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This thesis is concerned with various aspects of stationary and nonstationary time series analysis. In the nonstationary case, we study estimation of the Wold-Cram'er evolutionary spectrum, which is a time-dependent analogue of the spectrum of a stationary process. Existing estimators of the Wold-Cram'er evolutionary spectrum suffer from several problems, including bias in boundary regions of the time-frequency plane, poor frequency resolution, and an inability to handle the presence of purely harmonic frequencies. We propose techniques to handle all three of these problems. We propose a new estimator of the Wold-Cram'er evolutionary spectrum (the BCMTFSE) which mitigates the first problem. Our estimator is based on an extrapolation of the Wold-Cram'er evolutionary spectrum in time, using an estimate of its time derivative. We apply our estimator to a set of simulated nonstationary processes with known Wold-Cram'er evolutionary spectra to demonstrate its performance. We also propose an estimator of the Wold-Cram'er evolutionary spectrum, valid for uniformly modulated processes (UMPs). This estimator mitigates the second problem, by exploiting the structure of UMPs to improve the frequency resolution of the BCMTFSE. We apply this estimator to a simulated UMP with known Wold-Cram'er evolutionary spectrum. To deal with the third problem, one can detect and remove purely harmonic frequencies before applying the BCMTFSE. Doing so requires a consideration of the aliasing problem. We propose a frequency-domain technique to detect and unalias aliased frequencies in bivariate time series, based on the observation that aliasing manifests as nonlinearity in the phase of the complex coherency between a stationary process and a time-delayed version of itself. To illustrate this ``unaliasing'' technique, we apply it to simulated data and a real-world example of solar noon flux data. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2009-02-05 10:18:13.476

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Unsatisfactory performance of a control system may have different root causes, of which diagnosis and control have been subjects of interest. Numerous approaches have been used to identify the source of the oscillatory behavior of control systems. This work will focus on the nonlinearities introduced by process equipment, more specifically, static friction (stiction) in control valves. Using shape-based stiction detection methods and surrogate testing for time series, a new detection method is proposed for systems containing one or more sticky valves. Performance of this method is validated by both simulation and industrial data. The existence of stiction in a control valve may lead to oscillations in all loops of the process. In this work, frequency analysis of multi-loop processes oscillating due to stiction will be presented. Derivation of a general mathematical representation of the condition, under which oscillations occur in a multi-loop system because of stiction, is the contribution of the proposed analysis. The proposed condition for occurrence of oscillations provides a compensation framework for this problem. In this scheme, given dynamics of the system and severity of stiction, the appropriate tuning for the controller will be found which reduces or removes oscillations from the system. An alternative compensation algorithm will also be proposed, which aims removal of oscillations from systems for which the previously proposed approach cannot permanently remove undesirable oscillations. Achieving a non-oscillatory output without making the valve stem to move more aggressively, is the main characteristic of this algorithm. / Process Control

