(190l) Term Elimination and Optimal Experiments for Model Reduction

Models of complex systems, particularly thermofluid models
of chemical processes, tend to be computationally and mathematically complex,
consisting of many differential algebraic equations. Use of such models for
applications beyond simple simulation, including optimization and controls
development, can be infeasible due to their complexity. Model reduction methods
are applied to develop reduced order models that adequately reflect the
input-output behavior of higher-fidelity models, with significantly less
computational cost. Currently practiced model reduction techniques are
frequently based on projections [1], regressions, or surrogate modeling [2] [3]. The abstracted reduced models produced with these methods are effective for
approximating outputs, but do not generally retain the physically meaningful
parameters of the original model or system.

This work presents a novel method for the creation and
evaluation of reduced order models, using a high-fidelity model as a basis. The
proposed method consists of two key algorithmic processes. The first is a
method for generating reduced models from an original model by heuristically
directed term elimination. This process selectively removes or replaces
parameters, variables, functions, and equations form the original model,
creating a new candidate reduced model with each manipulation. The second key
process is the selection of the most suitable reduced models from the candidate
set by the evaluation of optimal experiments using a T-optimal design criterion.
The candidate set of reduced models for the optimal experiments are those that
are found to be suitable representations of the original for a nominal
experiment. Similar formulations using different design criteria have been previously
explored for use in the selection of kinetic models [4] [5]
and fault detection and isolation [6].

Eqs. (1) and (2) enumerate the optimal experiment design
problem, wherein  are
the outputs, state variables, equations, initial conditions, and parameters of
the original model while correspond
to the reduced model. The input trajectory  is selected
to maximize the weighted error in the outputs of the reduced model as compared
to the original, integrated over the duration of the experiment. The
parameter values of the reduced model, , are
adjusted to minimize error and better approximate the original model. The
resulting optimal design vector   characterizes
the experiment which will demonstrate the worst-case performance of the
parameterized candidate reduced model at representing the original model within
the state space of interest.  If the observed maximum error from the optimal
experiment is within a specified threshold, the reduced model can be considered
as suitable.

The proposed method is demonstrated by application to some
classic chemical process models, including homogenous and spatially discretized
reactor models. It is observed that the method can autonomously recreate and
select reduced models which match those identified in existing literature. It
is also shown that the optimal experiment design approach can more reliably
identify unsuitable reduced models as compared to experiments with nominal
inputs or those with inputs at minimum or maximum values. Application to larger
models of varying structure is performed in order to quantify the computational
cost advantages achievable by the selected reduced models.

  Acknowledgment

This work was sponsored by the UTC Institute for Advanced
Systems Engineering (UTC-IASE) of the University of Connecticut and the United
Technologies Corporation. Any opinions expressed herein are those of the
authors and do not represent those of the sponsor.

  References