Andrea Castelletti1, Stefano Galelli2, Matteo Giuliani1

1 Dipartimento di Elettronica, Informazione, e Bioingegneria, Politecnico di Milano, Milano, Italy 2 Pillar of Engineering Systems and Design, Singapore University of Technology and Design, Singapore

Improving Computational Efficiency in Modeling Complex Environmental Systems

Dynamic emulation modelling for the optimal operation of water systems: an overview

Pollock  n.  31  

H41J-01

Emulation modelling: reconciling science and decision making …

DM High fidelity Accuracy

Credibility Simplicity

DATA DRIVEN PROCESS BASED

DM

Emulation modelling: reconciling science and decision making …

Emulator: A low-order, computationally efficient model identified from an original large high fidelity model and then used to replace it in computationally intensive applications.

DM High fidelity Accuracy

Credibility Simplicity

DATA DRIVEN PROCESS BASED

DM

EMO’s application tree

Model Emulation

MODEL DIAGNOSTIC

Data assimilation

DECISION MAKING

Model identification

Sensitivity analysis

Optimal planning

What-if analysis

Optimal control

[Castelletti et al. 2012a]

Non-dynamic vs dynamic emulation

decision 1

de

cisi

on

2

objective 1

ob

jec

tive 2

time

sta

te

ext

driv

ers

time

HIGH FIDELITY MODEL

Non-dynamic emulator [Razavi et al. 2013]

Non-dynamic vs dynamic emulation

decision 1

de

cisi

on

2

objective 1

ob

jec

tive 2

time

sta

te

ext

driv

ers

time

HIGH FIDELITY MODEL

N-DEMo

Non-dynamic emulator [Razavi et al. 2013]

Non-dynamic vs dynamic emulation

decision 1

de

cisi

on

2

objective 1

ob

jec

tive 2

time

sta

te

ext

driv

ers

time

HIGH FIDELITY MODEL

N-DEMo

Non-dynamic emulator [Razavi et al. 2013]

Non-dynamic vs dynamic emulation

decision 1

de

cisi

on

2

objective 1

ob

jec

tive 2

time

sta

te

ext

driv

ers

time

HIGH FIDELITY MODEL

Dynamic emulator [Castelletti et al. 2012a]

Non-dynamic vs dynamic emulation

decision 1

de

cisi

on

2

objective 1

ob

jec

tive 2

time

sta

te

ext

driv

ers

time

HIGH FIDELITY MODEL

DEMo

Dynamic emulator

time

red

uc

ed

sta

te

[Castelletti et al. 2012a]

Non-dynamic vs dynamic emulation

decision 1

de

cisi

on

2

objective 1

ob

jec

tive 2

time

sta

te

ext

driv

ers

time

HIGH FIDELITY MODEL

DEMo

Dynamic emulator

time

red

uc

ed

sta

te

[Castelletti et al. 2012a]

How to build a Dynamic Emulator

Transform the state and input/decision vectors into lower dimension vectors through adoption of a suitable aggregation (PCA, SVD, etc)

2. Variable aggregation

Selection of the most relevant aggregated variables in explaining the model output (IVS, PMI, etc)

3. Variable selection

Selection of a family of models for the emulator, calibration, validation, and physical interpretation.

4. Emulator calib. & validation

MODEL REDUCTION

The dynamic emulator is used in the task is was designed for.

Model use

DEMo Design a sequence of simulation runs to construct a high dimension sample data-set.

1. DOE and simulation runs

[Castelletti et al. 2012a]

REAL TIME CONTROL OF MARINA BARRAGE

SINGAPORE

CASE STUDY

Singapore’s 4 national taps strategy

Malaysia

Indonesia

0 100 km

0 10 km

Singapore Strait

Marina Reservoir

(source: URA)

The 4 TAPS [Kristiana et al., 2011] 1. Local catchments water

2. Imported water

3. Reclaimed water (NEWater)

4. Desalinated water

Marina Barrage

Low tide High tide

Seepage

Pumps

Gates

Pipes

Actuators:

§  7 pumps §  9 weirs §  2 bottom pipes

Water quantity objectives:

§  Water supply §  Flood control §  Energy usage

Water quality objectives:

§  Maintain low salinity

[Galelli et al. 2014]

