A Bayesian Local Linear Wavelet Neural Network

Nonlinear dynamic systems are characterized with uncertainties in terms of structure and parameters. These uncertainties cannot be described by deterministic models. The modelling and identification of nonlinear dynamic systems through the measured experimental data is a problem in engineering and technical processes. Therefore, field of system identification have become an important area of research. Fuzzy technology is an effective tool for dealing with complex nonlinear processes that are characterized with uncertain factors. In this paper, a novel approach based on Local Linear method learning in dynamical filter weights neurons for the identification of non-linear dynamic systems is presented. The fuzzy wavelet neural network combines wavelet theory with fuzzy logic and neural networks. Learning fuzzy rules and parameter update in fuzzy wavelet neural network is based on gradient decent method. The proposed approach is said to be Fuzzy Local Linear Wavelet Neural Network based model. It has been explained through examples. The structure is tested for the identification with both wavelet neural network and Fuzzy Local Linear Wavelet Neural Network that shows the comparative performance.KeywordsSystem IdentificationNon-linear SystemWavelet Neural NetworkFuzzy Wavelet Neural NetworkLocal Linear Wavelet Neural NetworkFuzzy Local Linear Wavelet Neural Network

In this paper we have used a local linear wavelet neural network (LLWNN) model for pattern classification. The difference of the network with conventional wavelet neural network (WNN) is that the connection weights between the hidden layer and output layer of conventional WNN are replaced by a local linear model. Particle swarm optimisation (PSO) technique used for training the LLWNN. Simulation results for the classification of different benchmark datasets show the feasibility and effectiveness of the proposed method.

This work presents a new technique for the identification of multiple power quality disturbances in industrial power systems. This new technique is developed based on change detection filter (CDF) and machine intelligence techniques like the local linear radial basis function neural network (LLRBFNN) and decision tree (DT). The proposed change detection filter has been designed in one cycle back fashion for the multiple non–stationary transient power signal disturbances for localisation, and feature extraction. The extracted features are fed as inputs to either a LLRBFNN or a decision tree–based classifier (DTC) for characterisation of the power quality events. The performance of LLRBFNN and DTC are evaluated and compared with local linear wavelet neural network (LLWNN), wavelet neural network (WNN), radial basis function neural network (RBFNN), etc., to highlight the superior performance of the proposed classifiers.

This paper proposes a new hybrid approach, based on the combination of parametric and nonparametric models by adopting wavelet estimation approach, to model and predict the price electricity for Nord Pool market. Our hybrid methodology consists into two steps. The first step aims at modeling the conditional mean of the time series, using a generalized fractional model withk‐factor of Gegenbauer termed thek‐factor GARMA model; the parameters of this model are estimated using the wavelet approach based on the discrete wavelet packet transform (DWPT). The second step aims at estimating the conditional variance, so we adopt the local linear wavelet neural network (LLWNN) model. The proposed hybrid model is tested using the hourly log‐returns of electricity spot price from the Nord Pool market. The empirical results were compared with the predictions of the ARFIMA–LLWNN, thek‐factor GARMA–FIGARCH and the individual LLWNN models. It is shown that the proposed hybridk‐factor GARMA–LLWNN model outperforms all other competing methods. Hence it is a robust tool in forecasting time series.

This study investigates the performance of a novel neural network technique in the problem of price forecasting. To improve the prediction accuracy using each model’s unique features, this research proposes a hybrid approach that combines the -factor GARMA process, empirical wavelet transform and the local linear wavelet neural network (LLWNN) methods, to form the GARMA-WLLWNN process. In order to verify the validity of the model and the algorithm, the performance of the proposed model is evaluated using data from Polish electricity markets, and it is compared with the dual generalized long memory -factor GARMA-G-GARCH model and the individual WLLWNN. The empirical results demonstrated the proposed hybrid model can achieve a better predicting performance and prove that is the most suitable electricity market forecasting technique.

Radial Basis Function (RBF) Network is popularly used for solving pattern recognition problems. The training of RBF Network is faster compared to multi layer perceptron using error backpropagation. However, the RBF Network uses the pseudo inverse matrix to calculate weights from the hidden layer to the output layer. Thus calculation cost increases when the number of data and the number of hidden units increase. In addition, in RBF Network the decision of optimum number of hidden units is difficult. It is also more prone to overtraining, needing repeated train and test cycles to ascertain a proper number of the Network hidden units, so that generalization performance is good. In this work, we propose a technique to set up RBF network parameters which is fast, as well as the number of hidden units are automatically determined. We start with training a Self-Organizing Maps (SOM), which is a unsupervised training, though our samples are labeled. SOM can find the distribution of data in multidimensional space, and map it on a two dimensional display. The results of SOM network is used to calculate the RBF parameters. It is shown by experiments that using the proposed method, RBF network parameters can be determined much faster compared to existing technique. Moreover, the recognition rate for the test data was higher, showing better generalization performance.

