Hybrid Water Demand Forecasting Model Associating Artificial Neural Network with Fourier Series

This paper addressed the problem of water-demand forecasting for real-time operation of water supply systems. The present study was conducted to identify the best fit model using hourly consumption data from the water supply system of Araraquara, Sa approximate to o Paulo, Brazil. Artificial neural networks (ANNs) were used in view of their enhanced capability to match or even improve on the regression model forecasts. The ANNs used were the multilayer perceptron with the back-propagation algorithm (MLP-BP), the dynamic neural network (DAN2), and two hybrid ANNs. The hybrid models used the error produced by the Fourier series forecasting as input to the MLP-BP and DAN2, called ANN-H and DAN2-H, respectively. The tested inputs for the neural network were selected literature and correlation analysis. The results from the hybrid models were promising, DAN2 performing better than the tested MLP-BP models. DAN2-H, identified as the best model, produced a mean absolute error (MAE) of 3.3 L/s and 2.8 L/s for training and test set, respectively, for the prediction of the next hour, which represented about 12% of the average consumption. The best forecasting model for the next 24 hours was again DAN2-H, which outperformed other compared models, and produced a MAE of 3.1 L/s and 3.0 L/s for training and test set respectively, which represented about 12% of average consumption. DOI: 10.1061/(ASCE)WR.1943-5452.0000177. (C) 2012 American Society of Civil Engineers.

MODEL PARTITIONS AND COMPACT TEST CASE SUITES

We present a generalized test case generation method, called the G method. Although inspired by the W method, the G method, in contrast, allows for test case suite generation even in the absence of characterization sets for the specification models. Instead, the G method relies on knowledge about the index of certain equivalences induced at the implementation models. We show that the W method can be derived from the G method as a particular case. Moreover, we discuss some naturally occurring infinite classes of FSM models over which the G method generates test suites that are exponentially more compact than those produced by the W method.

A Poisson mixed model with nonnormal random effect distribution

In this paper, we propose a random intercept Poisson model in which the random effect is assumed to follow a generalized log-gamma (GLG) distribution. This random effect accommodates (or captures) the overdispersion in the counts and induces within-cluster correlation. We derive the first two moments for the marginal distribution as well as the intraclass correlation. Even though numerical integration methods are, in general, required for deriving the marginal models, we obtain the multivariate negative binomial model from a particular parameter setting of the hierarchical model. An iterative process is derived for obtaining the maximum likelihood estimates for the parameters in the multivariate negative binomial model. Residual analysis is proposed and two applications with real data are given for illustration. (C) 2011 Elsevier B.V. All rights reserved.