"INTELLIGENT" OPTIMAL DESIGN OF COMPOSITES

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• "INTELLIGENT" OPTIMAL DESIGN OF COMPOSITES
• Joseph ZARKA

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1. INTRODUCTION

• Serious Difficulties
• constitutive modeling ?
• random or unknown loading ?
• Initial state ?
• Experimental tests ?
• Numerical simulations ?

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2. LEARNING EXPERT SYSTEMS

• Unknown full solution
• One raw examples base built by EXPERTS
  experimentally or numerically or ..
• with
• input descriptors (numbers, alphanumeric,
  boolean, files...)
• output descriptors or conclusions classes or
  real numbers

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2. LEARNING EXPERT SYSTEMS

• Generally
• non statistically representative
• with few, fuzzy, missing information !!
• Any tool that can be applicable
• Learning neural network, computational
  learning, linear regression, fuzzy logic,
  symbolic learning

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2. LEARNING EXPERT SYSTEMS

• Optimization
• classical convexity of the cost function and the
  functions constraints
• all functions analytical and differentiable
• Real problems
• non-convexity of functions and only known by
  values !!
• Optimization genetic algorithm, annealing...

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2. LEARNING EXPERT SYSTEMS

• Prepare User format gt L.E.S format Split
  database into learning and test sets
• Learn Draw rules from learning set
• Inclear shows active descriptors and rules
• Test Evaluates rules with test set
• Conclude Rulesgt Conclusion Apply rules to
  solve new problems
• Optimize Deliver the best result under some
  constraints

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LES by LMS of Ecole Polytechnique
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LES by LMS of Ecole Polytechnique
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NEUROSHELL by Wards System
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NEUROSHELL by Wards System
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3. GENERAL METHODOLOGY

• 3.1. BUILDING THE DATA BASE
• EXPERTS gtall variables or descriptors which may
  take a part
• i) PRIMITIVE descriptors x (limited
  number)
• ii) INTELLIGENT descriptors XX (large
  number)
• with the actual whole knowledge
• simplified analytical models
• simplified analysis
• complex (but insufficient) beautiful theories !!

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3. GENERAL METHODOLOGY

• Experimental results or field observations
• Numerical analysis results
• General tools to describe
• geometry
• material properties
• loading
• signals, curves, images.

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3. GENERAL METHODOLOGY

• INPUT DESCRIPTORS
• i) Number
• ii) Boolean
• iii) Alphanumeric
• iv) Name of files
• data base access
• curve, signal
• pictures....

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3. GENERAL METHODOLOGY

• OUTPUT DESCRIPTORS or CONCLUSIONS
• i) classes (good, not good, leak, break...)
• ii) numbers (cost, weight,...)
• 50 examples in the data base
• 10 to 1000 descriptors
• 1 to 20 conclusionsMOST IMPORTANT (DIFFICULT)
  TASK

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3. GENERAL METHODOLOGY

• 3.2. GENERATING THE RULES with any Machine
  Learning tool
• i) Intelligent descriptors help the algorithms
• ii) Each conclusion explained as function or
  rules of some intelligent descriptors
• iii) with known Reliability
• if too low gt
• not enough data
• bad or missing intelligent descriptors

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3. GENERAL METHODOLOGY

• 3.3. OPTIMIZATION at two levels (Inverse Problem)
• i) independent intelligent descriptors
• may be impossible OPTIMAL SOLUTION
• but DISCOVERY OF NEW MECHANISMS
• ii) intelligent descriptors linked to primitive
  descriptors
• OPTIMAL SOLUTION
• technological possible !

