Transcript Towards an improved PEPT triangulation routine

Towards an improved PEPT triangulation routine
J Newling1, AJ Morrison1, N Fowkes2, I Govender1 and L Bbosa1
1 University
of Cape Town, Cape Town, South Africa
2University of Western Australia, Perth, Australia
Tumbling Mills
• Minerals industry (gold,
platinum, copper, etc …)
• Main aim is size reduction of
extracted ore
• Very energy-intensive,
however inefficient
• Aggressive environment,
in situ measurement not
feasible
• Models are empirical
Mill diameter 0.3 – 5m
Rotational speed 15 – 40 rpm
– Mill specific
– Ore specific
Positron Emission Particle Tracking
Positron Emission Particle Tracking
γ
γ
Positron Emission Particle Tracking
Sources of false events
True Pairing
Scattered Pairing
Random Pairing
Triangulation
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75% - 90% of recorded events are discarded
Proposal 1: Minimum perpendicular
distance method
Method
•Find the midpoint of the perpendicular between
successive lines of response
•Use the median of these midpoints to estimate the
particle location in that time interval
Motivation
•Avoid iteration by using the median to weight true
pairs
Shortcoming
•No guarantee that the closest approach is in the area
of the tracer particle
Proposal 1: Minimum perpendicular
distance method
Proposal 2: Density of lines
Method
•Discretise the field of the view into a 3D grid.
•Use the number of intersections of the LoRs with each
grid element to isolate the particle position
Motivation
•Discriminate against random and scattered events
Shortcoming
•Computationally expensive
Proposal 2: Density of lines
Dino Giovannoni & Matthew Bickell (Physics Honours)
From detected lines to line density…
… to probability distributions…
… to particle position.
Proposal 3: 2D triangulation
Method
•Divide LoR into coplanar sets and use these to reduce
the problem to a 2D one
Motivation
•Simplify the 3D case into a 2D problem
Shortcoming
•Drastically reduces the statistics
•Does not discriminate between true and false lines.
Proposal 4: Distance distribution
Method
•Use the current iterative method to calculate the
centroid
•Use the distribution of LoR distances from the centroid
to dynamically determine the fraction to discard
•Recalculate the centroid and repeat until some
convergence criteria is met.
Motivation
•Avoid having to calibrate the routine for each
experiment
Shortcoming
•Does not reduce the computational expense
Proposal 4: Distance distribution
Frequency
of events
Distance from centroid /mm
Conclusion