iSoGO Symposium on Interdisciplinary
Computation and Optimization
SICO 2014
Yellow Mountain, Anhui, China
December 20-25, 2014
INTERNATIONAL SOCIETY OF GLOBAL OPTIMIZATION
iSoGO Symposium on Interdisciplinary Computation and Optimization
December 20-25, 2014
Organized by:
CAD Center, Huanzhong University of Science &
Technology (HUST)
Tsinghua University
Central South University
Federation University Australia (FedUni)
Australian National University (ANU)
University of Technology, Sydney (UTS)
International Society of Global Optimization (iSoGO)
Yellow Mountain, Anhui, China
SICO 2014 Program
December 22, 2014
17:00-19:30
Onsite Registration and Welcome Reception
December 23, 2014 ( *: invited speaker)
Session A. Chair: David Gao
9:00-9:30
Numerical analysis of fully
anisotropic plane elasticity using
Green’s-functions-based-hybrid
elements
9:30-10:00
Investigation on the fracture
analysis of carbon nanotubes using
the atomic-based cellular automata
algorithm
10:00-10:30
Tea Break
Session B. Chair: Qinghua Qin
10:30-11:00
Multidisciplinary Reliability
Design Optimization with MultiSource Uncertainties
11:00-11:30
Canonical Duality-Triality Theory
for Solving Challenging Problems
in Nonconvex Mechanics with
Applications in Contact Problems
11:30-12:00
Canonical Duality Theory for
Solving Mixed Integer
Programming
Problems with Applications
12:00-14:00
Lunch
Qinghua Qin*
Xiaoqiao He*
Jihong Liu*
David Gao*
Ning Ruan*
Session C. Chair: Liang Gao
14:00-14:30
An extended finite-element method Manman Xu
for unified optimization of
continuum structure
14:30-14:50
A rapid subsystem feasible
Wenqiang Yuan
architecture and solving
approach for multidisciplinary
complex system
14:50-15:10
Sequential Kriging-based
Yaohui Li
Optimization Method with Duality
Transformation for black-box
15:10-15:40
functions
Tea Break
Session D. Chair: Yubo Yuan
15:40-16:00
A metamodel based algorithm for
mixed-integer nonlinear
optimization involving expensively
black-box functions
16:00-16:20
Process Decomposition Method in
MDO based on Interval
Uncertainty
16:20-16:40
An Improved N-dimensional
NURBs-based Metamodel
16:40-17:00
Machinery Equipment Fault
Prediction Research and Prospect
18:00
Symposium Banquet
Haoxing Jie
Ruobing Wang
Zhansi Jiang
Taotao Zhou
December 24, 2014
Session E. Chair: Jihong Liu
9:00-9:30
Trigonometric wavelet finite
element method in structural
analysis
9:30-10:00
A Three-Dimensional
Visualization and Applications for
Big Data Sets
10:00-10:30
Tea Break
Session F. Chair: Xiaoqiao He
10:30-11:00
Integrated design of cellular
materials and structures using the
topological shape optimization
11:00-11:30
Game Analysis on the Extreme
Behavior of Employees in
Enterprise
11:30-12:00
Radial basis functions and their
engineering applications
12:00-14:00
Lunch
Weixin Ren*
YuboYuan*
Liang Gao*
Guoshan Liu*
Zhuojia Fu*
Session G. Chair: Zhuojia Fu
14:00-14:30
WebMWorks: a web-based parallel Xiaoling Yin
computing environment of modeling, simulation and optimization
14:30-14:50
14:50-15:10
15:10-15:40
for multi-domain physical systems
Aerodynamic and Layout
Integration Optimization Design
for Hypersonic Vehicle
Dynamic Response Optimization
under Equivalent Static Loads
Transformed from Dynamic Loads
Based on Volume Strain Energy
Tea Break
Session H. Chair: David Gao (For potential participant)
15:40-16:00
16:00-16:20
16:20-16:40
16:40-17:00
18:00
Symposium dinner
Zhengze Zhao
Jianjian Qin
Abstracts of Invited Speakers
(According to last name)
Radial basis functions and their engineering applications
Zhuo-Jia FU
College of Mechanics and Materials, Hohai University, China
Radial basis functions (RBFs) are constructed in terms of 1D distance variable and appear to
have certain advantages over the traditional coordinates-based functions. In contrast to the
traditional meshed-based methods, the RBF collocation methods are mathematically simple
and truly meshless, which avoid troublesome mesh generation for high-dimensional problems
involving irregular or moving boundary. This talk will firstly introduce several popular RBF
methods, and then present their applications in heat conduction analysis for functionally
graded materials, plate bending analysis, engineering inverse analysis, exterior wave
propagation and anomalous diffusion.
