Búsqueda Armónica para optimizar la función Gumbel Mixta univariada

Abstract

Phenomena analyzed in the field of engineering with frequency analyses are usually extreme events such as floods and droughts. Such events frequently have as origin the simultaneous occurrence of two phenomena, and therefore are analyzed with two simultaneous probability distributions. Such is the case of the climatological and hydrometric series in Mexico which, due to its exposure to phenomena such as hurricanes, are analyzed with two-population probability distributions. The good use of these distributions depends on the correct estimation of their parameters. The application of a harmonic search meta-heuristic algorithm for the estimation of the parameters that optimize the univariate Gumbel Mixed function is presented. Annual maximum hydrometric data are used to compare the best-fit of the univariate distribution with traditional methodologies, such as maximum likelihood and the Rosenbrock algorithm. The results show that there is a decrease in the root mean square error and a fast convergence when a harmonic search algorithm is used. With the decrease of the error of fit, estimation of the design flows values is improved. The pseudocode of the algorithm for the implementation of the proposed methodology is presented.

Ajuste de la distribución de valores extremos de dos componentes (TCEV) por medio de máxima verosimilitud

“…La estimación de sus cinco parámetros de ajuste se ha resuelto por medio del método de los momentos L (Hosking & Wallis, 1997) y mediante optimización numérica restringida (Campos-Aranda, 2001). Por último, la distribución Gumbel mixta ha sido ajustada con base en algoritmos modernos de búsqueda (Molina-Aguilar et al, 2018); su FDP es similar a la Ecuación (3), ésta es:…”

Optimization of Parameters in the Generalized Extreme-Value Distribution Type 1 for Three Populations Using Harmonic Search

“…However, in Latin American countries, human settlements on riverbanks are very common. Material damage and loss of human life happens The incorporation of technology in hydrological studies, specifically in frequency distribution analyses, has allowed the exploration of the use of genetic algorithms [2] and meta-heuristic techniques [17].…”

“…The exploration of HS implementation in hydrology has led to parameter estimation in the nonlinear Muskingum model [34], in the same model using a hybrid algorithm [35], in optimal groundwater remediation designs [36], in the optimization of storage operation [37], the estimation of design storms [38], the conceptual modeling of rain-runoff transformation considering seasonal variations [39], the estimation of time of concentration in basins [40], and the adjustment of Extreme Value Distribution (Type I) for two populations in series of annual maximum flows [17].…”