The application of wavelets in the fields of mathematics and engineering has grown rapidly in the past few years. One interesting application is to use wavelets as the activation functions in neural networks. This paper discusses the theoretical background involving wavelets from which feedforward wavelet neural networks are simply a direct consequence and evaluates a design procedure for developing these multiresolution networks. Two different wavelet neural network design examples are presented in order to demonstrate the issues involved in the design of wavelet networks. One example is to use a wavelet neural network to solve a two dimensional nonlinear function approximation problem. The other example is to use a wavelet neural network for feathering the position of the solar arrays of the Space Station.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Process fault detection and diagnosis using neural networks—I. steady-state processes

Complexity control of a learning method is critical for obtaining good generalization with finite training data. We discuss complexity control in multilayer perceptron (MLP) networks trained via backpropagation. For such networks, the number of hidden units and/or network weights is usually used as a complexity parameter. However, application of backpropagation training introduces additional mechanisms for complexity control. These mechanisms are implicit in the implementation of an optimization procedure, and they cannot be easily quantified (in contrast to the number of weights or the number of hidden units). We suggest using the framework of statistical learning theory to explain the effect of weight initialization. Using this framework, we demonstrate the effect of weight initialization on complexity control in MLP networks.

The Sixth International Symposium on Neural Networks (ISNN 2009)

Complex plants seldom fulfill the conditions required for the direct feedback linearization(DFL) control. Aiming at the mathematic model not known exactly, wavelet neural network(WNN) identifier combined with H ∞ controller is proposed. WNN is used to approximate the unknown function, novel control and update laws for the weights in the WNN are derived to guarantee that the tracking error is uniformly ultimately bounded (UUB) in the sense of Lyapunov. In addition, a variable structure control and H ∞ robust compensator is designed to improve the tracking performance. This control method is used to the AC all-electrical tank gun control system, computer simulations show that the tracking accuracy is much better and the control system has strong adaptability and robustness.

Accurate Spectrum Prediction is a promising solution to save sensing energy and time, it also helps to increase throughput in cognitive radio systems. In this paper, we investigate the use of wavelet neural networks (WNN) in predicting future channel occupancy status. The proposed work builds upon existing concepts in open literature, gathered in a general framework for applying WNN. An experimental measurement in the 100–200 MHz band, are used for either training or validation of the proposed model. The trade-off between accuracy, utilization and parameters initialization have been explained, that helped in selecting a near optimal model. Computer simulations show the effectiveness of using WNN in spectrum prediction as compared to previous works in literature, in terms of predictive accuracy and stability in prediction.

An effective approach for fault diagnosis of aeroengine based on integration of wavelet analysis and neural networks is presented. The wavelet transform can accurately localizes the characteristics of a signal in time-frequency domains and in a view of the inter relationship of wavelet transform between exponent theory, the whole and local exponents obtained from wavelet transform coefficients as features are presented for extracting fault signals, which are inputted into radial basis function for fault pattern recognition. The fault diagnosis model of aero-engine is established and the improved Levenberg-Marquardt training algorithm is used to fulfill the network structure and parameter identification. By choosing enough samples to train the fault diagnosis network and the information representing the faults input into the neural network, the fault pattern can be determined. The robustness of wavelet neural network for fault diagnosis is discussed. The practical fault diagnosis for aeroengine vibration approves to be accurate and comprehensive.

Studies Hebbian learning in linear neural networks with emphasis on the self-association information principle. This criterion, in one-layer networks, leads to the space of the principal components and can be generalized to arbitrary architectures. The self-association paradigm appears to be very promising because it accounts for the fundamental features of Hebbian synaptic learning and generalizes the various techniques proposed for adaptive principal component networks. The authors also include a set of simulations that compare various neural architectures and algorithms.

Traditional neural network training is usually based on the maximum likelihood to obtain the appropriate network parameters including weights and biases given the training data. However, if the available data are finite and noisy, the maximum likelihood-based network training can cause the neural network after being trained to overfit the noisy data. This problem has been overcome by using the Bayesian inference applied to the neural network training in various applications. The Bayesian inference can allow values of regularization parameters to be found using only the training data. In addition, the Bayesian approach also allows different models (e.g., neural networks with different numbers of hidden units to be compared using only the training data). Neural networks trained with Bayesian inference can be also known as Bayesian neural networks (BNNs). This chapter focuses on BNNs for classification problems with considerations of model complexity of BNNs conveniently handled by a method known as the evidence framework.