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4. EFFECTIVE PROPERTIES OF AN ELASTIC AGGREGATE
PRIMITIVE DESCRIPTORS OF THE AGGREGATE

• MATERIALS matrix and inclusions
• GEOMETRY
• concentration, shape, number,
• random distribution of inclusions
• nb_inc Shaper C_x C_y dis1 dis2 dmin
  dmax

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4. EFFECTIVE PROPERTIES OF AN ELASTIC AGGREGATE
PRIMITIVE DESCRIPTORS OF THE AGGREGATE

• OUTPUT DESCRIPTORSor CONCLUSIONS
• Measured effective global coefficients
• here numerically computed coefficients

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4. EFFECTIVE PROPERTIES OF AN ELASTIC AGGREGATE

• Simple approximates values and
• Many papers were published
• Extremal Bounds were produced

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4. EFFECTIVE PROPERTIES OF AN ELASTIC AGGREGATE

• Voigt and Reuss Averages
• Self-consistent Model
• Hashin-Strickman bounds
• E. Kroner, S. Nemat-Nasser
• John. Willis, P. Ponte Castaneda, P. Suquet
  ...with also non linearity

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4. EFFECTIVE PROPERTIES OF AN ELASTIC AGGREGATE
PRIMITIVE DESCRIPTORS OF THE AGGREGATE
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4. EFFECTIVE PROPERTIES OF AN ELASTIC AGGREGATE
PRIMITIVE DESCRIPTORS OF THE AGGREGATE
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4. EFFECTIVE PROPERTIES OF AN ELASTIC AGGREGATE
PRIMITIVE DESCRIPTORS OF THE AGGREGATE
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4. EFFECTIVE PROPERTIES OF AN ELASTIC AGGREGATE
INTELLIGENT DESCRIPTORS OF THE AGGREGATE

• GEOMETRY

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4. EFFECTIVE PROPERTIES OF AN ELASTIC AGGREGATE
INTELLIGENT DESCRIPTORS OF THE AGGREGATE
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4. EFFECTIVE PROPERTIES OF AN ELASTIC AGGREGATE
INTELLIGENT DESCRIPTORS OF THE AGGREGATE
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4. EFFECTIVE PROPERTIES OF AN ELASTIC AGGREGATE
INTELLIGENT DESCRIPTORS OF THE AGGREGATE

• fichr volfrac L11P L21P L32P L66P nb_inc
  Shaper C_x C_y dis1 dis2 dmin dmax L11
  L22 L12 L31 L32 L66
• 66 0.052 13649 5108.6 4617.4
  4306.1 7 0.3 .0857 0.1257 0.0965
  0.1321 0.172 0.9209 14544 13452 4631.9
  4768.1 4585.3 4418.6
• 68 0.056 17185 7136.5 6392.7
  4996.8 7 0.3 0.0171 0.1114 0.0687 0.1157 0
  .2088 0.6812 18087 16907
  6473.5 6507.3 6368.4 5221.4
• 60 0.0624 18820 7565.3 6583.7
  5595 1 0.3 0.44 0.12 0 0 0 0 19634 18516 6667.5
  6654.1 6564.3 5930.3
• 62 0.0624 16114 7407.4
  6698.2 4383.5 1 0.3 0.3 0.18 0 0 0 0 17369 15864 6
  733.9 6895.9 6660.6 4576.5
• 59 0.0624 16913 7447.2
  6664.4 4766.4 20 0.7 0.002 0.029 0.1985 0.3578 0.1
  077 0.8938 17344 16747 6748.5 6735.1 665
  0.3 5000.2

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Without Berhens
34 34 189 4 fichr 6 Yinc 6 Pinc 6 Ymat 6 Pmat 6
volfrac 4 Linc 4 Minc 4 Kinc 4 Lmat 4 Mat 4
Kmat 4 L11P 4 L22P 4 L21P 4 L12P 4 L31P 4 L32P 4
L66P 6 nb_inc 6 Shaper 6 C_x 6 C_y 6 dis1 6
dis2 6 dmin 6 dmax 4 L11 4 L22 4 L21 4 L12 4
L31 4 L32 6 L66
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With Berhens
34 34 189 4 fichr 6 Yinc 6 Pinc 6 Ymat 6 Pmat 6
volfrac 4 Linc 4 Minc 4 Kinc 4 Lmat 4 Mat 4
Kmat 6 L11P 4 L22P 6 L21P 4 L12P 6 L31P 4 L32P 6
L66P 6 nb_inc 6 Shaper 6 C_x 6 C_y 6 dis1 6
dis2 6 dmin 6 dmax 4 L11 4 L22 4 L21 4 L12 4
L31 4 L32 6 L66
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4. EFFECTIVE PROPERTIES OF AN ELASTIC AGGREGATE
INTELLIGENT DESCRIPTORS OF THE AGGREGATE

