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 ScienceUniversity of California at Berkeley

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

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

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.

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 is pareto-optimal if there doesn’t exist any other solutions that dominate x. equally good; non-dominated;

Evolutionary MEMS Synthesis Approach

Done

Pareto rankingRank-based

fitness assignment

Design specifications

MEMS simulation (SUGAR or other tools)

Create initial designs

Yes

No

New generation of designs

Randomimmigrants

Pe%

Elitism

Pi%

1 - Pe% - Pi%Performance values

Meet specifications

Genetic operations:selection,crossover

mutation

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.

GA Building Blocks Block type

A number is assignment to represent one type;

Block ports (nodes) Nodes connected to other building blocks;

Variable Parameters

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

beama

y

x

Genetic Operations: Selection Fitness assignment for each individual: f

f is proportional to performance; Roulette wheel selection

p1

p2

p3

p4

pi

……

Pointer

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=λp1 + (1-λ)p2 Achieve building block parameter evolution.

Crossover (cont.)

Anchor Spring 2Spring 1

Anchor Mass Spring 1 Spring 2 Anchor

Parent 1:

Parent 2:

L2

L1 L2

Anchor

Spring 2

Spring 1

Mass Anchor

Mass Spring 1 Spring 2 AnchorChild 1:

Child 2:

Mass

Arithmetical crossover

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).

Example 1: Meandering SpringConcept 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 < w <20um, w < L < 400um, -pi/2 < theta <pi/2

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]…………

Example1: Crossoverparent 2N2=3

parent 1 N1=5

child 2child 1

child 2child 1

Parameter crossover for the first Nmin rows

Cut and splice

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

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

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 < w <20um,

w < L < 400um, -pi/2 < theta <pi/2

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….]

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)

Example 2: results

Solution 1f = 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

Example 2: results

f = 87368 Hz

Kx= 1.90 N/m

Ky= 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

Example 2: convergence curves

0 5 10 15 20 25 300

1

2

3

4

5

6x 105

Iterations (generations)

Th

e lo

wes

t n

atu

ral f

req

uen

cy (

rad

/s)

0 5 10 15 20 25 30-2

0

2

4

6

8

10

12

14

16

18

20

Stif

fnes

s in

y d

irec

tion

(N

/m)

Iterations (generations)

Average performance value in the pareto-set in each generation

Objective performance value

Example 2: convergence curves

0 5 10 15 20 25 30

0

10

20

30

40

50

60

Stif

fnes

s in

x d

irec

tion

(N

/m)

Iterations (generations)

Average performance value in rank 1 in each generation

Objective performance value

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.

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.

Proposed MEMS Synthesis Architecture

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

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)