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Open TURNS User’s Day #5
12 juin 2012
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Open TURNS User’s Day #5 Contents
Reception at EDF R&D Clamart
Open TURNS : Identity card
Consortium and Industrial Club
Web site
Open TURNS trainings
New features from the 0.14.0 release Scientific and technologic new features
New modules : FFTW, SVM, Matplotlib, MixMod (modifications)
Open TURNS and the Stochastic Processes « Processus gaussiens et leur simulation » (1h) : F. Poirion (ONERA)
« The Stochastic Processes in Open TURNS v1.0 » (30’) : A. Dutfoy (EDF R&D MRI)
Studies using Open TURNS Study 1 :« Modélisation de variables dépendantes pour l'étude de la dispersion de la signature
infrarouge» (30’) : S. Lefebvre (ONERA)
Study 2 : « Assistance à l’élaboration de gammes d’assemblage innovantes de structures composites » (30’) : L. Andalfatto (EADS-IW / ENS Cachan)
Study 3 : « Interfaces Open TURNS - Java, Matlab, Octave » (30’) : P. Rekapalli (EADS-IW)
Study 4 : « Open TURNS en mécanique » (30’) : A-L. Popelin (EDF)
Study 5 : « Analyse de sensibilité multi-échelle – Open TURNS / YACS » : Y. Caniou
Next works of the Consortium and Discussion
9h30 – 10h30
10h30 – 12h
14h – 16h
16h15 – 17h
9h – 9h30
12h – 12h30
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Open TURNS : identity card
Open TURNS aims at propagating uncertainties through a model until a given variable of interest. It proposes some functionalities in order to quantify uncertainties in order to rank their influence on the variable of interest. Open TURNS also enables to build meta models.
Partners 2005 – 2011 : EDF – R&D / EADS – Innovation Works / PhiMECA : transparency : to make the methodology and the associated software be accepted by certification or control entities
genericity : to benefit from different fields where the same approach is developped (mechanics, hydraulics, ...)
computing performance : to enable the treatment of complex industrial cases (parallélisation, distribution, ...)
Open TURNS : an open source platform dedicated to uncertainty treatment by probabilistic methods Open source Treatment of Uncertainty, Risk ‘N Statistics
sous LGPL licence
www.openturns.org
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Uncertainty Methodology
Open TURNS is the software associated to the Global Methodology of Treatment of Uncertainties developped first at EDF R&D in 1990 and then improved by contributions from other companies :
Step A : Study Specification : uncertain input variables, model, variable of interest, analysis criteria (range study, central dispersion, probability to exceed an extrem threshold)
Step B : Uncertainty Quantification : modelisation of the joint distribution of the input uncertain parameters
Step C : Uncertainty Propagation : quantification of the analysis criteria
Step C’ : Uncertainty Ranking
feedback
Step C : Uncertainty Propagation
Step C’ : Sensitivity Analysis, Ranking
ModelG(x,d)
ModelG(x,d)
Input Variables
Incertain : xFixed : d
Input Variables
Incertain : xFixed : d
Variable of interestZ = G(x,d)
Variable of interestZ = G(x,d)
Decision Criteria
Ex: Probability < 10-b
Step A : Study specification
Quantity of interest
ex: variance, probability, ..
Quantity of interest
ex: variance, probability, ..
Step B:
Uncertainty Quantification
joint distribution
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Uncertainty Methodology - Open TURNS
Numerous functionalities for each step of the Methodology in particular ....
Code linked to Open TURNS :
Generic Wrapper générique which enables to wrap OT to any code using input and output text files, with authomatic multithreading functionalities (parallélism multiprocessors / multicores)
Interface with python functions, which enables the realisation of complex wrappers without compilation
Standard Interface for the development of wrappers of any complexity (distributed wrapper, binary data) which require the development of an external wrapper
Salome compatibility : OpenTURNS composant of Salome, linked to YACS
Step B : Uncertainty Quantification
Estimation from data :
Distribution fittings (parametric or not),
Validation Tests (quantitative or graphical),
Estimation of the dependence : copula, correlation coefficient
Regression
Modelisation of Joint Distributions of dimension n :
• Combination Marginals + Copula,
• Parametric Distributions of dimension n (normal, student...)
