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tial sensitivity to abrupt changes from the input
ones fluctuations like the water flux, for instance.
Although it is not trivial to demonstrate that
there exists a phenomenology linked to variable
interactions, that sensitivity on the drum level
can be interpreted as that.
IV. PRESSURE TRAJECTORIES VERSUS MODEL
In order to confront data and model, one should
to evaluate (11) and (14) numerically. To this
end, the transfer functions are expressed as orthogonal
polynomials up to 5th order. For all kernels
the central assumption is that of expanding
onto polynomials as follows
Essentially a code was created in FORTRAN
capable to calculate all contribution as given
in (14) for instance. Diverse strategies for simulating
curves like the ones of Fig. 2-3 were
taken. In essence special attention was paid on
the drum pressure as the most representative
variable of the plant to be analyzed. We have
simulated to some extent of error such curve by
using Eq. 11 and 14. The main result is displayed
in Fig. 2 where the Eq. (14) is employed to
approximate the “data” as shown in last of Fig.
1. One can see that the simulation adjusts notably
the “right” curve of drum pressure (please
note that the vertical axis is multiplied by 0.34
in order to recover the values of plant as indicated
in Fig. 1) only when almost all contributions
are considered. These results clearly indicate
us a certain consistency of the hypothesis that
the variable interactions is a serious strategy to
model nonlinear systems with a notable accurately.
By the other hands, it also tells us that
the kernel expansion has a little impact on the
modeling of the drum pressure. Consequently,
one can arrive to state that the non-diagonal
terms does not holds a essential role in contrast
to the diagonal ones which returns valuable information
about the system even under dynamic
evolution, interactions themselves and intrinsic
fluctuations. A 7% of discrepancy is found. This
study would serve to go through the searching
of potential sources of instabilities which would
have negatives consequences at the mass delivery
electricity. Finally, in figure (3) it is shown
the possible scenarios where a low order diagonal
integrals produce clouded system identification
on the drum pressure with systematic error
above the 10%.
Figure 2. Data simulated
against identification curves
for different scenarios of
approxmation. Square
boxes denote the “right”
trajectory, whereas doterror
bars in various colors
the model adjusted in
its most representative
approximations as given in
Eq. (14).
Figure 3. Data simulated against identification curves for
different scenarios of approxmation of Eq. (11-14). Left
panel shows the weakness of model when only Eq. 11
is considered and a few interactions terms are included.
Right panel displays the curves when Eq. 14 is taken and
a various non diagonal terms. In all cases, the diagonal
terms appear to be as a substantial component for drum
pressure identification.
V CONCLUSIONS
In this report the application of diagonal integrals
from a variable interaction formalism aimed for
identifying slow systems have been achieved. Concretely
the drum pressure variable inside a tank
where become mixed the water vapor plus nature
gas necessary to generate turbine power have been
identified. The formalism applied adjusts well to data
in up to 7% discrepancy. In this case, the diagonal
part in third order of interactions is assumed. The
identification is consisting to the real data extracted
from plant. In somewhat the adjustability of model
to data depends strongly on the diagonal terms. The
non diagonal ones add more precision but all of them
are not relevant as a robust scheme of system identification.
ACKNOWLEDGMENT
H. N-Ch would like to thank to Mr. Oscar Rivera from
EDEGEL to whom we appreciated his willing in providing
us data from the combined cycle plant as well
as the lively atmosphere found at the FIEM UTP.
REFERENCES
[1] Narasimhan, “Multi-objective input signal design
for plant friendly identification of process systems”,
American Control Conference, 2004. Proceedings
of the 2004, IEEExplore.
[2] Thomas, J, Deville Y,” Fast Blind Separation of
Long Mixture Recordings Using Multivariate Polynomial
Identification”, IEEE Transactions on Signal
Processing, 56 pp.5704-5709 (2008).
[3] Jon Mathews and R. L. Walker, Mathematical
Methods of Physics, 2nd ed., Addison-Wesley Publishing
Company, Inc., pp.68–73.
[4] O. Rivera (Private Communication) and thesis to
submmited at the FIEM-UTP-2012.
CIENCIA, CULTURA Y TECNOLOGÍA - UNIVERSIDAD TECNOLÓGICA DEL PERÚ