersion conditions and lead to potential risk. In this paper, a double circular arc (DCA) model is firstly established to simulate the pipelines containing an isolated corrosion pit. Then, a burst pressure predictive equation of the pipelines with an isolated pit is provided. Next, the finite element method (FEM) is adopted to verify the accuracy of predictive equation. In the end, comparisons and discussions between the predictive equation and FEM are conducted. The results indicated that undetectable corrosion pits can largely decrease the ultimate carrying capability of pipelines. Furthermore, the DCA model is feasible to simulate the burst behavior of pipelines with an isolated corrosion pit. In addition, compared to FEM, the errors of burst pressure equation are less than 10% for the pipes with an isolated corrosion pit. Finally, accurately predicting the burst pressure and timely repair or replacement of the pipelines with pits can avoid drastic consequences. We provide a novel idea to predict the burst pressure of pipelines with group pits. It is rewarding to study the burst behavior of pitting pipelines and assess the integrity of pipelines.

Predictive models for the deep geometry of a thick-skinned thrust matched to crustal structure: Wind River Range, western USA

AbstractThe ability of models designed to use near-surface structural information to predict the deep geometry of a faulted block is tested for a thick-skinned thrust by matching the surface geometry to the crustal structure beneath the Wind River Range, Wyoming, USA. The Wind River Range is an ∼100-km-wide, thick-skinned rotated basement block bounded on one side by a high-angle reverse fault. The availability of a deep seismic-reflection profile and a detailed crustal impedance profile based on teleseismic receiver-function analysis makes this location ideal for testing techniques used to predict the deep fault geometry from shallow data. The techniques applied are the kinematic models for a circular-arc fault, oblique simple-shear fault, shear fault-bend fold, and model-independent excess area balancing. All the kinematic models imply that the deformation cannot be exclusively rigid-body rotation but rather require distributed deformation throughout some or all of the basement. Both the circular-arc model and the oblique-shear models give nearly the same best fit to the master fault geometry. The predicted lower detachment matches a potential crustal detachment zone at 31 km subsea. The thrust ramp is located close to where this zone dies out to the southwest. The circular-arc model implies that the penetrative deformation could be focused at the trailing edge of the basement block rather than being distributed uniformly throughout and thus helps to explain the line of second-order anticlines along the trailing edge of the Wind River block.Key points: (1) The circular-arc fault model and the oblique-shear model predict a lower detachment for the Wind River rotated block to be ∼31 km subsea, consistent with the crustal structure as defined by teleseismic receiver-function analysis. The thrust ramp starts where this zone dies out. (2) The kinematic models require distributed internal deformation within the basement block, probably concentrated at the trailing edge. (3) The uplift at the trailing edge of the rotated block is explained by the circular-arc kinematic model as a requirement to maintain area balance of a mostly rigid block above a horizontal detachment; the oblique-shear model can explain the uplift as caused by displacement on a dipping detachment.

Design and Optimization of Concentric Tube Robots Based on Surgical Tasks, Anatomical Constraints and Follow-the-Leader Deployment

Many neurological disorders are characterized by the focal and anatomically definable lesions within the brain parenchyma. Traditional treatment may introduce major trauma in neurosurgery and conventional medical devices can only trace straight trajectories. To overcome these problems, a design and optimization method for a patient-specific concentric tube robot (CTR) satisfying the constraints of anatomy, surgical tasks and follow-the-leader (FTL) deployment is proposed in this paper. CTR is a tentacle like continuum robot that can work inside confined and complex biological chambers with the ability of tracking complex 3D trajectories. It consists of pre-curved superplastic tubes with hollow cavities to accommodate the surgical tools. These merits make the CTR well suitable for minimally invasive surgeries. This paper introduces a design framework that utilizes preoperative MRI data to configure patient-specific CTR for single and multiple tasks with the minimum number of tubes. A constant curvature circular arc model is built to solve the problem of inverse kinematics. Two iterative optimization methods for single and multiple tasks are proposed to optimize the parameters of the CTR. Initial waypoints of the CTR are produced based on the FTL deployment. The waypoints are then refined using a Follow Shape Rapidly-exploring Random Tree algorithm (FSRRT) for cases that the initial configurations of the CTR cannot completely satisfy the FTL deployment. Simulations and experiments are carried out on a human brain model to validate the proposed methods. The parameters of CTR including the entire length, curvature, radius angle, number, diameter, arc length and the waypoints are obtained. The errors of the FTL deployment are found to be within 2.1mm.

