Review of The Hilbert-Huang Transform in Engineering, edited by Norden E. Huang and Nii O. Attoh-Okine: Taylor & Francis, CRC Press, Boca Raton, Fla., 2005. Price: $149.85. pp. 328.

The Hilbert-Huang Transform (HHT) is a signal processing tool developed for joint time-frequency representation of nonstationary signals. The well-known short-time Fourier Transform and the Wavelet Transform (WT) that are also employed for time-frequency analysis use predefined analyzing functions and are subject to limitations associated with the uncertainty principle. In implementing the HHT method, signals are decomposed into case-specific functions that are extracted from the original signal by means of a numerical data-driven algorithmic process, the so-called Empirical Mode Decomposition (EMD). These functions, the Intrinsic Mode Functions (IMF), are defined by two criteria: (1) the number of extrema and zero-crossing points must either be equal or differ by no more than one, and (2) the mean value of the envelope defined by the local maxima and the envelope of the local minima is zero at any time instant. The salient property of the IMFs is that they are monocomponent signals whose instantaneous frequency, lends itself to physical interpretation. The instantaneous frequency is taken equal to the derivative of the phase of the complex analytic signal, which has a spectrum identical to that of the real signal for positive frequencies and zero for negative frequencies. Applying the standard Hilbert spectral analysis (HSA) to all IMFs, the Hilbert Spectrum (HS) of the decomposed signal is derived. It depicts the temporal evolution of the amplitude and the instantaneous frequency of the complex analytic signal of all IMFs and thus constitutes a time-frequency representation of the original signal. The product of the EMD and HSA of the decomposed signal into IMFs is referred to, at least in this book, as the HHT.

This is a book that exclusively deals with the HHT. Its main purpose is to provide the reader with an overview of the HHT without pursuing thorough mathematical details. Further, it attempts to demonstrate the versatility of the method by including numerous applications of the HHT in various engineering fields including ocean, environmental, seismic, and structural engineering. The book is organized into 13 chapters, each one written by different authors in a strict technical paper format (abstract, introduction, theoretical background, numerical results, conclusions, and references). However, not all chapters reflect the same degree of rigorousness, completeness, and effectiveness in communicating their specific topic.

Chapter 1 serves as an introduction to the HHT, explaining the initial motivations for its development and providing a broad outline of the standard EMD algorithm, together with recent developments on its practical implementation. A normalized form of the Hilbert transform, a confidence limit analysis of the HHT, and the statistical significance of the IMFs are briefly discussed as well.

In Chapter 2, the superiority of the HHT over the traditional Fourier-based power density spectral estimation for the detection of extremely localized in-time rogue waves in ocean wave time histories is explored. Rogue waves exhibit significantly larger wave heights from the mean value of a developed sea and play a significant role in the design of off-shore structures and deep-sea vessels. Exploitation of the obtained Hilbert spectra to deduce the possible generating mechanisms of these transient waves is also attempted in accordance with assorted theoretical treatments.

In Chapter 3, the HHT is applied to three different sets of data to exemplify the potential of the method for ocean engineering and science studies. In particular, measurements of interannual sea surface height fluctuation in the Pacific, closely associated with the El Nino phenomenon and global climate change, are analyzed. Seasonal ocean color data of the Delaware Bay recorded by satellites used for oceanographic health monitoring of large ecosystems are considered as well. Records obtained by satellite multisensor remote sensing related to the exchange flow between the Mediterranean Sea and the Atlantic Ocean are also processed.

In Chapter 4, the HHT is used for the analysis of sea surface spatial data acquired by an airborne scanning laser system near Duck, N.C. 3 days after an extratropical storm passed through the area. The spatial evolution of the shoaling swell is studied in context to its Hilbert spectrum, and the energy flux of the sea-wave field is investigated. A comparison with a corresponding space-wavenumber representation obtained by wavelet analysis and with the standard Fourier-based spectrum is made to illustrate the potential of the HHT to provide enhanced spatial/wavenumber resolution.

