A model-based PID controller for Hammerstein systems using B-spline neural networks

In this paper, a new model-based proportional–integral–derivative (PID) tuning and controller approach is introduced for Hammerstein systems that are identified on the basis of the observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a B-spline neural network. The control signal is composed of a PID controller, together with a correction term. Both the parameters in the PID controller and the correction term are optimized on the basis of minimizing the multistep ahead prediction errors. In order to update the control signal, the multistep ahead predictions of the Hammerstein system based on B-spline neural networks and the associated Jacobian matrix are calculated using the de Boor algorithms, including both the functional and derivative recursions. Numerical examples are utilized to demonstrate the efficacy of the proposed approaches.

B-spline neural networks based PID controller for Hammerstein systems

A new PID tuning and controller approach is introduced for Hammerstein systems based on input/output data. A B-spline neural network is used to model the nonlinear static function in the Hammerstein system. The control signal is composed of a PID controller together with a correction term. In order to update the control signal, the multistep ahead predictions of the Hammerstein system based on the B-spline neural networks and the associated Jacobians matrix are calculated using the De Boor algorithms including both the functional and derivative recursions. A numerical example is utilized to demonstrate the efficacy of the proposed approaches.

Online modeling with tunable RBF network

In this paper, we propose a novel online modeling algorithm for nonlinear and nonstationary systems using a radial basis function (RBF) neural network with a fixed number of hidden nodes. Each of the RBF basis functions has a tunable center vector and an adjustable diagonal covariance matrix. A multi-innovation recursive least square (MRLS) algorithm is applied to update the weights of RBF online, while the modeling performance is monitored. When the modeling residual of the RBF network becomes large in spite of the weight adaptation, a node identified as insignificant is replaced with a new node, for which the tunable center vector and diagonal covariance matrix are optimized using the quantum particle swarm optimization (QPSO) algorithm. The major contribution is to combine the MRLS weight adaptation and QPSO node structure optimization in an innovative way so that it can track well the local characteristic in the nonstationary system with a very sparse model. Simulation results show that the proposed algorithm has significantly better performance than existing approaches.

The link between temporal attention and emotion: a playground for psychology, neuroscience, and plausible artificial neural networks

In this paper, we will address the endeavors of three disciplines, Psychology, Neuroscience, and Artificial Neural Network (ANN) modeling, in explaining how the mind perceives and attends information. More precisely, we will shed some light on the efforts to understand the allocation of attentional resources to the processing of emotional stimuli. This review aims at informing the three disciplines about converging points of their research and to provide a starting point for discussion.

Complex-valued B-spline neural networks for modeling and inverting Hammerstein systems

Many communication signal processing applications involve modelling and inverting complex-valued (CV) Hammerstein systems. We develops a new CV B-spline neural network approach for efficient identification of the CV Hammerstein system and effective inversion of the estimated CV Hammerstein model. Specifically, the CV nonlinear static function in the Hammerstein system is represented using the tensor product from two univariate B-spline neural networks. An efficient alternating least squares estimation method is adopted for identifying the CV linear dynamic model’s coefficients and the CV B-spline neural network’s weights, which yields the closed-form solutions for both the linear dynamic model’s coefficients and the B-spline neural network’s weights, and this estimation process is guaranteed to converge very fast to a unique minimum solution. Furthermore, an accurate inversion of the CV Hammerstein system can readily be obtained using the estimated model. In particular, the inversion of the CV nonlinear static function in the Hammerstein system can be calculated effectively using a Gaussian-Newton algorithm, which naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. The effectiveness of our approach is demonstrated using the application to equalisation of Hammerstein channels.

Towards optimizing the selection of neurons in affordable neural networks

This paper considers variations of a neuron pool selection method known as Affordable Neural Network (AfNN). A saliency measure, based on the second derivative of the objective function is proposed to assess the ability of a trained AfNN to provide neuronal redundancy. The discrepancies between the various affordability variants are explained by correlating unique sub group selections with relevant saliency variations. Overall this study shows that the method in which neurons are selected from a pool is more relevant to how salient individual neurons are, than how often a particular neuron is used during training. The findings herein are relevant to not only providing an analogy to brain function but, also, in optimizing the way a neural network using the affordability method is trained.

Single-carrier frequency domain equalisation for hammerstein communication systems using complex-valued neural networks

Single-carrier (SC) block transmission with frequency-domain equalisation (FDE) offers a viable transmission technology for combating the adverse effects of long dispersive channels encountered in high-rate broadband wireless communication systems. However, for high bandwidthefficiency and high power-efficiency systems, the channel can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such nonlinear Hammerstein channels, the standard SC-FDE scheme no longer works. This paper advocates a complex-valued (CV) B-spline neural network based nonlinear SC-FDE scheme for Hammerstein channels. Specifically, We model the nonlinear HPA, which represents the CV static nonlinearity of the Hammerstein channel, by a CV B-spline neural network, and we develop two efficient alternating least squares schemes for estimating the parameters of the Hammerstein channel, including both the channel impulse response coefficients and the parameters of the CV B-spline model. We also use another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a natural 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 B-spline neural network model obtained in time domain. Extensive simulation results are included to demonstrate the effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels.

The climate of Europe 6000 years ago

Palaeoclimates across Europe for 6000 y BP were estimated from pollen data using the modern pollen analogue technique constrained with lake-level data. The constraint consists of restricting the set of modern pollen samples considered as analogues of the fossil samples to those locations where the implied change in annual precipitation minus evapotranspiration (P–E) is consistent with the regional change in moisture balance as indicated by lakes. An artificial neural network was used for the spatial interpolation of lake-level changes to the pollen sites, and for mapping palaeoclimate anomalies. The climate variables reconstructed were mean temperature of the coldest month (T c ), growing degree days above 5  °C (GDD), moisture availability expressed as the ratio of actual to equilibrium evapotranspiration (α), and P–E. The constraint improved the spatial coherency of the reconstructed palaeoclimate anomalies, especially for P–E. The reconstructions indicate clear spatial and seasonal patterns of Holocene climate change, which can provide a quantitative benchmark for the evaluation of palaeoclimate model simulations. Winter temperatures (T c ) were 1–3 K greater than present in the far N and NE of Europe, but 2–4 K less than present in the Mediterranean region. Summer warmth (GDD) was greater than present in NW Europe (by 400–800 K day at the highest elevations) and in the Alps, but >400 K day less than present at lower elevations in S Europe. P–E was 50–250 mm less than present in NW Europe and the Alps, but α was 10–15% greater than present in S Europe and P–E was 50–200 mm greater than present in S and E Europe.

A fast adaptive tunable RBF network for nonstationary systems

This paper describes a novel on-line learning approach for radial basis function (RBF) neural network. Based on an RBF network with individually tunable nodes and a fixed small model size, the weight vector is adjusted using the multi-innovation recursive least square algorithm on-line. When the residual error of the RBF network becomes large despite of the weight adaptation, an insignificant node with little contribution to the overall system is replaced by a new node. Structural parameters of the new node are optimized by proposed fast algorithms in order to significantly improve the modeling performance. The proposed scheme describes a novel, flexible, and fast way for on-line system identification problems. Simulation results show that the proposed approach can significantly outperform existing ones for nonstationary systems in particular.