Chaotic Behaviour of Active Magnetic Bearing System by Time Series Analysis

Chaotic behaviour is one of the hardest problems that can happen in nonlinear dynamical systems with severe nonlinearities. It makes the system's responses unpredictable. It makes the system's responses to behave similar to noise. In some applications it should be avoided. One of the approaches to detect the chaotic behaviour is nding the Lyapunov exponent through examining the dynamical equation of the system. It needs a model of the system. The goal of this study is the diagnosis of chaotic behaviour by just exploring the data (signal) without using any dynamical model of the system. In this work two methods are tested on the time series data collected from AMB (Active Magnetic Bearing) system sensors. The rst method is used to nd the largest Lyapunov exponent by Rosenstein method. The second method is a 0-1 test for identifying chaotic behaviour. These two methods are used to detect if the data is chaotic. By using Rosenstein method it is needed to nd the minimum embedding dimension. To nd the minimum embedding dimension Cao method is used. Cao method does not give just the minimum embedding dimension, it also gives the order of the nonlinear dynamical equation of the system and also it shows how the system's signals are corrupted with noise. At the end of this research a test called runs test is introduced to show that the data is not excessively noisy.

On Time Series Analysis of Public Health and Biomedical Data

A time series is a sequence of observations made over time. Examples in public health include daily ozone concentrations, weekly admissions to an emergency department or annual expenditures on health care in the United States. Time series models are used to describe the dependence of the response at each time on predictor variables including covariates and possibly previous values in the series. Time series methods are necessary to account for the correlation among repeated responses over time. This paper gives an overview of time series ideas and methods used in public health research.

Environmental variables modeling based on remote sensing data using time series analysis: forestry and agricultural applications

En la actualidad, el seguimiento de la dinámica de los procesos medio ambientales está considerado como un punto de gran interés en el campo medioambiental. La cobertura espacio temporal de los datos de teledetección proporciona información continua con una alta frecuencia temporal, permitiendo el análisis de la evolución de los ecosistemas desde diferentes escalas espacio-temporales. Aunque el valor de la teledetección ha sido ampliamente probado, en la actualidad solo existe un número reducido de metodologías que permiten su análisis de una forma cuantitativa. En la presente tesis se propone un esquema de trabajo para explotar las series temporales de datos de teledetección, basado en la combinación del análisis estadístico de series de tiempo y la fenometría. El objetivo principal es demostrar el uso de las series temporales de datos de teledetección para analizar la dinámica de variables medio ambientales de una forma cuantitativa. Los objetivos específicos son: (1) evaluar dichas variables medio ambientales y (2) desarrollar modelos empíricos para predecir su comportamiento futuro. Estos objetivos se materializan en cuatro aplicaciones cuyos objetivos específicos son: (1) evaluar y cartografiar estados fenológicos del cultivo del algodón mediante análisis espectral y fenometría, (2) evaluar y modelizar la estacionalidad de incendios forestales en dos regiones bioclimáticas mediante modelos dinámicos, (3) predecir el riesgo de incendios forestales a nivel pixel utilizando modelos dinámicos y (4) evaluar el funcionamiento de la vegetación en base a la autocorrelación temporal y la fenometría. Los resultados de esta tesis muestran la utilidad del ajuste de funciones para modelizar los índices espectrales AS1 y AS2. Los parámetros fenológicos derivados del ajuste de funciones permiten la identificación de distintos estados fenológicos del cultivo del algodón. El análisis espectral ha demostrado, de una forma cuantitativa, la presencia de un ciclo en el índice AS2 y de dos ciclos en el AS1 así como el comportamiento unimodal y bimodal de la estacionalidad de incendios en las regiones mediterránea y templada respectivamente. Modelos autorregresivos han sido utilizados para caracterizar la dinámica de la estacionalidad de incendios y para predecir de una forma muy precisa el riesgo de incendios forestales a nivel pixel. Ha sido demostrada la utilidad de la autocorrelación temporal para definir y caracterizar el funcionamiento de la vegetación a nivel pixel. Finalmente el concepto “Optical Functional Type” ha sido definido, donde se propone que los pixeles deberían ser considerados como unidades temporales y analizados en función de su dinámica temporal. ix SUMMARY A good understanding of land surface processes is considered as a key subject in environmental sciences. The spatial-temporal coverage of remote sensing data provides continuous observations with a high temporal frequency allowing the assessment of ecosystem evolution at different temporal and spatial scales. Although the value of remote sensing time series has been firmly proved, only few time series methods have been developed for analyzing this data in a quantitative and continuous manner. In the present dissertation a working framework to exploit Remote Sensing time series is proposed based on the combination of Time Series Analysis and phenometric approach. The main goal is to demonstrate the use of remote sensing time series to analyze quantitatively environmental variable dynamics. The specific objectives are (1) to assess environmental variables based on remote sensing time series and (2) to develop empirical models to forecast environmental variables. These objectives have been achieved in four applications which specific objectives are (1) assessing and mapping cotton crop phenological stages using spectral and phenometric analyses, (2) assessing and modeling fire seasonality in two different ecoregions by dynamic models, (3) forecasting forest fire risk on a pixel basis by dynamic models, and (4) assessing vegetation functioning based on temporal autocorrelation and phenometric analysis. The results of this dissertation show the usefulness of function fitting procedures to model AS1 and AS2. Phenometrics derived from function fitting procedure makes it possible to identify cotton crop phenological stages. Spectral analysis has demonstrated quantitatively the presence of one cycle in AS2 and two in AS1 and the unimodal and bimodal behaviour of fire seasonality in the Mediterranean and temperate ecoregions respectively. Autoregressive models has been used to characterize the dynamics of fire seasonality in two ecoregions and to forecasts accurately fire risk on a pixel basis. The usefulness of temporal autocorrelation to define and characterized land surface functioning has been demonstrated. And finally the “Optical Functional Types” concept has been proposed, in this approach pixels could be as temporal unities based on its temporal dynamics or functioning.