Chapter 5 considers near-shore sea-wave data during different sea stages collected on the Pacific coast of Japan, which are then analyzed via the HHT. The shallow water effects and the boundary conditions of the coastline significantly contribute to the inherent nonstationarity of sea wave time histories. The limitations of Fourier analysis methods are addressed, vis-a-vis the appropriateness of the HHT method to draw useful conclusions about the phenomena associated with such types of records.

In Chapter 6, a hybrid EMD-matched filter algorithm is developed for the detection of man-made electromagnetic signals in the noisy underwater electromagnetic background. Marine vessels act as dipoles causing local fluctuations in the general background of geomagnetic and hydrodynamic non-Gaussian colored noise that characterizes the near-shore shallow-water environment. The proposed algorithm exploits the ability of the EMD to extract these transient electric dipole signatures out of electromagnetic field measurements and, thus, to effectively detect the presence of sea vessels.

In Chapter 7, joint time-frequency representations of experimental velocity signals observed in turbulent, fully developed open-channel flow, with and without the imposition of bed suction, are obtained by both the HHT and WT. The detection of certain patterns localized in time and frequency is pursued. A comparative study suggests that the HHT yields better localization in the time-frequency plane over the WT, stemming from the enhanced resolution that the Hilbert spectra attain.

Chapter 8 employs the HHT to analyze earthquake records pertaining to the Nisqually 2001 seismic event, toward detecting the potential nonlinear response of layered soil deposits. Furthermore, the HHT-based site amplification factor that is similar to the traditional Fourier-based amplification factor and the appropriately defined Hilbert damping spectrum are introduced. It is shown that they are promising tools for the quantification of the influence of the inelastic soil behavior to the so-called site-effect phenomena during a strong ground motion.

In Chapter 9, two methods incorporating the HHT are proposed for the simulation of artificial earthquake accelerograms as samples of an underlying nonstationary random-process compatible with a real earthquake record. The first method defines a random process in terms of its HHT by adding a uniformly distributed random-phase angle to the Hilbert spectral representation of a recorded accelerogram. In the second method, artificial time histories compatible with the IMF’s of a recorded accelerogram are appropriately defined and synthesized using the standard spectral representation technique. Summation of the generated time histories yields accelerograms sharing similar characteristics in the time and in frequency domain, with the recorded one.

In Chapter 10, crack detection in aluminum beam and plate specimens is pursued via signal processing of flexural wave propagation records using the HHT and WT. Further, the identification of the natural frequencies from the free-vibration responses of beams of different end support conditions is accomplished by utilizing the HHT, the WT, and the classical Fourier spectrum. A comparison of the results derived by the various methods suggests the HHT as a viable tool for structural health monitoring purposes.

In Chapter 11, the HHT is applied to nonstationary data obtained by a molecular dynamics computer-simulated model of a simple protein. It is concluded that the HHT provides useful insight into the dynamics of the protein. Further, it can be used to prescribe optimum digital filter specifications for the amplification of the effective frequencies of the simulated data associated with potential conformational change events in the structure of the protein. Filters thus obtained are adopted for efficient detection of spontaneous modifications in the molecular shape of proteins.

Chapter 12 proposes a technique to improve the capacity of the EMD to extract intermittent fluctuations of high frequency and of small amplitude from a dominant low frequency and large amplitude wave. This is achieved by appending a properly chosen artificial temporary waveform to the original data. This waveform can be readily disregarded after the decomposition into IMFs is obtained. Moreover, a second technique is described to effectively decompose and detect wave groups of similar frequencies in given field data by appropriately modulating the frequency content of their Hilbert transform representation.

Finally, Chapter 13 reviews the theory of HHT. It provides a summary of certain biomedical, chemistry and chemical en-gineering, financial, meteorological and atmospheric, ocean engineering, seismic, structural, health monitoring, and system identification applications that utilize the HHT. It also discusses some limitations of the method and contains further suggestions for potential future research.

Overall, the book provides a balanced presentation of the HHT from various points of view depending on the application of interest and demonstrates the versatility and applicability of this numerical technique in various technical fields. It can be a valuable reference text for researchers and practitioners in the plethora of engineering fields that deal with the processing of nonstationary data sets and focus on extracting physically meaningful information while capturing the evolution of the corresponding processes in time or space.