M. GUITON, T. PERDRIZET, Y. POIRETTE, G. HUWART, N ...

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OPTIMIZATION AND RELIABILITY DESIGN OF A FLOATING OFFSHORE WIND TURBINE

M. GUITON, T. PERDRIZET, Y. POIRETTE, G. HUWART, N. DELÉPINE (IFPEN PHYSICO-CHIMIE ET MÉCANIQUE APPLIQUÉES)

M. MUNOZ-ZUNIGA, A. COUSIN, D. SINOQUET (IFPEN SCIENCES ET TECHNOLOGIES DU NUMÉRIQUE)

J. GARNIER, (CMAP POLYTECHNIQUE)

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N E W E N E R G I E S

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CONTEXT : FLOATING OFFSHORE WIND TURBINE

Significant contribution to the 2 degrees scenario (IEA)

Extend operating sites for many countries (water-depth > 50m)

Facilitate social acceptance (farther offshore)

Higher average wind speed (↗wind turbine size, power up to 10 MW)

More steady wind (increased capacity factor)

emp.lbl.gov (2016)

SBM-IFPEN floater

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N E W E N E R G I E S

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CONTEXT : FLOATING OFFSHORE WIND TURBINE

Many cost reductions expected, implying optimization of design from the wind farm layout to the various components -> reduction of Levelized Cost of Energy comparable to onshore.

Large uncertainties (e.g. metocean during 20 years, highly non-linear multiphysics) -> high security factors (e.g. 10 for fatigue damage in standards). Large possible cost reductions with Reliability Based Design Optimizations.

Only few pilots, not yet database for classical Fault Analysis approaches.

[Floating Offshore Wind Vision Statement WindEurope, 2017]

Median LCOE

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É N E R G I E S N O U V E L L E S

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Stationary windows (10min for wind, 3h for wave)

Joint probability of wind and wave long term parameters 𝑃 𝑈,𝐻𝑠, 𝑇𝑝, 𝛽 = 𝑃 𝑈 𝑃 𝛽 𝑈 𝑃 𝐻𝑠 𝑈, 𝛽 𝑃(𝑇𝑝|𝑈, 𝐻𝑠) 𝑈 : the 10-min mean wind speed (should add Turbulence Intensity (i.e. cov))

𝐻𝑠: the significant wave height 𝑇𝑝 : the PSD peak period

𝛽 : wind/wave misalignment

CONTEXT : ENVIRONMENTAL UNCERTAINTY

[Preumont, 1994]

[Stewart et al, 2016])

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Like in offshore oil&gas, standards recommend to use discretized scatter diagrams -> several thousands environmental cases

Very large number of cases to estimate the Fatigue Limit State (service life of about 20 years)

Difficulty to select representative cases for Ultimate Limit State (return period of 50 years, e.g. standard environmental contour method [Saranyasoontorn & Manuel, 2006])

CONTEXT : ENVIRONMENTAL UNCERTAINTY

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CONTEXT : MODEL UNCERTAINTY

Multiphysics (aero-servo-hydrodynamics-elastic) codes to predict FOWT response

Strong non linearities require high CPU time domain simulations (several hours for one environmental case)

Validated by comparison to basin test which may not be representative of full scale behavior (incompatibility of Froude vs Reynolds similarities)

[Robertson et al, 2017]

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OUTCROSSING APPROACH FOR ULTIMATE STATE Perdrizet, T., Averbuch, D. (2011). “Short and long term extreme reliability analysis applied to floating wind turbine design”. OMAE 2011, Paper n° 50264. Murangira, A., Munoz-Zuniga, M. , Perdrizet., T. (2015). “Structural reliability assessment through metamodel based importance sampling with dimension reduction.” “https://hal.archives-ouvertes.fr/hal-01230454/document”.

https://hal.archives-ouvertes.fr/hal-01230454/document





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OUTCROSSING APPROACH FOR ULTIMATE STATE [PERDRIZET & AVERBUCH, 2011; MURANGIRA ET AL, 2015]

