HW3-1: 1-3 m Min. M For the design problem of the hollowed circular beam (shown below). δ 2R M =лpl(2Rt-t²) 5mpg (2Rt-1)]* προ 384E(R') d= s.t. $-0.0001/≤0 σ-σ≤0 20t-R≤0 0.02≤ R≤0.2 0.001 F R Radi RMSE PRESS R prediction Quadratic 33.71 201.55 0.01 0.9183 0.8910 0.9053 4.956 0.8352 0.005 0.9951 0.9901 0.2725 0.016 0.9995 OH. Fang Metamodeling 1 - Polynomial Regression 24
HW3-1: 1-3 m Min. M For the design problem of the hollowed circular beam (shown below). δ 2R M =лpl(2Rt-t²) 5mpg (2Rt-1)]* προ 384E(R') d= s.t. $-0.0001/≤0 σ-σ≤0 20t-R≤0 0.02≤ R≤0.2 0.001 F R Radi RMSE PRESS R prediction Quadratic 33.71 201.55 0.01 0.9183 0.8910 0.9053 4.956 0.8352 0.005 0.9951 0.9901 0.2725 0.016 0.9995 OH. Fang Metamodeling 1 - Polynomial Regression 24
Chapter8: Influence Lines
Section: Chapter Questions
Problem 10P
Related questions
Question
If you could help me answer these questions in matlab that would be great, I provided an additional picture detailing what the outcome should look like.
![HW3-1:
1-3 m
Min.
M
For the design problem of the hollowed circular beam (shown below).
δ
2R
M =лpl(2Rt-t²)
5mpg (2Rt-1)]*
προ
384E(R')
d=
s.t.
$-0.0001/≤0
σ-σ≤0
20t-R≤0
0.02≤ R≤0.2
0.001 <t≤0.01
p=7800 kg/m³
g=9.80 m/s²
E=210×10° Pa
P=50,000 N
Р
σ
(2Rt-t²
HW3-2.
For the design problem of the hollowed circular beam (shown in the figure of HW3-1),
a. Create a five-level factorial design matrix in HiPPO and map to the real ranges for R = [0.02 to 0.2] m and
-[0.001, 0.01] m. Show your design matrix including both the normalized and real design variables along
with the function values of M, 5, and σ for each design in your design matrix.
b. Create the quadratic PR models (with interactions) of M, &, and σ in HIPPO and create the 3D plots of
these three metamodels in Matlab. Briefly comment on the accuracy of the three metamodels by comparing
to the true function plots in HW2-3.
c. Create the GimOPT input file for this optimization problem using the three metamodels and obtain the
optimum solution. Report your solution and briefly comment on it by comparing to the true solution in
HW2-2. Note that these metamodels and their gradients can be saved to file in HiPPO. Also note that the
two functions for ♪ and σ are not the constraint functions by themselves; you need to apply their limit
values when creating the constraint functions for GimOPT.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2e99635-9351-4a90-90be-f1d1f0c280c7%2Ff6858b80-7866-4efc-83e7-0838a4dd6d8b%2Fyqnzzh_processed.png&w=3840&q=75)
Transcribed Image Text:HW3-1:
1-3 m
Min.
M
For the design problem of the hollowed circular beam (shown below).
δ
2R
M =лpl(2Rt-t²)
5mpg (2Rt-1)]*
προ
384E(R')
d=
s.t.
$-0.0001/≤0
σ-σ≤0
20t-R≤0
0.02≤ R≤0.2
0.001 <t≤0.01
p=7800 kg/m³
g=9.80 m/s²
E=210×10° Pa
P=50,000 N
Р
σ
(2Rt-t²
HW3-2.
For the design problem of the hollowed circular beam (shown in the figure of HW3-1),
a. Create a five-level factorial design matrix in HiPPO and map to the real ranges for R = [0.02 to 0.2] m and
-[0.001, 0.01] m. Show your design matrix including both the normalized and real design variables along
with the function values of M, 5, and σ for each design in your design matrix.
b. Create the quadratic PR models (with interactions) of M, &, and σ in HIPPO and create the 3D plots of
these three metamodels in Matlab. Briefly comment on the accuracy of the three metamodels by comparing
to the true function plots in HW2-3.
c. Create the GimOPT input file for this optimization problem using the three metamodels and obtain the
optimum solution. Report your solution and briefly comment on it by comparing to the true solution in
HW2-2. Note that these metamodels and their gradients can be saved to file in HiPPO. Also note that the
two functions for ♪ and σ are not the constraint functions by themselves; you need to apply their limit
values when creating the constraint functions for GimOPT.
Transcribed Image Text:•
Example 3-2: Create and compare the linear and quadratic PR models of
function R(x) using five design points.
7.0
-
Design points
True response
6.0
Design points
x
R(x)
-Linear Polynomial
5.0
0.00
0.0
.....Quadratic Polynomial
0.75
0.787108
|R(x)=sin x+0.25x³
4.0
1.50
1.841245
2.25
3.625729
R(x)
3.0
y = 2.2161x - 0.6951
R² = 0.9183
3.00
6.891120
2.0
PR models
fLP
=-0.695132+2.216115x
fop = 0.1172842+0.049672x+0.7221477x²
1.0
y=0.7221x²+0.0497x+0.1173
R² = 0.9951
0.0
0.5
1
1.5
2
2.5
3
35
-1.0
X
Model
Linear
F
Prob > F
R
Radi
RMSE
PRESS
R
prediction
Quadratic
33.71
201.55
0.01
0.9183
0.8910
0.9053
4.956
0.8352
0.005
0.9951
0.9901
0.2725
0.016
0.9995
OH. Fang
Metamodeling 1 - Polynomial Regression
24
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