Multivariate ARIMA Compositional Time Series Analysis

A compositional time series is obtained when a compositional data vector is observed atdifferent points in time. Inherently, then, a compositional time series is a multivariatetime series with important constraints on the variables observed at any instance in time.Although this type of data frequently occurs in situations of real practical interest, atrawl through the statistical literature reveals that research in the field is very much in itsinfancy and that many theoretical and empirical issues still remain to be addressed. Anyappropriate statistical methodology for the analysis of compositional time series musttake into account the constraints which are not allowed for by the usual statisticaltechniques available for analysing multivariate time series. One general approach toanalyzing compositional time series consists in the application of an initial transform tobreak the positive and unit sum constraints, followed by the analysis of the transformedtime series using multivariate ARIMA models. In this paper we discuss the use of theadditive log-ratio, centred log-ratio and isometric log-ratio transforms. We also presentresults from an empirical study designed to explore how the selection of the initialtransform affects subsequent multivariate ARIMA modelling as well as the quality ofthe forecasts

A time series analysis of meteorological factors and hospital outpatient admissions for cardiovascular disease in the Northern district of Guizhou Province, China

Findings on the effects of weather on health, especially the effects of ambient temperature on overall morbidity, remain inconsistent. We conducted a time series study to examine the acute effects of meteorological factors (mainly air temperature) on daily hospital outpatient admissions for cardiovascular disease (CVD) in Zunyi City, China, from January 1, 2007 to November 30, 2009. We used the generalized additive model with penalized splines to analyze hospital outpatient admissions, climatic parameters, and covariate data. Results show that, in Zunyi, air temperature was associated with hospital outpatient admission for CVD. When air temperature was less than 10°C, hospital outpatient admissions for CVD increased 1.07-fold with each increase of 1°C, and when air temperature was more than 10°C, an increase in air temperature by 1°C was associated with a 0.99-fold decrease in hospital outpatient admissions for CVD over the previous year. Our analyses provided statistically significant evidence that in China meteorological factors have adverse effects on the health of the general population. Further research with consistent methodology is needed to clarify the magnitude of these effects and to show which populations and individuals are vulnerable.

Multivariate ARIMA Compositional Time Series Analysis

A compositional time series is obtained when a compositional data vector is observed at different points in time. Inherently, then, a compositional time series is a multivariate time series with important constraints on the variables observed at any instance in time. Although this type of data frequently occurs in situations of real practical interest, a trawl through the statistical literature reveals that research in the field is very much in its infancy and that many theoretical and empirical issues still remain to be addressed. Any appropriate statistical methodology for the analysis of compositional time series must take into account the constraints which are not allowed for by the usual statistical techniques available for analysing multivariate time series. One general approach to analyzing compositional time series consists in the application of an initial transform to break the positive and unit sum constraints, followed by the analysis of the transformed time series using multivariate ARIMA models. In this paper we discuss the use of the additive log-ratio, centred log-ratio and isometric log-ratio transforms. We also present results from an empirical study designed to explore how the selection of the initial transform affects subsequent multivariate ARIMA modelling as well as the quality of the forecasts

