INTELLIGENT OPTIMAL DESIGN OF A BEAM DURING THE CRASH

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• INTELLIGENT OPTIMAL DESIGN OF A BEAM DURING THE
  CRASH
• Joseph ZARKA

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1. INTRODUCTION

• Serious Difficulties
• constitutive modeling ?
• random or unknown loading ?
• Initial state ?
• Experimental tests ?
• Numerical simulations ?
• Unknowns, Uncertainties, Errors !!!!

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• Optimization
• the objective function, as the constraint
  functions are non convex
• and non differentiable
• NEW APPROACH

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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, simulated
  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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3. GENERAL METHODOLOGY

• BUILDING THE DATA BASE OF EXAMPLES
• PRIMITIVE DESCRIPTION
• INTELLIGENT DESCRIPTION
• GENERATION OF THE RULES
• APPLICATIONS TO NEW EXAMPLES
• OPTIMIZATION

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3. GENERAL METHODOLOGY

• 1. BUILDING THE DATA BASE
• EXPERTS gtall variables or descriptors which may
  take a part
• PRIMITIVE descriptors x (limited number)
• 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
• Number
• Boolean
• Alphanumeric
• Name of files
• data base access
• curve, signal
• pictures....

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3. GENERAL METHODOLOGY

• OUTPUT DESCRIPTORS or CONCLUSIONS
• classes (good, not good, leak, break...)
• 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

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

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3. GENERAL METHODOLOGY

• 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. APPLICATION IN OPTIMAL DESIGN OF A BEAM

• Used in cars
• During a crash
• the maximal load must be limited !
• the dissipated energy for a given displacement
  must reach a maximum value !!
• Germany dedicated center gt 15 000 tests
• USA gt 8 000 numerical simulations

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4. APPLICATION IN OPTIMAL DESIGN OF A BEAM
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• Dedicated system
• for any cross section
• for any type of assembly
• to give the minimum load and the maximum
  dissipated energy
• the optimal design for any new requirements

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4. APPLICATION IN OPTIMAL DESIGN OF A BEAM

• PRIMITIVE DESCRIPTORS
• INPUT DESCRIPTORS
• 1. GEOMETRY OF NORMAL SECTION (NISA from EMRC)
• Numbering each NODE
• Definition of and numbering each MEMBER
  (connectivity and thickness)
• Definition of and numbering each external or
  internal CELL

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4. APPLICATION IN OPTIMAL DESIGN OF A BEAM
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4. APPLICATION IN OPTIMAL DESIGN OF A BEAM
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4. APPLICATION IN OPTIMAL DESIGN OF A BEAM

• 2. MATERIALS
• 3. ASSEMBLY OF THE PARTS
• Type weld, glue, bolt, ...
• weld
• continuous or by step
• number of spots

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4. APPLICATION IN OPTIMAL DESIGN OF A BEAM

• OUTPUT DESCRIPTORS
• 4. CONCLUSIONS
• Maximal Load
• Dissipated energy

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4. APPLICATION IN OPTIMAL DESIGN OF A BEAM

• dynamical CRASH simulation with RADIOSS.
• loading one end clamped and on the other one
  rigid mass of 100 kg is sent at the initial speed
  of 10m/s.
• resulting axial force and the dissipated energy
  in function of the time.a displacement of 15 mm.
• On a Silicon graphics workstation (Indy R 4400)
  1 to 2 hours !!!

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4. APPLICATION IN OPTIMAL DESIGN OF A BEAM

• INTELLIGENT DESCRIPTORS
• 1. GEOMETRY OF NORMAL SECTION
• Area
• Moments of inertia about centroid
• Product of inertia
• Torsional constant
• Coordinates of centroid
• Principal axes orientation

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4. APPLICATION IN OPTIMAL DESIGN OF A BEAM

• Eccentricities of shear center
• Depths of section
• Sections modulus
• Warping constant ...
• 2. MATERIALS
• Elastic constants
• Plastic constants
• Nothing is taken when same used materials !!!

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4. APPLICATION IN OPTIMAL DESIGN OF A BEAM

• 3. ASSEMBLY by welding most critical and
  difficult part !
• each spot weld gt small beam
• Total number of small beams with special
  properties
• Global Moment Elastic Torsion or properties
  during one elastic dynamic step loading

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4. APPLICATION IN OPTIMAL DESIGN OF A BEAM

• Generating the rules
• NRJ-INT -1.85e-02 IZZ 2.04e03 DZ
  4.842e-02 MOMENT-TORSION -6.9e-01 J
  -1.07e-04 SURF IYY -1.98e-04 SURF
  MOMENT-TORSION 1.24e-03 SURF IZZ -3.34e-04
  J 9.84e-07 IZZ J -1.25e-03 J
  -1.79e-04 DZ MOMENT-TORSION -7.5e-13 IZZ
  2 J 9.00e-07 IZZ 2 5.57e-06 IZZ 2
  8.76e-03 DZ 2 -4.08e-10 SURF IZZ
  2 1.955e-19 IZZ 2 J 2
• Similar expression for EFF-MAX

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OPTIMAL DESIGN

• Requirements
• Maximun load lt 150 000 N
• geometrical constraints
• find the solution to get the maximal value of the
  dissipated energy
• in the space of the intelligent descriptors
• solution NRJ-INT 6 672 127 with EFF-MAX 11
  200
• great improvment !!!!
• Meaning of the solution ?
• Does it exit ?
• How to obtain it ?

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4. APPLICATION IN OPTIMAL DESIGN OF A BEAM
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APPLICATION IN OPTIMAL DESIGN OF A BEAM
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4. APPLICATION IN OPTIMAL DESIGN OF A BEAM
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4. APPLICATION IN OPTIMAL DESIGN OF A BEAM
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4. APPLICATION IN OPTIMAL DESIGN OF A BEAM

• RADIOSS gtNRJ-INT 1 953 500 J and EFF-MAX
  155 540 N
• Improved technological solution
• The design office
• able to answer at once to any new requirements
• with at each time one optimal solution !!

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5. 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