ICIAM 2019 / Industry Day Methods and issues for the ... · Valencia 2019, 17th, July ICIAM 2019 /...
Transcript of ICIAM 2019 / Industry Day Methods and issues for the ... · Valencia 2019, 17th, July ICIAM 2019 /...
Valencia
2019, 17th, July
ICIAM 2019 / Industry Day
Methods and issues for the analysis of complex
systems by numerical simulation at EDF
Bertrand Iooss, EDF R&D
Many uncertainties for the energy production and the safety due to:
• hazards (demand, weather, …),
• incomplete system knowledge (ageing, physics, …),
• internal agressions (failures, …)
• external agressions (earthquake, …)
In order to better understand, prove the safety and optimize its industrial
processes, EDF R&D develops some physical numerical simulation codes
EDF(Electricité de France)
Electricity production and distribution systems
| 3
SALOME PLATFORM FOR SIMULATION
Numerical modelling of EDF components and structures
• Structural mechanics (Code_Aster)
• Thermohydraulics (Code_Saturne, NEPTUNE_CFD)
• Electromagnetism (Code_CARMEL3D)
• Neutronics (ANDROMEDE)
• Surface hydraulics (TELEMAC-MASCARET)
All these physics domains require generic functions for numerical simulations
Computation scheduling
(workflow, distribution)
Complex data processing
(fields, matrix, etc)
3D Modelling
(CAD, meshing, vizualisation)
+ +
Simulation Analytics: Exploring the computer code
Solutions and tools from numerical maths, approximation theory, structural reliability,
applied/theoretical proba/stats, operational research, optimization, machine learning,
geostatistics, data assimilation, scientific computing and visualization, data-analytics…
Keywords: VVUQ (Validation, Verification and Uncertainty Quantification)
DACE (Design & Analysis of Computer Experiments)
See GdR MASCOT-NUM (french academics/industry research group)
Numerical design of
experiments
Simulation
with the finite-
element modelOutput analysis
Computer code
Y = G(X)
X1
X2Integration of data
Simulation analytics in industrial context
Exploratory study : understand a phenomena, an experimental or industrial process
Safety study : evaluate a safety margin (failure probability, rare events)
Design study : optimizingand control the performances
• Environmental variables• Physical parameters• Process parameters
• Distributions of process outputs• Probability of failure• « Main » influential input
parameters• …
Process: Numericalsimulation code
Uncertainties
Design of experiments
Metamodel
Simulation analytics in industrial context
Exploratory study : understand a phenomena, an experimental or industrial process
Safety study : evaluate a safety margin (failure probability, rare events)
Design study : optimizing and control the performances
• Environmental variables• Physical parameters• Process parameters
• Distributions of process outputs• Probability of failure• « Main » influential input
parameters• …
Process: Numericalsimulation code
Uncertainties
Design of experiments
Metamodel
Example 1: Flood risk analysis
via a flood river modelUncertainty analysis: Impact of the uncertainties
of the flowrate and river bed hydraulic properties
Convergence and
confidence
intervals at 95 % of
the estimated
mean
Empirical pdf
based on
70000 Monte
Carlo
simulations
[Goeury et al. 2016]
Global sensitivity analysis via Sobol’ indices
(functional analysis of variance)
• The flowrate input factor explains about 80% of
the variance of the output variable
• Few interactions between the uncertain
variables
Example 1: River flood risk
SCF4
Conclusion and valorization:
- Strong interactions with modelers during the work
- Development of a prototype study with soft to provide interests of engineers and users
Improvement of the sensitivity analysis process via
successful academic collaborations
EDF / Institut de Mathématiques de Toulouse / Ecole des Mines de Saint-Etienne
Two kind of global sensitivity indices of the model Y = G(X) :
First-order and total Sobol’ indices:
Derivative-based global sensitivity measures (DGSM):
Development of inequality properties between DGSM and Sobol’ indices:
=> Sensitivity analysis with large number of inputs is made with a reasonable
computational cost (by using adjoint model)
constant Poincaré optimal the with )Var(
)(
i
i
Xi
X
Ti CY
CS
[ Lamboni et al. 2013
Roustant et al. 2017 ]
2
)(
i
iX
G X
)(Var)(Var;)(Var)(Var YXYTYXYS iiii
Simulation analytics in industrial context
Exploratory study : understand a phenomena, an experimental or industrial process
Safety study : evaluate a safety margin (failure probability, rare events)
Design study : optimizingand control the performances
• Environmental variables• Physical parameters• Process parameters
• Distributions of process outputs• Probability of failure• « Main » influential input
parameters• …
Process: Numericalsimulation code
Uncertainties
Design of experiments
Metamodel
Urgent demand of a nuclear power plant engineer :
Probability of non detection of an indesirable object inside a pipe?
Issue
Qualification on 20 mockup tests of a new NDC process
First step: Formalizing the problem
=> Compute Prob (Signal < threshold), with only 10 Signal values
Solution: Using some « universal » probabilistic inequalities
(concentration-types as Bienaymé-Tchebytchev, Camp-Meidell, …)
+ Adding a bootstrap step to take into account the uncertainties
𝑃 𝑋 ≤ 𝜇 − 𝑡 ≤ 1/(1 + 𝑡2/𝑘𝑠²)
Example 2: Safety process qualification
2.4
2.8
3.2
3.6
8.5
9.0
9.5
10.5
Histogram of SNTT0
SNTT0
Fre
quency
2.4 2.6 2.8 3.0 3.2 3.4 3.6
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Histogram of SNTT1
SNTT1
Fre
quency
8.0 8.5 9.0 9.5 10.5 11.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
10 tests without object
Pro
ba
threshold 10 tests with object
[ Blatman et al., 2017 ]
Urgent demand of a nuclear power plant engineer :
Probability of non detection of an indesirable object inside a pipe?