Time series analysis of lava flux

We have applied time series analytical techniques to the flux of lava from an extrusive eruption. Tilt data acting as a proxy for flux are used in a case study of the May–August 1997 period of the eruption at Soufrière Hills Volcano, Montserrat. We justify the use of such a proxy by simple calibratory arguments. Three techniques of time series analysis are employed: spectral, spectrogram and wavelet methods. In addition to the well-known ~9-hour periodicity shown by these data, a previously unknown periodic flux variability is revealed by the wavelet analysis as a 3-day cycle of frequency modulation during June–July 1997, though the physical mechanism responsible is not clear. Such time series analysis has potential for other lava flux proxies at other types of volcanoes.

A Time-Series Analysis of the H alpha Emission Line in V3885 Sagitarii

Flickering is a phenomenon related to mass accretion observed among many classes of astrophysical objects. In this paper we present a study of flickering emission lines and the continuum of the cataclysmic variable V3885 Sgr. The flickering behavior was first analyzed through statistical analysis and the power spectra of lightcurves. Autocorrelation techniques were then employed to estimate the flickering timescale of flares. A cross-correlation study between the line and its underlying continuum variability is presented. The cross-correlation between the photometric and spectroscopic data is also discussed. Periodograms, calculated using emission-line data, show a behavior that is similar to those obtained from photometric datasets found in the literature, with a plateau at lower frequencies and a power-law at higher frequencies. The power-law index is consistent with stochastic events. The cross-correlation study indicates the presence of a correlation between the variability on Ha and its underlying continuum. Flickering timescales derived from the photometric data were estimated to be 25 min for two lightcurves and 10 min for one of them. The average timescales of the line flickering is 40 min, while for its underlying continuum it drops to 20 min.

Structural Health Monitoring in Smart Structures Through Time Series Analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Time series analysis of jaw muscle contraction and tissue deformation during mastication in miniature pigs

Masticatory muscle contraction causes both jaw movement and tissue deformation during function. Natural chewing data from 25 adult miniature pigs were studied by means of time series analysis. The data set included simultaneous recordings of electromyography (EMG) from bilateral masseter (MA), zygomaticomandibularis (ZM) and lateral pterygoid muscles, bone surface strains from the left squamosal bone (SQ), condylar neck (CD) and mandibular corpus (MD), and linear deformation of the capsule of the jaw joint measured bilaterally using differential variable reluctance transducers. Pairwise comparisons were examined by calculating the cross-correlation functions. Jaw-adductor muscle activity of MA and ZM was found to be highly cross-correlated with CD and SQ strains and weakly with MD strain. No muscle’s activity was strongly linked to capsular deformation of the jaw joint, nor were bone strains and capsular deformation tightly linked. Homologous muscle pairs showed the greatest synchronization of signals, but the signals themselves were not significantly more correlated than those of non-homologous muscle pairs. These results suggested that bone strains and capsular deformation are driven by different mechanical regimes. Muscle contraction and ensuing reaction forces are probably responsible for bone strains, whereas capsular deformation is more likely a product of movement.

Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

Development of record-breaking statistics for climatological time-series analysis

The number of record-breaking events expected to occur in a strictly stationary time-series depends only on the number of values in the time-series, regardless of distribution. This holds whether the events are record-breaking highs or lows and whether we count from past to present or present to past. However, these symmetries are broken in distinct ways by trends in the mean and variance. We define indices that capture this information and use them to detect weak trends from multiple time-series. Here, we use these methods to answer the following questions: (1) Is there a variability trend among globally distributed surface temperature time-series? We find a significant decreasing variability over the past century for the Global Historical Climatology Network (GHCN). This corresponds to about a 10% change in the standard deviation of inter-annual monthly mean temperature distributions. (2) How are record-breaking high and low surface temperatures in the United States affected by time period? We investigate the United States Historical Climatology Network (USHCN) and find that the ratio of record-breaking highs to lows in 2006 increases as the time-series extend further into the past. When we consider the ratio as it evolves with respect to a fixed start year, we find it is strongly correlated with the ensemble mean. We also compare the ratios for USHCN and GHCN (minus USHCN stations). We find the ratios grow monotonically in the GHCN data set, but not in the USHCN data set. (3) Do we detect either mean or variance trends in annual precipitation within the United States? We find that the total annual and monthly precipitation in the United States (USHCN) has increased over the past century. Evidence for a trend in variance is inconclusive.