Goal is long term failure probability : 𝑃𝑓 𝑇𝐿𝑇 = ℙ𝑄,𝑋 ∃𝑡 ∈ 0, 𝑇𝐿𝑇 | 𝐺 𝑋(𝑡|𝑄) ≤ 0 with 𝑋 the short term input and 𝑄 long term environment parameter

𝑋 expanded in finite numbers of random variables 𝜉, 𝜉 (e.g. spectral with 𝑋 stationary Gaussian)

𝑋 𝑡|𝑄 = 𝑋 𝑡|𝑄 + 𝜉𝑖𝜎𝑖 cos 𝜔𝑖𝑡 − 𝑘𝑖𝑥 − 𝜉𝑖 𝜎𝑖 sin 𝜔𝑖𝑡 − 𝑘𝑖𝑥

𝑛

𝑖=1

Short term failure probability with outcrossing approach [Rice, 1944]

𝑃𝑓 𝑇𝑆𝑇|𝑄 ≤ ℙ𝜉 𝐺 𝑡 = 0, 𝜉, 𝜉 |𝑄 ≤ 0 + 𝔼𝜉|𝑄 𝜈+ 𝑡 𝑑𝑡

𝑡

0 with 𝜈+ the outcrossing rate

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Possible approaches

FORM based PHI2 approach [Der Kiureghian, 2000; Andrieu-Renaud et al, 2004]

Optimization to determine design point (e.g. Abdo-Rackwitz, IFPEN derivate free SQA). Less call to simulators to SQA

Simulation methods: subset [Au & Beck, 2001], IS, Kriging-IS [Dubourg, 2011]

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High number of short term variables 𝜉, 𝜉 (several hundreds), could be reduced with sufficient dimension reduction (SDR)

Find linear subspace of 𝜉 predictors that contains all information on regression/classification of 𝐺 against 𝜉 (Kernel dimension reduction method, KDR [Fukumizu, 2009])

Strong reduction of calls to simulator when coupled with Kriging-IS [Murangira et al, 2015]


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From short to long term failure probability Assumed long term Q parameters ergodic, independent outcrossing rates (no extreme clustering) -> Poisson distribution

𝑃𝑓 𝑇𝐿𝑇 ≈ 1 − 𝑒𝑥𝑝(−𝑇𝐿𝑇𝔼𝑄 𝜈+ 𝑄

Possibility to compute a design point with long and short term together -> reduction to 1 environmental case


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Failure scenario at t0 = 150 s

t = 130 s

V <11 m/s pitch

130s to 150s

gust V 16 m/s

platform pitch modified (lower) apparent wind speed

controller does not see the increased wind speed

no blade pitch correction

platform pitch strongly increased apparent wind speed and almost no pitch

t = 150 s : failure

large rotor thrust

failure at the tower base


wave wind

Blade pitch

Rotor thrust

Tower base moment

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Optimizing dynamic inter-array production cable configuration Poirette, Y., Guiton, M., Huwart, G., Sinoquet, D., Leroy, J-M. (2017). “An Optimization Method for the Configuration of Inter Array Cables for Floating Offshore Wind Farm”. OMAE 2017 61655

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OPTIMIZING DYNAMIC INTER-ARRAY POWER CABLE CONFIGURATION [POIRETTE ET AL, 2017]

IFPEN SQA optimizer for black-box software and non-linear constraints [Langouët, 2011]

Constrained sub-problems in the trust region of size 𝛥𝑘

𝑚𝑖𝑛𝑑 ≤𝛥𝑘𝑄𝑂𝑘 𝑑 s.t. 𝑄𝐶𝑘(𝑑) ≤ 0

𝑄𝑂𝑘 and 𝑄𝐶𝑘 quadratic interpolations of objective function and constraints

Case study to minimize material cost of power cable linked to an IFPEN floater with a 3,6 MW wind turbine (total mass of 425 tons). ULS constraints with 28 environmental cases.