Philosophiae Doctor - PhD / The Okavango Delta is recognized as one of the famous inland wetlands and its sustainable use is important for socio-economic development of Botswana. The Okavango delta comprises permanent swamps, seasonal swamps, and drylands on islands within the delta and the surrounding areas, sustained by Okavango river inflows from upstream and local rainfall. TheOkavango River splits into several distributary channels within the delta. Areas which are flooded annually vary in response to varying inflows into the delta. Peak inflows into the delta occur during the February to May period. Due to the low gradient over the delta, these inflows move slowly resulting in peak outflows from the delta occurring during the June to August period. The inundated area over the entire delta increases from May until it reaches maximum inAugust and starts to decrease from September, reaching minimum inundated area in the months of December and January. The incoming flood wave into the delta and maximum inundation is out of phase with the local rainfall season.Communities living within and around the delta derive their livelihoods from tourism, hunting, fishing, livestock rearing, and crop production. Crop production is carried out on drylands and within floodplains. Some of the households take advantage of the increase in soil moisture arising from this inundation along floodplains to cultivate their crops as the floods recede. This practice is locally referred to as molapo farming which highly depends on inundation of floodplains. The availability of floodplain inundation highly depends on the magnitude of inflows into the delta and the local rainfall which are highly variable resulting in uncertainty regarding successful crop production, availability of livestock grazing areas, and uncertainty in reliance on the wetlands resources such as fishing. The uncertainty experienced in timing of extreme events which cause flooding of resulting in water reaching areas or floodplains where it is not wanted, and also uncertainity in timing of low flows, therefore water not reaching some parts of the delta.Several hydrological studies have been carried out with the aim of improving the understanding of the spatial and temporal dynamics of flows throughout the delta including predicting areas that are likely to be inundated each year. The significant gap addressed by this research is to improve the understanding of the spatial and temporal influence of magnitude and timing of flows on floodplain inundation. Local rainfall on the delta is highly variable over time and space due to its convective nature. This research also addresses the rainfall temporal and spatial variations and its implications on floodplain inundation. The knowledge about spatial extent and duration of floodplain inundation should assist in predicting each year the viability of molapo farming. Three research site, Shorobe, Tubu and Xobe are selected as case studies to understand the dynamics of floodplain inundation induced either by inflows or local rainfall. Local rainfall during the December to March period enables the crops to reach maturity. The onset of the rainy season is very important in supporting sowing of crop seeds. Local rainfall on the delta varies considerably. Aerial rainfall interpolation shows a change in rainfall magnitudes over space in different rainfall months, i.e different parts of the delta receive different rainfall magnitudes in different months of the rainy season. The spatial variation is mainly associated with the migration of the ITCZ southwards first through East Africa during October andNovember and down over Southern Africa in December to February. The movement of the ITCZ brings rainfall concentration on the northern and eastern parts of the Okavango Delta during December to January and bringing rainfall concentration to the northwestern part of the delta around February. However, rainfall spatial correlation between stations can be poor even within the first 150 km therefore implying neighboring places do not experience floodplain inundation by rainfall at the same time. The poor spatial correlation of rainfall between neighboring stations reflects the erratic nature of rainfall in the Okavango Delta characterised by localized thunderstorms. Change detection shows change points in rainfall which can be associated with ENSO episodes. A change point is identified in 1976 and 1977 which can be associated with the El Nino episodes during those years and two change points identified in 1999 and 2004 which can be associated with the La Nina episodes, therefore rainfall induced floodplain inundation can also be associated with wet and dry ENSO episodes. Rainfall does not show any significant trends except for an increasing trend on 10th percentile of Shakawe rainfall. Rainfall also does not show any cyclic behavior. Rainfall over the Okavango Delta can be divided into three unique homogenious sub-regions; sub-region 1: the northern part following the GEV probability distribution and being the region with highest rainfall amounts; sub-region 2: the lower northern and the outlet parts of the Okavango Delta following the GPA distribution with moderate rainfall; and sub-region 3: the middle part of the delta extending to the western and the eastern fringes of the delta, following the P3 distribution and having the lowest rainfall.The main characteristic that defines the Okavango Delta flows at Mohembo is its cyclic behavior. Three significant cycles are identified, close to 10, 20 and 40 years. No significant trends are identified, only a decreasing trend in minimum flows. Change points are identified in 1979 and 1988 and these can be explained by the existing cyclicity since no major land use changes have taken place in the Okavango River Basin upstream before 1989. The existence of cyclicity in Okavango River flows at Mohembo also explains the periodic wetting and drying of different floodplains in the delta. A long period of low flows was experienced from 1983 until 2003 and floodplain inundation extent was greatly reduced, more especially during the 1993-2003. During the 1993-2003 period, flows could no longer reach Maun Bridge along Thamalakne River, therefore leaving molapo floodplains around Boteti River, Gomoti River and Thaoge River to dry out. The 10 and 40 year return floods are important as they indicate the probability of a flood magnitude which has potential to result in major inundation in the Okavango Delta. Therefore, flood magnitudes with recurrence interval 10 and 40 years have high probability of occurring and can cause major floodplain inundation as they can be above the 2009 flood of 969 m3/s, which was the return of major inundation of Okavango Delta floodplains after a long period of dryness. The Ngoqa-Maunachira distributary channel of the Okavango River receives 32% of flow volumes entering the Okavango Delta at Mohembo. 12 % of the Mohembo flow volumes reach the Jao-Boro distributary whilst 1% is received by the Thaoge distributary. Therefore more inundation is experienced along the Ngoqa-Maunachira system compared to the other two. Only about 2% of the Mohembo flow volumes leave the Okavango Delta through Boteti River. Long term shifting of flow direction amongst reaches along the Okavango Delta distributaries is evident more especially along the Ngoqa-Maunachira River system. This results in shifting of inundation. Sub-surface water respond significantly to local rainfall and inflows with high soil moisture conditions retained at 60 cm and 100 cm below the ground.

