Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Vessel Traffic Model

60 views

Published on

  • Be the first to comment

  • Be the first to like this

Vessel Traffic Model

  1. 1. Stochastic Modeling of Transit Vessel Traffic through the 
 Strait of Istanbul Safak Ozkan Photo: Paul Work Department of Civil Engineering Bosphorus University
  2. 2. OBJECTIVES: • to quantify casualty risk variation… 1)…along the Strait 2)…among different vessel sizes SCOPE: • Pilotage errors • Currents are assumed to be the predominant factor for vessel drift • Vessel lengths are limited to 50 - 200 m Present Study
  3. 3. the Strait of İstanbul • exchange of two distinct water systems between BLACK SEA – MEDDITERANEAN SEA
  4. 4. the simulation program rather acts like a numerical test in order to quantify the casualty risk relatively Present Study METHODOLOGY: • Stochastic Model • Random parameters include LOA and pilotage error • the autopilot • Physics Based Mathematical Simulation
  5. 5. • 12 maneuver points • the turn angles are @ Üsküdar, Ortaköy and Büyükdere ∼ 45o
 @ Yeniköy ∼ 80o • At Kandilli and Yeniköy the forward sight is blocked by the bends • Currents mount up to
 7-8 knots whilst northerly winds • narrowest section at Kandilli (app. 700 m) courtesy of Yüce, 1995 Physical Characteristics of the Strait
  6. 6. Hydrodynamics of the Strait • Count Marsigli identified a two layer flow in the Strait in year 1679 • The surface flow is 
 driven by sea-level differences, Δη • The lower layer flow is driven by density differences, ρMed – ρBS Courtesy of London Science Museum, Photo: Emre Otay
  7. 7. Department of Navigation, Hydrography and Oceanography, map no 9001 Surface Currents (Akyarlı and Arısoy, 1994) • Quantitative observations on sea level differences being made since 1918 • mean(Δη) ~ 30 – 35 cm (Büyükay, 1990) • Instantaneous difference -5 cm to 77 cm. (Akyarlı, 1997) • transient changes in Δη, and winds causes orkoz currents be formed.
  8. 8. (Örs, 1998) Surface Currents Department of Navigation, Hydrography and Oceanography, map no 9001 MODEL: • Shallow water equations • Slip boundary conditions at the solid boundaries • Reynolds number is artificially lowered (Laminar flow) REALITY: • Transient nature • Under certain circumstances north- going counter currents may develop (orkoz).
  9. 9. Casualty Statistics • over 300 vessels involved in casualties • Annually 50,000 vessels transit 
 the Strait • 10% of them are tankers with liquid cargo • Approximately every 12 minutes a vessel enters the Strait (Gören, 2002)
  10. 10. Present Regulations • Traffic Separation Scheme issued in 1994 • Maximum speed 
 10 knots • Vessels longer than 200 m cannot keep within the lanes • For vessels longer than 300 m, opposite direction is suspended for all vessel types Therefore vessels longer than 200 m are out of the scope of the present study
  11. 11. Ship Hydrodynamics • ship motion is represented with 3 DOF xDp RmFF xx =+ yDp RmFF yy =+ zzcurrh IMM φ=+/ Hydrodynamic forces on ship parts are analyzed separately : • Hull forces • Propeller forces • Rudder forces
  12. 12. Equations of Motion ∫ ∫ + ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + + =Δ Tt t ox t t Dpx x o o o x dttRdt m tFtF R )( )()( ∫ ∫ + ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + + =Δ Tt t oy t t Dpy y o o o y dttRdt m tFtF R )( )()( ∫ ∫ + ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + + =Δ Tt t oz t t currh z o o o dttdt m tMtM )( )()(/ φφ xDp RmFF xx =+ yDp RmFF yy =+ zzcurrh IMM φ=+/
  13. 13. Hull Forces • Hull forces are computed along the longitudinal axis and transverse axis of the vessel • The empirical equations are suitable for maneuvering vessels at low velocities. • Hull forces are due to viscous drag and lift forces tctvt eVVYF ,)( φ⋅−= φφρ eeVVACCF ctwsrfl ⋅⋅−+−= 2 2 1 )()(
  14. 14. • Propeller thrust is set constant such that the linear velocity of the vessel is around 10 knots during the navigation • For southbound vessels, calm water velocity is 8 knots • For southbound vessels, calm water velocity is 12 knots LOAsouthbound=125 m, complete navigation Propeller Forces