Campylobacter monitoring in German broiler flocks: an explorative time series analysis

Campylobacter, a major zoonotic pathogen, displays seasonality in poultry and in humans. In order to identify temporal patterns in the prevalence of thermophilic Campylobacter spp. in a voluntary monitoring programme in broiler flocks in Germany and in the reported human incidence, time series methods were used. The data originated between May 2004 and June 2007. By the use of seasonal decomposition, autocorrelation and cross-correlation functions, it could be shown that an annual seasonality is present. However, the peak month differs between sample submission, prevalence in broilers and human incidence. Strikingly, the peak in human campylobacterioses preceded the peak in broiler prevalence in Lower Saxony rather than occurring after it. Significant cross-correlations between monthly temperature and prevalence in broilers as well as between human incidence, monthly temperature, rainfall and wind-force were identified. The results highlight the necessity to quantify the transmission of Campylobacter from broiler to humans and to include climatic factors in order to gain further insight into the epidemiology of this zoonotic disease.

The Moderating Role of Electoral Pressure on Congressional Ideological Polarization: A Cross-Sectional Time-Series Analysis

Reelection and self-interest are recurring themes in the study of our congressional leaders. To date, many studies have already been done on the trends between elections, party affiliation, and voting behavior in Congress. However, because a plethora of data has been collected on both elections and congressional voting, the ability to draw a connection between the two provides a very reasonable prospect. This project analyzes whether voting shifts in congressional elections have an effect on congressional voting. Will a congressman become ideologically more polarized when his electoral margins increase? Essentially, this paper assumes that all congressmen are ideologically polarized, and it is elections which serve to reel congressmen back toward the ideological middle. The election and ideological data for this study, which spans from the 56th to the 107th Congress, finds statistically significant relationships between these two variables. In fact, congressman pay attention to election returns when voting in Congress. When broken down by party, Democrats are more exhibitive of this phenomenon, which suggest that Democrats may be more likely to intrinsically follow the popular model of representation. Meanwhile, it can be hypothesized that insignificant results for Republicans indicate that Republicans may follow a trustee model of representation.

Implementation of active surveillance cultures and associated infection control practices for the reduction of methicillin resistant Staphylococcus aureus in the healthcare setting: An interrupted time series analysis

OBJECTIVE. To determine the effectiveness of active surveillance cultures and associated infection control practices on the incidence of methicillin resistant Staphylococcus aureus (MRSA) in the acute care setting. DESIGN. A historical analysis of existing clinical data utilizing an interrupted time series design. ^ SETTING AND PARTICIPANTS. Patients admitted to a 260-bed tertiary care facility in Houston, TX between January 2005 through December 2010. ^ INTERVENTION. Infection control practices, including enhanced barrier precautions, compulsive hand hygiene, disinfection and environmental cleaning, and executive ownership and education, were simultaneously introduced during a 5-month intervention implementation period culminating with the implementation of active surveillance screening. Beginning June 2007, all high risk patients were cultured for MRSA nasal carriage within 48 hours of admission. Segmented Poisson regression was used to test the significance of the difference in incidence of healthcare-associated MRSA during the 29-month pre-intervention period compared to the 43-month post-intervention period. ^ RESULTS. A total of 9,957 of 11,095 high-risk patients (89.7%) were screened for MRSA carriage during the intervention period. Active surveillance cultures identified 1,330 MRSA-positive patients (13.4%) contributing to an admission prevalence of 17.5% in high-risk patients. The mean rate of healthcare-associated MRSA infection and colonization decreased from 1.1 per 1,000 patient-days in the pre-intervention period to 0.36 per 1,000 patient-days in the post-intervention period (P<0.001). The effect of the intervention in association with the percentage of S. aureus isolates susceptible to oxicillin were shown to be statistically significantly associated with the incidence of MRSA infection and colonization (IRR = 0.50, 95% CI = 0.31-0.80 and IRR = 0.004, 95% CI = 0.00003-0.40, respectively). ^ CONCLUSIONS. It can be concluded that aggressively targeting patients at high risk for colonization of MRSA with active surveillance cultures and associated infection control practices as part of a multifaceted, hospital-wide intervention is effective in reducing the incidence of healthcare-associated MRSA.^