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.

Autonomous ship collision free trajectory navigation and control algorithms

A new autonomous ship collision free (ASCF) trajectory navigation and control system has been introduced with a new recursive navigation algorithm based on analytic geometry and convex set theory for ship collision free guidance. The underlying assumption is that the geometric information of ship environment is available in the form of a polygon shaped free space, which may be easily generated from a 2D image or plots relating to physical hazards or other constraints such as collision avoidance regulations. The navigation command is given as a heading command sequence based on generating a way point which falls within a small neighborhood of the current position, and the sequence of the way points along the trajectory are guaranteed to lie within a bounded obstacle free region using convex set theory. A neurofuzzy network predictor which in practice uses only observed input/output data generated by on board sensors or external sensors (or a sensor fusion algorithm), based on using rudder deflection angle for the control of ship heading angle, is utilised in the simulation of an ESSO 190000 dwt tanker model to demonstrate the effectiveness of the system.

Adaptive modelling, estimation and fusion from data: a neurofuzzy approach

In a world of almost permanent and rapidly increasing electronic data availability, techniques of filtering, compressing, and interpreting this data to transform it into valuable and easily comprehensible information is of utmost importance. One key topic in this area is the capability to deduce future system behavior from a given data input. This book brings together for the first time the complete theory of data-based neurofuzzy modelling and the linguistic attributes of fuzzy logic in a single cohesive mathematical framework. After introducing the basic theory of data-based modelling, new concepts including extended additive and multiplicative submodels are developed and their extensions to state estimation and data fusion are derived. All these algorithms are illustrated with benchmark and real-life examples to demonstrate their efficiency. Chris Harris and his group have carried out pioneering work which has tied together the fields of neural networks and linguistic rule-based algortihms. This book is aimed at researchers and scientists in time series modeling, empirical data modeling, knowledge discovery, data mining, and data fusion.

Adaptive modelling with tunable RBF network using multi-innovation RLS algorithm assisted by swarm intelligence

In this paper, we propose a new on-line learning algorithm for the non-linear system identification: the swarm intelligence aided multi-innovation recursive least squares (SI-MRLS) algorithm. The SI-MRLS algorithm applies the particle swarm optimization (PSO) to construct a flexible radial basis function (RBF) model so that both the model structure and output weights can be adapted. By replacing an insignificant RBF node with a new one based on the increment of error variance criterion at every iteration, the model remains at a limited size. The multi-innovation RLS algorithm is used to update the RBF output weights which are known to have better accuracy than the classic RLS. The proposed method can produces a parsimonious model with good performance. Simulation result are also shown to verify the SI-MRLS algorithm.

Grey-box radial basis function modelling

A fundamental principle in data modelling is to incorporate available a priori information regarding the underlying data generating mechanism into the modelling process. We adopt this principle and consider grey-box radial basis function (RBF) modelling capable of incorporating prior knowledge. Specifically, we show how to explicitly incorporate the two types of prior knowledge: (i) the underlying data generating mechanism exhibits known symmetric property, and (ii) the underlying process obeys a set of given boundary value constraints. The class of efficient orthogonal least squares regression algorithms can readily be applied without any modification to construct parsimonious grey-box RBF models with enhanced generalisation capability.

Modelling and control of Hammerstein system using B-spline approximation and the inverse of De Boor algorithm

In this article a simple and effective controller design is introduced for the Hammerstein systems that are identified based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a B-spline neural network. The controller is composed by computing the inverse of the B-spline approximated nonlinear static function, and a linear pole assignment controller. The contribution of this article is the inverse of De Boor algorithm that computes the inverse efficiently. Mathematical analysis is provided to prove the convergence of the proposed algorithm. Numerical examples are utilised to demonstrate the efficacy of the proposed approach.

