Balaban Poster - Cyclotron Institute
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Geometry Simula.on 4 He @15MeV/A+ nat Au 228 Th Source Descrip.on of Hill Climbing (HC): Novel Techniques for the Posi3on Calibra3on of FAUST David Balaban, Cyclotron Ins,tute, Texas A&M University (REU student from University of Massachuse@s Amherst) Advisers: Sherry Yennello, Lauren Heilborn, Cyclotron Ins,tute, Texas A&M University. 0. Collect Data Posi.on plot aRer raw data collec.on for detector 21 Apply cuts on signal strength to filter out noise levels. The detectors are also stretched so they can fill region. 1. Signal Processing 2. Rota.on Rotate data by 45 degrees, the expected angle of the slope. This makes projec.ng and fiYng easier. Phase 1, Stripe Iden.fica.on with Kmeans: 3. Run Kmeans Algorithm KMeans is used to iden.fy loca.on of stripes. Colors shown are different Kvalues, best one must be selected. 4. Data Selec.on Kmeans will give approximate loca.on of stripe, can now do a linear fit to data. 5. Linear Fit Rotate lines back by 45 degrees. Colors show which points were used in fit 1. Ini.alize k random points 2. Calculate average posi.on of data associated with each point 3. Reset point to average posi.on 4. Repeat un.l convergence will use this method to iden.fy stripes in data • Define set of free parameters P • Define method eval(P) to evaluate parameters to a single value Problem: Tungsten mask blocks charged par.cles and creates striped paaern on detectors. Stripes on detectors will be displaced according to detector placement. Goal is to find how far they are from expected posi.ons 2 phase process: 1.) Iden.fy stripes on detector with the Kmeans algorithm 2.) Find set of linear transforma.ons applied to detector which will reposi.on the stripes to the expected values with the Hill Climbing algorithm The Forward Array Using Silicon Technology (FAUST) consists of 68 detectors, which iden.fy and measure the energy of charged par.cles. FAUST was recently upgraded to posi.onsensi.ve detectors which enable higher resolu.on in rela.ve momentum. Many different structural tolerances may result in inaccurate rela.ve posi.oning. This final posi.on must be accurately known for upcoming experiments. Overview: Descrip.on of Kmeans: Picture from: Thomas, Philip. “Midterm Review.” Ar.ficial Intelligence 383. University of Massachuseas Amherst, Amherst, MA. 25 Mar. 2014. Lecture. Plot showing the distribu.on of slopes found by Kmeans. Blue comes from data obtained from a beam, red from radioac.ve source, and orange from a simula.on. Plot showing the distribu.on of slope uncertainty. Less centered stripes give worse fits because the data is more square shape than rectangular. Explains devia.on from 1 in orange data on plot to the leR Phase 2, Ideal Detector Alignment with HC: •Beam and source agree closely for detectors with good data •Significant differences with the Simula.on •Number of stripes •Slope of stripes •Detectors are in fact moving. •Use Hill Climbing to find a set of transforma.ons which make beam and source data look more like simula.on •Hill Climbing can be applied to a variety of problems, however it’s performance can also be affected by a variety of factors •Extensive tes.ng must be done to fully understand it •Presently, only preliminary tests have been done for this algorithm Acknowledgements: Thank you to the SJY Research Group, the Cyclotron Institute, and Texas A&M University. This work was supported by the Robert A. Welch Foundation under Grant No. A-1266 and the U. S. Department of Energy under Grant No. DE-FG03-93ER-40773 and the National Science Foundation under Grant No. PHY-1263281. XPosi.on (cm) XPosi.on (cm) XPosi.on (cm) YPosi.on (cm) XPosi.on (cm) XPosi.on (cm) YPosi.on (cm) YPosi.on (cm) YPosi.on (cm) YPosi.on (cm) Count YPosi.on (cm) YPosi.on XPosi.on YPosi.on YPosi.on XPosi.on XPosi.on Setup: • Two ini.ally parallel lines are rotated randomly • Hill Climbing is told to make them parallel again through rota.ons • 6 free parameters for 3 rota.ons each Angle between Lines aRer Hill Climb (deg) Count beam source simula.on source Setup: • Ring of detectors rotated by .5 degrees about beamaxis • Each detector is rotated randomly within a given range • Hill Climbing is told to rotate ring such that the set of stripes are as close to expected as possible • 1 free parameter. eval(P) at the end of Hill Climb (θ.5)/.5 θ in degrees Black min/max rota.on: [.05 ˚, .05 ˚] Red min/max rota.on: [.1 ˚, .1 ˚] Green min/max range: [.2 ˚, .2 ˚] .5˚ •Geometry Simula.on •“Perfect World” expecta.on •Alpha par.cle simula.on perfect elas.c scaaering Black K=1 Red K=2 Green K=3 HC tries to find the global maximum of eval(P) by changing P. The picture to the leR shows a successful Hill Climb with one free parameter. Local maxima causes difficulty for successful HC. Picture from: "Hill Climbing." Wikipedia. Wikimedia Founda.on, 27 July 2014. Web. 03 Aug. 2014. P eval(P)
Transcript of Balaban Poster - Cyclotron Institute
Geometry Simula.on
4He @15MeV/A+ natAu 228Th Source
Descrip.on of Hill Climbing (HC):
Novel Techniques for the Posi3on Calibra3on of FAUST David Balaban, Cyclotron Ins,tute, Texas A&M University (REU student from University of Massachuse@s Amherst)
Advisers: Sherry Yennello, Lauren Heilborn, Cyclotron Ins,tute, Texas A&M University.