Canonical Duality-Triality Theory for Solving Challenging Problems in Nonconvex
Mechanics with Applications in Contact Problems
David Y. Gao1,2
1. Faculty of Science and Technology, Federation University Australia, Australia
2. Research School of Engineering, Australian National University, Australia
Computational problems in nonconvex mechanics are fundamentally difficult. In large
deformation mechanics, the nonconvexity usually leads to multi-solutions in the related
equilibrium equations. Each of these solutions represents certain possible state or phase of
the system. How to identify the global and local stability and extremality of these critical
solutions is a challenge task. In unilateral buckling of large deformed structures, the
solution could be local minimizer, which is very sensitive to external load. It is wellknown in computational science that traditional numerical approaches for solving
nonconvex minimization problems in global optimization are fundamentally difficult or
even impossible. Therefore, most of nonconvex optimization problems are considered as
NP-hard. Unfortunately, this well-known fact in computer science and global optimization
is not fully recognized in computational mechanics. It turns out that many local search
finite element methods have been used for solving nonconvex large deformation problems.
Canonical duality theory was developed from Gao and Strang’s original work on
nonconvex mechanics in 1989. This potentially useful theory is composed mainly of a
canonical dual transformation methodology, a complementary-dual principle, and a triality
theory. The canonical dual transformation is a versatile method which can be used to
model complex systems and to formulate perfect dual problems within a unified
framework; the complementary-dual principle solved an open problem in nonlinear
elasticity and presents an analytic solution form for general nonconvex problems in
continuous and discrete systems; the triality theory can be used to identify both global and
local extrema, and to develop effective canonical dual algorithms for solving a wide class
of nonconvex/nonsmooth/discrete variational/optimization problems. Combining with
mixed finite element method, a powerful canonical dual finite element method (CD-FEM)
was developed recently, which can be used for solving a large class of nonconvex
mechanics problems.
Starting from some very simple nonconvex problems in phase transitions of Ericksen’s bar
and post-buckling of large deformed beam, the speaker will first explain why most
nonconvex problems are NP-hard. Based on the pure complementary energy principle he
proposed in 1999, a complete set of analytical solutions can be obtained for one-D
problems in phase transitions. He will show that the global optimal solution is usually
nonsmooth and can’t be captured by any Newton type direct methods. For general 3-D
problems, a mixed finite element method and associated primal-dual algorithm will be
presented, which can be used for solving general nonconvex problems in large
deformation theory and complex systems.
He will show that certain unilateral buckling problems of large deformed structures are
NP-hard and can’t be solved by any other direct numerical methods. Finally, the speaker
will present a set of analytical solutions to 3-D nonlinear elasticity governed by St VenantKirchhoff constitutive law.
Integrated design of cellular materials and structures
using the topological shape optimization
Liang Gao
School of Mechanical Science and Engineering,
Huazhong University of Science and Technology, China
Integrated design of cellular materials and structures using the optimization methodology
shows great significance in both science and engineering. As the homogenization method
providing a rigorous way to predict the effective mechanical behavior of the microstructured materials, the topology optimization approaches are successfully used to design
the ultra-lightweight cellular materials to achieve specific multifunctional properties such as
energy absorption, anti-impact and thermal isolation. However, the optimal design will
never be obtained unless the loading and boundary conditions of the macrostructure are
considered. Therefore, this talk will discuss a systematic method to solve the two-scale
integrated design problem. The optimization process is divided into two levels, in which
the first level is macrostructure design by using the SIMP to describe the hierarchical
structural layout with intermediate densities, and the second level is material microstructure
design by integrating the numerical homogenization approach into a powerful parametric
level set method (PLSM). Several numerical cases will be given to showcase the
characteristics of the integrated design method.
