real time modeling of water infrastructure using hydraulic...
TRANSCRIPT
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
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
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)
Full 1D St. Venant equations
Conservation of mass:
Conservation of momentum:
Hydraulic computations
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
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
......
.....
Measured rain
Perturbated
rain
MIKE URBAN
MIKE URBAN
MIKE URBAN
......
.....
Observation
EnKF
Ensemble based updating
Ensemble Kalman Filter
q Value
Xi,3 Xi,2 Xi,1
X1
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)
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
Model setup: Link and weir
A =57 ha Tc = 60 min
Weir
Point at Link 7
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
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
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
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
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
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
• Drainage system results
04/10/2016 Surrogate modelling of inundation 19 DTU Environment, Technical University of Denmark
Preliminary results
• Elster Creek catchment, Melbourne, Australia
04/10/2016 Surrogate modelling of inundation 20 DTU Environment, Technical University of Denmark
Preliminary results
• Elster Creek catchment, Melbourne, Australia
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
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
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!
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.
20 October 2016
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Questions?