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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.

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.

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.

The purpose of this study is to develop a hybrid algorithm for segmenting tumor from ultrasound images of the liver.

After collecting the ultrasound images, contrast-limited adaptive histogram equalization approach (CLAHE) is applied as preprocessing, in order to enhance the visual quality of the images that helps in better segmentation. Then, adaptively regularized kernel-based fuzzy C means (ARKFCM) is used to segment tumor from the enhanced image along with local ternary pattern combined with selective level set approaches.

The proposed segmentation algorithm precisely segments the tumor portions from the enhanced images with lower computation cost. The proposed segmentation algorithm is compared with the existing algorithms and ground truth values in terms of Jaccard coefficient, dice coefficient, precision, Matthews correlation coefficient, f-score and accuracy. The experimental analysis shows that the proposed algorithm achieved 99.18% of accuracy and 92.17% of f-score value, which is better than the existing algorithms.

From the experimental analysis, the proposed ARKFCM with enhanced level set algorithm obtained better performance in ultrasound liver tumor segmentation related to graph-based algorithm. However, the proposed algorithm showed 3.11% improvement in dice coefficient compared to graph-based algorithm.

The image preprocessing is carried out using CLAHE algorithm. The preprocessed image is segmented by employing selective level set model and Local Ternary Pattern in ARKFCM algorithm. In this research, the proposed algorithm has advantages such as independence of clustering parameters, robustness in preserving the image details and optimal in finding the threshold value that effectively reduces the computational cost.

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 propose a level set method (LSM) for topology optimization of an electromagnetic system.

The classical shape optimization method has a meshing problem for shape changes and so the level set method is employed to overcome this difficulty, due to its efficient representation of evolving geometry. The velocity field is required to solve the level set equation of the Hamilton‐Jacobi equation. It is obtained using the continuum shape sensitivity in a closed form by the material derivative concept. The optimization problem is modeled as a coupled system of Poisson's equation and the level set equation. They are solved using a standard FEM in the time domain.

Numerical examples are shown to test an optimization problem in the electric and magnetic field system. The design goal is to obtain the maximum torque for an operating electrostatic actuator and synchronous reluctance motor (SynRM), respectively. The results of the optimal shape and topology for electromagnetic system are presented.

This paper presents a theoretical algorithm and numerical techniques for topology optimization of an electromagnetic system to generate the maximum torque using the level set method and design sensitivity analysis.

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.

Fuzzy languages and level sets are defined and illustrated by examples. Properties of level sets are presented. A fuzzy regular language theorem may be proved through the use of the properties of level sets. Level sets offer what appears to be a useful tool in theorem proving in fuzzy languages, pictorial databases, natural language translation and processing, and many others. Through the use of level sets, results obtained in formal languages may be used in fuzzy languages and related areas.

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.

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.