Norden E. Huang - Böcker

Data used to develop and confirm models suffer from several shortcomings: the total data is too limited, the data are non-stationary, and the data represent nonlinear processes. The Hilbert-Huang transform (HHT) is a relatively new method that has grown into a robust tool for data analysis and is ready for a wide variety of applications.This text presents the first thorough presentation of the formulation and application of the Hilbert-Huang Transform (HHT) in engineering. After an introduction and overview of recent advances, thirty leading international experts explore the use of the HHT in areas such as oceanography, nonlinear soil amplification, and non-stationary random processes. One chapter offers a comparative analysis between HHT wavelet and Fourier transforms, and another looks at the HHT applied to molecular dynamic simulations. The final chapter provides perspectives on the theory and practice of HHT and reviews applications in disciplines ranging from biomedical, chemical, and financial engineering to meteorology and seismology.The Hilbert-Huang Transform in Engineering features a variety of modern topics, and the examples presented include wide-ranging, real-life engineering problems. While the development of the HHT is not yet complete, this book clearly demonstrates the power and utility of the method and will undoubtedly stimulate further interest, theoretical advances, and innovative applications.

This volume consists of five excellent review papers. In the first paper, “A Review of Coastal Wave Modeling: The Physical and Mathematical Problems”, N E Huang presents a summary of the state-of-the-art of wave modeling in deep waters. He points out several shortcomings in existing modeling approaches and expresses the urgent need for developing a statistical theory of surface waves in shallow waters. Huang believes that the statistical theory can be formulated as the soliton turbulence. He also points out other important issues in wave modeling, including the air-sea interaction processes, and the physics of the wave-current and dissipation processes. In the second paper A C Radder focuses his discussion on the “Hamiltonian Dynamics of Water Waves”. He demonstrates that the Hamiltonian theory of surface waves can be formulated in terms of surface elevation and the velocity potential at the free surface as canonical variables. Several evolution equations, can be readily obtained. Radder also points out the need to develop a stochastic wave model in the shallow-water environment.The maximum runup is arguably the single most important parameter in the design of coastal structures and for the evaluation of the inundation potential of storm surges and tsunamis. C E Synolakis presents a thorough review of the “Exact Solutions of Shallow-Water Wave Equations”. For a single sloping beach, the evolution and runup of solitary, dipole, N and cnoidal waves are discussed. These solutions are then extended to more practical problems.The last two papers concern the flow and sediment motions near the seafloor. In their paper, “Boundary Layer and Sediment Dynamics Under Sea Waves”, P Blondeaux and G Vittori give an expert review of the recent contributions on the understanding of the interaction of the coherent vortex with cohesionless or partially cohesive sediments in a boundary layer. The formation and development of small-scale bedforms in the coastal regions are also discussed. Finally, in “Wave Scour Around Structures”, B M Sumer and J Fredsøe review the scouring processes around various types of structures. Many recent experimental data and theoretical developments are presented.

The Hilbert-Huang Transform (HHT) represents a desperate attempt to break the suffocating hold on the field of data analysis by the twin assumptions of linearity and stationarity. Unlike spectrograms, wavelet analysis, or the Wigner-Ville Distribution, HHT is truly a time-frequency analysis, but it does not require an a priori functional basis and, therefore, the convolution computation of frequency. The method provides a magnifying glass to examine the data, and also offers a different view of data from nonlinear processes, with the results no longer shackled by spurious harmonics — the artifacts of imposing a linearity property on a nonlinear system or of limiting by the uncertainty principle, and a consequence of Fourier transform pairs in data analysis. This is the first HHT book containing papers covering a wide variety of interests. The chapters are divided into mathematical aspects and applications, with the applications further grouped into geophysics, structural safety and visualization.