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Students are encouraged to attend the class. You may not be able to understand by just reading the lecture notes. Measurements in Fluid Mechanics 058:180:001 (ME:5180:0001) Time & Location: 2:30P - 3:20P MWF 218 MLH Office Hours: 4:00P – 5:00P MWF 223B-5 HL. Instructor: Lichuan Gui

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Instructor lichuan gui lichuan gui@uiowa edu http lcgui net

Students are encouraged to attend the class. You may not be able to understand by just reading the lecture notes.

Measurements in Fluid Mechanics058:180:001 (ME:5180:0001)Time & Location: 2:30P - 3:20P MWF 218 MLHOffice Hours: 4:00P – 5:00P MWF 223B-5 HL

Instructor: Lichuan Gui

lichuan-gui@uiowa.edu

http://lcgui.net


Instructor lichuan gui lichuan gui uiowa lcgui

Lecture 28. Direct Correlation & MQD Method


Instructor lichuan gui lichuan gui uiowa lcgui

Direct Correlation & MQD Method

g2(i+m,j+n)

m

n

Direct Correlation (w/o FFT)

Method 1: g2(i,j) limited in the window frame

j

N

A

g1(i,j)

i

o

M


Instructor lichuan gui lichuan gui uiowa lcgui

Direct Correlation & MQD Method

g2(i+m,j+n)

m

n

Direct Correlation (w/o FFT)

Method 2: g2(i,j) not limited in the window frame

j

A

N

g1(i,j)

i

o

M


Instructor lichuan gui lichuan gui uiowa lcgui

Direct Correlation & MQD Method

Particle Image Pattern Tracking

Tracking ensemble of particle images

2nd recording

Image pattern at (m,n)

1st recording

tracked image pattern


Instructor lichuan gui lichuan gui uiowa lcgui

Direct Correlation & MQD Method

MN dimensional vectors

Quadratic difference of the vectors

Minimum-quadratic-difference (MQD) method

Double exposure

Single exposures

Particle Image Pattern Tracking

Minimum-quadratic-difference (MQD) method


Instructor lichuan gui lichuan gui uiowa lcgui

Direct Correlation & MQD Method

Normalized MQD tracking functions

Particle Image Pattern Tracking

Modified MQD tracking function

- D*(m,n) and D(m,n) identical for determining particle image displacement

- 3-point Gaussian fit directly applied to D*(m,n)


Instructor lichuan gui lichuan gui uiowa lcgui

Direct Correlation & MQD Method

Particle Image Pattern Tracking

Correlation-based tracking method

Correlation-based tracking function


Instructor lichuan gui lichuan gui uiowa lcgui

Direct Correlation & MQD Method

Particle Image Pattern Tracking

Modified correlation-based tracking function

zero


Instructor lichuan gui lichuan gui uiowa lcgui

Direct Correlation & MQD Method

tr(m,n)/D*(m,n)

j

A

m

N

g2(i+m,j+n)

g1(i,j)

n

2

i

o

M

2

Particle Image Pattern Tracking

Tracking area & tracking radius

  Tracking radius


Instructor lichuan gui lichuan gui uiowa lcgui

Direct Correlation & MQD Method

Zero padding:

Periodical, with FFT:

Particle Image Pattern Tracking

Acceleration with FFT

No periodical, no FFT:

g1(i,j)

g2(i,j)


Instructor lichuan gui lichuan gui uiowa lcgui

Direct Correlation & MQD Method

0

Particle Image Pattern Tracking

Acceleration with FFT

for [‑ m < , ‑ n < ]


Instructor lichuan gui lichuan gui uiowa lcgui

Direct Correlation & MQD Method

Test computer: IBM 6×86 P166+

Correlation tracking with FFT

[pixel]

Particle Image Pattern Tracking

Computation time


Instructor lichuan gui lichuan gui uiowa lcgui

Direct Correlation & MQD Method

Particle Image Pattern Tracking

Evaluation error

Image pattern tracking methods

- periodical error distribution on particle image displacement (1 pixel period)

- MQD has higher accuracy for ideal PIV images, but more sensitive to noises

Correlation algorithm

- error dependent on particle image displacement, high accuracy at very small displacement

Evaluation error for ideal PIV recordings by using different algorithmswith a 64x64-pixel interrogation window

Imaging techniques for fluid flow and insect motion experiments


Instructor lichuan gui lichuan gui uiowa lcgui

Matlab function for reconstruction of evaluation sample

File name: sample2.m

function[g]=sample2(G,M,N,x,y,sr,mode)

%INPUT PARAMETERS

% G - gray value distribution of the PIV recording

% M - interrogation window width

% N - interrogation window height

% x - horizontal position of interrogation window

% y - vertical position of the interrogation window

% sr - search radius

% mode - (1) for first evaluation sample

% OUTPUT PARAMETERS

% g - gray value distribution of the evaluation sample

for i=1:M+2*sr

for j=1:N+2*sr

g(i,j)=double(G(i+x-int16(M/2)-sr,j+y-int16(N/2)-sr));

end

end

g=g-mean(mean(g)); % subtracted by mean gray value

if mode==1

for i=1:M+2*sr

for j=1:N+2*sr

if i>sr & i<=M+sr & j>sr & j<= N+sr

continue;

end

g(i,j)=0; % zero padding

end

end

end


Instructor lichuan gui lichuan gui uiowa lcgui

Class project: practice with option #2

Main program:

A1=imread('A001_1.bmp'); % input image file

A2=imread('A001_2.bmp'); % input image file

G1=img2xy(A1); % convert image to gray value distribution

G2=img2xy(A2); % convert image to gray value distribution

Mg=32; % interrogation grid width

Ng=32; % interrogation grid height

M=32; % interrogation window width

N=32; % interrogation window height

[nxny]=size(G1);

row=ny/Mg-1; % grid row number

col=nx/Ng-1; % grid column number

sr=12; % search radius

for i=1:col

for j=1:row

x=i*Mg;

y=j*Ng;

g1=sample2(G1,M,N,x,y,sr,1); % evaluation samples for correlation tacking

g2=sample2(G2,M,N,x,y,sr,2);

[C m n]=correlation(g1,g2);

[cm vxvy]=peaksearch(C,m,n,sr,0,0); % particle image displacement

U(i,j)=vx;

V(i,j)=vy;

X(i,j)=x;

Y(i,j)=y;

end

end

quiver(X,Y,U,V); % plot vector map