Stéphane Grihon Expert in Structure...

Surrogate models for Rapid Sizing of Structures An experience of surrogate models for structure optimization at AIRBUS

November 2014 PRESTO - Surrogate Models for Rapid Sizing of Structures - ESAZO - Ref. X020PR1424042 - Issue 1

ESAZO Stéphane Grihon

Expert in Structure Optimization

© AIRBUS Operations S.A.S. All rights reserved. Confidential and proprietary document.

Summary


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Introduction Various R&T approaches Gradual industrialization Conclusions & next steps


Summary


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PRESTO - Surrogate Models for Rapid Sizing of Structures - ESAZO - Ref. X020PR1424042 - Issue 1 November 2014

Strength analysis process Basis for structural optimisation

[ ] FDK =

GLOBAL ANALYSIS process: full aircraft / component level

LOCAL ANALYSIS : part / element level

STATIC LINEAR ANALYSIS

STRESS/STRENGTH -Metallic -Fatigue/Damage tolerance -Composite

SEMI-EMPIRICAL METHODS

GLOBAL FINITE ELEMENT MODEL

ELEMENTARY INTERNAL LOADS

external loads

[ ]DAN =

NASTRAN

ISAMI


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Sizing process

Structural Analysis & Design

Analysis tools (FE-based / analytical)

Input data Loads

Geometry

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


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

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Sizing variables

Typical structure optimisation variables with largest weight influence


Simplified formulation for strength sizing

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Structure sizing optimization

≥

≤≤

= ∑=

1),(..

)(

)(

,,,

..1

jiikji

i

Niis

NsRFts

sss

smMMin

Pi : element, j:load case, k: failure modes

si : sizing variables

),( NsRFVector 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 10000 elements, 100 critical load cases, 10 variables: 2000 hours for one iteration. Surrogate Models To reduce unitary calculation time from 1s to 10-4s


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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


Summary


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© AIRBUS Operations S.A.S. All rights reserved. Confidential and proprietary document. Page 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

1),(..

)(

≥NsRFts

smMin

k

sN (t,A)

Surrogate models: t(N), A(N)

Super-stringer level



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: 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

Limitations

0

1500

0 2 4 6 8

panel thickness (tp)

cros

s se

ctio

n ar

ea o

f the

str

inge

r Sr

Mitigated results



Analysis regression PS3 test-case

h

ba

ta tw t 2

t 1

h

ba

ta tw t 2 t

1

h

ba

ta tw t 2 t

1

h

ba

ta tw t 2 t

1

•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



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



Piecewise approach

• Subdivision of the load input space in 20 subdomains • Separation of local/global buckling modes with a classifier neural network

•To master these effects a piecewise approach was developed: 1) Manual (A.Merval PhD)

2) Fully automated (D.Bettebghor PhD) thanks to an EM classification approach: IMAGE concept

PhD theses

Parameters estimated wih an expectation minimization. Database clusterised

Approximation per cluster then recombination



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



Gradual increase of dimensionality

July 2010

MACROS step1

MACROS step 2

MACROS step3

•2008 state of the art: detailed report (curves,CPU, accuracy)

•2009 statement of work: new design variables, new reserve factors

•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

%0°, %90°,

width

length

•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)

Challenge input dimensions



Full surrogate model implementation COMBOX

Objective Value

1.50E+03

1.60E+03

1.70E+03

1.80E+03

1.90E+03

2.00E+03

2.10E+03

0 5 10 15 20 25 30

Iteration

Wei

ght

Objective Value

•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

CAESAM ISAMI-PS3

NASTRAN



Integration in optimization

Objective Value

1.67E+03

1.67E+03

1.68E+03

1.68E+03

1.69E+03

1.69E+03

1.70E+03

1.70E+03

0 5 10 15 20 25 30 35 40

Iteration

Wei

ght

MACROSPS3

Blue: convergence with MACROS Green: restart

with PS3

278s instead of 1216s for sensitivity analysis inside one iteration

Optimization results

As expected: Good accuracy Smoother convergence Reduced computational times



Summary

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PRESTO A new sizing tool

A new sizing tool has been implemented for rapid sizing of structures with main application to A350-1000 fuselage. Particularity: To support thin composite fuselage design and trade-off studies, strength analysis are performed upfront on predefined catalogues: discrete approach



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Catalogue concept in PRESTO

• Catalogues are a way to reduce sizing variables to a thickness and a cross-sectional area:



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.

Step3: see conclusion

IRT MDA-MDO



Summary

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Conclusion and next steps

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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.



© AIRBUS Operations S.A.S. All rights reserved. Confidential and proprietary document. 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.

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