design optimization by using support vector machines · n. strömberg, reliability-based design...
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Design Optimization by usingSupport Vector Machines
NAFEMS NORDIC 18, 24-25 April, Gothenburg
Niclas Strömberg, Ph.D., DocentÖrebro University
www.fema.se
• Computational contactmechanics
• Thermomechnical stresses• Topology optimization• Metamodel-based design
optimization• Reliability-based design
optimization
• TopoBox• MetaBox• BrakeBox
• MT502G - Mechanics• MT504G - Solid mechanics• MT506G - Machine elements
TEACHING
RESEARCH
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Outline• What is support vector machines• Two SVM-based approaches for TO and RBDO• TopoBox – an inhouse toolbox for TO• Orthotropic elasticity with mortar contact conditions• SVM-based postprocessing• MetaBox – an inhouse toolbox for sampling-based DO• Reliability-based design optimization• A new SQP-based RBDO approach• SVM-based limit surface• SVM-based adaptive sampling
Many years ago, deep learning …
N. Strömberg, Simulation of Rotary Draw Bending using Abaqus and a Neural Network, NAFEMS NORDIC, 24-25 November, Gothenburg, 2005.
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Today, support vector machines …
C. Cortes & V. Vapnik, Support-VectorNetworks, Machine Learning, 20, 273–297, 1995.
The kernel trick
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Examples – 2D and 3D bulls eye
SVM-based approaches
SVM-based limit state surfaceSVM-based postprocessing
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TopoBox - inhouse toolbox
Trade-off curve
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Topology optimization of a cutting tool
Lattice structure
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Topology optimization of a stamping die
SVM
Compliance formulation
1 e
For given density distribution, solve the state problem
Sensitivity analysis
Solve LP-problem
Convergence
Update density distribution
STOP
YES
NO
Filter sensitivities
1
0V)(
0)(
s.t. max
e
V
ρ
FdρK
dFρd
Tc ) ,(
min
?
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Maximizing potential energy
N. Strömberg & A. Klarbring, Topology Optimization of Structures in Unilateral Contact, Structural and Multidisciplinary Optimization 41, 57-64, 2010.
N. Strömberg, Topology Optimization of Structures with Manufacturing and Unilateral Contact Constraints by Minimizing an Adjustable Compliance-Volume Product, Structural and Multidisciplinary Optimization 42, 341-350, 2010.
Topology optimization with contact constraints
F
F
F
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Additive manufacturing
A. Jansson, L. Pejryd / Additive Manufacturing 9 (2016) 7–13 www.eos.info
Orthotropic elasticity
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The mortar integralLobatto rule
N. Strömberg, Topology Optimization of Orthotropic Elastic Design Domains with Mortar Contact Conditions, in the proceedings of 12th World Congress on Structural and Multidisciplinary Optimization, Braunschweig, Germany, June 5-9, 2017.
Michell’s benchmark
Michell, A. G. M. (1904) The limits of economy of material in frame-structures, Philosophical Magazine, Vol. 8(47), p. 589-597.
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Different build directions
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.64800
4900
5000
5100
5200
5300
5400
5500
5600
5700
SVM-based postprocessing
N. Strömberg, Automatic Postprocessing of Topology Optimization Solutions by using support vector machines, submitted, 2018.
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Orthotropic elasticity with mortar contacts
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.62.35
2.4
2.45
2.5
2.55
2.6
2.65
2.7
2.75
2.8
2.85105
SVM-based postprocessing
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Metamodel
Metamodel”Black box” Computer experiments DoE
Metabox 1.4
Design of experiments• Linear Koshal• Full factorial• Face centered cubic• Symmetrical Koshal• Quadratic Koshal• Spherical• Box-Behnken• S-optimal• Latin hypercube sampling• Halton sampling• Hammersley sampling
Metamodels• Linear regression• Quadratic regression• OPRM• Kriging with LRM• Kriging with QRM
Metamodels• A priori RBN with LRM• A priori RBN with QRM• A posteriori RBFN with LRM• A posteriori RBFN with QRM• Analytical model• Hybrid model of analytical
model and RBFN• Polynomial chaos expansion• Support vector machines• Support vector regression• Least square SVM & SVR
Solvers• Genetic algorithm• SLP• SQP• Succesive response surface
methodology• Newton’s method
Distributions• Normal• Lognormal• Gumbel• Gamma• Weibull
Solvers• RBDO with SLP• RBDO with SQP• FORM based RBDO• SORM based RBDO• Crude Monte Carlo• Quasi-Monte Carlo• Importance sampling• Multi-classification
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RBDO - an impact problemUnderrun protection system
RBDO - an impact problem
Deterministic
RBDO
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A new SQP-based RBDO approach
N. Strömberg, Reliability-based Design Optimization using SORM and SQP, Structural and Multidisciplinary Optimization, 56, 631–645, 2017.
A new SQP-based RBDO approach
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A new SQP-based RBDO approach
RBDO benchmark
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SVM-based limit surface
N. Strömberg, Reliability-based Design Optimization by using Support Vector Machines, to appear in the proceedings of the European Safety and Reliability Conference ESREL, Trondheim, Norway, 17-21 June, 2018.
SVM-based adaptive sampling
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“The devil is in the details”