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A regularization scheme for explicit level-set XFEM topology optimization

Markus J. GEISS, Jorge L. BARRERA, Narasimha BODDETI, Kurt MAUTE

《机械工程前沿(英文)》 2019年 第14卷 第2期   页码 153-170 doi: 10.1007/s11465-019-0533-2

摘要: Regularization of the level-set (LS) field is a critical part of LS-based topology optimization (TO) approaches. Traditionally this is achieved by advancing the LS field through the solution of a Hamilton-Jacobi equation combined with a reinitialization scheme. This approach, however, may limit the maximum step size and introduces discontinuities in the design process. Alternatively, energy functionals and intermediate LS value penalizations have been proposed. This paper introduces a novel LS regularization approach based on a signed distance field (SDF) which is applicable to explicit LS-based TO. The SDF is obtained using the heat method (HM) and is reconstructed for every design in the optimization process. The governing equations of the HM, as well as the ones describing the physical response of the system of interest, are discretized by the extended finite element method (XFEM). Numerical examples for problems modeled by linear elasticity, nonlinear hyperelasticity and the incompressible Navier-Stokes equations in two and three dimensions are presented to show the applicability of the proposed scheme to a broad range of design optimization problems.

关键词: level-set regularization     explicit level-sets     XFEM     CutFEM     topology optimization     heat method     signed distance field     nonlinear structural mechanics     fluid mechanics    

Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed

Yingjun WANG,David J. BENSON

《机械工程前沿(英文)》 2016年 第11卷 第4期   页码 328-343 doi: 10.1007/s11465-016-0403-0

摘要:

In this paper, an approach based on the fast point-in-polygon (PIP) algorithm and trimmed elements is proposed for isogeometric topology optimization (TO) with arbitrary geometric constraints. The isogeometric parameterized level-set-based TO method, which directly uses the non-uniform rational basis splines (NURBS) for both level set function (LSF) parameterization and objective function calculation, provides higher accuracy and efficiency than previous methods. The integration of trimmed elements is completed by the efficient quadrature rule that can design the quadrature points and weights for arbitrary geometric shape. Numerical examples demonstrate the efficiency and flexibility of the method.

关键词: isogeometric analysis     topology optimization     level set method     arbitrary geometric constraint     trimmed element    

Level set band method: A combination of density-based and level set methods for the topology optimization

Peng WEI, Wenwen WANG, Yang YANG, Michael Yu WANG

《机械工程前沿(英文)》 2020年 第15卷 第3期   页码 390-405 doi: 10.1007/s11465-020-0588-0

摘要: The level set method (LSM), which is transplanted from the computer graphics field, has been successfully introduced into the structural topology optimization field for about two decades, but it still has not been widely applied to practical engineering problems as density-based methods do. One of the reasons is that it acts as a boundary evolution algorithm, which is not as flexible as density-based methods at controlling topology changes. In this study, a level set band method is proposed to overcome this drawback in handling topology changes in the level set framework. This scheme is proposed to improve the continuity of objective and constraint functions by incorporating one parameter, namely, level set band, to seamlessly combine LSM and density-based method to utilize their advantages. The proposed method demonstrates a flexible topology change by applying a certain size of the level set band and can converge to a clear boundary representation methodology. The method is easy to implement for improving existing LSMs and does not require the introduction of penalization or filtering factors that are prone to numerical issues. Several 2D and 3D numerical examples of compliance minimization problems are studied to illustrate the effects of the proposed method.

关键词: level set method     topology optimization     density-based method     level set band    

XFEM schemes for level set based structural optimization

Li LI, Michael Yu WANG, Peng WEI

《机械工程前沿(英文)》 2012年 第7卷 第4期   页码 335-356 doi: 10.1007/s11465-012-0351-2

摘要:

In this paper, some elegant extended finite element method (XFEM) schemes for level set method structural optimization are proposed. Firstly, two- dimension (2D) and three-dimension (3D) XFEM schemes with partition integral method are developed and numerical examples are employed to evaluate their accuracy, which indicate that an accurate analysis result can be obtained on the structural boundary. Furthermore, the methods for improving the computational accuracy and efficiency of XFEM are studied, which include the XFEM integral scheme without quadrature sub-cells and higher order element XFEM scheme. Numerical examples show that the XFEM scheme without quadrature sub-cells can yield similar accuracy of structural analysis while prominently reducing the time cost and that higher order XFEM elements can improve the computational accuracy of structural analysis in the boundary elements, but the time cost is increasing. Therefore, the balance of time cost between FE system scale and the order of element needs to be discussed. Finally, the reliability and advantages of the proposed XFEM schemes are illustrated with several 2D and 3D mean compliance minimization examples that are widely used in the recent literature of structural topology optimization. All numerical results demonstrate that the proposed XFEM is a promising structural analysis approach for structural optimization with the level set method.

