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Modeling and Inverse Problems in the Presence of Uncertainty
book

Modeling and Inverse Problems in the Presence of Uncertainty

by H. T. Banks, Shuhua Hu, W. Clayton Thompson
April 2014
Intermediate to advanced content levelIntermediate to advanced
405 pages
13h
English
Chapman and Hall/CRC
Content preview from Modeling and Inverse Problems in the Presence of Uncertainty
Mathematical and Statistical Aspects of Inverse Problems 93
0 0.5 1 1.5 2
x 1
0
4
−5000
0
5000
Residuals vs Model
Model Solution
Residuals
0 0.5 1 1.5 2
x 1
0
4
−40
−30
−20
−10
0
10
20
30
40
Modified (sqrt) Residuals vs Model
Model Solution
Modified (sqrt) Residuals
FIGURE 3.13: Truncated residual plots for models N
j
k
= I[n](t
j
, z
j
k
; θ
0
) +
(I[n](t
j
, z
j
k
; θ
0
))
γ
e
E
kj
with γ = 0 (top) vs. γ = 1/2 (bottom) where γ = 1/2
works well!!
by
ˆw
j,k
=
I[n](t
j
, z
j
k
;
ˆ
θ
(l)
)
1/2
, I[n](t
j
, z
j
k
;
ˆ
θ
(l)
) > I
0
(I
0
)
1/2
, I[n](t
j
, z
j
k
;
ˆ
θ
(l)
) I
0
.
(3.81)
The cuto ff value I
0
> 0 is determined by the experimenter so that the resulting
residuals appear random. In the work that follows, I
0
= 1 × 10
4
.
Truncated ...
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Publisher Resources

ISBN: 9781482206432