Elti &Gdi tEvolutionary & Gradient-BdBased Optimization in ... · Elti &Gdi tEvolutionary &...

NATIONAL TECHNICAL UNIVERSITY OF ATHENSParallel CFD & Optimization Unit

Laboratory of Thermal Turbomachines

E l ti & G di t B dEvolutionary & Gradient-BasedOptimization in Engineering –

Methods & Industrial Applications

Kyriakos C. GIANNAKOGLOU, Professor [email protected]

http://velos0.ltt.mech.ntua.gr/research/http://velos0.ltt.mech.ntua.gr/research/

The Parallel CFD & Optimization Unit of NTUA

Research Activities: Development and parallelization (on CPUs and GPUs) of:

1. In-house aero-thermal analysis software (mostly CFD a/w),1. In house aero thermal analysis software (mostly CFD a/w),2. An optimization platform based on enhanced evolutionary algorithms, 3. Optimization tools based on adjoint methods for fluid flow/heat applications,4. Hybrid (gradient-based & stochastic) optimization methods.y (g ) p

Applications in: turbomachines, aircraft/car aerodynamics, energy production & management systems, etc

Research Group:p

~12 researchers

Funding:

EU Projects (FP6/7: HISAC ACFA HYDROACTION AQUAGEN RBF4AERO)EU Projects (FP6/7: HISAC, ACFA, HYDROACTION, AQUAGEN, RBF4AERO),projects funded directly by the Industry (Dassault Aviation, Volkswagen, Andritz Hydro,Schlumberger, etc), software developers & vendors (ICON, NUMECA, SOFISTIK, etc),state research projects Greek companies (Hellenic Aerospace Industry Public Powerstate research projects, Greek companies (Hellenic Aerospace Industry, Public PowerCorporation, various SMEs). Income from selling the optimization software EASY(provided at zero cost to University groups and a symbolic cost tocompanies/industries).

Parallel CFD & Optimization Unit, NTUA, Greece 2

companies/industries).

Outline

►Brief Introduction to Optimization methods:From the Analysis to the Optimization, without (??) extra pain!

►Gradient based & Gradient free methods:►Gradient-based & Gradient-free methods:Selecting the most appropriate Optimization method is important!Commercial or In-house (with access to its source code) Analysis s/w?Generic of tailored to the problem Optimization method?Generic of tailored to the problem Optimization method?Single- or Multi-Objective Optimization, Multi-Disciplinary Optimization.Important criterion: the number of design variables (optimization unknowns).Computational cost of Optimization methods (and its reduction).p p ( )Hybridization!

►Industrial Optimization– Suggestions, ideas & recipes:Relevant or irrelevant cases to the themes discussed in this event.Optimization in Aerodynamics/fluid mechanics always shows us the way!!

►Modern research areas in Optimization methods:Optimization of unsteady/transient processes…Optimization of processes involving multiphase flows, chemical reactions…Robust Optimization, Optimization under Uncertainties…Methods for low-cost computation of high-order derivatives…


Optimization Methods – Prerequisites / Classification

F(b)

(1) Problem Parameterization(2) Objective(s) – Objective Function(s)(2) Objective(s) Objective Function(s)(3) Constraint(s), equality-inequality, if any…(4) Evaluation-analysis software(5) Optimization-search method( ) p(6) (in most cases) An adequately powerful computer

Gradient-Free Methods(Stochastic optimization methods)

b

Gradient-Based Methods(Steepest Descent, CG, etc)( i di )

Individual-Based Methods

Population Based Methods(exact or approximate gradient)

Hessian-Based Methods(N t Q i N t th d )

Population-Based Methods

Hybridization!


(Newton or Quasi-Newton methods)(exact or approximate Hessian)

Hybridization!

Multi-Objective Optimization

F2min F1, min F2

Pareto Front F1


PART I: Stochastic Optimization methods

• Evolutionary Algorithms (EAs)

• Differential Evolution (DE)

• Particle-Swarm Optimization (PSO)Particle-Swarm Optimization (PSO)

• Ant-Colony Optimization (ACO)

• etc.

