Alternative Optimization Alternative Optimization TechniquesTechniques

Kirk Cameron, Ph.D.MacStat Consulting, Ltd.kcmacstat@qwest.net

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Ways to Skin a CatWays to Skin a Cat

• Optimization techniques for LTM have advanced over last several years– Improved mathematics– Increased complexity– Combination of statistical & physical data

• Highlight some alternate methods– Genetic algorithms– Kalman-type filtering, updating

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A Question of TradeoffsA Question of Tradeoffs

• Computational horsepower– More analysis time, computer power often required– More complex models, greater reliance on advanced

numerical methods• More complex data needs

– “Garbage in, garbage out” principle– More kinds and quantities of data typically needed– Needed information not always available

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It’s an Empirical ThingIt’s an Empirical Thing

• No optimization possible without data– Moving from simpler to more complex

techniques exposes a dilemma– Advanced approaches may look ‘slick,’ but

without extra data, results may be no better• Determine which data inputs are crucial

– 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 Devireddy– Department of Civil and Environmental Engineering – The Pennsylvania State University

• Contact info: preed@engr.psu.edu

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Genetic Algorithm BasicsGenetic Algorithm Basics

• Genetic algorithms search among all possible monitoring plans– Create an initial “population” of sampling plans– Sampling plans are represented as a string binary digits

• 1 – ith well sampled• 0 – ith well not sampled

– Judge each sampling plan based on how well it satisfies monitoring objectives

• Plans that satisfy design objectives are “highly fit”• Have higher likelihood of mating and passing traits

– Sampling plans undergo Darwinian “natural selection” until the best set of plans are evolved

0 1 00

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– Selection– Measure of the fitness of string– Fitness is rated in terms of the objective functions– Population members compete to mate & pass traits

– Mating

– Mutation

How do How do GAsGAs work?work?

Parents

1 1 1 1

0 1 00 0

0 0

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11

1

Crossover occurs with user specified

probability, Pc

1 1 1 1 1 1 1 0

Bit change occurs with user specified

probability, Pm

Children

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Multiobjective EvolutionMultiobjective Evolution

• The Nondominated Sorted Genetic Algorithm-II:– Population classified into fronts using non-dominated

sorting– Better ranking = Higher likelihood of passing traits– Entire tradeoffs evolved in single run

Cost

Estim

atio

n Er

ror

Cost

Estim

atio

n Er

ror

Rank = 1

Rank = 2

Rank = 3

Rank = 4

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Case Study: Enumerated Case Study: Enumerated TradeoffTradeoff

• Two-Objectives:– Minimize Cost– Minimize Relative Mapping

Error (termed SREE)

• 220 possible designs• Evaluated using a

nonlinear least squares interpolation

• Best published result– Reed et al. (2004) WRR– 38000 evaluations

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Case Study: Efficiency of New Case Study: Efficiency of New ToolsTools

• Results for 50 trials (using interactive archiving)– Reduced solution time from hours to seconds– New tool is up to 90% more efficient

2540074400Max. no. of design evaluations

799239889Avg. no. of design evaluations

140016800Min. no. of design evaluations

ε-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)

– Under development at RiverGlass Inc., Champaign, IL

• Software development company launched by the University of Illinois

• Project lead: Barbara Minsker, PhD minskerconsulting@insightbb.com

– Beta testing of AEMS expected to begin in late Summer 2005

• Completed functionality available now on a project basis – contact Dr. Minsker for more information

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AEMS CapabilitiesAEMS Capabilities– Build data-driven trend models based on historical

data (geostatistical or analytical models)– 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

– Identify temporal and spatial redundancies in existing monitoring regimes

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Redundancy Analyses with AEMSRedundancy Analyses with AEMS

• Method considers– Tradeoffs among multiple objectives (e.g.,

cost and error) with mathematical optimization– Uncertainty in identifying robust designs– Temporal and spatial redundancy

simultaneously• Applied at 2 BP sites and 1 DOE site

– 22-36% redundancy found in well sampling plans

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Number of Wells

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pb)

AEMS Identifies Monitoring AEMS Identifies Monitoring TradeoffsTradeoffs

•Each diamond is an optimal monitoring plan for a given level of sampling

•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, PE– Engineering Physicist– SAIC & Chalmers University of Technology

• Contact info: larry.m.deschaine@alum.mit.edu

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Information Content Fused Information Content Fused ApproachApproach

• Integrated algorithm(s) consist of:– Simulation models based on physics– Data models based on sampling– Uncertainty handled through (geo)-statistics

• Information content fusion (Data & Physics):– Signal processing (i.e. Kalman Filters, etc.)– Genetic Programming

• Optimal System Estimate– Optimal estimate of “system” 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 predictions– 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:– 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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0.05

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0.65

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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 –– 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

0 .0 0

2 0 .0 0

4 0 .0 0

6 0 .0 0

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0 2 4 6 8 1 0 1 2 1 4 1 6

T im e (y e a rs )

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mal

ized

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cent

ratio

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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, PE– Subterranean Research, Inc.

• Contact info: ddougher@subterra.com

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Fusion of Data, SimulationFusion of Data, Simulation

• Site-specific, consulting approach– Strong emphasis on decision-trees

• Simulation models first used to both:– 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

– 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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050

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MW-90B

SV-4SV-3

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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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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)

MW-202B

MW-37

MW-39

Distance (ft)500 1000 1500 2000 2500

-50

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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 assimilation– 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 (“opdate”) 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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““OpdateOpdate””--inging“Snapshot in time” (July, 1999), prior to and after updating the predicted concentration plumes with monitoring data.

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Retrospective Data Retrospective Data AssimilationAssimilation——OPDATE™OPDATE™

Linea

r Kri

ged

Bes

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g K

rige

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15 Events 8 Events 4 Events

Quarterly Semi-Annual Annual

Sce

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Updating Frequency

Sensitivity to Historical Sampling Frequency

When and Where DoErrors Occur?

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SummarySummary

• ‘Next Generation’ methods offer great promise… however– Many sites currently lack sufficiently detailed

data or right kind of data– More expertise required to correctly set-up,

implement• Power, adaptability of genetic algorithms,

Kalman filter techniques cannot be denied– Especially true as computer horsepower gets

faster & cheaper

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Summary (cont.)Summary (cont.)

• Each method being developed for real-world applications– Savannah River, BP, DOE, AF facilities– Some “scalability” possible, especially with genetic

algorithm approaches• Key benefits

– Formal incorporation of additional kinds of data– Enumeration of entire cost tradeoff curve, sort of