Stable Nonlinear Receding Horizon Regulator Using RBF Neural Network Models

The general stability theory of nonlinear receding horizon controllers has attracted much attention over the last fifteen years, and many algorithms have been proposed to ensure closed-loop stability. On the other hand many reports exist regarding the use of artificial neural network models in nonlinear receding horizon control. However, little attention has been given to the stability issue of these specific controllers. This paper addresses this problem and proposes to cast the nonlinear receding horizon control based on neural network models within the framework of an existing stabilising algorithm.

Adaptive B-spline neural network based nonlinear equalization for high-order QAM systems with nonlinear transmit high power amplifier

High bandwidth-efficiency quadrature amplitude modulation (QAM) signaling widely adopted in high-rate communication systems suffers from a drawback of high peak-toaverage power ratio, which may cause the nonlinear saturation of the high power amplifier (HPA) at transmitter. Thus, practical high-throughput QAM communication systems exhibit nonlinear and dispersive channel characteristics that must be modeled as a Hammerstein channel. Standard linear equalization becomes inadequate for such Hammerstein communication systems. In this paper, we advocate an adaptive B-Spline neural network based nonlinear equalizer. Specifically, during the training phase, an efficient alternating least squares (LS) scheme is employed to estimate the parameters of the Hammerstein channel, including both the channel impulse response (CIR) coefficients and the parameters of the B-spline neural network that models the HPA’s nonlinearity. In addition, another B-spline neural network is used to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can easily be estimated using the standard LS algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. Nonlinear equalisation of the Hammerstein channel is then accomplished by the linear equalization based on the estimated CIR as well as the inverse B-spline neural network model. Furthermore, during the data communication phase, the decision-directed LS channel estimation is adopted to track the time-varying CIR. Extensive simulation results demonstrate the effectiveness of our proposed B-Spline neural network based nonlinear equalization scheme.

Neural and wavelet network models for financial distress classification

This work analyzes the use of linear discriminant models, multi-layer perceptron neural networks and wavelet networks for corporate financial distress prediction. Although simple and easy to interpret, linear models require statistical assumptions that may be unrealistic. Neural networks are able to discriminate patterns that are not linearly separable, but the large number of parameters involved in a neural model often causes generalization problems. Wavelet networks are classification models that implement nonlinear discriminant surfaces as the superposition of dilated and translated versions of a single "mother wavelet" function. In this paper, an algorithm is proposed to select dilation and translation parameters that yield a wavelet network classifier with good parsimony characteristics. The models are compared in a case study involving failed and continuing British firms in the period 1997-2000. Problems associated with over-parameterized neural networks are illustrated and the Optimal Brain Damage pruning technique is employed to obtain a parsimonious neural model. The results, supported by a re-sampling study, show that both neural and wavelet networks may be a valid alternative to classical linear discriminant models.

Detection of Parkinson’s disease tremor-onset with a frequency analysing artificial neural network

Deep Brain Stimulator devices are becoming widely used for therapeutic benefits in movement disorders such as Parkinson's disease. Prolonging the battery life span of such devices could dramatically reduce the risks and accumulative costs associated with surgical replacement. This paper demonstrates how an artificial neural network can be trained using pre-processing frequency analysis of deep brain electrode recordings to detect the onset of tremor in Parkinsonian patients. Implementing this solution into an 'intelligent' neurostimulator device will remove the need for continuous stimulation currently used, and open up the possibility of demand-driven stimulation. Such a methodology could potentially decrease the power consumption of a deep brain pulse generator.

A new RBF neural network with boundary value constraints

We present a novel topology of the radial basis function (RBF) neural network, referred to as the boundary value constraints (BVC)-RBF, which is able to automatically satisfy a set of BVC. Unlike most existing neural networks whereby the model is identified via learning from observational data only, the proposed BVC-RBF offers a generic framework by taking into account both the deterministic prior knowledge and the stochastic data in an intelligent manner. Like a conventional RBF, the proposed BVC-RBF has a linear-in-the-parameter structure, such that it is advantageous that many of the existing algorithms for linear-in-the-parameters models are directly applicable. The BVC satisfaction properties of the proposed BVC-RBF are discussed. Finally, numerical examples based on the combined D-optimality-based orthogonal least squares algorithm are utilized to illustrate the performance of the proposed BVC-RBF for completeness.

Connecting mean field models of neural activity to EEG and fMRI data

Progress in functional neuroimaging of the brain increasingly relies on the integration of data from complementary imaging modalities in order to improve spatiotemporal resolution and interpretability. However, the usefulness of merely statistical combinations is limited, since neural signal sources differ between modalities and are related non-trivially. We demonstrate here that a mean field model of brain activity can simultaneously predict EEG and fMRI BOLD with proper signal generation and expression. Simulations are shown using a realistic head model based on structural MRI, which includes both dense short-range background connectivity and long-range specific connectivity between brain regions. The distribution of modeled neural masses is comparable to the spatial resolution of fMRI BOLD, and the temporal resolution of the modeled dynamics, importantly including activity conduction, matches the fastest known EEG phenomena. The creation of a cortical mean field model with anatomically sound geometry, extensive connectivity, and proper signal expression is an important first step towards the model-based integration of multimodal neuroimages.