Issue
Qualification on 20 mockup tests of a new NDC process
First step: Formalizing the problem
=> Compute Prob (Signal < threshold), with only 10 Signal values
Solution: Using some « universal » probabilistic inequalities
(concentration-types as Bienaymé-Tchebytchev, Camp-Meidell, …)
+ Adding a bootstrap step to take into account the uncertainties
𝑃 𝑋 ≤ 𝜇 − 𝑡 ≤ 1/(1 + 𝑡2/𝑘𝑠²)
Example 2: Safety process qualification
Conclusion and valorization: 1) With a threshold at 5, proba=3% with 95% confidence level
2) Authority agreement; 3) Publication for method acceptability
2.4
2.8
3.2
3.6
8.5
9.0
9.5
10.5
Histogram of SNTT0
SNTT0
Fre
quency
2.4 2.6 2.8 3.0 3.2 3.4 3.6
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Histogram of SNTT1
SNTT1
Fre
quency
8.0 8.5 9.0 9.5 10.5 11.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
10 tests without object
Pro
ba
threshold 10 tests with object
[ Blatman et al., 2017 ]
Simulation analytics in industrial context
Exploratory study : understand a phenomena, an experimental or industrial process
Safety study : evaluate a safety margin (failure probability, rare events)
Design study : optimizingand control the performances
• Environmental variables• Physical parameters• Process parameters
• Distributions of process outputs• Probability of failure• « Main » influential input
parameters• …
Process: Numericalsimulation code
Uncertainties
Design of experiments
Metamodel
Example 3: Optimization of a (bifacial)
photovoltaic energy production plant
inclination
elevation Distance inter stands
Time consuming EDF R&D computer code
(electrical model) with:
6 hours per model run
3 « controllable » input variables:
elevation (0,4m to 1m),
inclination = tilt (0°to 50°), distance inter-stands (2,5m to 10m)
2 uncertain input variables: meteo and albedo
Model output : the production (kWh) of a stand
[ Chiodetti, 2015 ]
inclinaison élevation Distance inter-stands
Transfer of « advanced » mathematical
tools to engineers : Optimization
methods of costly function
Issue:
Solution: EGO algo
Example 3: Optimization of a photovoltaic plant
Conclusion and valorization:
1) Maximum at 1080 kWh/kWp with tilt = 30°, elevation = 1m, distance = 6m , with 30 runs of G
2) Dissemination of the skills and communication about interests of advanced mathematical tools
)(min arg* XGXDX
Model GGaussian processmetamodel
X
Adaptive experimental design by maximizing EI(x) = E[ max( 0 , observed minimum – G(x) ) ]
predictor
lower CI
upper CI
Examples of mathematical & computational
challenges in VVUQ and DACE- Optimization process using expensive computer codes (« small data »
problem)
- Curse of dimensionality in the input space (optimized sampling, finding the
effective dimensions of the function, …)
- Robustness to ignorance (model error, epistemic uncertainties, …)
- Volumetry of the simulation outputs => needs of in-situ analysis (learning data
without intermediate storage)
- User-friendly software
A generic platform: OpenTURNS
Features
B, B’, C, C’
Stochastic processes
Metamodels
Optimization framework
Distributed and multi-thread
evaluation of a Python function
Basis algo and module contributions
www.openturns.org, documentation
Licence: open source, LGPL
Linux, Windows
Programing: Python, C++
GUI Persalys via SALOME_EDF
(Linux) https://www.salome-
platform.org/Baudin, Dutfoy, I. and Popelin. Open TURNS:
An industrial software for uncertainty
quantification in simulation. In: Handbook of
uncertainty quantification, Springer, 2017
References
M. Baudin, A. Dutfoy, B. Iooss and A-L. Popelin. Open TURNS: An industrial software for uncertainty
quantification in simulation. In: Handbook of uncertainty quantification, R. Ghanem, D. Higdon and H. Owhadi
(Eds), Springer, 2017
G. Blatman, T. Delage, B. Iooss and N. Pérot. Probabilistic risk bounds for the characterization of radiological
contamination. The European Journal of Physics - Nuclear Sciences & Technology (EPJ-N) 3, 23, 2017
Matthieu Chiodetti. Bifacial pv plants: performance model development and optimization of their configuration.
2015. Master Thesis, KTH Royal Institute of Technology
C. Goeury, T. David, R. Ata, S. Boyaval, Y. Audouin, N. Goutal, A-L.Popelin, M. Couplet, M. Baudin, and R.
Barate. Uncertainty quantication with on a real case with TELEMAC-2D. In C. Moulinec and D.R. Emerson,
editors, Proceedings of XXIIth TELEMAC-MASCARET User Conference, pages 44{51, Warrington, UK, 2016.
Science and Technolgy Facilities Council
M. Lamboni, B. Iooss, A-L. Popelin and F. Gamboa. Derivative-based global sensitivity measures: general
links with Sobol' indices and numerical tests. Mathematics and Computers in Simulation, 87:45-54, 2013
OpenTURNS platform: http://www.openturns.org/
O. Roustant, F. Barthe and B. Iooss. Poincaré inequalities on intervals - application to sensitivity analysis.
Electronic Journal of Statistics, Vol. 11, No. 2, 3081-3119, 2017
SALOME platform: https://www.salome-platform.org/
Thanks for your attention