ME 465
Project 2
Curve Fitting
机械工程作业代做 For the problem described below, develop the necessary model and perform the calculations of RMSE in Excel (see tips below).
Introduction
In this project, we will demonstrate the process of curve fitting using both linear regression(minimizing the RMSE) and Taylor series (see Chapter 6).
Tasks 机械工程作业代做
For the problem described below, develop the necessary model and perform the calculations of RMSE in Excel (see tips below). Use HEEDS to find the optimal values of the unknown coefficients.
Find a best fit polynomial of order 1, 3 and 5 (three different fits) for the function f(x)=sin(x)over the range (0° ≤ x ≤90). In other words, assume a model function of the
form:
and determine through optimization the values of ܽai for ݊n=1, 3 and 5 that minimize the RMSE between ݂(fx) and ݂
(x). When developing the data points representing the target curve,evaluate ݂f(x) at 5 degree increments in the given range.
Turn In
Your report should be typed. Use a 12 pt font and 1 inch margins. On the first page, include the pledge in the form below:
Pledge: I have neither given nor received any unauthorized assistance on this assignment.
Signature: __________________________________ Print Name: ________________________
1.Results of the optimization design study
a.Explain briefly the goals of the optimization exercise, the relevant equations and mathematical concepts.
b.Write a brief description of the study results, including any interesting observations.In other words, describe what you learned from the study in addition to the optimal values of the parameters. Include appropriate figures (cut and paste) to justify your conclusions. In particular, include and discuss the following plots:
i.A history plot of the objective versus evaluation number for each curve fit. 机械工程作业代做
ii.A graph of the analytical function ݂f(x) and the three best fit curves for ݊n= 1,3 and 5 versus x . Develop this plot in Excel and properly label the curves.
iii.A graph of the analytical function ݂f(x) , the best fit curve for ݊n= 1, and the first‐order Taylor series approximation versus x. Develop this plot in Excel and properly label the curves.
iv.A graph of the analytical function ݂f(x) , the best fit curve for ݊n= 3, and the third‐order Taylor series approximation versus x . Develop this plot in Excel and properly label the curves. 机械工程作业代做
v.A graph of the analytical function ݂f(x) , the best fit curve for ݊n= 5, and the fifth‐order Taylor series approximation versus ݔ . Develop this plot in Excel and properly label the curves.
2.Based on this exercise, answer the following questions in short answer format.
a.How many evaluations did you use to obtain the optimal solution? How did you determine this number?
b.Why are the best fit polynomial curves different than the Taylor series curves for a given polynomial order?
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