Calculation of the Volterra kernels of non-linear dynamic systems using an artificial neural network

Wray, J.; Green, Gary

doi:10.1007/bf00202758

Cited by 105 publications

(37 citation statements)

References 28 publications

(43 reference statements)

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“…Even if these equations were known the state variables are often not observable. An alternative approach to identification is to adopt a very general model (Wray and Green, 1994) and focus on the inputs and outputs. Consider the single input-single output (SISO) systeṁ…”

Section: Input-state-output Systems and Volterra Seriesmentioning

confidence: 99%

Functional integration and inference in the brain

Friston

2002

Progress in Neurobiology

271

201

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Self-supervised models of how the brain represents and categorises the causes of its sensory input can be divided into two classes: those that minimise the mutual information (i.e. redundancy) among evoked responses and those that minimise the prediction error. Although these models have similar goals, the way they are attained, and the functional architectures employed, can be fundamentally different. This review describes the two classes of models and their implications for the functional anatomy of sensory cortical hierarchies in the brain. We then consider how empirical evidence can be used to disambiguate between architectures that are sufficient for perceptual learning and synthesis.Most models of representational learning require prior assumptions about the distribution of sensory causes. Using the notion of empirical Bayes, we show that these assumptions are not necessary and that priors can be learned in a hierarchical context. Furthermore, we try to show that learning can be implemented in a biologically plausible way. The main point made in this review is that backward connections, mediating internal or generative models of how sensory inputs are caused, are essential if the process generating inputs cannot be inverted. Because these processes are dynamical in nature, sensory inputs correspond to a non-invertible nonlinear convolution of causes. This enforces an explicit parameterisation of generative models (i.e. backward connections) to enable approximate recognition and suggests that feedforward architectures, on their own, are not sufficient. Moreover, nonlinearities in generative models, that induce a dependence on backward connections, require these connections to be modulatory; so that estimated causes in higher cortical levels can interact to predict responses in lower levels. This is important in relation to functional asymmetries in forward and backward connections that have been demonstrated empirically.To ascertain whether backward influences are expressed functionally requires measurements of functional integration among brain systems. This review summarises approaches to integration in terms of effective connectivity and proceeds to address the question posed by the theoretical considerations above. In short, it will be shown that functional neuroimaging can be used to test for interactions between bottom-up and top-down inputs to an area. The conclusion of these studies points toward the prevalence of top-down influences and the plausibility of generative models of sensory brain function.

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Section: Input-state-output Systems and Volterra Seriesmentioning

confidence: 99%

Functional integration and inference in the brain

Friston

2002

Progress in Neurobiology

271

201

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“…In the Biology field, Wray & Green [13] have outlined a method for extracting the Volterra kernels from the weights and bias values of a time-delayed MLP (Multilayer Perceptron) Neural Network. Based on this idea, there have been several proposals for kernels calculation with different, often non standard, neural networks topologies [14][15] [16].…”

Section: Fig 5 Schematic Representation Of a Volterra Systemmentioning

confidence: 99%

“…Following the approach in [13], we expand the output of our network model, Equation (6) Expanding Equation (7) up to m = 2 derivative order and accommodating the terms according to the derivatives, yields Equation (8) which is the final form of the output of our Neural Network model. Considering in Equation (8) only the terms that contain the variable x a (t), and supposing that it represents the voltage vgs; then supposing also that the variable x b (t) represents the voltage vds, and that the output of the neural network represents the current Ids in a FET, comparing the double Volterra representation of the current in Equation (1) with the output of the Neural Network model, it is easy to recognize the terms between brackets in Equation (8) as the Volterra kernels of a Volterra series expansion for the relationship Ids(Vgs, Vds).…”

Section: Fig 6 Mlp Neural Network Modelmentioning

confidence: 99%

Novel Neural Network application to nonlinear electronic devices: building a Volterra series model

Stegmayer

Chiotti

2006

Int. Artif.

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Abstract. In this work we want to present a novel application of Neural Networks as a Black-Box model, which allows representing the nonlinear behavior of a vast number of RF electronic devices with the Volterra series approximation. We propose a simple approach for the generation of the Volterra model for a device, even in the case of a nonlinearity that depends on more than one variable, which allows obtaining a general model, independent of the physical circuit. In particular, we will show the results obtained for the analysis of a transistor and the generation of its analytical Volterra series model, built using a standard Neural Network model and its parameters.

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“…This model can able to approximate various nonlinearities in the data series, among other models [20][21][22] and can give an appropriate optimized data output (Deposition efficiency).…”

Section: Introductionmentioning

confidence: 99%

Prediction and Analysis of Deposition Efficiency of Plasma Spray Coating Using Artificial Intelligence Method

Behera¹,

Mishra²

2012

OJCM

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Modern industrial technologies call for the development of novel materials with improved surface properties, lower costs and environmentally suitable processes. Plasma spray coating process has become a subject of intense research which attempts to create functional layers on the surface is obviously the most economical way to provide high performance to machinery and industrial equipments. The present work aims at developing and studying the industrial wastes (Flay-ash, Quartz and illmenite composite mixture) as the coating material, which is to be deposited on Mild Steel and Copper substrates. To study and evaluate Coating deposition efficiency, artificial neural network analysis (ANN) technique is used. By this quality control technique, it is sufficient to describe approximation complex of inter-relationships of operating parameters in atmospheric plasma spray process. ANN technique helps in saving time and resources for experimental trials. The aim of this work is to outline a procedure for selecting an appropriate input vectors in ANN coating efficiency models, based on statistical pre-processing of the experimental data set. This methodology can provide deep understanding of various co-relationships across multiple scales of length and time, which could be essential for improvement of product and process performance. The deposition efficiency of coatings has a strong dependence on input power level, particle size of the feed material, powder feed rate and torch to substrate distance. ANN experimental results indicate that the projection network has good generalization capability to optimize the deposition efficiency, when an appropriate size of training set and network is utilized.

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Calculation of the Volterra kernels of non-linear dynamic systems using an artificial neural network

Cited by 105 publications

References 28 publications

Functional integration and inference in the brain

Functional integration and inference in the brain

Novel Neural Network application to nonlinear electronic devices: building a Volterra series model

Prediction and Analysis of Deposition Efficiency of Plasma Spray Coating Using Artificial Intelligence Method

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