Floods cause widespread damage to property and life in different parts of the world. Hence there is a paramount need to develop effective methods for design flood estimation to alleviate risk associated with these extreme hydrologic events. Methods that are conventionally considered for analysis of floods focus on estimation of continuous frequency relationship between peak flow observed at a location and its corresponding exceedance probability depicting the plausible conditions in the planning horizon. These methods are commonly known as at-site flood frequency analysis (FFA) procedures. The available FFA procedures can be classified as parametric and nonparametric. Parametric methods are based on the assumption that sample (at-site data) is drawn from a population with known probability density function (PDF). Those procedures have uncertainty associated with the choice of PDF and the method for estimation of its parameters. Moreover, parametric methods are ineffective in modeling flood data if multimodality is evident in their PDF. To overcome those artifacts, a few studies attempted using kernel based nonparametric (NP) methods as an alternative to parametric methods. The NP methods are data driven and they can characterize the uncertainty in data without prior assumptions as to the form of the PDF. Conventional kernel methods have shortcomings associated with boundary leakage problem and normal reference rule (considered for estimation of bandwidth), which have implications on flood quantile estimates. To alleviate this problem, focus of NP flood frequency analysis has been on development of new kernel density estimators (kdes). Another issue in FFA is that information on the whole hydrograph (e.g., time to the peak flow, volume of the flood flow and duration of the flood event) is needed, in addition to peak flow for certain applications. An option is to perform frequency analysis on each of the variables independently. However, these variables are not independent, and hence there is a need to perform multivariate analysis to construct multivariate PDFs and use the corresponding cumulative distribution functions (CDFs) to arrive at estimates of characteristics of design flood hydrograph. In this perspective, recent focus of flood frequency analysis studies has been on development of methods to derive joint distributions of flood hydrograph related variables in a nonparametric setting. Further, in real world scenario, it is often necessary to estimate design flood quantiles at target locations that have limited or no data. Regional Flood Frequency analysis (RFFA) procedures have been developed for use in such situations. These procedures involve use of a regionalization procedure for identification of a homogeneous group of watersheds that are similar to watershed of the target site in terms of flood response. Subsequently regional frequency analysis (RFA) is performed, wherein the information pooled from the group (region) forms basis for frequency analysis to construct a CDF (growth curve) that is subsequently used to arrive at quantile estimates at the target site. Though there are various procedures for RFFA, they are largely confined to only univariate framework considering a parametric approach as the basis to arrive at required quantile estimates. Motivated by these findings, this thesis concerns development of a linear diffusion process based adaptive kernel density estimator (D-kde) based methodologies for at-site as well as regional FFA in univariate as well as bivariate settings. The D-kde alleviates boundary leakage problem and also avoids normal reference rule while estimating optimal bandwidth by using Botev-Grotowski-Kroese estimator (BGKE). Potential of the proposed methodologies in both univariate and bivariate settings is demonstrated by application to synthetic data sets of various sizes drawn from known unimodal and bimodal parametric populations, and to real world data sets from India, USA, United Kingdom and Canada. In the context of at-site univariate FFA (considering peak flows), the performance of D- kde was found to be better when compared to four parametric distribution based methods (Generalized extreme value, Generalized logistic, Generalized Pareto, Generalized Normal), thirty-two ‘kde and bandwidth estimator’ combinations that resulted from application of four commonly used kernels in conjunction with eight bandwidth estimators, and a local polynomial–based estimator. In the context of at-site bivariate FFA considering ‘peakflow-flood volume’ and ‘flood duration-flood volume’ bivariate combinations, the proposed D-kde based methodology was shown to be effective when compared to commonly used seven copulas (Gumbel-Hougaard, Frank, Clayton, Joe, Normal, Plackett, and student’s-T copulas) and Gaussian kernel in conjunction with conventional as well as BGKE bandwidth estimators. Sensitivity analysis indicated that selection of optimum number of bins is critical in implementing D-kde in bivariate setting. In the context of univariate regional flood frequency analysis (RFFA) considering peak flows, a methodology based on D-kde and Index-flood methods is proposed and its performance is shown to be better when compared to that of widely used L-moment and Index-flood based method (‘regional L-moment algorithm’) through Monte-Carlo simulation experiments on homogeneous as well as heterogeneous synthetic regions, and through leave-one-out cross validation experiment performed on data sets pertaining to 54 watersheds in Godavari river basin, India. In this context, four homogeneous groups of watersheds are delineated in Godavari river basin using kernel principal component analysis (KPCA) in conjunction with Fuzzy c-means cluster analysis in L-moment framework, as an improvement over heterogeneous regions in the area (river basin) that are currently being considered by Central Water Commission, India. In the context of bivariate RFFA two methods are proposed. They involve forming site-specific pooling groups (regions) based on either L-moment based bivariate homogeneity test (R-BHT) or bivariate Kolmogorov-Smirnov test (R-BKS), and RFA based on D-kde. Their performance is assessed by application to data sets pertaining to stations in the conterminous United States. Results indicate that the R-BKS method is better than R-BHT in predicting quantiles of bivariate flood characteristics at ungauged sites, although the size of pooling groups formed using R-BKS is, in general, smaller than size of those formed using R-BHT. In general, the performance of the methods is found to improve with increase in size of pooling groups. Overall the results indicate that the D-kde always yields bona fide PDF (and CDF) in the context of univariate as well as bivariate flood frequency analysis, as probability density is nonnegative for all data points and integrates to unity for the valid range of the data. The performance of D-kde based at-site as well as regional FFA methodologies is found to be effective in univariate as well as bivariate settings, irrespective of the nature of population and sample size. A primary assumption underlying conventional FFA procedures has been that the time series of peak flow is stationarity (temporally homogeneous). However, recent studies carried out in various parts of the World question the assumption of flood stationarity. In this perspective, Time Varying Gaussian Copula (TVGC) based methodology is proposed in the thesis for flood frequency analysis in bivariate setting, which allows relaxing the assumption of stationarity in flood related variables. It is shown to be effective than seven commonly used stationary copulas through Monte-Carlo simulation experiments and by application to data sets pertaining to stations in the conterminous United States for which null hypothesis that peak flow data were non-stationary cannot be rejected.

