Using Evolutionary Computation to explore geometry and topology without ground structures
Download
1 / 37

Using Evolutionary Computation to explore geometry and topology without ground structures - PowerPoint PPT Presentation


  • 128 Views
  • Uploaded on

Using Evolutionary Computation to explore geometry and topology without ground structures. IASS-IACM 2008 Ithaca, NY USA. Dr. –Ing. Peter von Buelow University of Michigan TCAUP 30 May 2008. What are ground structures?. Definition

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Using Evolutionary Computation to explore geometry and topology without ground structures' - keona


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Slide1 l.jpg

Using Evolutionary Computation to explore geometry and topology without ground structures

IASS-IACM 2008

Ithaca, NY USA

Dr. –Ing. Peter von Buelow

University of Michigan

TCAUP

30 May 2008

Peter von Buelow University of Michigan 1 / 37


What are ground structures l.jpg
What are ground structures? topology without ground structures

Definition

A set of all admissible bars connecting a set of admissible joints.

(Dorn, et al. 1964)

Peter von Buelow University of Michigan 2 / 37


Examples of ground structures l.jpg
Examples of ground structures topology without ground structures

12 nodes and 39 bars (Deb et al., 1999)

210 nodes and 21945 (max) bars (Klarbring, 1995)

Peter von Buelow University of Michigan 3 / 37


Effect of ground structure on results with ec l.jpg
Effect of ground structure on results with EC topology without ground structures

  • Ground structures have 2 effects on EC:

  • Results

    • Resolution

    • Geometry

    • Topology

  • Computation

    • Chromosome

    • Population

    • Analysis

Peter von Buelow University of Michigan 4 / 37


Effect of ground structure on results l.jpg
Effect of ground structure on results topology without ground structures

With ground structure (505 kg) without ground structure (322 kg)

Other topologies found without using ground structure

Peter von Buelow University of Michigan 5 / 37


Effect of ground structure on ga computation ga computation depends on chromosome string length l.jpg
Effect of ground structure on GA computation topology without ground structuresGA computation depends on chromosome string length

Length = 39 (actually used)

Size of ground structure

½ of the incidence matrix

Length = n(n-1)/2 = 45

Length = 21945 (all possible)

Length = 153

Peter von Buelow University of Michigan 6 / 37


Distinction of geometry and topology l.jpg
Distinction of geometry and topology topology without ground structures

definitions

Peter von Buelow University of Michigan 7 / 37


Encoding topology without ground structure l.jpg
Encoding Topology without ground structure topology without ground structures

‘binary string’ from incidence matrix

Peter von Buelow University of Michigan 8 / 37


Breeding topology l.jpg
Breeding Topology topology without ground structures

one-point crossover

Peter von Buelow University of Michigan 9 / 37


Encoding geometry without ground structure l.jpg
Encoding Geometry without ground structure topology without ground structures

Array of real number nodal coordinates

Peter von Buelow University of Michigan 10 / 37


Breeding geometry l.jpg
Breeding Geometry topology without ground structures

Half Uniform Crossover breeding

Peter von Buelow University of Michigan 11 / 37


Procedure l.jpg
Procedure topology without ground structures

M - the master sends and gathers all topologies

S - each slave finds geometry for each topology

Peter von Buelow University of Michigan 12 / 37


Geometry generations l.jpg
Geometry Generations topology without ground structures

Random start with progenitor

Peter von Buelow University of Michigan 13 / 37


Geometry generations14 l.jpg
Geometry Generations topology without ground structures

Selection from generation 1

Peter von Buelow University of Michigan 14 / 37


Geometry generations15 l.jpg
Geometry Generations topology without ground structures

Setup parents for generation 2

Peter von Buelow University of Michigan 15 / 37


Geometry generations16 l.jpg
Geometry Generations topology without ground structures

Breed parents to fill generation 2

Peter von Buelow University of Michigan 16 / 37


Geometry generations17 l.jpg
Geometry Generations topology without ground structures

Select best for parents in next generation

Peter von Buelow University of Michigan 17 / 37


Geometry generations18 l.jpg
Geometry Generations topology without ground structures

Setup parents for next generation

Peter von Buelow University of Michigan 18 / 37


Geometry generations19 l.jpg
Geometry Generations topology without ground structures

Breed parents for next generation

Peter von Buelow University of Michigan 19 / 37


Geometry generations20 l.jpg
Geometry Generations topology without ground structures

Cycle 1 Generations 4-6

Peter von Buelow University of Michigan 20 / 37


Geometry generations21 l.jpg
Geometry Generations topology without ground structures

Cycle 1 Generations 26-28

Peter von Buelow University of Michigan 21 / 37


Geometry ga l.jpg
Geometry GA topology without ground structures

Best from one cycle

Peter von Buelow University of Michigan 22 / 37


Topology generations l.jpg
Topology Generations topology without ground structures

Mutate progenitor to start topology cycle

Peter von Buelow University of Michigan 23 / 37


Topology generations24 l.jpg
Topology Generations topology without ground structures

Select best for next generation

Peter von Buelow University of Michigan 24 / 37


Topology generations25 l.jpg
Topology Generations topology without ground structures

Set selection as parents for next generation

Peter von Buelow University of Michigan 25 / 37


Topology generations26 l.jpg
Topology Generations topology without ground structures

Breed parents to obtain full generation

Peter von Buelow University of Michigan 26 / 37


Topology generations27 l.jpg
Topology Generations topology without ground structures

Select best from full generation

Peter von Buelow University of Michigan 27 / 37


Topology generations28 l.jpg
Topology Generations topology without ground structures

Set selection as parents for next generation

Peter von Buelow University of Michigan 28 / 37


Topology generations29 l.jpg
Topology Generations topology without ground structures

Breed parents to obtain full generation

Peter von Buelow University of Michigan 29 / 37


Topology l.jpg
Topology topology without ground structures

Best individuals from cycles 1- 4

All individualsfrom cycle 1

Peter von Buelow University of Michigan 30 / 37


Topology31 l.jpg
Topology topology without ground structures

selection

list of ‘pretty good’

solutions

Peter von Buelow University of Michigan 31 / 37


Bridge design l.jpg
Bridge Design topology without ground structures

automatic generation

list of ‘pretty good’

solutions

Peter von Buelow University of Michigan 32 / 37


Interactive group design l.jpg
Interactive Group Design topology without ground structures

Idea generator

Peter von Buelow University of Michigan 33 / 37


User selections l.jpg
User Selections topology without ground structures

Peter von Buelow University of Michigan 34 / 37


Final bridge design l.jpg
Final Bridge Design topology without ground structures

Peter von Buelow University of Michigan 35 / 37


3d trusses l.jpg
3D Trusses topology without ground structures

Peter von Buelow University of Michigan 36 / 37


3d trusses37 l.jpg
3D Trusses topology without ground structures

Peter von Buelow University of Michigan 37 / 37


ad