Outline

2. Outline • Motivation • Mobility tracking in large scale cyberphysical systems • Application to the Sacramento – San-Joaquin Delta • Flow reconstruction from Lagrangian measurements • Constitutive equations • First approach: Quadratic Programming • Ensemble Kalman filtering based algorithm • Application: Georgianna Slough • Towards fleet coordination • Viability based optimal control • Application to submarine path planning • Future steps

3. Motivation Mobile sensing in infrastructure cyberphysical systems • Smartphones, mobile computational platforms: convergence of • Multi-media • Communication • Sensing • Unprecedented opportunities for infrastructure systems • Cyberphysical systems: • “Cyber”: information network • “Physical”: governed by some physical laws Success stories • Mobile century project (with Nokia): monitoring of highways • Mobile millenium project (with Nokia): monitoring of arterials • Floating sensor networks: today’s talk Goal of this project • Design, development and deployment of a mobile sensor network for monitoring distributed hydraulics networks • Creation of novel inverse modeling algorithms • Coordinated control algorithms for heterogeneous water robotics platforms (floating sensors, submarine, etc.)

4. Deployment area: Sacramento – San-Joaquin Delta • Challenging area for sensor • network deployment: • Tidal forcing (inversion) • Salt intrusion • Networked system Numerous environmental engineering applications • Salmon migration • Characterization of the mixing / hydrodynamics Two deployment areas: • Georgianna Slough (current) • 3-mile Slough (this summer)

5. June 2, 2004 June 5, 2004 Possible applications Response to unanticipated events could be improved using mobile sensing, for example in the case of: - Heavy Rains - Contaminant Spills - Levee Failures Example: 2004 Jones Tract Levee Failure • - Silt from flooded area • contaminated the Delta • - South pumps shut down • until contaminant cleared • - Fixed network insufficient • to determine safe startup - $1M/day, 3 day shutdown [Source: M. Stacey, 2005]

6. Traditional [Eulerian] sensing in the Delta Few key locations: 50 sensors for 1000 km of channel Inflexible (install once)‏; expensive to install and maintain Good for long term trends; not good for localized or medium-term phenomena

7. UC Berkeley [Eulerian] sensing “Deployable” Eulerian sensors: Underwater sensors, autonomy 15 days. Measure cross sectional velocity and stage Need to be deployed from crane operated boat Need to be anchored to the ground (because of drift)

8. Envisioned monitoring architecture Inverse modeling Server (UC Berkeley)

9. Envisioned monitoring architecture Cyberphysical infrastructure monitoring system • Distributed monitoring system (floating sensors, vehicles) • Position / velocity sensing (GPS based) • Additional sensing to be added later (salinity, CTD, etc.) • Wireless communication (cell phones, GSM modules, etc.) • Onboard communication infrastructure (linux gumstix) Past experience • Nokia Mobile Century project (100 vehicles) Additions to network • Fixed sensors (USGS) • Eulerian sensors • Submarine

10. Floating [Lagrangian] sensor network Current fleet: 10 passive GPS floats (courtesy M. Stacey), 10 GPS/wireless enabled drifters (manufactured at Berkeley) Target (2009) fleet of 100 (potentially using Nokia N95) Potential additional sensors: salinity, temperature, dissolved O2 To Berkeley Data Center via GPRS Short-range wireless

11. Vision: progressive instrumentation of the Delta Development of an autonomous monitoring system Fleet of intelligent robotic sensors: tidal surfing Link to Internet

12. Motivation State estimation method for two-dimensional shallow water equations in rivers using Lagrangian drifter positions as measurements The aim of this method is to compensate for the lack of knowledge of upstream and downstream boundary conditions that causes inaccuracy in the velocity field estimation Drifters report their positions and thus provide additional information of the state of the river We seek to incorporate Lagrangian measurements into a two-dimensional Shallow water model with poorly known upstream and downstream boundary conditions using an Ensemble Kalman Filter (EnKF)

13. Motivation

14. Outline • Motivation • Mobility tracking in large scale cyberphysical systems • Application to the Sacramento – San-Joaquin Delta • Flow reconstruction from Lagrangian measurements • Constitutive equations • First approach: Quadratic Programming • Ensemble Kalman filtering based algorithm • Application: Georgianna Slough • Towards fleet coordination • Viability based optimal control • Application to submarine path planning • Future steps

15. Constitutive equations Hydrodynamics equations: two dimensional shallow water equations Variables: Velocity field Total depth of water Coefficient of turbulence diffusion Free surface elevation

16. Constitutive equations Hydrodynamics equations: two dimensional shallow water equations Friction forces: given by Manning’s law Parameters: Manning’s coefficient Bed slope

17. Boundary and initial conditions Boundary conditions: Initial conditions:

18. Lagrangian drifter trajectories Internal (Lagrangian) conditions: motion of a given drifter is given by the integration of the equations of motion in water (continuous time nonlinear dynamical system) Initial drifter release position: assumed to be known (released by user).