Investigation on the fracture analysis of carbon nanotubes
using the atomic-based cellular automata algorithm
Xiaoqiao He
Department of Civil and Architectural Engineering,
City University of Hong Kong, Hong Kong
The cellular automata algorithm is introduced to study the fracture characteristic of carbon
nanotubes (CNTs). With the linkage between the atomistic potential and the classical cellular
automata algorithm, the atomic-based cellular automata algorithm (ACAA) is presented for
fracture analysis of CNTs. In ACAA simulation, a CNT is treated as a discrete hexagonal
system in which the nodes represent the carbon atoms and Tersoff–Brenner’s potential is
adopted to describe the interaction between atoms. The stress–strain response from elastic to
fracture is simulated to examine the effect of a vacancy on the tension characteristic of CNTs.
Simulation results reveal that an initial vacancy lowers tension strength significantly. The
study demonstrates that the ACAA model is an efficient method for fracture analysis of
CNTs.
Game Analysis on the Extreme Behavior of Employees in Enterprise
LIU Guo-shan1, XU Shi-qin1, Wei Zi-qiu2,
1. School of Business, Renmin University of China, China
2. School of Economics and Management, Hebei University of Technology, China
In recent years, events of employees suicide in high-tech enterprises such as Huawei emerge
in a row. Such a phenomenon has become the focus of scholars who have discussed the
reasons behind this sort of suicide and also proposed some measures to keep these extreme
events from occurrence. In this paper, we propose a multi-stage dynamic game model from
the perspective of economics, in which the players are composed of high-tech enterprise and
employees with the tendency of extreme behaviors. It not only reveals the internal mechanism
of such suicides but also effectively explains some points of view raised by other researchers.
The conclusion has laid a theoretical foundation for solving and preventing suicides from
happening and has provided the decision making of the relevant administration and
improvement of legislation with a new analysis tool.
Multidisciplinary Reliability Design Optimization with Multi-Source Uncertainties
Jihong Liu1 and Shikai Jing2
1 Beihang University
2 Beijing Institute of Technology
The complexity of engineering systems is increasing greatly, and more coupled disciplines
and multi-source uncertainties are involved in the design and development of complex
engineered systems (CESs). Actually, uncertainties are ubiquitous in design of CESs, which
can be mainly classified into alteatory uncertainty (AU) and epistemic uncertainty (EU). To
gain high reliability and safety of CESs, the Reliability-based MDO (RBMDO) which
considers uncertainties of design variables and parameters has become a hot research topic.
In this paper, the quantification of aleatory and epistemic uncertainties based on the
probability theory and convex set-theory, multidisciplinary comprehensive reliability
evaluation index, adaptive collaborative optimization strategy based on the intelligent
optimization algorithm, sequential multidisciplinary reliability analysis method based on
the concurrent subspace optimization (CSSO) and performance measure approach (PMA),
and hierarchical and hybrid sequential optimization and reliability assessment (HSORA)
RBMDO strategy under multi-source uncertainties have been researched. All of the
researches can expand and improve the RBMDO theoretical system, and also provide the
effective method for the design and optimization of CESs under multi-source uncertainties.
