On the Groupiness and Intermittency of Oceanic Whitecaps

The enhancement of wave breaking activity during wave group passage is investigated using coherent field observations of the instantaneous sea surface elevation and whitecap coverage from platform-based stereo video measurements in the central North Sea. Passing wave groups are shown to be associated with a two to threefold enhancement in the probability distribution of total whitecap coverage W whereas the enhancement of active whitecap coverage WA is approximately fivefold. Breaking time scales and intermittency characteristics are also investigated with the inclusion of a secondary data set of W and WA observations collected during a research cruise in the North Pacific. The time scale analysis suggests a universal periodicity in wave breaking activity within a representative sea-surface area encompassing approximately one dominant wave crest. The breaking periodicity is shown to be closely linked to the peak period of the dominant wave components, suggesting that long-wave modulation of wave breaking is a predominant mechanism controlling the intermittency of wave breaking across scales.publishedVersio

End-effect, stopping criterion, mode mixing and confidence limit for the Hilbert-Huang transform

Master'sMASTER OF ENGINEERIN

Empirical mode decomposition for analyzing acoustical signals

The present invention discloses a computer implemented signal analysis method through the Hilbert-Huang Transformation (HHT) for analyzing acoustical signals, which are assumed to be nonlinear and nonstationary. The Empirical Decomposition Method (EMD) and the Hilbert Spectral Analysis (HSA) are used to obtain the HHT. Essentially, the acoustical signal will be decomposed into the Intrinsic Mode Function Components (IMFs). Once the invention decomposes the acoustic signal into its constituting components, all operations such as analyzing, identifying, and removing unwanted signals can be performed on these components. Upon transforming the IMFs into Hilbert spectrum, the acoustical signal may be compared with other acoustical signals

Detecting and characterizing high-frequency oscillations in epilepsy: a case study of big data analysis

abstract: We develop a framework to uncover and analyse dynamical anomalies from massive, nonlinear and non-stationary time series data. The framework consists of three steps: preprocessing of massive datasets to eliminate erroneous data segments, application of the empirical mode decomposition and Hilbert transform paradigm to obtain the fundamental components embedded in the time series at distinct time scales, and statistical/scaling analysis of the components. As a case study, we apply our framework to detecting and characterizing high-frequency oscillations (HFOs) from a big database of rat electroencephalogram recordings. We find a striking phenomenon: HFOs exhibit on–off intermittency that can be quantified by algebraic scaling laws. Our framework can be generalized to big data-related problems in other fields such as large-scale sensor data and seismic data analysis.The final version of this article, as published in Royal Society Open Science, can be viewed online at: http://rsos.royalsocietypublishing.org/content/4/1/16074

Computer implemented empirical mode decomposition method, apparatus and article of manufacture

A computer implemented physical signal analysis method is invented. This method includes two essential steps and the associated presentation techniques of the results. All the steps exist only in a computer: there are no analytic expressions resulting from the method. The first step is a computer implemented Empirical Mode Decomposition to extract a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform. The final result is the Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

A computer implemented physical signal analysis method includes four basic steps and the associated presentation techniques of the results. The first step is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform which produces a Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum. The third step filters the physical signal by combining a subset of the IMFs. In the fourth step, a curve may be fitted to the filtered signal which may not have been possible with the original, unfiltered signal

Analysis of stationary and non-stationary phenomena in turbulent subcritical flow behind two parallel cylinders

