On the application of the single-phase level set method to naval hydrodynamic flows

The application of the single-phase level set approach to the numerical simulations of three-dimensional free surface flows around complex geometries, at both non-breaking and breaking regimes is presented. In this approach only the liquid phase is simulated and the level set function is used as tracking device to locate the free surface position. The extrapolation of the solution in the dummy points in the gaseous phase is such that second-order accuracy is maintained also in the points adjacent to the free surface; the time evolution of the level set function and the re-initialization step have been merged so to get a function which is a distance function everywhere, and satisfies, at the same time, the kinematic condition on the free surface. The implementation of this technique into a general purpose Reynolds averaged Navier-Stokes (RANS) equations solver developed at INSEAN [Di Mascio A, Broglia R, Favini B. A Second Order Godunov-type Scheme for Naval Hydrodynamics. Kluwer Academic/Plenum Publishers; 2001, p. 253-61], is described in details; capabilities of the algorithm in dealing with non-breaking and breaking flows in the naval hydrodynamic context will be demonstrated by using a submerged hydrofoil and two different ship hulls in straight course as test cases. Comparisons with both experimental data and numerical surface fitting computations are presented; convergence properties of the algorithm, as well as validation and verification assessment will be also discussed.     

On motion optimization of robotic manipulators with strong nonlinear dynamic coupling using support area level set algorithm

Aiming for a better dynamic performance from the robot beyond the physical limits set by the manufacturers, in this paper we propose to integrate the robot dynamics into motion planning and then to approximate the robot joint torques using parameterized B-splines. By introducing a high-dimensional non-linear fitness function, we transform the motion planning problem into an optimization of a non-linear fitness function, and then we develop the approach based on Support Area Level Set Algorithm (SALAS). It integrates dual-stage sampling strategies to avoid early convergence in a small search field and to improve the rate of convergence to the potential solution. The effectiveness of the proposed approach has been verified by the simulation of a two-link robotic manipulator.     

Flux-based level set method on rectangular grids and computation of first arrival time functions

Flux-based level set method is a finite volume method for the numerical solution of advective level set equation which describes the transport of level lines by an external velocity field and by a speed in normal direction. The method is introduced for rectangular grids without using any dimensional splitting. The second order accurate discretization scheme is derived with one free parameter in the definition of piecewise linear reconstruction. A significant improvement of the accuracy can be obtained by special choices of this parameter for two benchmark examples of linear conservation laws. Moreover, the flux-based level set method can be used for computation of first arrival time functions in the class of problems such as “boat sailing” or “fire spread” where some external velocity field (e.g., a water or wind flow) must be considered additionally to the speed of boat or fire. Numerical experiments confirm very good performance of the method for this type of problems.     

Dynamic cluster formation using level set methods

Density-based clustering has the advantages for: 1) allowing arbitrary shape of cluster and 2) not requiring the number of clusters as input. However, when clusters touch each other, both the cluster centers and cluster boundaries (as the peaks and valleys of the density distribution) become fuzzy and difficult to determine. We introduce the notion of cluster intensity function (CIF) which captures the important characteristics of clusters. When clusters are well-separated, CIFs are similar to density functions. But, when clusters become closed to each other, CIFs still clearly reveal cluster centers, cluster boundaries, and degree of membership of each data point to the cluster that it belongs. Clustering through bump hunting and valley seeking based on these functions are more robust than that based on density functions obtained by kernel density estimation, which are often oscillatory or oversmoothed. These problems of kernel density estimation are resolved using level set methods and related techniques. Comparisons with two existing density-based methods, valley seeking and DBSCAN, are presented which illustrate the advantages of our approach.     

Reservoir description using a binary level set model

We consider the inverse problem of permeability estimation for two-phase flow in porous media. In the parameter estimation process we utilize both data from the wells (production data) and spatially distributed data (from time-lapse seismic data). The problem is solved by approximating the permeability field by a piecewise constant function, where we allow the discontinuity curves to have arbitrary shape with some forced regularity. To achieve this, we have utilized level set functions to represent the permeability field and applied an additional total variation regularization. The optimization problem is solved by a variational augmented Lagrangian approach. A binary level set formulation is used to determine both the curves of discontinuities and the constant values for each region. We do not need any initial guess for the geometries of the discontinuities, only a reasonable guess of the constant levels is required.     

Automated grain boundary detection using the level set method

In this paper, we detect the grain boundary by using a novel automated algorithm which is based on the level set method (the LSM). The LSM starts with only one initial closed curve which can be arbitrary in both shape and location in the microphotograph. The curve splits and merges repeatedly until it reaches the boundaries of the objects. The evolution depends on the structure of the image. This method requires simple and feasible constraints which ensure the exclusion of the objects unsuitable for reliable measurements and strain analysis. The LSM has the following three advantages: (1) with a single image as input, segmentation is automated without human intervention, (2) the grain boundary detected by the LSM is a closed curve, and (3) simple post-processing maintains the shape of the boundary. The segmentation and strain analysis by the LSM are demonstrated and the results are compared with those from hand-drawn method.     

