experience in mathematical optimization
DESCRIPTION
Wells-Tool. Experience in mathematical optimization. Automatic shape optimisation. parameterized geometry. Directe optimisation “Response Surface” method Estimation of an continous approximate function by Neuronal net Polynomial approach Spline - PowerPoint PPT PresentationTRANSCRIPT
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Experience in mathematical optimization
Automatic shape optimisation
parameterized geometry
Wells-Tool
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Optimisation Methods
• Directe optimisation• “Response Surface” method
– Estimation of an continous approximate function by• Neuronal net• Polynomial approach• Spline
– Search for the optimum of the approximate function
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Parameter
Qu
alit
äts
fun
ktio
nberechnete Werte
Optimierung an der Response Surface
Response Surface Methode
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
1
2
3
assumed optimum
search direction
cost
fu
nct
ion
relaxation
• Gradient type algorithmus, with search direction• Opjective funktion is locally approximated and the minimum is
calculated along the search direction
EXTREME
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Self Adaptive Evolution (SAE)
• Start with a randomly chosen population
• New population is obtained by
– Mutation
– Crossover
– Survival of the fittest– Live time of each individual is exactly 1 generation
(Comma Strategie)
Evolution methode
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Parallel Optimisation
simultaneous simulation on different resources
each simulation is run in parallel
Research: Asynchronous, parallel optimisation
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Parallel OptimisationGrid Compting
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Applied Algorithm
randomly choseninitial parameter sets
CFD
CFD
CFD
CFD
CFD
survival of the fittest
new sets by discrete operation, e. g. mirror
new sets randomlywith weighting
CFD
CFD
CFD
CFD
gri
d p
ort
al
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Example Guide vane shape
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Guide vane geometry
Inlet angle, Outlet angle,
chamber line angle, Weighting factor inlet,
Weighting factor outlet,Overlapping,
Profile a, Profile b,
Trailing edge thickness
Geometry Parameterisation
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Automatic block structured mesh
Automatic Grid Generation
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Simulation
Results:
Flow patterns (e. g pressure distribution)
Overall quantities (e. g. efficiency, losses)
Restrictions (e. g. cavitation)
Typical computational time for one geometry: 1-4 hon a Cluster of HPC
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
9 free parameters:
- 45 different designs (individuals) per generation
- 8 generations- in total 360 calculations
Guide vane shape
optimized with evolution strategy
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Convergence
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Optimised Geometrie
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Test example: Draft tube cone
Assumption:Cone length
Optimisation: Outlet diameter
L
Din
Dout
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
0.4
0.5
0.6
0.7
0.8
0.9
1
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
Dra
ft tu
be e
ffici
ency
D_out/D_in
Test example: Draft tube cone
randomly chosen starting points
Cone length: 6 D_in
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
0.4
0.5
0.6
0.7
0.8
0.9
1
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
Dra
ft tu
be e
ffici
ency
D_out/D_in
Test example: Draft tube cone
survivors of the first generation
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
0.4
0.5
0.6
0.7
0.8
0.9
1
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
Dra
ft tu
be e
ffici
ency
D_out/D_in
Test example: Draft tube cone
survivors of the second generation
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
0.4
0.5
0.6
0.7
0.8
0.9
1
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
Dra
ft tu
be e
ffici
ency
D_out/D_in
Test example: Draft tube cone
survivors of the third generation
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
0.4
0.5
0.6
0.7
0.8
0.9
1
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
Dra
ft tu
be e
ffici
ency
D_out/D_in
Test example: Draft tube cone
computed pointssurvivors of the seventh generation
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
The draft tube contour can only be changed slightly.
Optimization of the area distribution
Draft tube area distribution
Application: Refurbishment of an existing power plant
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Area
Draft tube length length
area distribution
• Area distribution represented by B-Spline curves • Inlet and outlet kept constant• other cross sections scaled up
Draft tube area distribution
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Draft tube area distribution
Investigated area distribution during the optimisation
Design point
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
Draft tube area distribution
Design point
Obtained area distribution
original draft tube
maximum efficiency
minimum efficiency
draft tube efficiency increase: 8%overall efficiency increase: 0.4%
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IHS-Präsentation, 2008Ruprecht
University of StuttgartInstitute of Fluid Mechanics and Hydraulic Machinery, GermanyIHS
minimum efficiency
Overload
design point
part load
original draft tube
Draft tube area distribution