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SOM Neural Network for Particle Tracking Velocimetry. Aifeng Yao. What is Particle Tracking Velocimetry?.

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what is particle tracking velocimetry
What is Particle Tracking Velocimetry?
  • PIV is a method for measuring a 2D velocity vector map of a flow field at an instant in time by matching the images of small suspended seeding particles in the flow taken in a small time interval.

Particle tracking

Frame 1

Frame 2

displacement

Velocity=

How to match the particle images?

time interval

som for particle tacking
SOM for Particle Tacking
  • Neural Network Structure

Position vector xi

Weight vector wi

Sub-network 1

i=1,2,…,N

Weights vector Wj

Sub-network 2

Position vector Xj

j=1,2,…,M

som neural network implementation 1
SOM Neural Network Implementation (1)

1. Weight initialization, wi=xi, Wj=Xj (i=1,2,…,N, j=1,2,…,M)

2. Competition between neurons within radius Dmax

wisub-network 2, for Wj-wiDmax (j=1,2,…,M)

Euclidean distance dij=Wj-wi, min{dij}winner Wc

Awarding winner and its neighbors

Wk= Wk +c(wi-Wc), c=  for neurons Xc-XkR (neighbors)

  • (accumulation) 0 otherwise

Wjsub-network 1, for wi-WjDmax (i=1,2,…,N)

Repeat competition and awarding

som neural network implementation 2
SOM Neural Network Implementation (2)

3.Updating weightsfor both sub-networks

wi=wi+ wi (i=1,2,…,N)Wj=Wj+ Wj (j=1,2,…,M)

4.Decreasing neighborhood radius R

R=R*Rcoef

Increasing 

=*coef

5. Repeat step 2 to step 4

nearest neighbor matching

winner= Wj-wc  for j=1,2,…,M

result 1
Result (1)
  • Shear flow constant gradient
  • Ratio=254/254=1.0
  • Erroneous

matching=7

Net ratio

=247/254 =0.97

results 2
Results (2)
  • rotational flows with out-of-plane particles 20/200
  • matching = 171/180=0.95
  • Mismatch=

20

Net ratio=0.84

conclusions and suggestion
Conclusions and Suggestion
  • SOM alg. works well in Particle Tracking Velocimetry;
  • Extension to real experimental scenarios, # of particles, unmatchable particles,
  • Comparison to other alg. used in PTV, accuracy and speed.