基于H_RLE水平集结构的运动界面追踪研究

为实现快速、高效追踪运动界面,对水平集方法几种常用数据结构进行了研究,选用了H_RLE(分层行程编码)水平集结构作为运动界面存储结构,提出了一种基于H_RLE水平集结构的窄带重构方法,采用只对窄带内元素重新初始化的方法降低了重构窄带的时间复杂度,利用快速粒子水平集方法对旋转Zalesak圆盘界面进行了追踪,结果表明该方法追踪准确,界面所需的存储空间极大的减少了,同时平均处理速度也得到了大幅度的提高.     

区域电网动态仿真系统研究

通过分析目前电网存在的安全问题,讲述了以河北南部电网为仿真对象,研制区域电网动态仿真系统的必要性。该系统采用图形、数据库和仿真模型的一体化技术实现了电网仿真、变电站集控中心仿真和变电站仿真的一体化设计,基于人工智能技术开发了智能化的故障训练系统,同时还基于虚拟现实技术设计了三维互动巡检系统。该系统全面仿真了河北南部电网运行的主要环节,正确反映了变电站、综合自动化系统、集中监控系统、调度SCADA系统和电网的相互关系,提高了整个仿真系统的真实性和正确性。     

Topology optimization of hinge-free compliant mechanisms with multiple outputs using level set method

A method for topology optimization of hinge-free compliant mechanisms with multiple outputs using level set method is presented in this paper. The focus of this paper is on how to prevent generating the flexible hinges during the process of topology optimization of compliant mechanisms. In the proposed method, two types of mean compliances are introduced and built in the proposed multi-objective function for topology optimization of hinge-free compliant mechanisms with multiple outputs, therefore, the spring model widely used for topology optimization of compliant mechanisms is no longer needed. Some numerical examples are presented to illustrate the validity of the proposed method.     

Hybrid control synthesis for eventuality specifications using level set methods

This paper is concerned with the extraction of controllers for hybrid systems with respect to eventuality specifications. Given a hybrid system modelled by a hybrid automaton and a target set of states, the objective is to compute the maximal set of initial states together with the hybrid control policy such that all the trajectories of the controlled system reach the target in finite time. Due to the existence of set-valued disturbance inputs, the problem is studied in a game-theoretic framework. Having shown that a least restrictive solution does not exist, we propose a dynamic programming algorithm that computes the maximal initial set and a controller with the desired property. To implement the algorithm, reachable sets of pursuit-evasion differential games need to be computed. For that reason level set methods are employed, where the boundary of the reachable set is characterized as the zero level set of a Hamilton–Jacobi equation. The procedure for the numerical extraction of the controller is presented in detail and examples illustrate the methodology. Finally, to demonstrate the practical character of our results, a control design problem in the benchmark system of the batch evaporator is considered as an eventuality synthesis problem and solved using the proposed methodology.     

Eigenvalue topology optimization of structures using a parameterized level set method

Preventing a structure from resonance is important in many real-world applications. Because an external excitation frequency can be lower than the fundamental eigenfrequency or between the eigenfrequencies of a structure, there is a strong need for eigenfrequency optimization technology to optimize the fundamental eigenfrequency and, in addition, the k-th eigenfrequency and to maximize the gap between eigenfrequencies. However, previous optimization studies on vibrating elastic structures that used the level set method have been devoted to the optimization of the fundamental eigenfrequency, whereas the higher-order eigenfrequencies optimization problem has seldom been considered. This paper presents an eigenfrequency optimization technology that is based on the compactly supported radial basis functions (CS-RBFs) parameterized level-set method, using the fundamental eigenfrequency, the eigenfrequency of a given higher-order, and the gap between two consecutive eigenfrequencies as the optimization objectives. Furthermore, to address the oscillation problem of the objective function, we adopt an exponential weighted optimization model of a number of the lower eigenfrequencies for multiple eigenvalue optimizations, and we utilize mode-tracking technology for the single eigenvalue optimization.In addition, we further extend the CS-RBFs parameterized level-set method to an optimization that is performed with geometric constraints, which means that the size and position of the regular holes in the structure can be optimized with the shape and topology. This approach is useful in real-world applications. The effectiveness of this method is demonstrated by several widely investigated examples that have various objectives.     