Numerical analysis of fully anisotropic plane elasticity using
Green’s-functions-based-hybrid elements
Hui Wang 1, Qing-Hua Qin 2*, Yong-Peng Lei 1
1 Institute of Scientific and Engineering Computation, Henna University of Technology,
China
2 Research School of Engineering, Australian National University, Australia
In the paper, a new hybrid polygonal finite element based on anisotropic elastic Green’s
functions was developed for solving displacements and stresses in fully anisotropic plane
elastic materials. In the present hybrid finite element, the element interior displacement and
stress fields were approximated by the linear combination of anisotropic Green’s functions
which were derived by Lekhnitskii potential method related to anisotropic elasticity, while
the independent element frame fields were constructed by the interpolation of general shape
functions popularly used in the conventional finite element method. These two independent
elementary fields were linked by a new double-variable hybrid functional and a stiffness
equation in terms of nodal displacements was obtained. Because the approximated element
interior fields exactly satisfied the governing equations related to anisotropic elasticity, all
integrals in the stiffness equation were performed only along the element boundary. Besides,
the independence of these two elementary fields made that arbitrary-shaped hybrid polygonal
element can be constructed theoretically to achieve such advantages as high accuracy,
versatile element construction and mesh reduction. Finally, the present new hybrid polygonal
element was verified by making comparison of numerical results and exact solutions in an
anisotropic cantilever composite beam under uniform pressure and also the influence of
lamina angle on the anisotropy of materials was investigated.
Trigonometric wavelet finite element method in structural analysis
Wei-Xin Ren
School of Civil Engineering, Hefei University of Technology, China
Canonical Duality Theory for Solving Mixed Integer Programming
Problems with Applications
Ning Ruan1 and David Y. Gao1,2
3. Faculty of Science and Technology, Federation University Australia, Australia
4. Research School of Engineering, Australian National University, Australia
The canonical duality is a breakthrough methodological theory, which can be used to model
complicated phenomena with a unified solution form to a wide class of non-convex/discrete
problems in different fields. It reals an interesting duality pattern in complex systems, which
can be used to identify global extrema and to design efficient algorithms for solving
challenging problems.
Beginning with a simple quadratic 0-1 programming problem, the speaker will show that by
using canonical duality theory, the non-convex integer programming problems can be
reformulated as a concave maximization dual problem in continuous space, which can be
solved easily for many real-world problems.
Then the speaker will address the canonical duality theory for solving mixed integer
programming problem. The speaker will show how the canonical duality theory is precisely
developed, why this theory is efficient for solving mixed integer programming problems.
Applications will be illustrated by a mixed-integer quadratic fixed charge problem and a
general quadratic mixed integer programming problem.
A Three-Dimensional Visualization and Applications for Big Data Sets
Yubo Yuana , Ma Cheng-Longb
a Department of Computer Science and Engineering
East China University of Science and technology, China
b
Center of Research and Innovation
Wonders Information Corporation LTD., China
With the rapid development of information acquiring systems, such as images and videos
obtained by cameras or scanners from the banks, medical institutions, capital markets,
satellite systems, mobile communication, monitoring equipment and so on, every day, we
created 2.5 quintillion (1018) bytes of data. Nowadays, big data has become a hot topic in the
field of data engineering. The existing key issue is that how we can develop effective
software to deal with the problem generated by the decision problem from big data mining,
which is also a difficult problem. From the perspective of data integration, this paper focuses
on the visualization of big data sets in three-dimensional space and the technology to show
the important features or data points. This paper firstly analyzes the construction method of
the 3-D visualization set-valued mapping, and then proposes a 3-D visualization method
which based on K-means clustering method. Its main idea is that we first obtain the cluster
centers after using K-means for these high dimensional data sets, and then project the data
toward these cluster centers' direction respectively. After that, we get the correspondence
between the original data space and the coordinates in 3-D space, a optimization three
dimensional display called as 3-D visualization is done. To verify the effectiveness of this
method, three sections of experiments had been done on many well-known databases. The
first section is from UCI, including ten data sets, such as Iris and Wine and so on. The second
one is web images from Corel5k. The last one is the data set of text documents and is called
as syllabus from the MIT OpenCourse Ware project. All of the results can make sure that the
corresponding similarity of data points or attributes are displayed clearly and show that the
proposed algorithm's feasibility and scalability. Especially, the results on web images and
syllabus are very excellent. As a result, the proposed 3-D visualization method will make
significant influence on data classification and dimensionality reduction.
