Evolutionary Synthesis of MEMS Design
Transcript of Evolutionary Synthesis of MEMS Design
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Evolutionary Synthesisof MEMS Design
Ningning Zhou, Alice Agogino, Bo Zhu,Kris Pister*, Raffi Kamalian
Department of Mechanical Engineering,
*Department of Electrical Engineering andComputer Science
University of California at Berkeley
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Outline Introduction
MEMS GA representation
Genetic operations Synthesis example 1
Synthesis example 2
Conclusion and Future work
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Introduction to MEMS
Synthesis MEMS are extremely small (~um)
mechanical elements often integrated
together with electronic circuitry,manufactured in a similar way tocomputer microchips.
MEMS synthesis: automatically generate
functional and optimum solutions forMEMS 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 ofnatural 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 timeby genetic operations: selection, crossover, mutation;
The best fitted solution will be evolved towardobjective function.
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Multi-objective Genetic
Algorithms (MOGAs) Deal with multiple, often competing, objectives.
Present a set of pareto-optimal solutions:
A(1)
B(1)
D(1)
G(2)
H(2)
I(3)
f1
f2
A solution x ispareto-optimal ifthere doesnt exist
any other solutionsthat dominate x. equally good; non-dominated;
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Evolutionary MEMS Synthesis
Approach
Done
Pareto ranking
Rank-based
fitness assignment
Designspecifications
MEMS simulation(SUGAR or other tools)
Create initial
designs
Yes
No
New generation of designs
Random
immigrants
Pe%
Elitism
Pi%
1 - Pe% - Pi%Performance
values
Meetspecifications
Genetic operations:
selection,crossover
mutation
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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
Mass
(a) MEMS resonator with four
meandering springs
Anchor
+
spring2
Anchor
+
comb1
Anchor
+
comb2
Spring3
+anchor
Spring4
+anchor
(b) GA Building blocks and
their connectivity
Center
mass
Serpentine
spring
Comb
drive
anchor
beam
a
y
x
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Genetic Operations: Selection Fitness assignment for each individual: f
f is proportional to performance;
Roulette wheel selection
p1
p2
p3p4
pi
Pointer
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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.)Anchor Spring 2Spring 1
Anchor MassSpring 1 Spring 2 Anchor
Parent 1:
Parent 2:
L2
L1 L2
Anchor
Spring 2
Spring 1
MassAnchor
MassSpring 1 Spring 2 AnchorChild 1:
Child 2:
Mass
Arithmetical crossover
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Mutation Uniform mutation
Each design variable is replaced bya random number withinboundaries
Each design variable is mutated
independently according to themutation probability (very small).
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Example 1: Meandering
SpringConcept design:one anchor and N beams connectedsubsequently;
Design goal:generate a mechanical spring withdesignated Kx, Ky.
Design variables:number of beams N,length of beams L,
width of beams w,
angle of beams theta;
Design Constraint:2um < w
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Example 1: Parameter
Codingtype 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: Crossoverparent 2N2=3
parent 1
N1=5
child 2child 1
child 2child 1
Parameter crossover for the
first Nmin rows
Cut and splice
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Example 1: Results
N = 2
Kx= 2.00 N/m
Ky= 2.00 N/m
Solution 1
N = 3
Kx = 2.00 N/m
Ky = 2.00 N/m
Solution 2
Objectives: Kx= 2.00 N/m Ky= 2.00 N/m
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Example 1: Results (cont.)
Solution 5
N = 5
Kx= 1.92 N/m
Ky = 2.00 N/m
N = 5
Kx = 1.99 N/m
Ky = 1.98 N/m
Solution 6Solution 4
N = 3
Kx= 1.99 N/m
Ky = 2.03 N/m
Objectives: Kx= 2.00 N/m Ky= 2.00 N/m
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Example 2: Meandering
resonatorConcept 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 themass.
Design Constraint:2um < w
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Example 2: parameter codingtype 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) center
mass
1 2
34
Building block 2
(spring + anchor)
Building block 4
(Anchor + spring)
Building block 3
(spring + anchor)
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Example 2: results
Solution 1
f = 93746 Hz
Kx= 1.80 N/m
Ky= 0.567 N/m
f = 92632 Hz
Kx= 2.00 N/m
Ky= 0.559 N/m
Solution 3
Objectives: f=93723 Hz, Kx= 1.90 N/m, Ky= 0.56
N/m
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Example 2: results
f = 87368 Hz
Kx= 1.90 N/mKy= 0.52 N/m
Solution 6f = 94290 Hz
Kx= 1.84 N/m
Ky= 0.59 N/m
Solution 5
Objectives: f=93723 Hz, Kx= 1.90 N/m, Ky= 0.56
N/m
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Example 2: convergence
curves
0 5 10 15 20 25 30
0
1
2
3
4
5
6x 1 0
5
Iterations (generations)
Thelowestnatur
alfreque
ncy(rad/s)
0 5 10 15 20 25 30-2
0
2
4
6
8
10
12
14
16
18
20
Stiffnes s
inydi r
ection(N
/m)
Iterations (generations)
Average performance value in the pareto-set in each generation
Objective performance value
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Example 2: convergence
curves
0 5 10 15 20 25 30
0
10
20
30
40
50
60
Stiffnes si
nxdirection
(N/m)
Iterations (generations)
Average performance value in rank 1 in each generation
Objective performance value
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Conclusion A representation of MEMS designs with a rooted
acyclic tree of MEMS GA building blocks is proposedand shown to be effective and extensible for GA
MEMS synthesis. A crossover operator, with emphasis both on
configuration and variable parameter searching, isdeveloped and shown to be feasible.
Multi-objective genetic algorithms (MOGAs) were
successfully applied to MEMS device design synthesisto produce results not previously envisioned byhuman 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 reasoningtools help to choose an initial concept design forMOGA.
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Proposed MEMS SynthesisArchitecture
Devices (indexed by function, materials, etc.)
Building Blocks (clusters & primitives)
Case Library
Input
Specifications
Obtain & Select
Configurations
Optimize &
Simulate
Layout &
Fabrication
Add to
Case
Library
Test &
Evaluate
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Current MEMS Libraries None are indexed databases. All existing libraries relatively small and not
compatible with Sugar.
CaMEL (Consolidated Micromechanical ElementLibrary) 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)