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Evolutionary Synthesis of MEMS Design
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:
Evolutionary MEMS Synthesis Approach
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.)
Genetic Operations: Selection
Fitness assignment for each individual: f
f is proportional to performance;
Roulette wheel selection
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.)
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 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 < 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: Crossover
Example 1: Results
Example 1: Results (cont.)
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
Example 2: results
Example 2: results
Example 2: convergence curves
Example 2: convergence curves
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
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)