RESEARCH & DEVELOPMENT

Transcription

1 RESEARCH & DEVELOPMENT Modeling model uncertainty in structural reliability: a variety of approaches Emmanuel ARDILLON EDF-R&D, Industrial Risk Management Department Chatou, France Sylvie AUDEBERT EDF-R&D, Acoustics and Mechanical Analyses Department Clamart, France Exposé Journée AFM «Conception robuste» 10 avril 2015 (cf. Séminaire ESReDA n 46 Turin mai 2014

2 OUTLINES 1. General context 2. The SICODYN Project 3. Model uncertainty in general 4. Deterministic approach: the model coefficient 5. Probabilistic representation 5.1 Justification 5.2 the semi-probabilistic approach st common expression: corrective term nd common expression: unknown parameters in the model 5.5 Some common assumptions 5.6 Proposed representation 6. Conclusions E. Ardillon - EDF-R&D/MRI 46 th ESReDA Seminar, Torino, May 29, 2014

3 I - General Context 3 E. Ardillon - EDF-R&D/MRI

4 1 General context Physical models well recognized in the deterministic approach and consequently on the csp. Probabilistic approach considered as reasonably predictive Proportionnally little work has been performed on the MU issue But a significant basis in 30 years For some structures (dams, big bridges): high gap between calculated probabilities and failure frequencies experienced Notional probabilities Structural dynamics: more realistic predictions for some mechanical components needed (SICODYN Project) 4 E. Ardillon - EDF-R&D/MRI

5 II - The SICODYN Research Project 5 E. Ardillon - EDF-R&D/MRI

6 The 13 project partners Groups ASTRIUM EADS EDF NECS SULZER Pompes France Research centers CETIM SMEs ( employees) LMS SAMTECH SOPEMEA SMEs (<250 employees) PHIMECA Engineering VIBRATEC Academic ENS Cachan FEMTO ST INSA Lyon MSME 6 E. Ardillon - EDF-R&D/MRI

7 Project Objective Quantification et amélioration de la crédibilité des modèles en dynamique des structures par corrélation calcul-essai et estimation des incertitudes. Quantification et amélioration de la crédibilité des modèles en dynamique des structures par corrélation calcul-essai et estimation des incertitudes. 7 E. Ardillon - EDF-R&D/MRI

8 Verrous technologiques Application de méthodes à des structures complexes et industrielles à grand nombre de degrés de liberté Elaboration de modèles d assemblages boulonnés Prise en compte du milieu environnant 9, 00E-03 7, 00E-03 5, 00E-03 Pompe couplée Pompe non couplée 3, 00E-03 1, 00E-03 0,00 50,00 100,00 150,00 200,00 250, , 00-1, 00E-03 Influence des conditions aux limites sur la réponse vibratoire Estimation de l incertitude de modèle et de l incertitude numérique totale Amélioration de la robustesse des modèles vis-à-vis des incertitudes Etablissement de lois empiriques sur les coefficients de sécurité ou les marges Liens avec d autres projets Projet se situe dans la roadmap du groupe OCDS, en particulier ROMMA, EHPOC et CSDL (estimation d incertitudes, robustesse, réduction de modèles) 8

9 1 er démonstrateur : pompe Booster dans son environnement industriel en centrale thermique EDF La pompe Booster dans l atelier du constructeur SULZER Pompes France La pompe déconnectée in situ In situ La pompe connectée à ses tuyauteries d aspiration et de refoulement Modélisée en éléments finis 9

10 Les principaux composants de la pompe 10

11 Structuration scientifique du projet Lot 2 Observation de la variabilité expérimentale (benchmark) Lot 3 Observation de la variabilité numérique totale (benchmark) Lot 4 Corrélation calcul-essai modèle best compromise Lot 1 REX Etat de l art Boîte à outils méthodes Lot 5 Analyse de la variabilité numérique par confrontation des méthodes de quantification des incertitudes Lot 6 Comparaison des variabilités numériques observée et calculée Classification - capitalisation 11 Base de données de benchmarks Coefficients de sécurité

12 Incertitude de modèle sur les fréquences propres des différents composants (séparés) de la pompe 12

13 Pompe non connectée: corrélation calcul/expérience des modes de la pompe assemblée 13

14 Pompe non connectée: corrélation calcul/expérience des modes de la pompe assemblée 14

15 Pompe connectée aux tuyauteries d aspiration et de refoulement 15

16 Pompe non connectée: corrélation calcul/expérience des modes de la pompe assemblée 16

17 III - Model Uncertainty in general 17 E. Ardillon - EDF-R&D/MRI

18 3 Model uncertainty in general Main sources of MU in SRA link with the V&V procedure «Numerical» uncertainty - Are we solving the equations right? verification (step1) Errors in implementing the physico-mathematical model code verification Approximations resulting from the numerical algorithms solution verification FEA: mesh convergence Often considered as negligible after verification «Physical» uncertainty - Are we solving the right equations? validation (step 2) hidden or voluntarily omitted (=error) variables (reduced dimension) Model form: simplifications, approximations (e.g linear assumption, cross effects ignored) Potentially, step 3: calibration (pour réduire l incertitude «physique») Possibly followed by an additional validation step Other sources of MU Limit state considered (conservatism included) Extrapolation 18 E. Ardillon - EDF-R&D/MRI

