A DecisionMaking Framework for More Sustainable Urban Environments

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A Decision-Making Framework for More Sustainable
Urban Environments
Victoria Chen and Zehua Yang Industrial
Manufacturing Systems Engineering University of
Texas at Arlington (UTA)vchen_at_uta.edu
Julia Tsai Purdue University
Michael Chang, Ellis Johnson, Eva Lee, and Terry
Murphy Georgia Institute of Technology
Supported by TSE/EPA Contract R-82820701-0
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Outline

• Decision-Making Framework (DMF)
• Stochastic Dynamic Programming (SDP)
• Wastewater Treatment Application
• Metropolitan Atlanta Ozone Pollution Application

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A Modular Decision-Making Framework

• For time period/level/stage t
• xt state of system
  ut decision/control

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Applications

• Inventory Forecasting
• Determine optimal order quantities using
  forecasts for product demand.
• Airline Yield Management (Sabre)
• Develop an on-line YM policy for a real airline
  network.
• Water Resources (Italy)
• Determine optimal control of a water reservoir
  network.
• Wastewater Treatment System (EPA)
• Evaluate current and future technologies
  according to economic and sustainability
  measures.
• Ozone Pollution (EPA)
• Identify key times and locations for emissions
  reductions to avoid ground-level ozone
  exceedances.

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Stochastic Dynamic Programming (SDP)

• Objective Minimize expected cost over T stages.
• Optimal Value Function Ft(xt) in Stage t Minimum
  expected cost to operate the system over stages t
  through T.

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SDP Optimization Formulation
Objective Transition Constraints
For stage t xt is the vector of state
variables ut is the vector of decision
variables ?t is the vector of random
variables ct(.) is the cost function ft(.) is
the multivariate transition function ?t is the
set of constraints
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SDP Optimal Value Function

• For stages t through T
• Recursive formulation
• SDP solves backwards (t T,, 1) to determine
  the optimal value functions Ft(xt) in all stages.

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SDP Statistical Modeling Process
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Wastewater Treatment System

• Research with Jining Chen (Tsinghua U, China),
  Bruce Beck (U of Georgia), and Julia
  Tsai (Purdue U)
• Decision-Making Framework (DMF)
• Evaluate current and emerging technologies,
  including usage at a unconventional level.
• Provide most promising directions for future
  research.
• Liquid treatment line up to 11 levels.
• Solid treatment line up to 6 levels.
• Advantages over Typical Approach
• Comprehensive vs. isolated evaluation of
  processes.
• Exploration of many potential levels of
  treatment.

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Wastewater Treatment DMF

• Objective Minimize capital and operating costs
• size (land area, volume) odor emissions.
• Maximize robustness global desirability.
• Complication Dependencies between some
  technologies.
• Stages Levels of the treatment system (T 17)
• State xt entering Level t Liquid and solid
  attributes.
• Decision ut in Level t Technology process
  employed.
• Constraints Attribute quantities exiting each
  Level.
• Random Variables Performance and cost of the
  technologies.
• Transition xt1 xt ? quantity removed
  quantity added.

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Wastewater Treatment DMF

• Monitored attributes are the 20 SDP state
  variables

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Dependencies Between the Technologies
Diagnostic state variables indicate what
technology has been utilized in an earlier level.
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DMF Solution (Economic Cost)
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DMF Solution (Economic Cost)
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DMF Solution (Economic Cost)
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DMF Solution (Economic Cost)
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DMF Solution (Economic Cost)
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Controlling Ozone Pollution

• Research with Michael Chang (Georgia Tech),
  Melanie Sattler (UTA), and John Priest
  (UTA)
• Decision-Making Framework (DMF)
• Explore the necessary emissions reductions over
  time and space to prevent an ozone exceedance.
• Identify reductions in emissions that will lead
  to new control strategies.
• Provide information and guidance to government
  decision makers for creating new control
  strategies
• Advantages over Typical Approach
• Comprehensive approach vs. trial and error.
• Dynamic and focused vs. static control strategies.

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Ozone Pollution DMF

• Objective Minimize cost to avoid ozone
  exceedance days.
• Complications
• Ozone is not directly emitted, but is formed by
  the reaction of emitted pollutants, such as
  nitrogen oxides (NOx).
• State variables are temporally and spatially
  related.
• Stages Hours or groups of hours.
• State xt at the beginning of Stage t Ozone, NOx
  at different locations and at hours prior to
  stage t.
• Decision ut in Stage t Reductions of NOx by
  location.
• Constraint Ozone exceedance limit ? adds penalty
  cost
• Random Variables Uncertainty in how Ozone, NOx
  change over time and space.

