MEMS Design usingMEMS Design usingGenetic AlgorithmsGenetic Algorithms
Carlo H. Séquin
EECS Computer Science Division
University of California, Berkeley
CS 285
Genetic AlgorithmsGenetic Algorithms
Pursue several design variations in parallel(many phenotypes in each generation)
Evaluate their “fitness” (how well they meet the various design objectives Pareto set)
Use best designs to “breed” new off-springs(by modifying / combining their genes)
Expectation: Good traits will stick around,bad solution will be weeded out ...
The “genome” is the ultimate The “genome” is the ultimate parameterization of a design,parameterization of a design,given the proper proceduregiven the proper procedure
to interpret that codeto interpret that code
Without the proper framework, the genome is meaningless. (e.g., human DNA on a planet in the Alpha-Centauri System)
An ExperimentAn Experiment
Let ME students design a MEMS resonator
Students (initially) had no IC experience
Good programmers
Excited about Genetic Algorithms
Micro-Electromechanical SystemsMicro-Electromechanical SystemsMEMSMEMS
Created with a somewhat enhanced fabrication technology used for integrated circuits.
Many nifty devices and systems have been built: motors, steerable mirrors, accelerometers, chemo sensors ...
The Design of a MEMS ResonatorThe Design of a MEMS Resonator Filters
Accelerometers
Gyroscopes
Prevent horizontaloscillations !
Resonate vertically at desired frequency
Basic MEMS ElementsBasic MEMS Elements
Beam H-shaped center mass
Comb driveAnchor to substrate
A General Set-Up for OptimizationA General Set-Up for Optimization Poly-line suspensions at 4 corners.
Adjust resonant frequency F
Get Kx Ky into OK ranges
Minimize layout area
Need an Electro-Mechanical Simulator !Need an Electro-Mechanical Simulator !
“SUGAR”
“SPICE for the MEMS World”(open source just like SPICE)
Fast,Simple,
Capable.
DESIGN
MEASUREMENT SIMULATION
A Possible PhenotypeA Possible Phenotype
Adjust resonant frequency to 10.0 ± 0.5 kHz
Bring Kx / Ky into acceptable range ( >10 )
Minimize size of bounding box; core fixed
MEMS Actually Built and MeasuredMEMS Actually Built and Measured
Genetic Algorithm in Action !Genetic Algorithm in Action !
Area = 0.181 mm2; Kx/Ky = 12
Use 4-Fold Symmetry !Use 4-Fold Symmetry !
1st-order compensation of fabrication variations
Using 4-fold SymmetryUsing 4-fold Symmetry
Faster search ! Area = 0.171 mm2; Kx/Ky = 12
X,Y-Symmetry; Axis-Aligned BeamsX,Y-Symmetry; Axis-Aligned Beams
Area = 0.211 mm2; Kx/Ky = 118
Introduce Serpentine ElementIntroduce Serpentine Element
A higher-order composite subsystemwith only five parameters: N , Lh, Wh, Lv, Wv
N=3
Wv
Lh
Wh Lv
Proper Use of Serpentine Sub-DesignProper Use of Serpentine Sub-Design
That is what we had in mind ...
Proper Use of Serpentine ElementProper Use of Serpentine Element
Area = 0.143 mm2; Kx/Ky = 11Reduce X-dimension of layoutby introducing more serpentine loops
Trying to Reduce AreaTrying to Reduce Area
Area = 0.131 mm2; Kx/Ky = 4 !!
soft Kx flare out
Increasing Stiffness KIncreasing Stiffness Kxx
Connecting bars suppress horizontal oscillations
But branched suspensions may not be expressible in genome ( = underlying data structure ).
Using Cross-Linked SerpentinesUsing Cross-Linked Serpentines
Area = 0.126 mm2; Kx/Ky = 36
PROFESSIONAL DESIG
N
Why Does the G.A. Not Find This ?Why Does the G.A. Not Find This ?
Lack of expressibility of genome.
Solution space too large, too rugged ...
Sampling is too sparse !
Samples are not driven to local optima.
““Holey” Fitness SpaceHoley” Fitness Space
Open-ended engineering problems have complicated, higher-dimensional solution / fitness spaces.
1. Generation – a random sampling20. Generation – drifting to higher ground50. Generation – clustered near high mountains
A Rugged Solution SpaceA Rugged Solution Space
No phenotype is on the top of a peakNo phenotype is on the top of a peak
Good intermediate solutions may get lostGood intermediate solutions may get lost
What really happened here ?What really happened here ?
Major improvement steps came by engineering insights.
Genetic algorithm found good solutions for the newly introduced configurations.
With few enough parameters & clear objectives, greedy optimization may be more efficient.
With complex multiple objectives, G.A. may have advantage of parallel exploration.
What Are Genetic Algorithms Good For ?What Are Genetic Algorithms Good For ?
Exploring unknown territory
Generating a first set of ideas
Showing different subsystem solutions
How can this be harnessed most effectivelyin an engineering design environment ?
Uncharted TerritoryUncharted Territory
Task: Design a robot that climbs trees !Task: Design a robot that climbs trees !
How do you get started ??How do you get started ??
Making G.A. Useful for EngineeringMaking G.A. Useful for Engineering
G.A. by itself is not a good engineering tool
G.A.
Selectivebreeding Greedy
Optimization
Selection ofgood startingphenotypes
Suggestiveediting
Visualization
OPASYNOPASYNA Compiler for CMOS Operational AmplifiersA Compiler for CMOS Operational Amplifiers
H.Y. Koh, C.H. SH.Y. Koh, C.H. Séquin, P.R. Gray, 1990équin, P.R. Gray, 1990
Synthesizing on-chip operational amplifiers to given specifications and IC layout areas.
1. Case-based reasoning (heuristic pruning)selects from 5 proven circuit topologies.
2. Parametric circuit optimization to meet specs.
3. IC Layout generation based on macro cells.
MOS Operational Amplifier (1 of 5)MOS Operational Amplifier (1 of 5)
Only five crucial design parameters !
Op-Amp Design (OPASYN, 1990)Op-Amp Design (OPASYN, 1990)
Multiple Objectives:
power dissipation (mW)
output voltage swing (V)
output slew rate (V/nsec)
open loop gain ()
settling time (nsec)
unity gain bandwidth (MHz)
1/f-noise (V*Hz-½)
total layout area (mm2)
“Cost” of Design = weighted sum of deviations
OPASYN Search MethodOPASYN Search Method
Design-parameter spaceRegular sampling followed by gradient ascent
Hard design constraints
Fitness
Cost
MOS Op-Amp LayoutMOS Op-Amp Layout
Following circuit synthesis & optimization, other heuristic optimization procedures produce layout with desired aspect ratio.
Synthesis in Established FieldsSynthesis in Established Fields
Filter design and MOS Op-Amp synthesishave well-established engineering practices.
Efficiently parameterized designs as wellasrobust and efficient design procedures exist.
Experience is captured in special-purpose programs and used for automated synthesis.
But what if we need to design something in “uncharted engineering territory” ?
Top Related