Evolutionary Synthesis of MEMS Design

8/14/2019 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]




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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)


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)


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)

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Evolutionary Synthesis of MEMS Design

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