Model Based Exploration of Uncertainty in Non-linear Systems: Applying Systems & Control to Exploratory System Dynamics

Model Based Exploration of Uncertainty in Non-linear Systems: Applying Systems & Control to Exploratory System Dynamics

Kuipers, J.

Bombois, X.J.A. (mentor)
Pruyt, E. (mentor)

Mechanical, Maritime and Materials Engineering

Delft Center for Systems and Control

Systems & Control

2014-10-29

In this Master of Science thesis, the author introduces a new method to explore the consequences of uncertainty in System Dynamics (SD) models. This is important, as it allows the SD field to provide more robust decision support. The current methods search for relations between uncertainties and model outputs, without using the model equations. The research question is formulated as: How can the consequences of uncertainties be explored from the differential equations in SD models? The new method focusses on how the differential equations are influenced by uncertainties. This can later be translated to an impact on the output. Thesis thesis shows that, for a two dimensional analytic non-linear system with parameter uncertainty, a 1-on-1 mapping can be constructed that relates regions in the uncertain parameters space to properties of the differential equations. The properties that are used here are bifurcations; changes in properties of equilibrium points. All bifurcations for all equilibria in a system create a set of modes that represent the scope of the influence of the uncertain parameters. These modes have been made concise and insightful with several visualisation tools. When this method is applied to a small, but more complex SD model, a hybrid framework is adopted to account for conditional function. The simultaneous exploration of the changes in this hybrid partition and bifurcations lies outside the scope of this thesis. However, with the visualization tools that were employed before, a better understanding could be created in a base case with fixed parameter set. These visualisations allow to formulate more precise hypotheses about the influence of the uncertainty. In future research, it would be valuable to verify of these hypotheses could be answered under parameter uncertainty. In this way, the method has shown to contribute to the insightfulness of the consequences of parameter uncertainty in SD models.

SD (System Dynamics)
Non-linear Systems
Uncertainty

http://resolver.tudelft.nl/uuid:f441cff5-5760-46af-8ee2-35614d1f0bd6

Student theses

master thesis

(c) 2014 Kuipers, J.