C1 : (no compression) 𝜎 > 0

C2 : (tension) σ <2

3𝑅𝑒 = 660𝑀𝑃a

C3 : (curvature ) γ < 0.25𝑚−1

C4 : (sea bed contact): 𝑧𝑓𝑖𝑟𝑠𝑡𝑝𝑎𝑟𝑡 − 0.5𝐷𝑐 > 𝑊𝑎𝑡𝑒𝑟 𝑑𝑒𝑝𝑡ℎ

C5 : (no emersion) Z-position: 𝑧𝑏𝑢𝑜𝑦𝑠 + 0.5𝐷𝑐 < 0

C6 : (elongation) 𝑒 < 0.1%

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Cable only (L1c, Dc, Lc) Buoys (Db,Lb)

Stiffener (Ls, Dsb)

60 m

OPTIMIZING DYNAMIC INTER-ARRAY PRODUCTION CABLE CONFIGURATION [POIRETTE ET AL, 2017]

Parameters Top segment length 𝐿1𝑐 65𝑚; 95𝑚

Buoys segment length 𝐿𝑏 [30𝑚; 70𝑚]

Total length 𝐿𝑐 525𝑚; 555𝑚

Cable diameter 𝐷𝑐 120𝑚𝑚; 135𝑚𝑚

Buoys diameter 𝐷𝑏 𝐷𝑐; 4𝐷𝑐

Stiffener length 𝐿𝑠 3𝑚; 6𝑚

Stiffener base diameter 𝐷𝑠𝑏 2.5𝐷𝑐; 3.5𝐷𝑐

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Workflow 1. A Kriging meta-model is built with 600 points in parameter space (LHS), and 6 most severe DLC

2. Global Sensitivity Analysis of the parameters on the design constraints, based on the meta-model, to improve the optimization problem (parameter selection and definition domain).

3. Multi-start (1000 initial points) optimizations based on the meta model with SQA optimization algorithm. Fast computations.

4. Local optimization with SQA and the original model from best solutions of step 3.


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Example of optimization toward an admissible case which is a compromise between 3 active constraints (C3 max curvature, C1 no compression and C4 bottom contact)

The optimization deals efficiently with large change of parameters, despite the strong possible irregularity of constraints (max over 28 environmental cases)


• Constraints rewritten to be active when positive and normalized in [-100,100]

• Not converged cases correspond to lateral subsurface current which require more static increments before dynamic simulation

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Chance constraint optimization of a complex system, Application to the design

of a floating offshore wind turbine Cousin, A.; Garnier, J., Munoz-Zuniga, M., Guiton, M. (2019). “Chance constraint optimization of a complex system - Application to the design of a floating offshore wind turbine”. Poster at MascotNum

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Formulation for FLS (𝑥 deterministic, 𝜉 stochastic, z stationary Gaussian process)

𝑚𝑖𝑛𝑥∈Ω 𝑐 𝑥

𝑠. 𝑡 ℙ𝜉 𝐹𝑎𝑡𝑖𝑔𝑢𝑒 𝑥, 𝜉 > 𝜌 < 10−4

ℙ𝜉,𝑧 min𝑡∈ 0,𝑇𝑇𝑒𝑛𝑠𝑖𝑜𝑛 𝑥, 𝜉; 𝑧 𝑡 < 0 < 10−4

ℙ𝜉,𝑧 m𝑎𝑥𝑡∈ 0,𝑇𝑃𝑖𝑡𝑐ℎ 𝑥, 𝜉; 𝑧 𝑡 > 6° < 10−4

If linearization of simulator (e.g. frequency domain) -> Extreme Value Theory ℙ( 𝑚𝑎𝑥𝑡∈ 0,𝑇𝜁 𝑡 ≤ 𝛼) ≃ exp (−𝑒𝑎𝑇 𝑏𝑇−𝛼 )

CHANCE CONSTRAINT OPTIMIZATION OF A COMPLEX SYSTEM, APPLICATION TO THE DESIGN OF A FLOATING OFFSHORE WIND TURBINE [POSTER, THESIS A. COUSIN]

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For fatigue and non gaussian extreme constraints

Standard approaches based on FORM/SORM with double loop optimization (RIA and PMA) [Madsen et al, 1986; Tu et al, 1999]

Single loop optimization still based on FORM/SORM (SORA/SAP) [Du & Chen 2004; Cheng et al 2006]

Double loop with metamodels based simulation methods (less assumptions on limit state + confidence interval)

