Search results

The purpose of this paper is to present a new numerical technique, called adaptive level set method, for use with the finite element method.

A conventional level set method using the smeared Heaviside function has been employed for shape and topology optimizations. The smeared Heaviside function yields an indistinct interface boundary, and so can increase computational time and cause numerical errors. The adaptive level set method does not use the smeared Heaviside function. To coincide with the material interface, it processes the zero level as the boundary data of element meshing.

Usefulness and accuracy of shape optimization using the adaptive level set method are shown by comparison to the conventional level set method. A shape optimization procedure using the adaptive level set method is introduced. Numerical examples are employed to explain how the adaptive level set method is applied.

The adaptive level set method is proposed to relieve the interface problem of the conventional level set method. Shape variation in the optimization is calculated from the continuum sensitivity analysis.

Shape optimization using the level-set method is one of the most effective automatic design tools for electromagnetic machines. While level-set method has the advantage of being able to suppress unfeasible shape, it has a weakness of being unable to handle complex topology changes such as perforate at material region. With this method, it is only possible to define simple connected topology, and it is difficult to determine the optimal shape which has holes. Therefore, it is important to efficiently expand the searching area in the optimization process with level-set method.

In this paper, the authors introduce the newly defined hole sensitivity which is based on concept of topological derivatives, and combine it with level-set method to effectively create holes in the search process. Furthermore, they consider a variable bandwidth of gray scale, which indicates the transition width between air and magnetic body and combine it with the hole creation method described above. With these methods, the authors aim to expand the searching area in comparison with the conventional level-set method.

As a result of applying the proposed methods to a magnetic shielding problem, the multi-layered shielding which effectively reduces the magnetic flux in the target area, is successfully produced.

The proposed methods enable us to effectively create a hole and to expand the searching area in the topology optimization process unlike in the case of conventional level-set method.

Conventional level-set method tends to fall into local optima because optimization is conducted based on gradient method. The purpose of this paper is to develop a novel topology optimization in which simulated annealing (SA) is introduced to overcome the difficulties in level-set method.

Level-set based topology optimization for two-dimensional optimization problem.

It is shown in the numerical examples, where conventional and present methods are applied to shape optimization of ferrite inductor and Interior Permanent Magnetic (IPM)-motor, the present method can find solutions with better performance than those obtained by the conventional method.

SA is introduced to improve the search performances of level-set method.

The performance of three frequently used level set-based segmentation methods is examined for the purpose of defining features and boundary conditions for image-based Eulerian fluid and solid mechanics models. The focus of the evaluation is to identify an approach that produces the best geometric representation from a computational fluid/solid modeling point of view. In particular, extraction of geometries from a wide variety of imaging modalities and noise intensities, to supply to an immersed boundary approach, is targeted.

Two- and three-dimensional images, acquired from optical, X-ray CT, and ultrasound imaging modalities, are segmented with active contours, k-means, and adaptive clustering methods. Segmentation contours are converted to level sets and smoothed as necessary for use in fluid/solid simulations. Results produced by the three approaches are compared visually and with contrast ratio, signal-to-noise ratio, and contrast-to-noise ratio measures.

While the active contours method possesses built-in smoothing and regularization and produces continuous contours, the clustering methods (k-means and adaptive clustering) produce discrete (pixelated) contours that require smoothing using speckle-reducing anisotropic diffusion (SRAD). Thus, for images with high contrast and low to moderate noise, active contours are generally preferable. However, adaptive clustering is found to be far superior to the other two methods for images possessing high levels of noise and global intensity variations, due to its more sophisticated use of local pixel/voxel intensity statistics.

It is often difficult to know a priori which segmentation will perform best for a given image type, particularly when geometric modeling is the ultimate goal. This work offers insight to the algorithm selection process, as well as outlining a practical framework for generating useful geometric surfaces in an Eulerian setting.

The segmentation of printed circuit board (PCB) images is an important process in PCB inspection. The circuit traces, pads and vias in a PCB are dense and curved, and the PCB image obtained using different cameras or in different conditions may exhibit a large image gradient, which leads to inaccuracy and inefficiency in the PCB image segmentation. This paper aims to propose an improved local binary fitting level set method with prior graph cut, aiming to improve the accuracy and efficiency of the segmentation of PCB images obtained using different cameras or in different environments.

First, the paper constructs a 4-connected undirected graph using a given PCB image and classifies it based on the graph cut. Second, an adaptive initialization level set is implemented using the priori information obtained from the graph cut. Finally, the paper constructs a priori energy term using the prior information and introduces it into the energy function of the level set.

The approach results in an improved accuracy of segmentation in the context of a large gradient within the image. Experimental results demonstrate that the method can solve the deviation of artificially initialized level set from targets and improve the efficiency and accuracy of segmentation.

This study only considers level set method as the research object. Iteration of the level set method takes a long time for a given huge PCB picture, which makes it impossible to apply to scenes with high real-time requirements.

PCB image segmentation is an important process in the PCB inspection. Since template matching and morphology techniques are well-established, image segmentation quality has a significant impact on the accuracy of detection.

This paper studies the segmentation of PCB images, improves the efficiency and accuracy of segmentation and facilitates the subsequent applications, such as in the nondestructive testing of PCB.

The purpose of this paper is to develop the numerical simulated methodology for sloshing motion of fluid inside a two dimension rectangular tank, and parametric studies were performed for three parameters – excitation frequency, excitation amplitude, and liquid depth.

