6.4
Non-Linear Models ("Transforming" the Data)
8 pts
A material stress test gave you the following values of force (F, in lbf) versus
displacement (x, in mm). You want to develop the function F(x) to predict the
stress-strain relationship for different x in the future.
F
X
(lbf) (mm)
1
2
You found three possible models (below) for F(x) from a textbook. For each case
(A) write the problem out in matrix form r =y-Ac. Be sure to explicitly ...
2
3
4
4
6
5
define the vector c in terms of the unknown(s) in the model,
write out values of all the elements in the vector y and matrix A using
the provided data (similar to my posted solutions for problem 6.1)
(B) evaluate c from the least-squares best-fit using the MATLAB command: c = A \ y.
write out the result for the vector c (each element to at least 4 significant figures), and
use the values in c to write out the final equation for the best-fit model.
a) $F(x) = x^a - 1$ for one unknown a.
ax
b) $F(x) = \frac{ax^2}{b + x^2}$ for two unknowns a and b.
c) $F(x) = ax^2 + bx^4 + k$ for three unknowns a, b and k.
d) $F(x) = (1 + K)x^a e^{bx}$ for three unknowns K, a and b.