Effect of the Y/T on the burst pressure for corroded pipelines with high strength

Pipelines are the fifth type of transportation, which has the highest efficiency and the least environmental damage for gas or oil transmission. Recently, the pipeline failures due to corrosion defects have attracted people's attention in maintaining pipeline integrity. Based on the double circular arc (DCA) model and elastic-plastic theory, an analytical solution of the corroded pipelines under internal and external pressures was obtained. And then, a new burst pressure equation of the corroded pipelines with high strength was further provided according to the von Mises criterion and previous equations. Compared with previous equations, this equation greatly extends the application scope and increases the calculation accuracy. The accuracy of our equation is validated by comparing with the full-scale experimental data. The effects of the thickness to diameter ratio, corrosion ratio and yield strength on the burst pressure are carefully investigated. The results reveal that when the thickness to diameter ratio is less than 0.1, the calculated results show a good agreement with the experimental data for the corroded and high strength pipes. Our research can provide a foundation for replacing the corroded pipelines at the bottom of the sea. In addition, our research is beneficial for the engineering design and integrity assessment of oil and gas pipelines.

Bounded, minimal, and short representations of unit interval and unit circular-arc graphs. Chapter I: theory

This is the first of two chapters of a work in which we consider the unrestricted, minimal, and bounded representation problems for unit interval (UIG) and unit circular-arc (UCA) graphs. In the unrestricted version, a proper circular-arc (PCA) model ${\mathcal{M}}$ is given and the goal is to obtain an equivalent UCA model ${\mathcal{U}}$. In the bounded version, ${\mathcal{M}}$ is given together with some lower and upper bounds that the beginning points of ${\mathcal{U}}$ must satisfy. In the minimal version, we have to find a minimal model equivalent to ${\mathcal{M}}$, in which the circumference of the circle and length of the arcs must be simultaneously as small as possible. In this chapter we motivate these problems from an historical perspective, and we develop the theoretical framework required for the algorithms in Chapter II. We present new characterizations of those PCA models that have equivalent UCA models, and of those UCA models with a circle of circumference ${c}$ and the arcs of length $\ell$. We also prove that every UCA model is equivalent to a minimal one. We remark that all our results are of an algorithmic nature and can be readily employed to solve the problems at hand, even though these algorithms are not as efficient as those in Chapter II.

Bounded, minimal, and short representations of unit interval and unit circular-arc graphs. Chapter II: algorithms

This is the second and last chapter of a work in which we consider the unrestricted, minimal, and bounded representation problems for unit interval (UIG) and unit circular-arc (UCA) graphs. In the unrestricted version (${\rm R{\small EP}}$), a proper circular-arc (PCA) model $\mathcal M$ is given and the goal is to obtain an equivalent UCA model $\mathcal U$. In the bounded version (${\rm B{\small OUND}R{\small EP}}$), $\mathcal M$ is given together with some lower and upper bounds that the beginning points of $\mathcal U$ must satisfy. In the minimal version (${\rm M{\small IN}UCA}$), the circumference of the circle and the length of the arcs in $\mathcal U$ must be simultaneously as small as possible, while the separation of the extremes is greater than a given threshold. In this chapter we take advantage of the theoretical framework developed in Chapter I to design efficient algorithms for these problems. We show a linear-time algorithm with negative certification for ${\rm R{\small EP}}$, that can also be implemented to run in logspace. We develop algorithms for different versions of ${\rm B{\small OUND}R{\small EP}}$ that run in linear space and quadratic time. Regarding ${\rm M{\small IN}UCA}$, we first show that the previous linear-time algorithm for ${\rm M{\small IN}UIG}$ (i.e., ${\rm M{\small IN}UCA}$ on UIG models) fails to provide a minimal model for some input graphs. We fix this algorithm but, unfortunately, it runs in linear space and quadratic time. Then, we apply the algorithms for ${\rm M{\small IN}UIG}$ and ${\rm M{\small IN}UCA}$ (Chapter I) to find the minimum powers of paths and cycles that contain given UIG and UCA models, respectively.

