Inclusion of nonlinear demand-supply relationships within large-scale partial equilibrium linear programming models

This paper presents a new method for the inclusion of nonlinear demand and supply relationships within a linear programming model. An existing method for this purpose is described first and its shortcomings are pointed out before showing how the new approach overcomes those difficulties and how it provides a more accurate and 'smooth' (rather than a kinked) approximation of the nonlinear functions as well as dealing with equilibrium under perfect competition instead of handling just the monopolistic situation. The workings of the proposed method are illustrated by extending a previously available sectoral model for the UK agriculture.

Robust identification for linear-in-the-parameters models

In this paper new robust nonlinear model construction algorithms for a large class of linear-in-the-parameters models are introduced to enhance model robustness, including three algorithms using combined A- or D-optimality or PRESS statistic (Predicted REsidual Sum of Squares) with regularised orthogonal least squares algorithm respectively. A common characteristic of these algorithms is that the inherent computation efficiency associated with the orthogonalisation scheme in orthogonal least squares or regularised orthogonal least squares has been extended such that the new algorithms are computationally efficient. A numerical example is included to demonstrate effectiveness of the algorithms. Copyright (C) 2003 IFAC.

Comparing tube models for predicting the linear rheology of branched polymer melts

The hierarchical and "bob" (or branch-on-branch) models are tube-based computational models recently developed for predicting the linear rheology of general mixtures of polydisperse branched polymers. These two models are based on a similar tube-theory framework but differ in their numerical implementation and details of relaxation mechanisms. We present a detailed overview of the similarities and differences of these models and examine the effects of these differences on the predictions of the linear viscoelastic properties of a set of representative branched polymer samples in order to give a general picture of the performance of these models. Our analysis confirms that the hierarchical and bob models quantitatively predict the linear rheology of a wide range of branched polymer melts but also indicate that there is still no unique solution to cover all types of branched polymers without case-by-case adjustment of parameters such as the dilution exponent alpha and the factor p(2) which defines the hopping distance of a branch point relative to the tube diameter. An updated version of the hierarchical model, which shows improved computational efficiency and refined relaxation mechanisms, is introduced and used in these analyses.

Linear-wavelet models for non-linear identification applied to a pressure plant

A nonlinear regression structure comprising a wavelet network and a linear term is proposed for system identification. The theoretical foundation of the approach is laid by proving that radial wavelets are orthogonal to linear functions. A constructive procedure for building such models is described and the approach is tested with experimental data.

Linear-wavelet models applied to the identification of a two-link manipulator

This paper shows that a wavelet network and a linear term can be advantageously combined for the purpose of non linear system identification. The theoretical foundation of this approach is laid by proving that radial wavelets are orthogonal to linear functions. A constructive procedure for building such nonlinear regression structures, termed linear-wavelet models, is described. For illustration, sim ulation data are used to identify a model for a two-link robotic manipulator. The results show that the introduction of wavelets does improve the prediction ability of a linear model.

Linear-wavelet models for system identification

A model structure comprising a wavelet network and a linear term is proposed for nonlinear system identification. It is shown that under certain conditions wavelets are orthogonal to linear functions and, as a result, the two parts of the model can be identified separately. The linear-wavelet model is compared to a standard wavelet network using data from a simulated fermentation process. The results show that the linear-wavelet model yields a smaller modelling error when compared to a wavelet network using the same number of regressors.

Superensembles of linear viscoelastic models of polymer melts

The idea of incorporating multiple models of linear rheology into a superensemble, to forge a consensus forecast from the individual model predictions, is investigated. The relative importance of the individual models in the so-called multimodel superensemble (MMSE) was inferred by evaluating their performance on a set of experimental training data, via nonlinear regression. The predictive ability of the MMSE model was tested by comparing its predictions on test data that were similar (in-sample) and dissimilar (out-of-sample) to the training data used in the calibration. For the in-sample forecasts, we found that the MMSE model easily outperformed the best constituent model. The presence of good individual models greatly enhanced the MMSE forecast, while the presence of some bad models in the superensemble also improved the MMSE forecast modestly. While the performance of the MMSE model on the out-of-sample training data was not as spectacular, it demonstrated the robustness of this approach.

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Robust linear mixed models with skew-normal independent distributions from a Bayesian perspective

Linear mixed models were developed to handle clustered data and have been a topic of increasing interest in statistics for the past 50 years. Generally. the normality (or symmetry) of the random effects is a common assumption in linear mixed models but it may, sometimes, be unrealistic, obscuring important features of among-subjects variation. In this article, we utilize skew-normal/independent distributions as a tool for robust modeling of linear mixed models under a Bayesian paradigm. The skew-normal/independent distributions is an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal distribution, skew-t, skew-slash and the skew-contaminated normal distributions as special cases, providing an appealing robust alternative to the routine use of symmetric distributions in this type of models. The methods developed are illustrated using a real data set from Framingham cholesterol study. (C) 2009 Elsevier B.V. All rights reserved.

Improved score tests in symmetric linear regression models

The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n(-3/2)), n being the sample size. The corrections represent an improvement over the corresponding original Rao`s score statistics, which are chi-squared distributed up to errors of order O(n(-1)). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size.

Leverage analysis for linear mixed models

We consider a generalized leverage matrix useful for the identification of influential units and observations in linear mixed models and show how a decomposition of this matrix may be employed to identify high leverage points for both the marginal fitted values and the random effect component of the conditional fitted values. We illustrate the different uses of the two components of the decomposition with a simulated example as well as with a real data set.