• L11P 6.065885e04 Min 1.364900e04 Max
  1.076687e05
• L21P 2.399668e04 Min 5.108586e03 Max
  4.288477e04
• L32P 1.533811e04 Min 4.617410e03 Max
  2.605881e04
• L66P 2.408491e04 Min 3.997819e03 Max
  4.417200e04
• Shaper 6.500000e-01 Min 3.000000e-01 Max
  1.000000e00
• C_y 4.300005e-01 Min 0.000000e00 Max
  8.600010e-01
• dis1 1.517385e-01 Min 0.000000e00 Max
  3.034770e-01
• dmin 3.573515e-01 Min 0.000000e00 Max
  7.147030e-01
• dmax 5.720150e-01 Min 0.000000e00 Max
  1.144030e00

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4. EFFECTIVE PROPERTIES OF AN ELASTIC AGGREGATE
INTELLIGENT DESCRIPTORS OF THE AGGREGATE

• 4.886128371032892e-01B27.199760148713786e-01B
  15.745424421382571e-01B4-2.969919726949107e-01
  B3L11 SUM(A13A15)
• -4.347019108012945e025.316839278263813e02B6
  7.897379163532516e02B54.208787571884625e-01B
  26.818804488243249e-01B16.548424547358641e-01B
  4-1.587820070111455e-01B3L22 SUM(A19A21)
• 1.990435738582639e03B71.887591260190284e02B
  5-5.069423034625935e02B92.392386469571942e02
  B81.436020191892966e-01B23.344745151494068e-01
  B13.457936746809989e-01B4-5.089260475848305e-
  01B3L66 SUM(A40A42)

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4. EFFECTIVE PROPERTIES OF AN ELASTIC
AGGREGATEERROR OF THE MESO-MODELING
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4. EFFECTIVE PROPERTIES OF AN ELASTIC
AGGREGATEOPTIMIZATION
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5. OPTIMAL DESIGN OF WOVEN COMPOSITE MATERIALS

• Used in radomes
• Mechanical and electromagnetical properties !
• rather stiff structure but in the same time
  transparency to the waves !!

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5. OPTIMAL DESIGN OF WOVEN COMPOSITE MATERIALS

• Classical layer composite materials
• Woven composite materials
• elastic properties
• ultimate properties in tension, compression,
  flexion ...
• electromagnetic properties

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5. OPTIMAL DESIGN OF WOVEN COMPOSITE MATERIALS

• Woven composite materials
• hybrid composites several fibers but only one
  resine (RP13)
• only 16 specimens (AIA de Cuers-Pierrefeu)

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5. OPTIMAL DESIGN OF WOVEN COMPOSITE MATERIALS

• Specimen for mechanical tests
• Only 16 tests were performed for randomly
  designed woven composite materials

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5. OPTIMAL DESIGN OF WOVEN COMPOSITE MATERIALS

• Definition of the global mechanical data

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Data base on fibers
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Mechanical and electromagnetical results
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PROBLEM Optimal Design

• i) a few tests are available (no DOE!!),
• ii) simulated predictions are not very reliable
• iii) necessary to adjust its mechanical
  elastic/inelastic properties and its
  electromagnetic properties
• iv) and to take care of its weight and its price
  !
• gt NEW APPROACH

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First Fusion
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PARTICULAR PROCEDURE

• eps_th permittivity of the material

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PARTICULAR PROCEDURE

• Several quasi-analytical models for mechanical
  properties for
• one dimensionnal bundle,
• classical layered composites with straight
  bundles,
• waves on bundles
• or complex numerical simulations

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6. CONCLUSIONS

• ACTUAL APPROACH gt DESIGN OF THE FUTURE !!!
• ABSOLUTE NECESSITY also inControl of
  ProcessesSurvey of Structures...
• Linking automatic learning and optimization
  techniques with mechanical expertise