Population-based, randomized search of the design space.

Suitable for multi-objective and multi-disciplinary optimization problems.j p y p p

Pro(s): Gradient-Free, Plug&Play way of accommodating existing/commercial analysistools directly amenable to parallelizationtools, directly amenable to parallelization.

Con(s): Computationally expensive unless coupled with “computational intelligence”techniques.


(μ, λ) Evolutionary Algorithms (EAs) at a Glance

Offspring population(λ individuals)

Mutation( )

Evaluation(λ calls to the evaluation s/w)

Parent Selection CParent Selection(μ parents)

Crossover-Recombination

The (μ,λ) ΕΑ can reproduce almost any other known evolutionary algorithm, such asG i Al i h E l i S i


Genetic Algorithms, Evolution Strategies, etc.

Metamodel-Assisted EAs (MAEAs)

Problem-Specific Evaluation Model

(Exact/Costly Model)

SurrogateEvaluation Model

(Approximate/Cheap Model)(Approximate/Cheap Model)Performance

F

Design Variable

b

In each generation, instead of performing λ calls to the exact-costly evaluation s/w, themetamodel or surrogate evaluation model (less accurate, cheaper) is used to pre-

l h l i b Th l h λ λ f h l d


evaluate the population members. Then, only, the top λe<<λ of them are evaluated onthe expensive s/w.

MAEAs with Inexact Pre-Evaluation (IPE)

λ evaluations

Generation 1Generation 2

Generation 1Generation 3

IPE starts herestarts hereλe<<λ evaluations

Generation 4Generation 5Generation 6 Generation 4Generation 5Generation 6

More generations are needed; however, apart from the very first ones, the number ofcalls to the e pensi e e al ation tool per generation red ces to λ <<λ The al e of λ


calls to the expensive evaluation tool per generation reduces to λe<<λ. The value of λe

and the first generation relying upon IPE are user-controlled parameters.

Distributed Metamodel-Assisted EAs (DMAEAs)

Adjustable Parameters:j

Number of demes or islands

Communication topology

C i i fCommunication frequency

Migration algorithm

EA set-up per deme

A DEA or DMAEA with distinct exploration- & exploitation-oriented subpopulations is


p p p pa very efficient search method!

Expected Gain from DMAEAs

Standard EAMetamodel-Assisted EA (MAEA)Distributed EA (DEA)( )Distributed MAEA (DMAEA)

E l tiEvaluations

Similar behavior can be found in many other cases! A well-tuned DMAEA constantly


y youtperforms other variants, such as EAs, DEAs or MAEAs.

Optimization Study in Marine Engines

Marine Diesel Oil (MDO) combustion in a large two-stroke marine Diesel engine

Maker: Wärtsilä Switzerland

2 TType

2-TRT-flex58T-B

Bore 580 mm

Stroke 2416 mmStroke 2416 mm

Speed 105 RPM

Max. power output 2125 KW/cyl

Injection system Common Rail

Number of injectors 3

Improvement of the operation of a large two stroke marine diesel engine at full loadImprovement of the operation of a large two-stroke marine diesel engine, at full load,by implementing pilot injection, using CFD and EAs. The problem is solved as a two-objective optimization one: (a) min. NOx concentration & (b) min. specific fuel oilconsumption (SFOC); both are normalized with the corresponding values forconsumption (SFOC); both are normalized with the corresponding values forcontinuous injection (reference case). The main and pilot injection profiles areparameterized in terms of four design variables.

Evaluation Code (CFD) : KIVA 3Division of Marine EngineeringSchool of Naval Architecture &

12Parallel CFD & Optimization Unit, NTUA, Greece 12

Evaluation Code (CFD) : KIVA 3.Optimization S/W : EASY

Marine Engineering, NTUAProf. L. Kaiktsis


Design-Optimization Variables:

SOPI : Start Of the Pilot Injection

SOMI : St rt Of the M in InjectionSOMI : Start Of the Main Injection

PMF : Pilot Mass Fraction injected as part of the total fuel amount

MR : Total injected Mass Reduction with respect to the reference case ofcontinuous injection.

