# Steven R. Long's research while affiliated with California Institute of Technology and other places

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## Publications (32)

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert–Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulati...

Global climate variability is currently a topic of high scientific and public interest, with potential ramifications for the Earth's ecologic systems and policies governing world economy. Across the broad spectrum of global climate variability, the least well understood time scale is that of decade-to-century.1 The bases for investigating past chan...

Instantaneous frequency (IF) is necessary for understanding the detailed mechanisms for nonlinear and nonstationary processes. Historically, IF was computed from analytic signal (AS) through the Hilbert transform. This paper offers an overview of the difficulties involved in using AS, and two new methods to overcome the difficulties for computing I...

Determining trend and implementing detrending operations are important steps in data analysis. Yet there is no precise definition of “trend” nor any logical algorithm for extracting it. As a result, various ad hoc extrinsic methods have been used to determine trend and to facilitate a detrending operation. In this article, a simple and logical defi...

We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed...

The confidence limit is a standard measure of the accuracy of the result
in any statistical analysis. Most of the confidence limits are derived
as follows. The data are first divided into subsections and then, under
the ergodic assumption, the temporal mean is substituted for the
ensemble mean. Next, the confidence limit is defined as a range of
st...

A new method, the Hilbert–Huang Transform (HHT), developed initially for natural and engineering sciences has now been applied to financial data. The HHT method is specially developed for analysing non-linear and non-stationary data. The method consists of two parts: (1) the empirical mode decomposition (EMD), and (2) the Hilbert spectral analysis....

Using a process denoted here as the empirical mode decomposition and the Hilbert spectral analysis, the ages of the seiches on the Caribbean coast of Puerto Rico are determined from their dispersion characteristics with respect to time. The ages deduced from this method are less than a day; therefore, the seiches could be locally generated.

Traditionally, data from random ocean waves are presented in spectral functions. The spectra are the result of Fourier analysis. Fourier spectral analysis has dominated data analysis for, at least, the last hundred years. It has been the standard method for is examining the global amplitude-frequency distributions. Although Fourier transform valid...

We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed...

A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the `empirical mode decomposition' method with which any complicated data set can be decomposed into a finite and often small number of 'intrinsic mode functions' that admit well-behaved Hilbert transforms. This decomposition method is ada...

AbstractIt has long been recognized that the frequency downshift in the wave field evolution is a consequence of nonlinear wave-wave interactions and that the frequency downshift is also necessary for the wind wave field to grow. Yet the detailed mechanism for the frequency change is still unknown: Is the process continuous and gradual? Or, is the...

Using aircraft radar instruments designed for sea surface wave measurements, we have obtained fetch-limited directional wind wave spectra under steady off-shore wind conditions. The results from these observations in different areas at different times show that, up to a fetch of 150 km, the dominant waves propagate at an angle to the wind. The angl...

The blocking and trapping of waves and wave packets by inhomogeneous flow fields were studied in a laboratory setting. Evidence for multiple reflections and thus trapping within the current gradient zone near the blocking point are the main results obtained, and lead to the following conclusions: (1) a strong current gradient zone near the blocking...

Traditionally, investigation of statistical properties of ocean waves has been limited largely to global quantities related to elevation and amplitude such as the power spectral and various probability density functions. Although these properties give valuable information about the wave field, the results cannot be related directly to any portion o...

Controlled laboratory experiments have been conducted to study the kinematics of wave-current interactions. The results confirm the conservation of waves under the steady state condition. The data also show that the kinematic effect of the current on waves can be treated as a simple Doppler shift. After the Doppler correction, the kinematics of the...

The statistical properties of a water surface roughness structure subjected to wind and waves are analyzed in a laboratory wind wave channel. The surface slope is derived using elevation measurements and the pitot tube is employed to measure wind speed. The transient responses of the surface slope to a calm condition and low, medium, and high wind...

Using a threshold criterion governing the onset of wave breaking, we derived an analytical expression for the whitecap coverage of the ocean. This expression is a function of the wave steepness in terms of the significant slope and the ratio of the frictional velocity of the wind to the phase velocity of the energy-containing waves. Theoretically,...

Controlled laboratory experiments are reported which demonstrate directly and quantitatively the influence of wave conditions in determining the drag law at the air-sea interface under neutral stability conditions. It is concluded that the analytic form first proposed by Kitaigorodskii (1970) models the roughness scale very well when the sea is dom...

A laboratory investigation of the influence of wind on the evolution of mechanically generated regular (m.g.r.) waves is reported. Surface elevation measurements were made at four fetches for steep (0.1 less than ak(bar) less than 0.2, 2 Hz) m.g.r. waves, moderate (15 less than u(asterisk) less than 25 cm/s, 3-6 Hz) wind waves, and combinations of...

Statistical properties of wind-generated waves are studied under laboratory conditions. The properties studied include distributions of various zero crossings; crest, trough, and wave amplitudes; local maxima and minima; group length and number of waves per group; and the joint probability distribution of amplitude and period. The results indicate...

Laboratory measurements using both wave probes (contact and optical) and radar confirm the existence of a new type of overshoot phenomenon in the wind-wave development processes. This type of overshoot, which occurs at gravity-capillary wavelengths, is practically a function of local wind stress only. It is named the overshoot phenomenon of the thi...

On the basis of the mapping method developed by Huang et al. (1983), an analytic expression for the non-Gaussian joint probability density function of slope and elevation for nonlinear gravity waves is derived. Various conditional and marginal density functions are also obtained through the joint density function. The analytic results are compared...

