Data based constructive identification - overcoming the curse of dimensionality

The modelling of a nonlinear stochastic dynamical processes from data involves solving the problems of data gathering, preprocessing, model architecture selection, learning or adaptation, parametric evaluation and model validation. For a given model architecture such as associative memory networks, a common problem in non-linear modelling is the problem of "the curse of dimensionality". A series of complementary data based constructive identification schemes, mainly based on but not limited to an operating point dependent fuzzy models, are introduced in this paper with the aim to overcome the curse of dimensionality. These include (i) a mixture of experts algorithm based on a forward constrained regression algorithm; (ii) an inherent parsimonious delaunay input space partition based piecewise local lineal modelling concept; (iii) a neurofuzzy model constructive approach based on forward orthogonal least squares and optimal experimental design and finally (iv) the neurofuzzy model construction algorithm based on basis functions that are Bézier Bernstein polynomial functions and the additive decomposition. Illustrative examples demonstrate their applicability, showing that the final major hurdle in data based modelling has almost been removed.

Advanced methods in adaptive control for industrial applications

This volume is based on a seminar concerned with advanced methods in adaptive control for industrial applications which was held in Prague in May 1990 and which brought together experts in the UK and Czechoslovakia in order to suggest solutions to specific current and anticipated problems faced by industry.

Cluster analysis for multivariable process control

This paper describes the novel use of cluster analysis in the field of industrial process control. The severe multivariable process problems encountered in manufacturing have often led to machine shutdowns, where the need for corrective actions arises in order to resume operation. Production faults which are caused by processes running in less efficient regions may be prevented or diagnosed using a reasoning based on cluster analysis. Indeed the intemal complexity of a production machinery may be depicted in clusters of multidimensional data points which characterise the manufacturing process. The application of a Mean-Tracking cluster algorithm (developed in Reading) to field data acquired from a high-speed machinery will be discussed. The objective of such an application is to illustrate how machine behaviour can be studied, in particular how regions of erroneous and stable running behaviour can be identified.

Speech motor control in fluent and dysfluent speech production of an individual with apraxia of speech and Broca’s aphasia

Apraxia of speech (AOS) is typically described as a motor-speech disorder with clinically well-defined symptoms, but without a clear understanding of the underlying problems in motor control. A number of studies have compared the speech of subjects with AOS to the fluent speech of controls, but only a few have included speech movement data and if so, this was primarily restricted to the study of single articulators. If AOS reflects a basic neuromotor dysfunction, this should somehow be evident in the production of both dysfluent and perceptually fluent speech. The current study compared motor control strategies for the production of perceptually fluent speech between a young woman with apraxia of speech (AOS) and Broca’s aphasia and a group of age-matched control speakers using concepts and tools from articulation-based theories. In addition, to examine the potential role of specific movement variables on gestural coordination, a second part of this study involved a comparison of fluent and dysfluent speech samples from the speaker with AOS. Movement data from the lips, jaw and tongue were acquired using the AG-100 EMMA system during the reiterated production of multisyllabic nonwords. The findings indicated that although in general kinematic parameters of fluent speech were similar in the subject with AOS and Broca’s aphasia to those of the age-matched controls, speech task-related differences were observed in upper lip movements and lip coordination. The comparison between fluent and dysfluent speech characteristics suggested that fluent speech was achieved through the use of specific motor control strategies, highlighting the potential association between the stability of coordinative patterns and movement range, as described in Coordination Dynamics theory.

Regularization techniques for ill-posed inverse problems in data assimilation

Optimal state estimation from given observations of a dynamical system by data assimilation is generally an ill-posed inverse problem. In order to solve the problem, a standard Tikhonov, or L2, regularization is used, based on certain statistical assumptions on the errors in the data. The regularization term constrains the estimate of the state to remain close to a prior estimate. In the presence of model error, this approach does not capture the initial state of the system accurately, as the initial state estimate is derived by minimizing the average error between the model predictions and the observations over a time window. Here we examine an alternative L1 regularization technique that has proved valuable in image processing. We show that for examples of flow with sharp fronts and shocks, the L1 regularization technique performs more accurately than standard L2 regularization.

Iterative Methods for Equality-Constrained Least Squares Problems

We consider the linear equality-constrained least squares problem (LSE) of minimizing ${\|c - Gx\|}_2 $, subject to the constraint $Ex = p$. A preconditioned conjugate gradient method is applied to the Kuhn–Tucker equations associated with the LSE problem. We show that our method is well suited for structural optimization problems in reliability analysis and optimal design. Numerical tests are performed on an Alliant FX/8 multiprocessor and a Cray-X-MP using some practical structural analysis data.

