Resource allocation for complex systems in the presence of uncertainty.

摘要

The objective of the present work is to quantify and manage the confidence in model-based predictions associated with complex systems as exemplified by pollution transport in a watershed system. A probabilistic framework is adopted for representing uncertainty and a constrained optimization problem is posed, the solution of which provides the strategy for resource allocation that will maximize the target confidence. The hydrologic cycle, which involves multi-physics phenomena, is the driving force behind the transport of pollutants in the watershed. Mechanisms for pollutant transport which are addressed in this work include surface runoff and advection in streams and rivers. These different modes of transport when coupled together form an integrated transport model for a given watershed. The thesis addresses the flow of data and information between the components making up this model. Given the nature of this problem which features natural variability and complex boundary conditions, the properties of the parameters of the sub-models are modeled as spatially, and sometimes temporally, varying random processes. The Karhunen-Loeve expansion is used to represent these processes in terms of a denumerable set of random variables. Then, as a result, the predicted state variables are identified with their coordinates with respect to a basis formed by the Polynomial Chaos random variables. Once the coefficients in the Polynomial Chaos representation have been computed, a complete probabilistic characterization of the state variables processes can be obtained. It is worth noting that a treatment to the interaction across the interfaces of the sub-models is essential for the proper analysis of the propagation. An optimization algorithm scheme is then developed that incorporates budget constraint component, while minimizing the uncertainty of the final prediction by selectively reducing the uncertainty of the input parameters. The thesis makes original contributions to the computational modeling of integrated uncertain systems and to the management of uncertainty in the associated predictions.