This study presents the analysis of the bistable phenomenon for turbulent flows around two cylinders side-by-side using two methods for data analysis and chaos theory for dynamic analysis. The experimental data were acquired for various Reynolds numbers and pitch-todiameter ratio p/D of 1.16, 1.26, and 1.60, cylinders diameter was 25.1 mm. The experimental technique consists of measuring the velocity fluctuations in an aerodynamic channel using hot-wire anemometry. The study presents the application of the Hilbert-Huang transform (HHT) as a tool of analysis for non-stationary and non-linear signals. The method was first validated using single cylinders and then extended for two cylinders side-by-side. Results show that the HHT method may provide information about particular events in timefrequency space and about the physics of flow scales. The statistical analysis of the experimental data is performed to identify statistical patterns that can be used to characterize the bistable flow. The signals are scanned by a moving window for the statistical analysis, creating blocks of probability density functions (PDFs). The four first statistical moments of each PDF are calculated, and a tendency of behavior based on their variations is established. The dynamics of the bistable flow system are studied applying chaos theory tools, like the largest Lyapunov exponent. The strange attractors of the velocity-time series are reconstructed, and their topology is useful to understand the physics of the bistable system. Each flow wake mode is analyzed separately. A general model of the bistable flow is reconstructed using probability functions. The application of a set of tools in the analysis of the turbulent wake behind cylinders is useful for the comprehension of turbulent phenomena, producing meaningful results and allowing the identification of turbulent structures and flow scales, and a better understanding of the system dynamics.Este estudo apresenta a análise do fenômeno da biestabilidade no escoamento em torno de dois cilindros lado a lado usando dois métodos para análise de sinais, e teoria do caos para a análise da dinâmica. Os dados experimentais foram adquiridos para vários números de Reynolds e várias razões de aspecto p/D de 1,16, 1,26 e 1,60, o diâmetro dos cilindros é de 25,1 mm. A técnica experimental utilizada consiste em medir as flutuações de velocidade em um canal aerodinâmico utilizando anemometria de fio quente. O estudo apresenta a aplicação da transformada de Hilbert-Huang (HHT) como ferramenta de análise para sinais não estacionários e não lineares. O método é primeiramente validado utilizando sinais experimentais para um cilindro sobre escoamento turbulento e após aplicado ao escoamento sobre dois cilindros lado a lado. Resultados mostram que o método de HHT fornece não só uma definição mais precisa de eventos específicos no espaço tempo-frequência, mas também permite uma interpretação física mais significativa dos processos dinâmicos das escalas do escoamento. A análise estatística dos dados experimentais é feita com o objetivo de identificar padrões estatísticos que possam ser utilizados para caracterização do escoamento biestável. Para a análise estatística os dados são varridos por uma janela móvel, criando blocos de funções densidade de probabilidade (PDFs). Os quatro primeiros momentos estatísticos são calculados e é possível estabelecer uma tendência de comportamento baseada em suas variações. A dinâmica do sistema biestável é estudada aplicando ferramentas da teoria do caos, como o maior expoente de Lyapunov. O atrator estranho da série temporal da velocidade é reconstruído e sua topologia é utilizada para melhor compreensão do comportamento físico do fenômeno da biestabilidade. Cada esteira do escoamento biestável é analisada separadamente. Um modelo geral do escoamento biestável é reconstruído utilizando funções de probabilidade. A aplicação de um conjunto de ferramentas para a análise da turbulência das esteiras dos cilindros é útil para a melhor compreensão de fenômenos turbulentos, produzindo resultados significativos e permitindo a identificação de estruturas turbulentas e escalas do escoamento e um entendimento sobre a dinâmica do sistema

Edge-preserving Multiscale Image Decomposition based on Local Extrema

We propose a new model for detail that inherently captures oscillations, a key property that distinguishes textures from individual edges. Inspired by techniques in empirical data analysis and morphological image analysis, we use the local extrema of the input image to extract information about oscillations: We define detail as oscillations between local minima and maxima. Building on the key observation that the spatial scale of oscillations are characterized by the density of local extrema, we develop an algorithm for decomposing images into multiple scales of superposed oscillations. Current edge-preserving image decompositions assume image detail to be low contrast variation. Consequently they apply filters that extract features with increasing contrast as successive layers of detail. As a result, they are unable to distinguish between high-contrast, fine-scale features and edges of similar contrast that are to be preserved. We compare our results with existing edge-preserving image decomposition algorithms and demonstrate exciting applications that are made possible by our new notion of detail

An investigation into the dynamical and statistical properties of dominant ocean surface waves using close-range remote sensing

