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					   Intelligent Light Control using
           Sensor Networks

       Vipul Singhvi1,3, Andreas Krause2,
Carlos Guestrin2,3, Jim Garrett1, Scott Matthews1
         Carnegie Mellon University
                        1   Department of Civil and Environmental Engineering
                                                 2 School of Computer Science

                                            3 Center of Learning and Discovery
    Motivation
   Current built infrastructure
     Trillions of dollars investment

   Cost over the life cycle
   Research shows potential gains from
    reducing operating cost and
           Sensor networks
    improving occupant performance
                                          Life cycle building cost
                                             Maintenance and
     $10 Smart monitoring and actuation
            - $30 billion/yr from reduced    operation

           can significantly reduce cost and
       energy consumption                               Construction


           improve occupant performance
    $20 - $160 billion/yr gained from
    improvement in comfort leading to
    better occupant performance
   Reduction in energy cost related                   Salary cost over
    to reduced comfort &                               building life cycle
    performance: Complex tradeoff
    optimization
Motivating Scenario
                                                                Operator

                                             All lights
                                            0-10 levels
                              0
                             10

  Coordinate lighting to make everybody happy
                                                                  Controller
             Louvers




                                  Bob               Andy
            Strategy to exploit natural lighting
                         5
                         0                    5
                                              0
                                                                   Feed
                                                0
                                                5                  back



                       Predictive light control
 Louvers/
                                                           0
                                                           10
 Blinds                                 6
                                        0
Challenges

   Knowing the current state
       Light levels and occupants location
 Capturing occupant and operator
  preferences & happiness
 Optimization of tradeoff
       Occupants happier OR save more
        energy
Knowing the current state of the world

   Indoor Environment            Tracking occupants
       Light levels                  Smart tags
   Pervasive sensor                  RFID tags
    network                           Camera tracking
       Wireless or Wired




                        Desk
Preferences & Happiness
    Utility Theory: Framework to compare choices
     based on preferences
    Personal preference
    Attributes: Coolness, Horse Power, Mileage,
     COST….
    Representation complexity of utility function




    Lamborghini, Second Hand 2003   Toyota Corolla, New 2006
           model, $50,000                model,$30,000
    Building Operations: Occupants              Andy
                                          Bob   i
   Occupant preference:Comfort
       Light level
   Utility Function
     Task dependent
   Light levels
                Try to make everybody happy !
     Depends on lamp setting n

                         argmax
                                  i  a 
     Use sensing to learn effect of
      lamps on person i –  i
                            a
                                   i 1
     Control lamp settings a to max.
      occupant preferences,
      a=(a1,…,an), aj – level of lamp j
Building Operations: Operator
                                                                        Cheaper the better
   Operator preference: Cost




                                            Normalized utility
                                                                 1.00
       Operating cost                                           0.80
                                                                                              j
       Maintenance Cost                                         0.60

                                                                 0.40
   Decreases monotonically                                      0.20

    with the energy expended                                     0.00
                                                                           100          200        300

                                                                                 Operating Cost

   Utility function
                        n

                        
                        j 1
                               j   (a j )
       aj , jth lamp
Utility Maximization : Tradeoff

   Maximize system utility: Make occupants and operator
    happy!    Operator                              Occupants
                               n           n
               U  a   F (  j (a j ),   i (a))
                               j 1       i 1

       a = (a1,…….an)
   Scalarization technique                 n
                   U  a    *  (a)    i (a)
                                           i 1
          is the tradeoff parameter

                   a  arg max U (a)
                     *

                                      a
Utility Maximization: Complexity
                          n
U  a    *  (a)    i (a)                       a  arg max U (a)
                                                        *

                         i 1                                    a
                                     10 levels       10 levels
               10 levels a2             a4             a6




          10 levels a1            a4             a5 10 levels
                                10 levels

   Evaluating U(a) for combinations of all lamp setting
       for just 6 lamps the total number is 106
   Evaluating argmax U(a) is also over that big space
   Exponential in number of lamps!
Reducing Complexity
   Exploit problem                         a2             a4            a6
    structure: Zoning

                                      a1           a4             a5

                1 (a1 , a2 , a3 )   2 (a2 , a3 , a4 )            6
    a*  argmax                                               *  (ai )
            a    3 (a3 , a4 , a5 )   4 (a4 , a5 , a6 )        i 1


   Distributed action selection approach (Guestrin ’03)
       Exact solution to the coordination problem

                           n                             m
        a  argmax   i (ai1 ,..., aik )     j (a j )
          *

                  a       i 1                           j 1
Open-loop controller:
                  Coordinated Lighting

          Control law using
         Occupant utility and
         Coordination Graph
             approach
                                         a
Test Bed
   Control Schematics
   10 table lamps
   12 motes aka occupants
   Size: 146 * 30 in., 7 zones
                    146 in.