Cognitive process modelling of controllers in en route air traffic control

In recent years, various efforts have been made in air traffic control (ATC) to maintain traffic safety and efficiency in the face of increasing air traffic demands. ATC is a complex process that depends to a large degree on human capabilities, and so understanding how controllers carry out their tasks is an important issue in the design and development of ATC systems. In particular, the human factor is considered to be a serious problem in ATC safety and has been identified as a causal factor in both major and minor incidents. There is, therefore, a need to analyse the mechanisms by which errors occur due to complex factors and to develop systems that can deal with these errors. From the cognitive process perspective, it is essential that system developers have an understanding of the more complex working processes that involve the cooperative work of multiple controllers. Distributed cognition is a methodological framework for analysing cognitive processes that span multiple actors mediated by technology. In this research, we attempt to analyse and model interactions that take place in en route ATC systems based on distributed cognition. We examine the functional problems in an ATC system from a human factors perspective, and conclude by identifying certain measures by which to address these problems. This research focuses on the analysis of air traffic controllers' tasks for en route ATC and modelling controllers' cognitive processes.

On discrimination algorithms for ill-posed problems with an application to magnetic tomography

In this paper we explore classification techniques for ill-posed problems. Two classes are linearly separable in some Hilbert space X if they can be separated by a hyperplane. We investigate stable separability, i.e. the case where we have a positive distance between two separating hyperplanes. When the data in the space Y is generated by a compact operator A applied to the system states ∈ X, we will show that in general we do not obtain stable separability in Y even if the problem in X is stably separable. In particular, we show this for the case where a nonlinear classification is generated from a non-convergent family of linear classes in X. We apply our results to the problem of quality control of fuel cells where we classify fuel cells according to their efficiency. We can potentially classify a fuel cell using either some external measured magnetic field or some internal current. However we cannot measure the current directly since we cannot access the fuel cell in operation. The first possibility is to apply discrimination techniques directly to the measured magnetic fields. The second approach first reconstructs currents and then carries out the classification on the current distributions. We show that both approaches need regularization and that the regularized classifications are not equivalent in general. Finally, we investigate a widely used linear classification algorithm Fisher's linear discriminant with respect to its ill-posedness when applied to data generated via a compact integral operator. We show that the method cannot stay stable when the number of measurement points becomes large.

Optimal linearization trajectories for tangent linear models

We examine differential equations where nonlinearity is a result of the advection part of the total derivative or the use of quadratic algebraic constraints between state variables (such as the ideal gas law). We show that these types of nonlinearity can be accounted for in the tangent linear model by a suitable choice of the linearization trajectory. Using this optimal linearization trajectory, we show that the tangent linear model can be used to reproduce the exact nonlinear error growth of perturbations for more than 200 days in a quasi-geostrophic model and more than (the equivalent of) 150 days in the Lorenz 96 model. We introduce an iterative method, purely based on tangent linear integrations, that converges to this optimal linearization trajectory. The main conclusion from this article is that this iterative method can be used to account for nonlinearity in estimation problems without using the nonlinear model. We demonstrate this by performing forecast sensitivity experiments in the Lorenz 96 model and show that we are able to estimate analysis increments that improve the two-day forecast using only four backward integrations with the tangent linear model. Copyright © 2011 Royal Meteorological Society

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Gradient recovery in adaptive finite-element methods for parabolic problems

We derive energy-norm a posteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This appears to be the �rst completely rigorous derivation of ZZ estimators for fully discrete schemes for evolution problems, without any restrictive assumption on the timestep size. An essential tool for the analysis is the elliptic reconstruction technique.Our theoretical results are backed with extensive numerical experimentation aimed at (a) testing the practical sharpness and asymptotic behaviour of the error estimator against the error, and (b) deriving an adaptive method based on our estimators. An extra novelty provided is an implementation of a coarsening error "preindicator", with a complete implementation guide in ALBERTA in the appendix.

A modified PNN algorithm with optimal PD modeling using the orthogonal least squares method

In this paper a modified algorithm is suggested for developing polynomial neural network (PNN) models. Optimal partial description (PD) modeling is introduced at each layer of the PNN expansion, a task accomplished using the orthogonal least squares (OLS) method. Based on the initial PD models determined by the polynomial order and the number of PD inputs, OLS selects the most significant regressor terms reducing the output error variance. The method produces PNN models exhibiting a high level of accuracy and superior generalization capabilities. Additionally, parsimonious models are obtained comprising a considerably smaller number of parameters compared to the ones generated by means of the conventional PNN algorithm. Three benchmark examples are elaborated, including modeling of the gas furnace process as well as the iris and wine classification problems. Extensive simulation results and comparison with other methods in the literature, demonstrate the effectiveness of the suggested modeling approach.

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

From farmers’ perspective : pesticide use and pest control

Many studies have shown that farmers in developing countries often overuse pesticides and do not adopt safety practices. Policies and interventions to promote a safer use of pesticides are often based on a limited understanding of the farmers’ own perspective of pesticide use. This often results in ineffective policies and the persistence of significant pesticide-related health and environmental problems, especially in developing countries. This chapter explores potentials and limitations of different approaches to study pesticide use in agriculture from the farmers’ perspective. In contrast to the reductionist and mono-disciplinary approaches often adopted, this chapter calls for integrative methodological approaches to provide a realistic and thorough understanding of the farmers’ perspective on pesticide use and illustrates the added value of such an approach with three case studies of pesticide use in Iran, India, and Colombia.