ESD.77
ESD.77
Multidisciplinary System Design
Optimization
Spring 2010
Barge Design Optimization
Anonymous MIT Students
ESD.77
What is a barge?
Flat bottomed vessel, typically non self‐
propelled, used to carry low value, heavy or
bulky items.
2
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Motivation
•Interest in marine environment disciplines.
•Opportunity to use and bring together previous
academic experience.
•A common ship design problem would be extremely
complex to handle in one semester.
3
Multi‐disciplinary
ESD.77
M
φ
WL
WL"
WL
Z
φ
WL"
G
B
W
K
e
Hydrostatics
N
Image by MIT OpenCourseWare.
Ship Motion Degrees of Freedom
Heave
Yaw
Hydrodynamics
Surge
Pitch
Roll
Sway
Image by MIT OpenCourseWare.
Structural Mechanics
Compressive stress in deck
4
Tensile stress in keel
Image by MIT OpenCourseWare.
ESD.77
Problem Formulation
Design Variables
L
Length
B
Beam
D
Depth
t Plate Thickness
Lower Bound
90
20
4
12
Upper Bound
140
35
9
28
Unit
m
m
m
mm
v
kg
lcg
ω
H
Design Parameters
Speed
Payload vertical center of gravity
Payload longitudinal center of gravity
Peak spectral frequency
Significant wave height
Value
10
1.2D
0.5L
0.7
2.5
Unit
knots
rad/sec
m
ρ
Sea water density
1025
kg/m3
ρstr
Material thickness
7850
kg/m3
Design Objective is to maximize payload (P) s.t.
Barge cross‐section
N<60
T<6m
GM>0.15m
σk,sag<250MPa
σk,hog<250MPa
Inequality Constraints
Number of occurences of green water on deck per hour
Draft
Metacentric height
Keel stress at sagging wave
Keel stress at hogging wave
σd,sag<250MPa Deck stress at sagging wave
σd,hog<250MPa Deck stress at hogging wave
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ESD.77
Input/Output Diagram
v
Inputs
L,B,D,t
N
Hydrodynamics
Outputs
T
Hydrostatics
Hydrosta
tics
GM
P,wstr
σmax
Structural Mechanics
May 5,2010
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ESD.77
Modeling in MATLAB
Multidisciplinary Feasible (MDF) Model
• Payload, the objective function, is also required as
input by all modules.
• Feasibility is enforced at each optimization iteration.
May 5,2010
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ESD.77
Modeling in MATLAB
Hydrodynamics
Ship Motion Degrees of Freedom
• Curve fitting of experimental local
hydrodynamics properties from Lewis
theory to allow for a continuous design
space exploration.
• Seakeeping analysis for coupled heave
and pitch motions using 2D strip theory.
Heave
Yaw
Surge
Pitch
Roll
Sway
Image by MIT OpenCourseWare.
Assumption:
•Bretschneider spectrum with significant wave height of 2.5m and peak
spectral frequency of 0.7rad/sec
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ESD.77
Modeling in MATLAB
Hydrostatics
M
WL
WL"
WL
φ
Z
WL"
G
B
N
W
K
e
• Determines the vertical
metacentric height which is
evaluated against American
Bureau of Shipping (ABS) rules.
φ
Image by MIT OpenCourseWare.
Assumption:
•Vertical position of payload’s center of gravity at 1.2*D
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ESD.77
Modeling in MATLAB
Structural Mechanics
• Uses ABS parametric equations to determine
maximum keel and deck stresses in sagging and
hogging wave conditions.
Compressive stress in deck
Assumptions:
•Uniform longitudinal weight distribution.
Tensile stress in keel
Image by MIT OpenCourseWare.
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ESD.77
Simulation and Benchmarking
⎡ L ⎤ ⎡122⎤
⎢ ⎥ ⎢ ⎥
B⎥ ⎢ 30 ⎥
⎢
=
x=
⎢D⎥ ⎢ 6.1⎥
⎢ ⎥ ⎢ ⎥
⎣ t ⎦ ⎣ 16 ⎦
P=14,670tons
T=4.35m
N is the active
constraint
Source: McDonough Marine Service
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Initial Design Space Exploration
•4 Design variables
•3 Level (lower bound, mid, higher bound)
•JMP Statistical Software
•Generate DOE to capture main effect and two‐way
interactions
•48 runs (16 were unfeasible)
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Initial Design Space Exploration
Analysis of 32 feasible designs:
Recommended starting point
for numerical optimization:
⎡140⎤
⎢ ⎥
35 ⎥
⎢
x=
⎢9 ⎥
⎢ ⎥
⎣ 20 ⎦
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ESD.77
Gradient‐Based Optimization
SQP‐MATLAB’s “fmincon”:
•Ability to handle multiple variables
•Ability to handle design variables’ bounds
Results: P=23,530tons:
⎡137.8⎤
⎢
⎥
34.2 ⎥
*
⎢
x =
⎢ 8.7 ⎥
⎢
⎥
14.2
⎣
⎦
vs.
⎡140⎤
⎢ ⎥
35⎥
⎢
x=
⎢ 9 ⎥
⎢ ⎥
⎣ 20 ⎦
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ESD.77
Sensitivity Analysis
Sensitivity Analysis
Normalized Sensitivities
Variables:
Design V
Variable
t
D
B
L
‐0.2
Parameters:
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0
0.1
Normalized Sensitivities
Active constraints:
•N
•σd,hog
Design Parameter
H
ω
kg
v
‐0.6
‐0.5
‐0.4
‐0.3
‐0.2
‐0.1
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ESD.77
Post‐Optimality Analysis
•Hessian diagonal entries close to O(1)
•No improvement was achieved by trying to scale the
design variables
4
-2
Current Function Value: -23530.761
x 10
-2.05
Function value
-2.1
-2.15
-2.2
-2.25
-2.3
-2.35
-2.4
0
2
4
6
8
10
Iteration
12
14
16
18
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Heuristic Optimization
Genetic Algorithm:
•Easy implementation of fitness function
•Close to the optimum
⎡137.8⎤ ⎡138.7⎤
⎢
⎥
⎢ 34.6 ⎥
34.2 ⎥ *
⎢
⎥
⎢
Results: P=22,468tons at x =
vs. x =
⎢ 8.9 ⎥
⎢ 8.7 ⎥
⎢
⎥
⎢
⎥
⎣ 14.2 ⎦
⎣ 25.1 ⎦
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Global Optimum
Leveraging:
•DOE
•Gradient‐based optimization
•GA
⎡137.8⎤ ⎢
⎥
34.2 ⎥
*
⎢
Maximum Payload of P=23,530tons at x =
⎢ 8.7 ⎥ ⎢
⎥
14.2
⎣
⎦
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ESD.77
Multi‐Objective Optimization
Optimal Point
Utopia Point
Trade‐off analysis at optimal payload solution:
For an extra ton of payload we need to add 244kg of structural weight
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Conclusions
Model fidelity can be improved:
ƒCross‐section, scantlings, non‐uniform plate
thickness
ƒConsider most appropriate sea spectrum
ƒEvaluate all 6 degree of freedom motions
and most importantly roll.
But will make optimization more challenging.
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ESD.77
Back‐up
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MIT OpenCourseWare
http://ocw.mit.edu
ESD.77 / 16.888 Multidisciplinary System Design Optimization
Spring 2010
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