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