  15. 15. courtesy of Schilling Rudder Systems • Rudder is a symmetrical hydrofoil shadowed by the hull augmented by the propeller • Force developed on rudder is proportional to square of the inflow velocity Rudder Forces 2 nflowiL UF ∝
  16. 16. Rudder Forces courtesy of Schilling Rudder Systems • FL results in a turning moment on the hull • At stall point CL is maximum • Conventional rudders have stall angles at 35o • Beyond the stall point CL
  17. 17. Photo: Conny Wickberg Ship Maneuverability Turning Circle Test: A measurement of ship maneuverability
  18. 18. Turning Circle Test 925 m965 m Tactical Diameter 360 m394 mTransfer 1015 m1068 mAdvance Real Parameters (ESSO OSAKA) Simulation – simulation – IMO specifications (2002) on ship maneuverability require that the turning circle parameters be linearly related to vessel length
  19. 19. • The Strait is meshed with stations into 10 
 sub-regions where major course alterations take place. • Navigation runs are carried out in between every two successive stations separately. • Regions are meshed with checklines • Vessel positions are recorded where their Principals of the Simulation
  20. 20. ASSUMPTIONS & METHODOLOGY: • Main philosophy is to evaluate the mapping of the position distributions from one checkline to the next • Vessels are handled by an autopilot • The autopilot acts with a constant level of error in a region of course alteration • Surface current includes no eddies • Constant currents act at all points around the ship hull • The navigation of vessels is independent of the opposite direction traffic. Principals of the Simulation
  21. 21. RANDOM VARIABLES: • vessel length f(LOA), 
 all the vessel related parameters are related to LOA Principals of the Simulation • initial position f(xin) • autopilot error parameters f(ε ), f(τ )
  22. 22. Principals of the Simulation DISCRETIZATION of the INPUT VARIABLES: • Initial conditions, , are correlated to xin by curve fitting) • Whenever a random distribution is discretized, the shape of the distribution within the discretized bin is approximated with a constant shape function
  23. 23. Principals of the Simulation RE-COMBINATION of SCATTERED POSITION NODES: • the set of discrete position nodes have to be drawn back into a continuous form at the entrance of a navigation region • When the navigation run is completed we have a set of discrete position points scattered along the line (checkline or station) • this is achieved in two steps
  24. 24. Principals of the Simulation RE-COMBINATION of SCATTERED POSITION NODES: STEP 1 • Since the pilotage error is originally a continuous distribution, the position nodes originating from one single initial vessel represents a continuous distribution on the checkline
  25. 25. Principals of the Simulation RE-COMBINATION of SCATTERED POSITION NODES: STEP 1 • Position nodes are combined into a continuous distribution according to the shape functions • Shape functions represent the bin widths and the location of the discretised node within its corresponding bin
  26. 26. Principals of the Simulation RE-COMBINATION of SCATTERED POSITION NODES STEP 2 • In the end we have a number of continuous position distributions – for each initial vessel position – to be composed into the ultimate position distribution
  27. 27. Routes According to TSS • Routes are developed by locating the mid-lines of the TSS lanes • All vessel sizes incorporated in the program, i.e.
 (50 m < LOA < 200 m) are assumed to follow the same pre-determined routes
  28. 28. • At each time step the autopilot checks on the 
 route to pick a candidate 
 destination point lying on the pre-determined route at a specific distance from the vessel position. Maneuver Decider
  29. 29. Maneuver Decider • When an isosceles triangle is formed between vessel position and destination point maneuver is initiated • The autopilot is provided with the constraint variables 
 ΔRx ΔRy and Δφz
