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Introduction and Some Advances in Optimization of Engineering Systems
Shapour AzarmProfessor
Department of Mechanical EngineeringUniversity of Maryland
College Park, MD [email protected]
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
4
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
5
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
7
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
8
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)
9
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 +
10
Outline
Multi-Objective Sensitivity Analysis
Multi-Objective
Multi-Disciplinary Optimization
11
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
22
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
22
11
12
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
13
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
14
Outline
Multi-Objective
Multi-Disciplinary OptimizationApproximation
Assisted Optimization
15
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
16
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
17
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
18
Outline
Multi-Objective
Multi-Disciplinary Optimization
Design and Control
Optimization
19
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)
20
CoD:Approach
21
CoD:Example
22
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