A taxonomy for wavelet neural networks applied to nonlinear modelling

This article presents a novel classification of wavelet neural networks based on the orthogonality/non-orthogonality of neurons and the type of nonlinearity employed. On the basis of this classification different network types are studied and their characteristics illustrated by means of simple one-dimensional nonlinear examples. For multidimensional problems, which are affected by the curse of dimensionality, the idea of spherical wavelet functions is considered. The behaviour of these networks is also studied for modelling of a low-dimension map.

A new Jacobian matrix for optimal learning of single-layer neural networks

This paper investigates the learning of a wide class of single-hidden-layer feedforward neural networks (SLFNs) with two sets of adjustable parameters, i.e., the nonlinear parameters in the hidden nodes and the linear output weights. The main objective is to both speed up the convergence of second-order learning algorithms such as Levenberg-Marquardt (LM), as well as to improve the network performance. This is achieved here by reducing the dimension of the solution space and by introducing a new Jacobian matrix. Unlike conventional supervised learning methods which optimize these two sets of parameters simultaneously, the linear output weights are first converted into dependent parameters, thereby removing the need for their explicit computation. Consequently, the neural network (NN) learning is performed over a solution space of reduced dimension. A new Jacobian matrix is then proposed for use with the popular second-order learning methods in order to achieve a more accurate approximation of the cost function. The efficacy of the proposed method is shown through an analysis of the computational complexity and by presenting simulation results from four different examples.

Estimation of ternary liquid-liquid equilibria for arene/alkane/ionic liquid mixtures using neural networks

Neural network models have been explored for the prediction of the liquid-liquid equilibrium data and aromatic/aliphatic selectivity values. Four ternary systems composed of toluene, heptane, and the ionic liquids 1-ethyl-3-methylimidazolium ethylsulfate, or 1,3-dimethylimidazolium methylsulfate were investigated at 313.2 and 348.2 K.

Robust face recognition using posterior union model based neural networks

Face recognition with unknown, partial distortion and occlusion is a practical problem, and has a wide range of applications, including security and multimedia information retrieval. The authors present a new approach to face recognition subject to unknown, partial distortion and occlusion. The new approach is based on a probabilistic decision-based neural network, enhanced by a statistical method called the posterior union model (PUM). PUM is an approach for ignoring severely mismatched local features and focusing the recognition mainly on the reliable local features. It thereby improves the robustness while assuming no prior information about the corruption. We call the new approach the posterior union decision-based neural network (PUDBNN). The new PUDBNN model has been evaluated on three face image databases (XM2VTS, AT&T and AR) using testing images subjected to various types of simulated and realistic partial distortion and occlusion. The new system has been compared to other approaches and has demonstrated improved performance.

Application of auto-associative neural networks to transient fault detection in an IC engine

The tailpipe emissions from automotive engines have been subject to steadily reducing legislative limits. This reduction has been achieved through the addition of sub-systems to the basic four-stroke engine which thereby increases its complexity. To ensure the entire system functions correctly, each system and / or sub-systems needs to be continuously monitored for the presence of any faults or malfunctions. This is a requirement detailed within the On-Board Diagnostic (OBD) legislation. To date, a physical model approach has been adopted by me automotive industry for the monitoring requirement of OBD legislation. However, this approach has restrictions from the available knowledge base and computational load required. A neural network technique incorporating Multivariant Statistical Process Control (MSPC) has been proposed as an alternative method of building interrelationships between the measured variables and monitoring the correct operation of the engine. Building upon earlier work for steady state fault detection, this paper details the use of non-linear models based on an Auto-associate Neural Network (ANN) for fault detection under transient engine operation. The theory and use of the technique is shown in this paper with the application to the detection of air leaks within the inlet manifold system of a modern gasoline engine whilst operated on a pseudo-drive cycle. Copyright © 2007 by ASME.

A fast method for fuzzy neural modeling and refinement

In the identification of complex dynamic systems using fuzzy neural networks, one of the main issues is the curse of dimensionality, which makes it difficult to retain a large number of system inputs or to consider a large number of fuzzy sets. Moreover, due to the correlations, not all possible network inputs or regression vectors in the network are necessary and adding them simply increases the model complexity and deteriorates the network generalisation performance. In this paper, the problem is solved by first proposing a fast algorithm for selection of network terms, and then introducing a refinement procedure to tackle the correlation issue. Simulation results show the efficacy of the method.

Automated nonlinear system modelling with multiple neural networks

This article discusses the identification of nonlinear dynamic systems using multi-layer perceptrons (MLPs). It focuses on both structure uncertainty and parameter uncertainty, which have been widely explored in the literature of nonlinear system identification. The main contribution is that an integrated analytic framework is proposed for automated neural network structure selection, parameter identification and hysteresis network switching with guaranteed neural identification performance. First, an automated network structure selection procedure is proposed within a fixed time interval for a given network construction criterion. Then, the network parameter updating algorithm is proposed with guaranteed bounded identification error. To cope with structure uncertainty, a hysteresis strategy is proposed to enable neural identifier switching with guaranteed network performance along the switching process. Both theoretic analysis and a simulation example show the efficacy of the proposed method.

A heterosynaptic learning rule for neural networks

In this article we intoduce a novel stochastic Hebb-like learning rule for neural networks that is neurobiologically motivated. This learning rule combines features of unsupervised (Hebbian) and supervised (reinforcement) learning and is stochastic with respect to the selection of the time points when a synapse is modified. Moreover, the learning rule does not only affect the synapse between pre- and postsynaptic neuron, which is called homosynaptic plasticity, but effects also further remote synapses of the pre-and postsynaptic neuron. This more complex form of synaptic plasticity has recently come under investigations in neurobiology and is called heterosynaptic plasticity. We demonstrate that this learning rule is useful in training neural networks by learning parity functions including the exclusive-or (XOR) mapping in a multilayer feed-forward network. We find, that our stochastic learning rule works well, even in the presence of noise. Importantly, the mean leaxning time increases with the number of patterns to be learned polynomially, indicating efficient learning.

Improved structure optimization for fuzzy-neural networks

Fuzzy-neural-network-based inference systems are well-known universal approximators which can produce linguistically interpretable results. Unfortunately, their dimensionality can be extremely high due to an excessive number of inputs and rules, which raises the need for overall structure optimization. In the literature, various input selection methods are available, but they are applied separately from rule selection, often without considering the fuzzy structure. This paper proposes an integrated framework to optimize the number of inputs and the number of rules simultaneously. First, a method is developed to select the most significant rules, along with a refinement stage to remove unnecessary correlations. An improved information criterion is then proposed to find an appropriate number of inputs and rules to include in the model, leading to a balanced tradeoff between interpretability and accuracy. Simulation results confirm the efficacy of the proposed method.