Fuzzy-probabilistic modeling the flood characteristics using bivariate frequency analysis and α-cut decomposition

Water allocation in agricultural lands, optimal design of hydraulic structures and climatic phenomena are the events in water management science that face hydrological uncertainties. The purpose of this study is to estimate the characteristics of surface runoff based on probabilistic and fuzzy analysis. Separation and generation of basic hydrological information, probabilistic modeling, fuzzy analysis, and optimization to achieve the solution were the main steps of the decision-making problem. Long-term hydrological data of the study area were collected, analyzed and used as a basis for the simulation model. In this study, a copula-based stochastic method was developed to deal with uncertainties related to rainfall and runoff characteristics as well as to address the nonlinear dependence between multiple random variables. The relationship between rainfall variables and flood characteristics was formulated through fuzzy set theory. The feasible domain of the fuzzy problem was searched using the non-dominated sorting genetic algorithm to find the optimal extreme points. The obtained solutions were used as a fuzzy response to calculate the flood of the Baghmalek plain in Khuzestan province in southwestern Iran. The results showed that the maximum model error occurred in predicting rainfall depth and flood volume, and the maximum rainfall rate and runoff flow could be calculated more accurately. Moreover, the developed fuzzy-probabilistic model was able to predict more than 90% of flood events within the defined fuzzy range.

Application of a Reduced Order Model for Fuzzy Analysis of Linear Static Systems

This contribution proposes a strategy for performing fuzzy analysis of linear static systems applying α-level optimization. In order to decrease numerical costs, full system analyses are replaced by a reduced order model that projects the equilibrium equations to a small-dimensional space. The basis associated with the reduced order model is constructed by means of a single analysis of the system plus a sensitivity analysis. This reduced basis is enriched as the α-level optimization strategy progresses in order to protect the quality of the approximations provided by the reduced order model. A numerical example shows that with the proposed strategy, it is possible to produce an accurate estimate of the membership function of the response of the system with a limited number of full system analyses.