Parameter identification for the shallow water equations using modal decomposition
A parameter identification problem for systems
governed by first-order, linear hyperbolic partial differential
equations subjected to periodic forcing is investigated. The
problem is posed as a PDE constrained optimization problem
with data of the problem given by the measured input and
output variables at the boundary of the domain. By using
the governing equations in the frequency domain, a spatially
dependent transfer matrix relating the input variables to the
output variables is obtained. It is shown that by considering
a finite number of dominant oscillatory modes of the input,
an accurate representation of the output can be obtained. This
converts the original PDE constrained optimization problem to
one without any constraints. The optimal parameters can be
identified using standard nonlinear programming. The utility
of the proposed approach is illustrated by considering a river
reach in the SacramentoSan-Joaquin Delta, California, that
is subjected to tidal forcing. The dynamics of the reach are
modeled by linearized Saint-Venant equations. The available
data is the flow variables measured upstream and downstream
of the reach. The parameter identification problem is to estimate
the average free-surface width, the bed slope, the friction
coefficient and the steady-state boundary conditions. It is shown
that the estimated model gives an accurate prediction of the flow
variables at an intermediate location within the reach.
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