Multi-output Radial Basis Function Research Articles

Adaptive neural dynamic surface control of load/grid connected voltage source inverters with LC/LCL filters

Utilizing passive filters such as L, LC and LCL is preferred to cancel out high-frequency harmonics caused by pulse width modulation of voltage source inverters. However, the LC and LCL filters have shown better harmonic attenuation than the conventional L filter. Nevertheless, the control process of LC and LCL filters is more complicated due to their higher-order dynamics. The problem gets more challenging in the presence of uncertainties such as load and grid impedance variations. To overcome these challenges, two novel adaptive neural dynamic surface controllers are proposed for LC and LCL filters in the load and grid-connected modes, respectively. Meanwhile, the issue of computational complexity inherent in the conventional backstepping method is avoided here by utilizing the dynamic surface control technique. Furthermore, the matched and unmatched uncertainties of LC/LCL filters are approximated via multi-input multi-output radial basis function neural networks. Stability of the closed-loop systems is guaranteed by converging the tracking errors to a small neighborhood of the origin. Simulations are given to illustrate the effectiveness and potential of the proposed adaptive neural dynamic surface control methods under the load and grid impedance changes.

Generalized Hybrid Constructive Learning Algorithm for Multioutput RBF Networks.

An efficient generalized hybrid constructive (GHC) learning algorithm for multioutput radial basis function (RBF) networks is proposed to obtain a compact network with good generalization capability. By this algorithm, one can train the adjustable parameters and determine the optimal network structure simultaneously. First, an initialization method based on the growing and pruning algorithm is utilized to select the important initial hidden neurons and candidate ones. Then, by introducing a generalized hidden matrix, a structured parameter optimization algorithm is presented to train multioutput RBF network with fixed size, which combines Levenberg-Marquardt (LM) algorithm with least-square method together. Beginning from an appropriate number of hidden neurons, new neurons chosen from the candidates are added one by one each time when the training entraps into local minima. By incorporating an improved incremental constructive scheme, the training is built on previous results after adding new neurons such that the GHC learning algorithm avoids a trial-and-error procedure. Furthermore, based on the improved computation for LM training, the memory limitation problem is solved. The computational complexity analysis and experimental results demonstrate that better performance is efficiently achieved by this algorithm.

A fast multi-output RBF neural network construction method

This paper investigates the center selection of multi-output radial basis function (RBF) networks, and a multi-output fast recursive algorithm (MFRA) is proposed. This method can not only reveal the significance of each candidate center based on the reduction in the trace of the error covariance matrix, but also can estimate the network weights simultaneously using a back substitution approach. The main contribution is that the center selection procedure and the weight estimation are performed within a well-defined regression context, leading to a significantly reduced computational complexity. The efficiency of the algorithm is confirmed by a computational complexity analysis, and simulation results demonstrate its effectiveness.

Sparse multioutput radial basis function network construction using combined locally regularised orthogonal least square and D-optimality experimental design

A new construction algorithm for multi-output radial basis function (RBF) network modelling is introduce by combining a locally regularized orthogonal least squares (LROLS) model selection with a D-optimality experimental design. The proposed algorithm aims to achieve maximized model robustness and sparsity via two effective and complementary approaches. The LROLS method alone is capable of producing a very parsimonious RBF network model with excellent generalization performance. The D-optimality design criterion further enhances the model efficiency and robustness. A further advantage of the combined approach is that the user only needs to specify a weighting for the D-optimality cost in the combined RBF model selecting criterion and the entire model construction procedure becomes automatic. The value of this weighting does not influence the model selection procedure critically and it can be chosen with ease from a wide range of values.

Modelling a MIMO Chemical Process Using a RBF Network with Recursive OLS Updating

Abstract This paper describes neural network modelling techniques for multiinput multi-output (MIMO) non-linear systems. A multi-output radial basis function (RBF) network is employed for process modelling and a MIMO recursive orthogonal least squares (ROLS) algorithm is developed as a numerically robust method to update the weighting matrix in the network. In this way the degradation of the modelling error due to ill-conditioning in the training data is avoided. The modelling techniques are applied to a real MIMO chemical process rig. Real data experiments show that a neural model with high accuracy can be developed for MIMO non-linear processes.

Complex-valued radial basis function network, Part II: Application to digital communications channel equalisation

In the first part of this paper, a complex-valued multi-output radial basis function network was proposed and two learning algorithms were derived. This second part investigates the adaptive realisation of a Bayesian solution for 4-QAM digital communications channel equalisation using the complex single-output radial basis function network. It is shown that the optimal Bayesian equaliser is structurally equivalent to the complex radial basis function network, and this intimate connection is exploited to develop fast training algorithms for implementing a Bayesian equaliser based on the latter. A novel strategy of utilising decision feedback is employed to improve equaliser performance as well as to reduce computational complexity. The conventional decision feedback equaliser and the maximum likelihood sequence estimator are used as two benchmarks to assess the performance of this Bayesian decision feedback equaliser.

Orthogonal least-squares algorithm for training multioutput radial basis function networks

A constructive learning algorithm for multioutput radial basis function networks is presented. Unlike most network learning algorithms, which require a fixed network structure, this algorithm automatically determines an adequate radial basis function network structure during learning. By formulating the learning problem as a subset model selection, an orthogonal leastsquares procedure is used to identify appropriate radial basis function centres from the network training data, and to estimate the network weights simultaneously in a very efficient manner. This algorithm has a desired property, that the selection of radial basis function centres or network hidden nodes is directly linked to the reduction in the trace of the error covariance matrix. Nonlinear system modelling and the reconstruction of pulse amplitude modulation signals are used as two examples to demonstrate the effectiveness of this learning algorithm.