Conference, Proceedings

240
)]}
(
)[
(
{
)
(
)
(
T
)
(
M
L
)
(
)
1
( s
s
s
s
s
u
T
Y
u
X
P
u
u −
+
= −
+
(7a)
where
1
)
(
)
(
)
(
T
)
(
M
L
]
)
(
)
(
[
−
−
+
=
s
s
s
s
s
Ω
u
X
u
X
P μ
(7b)
I
Ω
u
X
u
X
Ω =
=
)
(
)
(
)
(
T
)
(
lub
)]
(
)
(
[
diag
s
s
s
s
(7c)
X – is the matrix of sensitive coefficients with elements
}
1,2,...,
{
NUP},
1,2,...,
{
NMP},
,...,
2
,
1
{
)
(
...
)
(
)
(
......
...
......
......
)
(
...
)
(
)
(
)
(
...
)
(
)
(
]
[
)
(
P
P
NUP
2
1
NUP
2
2
2
1
2
NUP
1
2
1
1
1
T
T
Nt
n
j
i
u
t
T
u
t
T
u
t
T
u
t
T
u
t
T
u
t
T
u
t
T
u
t
T
u
t
T
i
Nt
i
Nt
i
Nt
i
i
i
i
i
i
i
i
i
=
=
=
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
=
∇
=
=
T
u
X u
(7d)
Here NUP stand for the number of unknown parameters
The sensitivity coefficients with respect to the volumetric heat capacity and the thermal
diffusivity are given by
p
p
c
c
t
z
r
c
T
X p ρ
ϑ
−
=
ρ
∂
∂
=
ρ
)
,
,
(
)
(
)
(
(8)
[ ]
[ ]
f
g
m n
n
m
g
t
t
n
m
t
n
m
m
n
m
g
m n
n
m
t
n
m
m
n
m
p
r
a
t
t
t
t
t
e
t
e
R
B
A
t
t
t
e
R
B
A
H
c
q
a
T
X
g
n
m
n
m
n
m
r
≤
≤
⎪
⎪
⎩
⎪
⎪
⎨
⎧
+
γ
−
−
+
γ
γ
ω
≤
−
+
γ
γ
ω
ρ
=
=
∂
∂
=
∑∑
∑∑
∞
=
∞
=
−
γ
−
γ
−
∞
=
∞
=
γ
−
1 1
,
)
(
,
2
,
2
2
1 1
,
2
,
2
2
0
)
1
)
((
)
1
(
,
1
)
1
(
4
,
,
,
(9)
[ ]
[ ]
f
g
m n
n
m
g
t
t
n
m
t
n
m
n
n
m
g
m n
n
m
t
n
m
n
n
m
p
z
a
t
t
t
t
t
e
t
e
R
B
A
t
t
t
e
H
B
A
H
c
q
a
T
X
g
n
m
n
m
n
m
z
≤
≤
⎪
⎪
⎩
⎪
⎪
⎨
⎧
+
−
−
+
≤
−
+
=
=
∂
∂
=
∑∑
∑∑
∞
=
∞
=
−
−
−
∞
=
∞
=
−
1 1
,
)
(
,
2
,
2
2
1 1
,
2
,
2
2
0
)
1
)
((
)
1
(
,
1
)
1
(
4
,
,
,
γ
γ
γ
λ
γ
γ
λ
ρ γ
γ
γ
(10)