• Title/Summary/Keyword: Multivariate Gaussian function

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Modified Probabilistic Neural Network of Heterogeneous Probabilistic Density Functions for the Estimation of Concrete Strength

  • Kim, Doo-Kie;Kim, Hee-Joong;Chang, Sang-Kil;Chang, Seong-Kyu
    • International Journal of Concrete Structures and Materials
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    • v.19 no.1E
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    • pp.11-16
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    • 2007
  • Recently, probabilistic neural network (PNN) has been proposed to predict the compressive strength of concrete for the known effect of improvement on PNN by the iteration method. However, an empirical method has been incorporated in the PNN technique to specify its smoothing parameter, which causes significant uncertainty in predicting the compressive strength of concrete. In this study, a modified probabilistic neural network (MPNN) approach is hence proposed. The global probability density function (PDF) of variables is reflected by summing the heterogeneous local PDFs which are automatically determined by the individual standard deviation of each variable. The proposed MPNN is applied to predict the compressive strength of concrete using actual test data from a concrete company. The estimated results of MPNN are compared with those of the conventional PNN. MPNN showed better results than the conventional PNN in predicting the compressive strength of concrete and provided promising results for the probabilistic approach to predict the concrete strength by using the individual standard deviation of a variable.

Tail dependence of Bivariate Copulas for Drought Severity and Duration

  • Lee, Tae-Sam;Modarres, Reza;Ouarda, Taha B.M.J.
    • Proceedings of the Korea Water Resources Association Conference
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    • 2010.05a
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    • pp.571-575
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    • 2010
  • Drought is a natural hazard with different properties that are usually dependent to each other. Therefore, a multivariate model is often used for drought frequency analysis. The Copula based bivariate drought severity and duration frequency analysis is applied in the current study in order to show the effect of tail behavior of drought severity and duration on the selection of a copula function for drought bivariate frequency analysis. Four copula functions, namely Clayton, Gumbel, Frank and Gaussian, were fitted to drought data of four stations in Iran and Canada in different climate regions. The drought data are calculated based on standardized precipitation index time series. The performance of different copula functions is evaluated by estimating drought bivariate return periods in two cases, [$D{\geq}d$ and $S{\geq}s$] and [$D{\geq}d$ or $S{\geq}s$]. The bivariate return period analysis indicates the behavior of the tail of the copula functions on the selection of the best bivariate model for drought analysis.

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