Surrogate models for Rapid Sizing of Structures

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1 ESAZO Stéphane Grihon Expert in Structure Optimization Surrogate models for Rapid Sizing of Structures An experience of surrogate models for structure optimization at AIRBUS

2 Summary Introduction Various R&T approaches Gradual industrialization Conclusions & next steps Page 2

3 Summary Introduction Various R&T approaches Gradual industrialization Conclusions & next steps Page 3

4 Strength analysis process Basis for structural optimisation GLOBAL ANALYSIS process: full aircraft / component level GLOBAL FINITE ELEMENT MODEL STATIC LINEAR ANALYSIS [ K ] D = F N = external loads [ A]D NASTRAN ISAMI ELEMENTARY INTERNAL LOADS LOCAL ANALYSIS : part / element level STRESS/STRENGTH -Metallic -Fatigue/Damage tolerance -Composite SEMI-EMPIRICAL METHODS Page 4

5 Sizing process Structural Analysis & Design Input data Loads Geometry Analysis tools (FE-based / analytical) Structural responses Reserve Factors (failure modes) Ratios between structural responses and allowables (linked to material / geometry) : RF 1 : structure feasible RF< 1 : structure not feasible Structural design : Find Geometry with minimum weight and RF 1 Optimisation problem Structural design is an optimisation problem Page 5

6 Sizing variables Typical structure optimisation variables with largest weight influence Airframe structures: thin-walled structures stiffened panels (to withstand buckling) Sizing variables = - stiffener profile dimensions summarised as a stiffener area: A - panel lay-up (composite stacking) summarised as a thickness: t Page 6

7 Structure sizing optimization Simplified formulation for strength sizing Min s ( P) s s s. t. i M s RF i, j, k = m( s ( s i= 1.. N i, N i, j i ) ) 1 s i : sizing variables i : element, j:load case, k: failure modes RF( s, N ) Vector of <10 outputs: one RF per failure mode <10 geometrical inputs: sizing variables <10 internal load inputs: typically Nxx,Nxy,Nyy for a super-stringer Computed with a semi-empirical skill tool: 1s per unitary calculation (one internal load vector) But multiplied by elements, 100 critical load cases, 10 variables: 2000 hours for one iteration. Surrogate Models To reduce unitary calculation time from 1s to 10-4 s Page 7

8 Rapid sizing Accelerate sizing loops based on -Engineering approaches -IT means: High Performance Computing -Numerical techniques Multi-level decomposition Surrogate models To reduce non-recurring costs in airframe developments. To enable higher level trade-off studies Page 8

9 Summary Introduction Various R&T approaches Gradual industrialization Conclusions & next steps Page 9

10 Design curves Reduction of input variables via optimization We do not approximate RF but local optimization results: (P) is solved at elementary level with generic internal loads inputs. Results (t,a) are approximated as functions of internal loads: <10 inputs t(n), A(N) are used as gauge constraints in global level optimization Super-stringer level N s. t. Min s m( s) RF ( s, N) 1 k (t,a) Surrogate models: t(n), A(N) Page 10

11 Limitations Mitigated results This approach enables to work with a limited number of inputs and already solves part of the optimization problem. And it gives quite smooth response surfaces (integration effect) that can be used in other contexts (design curves) This approach is acceptable for rough preliminary sizing but does not provide an accurate representation of the feasible space: cross section area of the stringer Sr panel thickness (tp) Moreover: For several internal load components, different external load cases can contribute to the sizing. It is not possible to perform material exchange between panel and stringer Page 11

12 Analysis regression PS3 test-case Definition of a composite wing panel test-case with T stringers and thickness/percentages input for skin Use of PS3 semi-empirical ISAMI analysis tool to address all failure modes of a composite wing cover Approximation of RFs from PS3: tool for flat composite panel analysis (composite wing) 5 geometrical inputs 3 internal loads inputs First applications performed with neural networks ba t 1 tw h ta t 2 Page 12

13 Limitations Accuracy goal not met Approximation results were not as expected: 95% of samples below 5% error This was undersood as linked to Discontinuities in reserve factors: linked to leaps between failure modes, changes of theory Or zones of large variations: high gradients When we try to be more accurate we have a Gibbs effect: oscillations around the singularity Page 13

