Transcript Towards an improved PEPT triangulation routine
Towards an improved PEPT triangulation routine J Newling 1 , AJ Morrison 1 , N Fowkes 2 , I Govender 1 and L Bbosa 1 1
University of Cape Town, Cape Town, South Africa
2
University of Western Australia, Perth, Australia
Tumbling Mills
Mill diameter 0.3 – 5m Rotational speed 15 – 40 rpm • • • • • 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 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
600 500 400 300 200 100 0 600 400 400 300 200 200 0 100 75% - 90% of recorded events are discarded 500
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 particle position.
… to probability distributions…
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