alternative optimization techniques
TRANSCRIPT
Alternative Optimization Alternative Optimization TechniquesTechniques
Kirk Cameron, Ph.D.MacStat Consulting, [email protected]
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Ways to Skin a CatWays to Skin a Cat
⢠Optimization techniques for LTM have advanced over last several yearsâ Improved mathematicsâ Increased complexityâ Combination of statistical & physical data
⢠Highlight some alternate methodsâ Genetic algorithmsâ Kalman-type filtering, updating
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A Question of TradeoffsA Question of Tradeoffs
⢠Computational horsepowerâ More analysis time, computer power often requiredâ More complex models, greater reliance on advanced
numerical methods⢠More complex data needs
â âGarbage in, garbage outâ principleâ More kinds and quantities of data typically neededâ Needed information not always available
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Itâs an Empirical ThingItâs an Empirical Thing
⢠No optimization possible without dataâ Moving from simpler to more complex
techniques exposes a dilemmaâ Advanced approaches may look âslick,â but
without extra data, results may be no better⢠Determine which data inputs are crucial
â Forward thinking: how can this data be collected in the future?
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MultiobjectiveMultiobjective Groundwater Groundwater Monitoring DesignMonitoring Design
⢠Patrick Reed and Venkat Devireddyâ Department of Civil and Environmental Engineering â The Pennsylvania State University
⢠Contact info: [email protected]
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Genetic Algorithm BasicsGenetic Algorithm Basics
⢠Genetic algorithms search among all possible monitoring plansâ Create an initial âpopulationâ of sampling plansâ Sampling plans are represented as a string binary digits
⢠1 â ith well sampled⢠0 â ith well not sampled
â Judge each sampling plan based on how well it satisfies monitoring objectives
⢠Plans that satisfy design objectives are âhighly fitâ⢠Have higher likelihood of mating and passing traits
â Sampling plans undergo Darwinian ânatural selectionâ until the best set of plans are evolved
0 1 00
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â Selectionâ Measure of the fitness of stringâ Fitness is rated in terms of the objective functionsâ Population members compete to mate & pass traits
â Mating
â Mutation
How do How do GAsGAs work?work?
Parents
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0 0
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Crossover occurs with user specified
probability, Pc
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Bit change occurs with user specified
probability, Pm
Children
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Multiobjective EvolutionMultiobjective Evolution
⢠The Nondominated Sorted Genetic Algorithm-II:â Population classified into fronts using non-dominated
sortingâ Better ranking = Higher likelihood of passing traitsâ Entire tradeoffs evolved in single run
Cost
Estim
atio
n Er
ror
Cost
Estim
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n Er
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Rank = 1
Rank = 2
Rank = 3
Rank = 4
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Case Study: Enumerated Case Study: Enumerated TradeoffTradeoff
⢠Two-Objectives:â Minimize Costâ Minimize Relative Mapping
Error (termed SREE)
⢠220 possible designs⢠Evaluated using a
nonlinear least squares interpolation
⢠Best published resultâ Reed et al. (2004) WRRâ 38000 evaluations
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Case Study: Efficiency of New Case Study: Efficiency of New ToolsTools
⢠Results for 50 trials (using interactive archiving)â Reduced solution time from hours to secondsâ New tool is up to 90% more efficient
2540074400Max. no. of design evaluations
799239889Avg. no. of design evaluations
140016800Min. no. of design evaluations
Îľ-NSGA2 (New Tool)
Reed et al. 2003
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Case Study: Typical ResultCase Study: Typical Result
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Adaptive Environmental Monitoring Adaptive Environmental Monitoring System (AEMS)System (AEMS)
â Under development at RiverGlass Inc., Champaign, IL
⢠Software development company launched by the University of Illinois
⢠Project lead: Barbara Minsker, PhD [email protected]
â Beta testing of AEMS expected to begin in late Summer 2005
⢠Completed functionality available now on a project basis â contact Dr. Minsker for more information
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AEMS CapabilitiesAEMS Capabilitiesâ Build data-driven trend models based on historical
data (geostatistical or analytical models)â Assess new data in real time to
⢠Identify significant deviations from previous trends (spatial ortemporal), providing automated alerts
⢠Identify locations/times where additional data would be most beneficial to reducing risks
â Identify temporal and spatial redundancies in existing monitoring regimes
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Redundancy Analyses with AEMSRedundancy Analyses with AEMS
⢠Method considersâ Tradeoffs among multiple objectives (e.g.,
cost and error) with mathematical optimizationâ Uncertainty in identifying robust designsâ Temporal and spatial redundancy
simultaneously⢠Applied at 2 BP sites and 1 DOE site
â 22-36% redundancy found in well sampling plans
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Number of Wells
Max
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pb)
AEMS Identifies Monitoring AEMS Identifies Monitoring TradeoffsTradeoffs
â˘Each diamond is an optimal monitoring plan for a given level of sampling
â˘Shows tradeoffs between number of wells sampled ($) and interpolation errors
22% reduction in costsBenzene MCL
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Optimization of Large Scale Optimization of Large Scale Subsurface Environmental ImpactsSubsurface Environmental Impacts
⢠Larry M. Deschaine, PEâ Engineering Physicistâ SAIC & Chalmers University of Technology
⢠Contact info: [email protected]
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Information Content Fused Information Content Fused ApproachApproach