关键词: structural optimization     level set method     extended finite element method (XFEM)     computational accuracy and efficiency    

Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

Manman XU, Shuting WANG, Xianda XIE

《机械工程前沿(英文)》 2019年 第14卷 第2期   页码 222-234 doi: 10.1007/s11465-019-0534-1

摘要: Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises. In this study, we develop an isogeometric analysis (IGA)-based level set model for the formulation and solution of topology optimization in cases with maximum eigenfrequency. The proposed method is based on a combination of level set method and IGA technique, which uses the non-uniform rational B-spline (NURBS), description of geometry, to perform analysis. The same NURBS is used for geometry representation, but also for IGA-based dynamic analysis and parameterization of the level set surface, that is, the level set function. The method is applied to topology optimization problems of maximizing the fundamental eigenfrequency for a given amount of material. A modal track method, that monitors a single target eigenmode is employed to prevent the exchange of eigenmode order number in eigenfrequency optimization. The validity and efficiency of the proposed method are illustrated by benchmark examples.

关键词: topology optimization     level set method     isogeometric analysis     eigenfrequency    

Conceptual design of compliant mechanisms using level set method

Shi-kui CHEN, Michael Yu WANG

《机械工程前沿(英文)》 2006年 第1卷 第2期   页码 131-145 doi: 10.1007/s11465-006-0018-y

摘要: We propose a level set method-based framework for the conceptual design of compliant mechanisms. In this method, the compliant mechanism design problem is recast as an infinite dimensional optimization problem, where the design variable is the geometric shape of the compliant mechanism and the goal is to find a suitable shape in the admissible design space so that the objective functional can reach a minimum. The geometric shape of the compliant mechanism is represented as the zero level set of a one-higher dimensional level set function, and the dynamic variations of the shape are governed by the Hamilton-Jacobi partial differential equation. The application of level set methods endows the optimization process with the particular quality that topological changes of the boundary, such as merging or splitting, can be handled in a natural fashion. By making a connection between the velocity field in the Hamilton-Jacobi partial differential equation with the shape gradient of the objective functional, we go further to transform the optimization problem into that of finding a steady-state solution of the partial differential equation. Besides the above-mentioned methodological issues, some numerical examples together with prototypes are presented to validate the performance of the method.

关键词: splitting     minimum     dimensional optimization     Hamilton-Jacobi     topological    

Concurrent optimization of structural topology and infill properties with a CBF-based level set method

Long JIANG, Yang GUO, Shikui CHEN, Peng WEI, Na LEI, Xianfeng David GU

《机械工程前沿(英文)》 2019年 第14卷 第2期   页码 171-189 doi: 10.1007/s11465-019-0530-5

摘要: In this paper, a parametric level-set-based topology optimization framework is proposed to concurrently optimize the structural topology at the macroscale and the effective infill properties at the micro/meso scale. The concurrent optimization is achieved by a computational framework combining a new parametric level set approach with mathematical programming. Within the proposed framework, both the structural boundary evolution and the effective infill property optimization can be driven by mathematical programming, which is more advantageous compared with the conventional partial differential equation-driven level set approach. Moreover, the proposed approach will be more efficient in handling nonlinear problems with multiple constraints. Instead of using radial basis functions (RBF), in this paper, we propose to construct a new type of cardinal basis functions (CBF) for the level set function parameterization. The proposed CBF parameterization ensures an explicit impose of the lower and upper bounds of the design variables. This overcomes the intrinsic disadvantage of the conventional RBF-based parametric level set method, where the lower and upper bounds of the design variables oftentimes have to be set by trial and error. A variational distance regularization method is utilized in this research to regularize the level set function to be a desired distance-regularized shape. With the distance information embedded in the level set model, the wrapping boundary layer and the interior infill region can be naturally defined. The isotropic infill achieved via the mesoscale topology optimization is conformally fit into the wrapping boundary layer using the shape-preserving conformal mapping method, which leads to a hierarchical physical structure with optimized overall topology and effective infill properties. The proposed method is expected to provide a timely solution to the increasing demand for multiscale and multifunctional structure design.

关键词: concurrent topology optimization     parametric level set method     cardinal basis function     shell-infill structure design     conformal mapping    

Isogeometric analysis based on geometric reconstruction models

《机械工程前沿(英文)》 2021年 第16卷 第4期   页码 782-797 doi: 10.1007/s11465-021-0648-0

摘要: In isogeometric analysis (IGA), the boundary representation of computer-aided design (CAD) and the tensor-product non-uniform rational B-spline structure make the analysis of three-dimensional (3D) problems with irregular geometries difficult. In this paper, an IGA method for complex models is presented by reconstructing analysis-suitable models. The CAD model is represented by boundary polygons or point cloud and is embedded into a regular background grid, and a model reconstruction method is proposed to obtain the level set function of the approximate model, which can be directly used in IGA. Three 3D examples are used to test the proposed method, and the results demonstrate that the proposed method can deal with complex engineering parts reconstructed by boundary polygons or point clouds.