• Non Parametric Distribution of dimension n : kernel fitting (n), Sklar Copula
• Linear combination of pdf
• Linear combination of random variables,
• Random sum of independent discrete variables according to a Poisson process
• …
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Uncertainty Methodology - Open TURNS
Open TURNS = repository of innovant or recent algorithms the most recent and efficient algorithms of non uniform distribution generation
• Ziggurat method (2005) for the normal distribution
• sequential reject algorithm (1993) for the binomial distribution,
• Tsang & Marsaglia method (2000) for the gamma distribution,
• Lebrun algorithm (2012) for the MultiNomial distribution,
the most recent algorithms of evaluation of the CDF
• Marsaglia algorithm for the exact statistics of Kolmogorov (2003),
• Benton et Krishnamoorthy algorithm for the distributions non centered Student and non centered Chi2 (2003).
PhD results
• Sparse chaos expansion polynomials : G. Blatman (EDF/R&D/MMC) (2010)
• Accelerated simulation algorithm for the evaluation of low probabilities : M. Munoz (EDF/R&D/MRI) : (in projet)
Innovation : the internal data model is based on the multidimensional cumulative density function which enables :
the sampling approach : estimation of statistical characteristics of the output variable from a large numerical sample
and the analytical approach : exact partial or total résolution of some problems using the probabilistic modelisation and the implementation in Open TURNS of the function R n --> R p algebra until order 2:
• exact determination of the distribution of the sum of random variables thanks to the characteristic functions implemented for each distribution,
• exact representation of the distribution of a random variable such that its pdf is a linear comibnation of pdf,
• exact determination of the distribution of a random variable defined as the random sum according to a Poisson process of iid discrete random variables (for ex, cumulated failure times when failures follow a Poisson process)
• particular manipulations on distributions : extraction of marginals, extraction of dependence structure, ...
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Open TURNS in images
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Open TURNS in images
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Open TURNS in images
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Open TURNS in images
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Open TURNS : software, doc and Users
Open TURNS is ….
a C++ library giving functionalities for the treatment of uncertainties
a pyhton module offering high level operators
With a detailed documentation :
scientific documentation : Reference Guide,
Users documentation : Use Cases Guide, User Manual, Examples Guide
technical documentation : Architecture Guide, Wrapper Guide, Contribution Guide, Windows port doc.
… and a sympathetic community :
Openturns.org : official web site
a particular page share to communicate about the sofware
the annual Users day
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Open TURNS ans its Consortium
The Open TURNS Consortium is organised around two main committees in close collaboration :
Steering Committee : driving the evolution of the scientific content and the architecture, responsible for the releases, organisation of the User’s Day
Technical Committee : responsible for the scientific and technological content, audit of the different contributions, pro active to propose evolutions and partnerships
How to contribute to / interact with Open TURNS ?
Level 1 : the contributor wants to share around the tool by proposing new functionalities (developed under C++ or python with the module mechanism), a script (pre / post processing of data, coupling with other tools, ….)
GO TO share.openturns.org
Level 2 : the contributor wants to contribute to the official version of Open TURNS
Contribution to the C++ library, to the python TUI python
Open TURNS quality criteria to be respected (at the end) : code source + documentation, detailed in the Coding Rules Guide + Contribution Guide
don’t hesitate to contact the Open TURNS Consoritum as soon as possible!
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Open TURNS ans its User Club
Current situation :
The Open TURNS user's community is increasing :
• industrial : SNCF, Dassault-Aviation, MBDA, Astrium, Airbus, Michelin, Lafarge, Orange, EDF-SEPTEN, EDF-CIDEN,
• Research centers and universities : LNE, EDF-R&D, EADS-IW, ENS Cachan, IFMA, CEA
• Services : InModelia, IMACS, Phimeca
• projets ANR, européens, ...
Open TURNS is closer to the industrial computational chains :
• EDF : Salome et SalomeMeca, ...
• ERDF : plateform of computation for the safety of electric networks
• Other applications
Open TURNS is interfaced to:
• Matlab,
• SciLab,
• PhimecaSoft, ...
==> increasing needs in the community :
To train the users,
To enrich the tool with specific needs coming from various areas,
To adapt the tool to specific constraints,
To ensure the long-term maintenance and ensure the adequate quality of service, ...
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Open TURNS ans its User Club
Since 2012 : creation of the Open TURNS Users Club
Industrial people & Academics
To share best practices around the use of Open TURNS in uncertainty studies :
• discussions
• Scientific presentations around the uncertainty management methodology
• Use-case with the tool
To mutualize the developments to enrich the platform:
• Common requirements shared by several industrial to prototype scientfic developments ( module C++, production of python scripts, ...),
• The actions of developments and maintenance done by partners labelled by the Open TURNS consortium Open TURNS,
To organize training and communication actions
… you are welcome !