Abstracts of Contributed Speakers
(According to abstract number)
Machinery Equipment Fault Prediction Research and Prospect
Taotao Zhou1,2,Xianming Zhu1,2, Bo Tian1, Yan Liu1,2, and Weicai Peng1,2
Condition-based maintenance is a decision-making strategy based on real-time diagnosis of
impending failures and prognosis of future equipment health. If done successfully, CBM has
some benefits that reducing catastrophic failures, minimizing maintenance and logistical cost,
maximizing system security and availability and improving platform reliability. A CBM
system usually has four functional modules: feature extraction, diagnostics, prognostics and
decision support. Among them, fault prognostic is the most important enabling technology.
Generally, prognostic techniques can be classified into two categories: model-based
approaches and data-driven approaches. Various techniques and algorithms have been
developed depending on what models they usually adopt. Based on the review of some typical
approaches, advantages and disadvantages of these methodologies are discussed. From the
literature review, some increasing trends appeared in the research field of machine
prognostics are summarized.
Dynamic Response Optimization under Equivalent Static Loads Transformed
from Dynamic Loads Based on Volume Strain Energy
Huping Mao1, Jianjian Qin1, Yangang Zhang1, Jianjun Li2, and Xiaorui Dong1
1. College of Mechanical and Power Engineering, North University of China, China
2. School of Science North University of China, China
According to the complexity of dynamic analysis in the processing of structural dynamic
optimization, transformation method of equivalent static loads from dynamic loads based on
volume strain energy is proposed, and its application to dynamic response optimization.
Firstly, the critical points about dynamic response are identified by the spectral element
discrete of the solution space and Lagrange interpolation. Secondly, the mathematic model
for transformation of equivalent static loads from dynamic loads based on volume strain
energy is constructed by analyzing the relationship between work and volume strain energy.
The equivalent static loads are computed by a new global optimization method, DIRECT
algorithm. Thirdly, the mathematic model for dynamic response optimization is constructed.
Lastly, an examples of the diesel engine piston are used to illustrate the feasibility and
validity of the proposed method.
The Symplectic Method in Polar Coordinates for Linear Viscoelastic Materials
W.X. Zhang, Q.H. Qin and H. Wang
School of Civil Engineering and Architecture, Henan University of Technology, China
Research School of Engineering, Australian National University, Australia
In this study, a symplectic model is developed for analyzing viscoelastic problems with twodimensional annular-sector viscoelastic domain by way of the polar coordinate system and
Laplace transform. Making use of the method of separation of variables, all eigenvectors are
presented analytically. Since the eigenvectors forms a complete solution space, the solution of
the problem can be expressed in terms of linear combination of the eigenvectors. The
corresponding unknown coefficients are determined using prescribed conditions on the
circular boundary. Further, using the variable substitution method, the lateral boundary
conditions are transformed into a particular solution which can be determined by employing
the adjoint symplectic relations between eigenvectors. Numerical examples with some
particular boundary condition are considered to show the applicability and efficiency of the
proposed symplectic method. The symplectic model appears to provide a new numerical
means for solving engineering problems of annular-sector domain.
Solution to Global Minimization of Polynomials by Backward Differential Flow
Jinghao Zhu, Shangrui Zhao and Guohua Liu
Department of Mathematics, Tongji University, China
This paper presents a study on solutions to the global minimization of polynomials. The
backward differential flow by the K–T equation with respect to the optimization problem is
introduced to deal with a ball-constrained optimization problem. The unconstrained
optimization is reduced to a constrained optimization problem which can be solved by a
backward differential flow. Some examples are illustrated with an algorithm for computing
the backward flow.
Process Decomposition Method in MDO based on Interval Uncertainty
Ruobing Wang and Liangxian GU
National Key Labortory of Aerospace Flight Dynamics,
Northwest Polytechnical University, China
To reduce the computational cost of Uncertainty Multidisciplinary Design Optimization
(UMDO), a decomposition method based on interval uncertainty was proposed. In this
method, we constructed the Interval Coupling Strength Design Structure Matrix (ICSDSM) to
evaluate the coupling degree between each pair disciplines and the Interval Computational
Cost Matrix (ICCM) to assess the computational complexity in consideration of the
uncertainty of time-consuming in discipline analysis. Then, the genetic algorithm was
introduced in the decomposition optimization flow to find the best decomposition solution.