⢠Integrated algorithm(s) consist of:â Simulation models based on physicsâ Data models based on samplingâ Uncertainty handled through (geo)-statistics
⢠Information content fusion (Data & Physics):â Signal processing (i.e. Kalman Filters, etc.)â Genetic Programming
⢠Optimal System Estimateâ Optimal estimate of âsystemâ for locating plume at
given time, or time-space correlated estimates of long term monitoring programs
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Fundamentally Different From Fundamentally Different From EstimationEstimation
⢠Current methods typically gather data, calibrate model and use model for predictionsâ Models break down as physics becomes complex,
data sparse or input parameters not well known⢠This method fuses the information content via
signal processing / machine learning algorithms:â Integrated data/physics model provide optimal
estimates based on knowledge gained from both the physical simulator and the data, updated as new information is obtained
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0.050.10.150.20.250.30.350.40.450.50.550.60.650.70.750.80.850.9
Determining optimal well locations & their benefit to Determining optimal well locations & their benefit to understanding plume location understanding plume location ââ when to stop adding when to stop adding
wells, how to justifywells, how to justify
No wells [Max uncertainty]
Existing MW system [93.4% reduction]
Add One Well [98% reduction]
Add 2nd Well [98.5% reduction]
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LTM: Extend the reduction of uncertainty to include value of LTM: Extend the reduction of uncertainty to include value of historic samples in space and time historic samples in space and time --> Results in less > Results in less
samples needed to understand long term system behaviorsamples needed to understand long term system behavior
O p tim a l L o n g T e rm M o n ito rin g E x a m p le
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T im e (y e a rs )
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E stim a teU p p e r C o nf L im itL o w e r C o nf L im it
Samples are collected when the space-time correlated uncertainty exceeds preset limits
Excessive Uncertainty
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OPDATEOPDATE
⢠David Dougherty, PEâ Subterranean Research, Inc.
⢠Contact info: [email protected]
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Fusion of Data, SimulationFusion of Data, Simulation
⢠Site-specific, consulting approachâ Strong emphasis on decision-trees
⢠Simulation models first used to both:â Help plan remedy phases during RI, FS and
design LTM program⢠One goal of LTM design should be to improve simulation
model for anticipated future remedy/risk assessments
â Make predictions about future subsurface conditions
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Use of Model in LTM Planning: Placement of Use of Model in LTM Planning: Placement of MWsMWs Accounts for Different Phases of RemedyAccounts for Different Phases of Remedy
Distance (ft)500 1000 1500 2000 2500 3000
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MW-90B
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b) Optimized Pumping Condition
C-1 (Proposed)
MW-202B
MW-37
MW-39
Distance (ft)500 1000 1500 2000 2500
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Approximate Location of T-25 Perimiter
Approximate Location of Lake CochituateApproximate Location of Lake Cochituate
Distance (ft)
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sl)
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C-1 (Proposed)
MW-202B
MW-37
MW-39
Distance (ft)500 1000 1500 2000 2500
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Approximate Location of T-25 Perimiter Approximate Location
of Lake Cochituate
Distance (ft)
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sl)
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C-1 (Proposed)
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MW-39
Distance (ft)500 1000 1500 2000 2500
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Approximate Location of T-25 Perimiter Approximate Location
of Lake CochituateApproximate Location of Lake Cochituate
40201086420
TravelTime (yr)
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Retrospective AnalysisRetrospective Analysis
⢠Retrospective hydrologic data assimilationâ Applied to observed data to:
⢠1) add branches to LTM decision trees, and⢠2) improve quality of forecasts
⢠Measured data used to update and optimize (âopdateâ) simulation models
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Using Data AssimilationUsing Data Assimilation
Larger AdjustmentsEarly Time Late Time
Smaller AdjustmentsUse Observation Data to Update Models and UncertaintyAssessments
Predictive Model Forecast
Adjust c(x,y,z) based on measurements
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ââOpdateOpdateââ--ingingâSnapshot in timeâ (July, 1999), prior to and after updating the predicted concentration plumes with monitoring data.
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Retrospective Data Retrospective Data AssimilationAssimilationââOPDATEâ˘OPDATEâ˘
Linea
r Kri
ged
Bes
t Est
imat
e Lo
g K
rige
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15 Events 8 Events 4 Events
Quarterly Semi-Annual Annual
Sce
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ios
Updating Frequency
Sensitivity to Historical Sampling Frequency
When and Where DoErrors Occur?
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SummarySummary
⢠âNext Generationâ methods offer great promise⌠howeverâ Many sites currently lack sufficiently detailed
data or right kind of dataâ More expertise required to correctly set-up,
implement⢠Power, adaptability of genetic algorithms,
Kalman filter techniques cannot be deniedâ Especially true as computer horsepower gets
faster & cheaper
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Summary (cont.)Summary (cont.)
⢠Each method being developed for real-world applicationsâ Savannah River, BP, DOE, AF facilitiesâ Some âscalabilityâ possible, especially with genetic
algorithm approaches⢠Key benefits
â Formal incorporation of additional kinds of dataâ Enumeration of entire cost tradeoff curve, sort of