Topological shape optimization of geometrically nonlinear structures using level set method

Using the level set method, a topological shape optimization method is developed for geometrically nonlinear structures in total Lagrangian formulation. The structural boundaries are implicitly represented by the level set function, obtainable from “Hamilton-Jacobi type” equation with “up-wind scheme,” embedded into a fixed initial domain. The method minimizes the compliance through the variations of implicit boundary, satisfying an allowable volume requirement. The required velocity field to solve the Hamilton-Jacobi equation is determined by the descent direction of Lagrangian derived from an optimality condition. Since the homogeneous material property and implicit boundary are utilized, the convergence difficulty is significantly relieved.     

Individual tooth segmentation from CT images using level set method with shape and intensity prior

3D visualization of teeth from CT images provides important assistance for dentists performing orthodontic surgery and treatment. However, dental CT images present several major challenges for the segmentation of tooth, which touches with adjacent teeth as well as surrounding periodontium and jaw bones. Moreover, tooth contour suffers from topological changes and splits into several branches. In this work, we focus on the segmentation of individual teeth with complete crown and root parts. To this end, we propose adaptive active contour tracking algorithms: single level set method tracking for root segmentation to handle the complex image conditions as well as the root branching problem, and coupled level set method tracking for crown segmentation in order to separate the touching teeth and create the virtual common boundaries between them. Furthermore, we improve the variational level set method in several aspects: gradient direction is introduced into the level set framework to prevent catching the surrounding object boundaries; in addition to the shape prior, intensity prior is introduced to provide adaptive shrinking or expanding forces in order to deal with the topological changes. The test results for both tooth segmentation and 3D reconstruction show that the proposed method can visualize individual teeth with high accuracy and efficiency.     

Simultaneous optimization of cast part and parting direction using level set method

Parting direction is one of the main parameters that significantly affect mouldability and manufacturing costs of a cast part. In conventional optimal design of cast part, a parting direction is pre-selected by a designer and fixed throughout the optimization. However, when the optimization is performed with a different parting direction, the resulting design will also be different, and more importantly it will end up with different working performance. Therefore, we take the parting direction as a design variable in the optimization of a cast part so that the working performance can be optimized as much as possible. With these goals, a level set based method is proposed for the simultaneous optimization of cast part and parting direction. In each iteration, an optimal parting direction is first computed for the current structure, then the boundary of the current structure is updated by a design velocity that guarantees the design be moldable with the optimal parting direction. Therefore, although the parting direction may be changed during the optimization, the structure will always be moldable in the current parting direction. Numerical examples are provided in 3D.     

Topology optimization study of arterial bypass configurations using the level set method

We studied the arterial bypass design problem using a level set based topology optimization method. The blood flow in the artery was considered as the non-Newtonian flow governed by the Navier–Stokes equations coupled with the modified Cross model for the shear dependent viscosity. The fluid–solid interface is immersed in the design domain by the level set method and the fictitious porous material method. The sensitivity velocity derived by the level set based continuous adjoint method was utilized to control the evolution of the level set function. In order to accommodate the irregular analysis domains, the flow equations and the level set equations were computed on two different unstructured grids respectively. Three idealized arterial bypass configurations problems with the minimum flow shear stress objective were studied in the numerical examples. The results indicated that the optimal arterial bypass designs can effectively reduce integral of the squared shear rate in the artery and have a superior performance for the arterial grafting.     

Control of linear dynamic systems with set constrained disturbances

A linear dynamic system with input and observation uncertainties is studied. The uncertainties are constrained to be contained in specified sets. No probabilistic structure is assumed. The problem of keeping the state of the system in a specified region is investigated. Necessary and sufficient conditions for a solution to the problem and an algorithm that constructs the control are derived for open-loop and closed-loop control laws. The algorithm is also approximated by a bounding ellipsoid algorithm. Two special control laws, linear and "linear-plus-dead-band," are studied, and the regions that contain the state and control are characterized. Ellipsoids that bound the state and control are also derived, and a simple example of linear and linear-plus-dead-band control laws is presented.     

Fast level set image and video segmentation using new evolution indicator operators

We propose an effective level set evolution method for robust object segmentation in real images. We construct an effective region indicator and an multiscale edge indicator, and use these two indicators to adaptively guide the evolution of the level set function. The multiscale edge indicator is defined in the gradient domain of the multiscale feature-preserving filtered image. The region indicator is built on the similarity map between image pixels and user specified interest regions, where the similarity map is computed using Gaussian Mixture Models (GMM). Then we combine these two methods to develop a new mixing edge stop function, which makes the level set method more robust to initial active contour setting, and forces the level set to evolve adaptively based on the image content. Furthermore, we apply an acceleration approach to speed up our evolution process, which yields real time segmentation performance. Finally, we extend the proposed approach to video segmentation for achieving effective target tracking results. As the results show, our approach is effective for image and video segmentation and works well to accurately detect the complex object boundaries in real-time.