Automatic nonlinear predictive model-construction algorithm using forward regression and the PRESS statistic

An automatic nonlinear predictive model-construction algorithm is introduced based on forward regression and the predicted-residual-sums-of-squares (PRESS) statistic. The proposed algorithm is based on the fundamental concept of evaluating a model's generalisation capability through crossvalidation. This is achieved by using the PRESS statistic as a cost function to optimise model structure. In particular, the proposed algorithm is developed with the aim of achieving computational efficiency, such that the computational effort, which would usually be extensive in the computation of the PRESS statistic, is reduced or minimised. The computation of PRESS is simplified by avoiding a matrix inversion through the use of the orthogonalisation procedure inherent in forward regression, and is further reduced significantly by the introduction of a forward-recursive formula. Based on the properties of the PRESS statistic, the proposed algorithm can achieve a fully automated procedure without resort to any other validation data set for iterative model evaluation. Numerical examples are used to demonstrate the efficacy of the algorithm.

Bifurcation Analysis of Eigenstructure Assignment Control in a Simple Nonlinear Aircraft Model

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled � ight. The construction of a robust closed-loop control that extends the stable and decoupled � ight envelope as far as possible is pursued. For the study of these systems, nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and to investigate control effects on dynamic behavior. Linear feedback control designs constructed by eigenstructure assignment methods at a � xed � ight condition are investigated for a simple nonlinear aircraft model. Bifurcation analysis, in conjunction with linear control design methods, is shown to aid control law design for the nonlinear system.

Closed loop design for a simple nonlinear aircraft model using eigenstructure assignment

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled flight. The aim of this work is to construct a robust closed-loop control that optimally extends the stable and decoupled flight envelope. For the study of these systems nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and investigate control effects on dynamic behavior. In this work linear feedback control designs calculated by eigenstructure assignment methods are investigated for a simple aircraft model at a fixed flight condition. Bifurcation analysis in conjunction with linear control design methods is shown to aid control law design for the nonlinear system.

A simple theoretical model for the intensification of tropical cyclones and polar lows

A simple theoretical model for the intensification of tropical cyclones and polar lows is developed using a minimal set of physical assumptions. These disturbances are assumed to be balanced systems intensifying through the WISHE (Wind-Induced Surface Heat Exchange) intensification mechanism, driven by surface fluxes of heat and moisture into an atmosphere which is neutral to moist convection. The equation set is linearized about a resting basic state and solved as an initial-value problem. A system is predicted to intensify with an exponential perturbation growth rate scaled by the radial gradient of an efficiency parameter which crudely represents the effects of unsaturated processes. The form of this efficiency parameter is assumed to be defined by initial conditions, dependent on the nature of a pre-existing vortex required to precondition the atmosphere to a state in which the vortex can intensify. Evaluation of the simple model using a primitive-equation, nonlinear numerical model provides support for the prediction of exponential perturbation growth. Good agreement is found between the simple and numerical models for the sensitivities of the measured growth rate to various parameters, including surface roughness, the rate of transfer of heat and moisture from the ocean surface, and the scale for the growing vortex.

From a discrete to a continuum model of cell dynamics in one dimension

Multiscale modeling is emerging as one of the key challenges in mathematical biology. However, the recent rapid increase in the number of modeling methodologies being used to describe cell populations has raised a number of interesting questions. For example, at the cellular scale, how can the appropriate discrete cell-level model be identified in a given context? Additionally, how can the many phenomenological assumptions used in the derivation of models at the continuum scale be related to individual cell behavior? In order to begin to address such questions, we consider a discrete one-dimensional cell-based model in which cells are assumed to interact via linear springs. From the discrete equations of motion, the continuous Rouse [P. E. Rouse, J. Chem. Phys. 21, 1272 (1953)] model is obtained. This formalism readily allows the definition of a cell number density for which a nonlinear "fast" diffusion equation is derived. Excellent agreement is demonstrated between the continuum and discrete models. Subsequently, via the incorporation of cell division, we demonstrate that the derived nonlinear diffusion model is robust to the inclusion of more realistic biological detail. In the limit of stiff springs, where cells can be considered to be incompressible, we show that cell velocity can be directly related to cell production. This assumption is frequently made in the literature but our derivation places limits on its validity. Finally, the model is compared with a model of a similar form recently derived for a different discrete cell-based model and it is shown how the different diffusion coefficients can be understood in terms of the underlying assumptions about cell behavior in the respective discrete models.