Denne avhandlingen er basert på forskningsresultat som behandler statistiske og dynamiske egenskaper av dominante vinddrevne overflatebølger i åpent hav. Med uttrykket dominante bølger refererer vi her til de største bølgene, med størst energi, i en gitt sjøtilstand. Bølgedrevne prosesser er viktige både i klimasammenheng via atmosfære--hav interaksjon som drives i stor grad av bølgebrytning, samt for kommersiell og rekreasjonell offshorevirksomhet p.g.a. risikoen for å bli utsatt for f.eks. ekstreme enkeltbølger. Både bølgebrytning og ekstrembølgestatistikk er i skrivende stund ufullstendig representert i teoretiske og numeriske modeller. Arbeidet som presenteres i denne avhandlingen undersøker de ovennevnte temaene ved bruk av bølgeobservasjoner som er primært samlet inn på Ekofiskfeltet i den sentrale delen av Nordsjøen. Observasjonsdatasettene består av en langtidstidsserie av laser-altimetermålinger og stereoskopiske videodata fra Ekofisk, samt videomålinger av brytende bølger fra et forskningstokt i nordre Stillehavet. Forskningsresultatene er presentert i artikkelform med to publiserte verk og ett innlevert manuskript. Det blir påvist en tydelig forbindelse mellom økt bølgebrytning og dominante bølgegrupper, et resultat som tidligere har blitt påvist i laboratorie- og modelleksperiment, men sjeldent ved bruk av feltobservasjoner. Tredimensjonale stereo-rekonstruksjoner viser også at ekstreme bølgekammer, både brytende og ikke-brytende, følger nylig utviklet teori om ikke-lineær bølgegruppedynamikk. Dette funnet har konsekvenser f.eks. for estimering av geometriske og kinematiske bølgeegenskaper såsom steilhet og kamhastighet fra endimensjonale tidsseriemålinger. Som følge av en langtidsanalyse av endimensjonal bølgestatistikk blir det vist at enrettet, langkammet og bratt sjø mest sannsynlig leder til ekstreme enkeltbølger med statistiske egenskaper som avviker systematisk fra ordinære statistiske modeller. Tredimensjonal, kortsiktig tid-rom-statistikk av ekstreme bølgekammer blir også undersøkt v.h.a. stereomålingene fra Ekofisk. Her blir det vist at statistiske modeller utvidet fra endimensjonale til tredimensjonale bølgefelt i snitt er velegnet til å beskrive forekomsten av de høyeste bølgekammene, spesielt for relativt store tid-rom segment.The research presented in this thesis characterizes statistical and dynamical aspects of dominant wind-generated surface gravity waves inferred from field observations in intermediate-to-deep water. Dominant waves are the most energetic waves in a sea state, and as such, understanding their behavior is important in both engineering and geophysical contexts. Large waves impart considerable impact forces on marine structures such as oil and gas platforms and offshore wind turbines, and these forces may multiply manyfold when waves break. Wave breaking in deep water, often referred to as whitecapping, is also a key, though incompletely understood, process regulating the transfer of momentum, gas and heat across the air-sea interface, and must thus be accurately parameterized in large-scale weather and climate models. Current theory holds that the wave breaking process is closely linked kinematically and dynamically to the group structure inherent in ocean surface wave fields. Wave group dynamics is also believed to govern the characteristic shape and motion of so-called extreme or rogue waves, whose correct statistical description is central to many offshore activities. The work presented herein shows, using state-of-the-art stereoscopic imaging techniques employed at the Ekofisk platform complex in the central North Sea, that large-scale wave breaking activity in the open ocean is strongly enhanced in dominant wave groups. The topic of wave group-modulated wave breaking has received considerable attention in the past two decades from theoretical, numerical and laboratory perspectives; however, quantitative field studies of the phenomenon remain comparatively rare. The current results also support the general notion that the dominant waves in a given sea state regulate the breaking of shorter waves. The statistics of extreme wave crest elevations is investigated using a novel long-term laser altimeter data set, also located at the Ekofisk field. The validity of the extreme values is verified using a newly developed despiking methodology, and the quality controlled data set, which covers storm events over an 18-year period, is used to investigate the effects of wave steepness and directionality on crest height statistics. Narrow directional spread combined with high wave steepness is found to lead to crest height statistics that deviate the most from standard linear and second-order formulations. Finally, geometric wave shape and crest speed dynamics are analyzed for the highest wave crests encountered in three-dimensional, spatially and temporally resolved segments of the stereo-reconstructed sea surface fields. The directly measured crest steepness is found to conform to the classical breaking limit of Stokes, whereas crest steepness estimated from one-dimensional time series measurements using the linear gravity-wave dispersion relation are systematically higher. This may be at least in part explained by the observation that the directly measured crest speed just before, during and after the moment of maximum crest elevation slows down compared to the linear gravity-wave phase speed estimate. For the first time, the crest speed slowdown is shown with field measurements to apply to both breaking and non-breaking dominant wave crests.Doktorgradsavhandlin