14 Piecewise approach PhD theses To master these effects a piecewise approach was developed: 1) Manual (A.Merval PhD) Subdivision of the load input space in 20 subdomains Separation of local/global buckling modes with a classifier neural network 2) Fully automated (D.Bettebghor PhD) thanks to an EM classification approach: IMAGE concept Parameters estimated wih an expectation minimization. Database clusterised Approximation per cluster then recombination

15 Consolidation A new partnership: IRIAS/DATADVANCE, MACROS tool Use of gaussian/sigmoïdal approximations and mixture of experts (greedy approach) Application of boosting for high dimensional approximation Page 15

16 Gradual increase of dimensionality Challenge input dimensions %0, %90, length width MACROS step state of the art: detailed report (curves,cpu, accuracy) 2009 statement of work: new design variables, new reserve factors MACROS step 2 16 design variables (v1+8) with 1% accuracy: v1+8: 4 percentages in skin (0 and 90 percentages for left and right shells) 4 percentages in stringer (flange and web) MACROS step3 27 design variables (v2+11) with 1% accuracy: V2+11: Flange width, panel width, panel length UD material coefficients: 4 for skin and 4 for stringers Approximation of the complete set of reserve factors Page 16 July 2010

17 Full surrogate model implementation COMBOX Substitution of PS3 with a surrogate model built from MACROS inside the COMBOX optimization tool used for pre-sizing of all A350 boxes BOSS Quattro Objective Value 2.10E E E+03 Weight 1.80E+03 Objective Value CAESAM 1.70E E E Iteration ISAMI-PS3 NASTRAN Page 17

18 Integration in optimization Optimization results As expected: Good accuracy Smoother convergence Reduced computational times Objective Value Blue: convergence with MACROS 278s instead of 1216s for sensitivity analysis inside one iteration Weight 1.70E E E E E E E+03 MACROS PS3 Green: restart with PS3 1.67E Iteration Page 18

19 Summary Introduction Various R&T approaches Gradual industrialization Conclusions & next steps Page 19

20 PRESTO A new sizing tool A new sizing tool has been implemented for rapid sizing of structures with main application to A fuselage. Particularity: To support thin composite fuselage design and trade-off studies, strength analysis are performed upfront on predefined catalogues: discrete approach Page 20

21 Catalogue concept in PRESTO Catalogues are a way to reduce sizing variables to a thickness and a cross-sectional area: Page 21

22 PRESTO & surrogate models A step by step approach Surrogate models are progressively being integrated: Step1: Surrogate models with respect to internal loads have been introduced to compress look-up tables of Reserve Factors: Compression of RF databases by a factor 10 obtained! First step and PRESTO and MACROS are now linked for future steps: Step2 is to approximate with respect to catalogue inputs: t,a, to link PRESTO to continuous optimization approaches. IRT MDA-MDO Step3: see conclusion Page 22

23 Summary Introduction Various R&T approaches Gradual industrialization Conclusions & next steps Page 23

24 Conclusion and next steps Surrogate models identified as a very valuable technology for rapid sizing of structures Also linked to the kind of targeted tool with limited computational time and limited inputs Next step is to provide surrogate models from PRESTO and to deliver these surrogate models for: structure optimization tools detailed sizing in operational teams Idea is also to use them in a kind of stress cockpit to have quick sensitivity/curves plots for the designer in order to improve his knowledge of the strength analysis tool. Page 24

25 This document and all information contained herein is the sole property of AIRBUS Operations S.A.S. No intellectual property rights are granted by the delivery of this document or the disclosure of its content. This document shall not be reproduced or disclosed to a third party without the express written consent of AIRBUS Operations S.A.S. This document and its content shall not be used for any purpose other than that for which it is supplied. The statements made herein do not constitute an offer. They are based on the mentioned assumptions and are expressed in good faith. Where the supporting grounds for these statements are not shown, AIRBUS Operations S.A.S will be pleased to explain the basis thereof. AIRBUS, its logo, A300, A310, A318, A319, A320, A321, A330, A340, A350, A380, A400M are registered trademarks. Page 25

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