关键词: isogeometric analysis     reconstruction model     level set function     trimmed element     point cloud    

Maximum independent set in planning freight railway transportation

Gainanov Damir N., Mladenovic NENAD, Rasskazova V. A.

《工程管理前沿(英文)》 2018年 第5卷 第4期   页码 499-506 doi: 10.15302/J-FEM-2018031

摘要:

This work is devoted to the problem of planning of freight railway transportation. We define a special conflict graph on the basis of a set of acceptable train routes. The investigation aims to solve the classical combinatorial optimization problem in relation to the maximum independent set of vertices in undirected graphs. The level representation of the graph and its tree are introduced. With use of these constructions, the lower and upper bounds for the number of vertices in the maximum independent set are obtained.

关键词: independent set     algorithm     planning of transportation     two-sided estimate    

Operating mechanism and set pair analysis model of a sustainable water resources system

Chaoyang DU,Jingjie YU,Huaping ZHONG,Dandan WANG

《环境科学与工程前沿(英文)》 2015年 第9卷 第2期   页码 288-297 doi: 10.1007/s11783-014-0642-4

摘要: There is no alternative to the world’s water resources, and their increasing scarcity is making it difficult to meet the world population’s water needs. This paper presents a sustainable water resources system (SWRS) and analyzes the operating mechanism that makes it possible to evaluate the status of such a system. A SWRS can be described as a complex coupling system that integrates water resources, social, economic and ecological systems into a whole. The SWRS’s operating mechanism is composed of dynamic, resistance and coordination components, and it interacts with and controls the system’s evolution process. The study introduces a new approach, set pair analysis theory, to measure the state of a SWRS, and an evaluation index system is established using the subsystems and operating mechanism of a SWRS. The evaluation index system is separated into three levels (goal level, criteria level and index level) and divides the index standard into five grades. An evaluation model of the SWRS based on set pair analysis theory is constructed, and an example of SWRS evaluation in Shanghai is presented. The connection degrees of the index in the three levels are calculated, and the connection degree of the goal index is calculated to be 0.342, which classifies the city’s SWRS condition as grade 2. The sustainable use of water resources in the region is determined to be at a relatively adequate level that meets the requirements of sustainable development.

关键词: sustainable water resources system     operating mechanism     set pair analysis model     Shanghai    

Characteristics of plankton Hg bioaccumulations based on a global data set and the implications for aquatic

《环境科学与工程前沿(英文)》 2022年 第16卷 第3期 doi: 10.1007/s11783-021-1471-x

摘要:

• Hg bioaccumulation by phytoplankton varies among aquatic ecosystems.

关键词: Plankton     Hg bioaccumulation     Physiological characteristics     A cross-system analysis     Nutrient compositions     Global data set    

The research on structural damage identification using rough set and integrated neural network

Juelong LI, Hairui LI, Jianchun XING, Qiliang YANG

《机械工程前沿(英文)》 2013年 第8卷 第3期   页码 305-310 doi: 10.1007/s11465-013-0259-5

摘要:

A huge amount of information and identification accuracy in large civil engineering structural damage identification has not been addressed yet. To efficiently solve this problem, a new damage identification method based on rough set and integrated neural network is first proposed. In brief, rough set was used to reduce attributes so as to decrease spatial dimensions of data and extract effective features. And then the reduced attributes will be put into the sub-neural network. The sub-neural network can give the preliminary diagnosis from different aspects of damage. The decision fusion network will give the final damage identification results. The identification examples show that this method can simplify the redundant information to reduce the neural network model, making full use of the range of information to effectively improve the accuracy of structural damage identification.

关键词: rough set     integrated neural network     damage identification     decision making fusion    

统一集论与人工智能

张江,林华,贺仲雄

《中国工程科学》 2002年 第4卷 第3期   页码 40-47

摘要:

通过综合经典集合、模糊集合、可拓集合、Vague集合、粗糙集合、集对分析、FHW(模糊灰色物元空间)、FEEC(模糊可拓经济控制)等多种理论,提出了统一集概念,并详细讨论统一集的各种运算以及相关性质。从分析集合理论和人类思维形式之间的关系人手,把统一集理论初步应用到模式识别、聚类分析、逻辑推理、机器学习、智能决策等多种人工智能领域,指出了集合论及其运算系统与逻辑推理系统的等价关系。统一集能对现有的理论进行总结、统一,还为开辟崭新的集合论、逻辑推理方法提供很好的理论基础。

