Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools

We explore the recently developed snapshot-based dynamic mode decomposition (DMD) technique, a matrix-free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L-shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non-linear incompressible discontinuous Galerkin Navier?Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non-linear and linearised Navier?Stokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier?Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three-dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier?Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L-shaped geometry and control the most unstable 3D mode.

Decoding complex flow phenomena via Dynamic Mode Decomposition

In this thesis, the viability of the Dynamic Mode Decomposition (DMD) as a technique to analyze and model complex dynamic real-world systems is presented. This method derives, directly from data, computationally efficient reduced-order models (ROMs) which can replace too onerous or unavailable high-fidelity physics-based models. Optimizations and extensions to the standard implementation of the methodology are proposed, investigating diverse case studies related to the decoding of complex flow phenomena. The flexibility of this data-driven technique allows its application to high-fidelity fluid dynamics simulations, as well as time series of real systems observations. The resulting ROMs are tested against two tasks: (i) reduction of the storage requirements of high-fidelity simulations or observations; (ii) interpolation and extrapolation of missing data. The capabilities of DMD can also be exploited to alleviate the cost of onerous studies that require many simulations, such as uncertainty quantification analysis, especially when dealing with complex high-dimensional systems. In this context, a novel approach to address parameter variability issues when modeling systems with space and time-variant response is proposed. Specifically, DMD is merged with another model-reduction technique, namely the Polynomial Chaos Expansion, for uncertainty quantification purposes. Useful guidelines for DMD deployment result from the study, together with the demonstration of its potential to ease diagnosis and scenario analysis when complex flow processes are involved.

A novel spectral representation of electromyographic signals

Time/frequency and temporal analyses have been widely used in biomedical signal processing. These methods represent important characteristics of a signal in both time and frequency domain. In this way, essential features of the signal can be viewed and analysed in order to understand or model the physiological system. Historically, Fourier spectral analyses have provided a general method for examining the global energy/frequency distributions. However, an assumption inherent to these methods is the stationarity of the signal. As a result, Fourier methods are not generally an appropriate approach in the investigation of signals with transient components. This work presents the application of a new signal processing technique, empirical mode decomposition and the Hilbert spectrum, in the analysis of electromyographic signals. The results show that this method may provide not only an increase in the spectral resolution but also an insight into the underlying process of the muscle contraction.

EMD: A novel technique for the study of tremor time series

This paper introduces the Hilbert Analysis (HA), which is a novel digital signal processing technique, for the investigation of tremor. The HA is formed by two complementary tools, i.e. the Empirical Mode Decomposition (EMD) and the Hilbert Spectrum (HS). In this work we show that the EMD can automatically detect and isolate tremulous and voluntary movements from experimental signals collected from 31 patients with different conditions. Our results also suggest that the tremor may be described by a new class of mathematical functions defined in the HA framework. In a further study, the HS was employed for visualization of the energy activities of signals. This tool introduces the concept of instantaneous frequency in the field of tremor. In addition, it could provide, in a time-frequency-energy plot, a clear visualization of local activities of tremor energy over the time. The HA demonstrated to be very useful to perform objective measurements of any kind of tremor and can therefore be used to perform functional assessment.

Application of EMD as a novel technique for the study of tremor time series

This paper introduces the Hilbert Analysis (HA), which is a novel digital signal processing technique, for the investigation of tremor. The HA is formed by two complementary tools, i.e. the Empirical Mode Decomposition (EMD) and the Hilbert Spectrum (HS). In this work we show that the EMD can automatically detect and isolate tremulous and voluntary movements from experimental signals collected from 31 patients with different conditions. Our results also suggest that the tremor may be described by a new class of mathematical functions defined in the HA framework. In a further study, the HS was employed for visualization of the energy activities of signals. This tool introduces the concept of instantaneous frequency in the field of tremor. In addition, it could provide, in a time-frequency energy plot, a clear visualization of local activities of tremor energy over the time. The HA demonstrated to be very useful to perform objective measurements of any kind of tremor and can therefore be used to perform functional assessment.

