real time modeling of water infrastructure using hydraulic...
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Real time modeling of water infrastructure using hydraulic models and data assimilation
Smart Sustainable Cities seminar
DTU Lyngby
6th of February 2017
By
Asst. Prof.
Morten Borup
DTU Environment
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20 October 2016
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Contents
• Detailed urban hydrological models (HIFI models)
– Why online HIFI models
• The Ensemble Kalman Filter (EnKF)
• Surrogates of HIFI models
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Detailed urban hydrological models (HIFI models)
Mike Urban (DHI) model of Avedøre
WWTP catchment
1707 sub-catchments
6601 Manholes
7749 Pipe & channel sections
40 Pumps
40 Basins
Etc.
5 km
Can potentially be all-knowing: Water levels, volumes, flows, concentrations - everywhere
Outlet
The models can be made automatically - If the asset data base is well maintained! Can adapt to system
changes (as opposed to data driven models)
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Full 1D St. Venant equations
Conservation of mass:
Conservation of momentum:
Hydraulic computations
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Potential of online HIFI model • Warning system
• Real time control
• Online supervision of gauges
• Error detection
Not used because:
• Computational cost
• Very uncertain rain input
• Lack of update algorithm’s
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Main model input:
Rain data
Water consumption (waste water production)
5 km 5
Outlet
Detailed urban hydrological models (HIFI models)
Input data uncertain: All input data uncertain – Data assimilation is needed
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......
.....
Measured rain
Perturbated
rain
MIKE URBAN
MIKE URBAN
MIKE URBAN
......
.....
Observation
EnKF
Ensemble based updating
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Ensemble Kalman Filter
q Value
Xi,3 Xi,2 Xi,1
X1
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Ensemble Kalman Filter
q Value
Ensemble of models used to represent state uncertainty (model error)
Estimate of the error covariance can be calculated directly from ensemble:
Xi,3 Xi,2 Xi,1
X4
X5
X1 X2
X3
σ1,3 = 1
𝑁 − 1 (𝑋𝑖,1 − 𝑋,1)(𝑋𝑖,3 − 𝑋,3)
𝑁
𝑖
𝜎𝑧2 z
𝑋1,3= 𝑋1,3 + 𝜎𝑋1,3,𝑞
𝜎𝑞2+𝜎𝑧
2 (𝑧 − 𝑞)
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Ensemble Kalman Filter
z
Value Xi,1 Xi,2 Xi,3 q
𝜎𝑧2
Ensemble of models used to represent state uncertainty (model error)
Estimate of the error covariance can be calculated directly from ensemble:
σ1,3 =
1
𝑁 − 1 (𝑋𝑖,1 − 𝑋,1)(𝑋𝑖,3 − 𝑋,3)
𝑁
𝑖
𝑋1,3= 𝑋1,3 + 𝜎𝑋1,3,𝑞
𝜎𝑞2+𝜎𝑧
2 (𝑧 − 𝑞)
X4
X5
X1 X2
X3
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Model setup: Link and weir
A =57 ha Tc = 60 min
Weir
Point at Link 7
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Situation without update
20:00 22:00 00:00 02:00 04:00 06:00
12.4
12.6
12.8
13
13.2
13.4
13.6
time
Wate
r Level [m
]
Water level at link 7
Truth
Base
Ensemble of 20 – No update
Weir Link 7
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When updating using EnKF
3:00 4:00 5:0012
12.2
12.4
12.6
12.8
13
13.2
13.4
13.6
time
Wate
r Level [m
]
WL at Link7 chainage 935 - 5/11 2010
Base
Truth
Updated
Weir Link 7
It works
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Synthetic test on distributed system
• Updating using upstream wl gauge
• Downstream flow validation
Two rainfall observation scenarios: Scenario 1: Known rainfall error statistics Scenario 2: Rain observations 2.5 or 0 um/s
Two wl gauge scenarios: No bias: White noise on observation Bias: + Coloured noise (+5 cm)
R2
Downstream flow validation
Poor rain data + poor observations
=> good model
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Benefits in using EnKF for HIFI models
• Robust • Flexible • Good uncertainty estimates • Can utilize ensemble input • Can utilize most kinds of observations Drawbacks: - computational cost
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04/10/2016 Surrogate modelling of inundation 16 DTU Environment, Technical University of Denmark
Making Surrogates of HIFI models
• Division of system into compartments:
• Model volume of water with mass balance:
MU SM
Slides by Cecilie Thrysøe
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04/10/2016 Surrogate modelling of inundation 17 DTU Environment, Technical University of Denmark
Training data for SM
• Vol-Q relationships are extracted from steady state values
Rain input Original model output Training data
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• Drainage system results
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04/10/2016 Surrogate modelling of inundation 19 DTU Environment, Technical University of Denmark
Preliminary results
• Elster Creek catchment, Melbourne, Australia
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04/10/2016 Surrogate modelling of inundation 20 DTU Environment, Technical University of Denmark
Preliminary results
• Elster Creek catchment, Melbourne, Australia
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04/10/2016 Surrogate modelling of inundation 21 DTU Environment, Technical University of Denmark
Preliminary results
• Elster Creek catchment, Melbourne, Australia
• Steady state training data
• SM output
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04/10/2016 Surrogate modelling of inundation 22 DTU Environment, Technical University of Denmark
Preliminary results
• Elster Creek catchment, Melbourne, Australia
• Steady state training data
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04/10/2016 Surrogate modelling of inundation 23 DTU Environment, Technical University of Denmark
Preliminary results
• Elster Creek catchment, Melbourne, Australia
• Steady state training data
• Splitting compartment
• Splitting compartment gives the best results!
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04/10/2016 Surrogate modelling of inundation 24 DTU Environment, Technical University of Denmark
Conclusions
• EnKF can be used to make online models with HIFI models
• Surrogate models can be made for HIFI models to achieve large reduction in computational costs.
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20 October 2016
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