B-spline neural network based single-carrier frequency domain equalisation for Hammerstein channels

A practical single-carrier (SC) block transmission with frequency domain equalisation (FDE) system can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such Hammerstein channels, the standard SC-FDE scheme no longer works. We propose a novel Bspline neural network based nonlinear SC-FDE scheme for Hammerstein channels. In particular, we model the nonlinear HPA, which represents the complex-valued static nonlinearity of the Hammerstein channel, by two real-valued B-spline neural networks, one for modelling the nonlinear amplitude response of the HPA and the other for the nonlinear phase response of the HPA. We then develop an efficient alternating least squares algorithm for estimating the parameters of the Hammerstein channel, including the channel impulse response coefficients and the parameters of the two B-spline models. Moreover, we also use another real-valued B-spline neural network to model the inversion of the HPA’s nonlinear amplitude response, and the parameters of this inverting B-spline model can be estimated using the standard least squares algorithm based on the pseudo training data obtained as a byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse Bspline neural network model obtained in time domain. The effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels is demonstrated in a simulation study.

Validation of improved TAMANN neural network for operational satellite-derived rainfall estimation in Africa

Real-time rainfall monitoring in Africa is of great practical importance for operational applications in hydrology and agriculture. Satellite data have been used in this context for many years because of the lack of surface observations. This paper describes an improved artificial neural network algorithm for operational applications. The algorithm combines numerical weather model information with the satellite data. Using this algorithm, daily rainfall estimates were derived for 4 yr of the Ethiopian and Zambian main rainy seasons and were compared with two other algorithms-a multiple linear regression making use of the same information as that of the neural network and a satellite-only method. All algorithms were validated against rain gauge data. Overall, the neural network performs best, but the extent to which it does so depends on the calibration/validation protocol. The advantages of the neural network are most evident when calibration data are numerous and close in space and time to the validation data. This result emphasizes the importance of a real-time calibration system.

Modified radial basis function neural network using output transformation

A modified radial basis function (RBF) neural network and its identification algorithm based on observational data with heterogeneous noise are introduced. The transformed system output of Box-Cox is represented by the RBF neural network. To identify the model from observational data, the singular value decomposition of the full regression matrix consisting of basis functions formed by system input data is initially carried out and a new fast identification method is then developed using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator (MLE) for a model base spanned by the largest eigenvectors. Finally, the Box-Cox transformation-based RBF neural network, with good generalisation and sparsity, is identified based on the derived optimal Box-Cox transformation and an orthogonal forward regression algorithm using a pseudo-PRESS statistic to select a sparse RBF model with good generalisation. The proposed algorithm and its efficacy are demonstrated with numerical examples.

Prediction of Parkinson’s Disease tremor onset using a radial basis function neural network based on particle swarm optimization

Deep Brain Stimulation (DBS) has been successfully used throughout the world for the treatment of Parkinson's disease symptoms. To control abnormal spontaneous electrical activity in target brain areas DBS utilizes a continuous stimulation signal. This continuous power draw means that its implanted battery power source needs to be replaced every 18–24 months. To prolong the life span of the battery, a technique to accurately recognize and predict the onset of the Parkinson's disease tremors in human subjects and thus implement an on-demand stimulator is discussed here. The approach is to use a radial basis function neural network (RBFNN) based on particle swarm optimization (PSO) and principal component analysis (PCA) with Local Field Potential (LFP) data recorded via the stimulation electrodes to predict activity related to tremor onset. To test this approach, LFPs from the subthalamic nucleus (STN) obtained through deep brain electrodes implanted in a Parkinson patient are used to train the network. To validate the network's performance, electromyographic (EMG) signals from the patient's forearm are recorded in parallel with the LFPs to accurately determine occurrences of tremor, and these are compared to the performance of the network. It has been found that detection accuracies of up to 89% are possible. Performance comparisons have also been made between a conventional RBFNN and an RBFNN based on PSO which show a marginal decrease in performance but with notable reduction in computational overhead.

Artificial keys for botanical identification using a multilayer perceptron neural network (MLP)

In this paper, practical generation of identification keys for biological taxa using a multilayer perceptron neural network is described. Unlike conventional expert systems, this method does not require an expert for key generation, but is merely based on recordings of observed character states. Like a human taxonomist, its judgement is based on experience, and it is therefore capable of generalized identification of taxa. An initial study involving identification of three species of Iris with greater than 90% confidence is presented here. In addition, the horticulturally significant genus Lithops (Aizoaceae/Mesembryanthemaceae), popular with enthusiasts of succulent plants, is used as a more practical example, because of the difficulty of generation of a conventional key to species, and the existence of a relatively recent monograph. It is demonstrated that such an Artificial Neural Network Key (ANNKEY) can identify more than half (52.9%) of the species in this genus, after training with representative data, even though data for one character is completely missing.

On the utility of input selection and pruning for financial distress prediction models

Analyzes the use of linear and neural network models for financial distress classification, with emphasis on the issues of input variable selection and model pruning. A data-driven method for selecting input variables (financial ratios, in this case) is proposed. A case study involving 60 British firms in the period 1997-2000 is used for illustration. It is shown that the use of the Optimal Brain Damage pruning technique can considerably improve the generalization ability of a neural model. Moreover, the set of financial ratios obtained with the proposed selection procedure is shown to be an appropriate alternative to the ratios usually employed by practitioners.

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.

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.