Hammerstein model identification algorithm using Bezier-Bernstein approximation

A new identification algorithm is introduced for the Hammerstein model consisting of a nonlinear static function followed by a linear dynamical model. The nonlinear static function is characterised by using the Bezier-Bernstein approximation. The identification method is based on a hybrid scheme including the applications of the inverse of de Casteljau's algorithm, the least squares algorithm and the Gauss-Newton algorithm subject to constraints. The related work and the extension of the proposed algorithm to multi-input multi-output systems are discussed. Numerical examples including systems with some hard nonlinearities are used to illustrate the efficacy of the proposed approach through comparisons with other approaches.

Neurofuzzy network model construction using Bézier-Bernstein polynomial functions

Neurofuzzy modelling systems combine fuzzy logic with quantitative artificial neural networks via a concept of fuzzification by using a fuzzy membership function usually based on B-splines and algebraic operators for inference, etc. The paper introduces a neurofuzzy model construction algorithm using Bezier-Bernstein polynomial functions as basis functions. The new network maintains most of the properties of the B-spline expansion based neurofuzzy system, such as the non-negativity of the basis functions, and unity of support but with the additional advantages of structural parsimony and Delaunay input space partitioning, avoiding the inherent computational problems of lattice networks. This new modelling network is based on the idea that an input vector can be mapped into barycentric co-ordinates with respect to a set of predetermined knots as vertices of a polygon (a set of tiled Delaunay triangles) over the input space. The network is expressed as the Bezier-Bernstein polynomial function of barycentric co-ordinates of the input vector. An inverse de Casteljau procedure using backpropagation is developed to obtain the input vector's barycentric co-ordinates that form the basis functions. Extension of the Bezier-Bernstein neurofuzzy algorithm to n-dimensional inputs is discussed followed by numerical examples to demonstrate the effectiveness of this new data based modelling approach.

Generalized neurofuzzy network modeling algorithms using Bezier-Bernstein polynomial functions and additive decomposition

This paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are Bezier-Bernstein polynomial functions. This paper is generalized in that it copes with n-dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n. This new construction algorithm also introduces univariate Bezier-Bernstein polynomial functions for the completeness of the generalized procedure. Like the B-spline expansion based neurofuzzy systems, Bezier-Bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions, unity of support, and interpretability of basis function as fuzzy membership functions, moreover with the additional advantages of structural parsimony and Delaunay input space partition, essentially overcoming the curse of dimensionality associated with conventional fuzzy and RBF networks. This new modeling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate Bezier-Bernstein polynomial functions used in model construction. The overall network weights are then learnt using conventional least squares methods. Numerical examples are included to demonstrate the effectiveness of this new data based modeling approach.

State and society in the English countryside: the rural community movement 1918-1939

This paper assesses the relationship between state and society in interwar rural England, focusing on the hitherto neglected role of the Rural Community Councils (RCCs). The rise of statutory social provision in the early twentieth century created new challenges and opportunities for voluntaryism, and the rural community movement was in part a response. The paper examines the early development of the movement, arguing that a crucial role was played by a close-knit group of academics and local government officials. While largely eschewing party politics, they shared a commitment to citizenship, democracy and the promotion of rural culture; many of them had been close associates of Sir Horace Plunkett. The RCCs engaged in a wide range of activities, including advisory work, adult education, local history, village hall provision, support for rural industries and an ambivalent engagement with parish councils. The paper concludes with an assessment of the achievements of the rural community movement, arguing that it was constrained by its financial dependence on voluntary contributions.

Aesthetical and narrative uses of the trench in the Hollywood cinema of 1918-1930

Throughout history of painting, the representation of landscape has been considered a laboratory for the human gaze on the world. The First World War and its new approach to the battlefield altered deeply the classical forms of representation, and replaced them with a mechanised and fragmentary vision, which was related with the development of photography and cinema. As Vicente J. Benet has analysed, Hollywod cinema used these deep changes in its filmic versions of the conflict, although it organised them following a narrative logic. In this text we intend to study how the battlefield and, particularly, the trench, are inserted in this logic of the history of landscape painting. We do so through some Hollywood films from the period 1918-1930. Firstly, we approach the trench as a composition value which can structure the image and guide the camera movement. In the second place, we study how it creates a dialog between its inside, melodrama scenery, and the outside, battlefield and danger. In both cases, we conclude that the trench as a form and as a narrative element plays a structuring and integrative role with the storytelling logic.