Evolutionary Synthesis of MEMS Design

1
Evolutionary Synthesis of MEMS Design

• Ningning Zhou, Alice Agogino, Bo Zhu, Kris
  Pister, Raffi Kamalian
• Department of Mechanical Engineering,
• Department of Electrical Engineering and
  Computer Science
• University of California at Berkeley

2
Outline

• Introduction
• MEMS GA representation
• Genetic operations
• Synthesis example 1
• Synthesis example 2
• Conclusion and Future work

3
Introduction to MEMS Synthesis

• MEMS are extremely small (um) mechanical
  elements often integrated together with
  electronic circuitry, manufactured in a similar
  way to computer microchips.
• MEMS synthesis automatically generate functional
  and optimum solutions for MEMS design.
• Device design synthesis
• Fabrication process synthesis

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Evolutionary Approach

• Genetic algorithms are global stochastic
  optimization techniques based on the adaptive
  mechanics of natural genetics.
• Robust and non-problem specific.
• GAs code the parameter set of the optimization
  problem as finite-length string.
• GAs start the searching from a population of
  random points, improve the quality of the
  population over time by genetic operations
  selection, crossover, mutation
• The best fitted solution will be evolved toward
  objective function.

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Multi-objective Genetic Algorithms (MOGAs)

• Deal with multiple, often competing, objectives.
• Present a set of pareto-optimal solutions

f2
H(2)

• A solution x is pareto-optimal if there
  doesnt exist any other solutions that dominate
  x.
• equally good non-dominated

A(1)
I(3)
B(1)
G(2)
D(1)
f1
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Evolutionary MEMS Synthesis Approach
Random immigrants
Create initial designs
Pi
MEMS simulation (SUGAR or other tools)
New generation of designs
Pe
1 - Pe - Pi
Performance values
Genetic operations selection,crossover mutation
Elitism
Meet specifications
No
Design specifications
Pareto ranking Rank-based fitness assignment
Yes
Done
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MEMS GA Representation

• A MEMS device is decomposed into parameterized
  MEMS GA building blocks.
• Basic or primitive elements anchors, beams etc.
• Clusters springs(several beams), comb-drive etc.
• Represented by subnets in SUGAR.
• A rooted acyclic tree of building components.
• Acyclic open-chain structure.
• Rooted A reference node.

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GA Building Blocks

• Block type
• A number is assignment to represent one type
• Block ports (nodes)
• Nodes connected to other building blocks
• Variable Parameters

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MEMS GA Representation (cont.)
Anchor spring1
Anchor spring2
Anchor comb1
Anchor comb2
Mass
Spring3 anchor
Spring4 anchor

• MEMS resonator with four
• meandering springs

(b) GA Building blocks and their
connectivity
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Genetic Operations Selection

• Fitness assignment for each individual f
• f is proportional to performance
• Roulette wheel selection

Pointer
p1
p2
pi
p3
p4

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Genetic Operation Crossover

• Cut and splice crossover
• Analogous to the traditional one-point crossover
• Cut each parent into two pieces and exchange
• Achieve configuration evolution.
• Parametric Crossover
• Analogous to the traditional uniform crossover
• Arithmetical crossover for selected building
  block parameters c?p1 (1-?)p2
• Achieve building block parameter evolution.

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Crossover (cont.)
L2
Mass
Anchor
Spring 2
Spring 1
Parent 1
Parent 2
Anchor
Mass
Spring 1
Spring 2
Anchor
L2
L1
Anchor
Anchor
Spring 1
Mass
Spring 1
Spring 2
Child 1
Arithmetical crossover
Anchor
Spring 2
Mass
Child 2
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Mutation

• Uniform mutation
• Each design variable is replaced by a random
  number within boundaries
• Each design variable is mutated independently
  according to the mutation probability (very
  small).