19. Lagrangian drifter trajectories Internal (Lagrangian) conditions: motion of a given drifter is given by the integration of the equations of motion in water (continuous time nonlinear dynamical system) Initial drifter release position: assumed to be known (released by user).

20. Outline • Motivation • Mobility tracking in large scale cyberphysical systems • Application to the Sacramento – San-Joaquin Delta • Flow reconstruction from Lagrangian measurements • Constitutive equations • First approach: Quadratic Programming • Ensemble Kalman filtering based algorithm • Application: Georgianna Slough • Towards fleet coordination • Viability based optimal control • Application to submarine path planning • Future steps

21. Linearization of the constraints Low Froude number conditions (subcritical): Linearization of the equations around a nominal flow Linearized equations: Nominal flow does not need to be static or uniform:

22. Implicit discretization of the constraints Implicit discretization scheme: Example (equation for u component of the velocity) Implicit discretization scheme: Implicit Euler in time, second order centered in space.

23. Data assimilation functional L2 error of measurements vs. prediction: minimize the discrepancy between measured flow and estimated flow Variables used in the assimilation: State, observer operator, observation vector, covariance. State to estimate Initial state Background term Observation vector Background covariance Observation covariance Observation operator

24. Data assimilation functional Problem of semi definiteness: add term to make result semi definite (guess term) Variables used in the assimilation: State, observer operator, observation vector, covariance. State to estimate Initial state Background term Observation vector Background covariance Observation covariance Observation operator

25. Quadratic program formulation Assemble cost functional and constraints: quadratic cost functional, implicit linear constraints (flow dynamics), knowledge of bounding box for functions. Results in quadratic program: minimization w.r.t. the initial state

26. Outline • Motivation • Mobility tracking in large scale cyberphysical systems • Application to the Sacramento – San-Joaquin Delta • Flow reconstruction from Lagrangian measurements • Constitutive equations • First approach: Quadratic Programming • Ensemble Kalman filtering based algorithm • Application: Georgianna Slough • Towards fleet coordination • Viability based optimal control • Application to submarine path planning • Future steps

27. State augmentation Used method:

28. Discretized system System discretization:

29. Estimation framework Used method: hybrid systems framework

30. Observation operator

31. Ensemble Kalman filtering algorithm

32. Outline • Motivation • Mobility tracking in large scale cyberphysical systems • Application to the Sacramento – San-Joaquin Delta • Flow reconstruction from Lagrangian measurements • Constitutive equations • First approach: Quadratic Programming • Ensemble Kalman filtering based algorithm • Application: Georgianna Slough • Towards fleet coordination • Viability based optimal control • Application to submarine path planning • Future steps

33. Bathymetry

34. Twin experiments (water) To test the algorithm, we set up twin experiments First model • Mikes (SWE solver) • Calibrated forward sim • “ground truth” Second model – Telemac (SWE solver) • Running EnKF algorithm to estimate the state of the system

35. Implementation in twin experiments

36. Tidal forcing

37. Results (I)

38. Results (II)

39. Results (III)

40. Results (IV)

41. Results (V)

42. Results (VI) Example of error analysis: comparison between QP and EnKF

43. Example of use of current reconstruction

44. Towards active sensing

45. Lagrangian team

46. Conclusion, future steps Reconstruction of currents and additional sensing can be done using • Shallow water equation model • Inverse modeling (presently shown: EnKF) • Other techniques: adjoint based optimization, nudging Autonomous path planning • Requires knowledge of the currents • Can be done using optimal control (implemented with viability) • Has been tried in the Georgianna Slough Upcoming steps include • Development of a communication infrastructures • Real time inverse modeling • Augmentation of drifter fleet (heterogeneous fleet) • Coordination of autonomous fleet • Adaptive sampling (using submarine) • Tidal surfing • Autonomous drifters

47. Moving Lagrangian Sensors, coming soon on a highway or canal near you.... Mobile Millennium

48. Architecture

49. Lagrangian sensors on the highway…

50. A glimpse of Mobile Century (February 8th, 2008)