The simulation results of optimizing hypersonic flight vehicle by UMDO show that the
method (developed) is universal and easy in application, and it can significantly reduce the
overall computational cost.
Sequential Kriging-based Optimization Method with Duality Transformation
for black-box functions
Yaohui Li1,2, David Y. Gao3, Yizhong Wu1 and Zhengdong Huang1
1 National CAD Supported Software Engineering Centre,
Huazhong University of Science and Technology, China
2 College of Mechanical and Electrical Engineering, Xuchang University, China
3 Federation University Australia, Australia
In this paper, a sequential Kriging-based optimization method with duality transformation
(SKOM-DT), combining Kriging surrogate model, duality-triality theory and trust region
strategy to solve black-box unconstrained optimization problems, is studied. We firstly
introduce the duality-triality theory to transform the non-convex optimization problem based
on Kriging model into a simple convex programing problem in order to quickly get accurate
global minimums. Then, trust region strategy which can improve accuracy and convergence
rate is adopted to find next evaluation point by searching an optimal solution from the
transformed optimization problem. Our proposed method not only can overcome the
computational troubles caused by ill-condition matrix, but also can effectively balance local
and global search capacity. Some well-known numerical test problems and a real engineering
example are investigated to illustrate the applicability, effectiveness and reliability of SKOMDT in contrast with typical EGO (Efficient Global Optimization) method.
A Metamodel Based Algorithm for Mixed-Integer Nnonlinear
Optimization Involving Expensively Black-Box Functions
Haoxiang Jie, Yizhong Wu, Boxing Wang, Liping Chen
National CAD Supported Software Engineering Centre,
Huazhong University of Science and Technology, China
In this paper, we propose a metamodel based optimization method, called as METADIR, to
solve mixed-integer nonlinear optimization involving black-box and computational-expensive
functions. The new proposed method is the extension of AMGO method, which is presented
for unconstrained continuous problems. The METADIR adopts extended DIRECT algorithm
to constantly subdivide the design space and identify the sub-region that may contain the
optimal value. When iterative points gather into a sub-region to some extent, we terminate the
search progress of DIRECT and construct a local metamodel in this potential optimal subregion. And then an auxiliary optimization problem extended from AMGO is established
based on the local metamodel to obtain the iterative points, which are then applied to update
the metamodel. To show the performance of METADIR on both continuous and mixedinteger problems, Numerical tests are presented on both kinds of problems. The METADIR
method is compared with the original DIRECT on continuous problems, and compared with
SO-MI and GA on mixed-integer problems. Test results show that the proposed method has
satisfactory accuracy and needs less function evaluations.
An extended finite-element method for unified optimization of continuum structure
a
a
a
b
ManmanXu , ShutingWang , Tao Liu , JieZhang
a School of Mechanical Science and Engineering, b School of Energy and Power
Engineering, Huazhong University of Science and Technology, China
The aim of this article is to provide a systematic method to perform approach on topology
optimization with zigzag boundary. A modeling method with an extended Finite Element
Method (XFEM) is presented to address the problem of zigzag boundary in topology
optimization by considering parameterized level set method. The difficulties of high-density
mesh and structure re-meshing can be avoided since XFEM grid is independent of the
geometry interface of the structure. Meanwhile, in the XFEM scheme, a level set function is
used to describe the geometry interface, which is unified to the level set model of structural
optimization seamlessly. Two well-studied examples about static and dynamic structural
optimization problems can illustrate the high accuracy and smooth boundary in unified
optimization of this modeling method. It implies that the method can be applied for other
optimization problems.