A numerically simulated methodology by using the cell‐centered pressure‐based SIMPLE scheme and level set method for the sloshing motion of fluid in a rectangular tank has been developed. The convection term in the Navier‐Stokes equations and the equations used in the level set method were treated by the second‐order upwind scheme. The temporal derivative terms were solved by the three‐level second order scheme. The diffusion term in the Navier‐Stokes equations alone was solved by the central‐difference scheme. All algebraic equations were solved by the point Gauss‐Seidel method. A fully implicit scheme to treat the level set distancing equation, written as the advection equation, was developed. In addition, the level set distancing equation was solved by the iterative procedure to determine the variation of free surface.

For given excitation amplitude together with a liquid depth, the free surface displacement increases when the excitation frequency is less than the resonance frequency of tank. However, the free surface displacement decreases when the excitation is greater than the resonant frequency of the tank. It is noted that the maximum free surface displacement is generated under the circumstance for which the excitation frequency approaches the resonant frequency. The excitation amplitude and the excitation frequency have a substantial effect on the impact pressure on the wall of the tank being investigated.

The sloshing motion of fluid in a rectangular tank has been studied by researchers and scholars using many numerical methods; however, literature employing the level set method to study the sloshing motion of fluid is limited. In this study, the cell‐centered pressure‐based SIMPLE scheme and level set method can be employed to predict the sloshing motion. The numerical methodology can help the engineer to predict sloshing motion of fluid.

Moving interface problems exist commonly in nature and industry, and the main difficulty is to represent the interface. The purpose of this paper is to capture the accurate interface, a novel three-dimensional one-layer particle level set (OPLS) method is presented by introducing Lagrangian particles to reconstruct the seriously distorted level set function.

First, the interface is captured by the level set method. Then, the interface is corrected with only one-layer particles advected with the flow to ensure that the level set function value of the particle is equal to 0. When interfaces are merged, all particles in merged regions are deleted, while the added particles near the generated interface are used to determine the interface as the interface is separated.

The OPLS method is validated with well-known benchmark examples, such as the long-term advection of a sphere, the rotation of a three-dimensional slotted disk and sphere, single vortex in a box, sphere merging and separation, deformation of a sphere. The simulation results indicate that the proposed method is found to be highly reliable and accurate.

This method exhibits excellent conservation of the area bounded by the interface. The extraordinary performance is also shown in dealing with complex interface topological changes.

Structural performance of additively manufactured parts is deposition path-dependent because of the induced material anisotropy. Hence, this paper aims to contribute a novel idea of concurrently performing the deposition path planning and the structural topology optimization for additively manufactured parts.

The concurrent process is performed under a unified level set framework that: the deposition paths are calculated by extracting the iso-value level set contours, and the induced anisotropic material properties are accounted for by the level set topology optimization algorithm. In addition, the fixed-geometry deposition path optimization problem is studied. It is challenging because updating the zero-value level set contour cannot effectively achieve the global orientation control. To fix this problem, a level set-based multi-step method is proposed, and it is proved to be effective.

The proposed concurrent design method has been successfully applied to designing additively manufactured parts. The majority of the planned deposition paths well match the principle stress direction, which, to the largest extent, enhances the structural performance. For the fixed geometry problems, fast and smooth convergences have been observed.

The concurrent deposition path planning and structural topology optimization method is, for the first time, developed and effectively implemented. The fixed-geometry deposition path optimization problem is solved through a novel level set-based multi-step method.

The purpose of this paper is to develop an effective numerical algorithm for a gas-melt two-phase flow and use it to simulate a polymer melt filling process. Moreover, the suggested algorithm can deal with the moving interface and discontinuities of unknowns across the interface.

The algebraic sub-grid scales-variational multi-scale (ASGS-VMS) finite element method is used to solve the polymer melt filling process. Meanwhile, the time is discretized using the Crank–Nicolson-based split fractional step algorithm to reduce the computational time. The improved level set method is used to capture the melt front interface, and the related equations are discretized by the second-order Taylor–Galerkin scheme in space and the third-order total variation diminishing Runge–Kutta scheme in time.

The numerical method is validated by the benchmark problem. Moreover, the viscoelastic polymer melt filling process is investigated in a rectangular cavity. The front interface, pressure field and flow-induced stresses of polymer melt during the filling process are predicted. Overall, this paper presents a VMS method for polymer injection molding. The present numerical method is extremely suitable for two free surface problems.

For the first time ever, the ASGS-VMS finite element method is performed for the two-phase flow of polymer melt filling process, and an effective numerical method is designed to catch the moving surface.

In this paper, a numerical approach to the topology optimization is proposed to design the permanent magnet excited machines with improved high-speed features. For this purpose the modified multi-level set method (MLSM) was proposed and applied to capture the shape of rotor poles on the fixed mesh using FE analysis. The paper aims to discuss these issues.

This framework is based on theories of topological and shape derivative for the magnetostatic system. During the iterative optimization process, the shape of rotor poles and its evolution is represented by the level sets of a continuous level set function f. The shape optimization of the iron and the magnet rotor poles is provided by the combining continuum design sensitivity analysis with level set method.

To obtain an innovative design of the rotor poles composed of different materials, the modified MLSM is proposed. An essential advantage of the proposed method is its ability to handle a topology change on a fixed mesh by the nucleating a small hole in design domain that leads to more efficient computational scheme then standard level set method.

The proposed numerical approach to the topology design of the 3D model of a PM machine is based on the simplified 2D model under assumption that the eddy currents in both the magnet and iron parts are neglected.

The novel aspect of the proposed method is the incorporation of the Total Variation regularization in the MLSM, which distribution is additionally modified by the gradient derivative information, in order to stabilize the optimization process and penalize oscillations without smoothing edges.