Introduction and Some Advances in Optimization of Engineering Systems

Shapour AzarmProfessor

Department of Mechanical EngineeringUniversity of Maryland

College Park, MD 20742azarm@umd.edu

https://enme.umd.edu/clark/faculty/507/Shapour-Azarm

Flexible Carbon Capture Technologies for a Renewable-Heavy Grid ARPA-E Workshop; Dr. Scott Litzelman

Crystal City Marriott, Arlington, VAJuly 31, 2019

2

Outline

Multi-Objective Sensitivity Analysis

Multi-Objective

Multi-Disciplinary Optimization

Multi-ObjectiveRobust/Flexible

Optimization

Approximation Assisted

Optimization

Design and Control

Optimization

3

Big Picture

Source:https://i.pinimg.com/originals/5a/a4/83/5aa4836d523f93dd5ce5f55b64a29649.jpg

• Optimizing design, operation and control of engineering systems, e.g. CCS, may require considerations of:

– multiple subsystems (disciplines)

– multiple objectives and constraints

– uncertainty– computationally

expensive simulations

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Terminology:Multi-Objective Optimization

f1 (e.g. emission)

f2(e.g. cost) feasible domain

Pareto solutions

Pareto (1896)

Minimize

Minimize

• f1,…, fM: objectives such as cost, emission intensity, NPV• x: decision variables such as size, pressure, flow rate; changed during optimization

• p: parameters such as material, temperature, fixedduring optimization• gj: constraint such as limit on emission, stress, budget[There might be equality constraints as well!]

minimize/maximize ( , ) 1, ,

subject to ( , ) 0 1, ,j

f m Mm

g j J

=

≤ =

x px

x p

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Terminology:Multi-Disciplinary Optimization (MDO)

f2

f1

f2

f1

psh,2

psh,1

Tolerance Range

Nominal value psh,0

Subsystem 1

Subsystem 2

y12 y21

p1

p2

x2

xsh, psh

f2, g2

x1 f1, g1

f, g f1

f2 Nominal AOVR

Hu et al. 2013, “New Approximation Assisted Multi-objective collaborative Robust Optimization Under Interval Uncertainty,” Structural and Multidisciplinary Optimization, 47(1)

Li and Azarm 2008, “Multiobjective collaborative Robust Optimization (McRO) with Interval Uncertainty and Interdisciplinary Uncertainty Propagation,” Journal of Mechanical Design (ASME Trans), 130(8)

6

Outline

Multi-Objective

Multi-Disciplinary Optimization

Multi-ObjectiveRobust/Flexible

Optimization

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Multi-Objective Robust/Flexible Optimization (MORO/MOFO):

What is the Problem?• Robust Optimization:

Optimize design xd and operational variables xop for all realizations of uncertainty

• Flexible Optimization:Optimize design xd for all realizations of uncertainty while using operational variables xop to mitigate or eliminate effects of uncertainty

Li et al. 2006, “A New Deterministic Approach using Sensitivity Region Measures for Multi-Objective and Feasibility Robust Design Optimization,” Journal of Mechanical Design (ASME Trans), 128(4) Azarm and Lee, 2016, “Multi-objective Robust Design Optimization with Operational Flexibility under Interval Uncertainty,” ASME IDETC

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Known range of uncertaintymaps into

objective space

Robust

Non-robustp1

p2

f1

f2

Feasibly robust

Feasibly non-robust

g2

g1

p1

p2

Known range of uncertainty maps into

constraint space

MORO/MOFO:Approach (Basic Idea)

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MORO/MOFO:Centrifugal Impeller Example

1 1 2 21 1 2, ;

2 1 2

1 1 2 , min

min ( , , , ),

( , , , ): 1 ( , , , ) / 0

d d op exitexitx x x p

out exit

exit exit exit no al

f p

f PW ps.t. g p p p

β βη β β

β ββ β

= = == − Ω

= − Ω= −∆ Ω ∆ ≤

2 1 2 min

3 1 2

4 1 2

5 1 2

1 ( , , , )/ 0 ( , , , ) 1 0 ( , , , ) 0.6 0 ( , ,

exit no al

exit

PS exit

SS e

g pg pg pg p

η β β ηη β βµ β βµ β β

= − Ω ≤= Ω − ≤= Ω − ≤=

1 2

, min , min

min min

, ) 0.6 0 25 40; 40 60 10 : -10 10

xit

exit no al exit exit no al

no al no al

p p pβ β

Ω − ≤≤ ≤ ≤ ≤

∆ ≤ ∆ ≤ ∆ +

∀Ω Ω ≤ Ω ≤ Ω +

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Outline

Multi-Objective Sensitivity Analysis

Multi-Objective

Multi-Disciplinary Optimization

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Multi-Objective Sensitivity Analysis (MOSA)What is the Problem?

• Determine key parameters for uncertainty reduction!

