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Homework answers / question archive / Metamodeling Polynomial Regression HW3-1: (30 points) For the design problem of the hollowed circular beam (shown below), a

Metamodeling Polynomial Regression HW3-1: (30 points) For the design problem of the hollowed circular beam (shown below), a

Computer Science

Metamodeling Polynomial Regression

HW3-1: (30 points) For the design problem of the hollowed circular beam (shown below),

a. Create a three-level factorial design matrix in HiPPO and map to the real ranges for R = [0.02 to 0.2] m and

t = [0.001, 0.01] m. Show your design matrix including both the normalized and real design variables along with the function values of M, G, and V for each design in your design matrix.

b. Create the quadratic PR models (with interactions) of M, G, and V 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 G and V are not the constraint functions by themselves; you need to apply their limit values when creating the constraint functions for GimOPT.

HW3-2: (40 points) 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 t = [0.001, 0.01] m. Show your design matrix including both the normalized and real design variables along with the function values of M, G, and V for each design in your design matrix.

b. Create the quadratic PR models (with interactions) of M, G, and V 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 G and V are not the constraint functions by themselves; you need to apply their limit values when creating the constraint functions for GimOPT.

 

 

PROBLEM SET ASSIGNMENT INSTRUCTIONS

OVERVIEW

The purpose of the homework problem sets is to reinforce material covered during class lectures and notes. Problem sets will play an important role in preparing you for your projects and quizzes.

INSTRUCTIONS

Each set of problems will be located in the Problem Set: [Title] Template document corresponding to each assignment in Canvas.

 

For each Problem Set Assignment, you will:

1.            Submit a single PDF via Canvas before the deadline.

2.            Your submission file should include your answers to all questions. Problems with no answers will receive zero points.

3.            For design optimization problems, always include your standard formulation before showing your solutions.

4.            For solutions obtained from the software (GimOPT etc.), you may show an excerpt from the output file, but do not include the entire output file, nor should you include the input file.

5.            Save all your input and output files for the assignments in case the instructor has questions on your solutions.
 

use MATLAB instead of GimOPT for solving design optimization problems. To perform design optimization in MATLAB for the case where all of the elements (objective function, design variable limits, design constraints) can be expressed in equation form. You may use this method rather than GimOPT for your homework assignments if you prefer. In that case, include the Live Script (*.mlx) in your homework submission. Do not worry aboutwhere it tells you to compare with previous homework(HW2-3 and HW2-2)

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