System Identification of Nonlinear Thermochemical Systems with Dynamical Instabilities
Thermochemical systems appear in applications as widespread as in
combustion engines, in industrial chemical plants and inside
biological cells. Science in all these areas is going towards a more
model based thinking, and it is therefore important to develop good
methods for system identification, especially fit for these kind of
systems. The presented systems are described as nonlinear differential
equations, and the common feature of the models is the presence of a
boundary between an oscillating and a non-oscillating region, i.e. the
presence of a bifurcation. If it is known that a certain input signal
brings the system to a bifurcation manifold, and this is the case for
many thermochemical systems, this knowledge can be included as an
extra constraint in the parameter estimation. Except for special
cases, however, this constraint can not be obtained analytically. For
the general case a reformulation, adding variables and equally many
constraints, have been done. This formulation allows for efficient use
of standard techniques from constrained optimization theory. For
systems with large state spaces the parameter vector describing the
initial state becomes big (sometimes > 1000), and special treatment is
required. New theory for such treatment have been shown, and the
results are valid for systems operating close to a Hopf
bifurcation. Through a combined center manifold and normal form
reduction, the initial state is described in minimal degrees of
freedom. Experiment designs are presented that force the minimal
degrees of freedom two be 2 or 3, independently of the dimension of
the state space. The initial state is determined by solving a
sub-problem for each step in the ordinary estimation process. For
systems starting in stationary oscillations the normal form reduction
reveals the special structure of this sub-problem. Therefore it can be
solved in a straight-forward manner, that does not have the problem of
local minima, and that does not require any integration of the
differential equations. It is also shown how the knowledge, coming
from the presence of a bifurcation, can be used for model
validation. The validation is formulated as a test quantity, and it
has the benefit that it can work also with uncalibrated sensors,
i.e. with sensors whose exact relation to the state variables is not
known. Two new models are presented. The first is a multi-zonal model
for cylinder pressure, temperature and ionization currents. It is a
physically based model with the main objectives of understanding the
correlation between the ionization curve and the pressure peak
location. It is shown that heat transfer has a significant effect on
this relation. It is further shown that the combination of a
geometrically based heat transfer model and a dynamical NO-model
predicts the correct relationship between the pressure and ionization
peak location within one crank angel degree. The second developed
model is for the mitogenic response to insulin in fat cells. It is
the first developed model for this specific pathway and the model has
been compared and estimated to experimental data. Finally, a
16-dimensional model for activated neutrophils has been used to
generate virtual data, on which the presented methods have been
applied, and on which the performance of the methods were
demonstrated.
Gunnar Cedersund
2004
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Senast uppdaterad: 2021-11-10
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