关键词: 统一集     人工智能     集合     运算     逻辑推理    

Application of random set method in a deep excavation: based on a case study in Tehran cemented alluvium

Arash SEKHAVATIAN, Asskar Janalizadeh CHOOBBASTI

《结构与土木工程前沿(英文)》 2019年 第13卷 第1期   页码 66-80 doi: 10.1007/s11709-018-0461-y

摘要: The design of high-rise buildings often necessitates ground excavation, where buildings are in close proximity to the construction, thus there is a potential for damage to these structures. This paper studies an efficient user-friendly framework for dealing with uncertainties in a deep excavation in layers of cemented coarse grained soil located in Tehran, Iran by non-deterministic Random Set (RS) method. In order to enhance the acceptability of the method among engineers, a pertinent code was written in FISH language of FLAC2D software which enables the designers to run all simulations simultaneously, without cumbersome procedure of changing input variables in every individual analysis. This could drastically decrease the computational effort and cost imposed to the project, which is of great importance especially to the owners. The results are presented in terms of probability of occurrence and most likely values of the horizontal displacement at top of the wall at every stage of construction. Moreover, a methodology for assessing the credibility of the uncertainty model is presented using a quality indicator. It was concluded that performing RS analysis before the beginning of every stage could cause great economical savings, while improving the safety of the project.

关键词: uncertainty     reliability analysis     deep excavations     random set method     finite difference method    

Data mining diagnosis system based on rough set theory for boilers in thermal power plants

YANG Ping

《机械工程前沿(英文)》 2006年 第1卷 第2期   页码 162-167 doi: 10.1007/s11465-006-0017-z

摘要: Large amounts of data in the SCADA systems databases of thermal power plants have been used for monitoring, control and over-limit alarm, but not for fault diagnosis. Additional tests are often required from the technology support center of manufacturing companies to diagnose faults for large-scale equipment, although these tests are often expensive and involve some risks to equipment. Aimed at difficulties in fault diagnosis for boilers in thermal power plants, a hybrid-intelligence data-mining system based only on acquired data in SCADA systems is structured to extract hidden diagnosis information directly from the SCADA systems databases in thermal power plants. This makes it possible to eliminate additional tests for fault diagnosis. In the system, a focusing quantization algorithm is proposed to discretize all variables in the preparation set to improve resolution near the change between normal value to abnormal value. A reduction algorithm based on rough set theory is designed to find minimum reducts from all discrete variables in the preparation set to represent diagnosis rules succinctly. The diagnosis rules mining from SCADA systems database are expressed directly by variables in the database, making it easy for engineers to understand and use in industry applications. A boiler fault diagnosis system is designed and realized by the proposed approach, its running results in a thermal power plant of Guangdong Province show that the system can satisfy fault diagnosis requirement of large-scale boilers and its accuracy rangers from 91% to 98% in different months.

标题 作者 时间 类型 操作

A regularization scheme for explicit level-set XFEM topology optimization

Markus J. GEISS, Jorge L. BARRERA, Narasimha BODDETI, Kurt MAUTE

期刊论文

Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed

Yingjun WANG,David J. BENSON

期刊论文

Level set band method: A combination of density-based and level set methods for the topology optimization

Peng WEI, Wenwen WANG, Yang YANG, Michael Yu WANG

期刊论文

XFEM schemes for level set based structural optimization

Li LI, Michael Yu WANG, Peng WEI

期刊论文

Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency

Manman XU, Shuting WANG, Xianda XIE

期刊论文

Conceptual design of compliant mechanisms using level set method

Shi-kui CHEN, Michael Yu WANG

期刊论文

Concurrent optimization of structural topology and infill properties with a CBF-based level set method

Long JIANG, Yang GUO, Shikui CHEN, Peng WEI, Na LEI, Xianfeng David GU

期刊论文

Isogeometric analysis based on geometric reconstruction models

期刊论文

Maximum independent set in planning freight railway transportation

Gainanov Damir N., Mladenovic NENAD, Rasskazova V. A.

期刊论文

Operating mechanism and set pair analysis model of a sustainable water resources system

Chaoyang DU,Jingjie YU,Huaping ZHONG,Dandan WANG

期刊论文

Characteristics of plankton Hg bioaccumulations based on a global data set and the implications for aquatic

期刊论文

The research on structural damage identification using rough set and integrated neural network

Juelong LI, Hairui LI, Jianchun XING, Qiliang YANG

期刊论文

统一集论与人工智能

张江,林华,贺仲雄

期刊论文

Application of random set method in a deep excavation: based on a case study in Tehran cemented alluvium

Arash SEKHAVATIAN, Asskar Janalizadeh CHOOBBASTI

期刊论文

Data mining diagnosis system based on rough set theory for boilers in thermal power plants

YANG Ping

期刊论文