Fuel injection profile

Studies with single- and twin-needleinjectors will be presented. A twin-needle

Division of Marine EngineeringSchool of Naval Architecture &

j pinjector allows different orientation of fuelinjection for the pilot and main injection.




MDO combustion in RT-flex58T-B under Partially Premixed Compression IgnitionPilot

InjectionMain Injection

A lAngle α

Angle β

Spatial distribution of temperaturePilot

InjectionMain

Injection Twin-needle injectorj j





7

Case H102

103

ReferenceUnconstrained Case of Present StudyUnconstrained Case of Andreadis et al.Pareto fronts

Results of Unconstrained & Constrained Optimization using EAs

4

5

6

eat R

elea

se

Reference

99

100

101

efer

ence

Cas

e]

Constrained Case of Present study (Pressure, Work) Constrained Case of Andreadis et al. (Pressure, Work)

H I

KJ

1

2

3

Rat

e of

He

97

98

99

SFO

C [%

of R

e K

EF G

-40 -20 0 20 40 600

Crank Angle [deg.]

75 80 85 90 95 100 10595

96

NOx [% of Reference Case]

G





S i d i il i j iSpray propagation during pilot injection

Andreadis et al. Int. J. Engine Research

Pananakis et al. 25th ILASS Conf. (2013)

C H● Utilization of available

cylinder volume

(2011) Case C

Case H

● No impact of fuel oncylinder wall

● Hi h di i

● Fuel liquid films oncylinder wall

● Higher dispersion of fuel droplets

● Good air-fuel mixingduring pilot injection

The pilot injection parameters are very similar but the injection angles are substantially different, since single-needle injectors are considered in Case C, where pilot injection , g j , p jis associated with wall wetting, with fuel still remaining in the near-wall region at the Top Dead Center (TDC). This is avoided for injection from twin needle valves, due to the modified injection angles.



Thus, in Case H, a Partially Premixed Compression Ignition (PPCI) is attained.


Biomass Pyrolysis Process

Use of EA for the determination of a kinetic model and its parameters, to be used in biomass pyrolysis process.

Fuel : Straw

Experimental thermogravimetric analysis (TGA) using a heating rate of 10 oC/min

To describe the mass loss during pyrolysis an independent parallel reaction modelTo describe the mass loss during pyrolysis, an independent parallel reaction modelwas adopted and mathematically fitted, in order to determine its constants (usingEas, namely EASY).

Biomass pyrolysis is modeled using three (N=3) components: HemicelluloseBiomass pyrolysis is modeled using three (N=3) components: Hemicellulose,Cellulose and Lignin.

Lab. Steam BoilersSchool of Mechanical


School of Mechanical Engineering, NTUA

Prof. S. Karellas


Overall (mass loss) rate of

Independent Parallel Reaction Model

Thermal decomposition of the( )conversion for N reactions:

)1(, RTE

ji aeAda

j

i

−=−

Nida

cdm jij 1, == ∑

pindividual components

)1( , jii aeAdt

=Nidt

cdt i

i ,..,1, == ∑

9 Design variables: Determine the contribution (c) of each component

iii AEc ,, to dm/dt, the activation energy (E) and pre-exponential factor (A).

Objective Function: 2

1.min ∑

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛=

K

j

jjobj dt

dmdt

dmF

1 exp= ⎥⎦

⎢⎣ ⎠⎝⎠⎝j compdtdt




Prof. S. Karellas


Optimization Results – DMAEA vs. EA Optimal Solution




Prof. S. Karellas

Design of HYDROMATRIX®

The design of a Hydromatrix® which comprises a number of “small” axial flowThe design of a Hydromatrix®, which comprises a number of small axial flowturbine generator units forming a factory-assembled grid or “matrix”, was carried outin Andritz-Hydro, using EASY. A Hydromatrix® has a lot of advantages compared toconventional designs (lower cost to power ratio): min. civil construction works, min.


conventional designs (lower cost to power ratio): min. civil construction works, min.time for project schedules, construction & installation, min. environmental inflict, etc.