SEA SEA

The high fidelity model

2D view 3D view

barrage

cross-section

observation point

m0-1-2-3-4-5-6-7

The DELFT3D-FLOW hydrodynamic model calculates non-steady flow and transport phenomena (i.e., temperature and salinity conditions)

§  5 states per cell = 5,500 state variables §  Real-to-run time ratio 100:1

[Zijl and Twigt 2007]

The real time control framework

DEFLT3D FLOW

DYNAMIC EMULATOR

MODEL PREDICTIVE CONTROL

- STATE - OBJECTIVES

RELEASE DECISIONS

MODEL REDUCTION

- OPTIMAL POLICY HYDROMETEO

DRIVERS

EVALUATION via SIMULATION

-1.71

2.54

12.47

2.06

2.12

6.81

Temp1

log(Lev) Algae

2 54

7

0666

Legend

6.2.45 10 6.3.84 10

7.14.26 107.4.01 10

size: Irr1

orientation: Sed

color: approachNSPCAbased

expertbased

PARETO Front

FAST SIMULATION

- REDUCED STATE - OBJECTIVES

-  STREAMFLOW PREDICTIONS

- OBJECTIVES

STREAMFLOW FORECAST

(SOBEK)

RELEASE DECISION

GENERATOR

Building a dynamic emulator of salinity @ the dam

Transform the state and input/decision vectors into lower dimension vectors through adoption of a suitable aggregation.

2. Variable aggregation

Selection of the most relevant aggregated variables in explaining the model output.

3. Variable selection

Selection of a family of models for the emulator, calibration, validation, and physical interpretation.

4. Emulator calib. & validation

MODEL REDUCTION

The dynamic emulator is used in the task is was designed for.

Model use

DEMo Design a sequence of simulation runs to construct a high dimension sample data-set.

1. DOE and simulation runs

[Castelletti et al. 2012a]

Building a dynamic emulator of salinity @ the dam

Transform the state and input/decision vectors into lower dimension vectors through adoption of a suitable aggregation.

2. Variable aggregation

Selection of the most relevant aggregated variables in explaining the model output.

3. Variable selection

Selection of a family of models for the emulator, calibration, validation, and physical interpretation.

4. Emulator calib. & validation

MODEL REDUCTION

The dynamic emulator is used in the task is was designed for.

Model use

DEMo 300,000 samples by pseudo random sampling = 5,500 state variables

1. DOE and simulation runs

[Castelletti et al. 2012a]

Building a dynamic emulator of salinity @ the dam

Hierarchical Agglomerative Time Series Clustering [Magni et al., 2008] = 5,500 to 32 states

2. Variable aggregation

Selection of the most relevant aggregated variables in explaining the model output.

3. Variable selection

Selection of a family of models for the emulator, calibration, validation, and physical interpretation.

4. Emulator calib. & validation

MODEL REDUCTION

The dynamic emulator is used in the task is was designed for.

Model use

DEMo 300,000 samples by pseudo random sampling = 5,500 state variables

1. DOE and simulation runs

[Castelletti et al. 2012a]

Variable aggregation

Cluster 1 (Salinity): saline layer.

m0-1-2-3-4-5-6-7

Variable aggregation

m0-1-2-3-4-5-6-7

Cluster 2 (Salinity): saline layer.

Variable aggregation

m0-1-2-3-4-5-6-7

Cluster 3 (Salinity): saline layer.

Variable aggregation

m0-1-2-3-4-5-6-7

Cluster 4 (Salinity): ‘buffer zone’ at a depth of 4 – 5 m, between the saline layer and the freshwater area.

Variable aggregation

m0-1-2-3-4-5-6-7

Cluster 5 (Salinity): upper layers of the reservoir (max depth of about 4 m), with a uniform salinity of 3 ppt.

Building a dynamic emulator of salinity @ the dam

Hierarchical Agglomerative Time Series Clustering [Magni et al., 2008] = 5,500 to 32 states

2. Variable aggregation

Selection of the most relevant aggregated variables in explaining the model output.

3. Variable selection

Selection of a family of models for the emulator, calibration, validation, and physical interpretation.

4. Emulator calib. & validation

MODEL REDUCTION

The dynamic emulator is used in the task is was designed for.