Double circular arc model based on average shear stress yield criterion and its application in the corroded pipe burst

Corrosion is one of the major causes of damage in offshore and onshore pipes. Based on the double circular arc (DCA) model and the average shear stress yield (ASSY) criterion for isotropic hardening materials, a new burst pressure equation for corroded pipes is developed in this paper. The ASSY criterion is a weighted average of the maximum shear stress and the octahedral shear stress and it is adopted to predict the burst pressure of the pipelines with corrosion defects. The accuracy of our predictive equations is validated respectively by both the ideal and corroded pipes. Firstly, the burst pressure equation of a corroded pipe is degraded into an ideal pipe's. Then we compare the calculated results with the full-scale experimental data. The calculated results are consistent with the experimental data for the ideal pipes. Again, we make a comparison of the predicted burst pressures of corroded pipes with the ones from the elastic-plastic finite element method (FEM) and the experiment. The calculated results show a good agreement with the numerical calculations and experimental data for the corroded pipes. Our research reveals that the corrosion defects can decrease the burst pressure for a pipe; the yield criterion and the strain hardening exponent are crucial to accurately capture the burst pressure. Our research is beneficial to evaluate the integrity of the corroded pipes.

Solving the canonical representation and Star System Problems for proper circular-arc graphs in logspace

We present a logspace algorithm that constructs a canonical intersection model for a given proper circular-arc graph, where canonical means that isomorphic graphs receive identical models. This implies that the recognition and the isomorphism problems for these graphs are solvable in logspace. For the broader class of concave-round graphs, which still possess (not necessarily proper) circular-arc models, we show that a canonical circular-arc model can also be constructed in logspace. As a building block for these results, we design a logspace algorithm for computing canonical circular-arc models of circular-arc hypergraphs. This class of hypergraphs corresponds to matrices with the circular ones property, which play an important role in computational genomics. Our results imply that there is a logspace algorithm that decides whether a given matrix has this property.Furthermore, we consider the Star System Problem that consists in reconstructing a graph from its closed neighborhood hypergraph. We show that this problem is solvable in logarithmic space for the classes of proper circular-arc, concave-round, and co-convex graphs.Note that solving a problem in logspace implies that it is solvable by a parallel algorithm of the class AC1. For the problems under consideration, at most AC2 algorithms were known earlier.

On the isomorphism problem for Helly circular-arc graphs

The isomorphism problem is known to be efficiently solvable for interval graphs, while for the larger class of circular-arc graphs its complexity status stays open. We consider the intermediate class of intersection graphs for families of circular arcs that satisfy the Helly property. We solve the isomorphism problem for this class in logarithmic space. If an input graph has a Helly circular-arc model, then our algorithm constructs it canonically, which means that the models constructed for isomorphic graphs are equal.

Numerical study on pull-out behaviour of cavern-type rock anchorages

이 논문은 케이블 인발하중이 작용하는 현수교의 지중정착식 앵커리지 캐번 터널에 대한 거동과 관련된 연구이다. 수치해석 결과와 이중곡선 관계식에 의한 추정식에서 얻어진 극한인발저항력(<TEX>$P_u$</TEX>) 결과와 비교를 통하여 앵커리지 거동, 앵커리지 설계 방법, 파괴면의 각도, <TEX>${\delta}$</TEX> 등을 분석하였다. 연구결과 <TEX>$P/{\gamma}/H$</TEX>와 변위와의 선형 상관관계, <TEX>$P_u/{\gamma}/H$</TEX>와 H/b와의 선형 상관관계를 활용하면 앵커리지 캐번 터널의 설치 심도를 쉽게 결정 할 수 있을 것으로 나타났다. 또한 수치해석에 의한 최대전단변형률 분포도와 소성영역 분포도를 분석한 결과 지반파괴 형태는 현재 사용되는 지반 콘 보델 보다는 원호모델에 더 가까운 것으로 나타났다. 이 연구에서는 계산이 간편하도록 원호모델을 단순화한 이중곡선 모델을 제안하였다. 수치해석 결과로부터 얻어진 평균 파괴각을 이중곡선 모델에 적용한 결과, 이중곡선 모델을 적용한 추정식에서 얻어진 극한인발저항력은 수치해석에서 얻어진 극한인발저항력 결과와 잘 일치하는 것으로 나타났다. This paper is a study for behaviour of cavern type anchorage tunnels for suspension bridges with cable tension. Anchorage behaviour, design method for anchorage, and failure surface angle, <TEX>${\delta}$</TEX> are analyzed by comparing numerical analysis results and ultimate pullout capacities(<TEX>$P_u$</TEX>) using bilinear corelation equation. Results show that design depths for cavern type anchorage tunnels are easily checked with linear relationships for <TEX>$P/{\gamma}/H$</TEX> vs. displacement and <TEX>$P_u/{\gamma}/H$</TEX> vs. H/b. The analysis results of maximum shear strain distribution and plastic status show that failure shapes are closer to circular arc model than soil cone model which frequently used. To an easy calculation of the ultimate pullout capacity, we propose a simple bilinear failure model in this study. The calculated ultimate pullout capacities from the proposed bilinear corelation equation using two failure angles results are similar to the ultimate pullout capacities from numerical analysis.