  30. 30. Autopilot ∫ ∫ + ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + + =Δ Tt t ox t t Dp x o o o xx dttRdt m tFtF R )( )()( ∫ ∫ + ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + + =Δ Tt t oy t t Dp y o o o yy dttRdt m tFtF R )( )()( ∫ ∫ + ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + + =Δ Tt t oz t t currp z o o o dttdt m tMtM )( )()(/ φφ • The autopilot physically has the control of the rudder angle, γ (t) • There are 3 constraint equations to be satisfied • Therefore a physical model for γ (t) must be constructed which must bring in only 3 unknowns.
  31. 31. ( )2 21 2 22 TTTTl o Δ−Δ− + =Δ+ γγ γ ( )2 21 1 1 TTTTl oo Δ−Δ− + =Δ+ γγ γ • The physical model for γ`(t) is a partially defined function which includes only 3 unknowns: γ1 , γ2 , T a Physical Model for γ (t)
  32. 32. • 3 equations – 3 unknowns • the equations are implicit integral equations • discretization of the equations yield non-linear terms • Newton-Raphson method is used a Physical Model for γ (t) ∫ ∫ + ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + + =Δ Tt t ox t t Dp x o o o xx dttRdt m tFtF R )( )()( ∫ ∫ + ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + + =Δ Tt t oy t t Dp y o o o yy dttRdt m tFtF R )( )()( ∫ ∫ + ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + + =Δ Tt t oz t t currp z o o o dttdt m tMtM )( )()(/ φφ Equations: Unknowns: γ1 γ2 T
  33. 33. Human errors are primarily classified in two categories • lack of ship-handling skills • lack of knowledge (Poyraz and Paksoy, 1998; Oğuzülgen 1995) • ε, (handling error), 
 set γ(t) = ε ⋅ γ`(t) • τ, (delay error),
 during the computations of γ`(t), the magnitude and the direction of surface currents are perceived with a time delay Autopilot Error Parameters τ and ε perfect pilotage corresponds to ε = 100%, τ = 0 sec.
  34. 34. pure handling, ε , and pure delay, τ , errors
  35. 35. Position Distributions • All the simulation program does is 
 evaluate the probability distributions of vessels along the checklines • The casualty risks are evaluated afterwards in a post-processing
  36. 36. Ramming and Grounding INPUT: • Q=50,000 vessels/year • f(LOA) Investigate the casualty risk variation • vessel length, LOA • travel direction • casualty type • regions of the Strait
  37. 37. Casualty Model – Collision Risk x { } dxXxSdxXxN SN )()(∫ ∫=ξ groundingzone collision zone 2 Q∝ξ
  38. 38. Casualty Model – Collision Risk High risk regions are (simulation) •Yeniköy •Büyükdere – Sarıyer •Kandilli
  39. 39. Casualty Model – Ramming and Grounding groundingzone ∫=Λ dxXxN N )( Q∝Λ
  40. 40. Casualty Model – Ramming and Grounding High risk regions are (simulation) •Ortaköy – Kanlıca
  41. 41. Comparison with Statistical Data • Collision risk is overestimated for larger vessels (Probably due to better ship-handling provided for larger vessels) – simulation – – statistical data – (Gören, 2002)
  42. 42. Comparison with Statistical Data (Gören, 2002) SIMULATION: 31.1≅ Λ ξ MEASURED: 95.1≅ Λ ξ • R/G seem to be over-estimated (Error is primarily due to constant shape functions)
  43. 43. Conclusion • CRG risk is evaluated with stochastic simulation • southbound vessels are at a more disadvantageous situation in terms of rudder control • vessel lengths directly correlate with CRG risk • High risk regions: Yeniköy, Kandilli and Büyükdere • Collision risk is higher than R/G risk • ξ ∝ Q2 • Λ ∝ Q
  44. 44. • Higher order shape functions must be incorporated • Different routes lying within the TSS lanes may be incorporated • Water currents be solved numerically as a function of Δη and ρMed – ρBS • Ship hydrodynamic forces be elaborated to include the shallow water and narrow channel effects • A detailed bathymetry data can be supplied for better representation of grounding zones for Further Improvements of the Simulation
  45. 45. Future Prospects Offered by This Study • Real time simulations can be implemented with extensive simultaneous surface current measurements • Similar channels can be analyzed with this mathematical simulation program for quantitative risk level comparison with the Strait of İstanbul

×