Chemical Engineering Hand Written_Notes_Part_101

Chemical Engineering Hand Written_Notes_Part_101 - 204 5....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
204 5. OPTIMIZATION AND RELATED NUMERICAL SCHEMES The f rst two approaches use the linear least square formulation as basis while the nonlinear programming approaches is a separate class of algorithms. 8.1. Weighted Least Square For Analytically Linearizable Models. Many nonlinear-in-parameter forms can be converted into linear-in-parameter forms by means of some linearizing transformations. In such cases, it appears that we can apply linear least square to obtain parameter estimates. However, this may not minimize e T We as explained below Consider linearizable form of model (8.7) b y = θ 0 [ f 1 ( x )] θ 1 [ f 2 ( x )] θ 2 ······ [ f m ( x )] θ m which can be transformed as (8.8) ln b y =ln θ 1 + θ 2 ln [ f 1 ( x )] + θ 3 ln [ f 2 ( x )] ··· θ m ln [ f m ( x )] Now, parameter set that minimizes (8.9) e Ψ = N X i =1 (ln y i ln b y i ) 2 = N X i =1 ( e i ) 2 may not minimize (8.10) Ψ = N X i =1 ( y i b y i ) 2 = N X i =1 ( e i ) 2 A rigorous approach to avoid this problem is to use nonlinear programming of Gauss-Newton approach. However, it is often possible to use weighted coe
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/26/2011 for the course EGN 3840 taught by Professor Mr.shaw during the Fall '11 term at FSU.

Page1 / 2

Chemical Engineering Hand Written_Notes_Part_101 - 204 5....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online