Normal Helly circular-arc graphs and its subclasses

A Helly circular-arc model M=(C,A) is a circle C together with a Helly family A of arcs of C. If no arc is contained in any other, then M is a proper Helly circular-arc model, if every arc has the same length, then M is a unit Helly circular-arc model, and if there are no two arcs covering the circle, then M is a normal Helly circular-arc model. A Helly (resp. proper Helly, unit Helly, normal Helly) circular-arc graph is the intersection graph of the arcs of a Helly (resp. proper Helly, unit Helly, normal Helly) circular-arc model. In this article we study these subclasses of Helly circular-arc graphs. We show natural generalizations of several properties of (proper) interval graphs that hold for some of these Helly circular-arc subclasses. Next, we describe characterizations for the subclasses of Helly circular-arc graphs, including forbidden induced subgraphs characterizations. These characterizations lead to efficient algorithms for recognizing graphs within these classes. Finally, we show how these classes of graphs relate with straight and round digraphs.

Investigation on Numerical Calculation of Thermal Boundary Resistance between Superconducting Magnets

Aiming at the problem that thermal boundary resistance (TBR) has an effect on heat transportation of superconducting magnet when Superconducting Magnetic Energy Storage (SMES) is cooled directly, from perspective of numerical calculation, truncated cone, circular arc and triangular models are used to simulate the solid to solid contact surface, and finite element method is adopted to carry on numerical simulation calculation for thermal boundary resistance. With comparison and analysis of the calculation results of the three models, knowing that the value calculated with the triangular model when its control angle is 30° is close to the measured value and its relative error is 17%. Meanwhile, the error source is analyzed. This dissertation can be a good reference to the research on superconducting magnet heat transportation.

Roll-over shapes of the ankle–foot and knee–ankle–foot systems of able-bodied children

Background The roll-over shape is the effective rocker shape that a lower limb system conforms to during a step. The roll-over shape concept has been explored in detail in adults and has been successfully used in the design, evaluation, and alignment of lower limb prostheses and orthoses. No such analysis exists for the pediatric population. Therefore, the purpose of this study was to investigate the ankle–foot and knee–ankle–foot roll-over shapes in able-bodied children, values that could serve as tools for design and evaluation of lower limb pediatric prostheses and orthoses. Methods This study describes a multi-center retrospective review of existing motion analysis data ( n = 153 from three centers). Roll-over shapes were calculated by transforming center of pressure data from a laboratory-based coordinate system into two body-based coordinate systems. Roll-over shapes were then characterized using a circular arc model. Best-fit radii of roll-over shapes for children in three age groups (3–7 years, 8–11 years, and 12–17 years) were compared using the Kruskal–Wallis test. Findings No significant changes were found in roll-over shape radii between the three age groups ( P = 0.54 for ankle–foot roll-over shape radii; P = 0.12 for knee–ankle–foot roll-over shape radii). The weighted mean of median radii for ankle–foot and knee–ankle–foot roll-over shapes from the three centers were approximately 22% and 17% of body stature, values similar to those seen in adults. Interpretation Children produce nearly circular knee–ankle–foot roll-over shapes at a young age that are similar to those seen in adults when scaled by body stature.

Linear-Time Recognition of Helly Circular-Arc Models and Graphs

A circular-arc model ℳ is a circle C together with a collection $\mathcal{A}$ of arcs of C. If $\mathcal{A}$ satisfies the Helly Property then ℳ is a Helly circular-arc model. A (Helly) circular-arc graph is the intersection graph of a (Helly) circular-arc model. Circular-arc graphs and their subclasses have been the object of a great deal of attention in the literature. Linear-time recognition algorithms have been described both for the general class and for some of its subclasses. However, for Helly circular-arc graphs, the best recognition algorithm is that by Gavril, whose complexity is O(n 3). In this article, we describe different characterizations for Helly circular-arc graphs, including a characterization by forbidden induced subgraphs for the class. The characterizations lead to a linear-time recognition algorithm for recognizing graphs of this class. The algorithm also produces certificates for a negative answer, by exhibiting a forbidden subgraph of it, within this same bound.

