文档介绍：Con v ex Mo deling
A Generalization Of
In terv al Analysis F or Nonprobabilist ic
T reatmen t Of Uncertain t y
Isaac Elishak o
the b eha vior of those whic h cannot b e observ ed
Abstr act
This pap er reviews some new
dev elopmen ts is con v ex mo deling of uncer
I I
Convex Modeling
tain t y in structural approac hes to engineer
V ery often
the information on uncertain v ariables
ing
Con v ex mo deling
on one hand
repre
is fragmen tary
Indeterminacy ab out the uncertain
sen ts an alternativ e plemen ttotra
v ariables in v olv ed could b e form ulated in terms of
ditional probabili sti c metho ds
and on the
these v ariables b elonging to certain sets
suc has
other hand
it is a generalization of the math
ematical theory of in terv al analysis
a
The uncertain parameter x is b ounded
j
I
Pr obabilistic Models
a
a
x
j
j
j
A structure can b e mo deled as a system sub ject to
where a
and a are lo w er and upp er v alues
j
j
in
uences
disturbances
excitations
and so forth
resp ectiv ely
that the v ariable x can tak e
j
designated as inputs
W e are usually in terested in
b
The uncertain function has en v elop e b ounds
the resp onse of the system
its dynamic displace
men ts
stresses
or strains designated as outputs
In
x
t
x
t
x
t
form ulating the probabilist