Run-time Optimized Double Correlated Discrete Probability Propagation for Process Variation Characterization of NEMS Cantilevers.
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Run-time Optimized Double Correlated Discrete Probability Propagation for Process Variation Characterization of NEMS Cantilevers
Rasit Onur Topaloglu PhD student [email protected] of California, San DiegoComputer Science and Engineering Department 9500 Gilman Dr., La Jolla, CA, 92093
v(x) : transverse deflection
u(x) : axial deflection
(x) : angle of rotation
the force vector is
l=100 w=h=2 l=110 w=h=2
dy=3.0333e-6 dy = 4.0333e-6
W
L
h
dy
W
L
h
dy
Probability Discretization Theory: Discretization Operation
pdf(X)
pdf(X)
X
spdf(X)=(X)
spdf(X)
wi : value of i’th impulse
X
N in QN indicates number or bins
Propagation Operation
Xi, Y : random variables
pXs : probabilities of the set of all samples s belonging to X
Resulting spdf(X)
Unite into one bin
Impulses after F
where :
W
L
h
dy
ex. L_s=a W_s+b Randn() where=a/sqrt(a2+b2)
MC 100 pts
MC 1000 pts
MC 10000 pts
=3.0409-6
=3.0407e-6
=3.0352e-6
DC-FDPP
Compared with MC 10000 pts
=0.425%
max=1.88%
min=3.67%
=3.0481e-6
max=3.5993e-6
min=2.61e-6