Probability density estimation with tunable kernels using orthogonal forward regression

A generalized or tunable-kernel model is proposed for probability density function estimation based on an orthogonal forward regression procedure. Each stage of the density estimation process determines a tunable kernel, namely, its center vector and diagonal covariance matrix, by minimizing a leave-one-out test criterion. The kernel mixing weights of the constructed sparse density estimate are finally updated using the multiplicative nonnegative quadratic programming algorithm to ensure the nonnegative and unity constraints, and this weight-updating process additionally has the desired ability to further reduce the model size. The proposed tunable-kernel model has advantages, in terms of model generalization capability and model sparsity, over the standard fixed-kernel model that restricts kernel centers to the training data points and employs a single common kernel variance for every kernel. On the other hand, it does not optimize all the model parameters together and thus avoids the problems of high-dimensional ill-conditioned nonlinear optimization associated with the conventional finite mixture model. Several examples are included to demonstrate the ability of the proposed novel tunable-kernel model to effectively construct a very compact density estimate accurately.

A linear model of gravity wave drag for hydrostatic sheared flow over elliptical mountains

An analytical model of orographic gravity wave drag due to sheared flow past elliptical mountains is developed. The model extends the domain of applicability of the well-known Phillips model to wind profiles that vary relatively slowly in the vertical, so that they may be treated using a WKB approximation. The model illustrates how linear processes associated with wind profile shear and curvature affect the drag force exerted by the airflow on mountains, and how it is crucial to extend the WKB approximation to second order in the small perturbation parameter for these effects to be taken into account. For the simplest wind profiles, the normalized drag depends only on the Richardson number, Ri, of the flow at the surface and on the aspect ratio, γ, of the mountain. For a linear wind profile, the drag decreases as Ri decreases, and this variation is faster when the wind is across the mountain than when it is along the mountain. For a wind that rotates with height maintaining its magnitude, the drag generally increases as Ri decreases, by an amount depending on γ and on the incidence angle. The results from WKB theory are compared with exact linear results and also with results from a non-hydrostatic nonlinear numerical model, showing in general encouraging agreement, down to values of Ri of order one.

Selection-mutation balance models with epistatic selection

We present an application of birth-and-death processes on configuration spaces to a generalized mutation4 selection balance model. The model describes the aging of population as a process of accumulation of mu5 tations in a genotype. A rigorous treatment demands that mutations correspond to points in abstract spaces. 6 Our model describes an infinite-population, infinite-sites model in continuum. The dynamical equation which 7 describes the system, is of Kimura-Maruyama type. The problem can be posed in terms of evolution of states 8 (differential equation) or, equivalently, represented in terms of Feynman-Kac formula. The questions of interest 9 are the existence of a solution, its asymptotic behavior, and properties of the limiting state. In the non-epistatic 10 case the problem was posed and solved in [Steinsaltz D., Evans S.N., Wachter K.W., Adv. Appl. Math., 2005, 11 35(1)]. In our model we consider a topological space X as the space of positions of mutations and the influence of epistatic potentials

Bayesian estimation of co-integrating thresholds in the term structure of interest rates.

Threshold Error Correction Models are used to analyse the term structure of interest Rates. The paper develops and uses a generalisation of existing models that encompasses both the Band and Equilibrium threshold models of [Balke and Fomby ((1997) Threshold cointegration. Int Econ Rev 38(3):627–645)] and estimates this model using a Bayesian approach. Evidence is found for threshold effects in pairs of longer rates but not in pairs of short rates. The Band threshold model is supported in preference to the Equilibrium model.

Autonomous intelligent cruise control using a novel multiple-controller framework incorporating fuzzy-logic-based switching and tuning

This paper presents a novel intelligent multiple-controller framework incorporating a fuzzy-logic-based switching and tuning supervisor along with a generalised learning model (GLM) for an autonomous cruise control application. The proposed methodology combines the benefits of a conventional proportional-integral-derivative (PID) controller, and a PID structure-based (simultaneous) zero and pole placement controller. The switching decision between the two nonlinear fixed structure controllers is made on the basis of the required performance measure using a fuzzy-logic-based supervisor, operating at the highest level of the system. The supervisor is also employed to adaptively tune the parameters of the multiple controllers in order to achieve the desired closed-loop system performance. The intelligent multiple-controller framework is applied to the autonomous cruise control problem in order to maintain a desired vehicle speed by controlling the throttle plate angle in an electronic throttle control (ETC) system. Sample simulation results using a validated nonlinear vehicle model are used to demonstrate the effectiveness of the multiple-controller with respect to adaptively tracking the desired vehicle speed changes and achieving the desired speed of response, whilst penalising excessive control action. Crown Copyright (C) 2008 Published by Elsevier B.V. All rights reserved.

