AAE550_Class37_2011

# AAE550_Class37_2011 - AAE 550 Class 37 Fall 2011 1 Class...

This preview shows pages 1–4. Sign up to view the full content.

1 AAE 550 Class 37 Fall 2011 1 Class 37: Approximation Techniques II - Response Surfaces Response surface coefficients – Least squares regression Design of experiments – Full-Factorial Design (FFD) – Central-Composite Design (CCD) – Face-centered CCD – Box and Behnken design – Saturated D-optimal design 2 Response Surface Coefficients ( 29 0 1 1 ˆ n n n i i ij i j i i j i f a a x a x x = = = = + + ∑∑ x Once a response surface model (here, a quadratic equation) is chosen, coefficients must be determined ( a 0 , a i , a ij are unknown) Note the index convention used here

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 AAE 550 Class 37 Fall 2011 3 Response Surface Coefficients Use some form of linear regression to find coefficients Run several “exact” (or “actual”) analyses, f ( x i ) f = X a + ε 4 Response Surface Coefficients ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 1 2 1 1 2 2 1 1 1 1 1 1 2 2 1 2 1 1 2 2 2 2 2 2 2 2 2 2 1 2 1 1 0 1 2 11 12 22 1 2 1 2 2 2 1 1 1 dp dp dp dp dp dp dp dp n n n n n n n n a x x x x x x x x x x x a a a a f f x x x x x x x f a = + ε ε ε x x x Two-variable example ( x 1 ) i = first variable of “data point” i ( x 2 ) i = second variable of “data point” i n dp = number of “data points”
3 AAE 550 Class 37 Fall 2011 5 Response Surface Coefficients Regression finds a to minimize error minimize ( 29 ( 29 2 2 1 1 dp dp n n i i i i L f Xa = = = ε = - this is a “least-squares” problem 6 Response Surface Coefficients Least squares solution [ ] f X X X a T T 1 - = Generalized least squares – Solve in Matlab using either: a = X\f (simplistic and easy) or lsqlin (provides additional info)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/14/2012 for the course IE 530 taught by Professor Ravindran during the Spring '97 term at Purdue University-West Lafayette.

### Page1 / 16

AAE550_Class37_2011 - AAE 550 Class 37 Fall 2011 1 Class...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online