This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: EAS6939 Homework #6 1. In engineering, the random wind pressure ( Y ) is typically modeled as a quadratic transformation of the random wind speed ( X ). If 2 ~ ( , ) x x X N μ σ and Y = X 2 , find approximation of Y based on the firstorder Taylor series expansion about mean of X and equivalent linearization. For equivalent linearization, consider Y L = aX + b , where a and b are optimal parameters. Calculate the mean and variance of the above approximations of Y . Solution: 1) Firstorder Taylor series expansion: 2 ( ) ( ) 2 x L x x x x x dY Y Y X X dX μ μ μ μ μ = = + − = − Therefore, the approximate mean and variance are 2 2 [ ] 2 [ ] Y L x x x E Y E X μ μ μ μ = = − = 2 2 2 2 (2 ) [ ] 2 Y x x x Var X σ μ μ σ = = 2) Equivalent linearization: The model parameters a and b can be obtained from: 2 , minimize [ ] L a b E Y Y − For a general case, the minimizing conditions become 2 3 2 [ ] [ ] [ ] [ ] [ ] aE X bE X E X aE X b E X + = + = From class, 2 2 2 [ ] x x E X σ μ = + 3 2 3 [ ] 2 x x x E X μ σ μ = + Therefore, parameters a and b are calculated by 2 2 2 x x...
View
Full
Document
This note was uploaded on 02/15/2012 for the course EAS 6939 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff

Click to edit the document details