Sensitivity Factors from FORM method¶
Sensitivity Factors are evaluated under the following context:
denotes a random input vector, representing the
sources of uncertainties,
its joint density probability,
the limit state function of the model. We denote by:
(1)¶
the event considered here and
its boundary (also called limit state surface).
The probability content of the event
is
:
(2)¶
In this context, the probability can often be
efficiently estimated by FORM or SORM approximations.
The FORM importance factors offer a way to analyze the sensitivity of
the probability the realization of the event with respect to the
parameters of the probability distribution of
.
A sensitivity factor is defined as the derivative of the Hasofer-Lind
reliability index with respect to the parameter . The
parameter
is a parameter in a distribution of the
random vector
.
If
represents the vector of all the parameters
of the distribution of
which appear in the definition
of the isoprobabilistic transformation
, and
the design point associated to the event
considered in (1) in the
-space, and if the mapping of the limit
state function by the
is denoted by:
then the sensitivity factors vector is defined as:
The sensitivity factors indicate the importance on the Hasofer-Lind
reliability index (refer to ) of the value of the parameters used to
define the distribution of the random vector .
In other words, the FORM sensitivity factors rank the importance of the parameters of the input components in the realization of the event defined in (1).