Objectives (metrics):Objectives 1/2 (f1,f2) : Given swirl and axial velocity distributions at the exitaxial velocity distributions at the exit

Objective 3 (f2): Uniform loading

Objective 4 (f4): Cavitation indexFullLoad

Objective 5 (f5): Pumping area

PartLoad

BestEffic

Th H d i ® bl d d l d i 52 d iThe Hydromatrix® runner blade was modeled using 52 designvariables and the design was carried out with 5 objectives, at 3operating points. EASY handled this design problem as a two-

bj ti ( i i ht )


objective case (via weights):

(a) min. F1(f1,f2, at the 3 OPs) & (b) min. F2(f3,f4,f5, at the 3 OPs)


F2

F1

EAs or MAEAs with the PCA of design variables:EAs or MAEAs with the PCA of design variables:

With the same computing cost (number of evaluations), the MAEA with PCAassisting the evolution operators outperforms MAEA. The computed fronts of non-dominated solutions by the two methods at the same cost are shown for the


dominated solutions by the two methods, at the same cost, are shown for theHydromatrix® runner design problem.

Design-Optimization of a Francis Runner

The design of the Francis runner, at 3 operating points, was carried out by Andritz-Hydro, with two objectives: (a) exit velocity profiles’ quality and (b) uniformity of the blade loading and two constraints (head and cavitation). There are 372 design variables, in total!

Due to the extremely high problem dimension, the Principal Component Analysis (PCA) of the continuously evolving front of non-

dominated solutions assists (a) the application of the evolution operators (EA(PCA) or MAEA(PCA)) and (b) the metamodel training


by cutting off the less important components of the training patterns (M(PCA)AEA). Both are combined in M(PCA)AEA(PCA).

Optimization of Geothermal ORC Systems

y

R-134aR-410AR-407C

all e

ffic

ien

c R-600a

Ove

r

Design- Optimization of an innovative Organic Rankine Cycle (ORC) System for electricity production using low-enthalpy geothermal energy, with three objectives. Design carried out at the Center for Renewable Energy Sources (CRES) using EASY


Design carried out at the Center for Renewable Energy Sources (CRES), using EASY, for the EU-funded project LOW-BIN.

Optimization of Ground Source Heat Pump Systems

Design of a Ground Source Heat Pump with two objectives: (a) max. coefficient of performance, COP & (b) min. heat exchangers’ surface. GSHPs are used for heating and cooling buildings Design performed by CRES using EASY for the EU-funded


and cooling buildings. Design performed by CRES, using EASY, for the EU-funded project GROUND-MED.

Solution of Unit Commitment Problems using EASY

EASY was used to solve Unit Commitment problems. With M power units (gas, steam,wind turbines etc.) and a given energy demand for a T-hour scheduling horizon, theobjective is to schedule all units so as to operate with min. Total Operating Cost (TOC)objective is to schedule all units so as to operate with min. Total Operating Cost (TOC)while meeting constraints (min. STUP/SHDN times, ramp, spinning reserve, etc).The method has been extended to handle problems with probabilistic unit outages(Monte Carlo simulations). In collaboration with the Public Power Corporation,


( ) p ,Greece.

PART II: Deterministic Optimization methods

Deterministic Optimization Methods:

Gradient-based methods quasi-Newton or exact Newton methodsGradient-based methods, quasi-Newton or exact Newton methods.

Assisted by the adjoint variable method in fluid mechanics (gradient or Hessiancomputation)

Pro(s): Fast!

Con(s): Need to compute the gradient of F, or even the Hessian. May be trapped intolocal minima.

Hybrid Optimization Methods!Hybrid Optimization Methods!

Continuous Adjoint: First-differentiate, then-discretize

Di Adj i Fi di i h diff iDiscrete Adjoint: First-discretize, then-differentiate

Starting Point: The set of PDEs governing the analysis problem.