(contacts : [email protected], [email protected], [email protected])
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Open TURNS – www.openturns.org
Quick access to main parts of the website by left and upper menu
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Open TURNS – www.openturns.org
Easy acces to the download page
Documentation
Version 1.0 => 168 downloads between the 22th of april and the 1st of june
France : 68 %
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Open TURNS – Trainings
EDF
« Uncertainty Management : Open TURNS »
• 3 days to learn the use of Open TURNS : python TUI, wrapping aspects, application of the methodologie from step A to step C & C’
• next session in october 2013, ITECH ref : 4888
contact : Corine Tripet : 01 47 65 58 41
MAI : 26 to 28 novembre 2012, Uncertainty Management in Computational Mechanics
General Methodology, Probabilistic Fatigue Design, etc… & illustrations with OpenTURNS
contact : Marc Berveiller, EDF : 01 60 73 73 66
PHIMECA
Several 2 days sessions on the different steps from the methodology:
Probability & Statistics
Response Surfaces Models
Uncertainty propagation methods for sensitivity & dispersion analysis
Uncertainty propagation methods for reliability evaluation
Introduction to the use of OpenTURNS : 2 days
Introduction to the use of PhimecaSoft : 2 days
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New features from the 0.14.0
Python types capabilities
Numpy array / matrix ↔ Open TURNS Matrix conversion Available for all Matrix types : Matrix, SymmetricMatrix, ComplexMatrix, Tensor, … Both ways numpy.array ↔ ot.Matrix: a0 = np.array( ((1.+3j,0.),(3.+7j,4.-9j)) ) m0 = ot.ComplexMatrix( a0 ) a1 = np.array( m0 )
Implicit conversion for Indices, Description, CorrelationMatrix, CovarianceMatrix types No need to specify these types anymore: v0.15 : marginal = distribution.getMarginal( Indices( [ 1, 2, 4 ] ) ) v1.0 : marginal = distribution.getMarginal( [ 1, 2, 4 ] ) Python philosophy : hidden basic types, shorter scripts
More operators for NumericalPoint, NumericalSample, Matrix NumericalPoint : __div__ → x / 3.0 NumericalPoint : __rmul__ → 3.0 * x NumericalSample : __eq__ → if xs == y: Matrix : __rmul__ → 3.0 * m
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New features from the 0.14.0
Scientific aspects
Chaos polynomial expansion, sparse chaos :
• Othonormalised polynomials for the discrete distributions : CharlierFactory, MeixnerFactory, KrawtchoukFactory
• Model selection: Kfold
• Projection algorithm: PenalizedLeastSquaresAlgorithmFactory
Additional distributions and factories :
• 1 D continuous distributions : LogUniform, LogUniformFactory
• 1 D discrete distributions : NegativeBinomial
• N D continuous distribution: MinCopula
Numerical models :
• Vectorial functions : AggregatedNumericalMathEvaluationImplementation, AnalyticalNumericalMathEvaluationImplementation, DatabaseNumericalMathEvaluationImplementation
• Process rransformations :DynamicalFunction, TemporalFunction, SpatialFunction,, BoxCoxFactory, BoxCoxTransform, InverseBoxCoxTransform, InverseTrendTransform,, TrendFactory, TrendTransform
• Differentiation: BlendedStep
Last Releases : 0.15.0 in April 2011; 1.0 in April 2012.
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New features from the 0.14.0
Scientific aspects
Processes (1.0)
• Families of processes: CompositeProcess, Process, RandomWalk, ARMA, WhiteNoise, SpectralNormalProcess, TemporalNormalProcess
• Second order models : CovarianceModel, CauchyModel, ExponentialCauchy, ExponentialModel, StationaryCovarianceModel, SecondOrderModel, SpectralModel, SpectralModelFactory, UserDefinedSpectralModel
• Statistiocal estimation : WelchFactory, WhittleFactory
• Filtrage: FilteringWindows, Hamming, Hanning
• Event : Domain, EventDomainImplementation, EventProcess
• Data contenairs : ProcessSample, RegularGrid, TimeSeries
Diverse
• Numerical analysis :
• Linear algebra : ComplexMatrix, HermitianMatrix, TriangularComplexMatrix, SquareComplexMatrix
• Fourier transform : FFT, KissFFT
• Design of Experiments : GaussProductExperiment, RandomizedLHS, RandomizedQuasiMonteCarlo, HaselgroveSequence, ReverseHaltonSequence
• Graphical analysis : SimulationSensitivityAnalysis
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Some new modules : MixMod & FFTW
See presentation .pdf
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Some new modules : Matplotlib based module
New graphing module
Allows to visualize Open TURNS graphs through python matplotlib plotting library
Replaces graphing with R command line, Rpy2, ...
