This research focuses on the development of a solution strategy for the optimization of
large-scale dynamic systems under uncertainty. Uncertainty resides naturally within the
external forces posed to the system or from within the system itself. For example, in chemical
process systems, external inputs include flow rates, temperatures or compositions; while
internal sources include kinetic or mass transport parameters; and empirical parameters
used within thermodynamic correlations and expressions. The goal in devising a dynamic
optimization approach which explicitly accounts for uncertainty is to do so in a manner
which is computationally tractable and is general enough to handle various types and
sources of uncertainty. The approach developed in this thesis follows a so-called multiperiod
technique whereby the infinite dimensional uncertainty space is discretized at numerous
points (known as periods or scenarios) which creates different possible realizations of the
uncertain parameters. The resulting optimization formulation encompasses an approximated
expected value of a chosen objective functional subject to a dynamic model for all the
generated realizations of the uncertain parameters. The dynamic model can be solved,
using an appropriate numerical method, in an embedded manner for which the solution
is used to construct the optimization formulation constraints; or alternatively the model
could be completely discretized over the temporal domain and posed directly as part of the
optimization formulation.
Our approach in this thesis has mainly focused on the embedded model technique for
dynamic optimization which can either follow a single- or multiple-shooting solution method.
The first contribution of the thesis investigates a combined multiperiod multiple-shooting
dynamic optimization approach for the design of dynamic systems using ordinary differential
equation (ODE) or differential-algebraic equation (DAE) process models. A major aspect
of this approach is the analysis of the parallel solution of the embedded model within the
optimization formulation. As part of this analysis, we further consider the application of
the dynamic optimization approach to several design and operation applications. Another
vmajor contribution of the thesis is the development of a nonlinear programming (NLP) solver
based on an approach that combines sequential quadratic programming (SQP) with an
interior-point method (IPM) for the quadratic programming subproblem. A unique aspect of
the approach is that the inherent structure (and parallelism) of the multiperiod formulation
is exploited at the linear algebra level within the SQP-IPM nonlinear programming algorithm
using an explicit Schur-complement decomposition. Our NLP solution approach is further
assessed using several static and dynamic optimization benchmark examples. / Thesis / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/19092 |
| Date | January 2016 |
| Creators | Washington, Ian D. |
| Contributors | Swartz, Christopher L.E., Chemical Engineering |
| Source Sets | McMaster University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
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