Environmental Engineering Reference
In-Depth Information
Where
x
,
is normally dis-
tributed with and
are the gradient and Hessian of at respectively, and de-
note the real and complex domains, respectively, and
M
is the number
of random variables in the circuit. The mean of is obtained by
taking expectation of (6.39) and neglecting the moments whose order is
higher than two
where
is the covariance of
The variance of the
response, denoted by
is obtained form
Substituting (6.40) into (6.41) and neglecting the moments whose order
exceeds 2 give
Eqs.(6.40) and (6.42) demonstrate that when up to the second-order
moments are considered, and are linear functions of
the covariance of the circuit parameters. The method is hence referred
to as the
first-order second-moment
(FOSM) method. It should be noted
that in derivation of FOSM method, the objective function is expended
at the mean of
x
. Recent study shows that approximation can also be
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