Chapter 9. Model Calibration. John Hourdakis Center for Transportation Studies, U of Mn

Transcription

1 Chapter 9 Model Calbraton John Hourdaks Center for Transportaton Studes, U of Mn Hourd00@tc.umn.edu

2 Why Calbrate? Computers Cannot Magcally Replcate Realty! Smulaton Models Are Desgned to be General Drver Behavor and Road Characterstcs Depend on Locaton.e. Mnnesota vs Calforna Vehcle Characterstcs (Horsepower, Sze, etc.) Weather Condtons (Dry, Wet, Ice, etc.) Day or Nght Mcroscopc Smulators Can Adapt and Replcate Almost Any Condton f the Model Parameters Are Properly Adjusted What s Realstc and What s Not? 2

3 Example of a Dsaster Half of an Ordnary Double Cloverleaf Freeway Speed 65 mph, Ramps 45 mph Turnng Warnngs More Than 2000 Feet Away Lot s of Traffc: 6500 veh/hour on Manlne Three Vehcle Types: Car, Truck, and Sem-Traler 3

4 Smulaton Results From 5 Scenaros Same Demands, Speed Lmts, Turnngs, Most of Model Parameters. Changed Car and Sem-Traler : Acceleraton Normal Deceleraton Maxmum Deceleraton (Emergency Stop) Average Speed Average Flow Total Travel Tme Av. Delay LOS +2f/s mph 683 vph 257 hours 9 sec/veh D +f/s mph 6200 vph 484 hours 4 sec/veh F BASE 46.7 mph 6396 vph 234 hours 9 sec/veh D -f/s mph 652 vph 393 hours 30 sec/veh E -2f/s mph 5500 vph 536 hours 57 sec/veh F 4

5 Calbraton Procedure Hstorcal system nput data H storcal system np ut data Actual system Smulaton Model System output data Comp are Model output data Vald? No Calbrate 5

6 REALITY Current Traffc Measurements, etc. Need to KNOW the Network to be Replcated Dependng on the Scope of the Project, Two or More of the Followng Are Needed : Manlne Volumes (Every X Feet) Manlne Speeds (Every X Feet) Travel Tmes (Lnk or Between O/D Pars) Bottleneck Capacty (Measured, Not Theoretcal) Entrance Ramp Queues Intersecton Queues and Queue Dscharge Rates 6

7 Modelng Parameters Global Parameters Vehcle Parameters Sze and Power Drver Behavor Car-Followng Model Parameters Reacton Tme Speed Dstbuton Among Lanes (Overtakng Manuevers) Local Secton Parameters Curvature and Grade Speed Lmt or Free Flow Speed Lane Changng Dstances Headway/Hestaton Factor 7

8 Model Parameter Issues Drver/Vehcle Characterstcs Lterature Does Not Provde Adequate Informaton Not Common to All Smulators No Info on Effects of Weather/Pavement/Ambent Condtons Car-Followng Parameters Depend on the Smulator s Car-Followng Model Employed. Most Smulators Do Not Adequately Descrbe the Modelng Process (f at all). User Has No Sense of Model Parameter Effects on Results. 8

9 Calbraton Issues Very Important For Model Accuracy and Robustness Accuracy Depends on Measurement Granularty Averages Over Several Days s a Bad Choce Mght Need Addtonal Informaton to be Collected n Turbulent Sectons (Bottlenecks, Weavng Areas, etc.) Smulaton Objectve Affects Calbraton When Adaptve Control Strateges Are Smulated, Strcter Valdaton s Needed Modelng of an Isolated Interchange n Rural Mnnesota Wll be Restrctve 9

10 Calbraton Issues VERY TIME CONSUMMING PROCESS Currently Smulators Do Not Provde a Methodology or Tools to Assst n Calbraton Often Users End Up n Endless Tral-and-Error Cycles Sporadc Attempts Made n Lterature to Streamlne the Process But: Focused on a Partcular Smulator Too Complex or too Nave to be Effectvely Used n Practce No Wdely Accepted Methods/Standards Currently Avalable 0

11 Before Calbraton! Check Geometry For Correctness Dsjoned Sectons Stuck Vehcles (Szes of Accel/Decel Lanes) Verfy Locaton of Detectors Check Input For Accuracy Entrance Volume Comparson (Perfect Match) Ext Volume Comparson (Match Sum Over All Hours) Volume Totals on Manlne Statons Should Match

12 Practcal Calbraton Methodology (Employed on Twn Ctes Freeways) Need Smultaneous Boundary and Manlne Staton Measurements. Technque: upstream manlne detector statons Objectve s to Match the Smulated and Actual Manlne Traffc Measurements Traffc Measurements Used: Volume and Speed Occupancy Affected by Detector Senstvty (Unknown) Perform Calbraton n Stages: Frst 2 Stages Based on Volume and Speed n That Order Further Improvements n Optonal 3 rd Stage: Dependng on Objectve.e. For Ramp Control -> Queue Length 2

13 Goodness-of-Ft Test Measures Recommended Goodness-of-Ft Measures:. RMS Percent Error = (Measures Overall % Error) n n = x y y 2 2. Correlaton Coeffcent = (Measures Lnear Assocaton) CORL = n n = ( x x)( y σ x σ y y) Where x s the Smulated Traffc Measurement at Tme x s the Mean of the Smulated Traffc Measurements y s the Actual Traffc Measurement at Tme y s the Mean of the Actual Traffc Measurements σ x s the Standard Devaton of the Smulated Traffc Measurement σ y s the Standard Devaton of the Actual Traffc Measurements n s the Number of Traffc Measurement Observatons 3