Kriging with adaptative design of experiment [Dubourg, 2011; Moustapha & Sudret 2019; Huchet et al; 2019; Hawchar et al, 2018]

Polynomial chaos, neural network

Single loop with metamodels or double loop Lagrangian formulation

CHANCE CONSTRAINT OPTIMIZATION OF A COMPLEX SYSTEM, APPLICATION TO THE DESIGN OF A FLOATING OFFSHORE WIND TURBINE [POSTER, THESIS A. COUSIN]

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Robertson, A. et al (2017). “OC5 Project Phase II: Validation of Global Loads of the DeepCwind Floating Semisubmersible Wind Turbine”. EERA DeepWind'2017.

Preumont, A. (1994) “Random vibration and analysis”. Springer-Verlag.

Saranyasoontorn , K. Manuely , L. (2006). “Design Loads for Wind Turbines using the Environmental Contour Method”, 44th AIAA Aerospace Sciences Meeting and Exhibit.

Andrieu-Renaud, C., Sudret, B., Lemaire, M. (2004). “The PHI2 method: a way to compute time-variant reliability”. Reliability Engineering and System Safety, 84:75-86.

Der Kiureghian, A. (2000). “The Geometry of Random Vibrations and Solutions by FORM and SORM”. Probabilistic Engineering Mechanics, 15: 81-90.

Perdrizet, T., Averbuch, D. (2011). “Short and long term extreme reliability analysis applied to floating wind turbine design”. OMAE 2011, Paper n° 50264.

Murangira, A., Munoz-Zuniga, M. , Perdrizet., T. (2015). “Structural reliability assessment through metamodel based importance sampling with dimension reduction.” “https://hal.archives-ouvertes.fr/hal-01230454/document”.

Au, S.-K., Beck, J., (2001). “Estimation of small probabilities of failure in high dimensions by subset simulation”. Probabilistic Engineering Mechanics 16, 263–277.

Fukumizu, K. Francis R. Bach and M. Jordan. (2009). “Kernel dimension reduction in regression”. The Annals of Statistics. 37(4), 1871-1905.

Poirette, Y., Guiton, M., Huwart, G., Sinoquet, D., Leroy, J-M. (2017). “An Optimization Method for the Configuration of Inter Array Cables for Floating Offshore Wind Farm”. OMAE 2017 61655

REFERENCES







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Langouët, H. (2011). « Optimisation sans dérivées sous contraintes : deux applications industrielles en ingénierie de réservoir et en calibration des moteurs ». Thèse Univ. Nice-Sophia Antipolis.

Dubourg, V. (2011). “Adaptive surrogate models for reliability analysis and reliability-based design optimization”. Thèse Univ. Blaise Pascal Clermont-Ferrand.

Leadbetter, M.R., Lindgren, G., Rootzén, H. (1983). “Extremes and Related Properties of Random Sequences and Processes”. Springer-Verlag.

Huchet, Q. (2018). “Kriging based methods for the structural damage assessement of offshore wind turbines”. Thèse Univ. Clermont Ferrand.

Moustapha, M., Sudret, B. (2019). “Surrogate-assisted reliability-based design optimization: a survey and a new general framework”. Chair of Risk, Safety and Uncertainty Quantification.

Hawchar, L., El Soueidy, C-P., Schoefs, F. (2019). “Global kriging surrogate modeling for general time-variant reliability-based design optimization problems”. Structural and Multidisciplinary Optimization (2018) 58:955–968.

Madsen, H.O., Krenk S. and Lind, N.C., (1986). “Methods of structural safety”. Prentice Hall, Englewood Cliffs.

Tu, J., Choi, K.K. and Park, Y.H., (1999). “A new study on reliability-based design optimization”. Journal of Mechanical Design, 121(4), pp. 557-64.

Du, X. and Chen, W., (2004). “Sequential Optimization and Reliability Assessment method for Efficient Probabilistic Design”. ASME J. Mech. Des., 126(2), pp. 225-233.

Cheng, G.D., Xu, L. and Jiang, L., (2006). “Sequential approximate programming strategy for reliability-based optimization”. Computers and Structures, 84(21), pp. 1353-67.

REFERENCES

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