Using zero-norm constraint for sparse probability density function estimation

A new sparse kernel probability density function (pdf) estimator based on zero-norm constraint is constructed using the classical Parzen window (PW) estimate as the target function. The so-called zero-norm of the parameters is used in order to achieve enhanced model sparsity, and it is suggested to minimize an approximate function of the zero-norm. It is shown that under certain condition, the kernel weights of the proposed pdf estimator based on the zero-norm approximation can be updated using the multiplicative nonnegative quadratic programming algorithm. Numerical examples are employed to demonstrate the efficacy of the proposed approach.

Modeling of complex-valued Wiener systems using B-spline neural network

In this brief, a new complex-valued B-spline neural network is introduced in order to model the complex-valued Wiener system using observational input/output data. The complex-valued nonlinear static function in the Wiener system is represented using the tensor product from two univariate B-spline neural networks, using the real and imaginary parts of the system input. Following the use of a simple least squares parameter initialization scheme, the Gauss-Newton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first-order derivatives recursion. Numerical examples, including a nonlinear high-power amplifier model in communication systems, are used to demonstrate the efficacy of the proposed approaches.

On combination of SMOTE and particle swarm optimization based radial basis function classifier for imbalanced problems

The combination of the synthetic minority oversampling technique (SMOTE) and the radial basis function (RBF) classifier is proposed to deal with classification for imbalanced two-class data. In order to enhance the significance of the small and specific region belonging to the positive class in the decision region, the SMOTE is applied to generate synthetic instances for the positive class to balance the training data set. Based on the over-sampled training data, the RBF classifier is constructed by applying the orthogonal forward selection procedure, in which the classifier structure and the parameters of RBF kernels are determined using a particle swarm optimization algorithm based on the criterion of minimizing the leave-one-out misclassification rate. The experimental results on both simulated and real imbalanced data sets are presented to demonstrate the effectiveness of our proposed algorithm.

B-spline neural network based digital baseband predistorter solution using the inverse of De Boor algorithm

In this paper a new nonlinear digital baseband predistorter design is introduced based on direct learning, together with a new Wiener system modeling approach for the high power amplifiers (HPA) based on the B-spline neural network. The contribution is twofold. Firstly, by assuming that the nonlinearity in the HPA is mainly dependent on the input signal amplitude the complex valued nonlinear static function is represented by two real valued B-spline neural networks, one for the amplitude distortion and another for the phase shift. The Gauss-Newton algorithm is applied for the parameter estimation, in which the De Boor recursion is employed to calculate both the B-spline curve and the first order derivatives. Secondly, we derive the predistorter algorithm calculating the inverse of the complex valued nonlinear static function according to B-spline neural network based Wiener models. The inverse of the amplitude and phase shift distortion are then computed and compensated using the identified phase shift model. Numerical examples have been employed to demonstrate the efficacy of the proposed approaches.

A Wiener model for memory high power amplifiers using B-spline function approximation

In this paper we introduce a new Wiener system modeling approach for memory high power amplifiers in communication systems using observational input/output data. By assuming that the nonlinearity in the Wiener model is mainly dependent on the input signal amplitude, the complex valued nonlinear static function is represented by two real valued B-spline curves, one for the amplitude distortion and another for the phase shift, respectively. The Gauss-Newton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first order derivatives recursion. An illustrative example is utilized to demonstrate the efficacy of the proposed approach.

Nitrogen fluxes from the landscape are controlled by net anthropogenic nitrogen inputs and by climate

The flux of nitrogen (N) to coastal marine ecosystems is strongly correlated with the “net anthropogenic nitrogen inputs” (NANI) to the landscape across 154 watersheds, ranging in size from 16 km2 to 279 000 km2, in the US and Europe. When NANI values are greater than 1070 kg N km−2 yr−1, an average of 25% of the NANI is exported from those watersheds in rivers. Our analysis suggests a possible threshold at lower NANI levels, with a smaller fraction exported when NANI values are below 1070 kg N km−2 yr−1. Synthetic fertilizer is the largest component of NANI in many watersheds, but other inputs also contribute substantially to the N fluxes; in some regions, atmospheric deposition of N is the major component. The flux of N to coastal areas is controlled in part by climate, and a higher percentage of NANI is exported in rivers, from watersheds that have higher freshwater discharge.