Applications of the Adjoint Method in Turbomachinery

Reference Blade 1.32

1.34

1.26

1.28

1.3

1.32

ntro

py G

ener

atio

n Reference Blade

Row 1 Row 2

1.22

1.24

0 5 10 15 20 25 30 35

Ent

Cycle

Optimal Blade Optimal BladeOptimal Blade Optimal Blade

Design-Optimization of a 3D peripheral compressor rows, for minimal viscous losses, ith geometrical constraints sing the contin o s adjoint method


with geometrical constraints, using the continuous adjoint method.Turbulence model : Low-Reynolds number Spalart-Allmaras.

Applications of the Adjoint Method in Turbomachinery

pinit

popt

Optimization of a Francis turbine blade, targeting a 1.5m increase in the


Optimization of a Francis turbine blade, targeting a 1.5m increase in the hydraulic height, subject to a number of flow constraints, incl. cavitation.

Applications of the Adjoint Method in Car Industry

Volkswagen L1 Car:● Half-model, low-Re mesh (y+~1), 18 M cells●(Continuous) Adjoint to [RANS & Spalart Allmaras]●(Continuous) Adjoint to [RANS & Spalart-Allmaras].● Drag reduction.

Velocity Adjoint velocity

Sensitivity

Sensitivity Map

Sensitivity map:Direction of favorable surface displacement

for reducing drag: d i d bl d


Sensitivity Mapred - inwards, blue – outwards.

Applications of the Adjoint Method in Car Industry

Convergence: Optimizing ONLY the Spoiler Overall deformation less than 20mm

BaselineOptimized

For an aerodynamically already nearly perfect car:

>2% drag reduction

30% lift improvement (not included in F!!!!)


Baseline Optimized

Topology Optimization & Continuous Adjoint Method

Unconstrained

With constraint onWith constraint on the mass flowrate per exit

With constraint on the

The adjoint method is used to solve topology optimization problems in fluid mechanics & heat transfer. Due

h i l hi h b f Flow swirl at the exitto the excessively high number of design variables, the adjoint method suits perfectly to this purpose.Example: Design of a manifold with


Example: Design of a manifold with a single inlet and four outlets.

Topology Optimization & Continuous Adjoint Method

gear box

outlet

inlet

Topology optimization of an air-conditioning duct of a passenger car, targeting min. total pressure losses. The optimal design (yields 45% less total pressure losses.

Starting Geometry: Optimal Geometry:Starting Geometry: F = 0.25 m5/s3

Optimal Geometry:F = 0.177m5/s3

Topology optimization of the plenum chamber of a student racing car, targeting min. l l b ddi i ll i fl id l i Th i l


total pressure losses, by additionally using a fluid volume constraint. The optimal design yields a 29% reduction in the objective function value.

Closure

Once a reliable analysis method is available, next step is to optimize the “system”.

A f i i i h d i il bl f l d l l iA great gamut of optimization methods is available from plug-and-play evolutionaryalgorithms to tailored-to-the problem gradient-based methods.

Evolutionary algorithms are nice is there is a moderate number of unknowns and/or theEvolutionary algorithms are nice is there is a moderate number of unknowns and/or theoptimization is not to be repeated on a daily basis. They might be the only choice if theexisting analysis s/w is a “black-box”.

In their standard form, EAs are quite slow. However, nowadays, there are interestingways to lower the CPU cost and/or the wall clock time.

Gradient-based methods, usually based on the adjoint method to compute the gradientof the objective function, are much faster but can be trapped into a local (rather than theglobal) minimum. Programming adjoint methods require a certain investment in time.g ) g g j q

Hybridization seems to be the best way to use them. EAs are responsible for theexploration of the search space whereas gradient-based for the refinement of promising


p p g p gsolutions.

Many Thanks to:

Dr. A. AsoutiDr. E. KontoleontosD E P i Ki h iDr. E. Papoutsis-KiachagiasDr. D. PapadimitriouDr. S. Kyriacou


Elti &Gdi tEvolutionary & Gradient-BdBased Optimization in ... · Elti &Gdi tEvolutionary &...

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