Environmental Engineering Reference
In-Depth Information
High Dynamic
Order Model
y
k
u
k
Low Dynamic
Order Model
y
k
DYNAMIC MODEL EMULATION
1. Define the nominal hig
h
order
model deep parameters:
X
.
.
2. Using the nomin
a
l set of
parameter values
X
, perform
planned experiments no the high
order model with training input
u
k
and perform Dominant Mode
Analysis (DMA) to obtain a
nominal, reduced dynamic order,
Transfer Function (TF) Model with
estimated coefficient vector
.
.
.
.
Low
Dynamic
Order
Model
Coefficients
.
.
q
.
High
Dynamic
Order
Model
Parameters
X
3. Repeat 2. over a selected region
of the high order model para-
meter domain
'P
to obtain a Monte
Carlo randomized sample of TF
coefficient vectors
(
i
)
associated
with
X
(
i
)
,
i
= 1,2,...
N
,
q
4. Mapping of the Monte Carlo
sample {
q
(
i
)
,
X
(
i
)
},
i
= 1,2,...
N
, by
non-parametric regression, tensor
product cubic spline or Gaussian
Process Emulation.
.
.
.
5. Validation: extrapolation to
untried
X
+
and new input
sequences
u
k
using interpolated
reduced order model coefficients
from the mapping results in 4. and
different input variables (this
includes uncertainty and sensitivity
analysis).
.
Figure 7.7
The process of DBM emulation model synthesis.
HEC-RAS hydrological model. Of course, this approach
is not limited to environmental models such as these: for
instance, Young and Ratto also describe, in considerable
detail, the DBM emulation of a very large econometric
model used by the EU.
hydrological example, where a 15
th
-order Nash-Cascade
model is emulated by a 4
th
-order DBM model. Here,
we will briefly consider another, more recent, hydro-
logical example (Beven
et al
., 2009; Young
et al
., 2009),
which is concerned with the DBM emulation of the large
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