14 4 Goodness-of-Ft Measures (Cont.) 3. Thel s U (Consders the Dsproportonate Weght of Large Errors) 3 Components of Thel s U Us (Measure of Varance Proporton, Close to Satsfactory) Uc (Measure of Covarance Proporton or Unsystematc Error, Close to 0 Satsfactory) Um (Measure of Bas Proporton or Systematc Error, Close to 0 Satsfactory) Where σ y and σ x are the Standard Devatons of the Actual and Smulated Seres r s the Correlaton Coeffcent Between the Two Seres = = = + n n n x n y n x y n ) ( = = n x y s x y n U 2 2 ) ( ) ( σ σ = = n x y c x y n r U 2 ) ( ) ( 2 σ σ = = n m x y x y n U 2 2 ) ( ) (

15 Examples vo lu m e (v eh c le s/5- m n) actual volume smulated volume vo lu me (veh cles/5-mn) actual volume s mulated volume tme n 5-mn ncrements from mdnght tme n 5-mn ncreme nts from mdnght Fgure (a): Illustraton of unsatsfactory Um Fgure (b): Illustraton of unsatsfactory Uc vo lu m e (v eh c le s/5- m n) actual volume s mulated volume vo lu me (veh cles/5-mn) s mulated volume actual volume tme n 5-mn ncrements from mdnght Fgure (c): Illustraton of unsatsfactory Uc tme n 5-mn ncrements from mdnght Fgure (d): Illustraton of unsatsfactory Us 5

16 Stage : Volume-Based Calbraton Objectve s to Match Smulated and Actual Manlne Staton Volumes Smulaton Model Calbrated Begnnng Upstream and Proceedng Downstream Global Parameters Are Calbrated Frst: Usually Accomplshed n Frst Few Statons Tral & Error Iteratve Process For Each Parameter RMSP, r and U are the Metrcs Used n Each Iteratons Local Parameters Calbrated at All Statons Um, Uc and Us are the Metrcs Used at Ths Pont. 6

17 Stage 2: Speed-based Calbraton Objectve s to Match Smulated and Actual Manlne Staton Speeds and Bottleneck Locatons Actual Speeds Derved From Volume, Occupancy, and Effectve Vehcle Length (For Sngle Loop Detectors) Speed Contour Graphs Used For Comparng (Vsually) Smulated and Actual Speeds. If Speed Contours Exhbt Sgnfcant Dscrepancy, Revse Global Parameters From Stage 2. Begnnng Upstream and Proceedng Downstream, Calbrate Local Parameters Untl Manlne Speeds and All Bottleneck Locatons n the 2 Contour Graphs Match 7

18 Stage 3: Applcaton Dependent For Adaptve Ramp control: Compare Queue Lengths Local Smulaton Parameters Affectng Detector Output Need Further Calbraton n Ths Stage Smulated Entrance Ramp Queues Should Match Actual Ones Queue Measurements From 30 sec Detector Counts Queue = Metered Demand - Actual Demand (Upstream) Over-Calbraton to be Avoded to Ensure Generalty Repeat Smulaton Wth Dfferent Random Seeds Smulate Addtonal Days 8

19 Example of Calbraton AIMSUN Mcrosmulator Mn/DOT Ramp Meterng Evaluaton. 2 Test Stes (Only One Presented) TH 69 Northbound n Mnneapols, MN 2 Mles Long: From I-494 to 63 rd Avenue N 24 Entrance Ramps, 25 Ext Ramps 30 Detector Statons. 5-Mnute Volume and Occupancy March 2 st to 23 rd, :00 to 20:00 hrs 9

20 Test ste : TH 69NB A A B B A A B B 20

21 Stage Results (Volume) Goodness-of- Ft Measure r RMSP U Um Us Uc Values % Smulator Iteratons Requred, 2 Months (!) Irregulartes n Input Data Observed Due to Sensor Msplacement 2

22 22 Actual Speed Contour TIME TIME Upstream Upstream Downstream Downstream

23 Speed (sm ulaton) Stage 2 Results Stage 2 Results (Speed) (Speed) Smulated Speed After Stage 2 (About 200 Iteratons) Actual Speed Smulated Speed After Stage

24 Stage 3 Results (Queues) Smulated and Actual Queues Dd Not Match Before Ths Stage 3 rd Stage Requred About 00 Iteratons Example Ramp real queue smulaton queue after stage 3 smulaton queue before stage tme (5-mn ncrements from mdnght) Smulaton vs Real Queues 24

25 Valdaton Accuracy (Volume) RMS% r U Um Us Uc March 2 st (valdaton) March 22 nd (valdaton) March 23 rd (Calbraton) Over All Statons. 25

26 Results (Calbrated Parameters) AIMSUN Mcroscopc Smulator Parameter Intal After stage After stage 2 After stage 3 Max. desred speed (kmph) Max. acc. rate (m/s 2 ) Normal dec. rate (m/s 2 ) Max. dec. rate (m/s 2 ) Reacton tme (sec) Percent overtake Percent recover Max. speed dfference (kmph) Max. speed dfference on-ramp (kmph) Av. secton speed (regular secton, kmph) Av. secton speed (weavng secton, kmph) Av. secton speed (ramp secton, kmph)

27 Concluson Garbage In >>> Garbage Out Smulaton Useless/Dangerous Wthout Calbraton Questons? 27