Model use

DEMo 300,000 samples by pseudo random sampling = 5,500 state variables

1. DOE and simulation runs

[Castelletti et al. 2012a]

Building a dynamic emulator of salinity @ the dam

Hierarchical Agglomerative Time Series Clustering [Magni et al., 2008] = 5,500 to 32 states

2. Variable aggregation

Recursive Variable Selection [Galelli and Castelletti, 2013a] = 32 to 1 state

3. Variable selection

Selection of a family of models for the emulator, calibration, validation, and physical interpretation.

4. Emulator calib. & validation

MODEL REDUCTION

The dynamic emulator is used in the task is was designed for.

Model use

DEMo 300,000 samples by pseudo random sampling = 5,500 state variables

1. DOE and simulation runs

[Castelletti et al. 2012a]

Building a dynamic emulator of salinity @ the dam

Hierarchical Agglomerative Time Series Clustering [Magni et al., 2008] = 5,500 to 32 states

2. Variable aggregation

Recursive Variable Selection [Galelli and Castelletti, 2013a] = 32 to 1 state

3. Variable selection

Extremely Randomized Trees [Galelli and Castelletti, 2013b]

4. Emulator calib. & validation

MODEL REDUCTION

The dynamic emulator is used in the task is was designed for.

Model use

DEMo 300,000 samples by pseudo random sampling = 5,500 state variables

1. DOE and simulation runs

[Castelletti et al. 2012a]

Variable selection

Cluster 2 salinity

Salinity @ dam

Release from pipes

Groundwater seepage

CONTROL

EXTERNAL DRIVER

STATE OUTPUT

Seepage

Pumps

Gates

Pipes SEA

Emulator calibration and validation

R2 – cross-validation (April – December

2009)

0.989

R2 – validation (January – December

2010)

0.970

Building a dynamic emulator of salinity @ the dam

Hierarchical Agglomerative Time Series Clustering [Magni et al., 2008] = 5,500 to 32 states

2. Variable aggregation

Recursive Variable Selection [Galelli and Castelletti, 2013a] = 32 to 1 state

3. Variable selection

Extremely Randomized Trees [Galelli and Castelletti, 2013b]

4. Emulator calib. & validation

MODEL REDUCTION

The dynamic emulator is used in the task is was designed for.

Model use

DEMo 300,000 samples by pseudo random sampling = 5,500 state variables

1. DOE and simulation runs

[Castelletti et al. 2012a]

Building a dynamic emulator of salinity @ the dam

Hierarchical Agglomerative Time Series Clustering [Magni et al., 2008] = 5,500 to 32 states

2. Variable aggregation

Recursive Variable Selection [Galelli and Castelletti, 2013a] = 32 to 1 state

3. Variable selection

Extremely Randomized Trees [Galelli and Castelletti, 2013b]

4. Emulator calib. & validation

MODEL REDUCTION

Model Predictive Control [Scattolini, 2007]

Model use

DEMo 300,000 samples by pseudo random sampling = 5,500 state variables

1. DOE and simulation runs

[Castelletti et al. 2012a]

Real time control with and without quality target

Period: April 2009 – December 2010

Objective (minimize) Without wq With wq

Water deficit [Mm3/year] 75.04 74.81

Flood control [hours/year] 305.67 302.15

Energy usage [Mm3/year] 17.28 16.19

Min salinity [ppt] 9.95 5.63

Max salinity [ppt] 30.97 29.52

Mean salinity [ppt] 28.41 22.24

Salinity simulated with DELTF3d Flow at the observation point (water column)

Obj.: water quantity Obj.: water quantity

Obj.: water quantity + quality Obj.: water quantity + quality

April – December 2009 January – December 2010

cross-section

observation point

Real time control with and without quality target

Salinity simulated along the cross-section (dry period vs. wet period)

Obj.: water quantity

Distance from the barrage Distance from the barrage

Water intake Water intake

cross-section

observation point

Obj.: water quantity + quality

Real time control with and without quality target

Conclusions

DEMo as a tool to put more science into decision-making, by …

… preserving the accuracy of the original high fidelity model

… providing some explanatory capability and thus credibility

… allowing to solve complex task such as real time control.

Thanks

Andrea Castelletti andrea.castelletti@polimi.it

Politecnico di Milano Italy