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.

An introduction to radial basis functions for system identification: a comparison with other neural network methods

A look is taken at the use of radial basis functions (RBFs), for nonlinear system identification. RBFs are firstly considered in detail themselves and are subsequently compared with a multi-layered perceptron (MLP), in terms of performance and usage.

Belowground biomass functions and expansion factors in high elevation Norway spruce

Biomass allocation to above- and belowground compartments in trees is thought to be affected by growth conditions. To assess the strength of such influences, we sampled six Norway spruce forest stands growing at higher altitudes. Within these stands, we randomly selected a total of 77 Norway spruce trees and measured volume and biomass of stem, above- and belowground stump and all roots over 0.5 cm diameter. A comparison of our observations with models parameterised for lower altitudes shows that models developed for specific conditions may be applicable to other locations. Using our observations, we developed biomass functions (BF) and biomass conversion and expansion factors (BCEF) linking belowground biomass to stem parameters. While both BF and BCEF are accurate in belowground biomass predictions, using BCEF appears more promising as such factors can be readily used with existing forest inventory data to obtain estimates of belowground biomass stock. As an example, we show how BF and BCEF developed for individual trees can be used to estimate belowground biomass at the stand level. In combination with existing aboveground models, our observations can be used to quantify total standing biomass of high altitude Norway spruce stands.

Wiener System identification using B-spline functions with De Boor recursion

A simple and effective algorithm is introduced for the system identification of Wiener system based on the observational input/output data. The B-spline neural network is used to approximate the nonlinear static function in the Wiener system. We incorporate the Gauss-Newton algorithm with De Boor algorithm (both curve and the first order derivatives) for the parameter estimation of the Wiener model, together with the use of a parameter initialization scheme. The efficacy of the proposed approach is demonstrated using an illustrative example.

Asymptotic expansions for Taylor coefficients of the composition of two functions

We give an asymptotic expansion for the Taylor coe±cients of L(P(z)) where L(z) is analytic in the open unit disc whose Taylor coe±cients vary `smoothly' and P(z) is a probability generating function. We show how this result applies to a variety of problems, amongst them obtaining the asymptotics of Bernoulli transforms and weighted renewal sequences.