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Ozone Pollution DMF

• Transition Atmospheric Chemistry Module
• E1 NOx emissions between 6am?9am
• E2 NOx emissions between 9am?12pm

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Atlanta Urban Airshed Model (UAM)

• U.S. EPA (1990)
• UAM An advanced three-dimensional, photochemical
  air quality grid model that encompasses a
  160?160 km square region containing the
  metropolitan area.
• Spatial modeling grid 40?40
• Point sources 102
• Temporal modeling 24 hours
• July 29 - August 1, 1987 episode
• Computational Issues one UAM simulation run gt
  one hour
• Impractical to implement within SDP optimization
• Instead develop a metamodel of the UAM.

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Atmospheric Chemistry Metamodel
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Atlanta Modeling Domain

1-15 were Georgia
Power
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Preliminary Metamodeling

• Transition Function Metamodel Setup
• All 5?5 grid regions and 15 significant point
  sources
• Reduce 24 hours ? five 3-hour time periods
• time period 0 from 4 a.m. to just before 7 a.m.
• time period 1 from 7 a.m. to just before 10
  a.m.
• time period 2 from 10 a.m. to just before 1
  p.m.
• time period 3 from 1 p.m. to just before 4 p.m.
• time period 4 from 4 p.m. to just before 7 p.m.
• Total NOx over each time period for each grid
  region and point source ? 5(2515) 200
  predictor variables
• Maximum hourly-averaged ozone at the 4 stations
  and in time periods 1, 2, 3, 4 ? 16 response
  variables

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Preliminary Metamodeling

• Transition Function Metamodel Fit
• Experimental Design A 500-point Latin hypercube
  design determined variations in NOx emissions
  from zero up to the nominal value.
• Statistical Model Multiple linear regression
  models at each of the 4 Atlanta monitoring
  stations for maximum ozone in time period p 1,
  2, 3, 4, as a function of
• maximum ozone at the 4 Atlanta monitoring
  stations in time periods earlier than p
• total NOx emissions over the 25 grid regions and
  at the 15 point sources in time periods p and
  earlier
• Achieved regression R2 gt 0.90 for all except
  sites Tucker and S. Dekalb in time period 2.

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State and Decision Variables

• Initial State Space for Stage t For all time
  periods lt t,
• maximum ozone at the 4 Atlanta monitoring sites
• total NOx emissions over the 25 grid regions and
  at the 15 point sources
• ? Stage 1 44 dimensions
• Stage 2 88 dimensions
• Stage 3 132 dimensions
• Stage 4 176 dimensions
• Initial Decision Space for Stage t For time
  period t,
• total NOx emissions over the 25 grid regions and
  at the 15 point sources
• ? 40 dimensions

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State and Decision Variables

• Key Only those variables included in the
  metamodels need to be maintained in the state and
  decision spaces.
• Reduced State Space ? Stage 1 17 dimensions
• Stage 2 25 dimensions
• Stage 3 23 dimensions
• Stage 4 19 dimensions
• Reduced Decision Space ? Stage 1 17 dimensions
• Stage 2 9 dimensions
• Stage 3 9 dimensions
• Stage 4 3 dimensions
• SDP Dimensionality The dimension of the SDP
  optimization problem is the largest state space
  dimension ? 25

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Emissions Reductions Decisions for Atlanta
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Last Period SDP Optimal Value Function
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Metamodel Refinement

• Multivariate Adaptive Regression Splines (MARS)
• Employed new robust MARS algorithm that favors
  lower-order terms.
• Maximum ozone model for S. Dekalb in time period
  2.
• ? R2 98.6
• Maximum ozone model for Tucker in time period 2.
• ? R2 91.5
• Resulting metamodels were clearly curvilinear.
• Undesirable chemical reaction in which high NOx
  leads to low ozone.
• However, SDP transition functions must be
  monotonic in order to guarantee convexity for the
  optimization.

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Maximum Ozone at S. Dekalb in Period 2
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Restructured S. Dekalb Metamodel
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On-going and Future Work

• DMF and SDP
• Alternate experimental designs / statistical
  models
• Parallel computing
• Wastewater Treatment
• Verify technology selections via simulation
• Consider other objectives (odor emissions,
  robustness)
• Ozone Pollution
• Complete SDP solution for Atlanta
• Simulate solution via Atlanta Urban Airshed Model
• Refine transition function metamodels
• Transfer Atlanta DMF to Dallas/Fort-Worth

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References

• Chen, V. C. P. (1999). Application of
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• Chen, V. C. P., D. Ruppert, and C. A. Shoemaker
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• Chen, V. C. P., Chen, J., and Beck, M. B. (2000).
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• Chen, V. C. P. (2001). Measuring the Goodness
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References

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References

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