LT1: Development, Calibration and Validation of Bus Following Model

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LT1: Development, calibration and validation of bus-following model to support analysis and evaluation of alternative BRT strategies under different scenarios

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LT1: Development, Calibration and Validation of Bus Following Model

  1. 1. LT1: Development, calibration and validation of bus-following model to support analysis and evaluation of alternative BRT strategies under different scenarios Luis Antonio Lindau Paula Manoela dos Santos
  2. 2. Mile- OUTPUTSstones M1 Do vehicle-following literature review M2 Check potential of existing models to represent bus behavior M3 Select data collection technique M4 Plan field data collection M5 Collect data M6 Process data M7 Define bus-following model M8 Final report Transit Leaders Roundtable MIT, June 2011
  3. 3. Comparing: GHR and Gipps GHR reveled unstable for typical Gipps is attractive for successive bus stopping maneuvers. stopping buses. 1 0,6 0,5 0,4 0 0,2acceleration (m/sΒ²) 0 20 40 60 80 100 120 140 acceleration (m/sΒ²)) -0,5 0 0 50 100 150 200 -1 -0,2 -1,5 -0,4 -2 -0,6 -2,5 time (s) -0,8 time (s)
  4. 4. Data collection (manual vs. automatic) Reported last year
  5. 5. Solution: image recognition software Kinovea 0.8.15 β€’ Developed for studying athletic techniques β€’ free and open source β€’ 33 info/s
  6. 6. Paralaxis correction 𝐢1 +𝐢2 𝑋 𝑓 +𝐢3 π‘Œ 𝑓 𝐢6 +𝐢7 𝑋 𝑓 +𝐢8 π‘Œ 𝑓 π‘‹π‘Ÿ = 𝐢4 𝑋 𝑓 +𝐢5 π‘Œ 𝑓 +1 π‘Œπ‘Ÿ = 𝐢4 𝑋 𝑓 +𝐢5 π‘Œ 𝑓 +1Bleyl, R. L. (1972) Traffic analysis of time lapse photographs without employing a perspective grid. TrafficEngineering, p. 29-31.
  7. 7. Methodology Find a setting to film Locate and measure 4 reference pointsFilm making (with vehicle loading Film analysis with image recognition estimation) softwareData collection (distance vs. time) Calibration of parameters
  8. 8. Calibrated modelsFREE FLOW 𝑣(𝑑) π‘Ž 𝑑 + 𝑑𝑑 = 𝐴 π‘šπ‘Žπ‘₯ Γ— 1 βˆ’ 𝑉 𝑑𝑒𝑠BUS STOPPING𝑣𝑛 𝑑 + 𝑇 = 𝑏𝑛 Γ— 𝑇 + 𝑏 𝑛 2 Γ— 𝑇 2 βˆ’ 𝑏 𝑛 Γ— 2 Γ— π‘₯ π‘‘π‘Žπ‘Ÿπ‘”π‘’π‘‘ βˆ’ π‘₯ 𝑛 (𝑑) βˆ’ 𝑣 𝑛 (𝑑) Γ— 𝑇 Static target: next station
  9. 9. Data analysis Software output Real distance calculation TrackLabel : 18:39:03 corrected parameters Coords (x,y:px; t:time) t (s) Xv (m) Yv (m) h (m) d (m) x y t 0 5,1242567 6,0919539 7,96052191 0 23 27 0 0,5 5,07053561 5,88621922 7,76903521 0,1914867 23 26 500 0,634 4,8952569 5,84434539 7,62364173 0,33688018 22 26 634 22 25 834 0,834 4,84202476 5,63956763 7,43302945 0,52749246 21 25 1067 1,067 4,66758358 5,59817115 7,28874863 0,67177328 21 24 1101 1,101 4,61483563 5,39434269 7,09898873 0,86153319 21 23 1334 1,334 4,56224048 5,19110469 6,91097722 1,04954469 20 23 1401 1,401 4,38895678 5,15053206 6,766899 1,19362291 20 22 1535 1,535 4,3368393 4,94823141 6,57975449 1,38076742 19 22 1668 1,668 4,16437691 4,90812353 6,43674697 1,52377494 19 21 1701 1,701 4,1127325 4,70675283 6,25044725 1,71007466