19 3 Model uncertainty in general Model uncertainty rather (more general) than model error Error: identifiable inaccuracy (deliberate simplifications, programming errors) Model uncertainty : epistemic? Some contributions can be reduced Voluntary approximations (model form, cross effects) Most errors (numerical and physical uncertainty) Hidden variables: knowledge improvement Other cannot Remaining error Remaining lack of knowledge : a compromise btw. Realistic representation and Industrial feasability Perfect accuracy not always required: conservative predictions may be sufficient 19 E. Ardillon - EDF-R&D/MRI

20 3 Model uncertainty in general Other sources of uncertainty in SRA Phenomenological uncertainty Novel structures, behavior partially unknown Epistemic «Decision» uncertainty Limit state violation Prediction uncertainty Knowledge increase versus time Epistemic Statistical uncertainty Data sample size Epistemic Human factor At every stage of the structural life cycle Human factor = involved in most failure cases Some types of human error could be probabilized, some not 20 E. Ardillon - EDF-R&D/MRI

21 IV - Deterministic approach: the model coefficient 21 E. Ardillon - EDF-R&D/MRI

22 4 Deterministic approach: a long-time concern solved by the model coefficient Traditionnally, fundamental role played by the safety coefficient in Civil Engineering High stakes (safety of facilities) All industrial branches are concerned Representative values Cas «R S»: R k / S k > k Safety margin Safety factor Besides the model uncertainty has to be accounted for model coefficient But what does it really represent? Model uncertainty Possibly: measurement uncertainty Possibly: a certain part of the uncertainties that can hardly be quantified A non rigorous concept 22 E. Ardillon - EDF-R&D/MRI

23 Tableau 6.1 Décomposition de l incertitude de modèle pour les structures (coefficients de variation) 4 Deterministic approach: a long-time concern solved by the model coefficient 23 E. Ardillon - EDF-R&D/MRI

24 V - Probabilistic representation 24 E. Ardillon - EDF-R&D/MRI

25 5 Probabilistic representation 5.1 Model uncertainty can be probabilized Ditlevsen s early works (1982) Formalizing the problem Variable change V: V(X 1 )= X 1 + h(x 1, ) V(X 2 )= X 2 Corresponds to : G i (X) = X 2 -f i (X 1 ) G p (X) = G i (V(X)) = X 2 -f i (X 1 + h(x 1, )) X 2 Failure set G(X) 0 Idealized surface G i (X) =0 A given disturbed surface G p (X) =0 Real surface G r (X) =0 X 1 25 E. Ardillon - EDF-R&D/MRI

26 5.2 Semi-probabilistic approach Random variable consistent with the corresponding model coefficient G(X(t), F(t)) = 26 E. Ardillon - EDF-R&D/MRI

27 5 Probabilistic representation 5.3 First common expression: a corrective term 27 E. Ardillon - EDF-R&D/MRI

28 5 Probabilistic representation 5.3 First common expression: a corrective term Suggested form of the corrective term: (X, θ) =. Number p of parameters as limited as possible Parameters sequentially removed (in case of high uncertainty) Parameters correlated or not h i functions correlated or not h i functions may correspond to some components of G(X) 28 E. Ardillon - EDF-R&D/MRI

29 5 Probabilistic representation nd common expression: unknown parameters in the model 29 E. Ardillon - EDF-R&D/MRI

30 5 Probabilistic representation 5.5 Some common assumptions Unbiased basic model Only an error term, with a correlation matrix Non diagonal terms = 0 Constant terms (homoskedasticity) Error term = gaussian Basic model: simplified expression following standards 30 E. Ardillon - EDF-R&D/MRI

31 5 Probabilistic representation 5.6 Proposed representation A synthetized representation can be issued to distinguish between unknown physical and statistical parameters 31 E. Ardillon - EDF-R&D/MRI

32 VI - Evaluations pratiques d incertitudes de modèle 32 E. Ardillon - EDF-R&D/MRI

33 Synthèse d évaluations rencontrées dans l état de l art 33 E. Ardillon - EDF-R&D/MRI

34 VI - Conclusions 34 E. Ardillon - EDF-R&D/MRI

35 6 Conclusions Model uncertainty becomes a growing concern for safety of facilities and scientific knowledge A current industrial example of interest is provided by the SICODYN French research project (13 partners) in structural dynamics MU is a long-time concern in Civil Engineering solved by the model coefficient: an empirical and non rigorous concept A probabilistic representation for model uncertainty is acceptable and the semi-probabilsitic approach enables to link model coefficients with corresponding random variables Two common representations exist in the littérature (additional corrective term or unknown parameters included in the model) A synthetized representation can be issued to distinguish between unknown physical and statistical parameters 35 E. Ardillon - EDF-R&D/MRI