Objective: Optimally determine, with minimum investment (cost), the amount of uncertainty reduction needed in input parameters that results in minimum transmitted uncertainty in system outputs (or performance)

Li et al. 2009, “Interval Uncertainty Reduction and Sensitivity Analysis with Multi-Objective Design Optimization,” Journal of Mechanical Design (ASME Trans), 131

Li et al. 2010, “Optimal Uncertainty Reduction for Multi-Disciplinary Multi-Output Systems Using Sensitivity Analysis,” Structural and Multidisciplinary Optimization, 40

Subsystem 2(SS2)

Subsystem 1(SS1)

Multi-Disciplinary, Multi-Objective Sensitivity Analysis (MiMOSA)

∆±

∆±∆±

nn pp

pppp

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11How much How much reduction in input reduction in input uncertainty (uncertainty (ΔΔpp), ), at both system at both system

and subsystems?and subsystems?

To optimally To optimally decrease output decrease output uncertainty (uncertainty (ΔΔf f ))aat both system t both system and subsystemsand subsystems

System (SS0)

∆±

∆±∆±

MM ff

ffff

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MOSA/MiMOSAApproach (Basic Idea)

• minimize investment in uncertainty reduction of inputs, while also

• minimize uncertainty in outputs

Investmentmetric

Rf

α = 0

α = 1

RTR

Tolerance Region

p0

p1

p2

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.05 0.1 0.15 0.2

α for tNi

α for ρNi

Decision Variable Comparison for the

Battery Subsystem (SS1)Solutions

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5R f ,SS2 (%)

Inve

stmen

t SS2

Total Normalized Range

Stator outer radius

Gap length αΙ

Total Normalized Range

Stator outer radius

Gap length αΙΙ

Total Normalized Range

Stator outer radius

Gap length αΙΙΙ

SS2

RSS2 (%)

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7

Inve

stmen

t SS0

Rf,SS0 (%)

Highest Rf:Most Important

Subsystem

MiMOSACordless Grinder Example

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Outline

Multi-Objective

Multi-Disciplinary OptimizationApproximation

Assisted Optimization

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Mehr and Azarm, 2005, “Bayesian Meta-Modeling of Engineering Design Simulations: A Sequential Approach with Adaptation to Irregularities in the Response Behavior,” International Journal for Numerical Methods in Engineering, 62

Abdelaziz et al. 2010, “Approximation Assisted Optimization for Novel Compact Heat Exchanger Designs,” HVAC&R Research, 16(5)

Approximation Assisted Optimization (AAO)What is the Problem?

Multi-objective optimizer

1. DOE

2. Meta(surrogate) modeling

3. ValidationObjective: Optimization of a system that has computationally expensive simulation

Heat Exchanger

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Parameterize Geometry

Optimization

Optimizer New Design(Nt, Din, Hs, Vs, w, v)

Assemble HX (CoilDesigner)

Heat load, HX Volume, Material, Air & water pressure drop etc.

Optimized HX

Volume

Air

DP

Current Technology

New designs

Concept Heat Exchanger

Approximation

DOE

PPCFD

Air DP/HTC

* Parameterized Parallel CFD, Abdelaziz, 2007, Aute et al., 2008

AAO:Approach

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max

max

min ADP, V

s.t.1kW

ADP ADPRDP RDP

[ , , , , , ]

HX

in

Q

HX Nt D Hs Vs w v

=≤≤≡

0

10

20

30

40

50

60

70

0 100 200 300 400 500 600 700

Air

DP

[Pa]

HX Volume [cm³]

NGHX Designs

Baseline Microchannel Coil

Parameter Value

Inputs Din, Hs, Vs, w, v

Responses Air DP, HTC

DOE SFCVT, SO

Metamodel Kriging

Initial 100

New points 100 each

Verification 250

MAS ≥80, 0.1

Approximation:

AAO:Heat Exchanger Example

Aute et al., 2008

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Outline

Multi-Objective

Multi-Disciplinary Optimization

Design and Control

Optimization

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Co-Design: Design and Control Optimization (CoD)What is the Problem?

• Connected systems may require design of both Plant and Control, or Co-Design

• Objective: Develop decentralized methods for coordinated design of Plant (P) and Control (C) for connected engineering systems

Chanekar et al. 2018, “Co-design of Linear Systems using Generalized Benders Decomposition,” Automatica, 89

Liu et al. 2017, “On Decentralized Optimization for a Class of Multisubsystem Co-design Problems,” Journal of Mechanical Design (ASME Trans), 139(12)

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CoD:Approach

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CoD:Example

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Final Remarks

• Optimization is a necessity for design, operation and control of engineering systems, including CCS systems, when we

– have multiple objectives, and constraints (with limits on resources, budget, etc.),

– want optimized solutions which are relatively “insensitive” to uncertainty

– want to explore tradeoffs between investment in uncertainty reduction of input parameters vs. reduction in system/subsystem output uncertainty

– have computationally expensive simulations while performing optimization