By Brunello Tirozzi, Silvia Puca, Stefano Pittalis, Antonello Bruschi, Sara Morucci, Enrico Ferraro, Stefano Corsini

ISBN-10: 0817643478

ISBN-13: 9780817643478

ISBN-10: 0817644598

ISBN-13: 9780817644598

Increasingly, neural networks are used and carried out in a variety of fields and became important instruments in probabilistic research and prediction concept. This book—unique within the literature—studies the appliance of neural networks to the research of time sequence of sea information, specifically major wave heights and sea degrees. the actual challenge tested as a kick off point is the reconstruction of lacking info, a common challenge that looks in lots of instances of information analysis.

Specific issues coated include:

* Presentation of basic info at the phenomenology of waves and tides, in addition to comparable technical information of assorted measuring strategies utilized in the study

* Description of the version of wind waves (WAM) used to figure out the spectral functionality of waves and expect the habit of SWH (significant wave heights); a comparability is made up of the reconstruction of SWH time sequence got by way of neural community algorithms as opposed to SWH computed by way of WAM

* ideas of synthetic neural networks, approximation thought, and extreme-value conception essential to comprehend the most purposes of the book.

* program of man-made neural networks (ANN) to reconstruct SWH and sea degrees (SL)

* comparability of the ANN procedure and the approximation operator method, exhibiting the benefits of ANN

* exam of extreme-event research utilized to the time sequence of sea facts in particular locations

* Generalizations of ANN to regard analogous difficulties for different kinds of phenomena and data

This e-book, a cautious mix of concept and functions, is a superb advent to using ANN, that may inspire readers to attempt analogous ways in different vital program parts. Researchers, practitioners, and complex graduate scholars in neural networks, hydraulic and marine engineering, prediction conception, and knowledge research will enjoy the effects and novel rules provided during this resource.

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Extra info for Neural Networks and Sea Time Series: Reconstruction and Extreme-Event Analysis (Modeling and Simulation in Science, Engineering and Technology)

Example text

Thus we have, for example, Wk (n + 1) = Wk (n), k = j, W j (n + 1) = W j (n) + h. 16) Then the new value of the error L E(W(n + 1)) is computed. If L E(W(n + 1)) ≤ L E(W(n)) then the new value W(n+1) of the weights is accepted. 17) L E is the “energy” change L E = L E(W(n + 1)) − L E(W(n)). This dynamic accepts with a certain probability transitions in which the “energy” L E increases. The parameter β > 0 is equal to the inverse “temperature” T of a system β = 1/T . Once we introduce the analogy of the error function L E with the energy of the system it is quite natural that the control parameter β is the inverse temperature.

We made a rigorous derivation of an equation for the SWH η, using the approach of pseudo differential operators, starting again from the free boundary problem of the first section but there is no stochastic behavior in it (Dobrokhotov, Tirozzi and Tudorovsky [61]). Instead the approach followed in this book is to make the statistical analysis of the waves using NNs. This approach has been shown to be useful as can be seen from the results of Chapter 7, where a comparison of the output of NN and WAM is made.

16). The relation between ω and k is the dispersion relation. It is characteristic of the waves (called gravity waves) obtained √ in the linear approximation. For small k it gives the well-known relation v ∼ g D where v = ω/k is the velocity of propagation of the wave. It can also be used to estimate the propagation velocity of a tsunami since the linear theory is considered to be valid for tsunami propagation in deep waters. For a more realistic description of waves propagating in the ocean it is necessary to consider a group of waves.

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Neural Networks and Sea Time Series: Reconstruction and Extreme-Event Analysis (Modeling and Simulation in Science, Engineering and Technology) by Brunello Tirozzi, Silvia Puca, Stefano Pittalis, Antonello Bruschi, Sara Morucci, Enrico Ferraro, Stefano Corsini


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