Thouless-Anderson-Palmer equation for analog neural network with temporally fluctuating white synaptic noise

Effects of synaptic noise on the retrieval process of associative memory neural networks are studied from the viewpoint of neurobiological and biophysical understanding of information processing in the brain. We investigate the statistical mechanical properties of stochastic analog neural networks with temporally fluctuating synaptic noise, which is assumed to be white noise. Such networks, in general, defy the use of the replica method, since they have no energy concept. The self-consistent signal-to-noise analysis (SCSNA), which is an alternative to the replica method for deriving a set of order parameter equations, requires no energy concept and thus becomes available in studying networks without energy functions. Applying the SCSNA to stochastic network requires the knowledge of the Thouless-Anderson-Palmer (TAP) equation which defines the deterministic networks equivalent to the original stochastic ones. The study of the TAP equation which is of particular interest for the case without energy concept is very few, while it is closely related to the SCSNA in the case with energy concept. This paper aims to derive the TAP equation for networks with synaptic noise together with a set of order parameter equations by a hybrid use of the cavity method and the SCSNA.Comment: 13 pages, 3 figure

Structural damage identification utilising PCA-compressed frequency response functions and neural network ensembles

This paper presents a damage detection method that utilises FRF data to identify damage in beam structures. The proposed method uses artificial neural networks (ANNs) to map changes in FRFs to damage characteristics. To obtain suitable patterns for ANN inputs, the size of the FRFs is reduced adopting Principal Component Analysis (PCA) techniques. A hierarchy of neural network ensembles is created to take advantage of individual differences from sensor signals. To simulate field applications, the time history data are polluted with white Gaussian noise. The method involves finite element modelling of undamaged and damaged steel beams. By performing transient analysis with the numerical beams, the time histories are obtained and subsequently polluted with different levels of white Gaussian noise. FRFs are determined and compressed utilising PCA techniques. The PCA-reduced FRFs are then used as input patterns for training and testing of neural network ensembles giving the characteristics of the damage. © 2009 Taylor & Francis Group, London

Dynamic-based damage identification using neural network ensembles and damage index method

This paper presents a vibration-based damage identification method that utilises a "damage fingerprint" of a structure in combination with Principal Component Analysis (PCA) and neural network techniques to identify defects. The Damage Index (DI) method is used to extract unique damage patterns from a damaged beam structure with the undamaged structure as baseline. PCA is applied to reduce the effect of measurement noise and optimise neural network training. PCA-compressed DI values are, then, used as inputs for a hierarchy of neural network ensembles to estimate locations and severities of various damage cases. The developed method is verified by a laboratory structure and numerical simulations in which measurement noise is taken into account with different levels of white Gaussian noise added. The damage identification results obtained from the neural network ensembles show that the presented method is capable of overcoming problems inherent in the conventional DI method. Issues associated with field testing conditions are successfully dealt with for numerical and the experimental simulations. Moreover, it is shown that the neural network ensemble produces results that are more accurate than any of the outcomes of the individual neural networks

Dissipativity analysis of stochastic fuzzy neural networks with randomly occurring uncertainties using delay dividing approach

This paper focuses on the problem of delay-dependent robust dissipativity analysis for a class of stochastic fuzzy neural networks with time-varying delay. The randomly occurring uncertainties under consideration are assumed to follow certain mutually uncorrelated Bernoulli-distributed white noise sequences. Based on the Itô's differential formula, Lyapunov stability theory, and linear matrix inequalities techniques, several novel sufficient conditions are derived using delay partitioning approach to ensure the dissipativity of neural networks with or without time-varying parametric uncertainties. It is shown, by comparing with existing approaches, that the delay-partitioning projection approach can largely reduce the conservatism of the stability results. Numerical examples are constructed to show the effectiveness of the theoretical results