Outputs nicer, more customizable plots
Available as an independent python module until next release
view = View( graph )
view.save( 'curve.png' )
view.show()
pyplot.text( 0.15, 0.6, 'Zou!')
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New matplotlib based module
Curve
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New matplotlib based module
Contour
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New matplotlib based module
Histogram
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New matplotlib based module
Qqplot
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New matplotlib based module
Cloud
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New matplotlib based module
CobWeb
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New matplotlib based module
Staircase
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New matplotlib based module
Convergence graph
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Open TURNS : its logo
The Galton Board (1822 - 1911) : british explorer, geograph, inventor, meteorologist, proto-geneticist, psychometrician, statistician
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Open TURNS and the Stochastic Processes
« Processus gaussiens et leur simulation » : F. Poirion (ONERA)
« Les processus stochastiques dans Open TURNS v1.0 » : A. Dutfoy (EDF R&D MRI)
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Open TURNS and the Stochastic Processes
Process
getRealization
getTimeGrid
getSample
getMarginalProcess
RegularGrid
Process
TimeSeries
ProcessSample : collection of n TimeSeries
: de dimension m <d
computeTemporalMean
computeMean
computeQuantilePerComponent
NumericalSample
TimeSeries
TimeSeries
computeTemporalMean
drawMarginal(i)
ARMA
RandomWalk SpectralNormalProcess
TemporalNormalProcess
WhiteNoise
CompositeProcess
NumericalPoint
Graph
where
(X(,t)), tR
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Open TURNS and the White Noise & Random Walk
WhiteNoise
WhiteNoise(myDistribution, myTimeGrid)
RandomWalk
RandomWalk(myOrigin, myDistribution, myTimeGrid)
Distribution RegularGridDistribution RegularGridNumericalPoint
P(-1) = 0.9; P(10) = 0.1
N(0,1)
N(0,1)
White noise Random walk
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Open TURNS and the ARMA processes
ARMA
ARMA models stationnary processes :
ARMA(myARCoef, myMACoef,myWNdist) (a)
ARMA(myARCoef, myMACoef,myWNdist, myCurrentState) (b)
• getRealization()
does not depend on the current state
TimeSeries
==> thermalization step
add Nther instants to the time grid
generate the process on the new time grid
erase the first Nther instants
by default, Nther = f(roots of the AR polynomials)
! authomatically performed with (a) creation
• getSample(n) ProcessSample
• getPossibleFuture(Nit,n)
must take into account the influence of the current state on the first instants
==> NO thermalization step
! creation (b) is mandatory
• getPossibleFuture(Nit) TimeSeries
ProcessSample
! Care : Beyond Nther instants, the future has no link with the present
ARCoefficient
MACoefficient
ARMAStateWhiteNoise
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Open TURNS and the ARMA estimation (1d)
Principles : White noise : Gaussian(0,2) Whittle likelihood function which is a ratio between an estimate of the spectral density function of the data and the analytical spectral density function of an ARMA(p,q) process Welch method to estimate the spectral density function of the data using a tappering window (Hamming, Hanning)
Estimation : for a given (p,q) for a range on p and a range on q : (pIndices, qIndices) decision criteria : corrected AIC other information : BIC and AIC criteria
The AIC and AIC c criteria select the best structure - AICc penalizes the high (p,q)
The BIC criteria selects the best prediction model
For n-> , the three selections (p,q) converge
WhittleFactory
• build (TS or PS) :• getHistory()
WhittleFactory(p,q) (a)
WhittleFactory(pIndices,qIndices) (b)
criterion = NumericalPoint()
criterion : in order to get the evaluation of the 3 criteria : AICc, AIC, BIC
• build (TS or PS, criterion) : ARMA WhittleFactoryStateCollection
stores all theARMA(p,q) models of the range ranks the models with respect to the AICc criteria stores the evaluation of the 3 criteria for each ARMA(p,q)
TimeSeries
ProcessSample
NumericalPoint
Indice
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Open TURNS and the Normal processes
Normal processes
• if stationnary, defined by its stationnary covariance function
• if stationnary, defined by its spectral density function
ExponentialModel
CauchyModel
UserDefinedModel
TemporalNormalProcess SpectralNormalProcess
==> ==>
SecondOrderModel
ExponentialCauchyModel
in order to insure the coherence between the covariance function and the spectral density function
==>
WechFactory
• may be estimated from data (non parametric Welch estimator)
• defined by its covariance function
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Open TURNS and the trend computation
Principles : In general, the time series (Yt)t writes :
(Xt)t stationnaryThe objective here is to identify the trend function f and to remove it from the observed time series in order to analyse the stationary time series (Xt)t .