0. Collect Data
Posi.on plot aRer raw data collec.on for detector 21 Apply cuts on signal strength to filter
out noise levels. The detectors are also stretched so they can fill region.
1. Signal Processing
2. Rota.on
Rotate data by 45 degrees, the expected angle of the slope. This makes projec.ng and fiYng easier.
Phase 1, Stripe Iden.fica.on with K-‐means:
3. Run K-‐means Algorithm
K-‐Means is used to iden.fy loca.on of stripes. Colors shown are different K-‐values, best one must be selected.
4. Data Selec.on
K-‐means will give approximate loca.on of stripe, can now do a linear fit to data.
5. Linear Fit
Rotate lines back by 45 degrees. Colors show which points were used in fit
1. Ini.alize k random points 2. Calculate average posi.on of data associated with each
point 3. Reset point to average posi.on 4. Repeat un.l convergence will use this method to iden.fy stripes in data
• Define set of free parameters P • Define method eval(P) to evaluate parameters to a single value
Problem:
Tungsten mask blocks charged par.cles and creates striped paaern on detectors. Stripes on detectors will be displaced according to detector placement. Goal is to find how far they are from expected posi.ons 2 phase process: 1.) Iden.fy stripes on detector with the K-‐means algorithm 2.) Find set of linear transforma.ons applied to detector which will reposi.on the stripes to the expected values with the Hill Climbing algorithm
The Forward Array Using Silicon Technology (FAUST) consists of 68 detectors, which iden.fy and measure the energy of charged par.cles. FAUST was recently upgraded to posi.on-‐sensi.ve detectors which enable higher resolu.on in rela.ve momentum. Many different structural tolerances may result in inaccurate rela.ve posi.oning. This final posi.on must be accurately known for upcoming experiments.
Overview:
Descrip.on of K-‐means:
Picture from: Thomas, Philip. “Midterm Review.” Ar.ficial Intelligence 383. University of
Massachuseas Amherst, Amherst, MA. 25 Mar. 2014. Lecture.
Plot showing the distribu.on of slopes found by K-‐means. Blue comes from data obtained from a beam, red from radioac.ve source, and orange from a simula.on.
Plot showing the distribu.on of slope uncertainty. Less centered stripes give worse fits because the data is more square shape than rectangular. Explains devia.on from 1 in orange data on plot to the leR
Phase 2, Ideal Detector Alignment with HC:
• Beam and source agree closely for detectors with good data • Significant differences with the Simula.on
• Number of stripes • Slope of stripes
• Detectors are in fact moving.
• Use Hill Climbing to find a set of transforma.ons which make beam and source data look more like simula.on • Hill Climbing can be applied to a variety of problems, however it’s performance can also be affected by a variety of factors • Extensive tes.ng must be done to fully understand it • Presently, only preliminary tests have been done for this algorithm
Acknowledgements: Thank you to the SJY Research Group, the Cyclotron Institute, and Texas
A&M University. This work was supported by the Robert A. Welch Foundation under Grant No. A-1266 and the U. S. Department of Energy under Grant No. DE-FG03-93ER-40773 and the National Science Foundation under Grant No. PHY-1263281.
X-‐Posi.on (cm) X-‐Posi.on (cm)
X-‐Posi.on (cm) Y-‐Posi.on (cm)
X-‐Posi.on (cm)
X-‐Posi.on (cm)
Y-‐Posi.on (cm)
Y-‐Posi.on (cm)
Y-‐Posi.on (cm)
Y-‐Posi.on (cm)
Count Y-‐Posi.on (cm
)
Y-‐Posi.on
X-‐Posi.on
Y-‐Posi.on
Y-‐Posi.on
X-‐Posi.on X-‐Posi.on
Setup: • Two ini.ally parallel lines are rotated randomly • Hill Climbing is told to make them parallel again through rota.ons • 6 free parameters for 3 rota.ons each
Angle between Lines aRer Hill Climb (deg)
Count
beam source simula.on
source
Setup: • Ring of detectors rotated by .5 degrees about beam-‐axis • Each detector is rotated randomly within a given range • Hill Climbing is told to rotate ring such that the set of stripes
are as close to expected as possible • 1 free parameter.
eval(P) at the end of Hill Climb
(θ-‐.5)/.5 θ in degrees
Black min/max rota.on: [-‐.05 ˚, .05 ˚] Red min/max rota.on: [-‐.1 ˚, .1 ˚] Green min/max range: [-‐.2 ˚, .2 ˚]
.5˚
• Geometry Simula.on • “Perfect World” expecta.on • Alpha par.cle simula.on perfect elas.c scaaering
Black K=1 Red K=2 Green K=3
HC tries to find the global maximum of eval(P) by changing P.
The picture to the leR shows a successful Hill Climb with one free parameter. Local maxima causes difficulty for successful HC.
Picture from: "Hill Climbing." Wikipedia. Wikimedia Founda.on, 27 July 2014.
Web. 03 Aug. 2014.
P
eval(P)