Aerodynamic and Layout Integration Optimization Design for Hypersonic Vehicle
Cheng-ze Zhao, Liang-xian Gu, Ao Li, Ruo-bing Wang
College of Astronautics, Northwest Polytechnical University, China
Hypersonic vehicle usually adopted the wave-rider or lifting-body configuration which
generally are low in volumetric capacity utility ratio and its capacity changes axially. A large
number of equipments need to be arranged within many constraints. It shows a serious
interdisciplinary cross-coupling among aerodynamic, layout and mass disciplines, etc. The
capacity constraint was connection between aerodynamic and layout in the traditional design,
which always makes a waste of layout space. In this paper, geometric parameters of the
precise shape was passed to the internal layout model, considering the constraint factors of the
aerodynamic, internal equipment size and volumetric capacity, and to synthetically optimize
the shape parameters and internal layout, to make the aircraft haven excellent aerodynamic
performance with greater load capacity, better quality characteristics and handling
characteristics.
Interval-based uncertainty analysis and optimization design for structures
Chao Jiang, Hunan University, China
Uncertainties associated with manufacturing imperfection, usage variation and imprecise
knowledge widely exist in practical engineering problems, and quantifying and controlling
their effects on the structural performance is of great importance for current product design. In
the past decades, the non-probabilistic interval model has been developed for uncertainty
analysis and reliability design, in which the variation bounds of the uncertain parameters are
only required rather than their precise probability distributions. Thus, it provides a potential
and promising way to conduct the reliability analysis and design for many complex problems
with limited experimental samples. In recent years, we conducted a systematic study for
interval-based uncertainty analysis and optimization design, through which we expect to
improve the reliability design level of many complex structures lacking sufficient experiment
data: (1) An interval optimization model was proposed for general nonlinear optimization
problems with uncertainty, through which the uncertain optimization could be transformed to
a conventional deterministic optimization; (2) Several efficient algorithms were formulated to
solve the transformed deterministic optimization which was a complex nesting optimization
problem; (3) A new interval model, namely the multidimensional parallelepiped model, was
proposed to deal with the important multi-source uncertainty problem, based on which an
interval optimization method was also proposed to conduct the optimization design for
structures with both the independent and dependent uncertain parameters; (4) A nonlinear
interval optimization method considering tolerance design was developed, through which we
could not only provide the optimal basic dimensions of the structure but also their maximal
tolerances that the structure could bear; (5) The above developed models and methods were
applied to the uncertainty analysis and design of many practical products and structures, such
as vehicle body, engineering machinery, etc.
WebMWorks: a web-based parallel computing environment of modeling, simulation
and optimization for multi-domain physical systems
Yin Xiao-Liang,Wu Yi-Zhong,Ding Jian-Wan, ChenLi-Ping
National CAD supported software engineering centre,
Huazhong University of Science and Technology, China
To meet with the requirements of modeling, simulation and optimization for multi-domain
physical systems based on Modelica, WebMWorks, a web-based parallel computing
environment has been designed and implemented. Firstly, an interactive graphic user interface
for modeling and post-processing on web browser was implemented where users can build
interdisciplinary model like under the standalone platform. Secondly, Service-Oriented
Architecture (SOA) based architecture was applied to supply compiling and solving services
which run on cloud-like simulation servers, so WebMWorks can manage and dispatch largescale simulation tasks in parallel simultaneously on multiple computing nodes. Lastly, an
RBF-based optimization module was implemented to run on the simulation servers and test
effect of the environment.
Elastodynamic Transformation Method and Perfectly Matched Layers
Zheng Chang1, Gengkai Hu2 and Xi-Qiao Feng1
1 Tsinghua University
2 Beijing Institute of Technology
Manipulating wave by spatially distributing materials is an inverse problem, in which heavy
mathematical algebra is usually involved due to non-unique solution. In this context,
transformation method (TM) provides an effective tool to construct directly one solution of
the above inverse problem for different physics. The key idea of TM is based on the forminvariance of the physical governing equations under a spatial mapping, so a geometric effect
can be mimicked by materials. With this method, many innovative paradigms, such as
invisibility cloaks, have been proposed and experimentally realized. In this talk, we review
some recent results obtained in elastodynamic TM, and report one of its application in the
design and realization of the perfectly matched layer (PML) for elastic waves.