==> We decompose f over the functional basis B :
Coefficients identification : algorithms which combine cross validation techniques and advanced regression strategies, in order to provide the estimation of the coefficients associated to the best model among the basis functions (sparse model).
==> Construction of the ‘Trend Factory’ :
TrendFactory TrendFactory(myBasisSequenceFact, myFittingAlgo)
BasisSequenceFactory FittingAlgo
ex : LAR CorrectedLeaveOneOut
KFold==> generates a sub basis of B
==> estimates the empirical error
ex :
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Open TURNS and the trend computation
This ‘Trend Factory’ is used to create a trend transform : • with a particular functional basis B• and a particluar time serie
• build(myTimeSeries, myFunctionBasis) TrendTransformTrendFactory
TimeSeries NumericalMathFunctionCollection
• add the trend to (Xt)t :
>> myYTimeSeries = myTrendTranform(Xt )
• remove the trend from (Yt)t :
>> myXTimeSeries = myTrendTranform . getInverse( )(Yt )
• evaluate the trend at t :
>> trend_t = myTrendTranform.getFunction ()(t)
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Open TURNS and the Box Cox transform
Principles : the Box Cox transform h : (Yt)t -> (h(Yt))t with a stabilized variance (if it exists) : such that Var[h(Y t)_] is constant with respect to the time for each i.For each scalar marginal process :
In general, the Box Cox transformation writes (where is scalar) :
• may be estimated from the data or given by the User
==> For ex, if then :
==> For ex : if then :
BoxCoxFactory • BoxCoxFactory()
if (Yt)t has negative values, translate it of alpha : (alpha + Yt)t is a positive time series
• BoxCoxFactory(alpha)
==> More generally : if then :
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Open TURNS and the Box Cox transform
This ‘Box Cox Factory’ is used to create a Box Cox transform with a particular time series where the factor is estimated from the data
• build(myTimeSeries) BoxCoxTransformBoxCoxFactory
TimeSeries
• transform (Yt)t into (h(Yt))t :
>> myStabilizedTS = myBoxCoxTranform(myYt )
• transform (h(Yt))t into (Yt)t
>> myYt = myBoxCoxTranform.getInverse()(myStabilizedTS )
or :
or :
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Open TURNS and the Box Cox and Trend transforms
We illustrate the full process of analysis
Box Cox transform : stabilization of the variance = 0.046
Trend suppression : LAR & cross validationbasis : polynomials of degree 4linear trend
ARMA(0,1)
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Open TURNS and the propagation of processes
Dynamical function :
TemporalFunction SpatialFunction
DynamicalFunction
Event :
Monte Carlo estimation :
Composite Process :
TemporalFunction(myFunctiong)
NumericalMathFunction
SpatialFunction(myFunctiong)
NumericalMathFunction
DynamicalFunction(myTemporalFunction)
myYt = CompositeProcess(f,myXt)
DynamicalFunction(mySpatialFunction)
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Studies with Open TURNS
Study 1 : « Modélisation de variables dépendantes pour l'étude de la dispersion de la signature infrarouge » - S. Lefebvre - ONERA
Study 2 : « Assistance à l’élaboration de gammes d’assemblage innovantes de structures composites » : L. Champaney » – L. Andalfatto EADS-IW / ENS-CACHAN
Study 3 : « Interfaces Open TURNS - Java, Matlab, Octave » - P. Rekapalli – EADS-IW
Study 4 : « Open TURNS in Mecanics » – AL Popelin - EDF R&D
Study 5 : « Analyse de sensibilité multi-échelle – Open TURNS / YACS » – Y. Caniou - PhiMECA
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Perspectives
Processus stochastiques : new developments to come
Dickey-Fuller stationarity test
Multidimensional ARMA estimation
Estimation of the covariance function stationnary : FFT algorithm, non stationnary : crude sample autocovariance function
Bayesian modelisation
Bayesian updating of « a priori » distribution in conjunction with physical models
Use Case discussion meeting : 19 juin 2012
OpenTURNS in its environment…
Python friendly
Automatic conversion (e.g. array/matrix)
Use of MatPlotLib library for the visualisation
Other ideas ?
Use of the module mecanism in order to extend the OpenTURNS capabilities
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Discussion
Some ideas ...
points on which you would like some improvements ?
additional functionnalities ?
how to improve the Open TURNS diffusion ?
It’s up to you !
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The end ....
Thanks for your participation ... and see you next year !