Stress field control of eruption dynamics at a rift volcano: Nyamuragira, D.R.Congo

Using the record of 30 flank eruptions over the last 110 years at Nyamuragira, we have tested the relationship between the eruption dynamics and the local stress field. There are two groups of eruptions based on their duration (< 80days >) that are also clustered in space and time. We find that the eruptions fed by dykes parallel to the East African Rift Valley have longer durations (and larger volumes) than those eruptions fed by dykes with other orientations. This is compatible with a model for compressible magma transported through an elastic-walled dyke in a differential stress field from an over-pressured reservoir (Woods et al., 2006). The observed pattern of eruptive fissures is consistent with a local stress field modified by a northwest-trending, right lateral slip fault that is part of the northern transfer zone of the Kivu Basin rift segment. We have also re-tested with new data the stochastic eruption models for Nyamuragira of Burt et al. (1994). The time-predictable, pressure-threshold model remains the best fit and is consistent with the typically observed declining rate of sulphur dioxide emission during the first few days of eruption with lava emission from a depressurising, closed, crustal reservoir. The 2.4-fold increase in long-term eruption rate that occurred after 1977 is confirmed in the new analysis. Since that change, the record has been dominated by short-duration eruptions fed by dykes perpendicular to the Rift. We suggest that the intrusion of a major dyke during the 1977 volcano-tectonic event at neighbouring Nyiragongo volcano inhibited subsequent dyke formation on the southern flanks of Nyamuragira and this may also have resulted in more dykes reaching the surface elsewhere. Thus that sudden change in output was a result of a changed stress field that forced more of the deep magma supply to the surface. Another volcano-tectonic event in 2002 may also have changed the magma output rate at Nyamuragira.

Information-based data selection for ensemble data assimilation

Ensemble-based data assimilation is rapidly proving itself as a computationally-efficient and skilful assimilation method for numerical weather prediction, which can provide a viable alternative to more established variational assimilation techniques. However, a fundamental shortcoming of ensemble techniques is that the resulting analysis increments can only span a limited subspace of the state space, whose dimension is less than the ensemble size. This limits the amount of observational information that can effectively constrain the analysis. In this paper, a data selection strategy that aims to assimilate only the observational components that matter most and that can be used with both stochastic and deterministic ensemble filters is presented. This avoids unnecessary computations, reduces round-off errors and minimizes the risk of importing observation bias in the analysis. When an ensemble-based assimilation technique is used to assimilate high-density observations, the data-selection procedure allows the use of larger localization domains that may lead to a more balanced analysis. Results from the use of this data selection technique with a two-dimensional linear and a nonlinear advection model using both in situ and remote sounding observations are discussed.

Body-centric modelling, identification, and acceleration tracking control of a quadrotor UAV

This paper presents the mathematical development of a body-centric nonlinear dynamic model of a quadrotor UAV that is suitable for the development of biologically inspired navigation strategies. Analytical approximations are used to find an initial guess of the parameters of the nonlinear model, then parameter estimation methods are used to refine the model parameters using the data obtained from onboard sensors during flight. Due to the unstable nature of the quadrotor model, the identification process is performed with the system in closed-loop control of attitude angles. The obtained model parameters are validated using real unseen experimental data. Based on the identified model, a Linear-Quadratic (LQ) optimal tracker is designed to stabilize the quadrotor and facilitate its translational control by tracking body accelerations. The LQ tracker is tested on an experimental quadrotor UAV and the obtained results are a further means to validate the quality of the estimated model. The unique formulation of the control problem in the body frame makes the controller better suited for bio-inspired navigation and guidance strategies than conventional attitude or position based control systems that can be found in the existing literature.

e-Leadership through strategic alignment: an empirical study of small and medium sized enterprises in the digital age

Small and medium sized enterprises (SMEs) play an important role in the European economy. A critical challenge faced by SME leaders, as a consequence of the continuing digital technology revolution, is how to optimally align business strategy with digital technology to fully leverage the potential offered by these technologies in pursuit of longevity and growth. There is a paucity of empirical research examining how e-leadership in SMEs drives successful alignment between business strategy and digital technology fostering longevity and growth. To address this gap, in this paper we develop an empirically derived e-leadership model. Initially we develop a theoretical model of e-leadership drawing on strategic alignment theory. This provides a theoretical foundation on how SMEs can harness digital technology in support of their business strategy enabling sustainable growth. An in-depth empirical study was undertaken interviewing 42 successful European SME leaders to validate, advance and substantiate our theoretically driven model. The outcome of the two stage process – inductive development of a theoretically driven e-leadership model and deductive advancement to develop a complete model through in-depth interviews with successful European SME leaders – is an e-leadership model with specific constructs fostering effective strategic alignment. The resulting diagnostic model enables SME decision makers to exercise effective e-leadership by creating productive alignment between business strategy and digital technology improving longevity and growth prospects.