PML is an artificial layer introduced in the simulation of wave propagation as a boundary
condition, which absorbs all incident waves without any reflection. Such a layer is generally
thought to be unrealizable due to its complicated material formulation. In this context, we
introduce complex coordinate transformation into the elastodynamic TM and propose a novel
method to design elastodynamic PML. To simplify the material parameters of the PML, the
conformal transformation technique is applied. As a result, the simplified PML can be
formulated in terms of conventional constitutive parameters and then can be easily realized by
functionally graded viscoelastic materials. We perform numerical simulations to validate the
material realization and performance of this PML.
Robust optimization of components sizing for battery electric vehicles
Yu Limina Xiong Huiyuana,b Zong Zhijiana,b
aCollege of Engineering, Sun Yat-Sen University, China
bInstitute of Dongguan-Sun Yat-Sen University, China
This paper presents a methodology for deriving the robust optimization design of a holistic
components sizing for BEVs. Design parameters are raised based on components analysis and
a multi-objective function including driving range, cycle energy consumption and component
cost is defined. The vehicle dynamic performance requirements are defined as constraints.
Components’ parametric model and vehicle performance simulation model are built based on
Modelica. Adaptive simulated annealing and robust optimization based on six sigma are
carried out respectively to solve the problem. A comparative analysis of the two methods had
been analyzed based on Monte Carlo method. Simulation results showed that 21.6% and 20.6%
of the multi-objective function can be improved in ASA optimal design and six sigma robust
design compared with the original system. Although the robust design had a lower
improvement, the robustness of vehicle performances had been raised effectively. The results
indicate that the overall vehicle performance of robust design scheme achieves high quality
under uncertainty factors.
A rapid subsystem feasible architecture and solving approach
for multidisciplinary complex system
Wenqiang Yuan 1 and Yusheng Liu2
1 Zhejiang University
2 State key Lab. Of CAD &CG
The collaborative optimization design for multidisciplinary engineering system is extremely
complicated, which is decomposed to several individual disciplines for obtaining optimal
solutions, the disciplines take advantage of some couplings for information transfer. However,
the coupling existence leads to iterative solving and more time cost. Some existing strategies
such as discipline reorder, coupling suspension and coupling ignore, can reduce the execution
cost in some degrees using different techniques, meanwhile, these architectures also involve
some drawbacks, such as, low search efficiency because of overwhelmed constraints at the
system level, huge iterative computation time for maintaining the system consistency. In this
study, a new rapid subsystem feasible architecture is proposed, the disciplines are clustered
into some subsystems by analyzing the interdisciplinary sensitivities, the coupling variables
among the subsystems need to be decoupled to ensure the independence each other, for each
subsystem the serialization process is executed to ensure no coupling loops exist and the
subsystem can be solved with no iteration, this strategy can reduce the time cost for solving
the disciplines in a large degree. A local optimization model is constructed for each subsystem,
this strategy is to maintain the scale of the global optimizer and ensure the mutual
independence and parallelism. The proposed three-layer architecture ensures the subsystem
feasibility and improves the execution efficiency. Finally two analytical mathematical
optimization problems and one practical engineering optimization problem are adopted to
demonstrate the effectiveness of the proposed architecture.
An Improved N-dimensional NURBs-based Metamodel
Zhansi Jiang, Liquan Ma and Yanxue Wang
Department of Electromechanical Engineering,
Guilin University of Electronic Technology, China
Non Uniform Rational B-splines (NURBs) are proved to be very promising for metamodeling
in engineering problems, because they have unique properties such as local modification
scheme, strong convex hull property, and infinitely differentiability, etc. Since NURBs are
defined by control points, knot vector, and weights associated with control points, the
precision of NURBs is influenced by all of the parameters. In order to improve the precision
and calculating efficiency, an enhanced method of building NURBs metamodel is presented.
Some improvements are made in many aspects, such as: improving the date normalization
formula and the calculating method of weight coefficient. Compared with the existing
methods, this method can calculation the weight coefficient of each control point more
quickly, because it adopts a new method of calculating the correlation vector and correlation
matrix. It avoids the inverse operation of correlation matrix, which may cause singular.
Several classic numerical examples show that the presented method is effective for building
approximate model with higher accuracy than existing NURBs metamodel.