Dual-orthogonal radial basis function networks for nonlinear time series prediction

A new structure of Radial Basis Function (RBF) neural network called the Dual-orthogonal RBF Network (DRBF) is introduced for nonlinear time series prediction. The hidden nodes of a conventional RBF network compare the Euclidean distance between the network input vector and the centres, and the node responses are radially symmetrical. But in time series prediction where the system input vectors are lagged system outputs, which are usually highly correlated, the Euclidean distance measure may not be appropriate. The DRBF network modifies the distance metric by introducing a classification function which is based on the estimation data set. Training the DRBF networks consists of two stages. Learning the classification related basis functions and the important input nodes, followed by selecting the regressors and learning the weights of the hidden nodes. In both cases, a forward Orthogonal Least Squares (OLS) selection procedure is applied, initially to select the important input nodes and then to select the important centres. Simulation results of single-step and multi-step ahead predictions over a test data set are included to demonstrate the effectiveness of the new approach.

An urban solar flux island: measurements from London

Solar irradiance measurements from a new high density urban network in London are presented. Annual averages demonstrate that central London receives 30 ± 10 Wm-2 less solar irradiance than outer London at midday, equivalent to 9 ± 3% less than the London average. Particulate matter and AERONET measurements combined with radiative transfer modeling suggest that the direct aerosol radiative effect could explain 33 to 40% of the inner London deficit and a further 27 to 50% could be explained by increased cloud optical depth due to the aerosol indirect effect. These results have implications for solar power generation and urban energy balance models. A new technique using ‘Langley flux gradients’ to infer aerosol column concentrations over clear periods of three hours has been developed and applied to three case studies. Comparisons with particulate matter measurements across London have been performed and demonstrate that the solar irradiance measurement network is able to detect aerosol distribution across London and transport of a pollution plume out of London.

The climate response to CO2 of the Hadley Centre coupled AOGCM with and without flux adjustment

Coupled atmosphere‐ocean general circulation models have a tendency to drift away from a realistic climatology. The modelled climate response to an increase of CO2 concentration may be incorrect if the simulation of the current climate has significant errors, so in many models, including ours, the drift is counteracted by applying prescribed fluxes of heat and fresh water at the ocean‐atmosphere interface in addition to the calculated surface exchanges. Since the additional fluxes do not have a physical basis, the use of this technique of “flux adjustment” itself introduces some uncertainty in the simulated response to increased CO2. We find that the global‐average temperature response of our model to CO2 increasing at 1% per year is about 30% less without flux adjustment than with flux adjustment. The geographical patterns of the response are similar, indicating that flux adjustment is not causing any gross distortion. The reduced size of the response is due to more effective vertical transport of heat into the ocean, and a somewhat smaller climate sensitivity. Although the response in both cases lies within the generally accepted range for the climate sensitivity, systematic uncertainties of this size are clearly undesirable, and the best strategy for future development is to improve the climate model in order to reduce the need for flux adjustment.

Centennial changes in the heliospheric magnetic field and open solar flux: the consensus view from geomagnetic data and cosmogenic isotopes and its implications

Svalgaard and Cliver (2010) recently reported a consensus between the various reconstructions of the heliospheric field over recent centuries. This is a significant development because, individually, each has uncertainties introduced by instrument calibration drifts, limited numbers of observatories, and the strength of the correlations employed. However, taken collectively, a consistent picture is emerging. We here show that this consensus extends to more data sets and methods than reported by Svalgaard and Cliver, including that used by Lockwood et al. (1999), when their algorithm is used to predict the heliospheric field rather than the open solar flux. One area where there is still some debate relates to the existence and meaning of a floor value to the heliospheric field. From cosmogenic isotope abundances, Steinhilber et al. (2010) have recently deduced that the near-Earth IMF at the end of the Maunder minimum was 1.80 ± 0.59 nT which is considerably lower than the revised floor of 4nT proposed by Svalgaard and Cliver. We here combine cosmogenic and geomagnetic reconstructions and modern observations (with allowance for the effect of solar wind speed and structure on the near-Earth data) to derive an estimate for the open solar flux of (0.48 ± 0.29) × 1014 Wb at the end of the Maunder minimum. By way of comparison, the largest and smallest annual means recorded by instruments in space between 1965 and 2010 are 5.75 × 1014 Wb and 1.37 × 1014 Wb, respectively, set in 1982 and 2009, and the maximum of the 11 year running means was 4.38 × 1014 Wb in 1986. Hence the average open solar flux during the Maunder minimum is found to have been 11% of its peak value during the recent grand solar maximum.

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.

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.

How is open solar magnetic flux lost over the solar cycle?

The Sun's open magnetic field, magnetic flux dragged out into the heliosphere by the solar wind, varies by approximately a factor of 2 over the solar cycle. We consider the evolution of open solar flux in terms of a source and loss term. Open solar flux creation is likely to proceed at a rate dependent on the rate of photospheric flux emergence, which can be roughly parameterized by sunspot number or coronal mass ejection rate, when available. The open solar flux loss term is more difficult to relate to an observable parameter. The supersonic nature of the solar wind means open solar flux can only be removed by near-Sun magnetic reconnection between open solar magnetic field lines, be they open or closed heliospheric field lines. In this study we reconstruct open solar flux over the last three solar cycles and demonstrate that the loss term may be related to the degree to which the heliospheric current sheet (HCS) is warped, i.e., locally tilted from the solar rotation direction. This can account for both the large dip in open solar flux at the time of sunspot maximum as well as the asymmetry in open solar flux during the rising and declining phases of the solar cycle. The observed cycle-to-cycle variability is also well matched. Following Sheeley et al. (2001), we attribute modulation of open solar flux by the degree of warp of the HCS to the rate at which opposite polarity open solar flux is brought together by differential rotation.

Multi-layer radial basis function networks: an extension to the radial basis function

This paper presents the initial research carried out into a new neural network called the multilayer radial basis function network (MRBF). The network extends the radial basis function (RBF) in a similar way to that in which the multilayer perceptron extends the perceptron. It is hoped that by connecting RBFs together in a layered fashion, an equivalent increase in ability can be gained, as is gained from using MLPs instead of single perceptrons. The results of a practical comparison between individual RBFs and MRBF's are also given.

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.

Permeate flux modeling of membrane distillation

This paper concerns the modeling of membrane distillation. The model developed has been used to predict permeate fluxes using different initial operating conditions. PVDF and PTFE membranes were successfully used in a flat plate module to experimentally confirm the theoretical results. The correlation between theory and experiment was close for both membranes. The PTFE membranes produced higher fluxes than PVDF. A Versapor membrane was also used for this work. This membrane is a composite, with a thin porous layer on a support layer. It was found not to be suitable for membrane distillation. A comparison of the heat flux was also carried out. Again, there was good correlation between theory and experiment