Neural correlates of true and false memory in mild cognitive impairment

The goal of this research was to investigate the changes in neural processing in mild cognitive impairment. We measured phase synchrony, amplitudes, and event-related potentials in veridical and false memory to determine whether these differed in participants with mild cognitive impairment compared with typical, age-matched controls. Empirical mode decomposition phase locking analysis was used to assess synchrony, which is the first time this analysis technique has been applied in a complex cognitive task such as memory processing. The technique allowed assessment of changes in frontal and parietal cortex connectivity over time during a memory task, without a priori selection of frequency ranges, which has been shown previously to influence synchrony detection. Phase synchrony differed significantly in its timing and degree between participant groups in the theta and alpha frequency ranges. Timing differences suggested greater dependence on gist memory in the presence of mild cognitive impairment. The group with mild cognitive impairment had significantly more frontal theta phase locking than the controls in the absence of a significant behavioural difference in the task, providing new evidence for compensatory processing in the former group. Both groups showed greater frontal phase locking during false than true memory, suggesting increased searching when no actual memory trace was found. Significant inter-group differences in frontal alpha phase locking provided support for a role for lower and upper alpha oscillations in memory processing. Finally, fronto-parietal interaction was significantly reduced in the group with mild cognitive impairment, supporting the notion that mild cognitive impairment could represent an early stage in Alzheimer’s disease, which has been described as a ‘disconnection syndrome’.

Final warming of the Southern Hemisphere polar vortex in high- and low-top CMIP5 models

The final warming date of the polar vortex is a key component of Southern Hemisphere stratospheric and tropospheric variability in spring and summer. We examine the effect of external forcings on Southern Hemisphere final warming date, and the sensitivity of any projected changes to model representation of the stratosphere. Final warming date is calculated using a temperature-based diagnostic for ensembles of high- and low-top CMIP5 models, under the CMIP5 historical, RCP4.5, and RCP8.5 forcing scenarios. The final warming date in the models is generally too late in comparison with those from reanalyses: around two weeks too late in the low-top ensemble, and around one week too late in the high-top ensemble. Ensemble Empirical Mode Decomposition (EEMD) is used to analyse past and future change in final warming date. Both the low- and high-top ensemble show characteristic behaviour expected in response to changes in greenhouse gas and stratospheric ozone concentrations. In both ensembles, under both scenarios, an increase in final warming date is seen between 1850 and 2100, with the latest dates occurring in the early twenty-first century, associated with the minimum in stratospheric ozone concentrations in this period. However, this response is more pronounced in the high-top ensemble. The high-top models show a delay in final warming date in RCP8.5 that is not produced by the low-top models, which are shown to be less responsive to greenhouse gas forcing. This suggests that it may be necessary to use stratosphere resolving models to accurately predict Southern Hemisphere surface climate change.

Method for exploratory cluster analysis and visualisation of single-trial ERP ensembles

Background: The validity of ensemble averaging on event-related potential (ERP) data has been questioned, due to its assumption that the ERP is identical across trials. Thus, there is a need for preliminary testing for cluster structure in the data. New method: We propose a complete pipeline for the cluster analysis of ERP data. To increase the signalto-noise (SNR) ratio of the raw single-trials, we used a denoising method based on Empirical Mode Decomposition (EMD). Next, we used a bootstrap-based method to determine the number of clusters, through a measure called the Stability Index (SI). We then used a clustering algorithm based on a Genetic Algorithm (GA)to define initial cluster centroids for subsequent k-means clustering. Finally, we visualised the clustering results through a scheme based on Principal Component Analysis (PCA). Results: After validating the pipeline on simulated data, we tested it on data from two experiments – a P300 speller paradigm on a single subject and a language processing study on 25 subjects. Results revealed evidence for the existence of 6 clusters in one experimental condition from the language processing study. Further, a two-way chi-square test revealed an influence of subject on cluster membership.

EMD performance comparison: single vs double floating points

Empirical mode decomposition (EMD) is a data-driven method used to decompose data into oscillatory components. This paper examines to what extent the defined algorithm for EMD might be susceptible to data format. Two key issues with EMD are its stability and computational speed. This paper shows that for a given signal there is no significant difference between results obtained with single (binary32) and double (binary64) floating points precision. This implies that there is no benefit in increasing floating point precision when performing EMD on devices optimised for single floating point format, such as graphical processing units (GPUs).

Atenuação de ruídos coerentes utilizando decomposição em modos empíricos

The seismic processing technique has the main objective to provide adequate picture of geological structures from subsurface of sedimentary basins. Among the key steps of this process is the enhancement of seismic reflections by filtering unwanted signals, called seismic noise, the improvement of signals of interest and the application of imaging procedures. The seismic noise may appear random or coherent. This dissertation will present a technique to attenuate coherent noise, such as ground roll and multiple reflections, based on Empirical Mode Decomposition method. This method will be applied to decompose the seismic trace into Intrinsic Mode Functions. These functions have the properties of being symmetric, with local mean equals zero and the same number of zero-crossing and extremes. The developed technique was tested on synthetic and real data, and the results were considered encouraging

Classificação de sinais acústicos utilizando a transformada wavelet discreta e a decomposição de modo empírico: aplicações na área de alimentos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Global and regional sea level variations in the recent past and future: insight from observations and modeling

