Instructor: Lichuan Gui lichuan-gui@uiowa

Measurements in Fluid Mechanics058:180 (ME:5180)Time & Location: 2:30P - 3:20PMWF 3315 SCOffice Hours: 4:00P – 5:00PMWF223B-5 HL Instructor: Lichuan Gui lichuan-gui@uiowa.edu Phone: 319-384-0594 (Lab), 319-400-5985 (Cell) http://lcgui.net

Lecture 33. Peak-locking effect

Individuale reading of X: Mean value 0 RMS fluctuation (random error) RMS error Evaluation Errors • Bias & random error for replicated measurement Measuring variable X for N times

3232-pixel window Peak-locking Effect • Example: PIV test in a thermal convection flow One of PIV recordings

Histogram of U & V Peak-locking Effect • Example: PIV test in a thermal convection flow One of vector maps

Correlation-based interrogation Correlation-based tracking MQD-tracking Peak-locking Peak-locking Effect • Example: PIV test in a thermal convection flow Histograms resulting from different algorithms Is the peak-locking an error? Why does the peak-locking exist? How to reduce the peak-locking effect?

Histogram for measuring 0.5 pixels    Source of Peak-locking • Probability density function (PDF) Probability to get X when measuring Xo

Distribution density function of true value Xo in region [a,b]: Distribution density function of measured value X: Histogram of measured variable X: Source of Peak-locking • Distribution density function (DDF) - (Xo)/(b-a): probability to find true value Xo in region [a,b] - Physical truth to be investigated - (X)/(b-a): probability to get value X when measuring Xo in region [a,b] - Investigated phenomenon - Defined in region [-,+]: - Number of samples in [X-/2,X +/2] - M: average number in 

Possible sources of peak-locking Source of Peak-locking • Distribution density function (DDF) • Histogram determined by • Sample number M • Sub region size  • Physical truth (Xo) • Bias error (Xo) • Random error (Xo)

Bias & Random Error Distribution • Simulation of Gaussian particle images Test results with simulated PIV recording pairs - particle image diameter: 2  5 pixels - particle image brightness: 130  150 - particle image number density: 20 particles in 3232-pixel window - vector number used for statistics: 15,000 CDWS – Correlation-based discrete window shift (=DWS) CCWS – Correlation-based continuous window shift (=CWS) FCTR – FFT accelerated correlation-based tracking w/o single pixel random noise with single pixel random noise (CDWS=DWS, CCWS=CWS, FCTR=correlation-base tracking)

Peak-locking Factor • DDFs and histograms for the test results

Simulation of error distributions: Simulated error distributions Response of peak-locking factor Peak-locking Factor • Response of  to bias and random error distribution   very sensitive to bias error amplitude A   sensitive to random error amplitude A when >0.02   not sensitive to constant portion of random error 0

Peak-locking Factor • Response of  to bias and random error distribution Contours of peak-locking factor for o=0.025  Peaks locked at integer pixels in bright area and at midpixels in dark area  Peak-locking minimum around A=0  Increasing A increaes  for A<0 but reduces  for A>0

Increasing A when A>0 for CCWS Peak-locking Factor • Influence of particle size on  Test results   increases with incresing particle size by CDWS   descreses with incresing particle size by FCTR & CCWS   increases when particle szie too small by FCTR & CDWS   smallest when particle szie too small by CCWS   generally smallest by FCTR (for Gaussian image profile)

Peak-locking Factor • Influence of particle number density on  Test results   not sensitive to particle image number density   generally smallest by FCTR (for Gaussian image profile)

Peak-locking Factor • Influence of window size on  Test results   decreases with incresing window size by CDWS   slightly increses with incresing window size by CCWS   slightly decrease with incresing window size by FCTR   generally smallest by FCTR (Gaussian image profile)

Image samples of different quality Non-Gaussian Particle Images • Influence of particle image profile

Gray value histogram & evaluation sample Histogram of particle image displacement Application Examples • PIV measurement in a thermal convection flow - Overexposed particle images - Particle image diameter 3  4 pixels - No peak-locking for CCWS

Gray value histogram & evaluation sample Histogram of particle image displacement Application Examples • PIV measurement in a wake vortex flow - Particle image diameter 1 pixels - Least peak-locking for CCWS

Gray value histogram & evaluation sample Histogram of particle image displacement Application Examples • PIV measurement in a micro channel flow - Particle image diameter 4  6 pixels - Mid-pixel peak-locking for CCWS

References • Guiand Wereley (2002) A correlation-based continues window shift technique for reducing the peak locking effect in digital PIV image evaluation. Exp Fluids 32: 506-517

Matlabprogram for showing peak-locking effect 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=16; % interrogation grid width Ng=16; % 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/Mg-1; % grid column number sr=12; % search radius for i=1:col % correlation interrogation begin for j=1:row x=i*Mg; y=j*Ng; g1=sample01(G1,M,N,x,y); g2=sample01(G2,M,N,x,y); [C m n]=correlation(g1,g2); [cm vxvy]=peaksearch(C,m,n,sr,0,0); U(i,j)=vx; V(i,j)=vy; X(i,j)=x; Y(i,j)=y; end end % correlation interrogation end nn=0; % count number of displacements with 0.1 pixel steps for k=-120:120 nn=nn+1; D(nn)=double(k/10); Px(nn)=0; Py(nn)=0; for i=1:col for j=1:row if U(i,j)>= D(nn)-0.05 & U(i,j) < D(nn)+0.05 Px(nn)=Px(nn)+1; end if V(i,j)>= D(nn)-0.05 & V(i,j) < D(nn)+0.05 Py(nn)=Py(nn)+1; end end end end plot(D,Px,'r*-') % make plots hold on plot(D,Py,'b*-') hold off

Instructor: Lichuan Gui lichuan-gui@uiowa