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Example 1 Meandering Spring

• Concept design one anchor and N beams connected
  subsequently
• Design goal generate a mechanical spring with
  designated Kx, Ky.
• Design variables number of beams N,
• length of beams
  L,
• width of beams
  w,
• angle of beams
  theta
• Design Constraint 2um lt w lt20um,
• w lt L lt
  400um,
• -pi/2 lt theta
  ltpi/2

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Example 1 Parameter Coding

• type node variables
• anchor 1
• beam 1 2 L1 w1 theta1
• beam 2 3 L2 w2 theta2
• beam 3 4 L3 w3 theta3

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Example1 Crossover
parent 2 N23
parent 1 N15
Parameter crossover for the first Nmin rows
child 2
child 1
Cut and splice
child 2
child 1
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Example 1 Results
Objectives Kx 2.00 N/m Ky 2.00 N/m
Solution 2
N 3 Kx 2.00 N/m Ky 2.00 N/m
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Example 1 Results (cont.)
Objectives Kx 2.00 N/m Ky 2.00 N/m
Solution 6
Solution 5
Solution 4
N 5 Kx 1.99 N/m Ky 1.98 N/m
N 3 Kx 1.99 N/m Ky 2.03 N/m
N 5 Kx 1.92 N/m Ky 2.00 N/m
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Example 2 Meandering resonator

• Concept design four meandering spring and one
  center mass
• Design goal generate a resonator with designated
  lowest resonant frequency f, stiffness Kx, Ky.
• Design variables parameters of each spring and
  the mass.
• Design Constraint 2um lt w lt20um,
• w lt L lt
  400um,
• -pi/2 lt theta
  ltpi/2

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Example 2 parameter coding

• type node variables
• mass 1 2 3 4 L W
• spring1 1 L1 w1 theta1.
• spring2 2 L1 w1 theta1.
• spring3 3 L1 w1 theta1.
• spring4 4 L1 w1 theta1.

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Example 2 schematic
Building block 1 (Anchor spring)
Building block 2 (spring anchor)
2
1
center mass
3
4
Building block 3 (spring anchor)
Building block 4 (Anchor spring)
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Example 2 results
Objectives f93723 Hz, Kx 1.90 N/m, Ky 0.56
N/m
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Example 2 results
Objectives f93723 Hz, Kx 1.90 N/m, Ky 0.56
N/m
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Example 2 convergence curves
Average performance value in the pareto-set in
each generation
Objective performance value
The lowest natural frequency (rad/s)
Stiffness in y direction (N/m)
Iterations (generations)
Iterations (generations)
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Example 2 convergence curves
Average performance value in rank 1 in each
generation
Objective performance value
Stiffness in x direction (N/m)
Iterations (generations)
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Conclusion

• A representation of MEMS designs with a rooted
  acyclic tree of MEMS GA building blocks is
  proposed and shown to be effective and extensible
  for GA MEMS synthesis.
• A crossover operator, with emphasis both on
  configuration and variable parameter searching,
  is developed and shown to be feasible.
• Multi-objective genetic algorithms (MOGAs) were
  successfully applied to MEMS device design
  synthesis to produce results not previously
  envisioned by human designers.

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Future Work

• Feedback from fabrication and testing on final
  Pareto set.
• Develop heuristic rules to ensure valid
  geometrical, functional producible designs.
• Compare simulated annealing to genetic algorithms
  for MEMS device synthesis.
• Develop library of MEMS devices (indexed by
  function, materials, etc.) with useful GA
  building blocks (clusters primitives).
• Develop knowledge-based and case-based reasoning
  tools help to choose an initial concept design
  for MOGA.

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Proposed MEMS Synthesis Architecture
Input Specifications
Add to Case Library
Case Library
Devices (indexed by function, materials, etc.)
Building Blocks (clusters primitives)
Test Evaluate
Optimize Simulate
Layout Fabrication
Obtain Select Configurations
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Current MEMS Libraries

• None are indexed databases.
• All existing libraries relatively small and not
  compatible with Sugar.
• CaMEL (Consolidated Micromechanical Element
  Library)
• Non-Parametrized (springs, hinges, sliders,
  actuators, accelerometers, gear trains, test
  structures, etc.)
• Parametrized (comb drive, side drive, bearings,
  springs, test structures, etc.)
• Commercial CAD tool libraries (e.g., MEMSCAP,
  Tanner, Coventor)