From an extension of the Wallops Spectrum (Huang et al., 1981) for the deep water waves, spectral models for waves in finite water depths are developed. Stokes wave expansions are found to offer a good approximation for intermediate water depth. The spectral function in this case is controlled by three parameters: the significant slope, the nondime...

Probability density function of the surface elevation of a nonlinear random wave field is obtained. The wave model is based on the Stokes expansion carried to the third order for both deep water waves and waves in finite depth. The amplitude and phase of the first-order component of the Stokes wave are assumed to be Rayleigh and uniformly distribut...

Based on theoretical analysis and laboratory data, we proposed a unified two-parameter wave spectral model as $\phi(n) = \frac{\beta g^2}{n^m n_0^{5-m}} {\rm exp} \left\{-\frac{m}{4}\left(\frac{n_0}{n}\right)^4\right\}$ with of the wave field which is defined as $\sect = \frac{(\overline{\zeta^2})^{\frac{}1{2}}}{\lambda_0},$ where $\overline{\zeta^...

The significant slope of a random wave field is found to be an important parameter in empirical wind-wave studies. This significant slope Ss is defined as Ss = (ζ²)½/λ0, with ζ² as the mean-square surface elevation and λ0 as the wavelength corresponding to the waves at the peak of the spectrum. With this parameter, the relationship between Ẽ and ñ...

Laboratory experiments were performed to measure the surface elevation probability density function and associated statistical properties for a wind-generated wave field. The laboratory data along with some limited field data were compared. The statistical properties of the surface elevation were processed for comparison with the results derived fr...

Laboratory measurements utilizing a laser probe are made for the slopes of wind waves generated on both positive and negative currents at different values of fetch. The data are then processed electronically to yield an average wave-slope spectrum in frequency space with 128 degrees of freedom. These spectra are used to obtain the growth of the spe...

A new laser device has been used to make direct wave-slope measurements in the capillary-gravity range. Owing to the design principles, the digital nature of the system and the use of a laser beam as a probe, the earlier problems of intensity variations and meniscus effects were avoided. Using this new technique, wave-slope spectra both down and ac...

## Citations

... One spectral analysis tool, the Holo-spectral analysis (HHSA) proposed by Huang et al. (2016) [48], was proposed to analyze both the amplitude modulation (AM) and the carrier frequency (frequency modulation, FM) information in a measured signal. The HHSA was constructed based on the structure of two-layer empirical mode decompositions (EMD), in which the EMD is a signal decomposition method used to extract meaningful oscillation features into intrinsic mode functions (IMF) by means of recursively applying a sifting process [49]. ...

... e town's leisure and sports culture features mainly fall into two categories: Fangchenggang sports features the town is mainly made up of sailing boats and motor boats on the water, and the beautiful south sports features the town is made up of fishing and kart competitions. e subsidies of stadiums and gymnasiums have a strong locational effect on urban development [18], and the influence of marketing on host cities is strongly correlated with the exposure of sports events [19], so national sports organizations can strengthen the sponsorship of sports towns [20]. ...

... where h is the crest height, and H s is the significant wave height. Tayfun (1980) and Huang et al. (1986) ...

... Each IMF is more general than a simple harmonic function due to time-dependent amplitudes and frequencies. More details on the EMD method can be found in Huang et al. (1998Huang et al. ( , 2003. ...

... The wave spectrum is typically given as a parameterized function. Spectral models include the PM (Pierson-Moskowitz) [1] and BM (Bretschneider-Mitsuyasu) spectrums [2,3] for fully grown wind waves; JONSWAP (Joint North Sea Wave Observation Project) [4] and TMA spectrums [5] for deep sea and finite water depth; and Wallops spectrum [6] for shallow waters. Several studies have been conducted to reproduce and parameterize the wave spectrum in various regions [7][8][9][10][11][12]. ...

... The core idea of EMD is to decompose one complex signal into several intrinsic mode functions (IMFs) and a residual. Each IMF contains the information of different time scales, and the residual denotes the slow change of the signal [28]. Considering the modal aliasing phenomenon in EMD, we adopt an improved approach, namely complementary ensemble empirical mode decomposition (CEEMD) [29]. ...

... The wavelet analysis could bear some resolution rates in frequency and at the same time hold signal characteristics in time. However, the Heisenberg imprecise measure theory limits the advancement wavelet analysis precision in frequency and time, and the illusive harmonious wave could also be engendered [10] [11]. Comparing to the wavelet transform, the Hilbert transform could obtain more elaborate partial characteristics but disagree with the signal of width [10]. ...

... Away from the wavemaker-generated frequency, the values of MSC gradually decrease. Huang et al. (1996Huang et al. ( , 1998 suggested an improved Hilbert-Huang transform (HHT) that is based on Empirical Mode Decomposition (EMD) and Hilbert transform. First, the EMD is applied to the original record as follows: ...

... In the field of cybersecurity many SP tools have been used for features extraction and data preprocessing along with ML classifiers/ clusters. For example, Hilbert Huang Transform (HHT) [34,35] which is used along with deep learning networks [36] and Support Vector Machine (SVM) [37]. Fast Fourier Transform (FFT) which is used within deep learning [38] to detect attacks like false alarm rate (FAR), precision and the detection rate (DR....) in smart island. ...

... Section 3 delves into the technical details. Huang et al. (2009) appear to have been the first. They use EMD to remove noise from monthly global temperature anomaly series to derive annual series. ...