Spatio-temporal variation in activation rates during ventricular fibrillation (VF)provides insight into mechanisms of sustained re-entry during VF. This study had three objectives related to spatio-temporal dynamics in activation rates during VF. The first objective was to quantify spatio-temporal variability in activation rates,that is, in dominant frequencies, computed from epicardial electrograms recorded during VF in swine. Results showed that temporally and spatially, dominant frequencies variedas much as 20% of the mean dominant frequency, and the mean dominant frequencies increased during first 30 sec of VF. These results suggest that activation rates are nonstationary during VF. The second objective of the study was to develop a new stimulation protocol for quantifying restitution of action potential duration (APD) by independently controlling diastolic intervals (DI). A property of cardiac cells that determines spatio-temporal variability in dominant frequencies is restitution of APD, which relates APD to the previous DI. Independent control of DI permits explicit determination of the role of memory in restitution. Restitution functions quantified using mathematical models of activation and our stimulation protocol, showed significant hysteresis. That is, for adiastolic interval, the action potential durations were as much as 15% longer during periods when the DI were decreasing than when the DI were increasing. We verified the feasibility of implementing our protocol experimentally in isolated and perfused rat hearts with action potentials recorded using floating glass microelectrodes. The third objective of our study was to verify that spatio-temporal variability in dominant frequencies during VF could be modified using spatially distributed pacing strength stimuli. Simulated VF was induced in 400x400 and 400x800 matrices of cells. Electrical function of cells was simulated using the Luo-Rudy model. Stimulators were arranged in the matrices such that there were 5 rows of line stimulators. Results showed that it was possible to modify activations in almost 54% of the area and to modify spatio-temporal variability in activation during VF into a desired pattern by the use of synchronized pacing from multiple sites. These results support further exploration of distributed stimulation approach for potential improvements in defibrillation therapy.

There are around 10,426 bird species around the world. Recognizing the bird species for an untrained person is almost impossible either by watching or listening them. In order to identify the bird species from their sounds, there is a need for an application that can detect the bird species from its sound. Time-frequency domain analysis techniques are used to implement the application. We implemented two time-frequency domain feature extraction methods. In feature extraction, a signature matrix which consist of extracted features is created for bird sound signals. A database of signature matrix is created with bird chirps extracted features. We implemented two feature classification methods. They are auto-correlation feature classification method and reference difference feature classification method. An unknown bird chirp is compared with the database to detect the species name. The main aim of the research is to implement the time-frequency domain feature extraction method, create a signature matrix database, implement two feature classification methods and compare them. At last, bird species were identified in the research and the auto-correlation classification method detects the bird species better than the reference difference classification method.

This thesis develops a new method for time-frequency signal processing and examines the relevance of the new representation in studies of neural coding in songbirds. The method groups together associated regions of the time-frequency plane into objects defined by time-frequency contours. By combining information about structurally stable contour shapes over multiple time-scales and angles, a signal decomposition is produced that distributes resolution adaptively. As a result, distinct signal components are represented in their own most parsimonious forms.  Next, through neural recordings in singing birds, it was found that activity in song premotor cortex is significantly correlated with the objects defined by this new representation of sound. In this process, an automated way of finding sub-syllable acoustic transitions in birdsongs was first developed, and then increased spiking probability was found at the boundaries of these acoustic transitions. Finally, a new approach to study auditory cortical sequence processing more generally is proposed. In this approach, songbirds were trained to discriminate Morse-code-like sequences of clicks, and the neural correlates of this behavior were examined in primary and secondary auditory cortex. It was found that a distinct transformation of auditory responses to the sequences of clicks exists as information transferred from primary to secondary auditory areas. Neurons in secondary auditory areas respond asynchronously and selectively -- in a manner that depends on the temporal context of the click. This transformation from a temporal to a spatial representation of sound provides a possible basis for the songbird's natural ability to discriminate complex temporal sequences.

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