This work is focused on the analysis of sea–level change (last century), based mainly on instrumental observations. During this period, individual components of sea–level change are investigated, both at global and regional scales. Some of the geophysical processes responsible for current sea-level change such as glacial isostatic adjustments and current melting terrestrial ice sources, have been modeled and compared with observations. A new value of global mean sea level change based of tide gauges observations has been independently assessed in 1.5 mm/year, using corrections for glacial isostatic adjustment obtained with different models as a criterion for the tide gauge selection. The long wavelength spatial variability of the main components of sea–level change has been investigated by means of traditional and new spectral methods. Complex non–linear trends and abrupt sea–level variations shown by tide gauges records have been addressed applying different approaches to regional case studies. The Ensemble Empirical Mode Decomposition technique has been used to analyse tide gauges records from the Adriatic Sea to ascertain the existence of cyclic sea-level variations. An Early Warning approach have been adopted to detect tipping points in sea–level records of North East Pacific and their relationship with oceanic modes. Global sea–level projections to year 2100 have been obtained by a semi-empirical approach based on the artificial neural network method. In addition, a model-based approach has been applied to the case of the Mediterranean Sea, obtaining sea-level projection to year 2050.

A novel detection method for determining a surgeon's fatigue and hand tremor

The thesis presents new methodology and algorithms that can be used to analyse and measure the hand tremor and fatigue of surgeons while performing surgery. This will assist them in deriving useful information about their fatigue levels, and make them aware of the changes in their tool point accuracies. This thesis proposes that muscular changes of surgeons, which occur through a day of operating, can be monitored using Electromyography (EMG) signals. The multi-channel EMG signals are measured at different muscles in the upper arm of surgeons. The dependence of EMG signals has been examined to test the hypothesis that EMG signals are coupled with and dependent on each other. The results demonstrated that EMG signals collected from different channels while mimicking an operating posture are independent. Consequently, single channel fatigue analysis has been performed. In measuring hand tremor, a new method for determining the maximum tremor amplitude using Principal Component Analysis (PCA) and a new technique to detrend acceleration signals using Empirical Mode Decomposition algorithm were introduced. This tremor determination method is more representative for surgeons and it is suggested as an alternative fatigue measure. This was combined with the complexity analysis method, and applied to surgically captured data to determine if operating has an effect on a surgeon’s fatigue and tremor levels. It was found that surgical tremor and fatigue are developed throughout a day of operating and that this could be determined based solely on their initial values. Finally, several Nonlinear AutoRegressive with eXogenous inputs (NARX) neural networks were evaluated. The results suggest that it is possible to monitor surgeon tremor variations during surgery from their EMG fatigue measurements.

Towards a unified understanding of event-related changes in the EEG:the Firefly model of synchronization through cross-frequency phase modulation

Although event-related potentials (ERPs) are widely used to study sensory, perceptual and cognitive processes, it remains unknown whether they are phase-locked signals superimposed upon the ongoing electroencephalogram (EEG) or result from phase-alignment of the EEG. Previous attempts to discriminate between these hypotheses have been unsuccessful but here a new test is presented based on the prediction that ERPs generated by phase-alignment will be associated with event-related changes in frequency whereas evoked-ERPs will not. Using empirical mode decomposition (EMD), which allows measurement of narrow-band changes in the EEG without predefining frequency bands, evidence was found for transient frequency slowing in recognition memory ERPs but not in simulated data derived from the evoked model. Furthermore, the timing of phase-alignment was frequency dependent with the earliest alignment occurring at high frequencies. Based on these findings, the Firefly model was developed, which proposes that both evoked and induced power changes derive from frequency-dependent phase-alignment of the ongoing EEG. Simulated data derived from the Firefly model provided a close match with empirical data and the model was able to account for i) the shape and timing of ERPs at different scalp sites, ii) the event-related desynchronization in alpha and synchronization in theta, and iii) changes in the power density spectrum from the pre-stimulus baseline to the post-stimulus period. The Firefly Model, therefore, provides not only a unifying account of event-related changes in the EEG but also a possible mechanism for cross-frequency information processing.

Atenuação de ruídos coerentes utilizando decomposição em modos empíricos

The seismic processing technique has the main objective to provide adequate picture of geological structures from subsurface of sedimentary basins. Among the key steps of this process is the enhancement of seismic reflections by filtering unwanted signals, called seismic noise, the improvement of signals of interest and the application of imaging procedures. The seismic noise may appear random or coherent. This dissertation will present a technique to attenuate coherent noise, such as ground roll and multiple reflections, based on Empirical Mode Decomposition method. This method will be applied to decompose the seismic trace into Intrinsic Mode Functions. These functions have the properties of being symmetric, with local mean equals zero and the same number of zero-crossing and extremes. The developed technique was tested on synthetic and real data, and the results were considered encouraging