          7 6 5               4 3 2 1
Coordinated Lighting: Results
                                                     30%
              Coordinated
              Illumination
                                                           Energy
                                                           Cost
  Greedy                                        Measured
  Heuristic                                     utility
                                          0.4



• Comparison to greedy approach
   •Each occupant comes and actuates the light
   •Caveat: cannot reduce the level of a already ON light
• At  = 0.4, reduction in comfort = 7% but reduction in
  energy cost = 30%
Coordinated Lighting

   Performs significantly better than typical
    greedy approach
   Solves the complex optimization using the
    structure of the problem (zoning)
                                    Predictive
                                   light control

                                 Natural Lighting


                                   Coordinated
                                     Lighting
 Closed-loop controller:
                       Daylight Harvesting
    Sense natural light levels
    Actuate lamps to compensate for extra light

                  Control law
             Online sensing using
               sensor network                      a

Current Light
Level
Day Light Harvesting: Sun Simulation
                                             Sun Lamps
                              Simulated sun using
                               overhead lamps

                              Variability using the real
                               sunlight data from
                               Pittsburgh
                           Measured intensities at center
    Real sun intensities
Daylight Harvesting: Utility Redefined
                                                                    Sun Lamps


   Represents the sunlight
    intensity at time t and
    point in space x,
          :T  X  R
   New utility definition
                        n                           m
        U (a, t , x)    i ,xi (a,(t , xi ))     j ( a j )
                       i 1                         j 1

   Maximization problem
             a* (t , x)  argmax U (a, t , x)
                                      a
Running the Simulations
Day Light Harvesting: Evaluation
    Gamma values (0.01, 0.4), same setup
           Energy
           Cost                   Measured
                                  Utility



                    Measured                  Energy
                    Utility                   Cost


    Gamma = 0.01, 15% of energy savings
    Gamma = 0.4, 55% of energy savings
    Loss in occupant utility due to too much light
        Shading, Louvers
Day light harvesting

   Builds on the coordinated lighting approach
   Saves significant (~50%)energy cost during
    sun time
   Long term sensor
                                      Predictive
    deployment: battery life         light control
   Sensor scheduling
       Save battery life          Natural Lighting


                                     Coordinated
                                       Lighting
Active Sensing aka Sensor Scheduling
   Spatial correlation in sunlight distribution
   Temporal correlation in sunlight intensity
   Use only a small number of sensor
   Estimate the light levels at other times and
        When and Where to sense!
    locations


              ?      Desk

                            ?       ?
                                ?
Active Sensing: Scheduling
   Use sunlight observation (samples) to estimate the
    current sunlight intensity distribution

                                                                           
                                                                              
           P ( 1 , 1 )  1,1 ,..., ( l ,  r )  l ,r | ( ,  )   
                                                                             

   The utility formulation then changes to conditional
    expected utility
                              n                                                   m
    EU (a, t , x | O  o)     P ((t , xi )   | O  o) i ,x (a,  )     j (a j )
                             i 1                                                 j 1

                             Sunlight Distribution Conditioned
                                      on observation

   Choose a set of observations that yields best
    maximum expected utility values
Active Sensing
   Calculating a set of observation that maximize

    J (O)   P(O  o)( max EU (a, t , x | O(1:t )  o(1:t ) ))
                                  a
              o             tT


                      O  argmax J (O)
                        *

                                      O

   More observation: better accuracy but high
    battery cost
   Constraint the observations to a budget
       Allocate strategically to max. EU
Active Sensing: Single Sensor
                   O  argmax J (O)
                       *

                                   O

   Optimal solution for single sensor budget allocation
    in polynomial time (Krause & Guestrin ’05)

     X1          X2          X3          X4         X5
   Xi where i is the time step, (5 times steps, Budget 2)
   For just 2 sensors: complexity is NP-hard
      X1
      X           X2
                  X           X3
                              X           X4
                                          X           X5
                                                      X
       1           2           3           4           5

      Y1          Y2          Y3          Y4          Y5
    Active Sensing: Heuristic
   Heuristic for solving multiple sensor
     Coordinate ascent scheme (uses optimal solution
      for single sensor)
                 Optimize sensor 1
      X1        X2        X3       X4         X5

      Y1        Y2        Y3        Y4        Y5

                 Optimize sensor 2
   Guaranteed to improve score on each iteration,
    guaranteed to not perform worse than independent
    scheduling
   Can be used for more than 2 sensors
Active Sensing: Results
                  No sensing



                                               Energy Cost




      1 obs./sensor        10
                           obs./sensor
                                              Measured Utility




   3 sensors, upto 10 readings per sensor in a day
   Energy saving are close approximation compared to
    sensing continuously
   Even a small number of readings (3) provides results
    as good as continuous
Active Sensing for Daylight Harvesting
   Exploit temporal correlation in sunlight
    intensity to schedule sensing
   Significant reduction in sensing requirement
    for comparable performance
   Can be integrated in the coordinated lighting
    formulation                       Predictive
                                    light control

                                   Natural Lighting

                                    Coordinated
                                      Lighting
Predictive light control

   Probabilistic model on mobility
       People move independent of each other
   Modeled using a random walk
       Stay in same position
       Move left, move right



              Zone 2        Zone 2   Zone 1
Integrating mobility

    Assuming full observability

                                 ( t 1)                          t 1
                         P( x    i          .| x , x )   t
                                                          i       i
    Computing expected utility
                           n                                                          m
    EU (a, t , x , x )    x P ( x
              t   t 1                  t 1
                                        i       xi ) E ( i , xi (a, ( xi , t ))     j (a j )
                          i 1                                                        j 1

                                 Probability of
                                    motion
                   Predictive Lighting: Results
                                              Using prediction
                        Occupant Utility
                                              Without
Normalized Scale




                                              prediction
                                 Energy Cost                              Occupant
                                                                          Utility
                                          Total Utility




                                                                 Energy
                                                                 Cost




                  20 step random walk
                  Total utility increase of about 25%
                  Low values of trade-off parameter, system prefers
                   occupants comforts
 Conclusion
Coordinated lighting strategy
•Maximizes happiness using utility maximization
•Solves complex coordination problem

           Day light harvesting
             •Exploits natural light sources using sensors
             •50-70% reduction in energy consumption

Active sensing
   •Sensor scheduling using sunlight distribution
   • Substantial increase in network life time

        Predictive Light control
           •Captures occupant mobility
           •Higher total utility for the system

				
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