Dynamic Behavior of SMA Actuated Catheter

Introduction: While catheters have proven effective in numerous cardiovascular procedures, their functionality and versatility can be greatly improved by incorporating active steering capabilities to the catheter tip. Shape memory alloy (SMA) actuation is ideally suited to this application, as these materials offer superior power density, energy density and biocompatibility. In this research, we investigate the transient behavior of an SMA-actuated active catheter to optimize its design and enable precise computer-controlled navigation. Methods: The active catheter prototype consists of a central beam actuated by a single SMA tendon, both enclosed by an outer Teflon sleeve. Joule heating is used to generate tip deflections, which are measured in real time using a dual-camera imaging system. SMA actuation is described using the Seelecke-Muller-Achenbach single-crystal model whose parameters are experimentally derived from stress-strain characteristics of the SMA tendon measured at different temperatures. These characteristics are used to optimize the design parameters of the catheter to maximize the bending response. The effects of outer sleeve thickness on the transient behavior of the catheter are also studied. Results: The catheter’s bending mechanics are described using a circular arc model, which is experimentally validated. Catheter actuation is found to be slower with increased sleeve thickness, as explained by heat transfer analysis. Dynamic simulation of the system model shows excellent correlation to experimental data for low frequency actuation.

Modeling the dynamic behavior of a shape memory alloy actuated catheter

In this paper we investigate the transient behavior of a simple active catheter: a centraltube actuated by a single nitinol tendon enclosed by an outer sleeve. Dynamic models aredeveloped to characterize the transient behavior and optimize the design of anexperimental prototype. The bending mechanics are derived using a circular arcmodel and are experimentally validated. Nitinol actuation is described using theSeelecke–Muller–Achenbach model for single-crystal shape memory alloys usingexperimentally determined parameters. The dynamic characteristics of this active cathetersystem are simulated and compared with experimental results. Joule heating is used togenerate tip deflections, which are computed in real time using a dual-camera imagingsystem. The effects of outer sleeve thickness on heat transfer and transient responsecharacteristics are studied.

Unit Circular-Arc Graph Representations and Feasible Circulations

In a recent paper, Duran et al. [J. Algorithms, 58 (2006), pp. 67-78] described an algorithm of complexity $O(n^2)$ for recognizing whether a graph $G$ with $n$ vertices and $m$ edges is a unit circular-arc (UCA) graph. Furthermore, the following open questions were posed in the above paper: (i) Is it possible to construct a UCA model for $G$ in polynomial time? (ii) Is it possible to construct a UCA model, whose extremes of the arcs correspond to integers of polynomial size? (iii) If (ii) is true, could such a model be constructed in polynomial time? In the present paper, we describe a characterization of UCA graphs, based on network circulations. The characterization leads to a different recognition algorithm and to answering these questions in the affirmative. We construct a UCA model whose extremes of the arcs correspond to integers of size $O(n)$. The proposed algorithms, for recognizing UCA graphs and constructing UCA models, have complexities $O(n+m)$. Furthermore, the complexities reduce to $O(n)$, if a proper circular-arc (PCA) model of $G$ is already given as the input, provided the extremes of the arcs are ordered. We remark that a PCA model of $G$ can be constructed in $O(n+m)$ time, using the algorithm by Deng, Hell, and Huang [SIAM J. Comput., 25 (1996), pp. 390-403]. Finally, we also describe a linear time algorithm for finding feasible circulations in networks with nonnegative lower capacities and unbounded upper capacities. Such an algorithm is employed in the model construction for UCA graphs.

Roll-over shapes of the able-bodied knee–ankle–foot system during gait initiation, steady-state walking, and gait termination

A few investigators have described the movement of the center of pressure (COP) of the ground reaction force and the activation patterns of the lower limb muscles during gait initiation and termination. This study examines the effective rocker (roll-over shape) behavior of the knee–ankle–foot (KAF) system during gait initiation, steady-state walking (i.e. constant speed gait), and gait termination. The KAF roll-over shapes were characterized by transforming COP data of 10 able-bodied subjects from a laboratory-based coordinate system into a leg-based coordinate system. The resulting roll-over shapes (effective rockers) were characterized using a circular arc model. The KAF roll-over shapes exhibit an overall “flexed” orientation during the first step of gait initiation and an “extended” orientation during the last step of gait termination. Understanding the behavior of the anatomical KAF system during gait initiation and termination may aid in the design of prosthetic components, i.e. mechanical devices that replace complete anatomical structures. Prostheses that intend to mimic the overall behavior of physiological KAF systems (biomimetic designs) could be manufactured using approaches that are much simpler than attempting to reconstruct the complexity of the lower limb.