  10. 10. Data analysis Real distance calculation Model distance calculation (from the linear acceleration model) Real Model t (s) Xv (m) Yv (m) h (m) d (m) a (m/sΒ²) minΒ²(m/s) v d d (m) 0 5,1242567 6,0919539 7,96052191 0 0 0 0 0 0,5 5,07053561 5,88621922 7,76903521 0,1914867 0,89368685 0,446843423 0,001019845 0,223421710,634 4,8952569 5,84434539 7,62364173 0,33688018 0,86023957 0,562115526 0,001454277 0,298745190,834 4,84202476 5,63956763 7,43302945 0,52749246 0,85161119 0,732437764 0,00676666 0,445232751,067 4,66758358 5,59817115 7,28874863 0,67177328 0,83886217 0,92789265 0,000106948 0,661431731,101 4,61483563 5,39434269 7,09898873 0,86153319 0,82423192 0,955916535 0,028089857 0,693932891,334 4,56224048 5,19110469 6,91097722 1,04954469 0,82213426 1,147473819 0,007788133 0,961294291,401 4,38895678 5,15053206 6,766899 1,19362291 0,80779575 1,201596134 0,023049822 1,041801241,535 4,3368393 4,94823141 6,57975449 1,38076742 0,80374457 1,309297907 0,026738876 1,217247161,668 4,16437691 4,90812353 6,43674697 1,52377494 0,79568284 1,415123726 0,013998753 1,405458611,701 4,1127325 4,70675283 6,25044725 1,71007466 0,78776154 1,441119856 0,06607938 1,45301557 Minimize the sum of squared differences toAmax the 𝑣(𝑑) obtain Vdes π‘Ž 𝑑 + 𝑑𝑑 = 𝐴 π‘šπ‘Žπ‘₯ Γ— 1 βˆ’ best alignment𝑉 𝑑𝑒𝑠 0,83413911 15,9777749
  11. 11. Data analysis: acceleration 8 50 observed acceleration 45 7 observed speedspeed (m/s) – acceleration (m/sΒ²) real distance 40 6 35 5 distance (m) 30 4 25 20 3 15 2 10 1 5 0 0 0 2 4 6 8 10 12 time (s)
  12. 12. Data analysis: acceleration 8 50 observed speed 45 7 speed modeledspeed (m/s) – acceleration (m/sΒ²) 40 observed acceleration 6 acceleration modeled 35 real distance 5 distance (m) distance modeled 30 4 25 20 3 15 2 10 1 5 0 0 0 2 4 6 8 10 12 time (s)
  13. 13. Acceleration by occupancy level 1,60 1,40 level 1 1,20acceleration (m/sΒ²) level 2 1,00 level 3 0,80 0,60 level 4 0,40 level 5 0,20 average 0,00 0 1 2 3 4 5 6 bus load levels Level 1 Level 2 Level 3 Level 4 Level 5 Acceleration 1,07 0,94 0,92 0,81 0,80 (m/sΒ²) (0,11) (0,16) (0,09) (0,17) (0,14) Time to reach 33 35 34 40 49 60km/h (s) (7,49) (7,00) (3,60) (7,74) (16,74)
  14. 14. Data analysis: deceleration 25distance (m) – speed (m/s) 20 15 10 observed distance 5 observed speed 0 0 2 4 6 8 10 12 14 time (s)
  15. 15. Data analysis: deceleration 25distance (m) – speed (m/s) 20 15 10 modeled distance modeled speed 5 observed distance observed speed 0 0 2 4 6 8 10 12 14 time (s)
  16. 16. Deceleration by occupancy level 7,00 6,00 level 1 5,00deceleration (m/sΒ²) level 2 4,00 level 3 3,00 level 4 2,00 1,00 average 0,00 0 1 2 3 4 5 bus load levels Level 1 Level 2 Level 3 Level 4 Ο„=1s 1,80 1,58 1,44 1,29 (0,52) (0,78) (0,63) (0,52) Deceleration (m/sΒ²) Ο„=0,66s 2,13 1,97 1,70 1,51 (0,66) (1,20) (2,20) (2,69)

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