Factorial Probabilistic Methodologies for Water Resources and Hydrologic Systems Analysis Under Interactive Uncertainties

Abstract

Water resources issues have become increasingly prominent worldwide. Optimization and simulation techniques are recognized as powerful tools to deal with water resources issues in an effective and efficient way. Nevertheless, various uncertainties and complexities exist in water resources and hydrologic systems, posing significant challenges to water resources planning and hydrologic predictions. Advanced optimization and simulation methodologies are thus desired to address the challenges involved in solving complex water resources problems.

In this dissertation research, a set of factorial probabilistic methods have been developed, which mainly deal with two types of problems: one is the inexact optimization for water resources planning and management, and the other is the uncertainty quantification for hydrologic simulations. The proposed methodologies include: (a) an inexact two-stage mixed-integer programming model with random coefficients (ITMP-RC); (b) an inexact probabilistic-possibilistic programming model with fuzzy random coefficients (IPP-FRC); (c) a risk-based factorial probabilistic inference (RFPI) method; (d) a multi-level Taguchi-factorial two-stage stochastic programming (MTTSP) method; (e) a risk-based mixed-level factorial-stochastic programming (RMFP) method; (f) a multi-level factorial-vertex fuzzy-stochastic programming (MFFP) method; (g) a factorial probabilistic collocation (FPC) method; and (h) a factorial possibilistic-probabilistic inference (FPI) method.

ITMP-RC and IPP-FRC methods improve upon existing inexact optimization methods by addressing randomness and fuzziness in the coefficients of the objective function. RFPI, MTTSP, RMFP, and MFFP methods that combine the strengths of optimization techniques and statistical experimental designs are capable of exploring parametric interactions as well as revealing their effects on system performance, facilitating informed decision making. FPC and FPI are factorial probabilistic simulation methods, which have been applied to the Xiangxi River watershed in China to enhance our understanding of hydrologic processes. FPC improves upon the well-known polynomial chaos expansion technique by facilitating the propagation of parameter uncertainties in a reduced dimensional space, which is useful for representing high-dimensional and complex stochastic systems. FPI is able to simultaneously take into account probabilistic inference and human reasoning in the model calibration process, achieving realistic simulations of catchment behaviors. The proposed methods are useful for optimization of water resources systems and for simulation of hydrologic systems under interactive uncertainties.