Academic literature on the topic 'High frequency averaging'

This paper presents the optimization of input amplitudes for mechanical control-affine systems with high-frequency, high-amplitude inputs. The problem consists of determining the input waveform shapes and the relative phases between inputs to minimize the input amplitudes while accomplishing some control objective. The effects of the input waveforms and relative phases on the dynamics are investigated using averaging. It is shown that of all zero-mean, periodic functions, square waves require the smallest amplitudes to accomplish a control objective. Using the averaging theorem the problem of input optimization is transformed into a constrained optimization problem. The constraints are algebraic nonlinear equalities in terms of the amplitudes of the inputs and their relative phases. The constrained optimization problem may be solved using analytical or numerical methods. A second approach uses finite Fourier series to solve the input optimization problem. This second approach confirms the earlier results concerning minimum amplitude inputs and is then applied to the problem of minimizing control energy.

A frequency averaging framework is proposed for the solution of complex linear dynamic systems. It is remarkable that, while the mid-frequency region is usually very challenging, a smooth transition from low- through mid- and high-frequency ranges is possible and all ranges can now be considered in a single framework. An interpretation of the frequency averaging in the time domain is presented and it is explained that the average may be evaluated very efficiently in terms of system solutions.

We consider microstructured thin elastic plates that have an underlying periodic structure, and develop an asymptotic continuum model that captures the essential microstructural behaviour entirely in a macroscale setting. The asymptotics are based upon a two-scale approach and are valid even at high frequencies when the wavelength and microscale length are of the same order. The general theory is illustrated via one- and two-dimensional model problems that have zero-frequency stop bands that preclude conventional averaging and homogenization theories. Localized defect modes created by material variations are also modelled using the theory and compared with numerical simulations.

An internet-based, real-time, Global Positioning System (GPS) ---synchronized relative to the wide-area frequency-monitoring network (FNET) ---has been developed at Virginia Tech. In this FNET system, an algorithm that employs the relationship between phasor angles and deviated frequency [13] is used to calculate both frequency and its rate of change. Tests of the algorithm disclose that, for non-pure sinusoidal input (as compared to pure sinusoidal input), significant errors in the output frequency will result. Three approaches for increasing the accuracy of the output frequency were compared. The first---increasing the number of samples per cycle N---proved ineffective. The second---using the average of the first estimated frequencies rather than the instant first estimated frequency as the resampling frequency---produces a moderate increase in accuracy of the frequency estimation. The third---multiple resampling---significantly increased accuracy. But both the second and the third become ineffective to the extent the input is not pure sinusoidal. From a practical standpoint, attention needs to be paid toward eliminating noise in the input data from the power grid so as to make it more purely sinusoidal. Therefore, it will be worthwhile to test more sophisticated digital filters for processing the input data before feeding it to the algorithm.
Master of Science

Cette thèse étudie la problématique du fonctionnement sans capteur et à basse vitesse des moteurs synchrones à aimant permanent par l'injection des signaux. Nous nous focalisons sur les effets de la saturation magnétique car leur compensation est primordiale pour résoudre cette problématique. Nous proposons une méthode originale pour modéliser la saturation magnétique en utilisant une approche énergétique (les formulations Lagrangienne et Hamiltonienne), où les symétries physiques sont exploitées pour simplifier l'expression de l'énergie magnétique. Les données expérimentales montrent qu'un polynôme de degré 4 est suffisant pour décrire avec précision les effets de la saturation. Ensuite, nous proposons une analyse claire et originale basée sur la moyennisation de second ordre et qui explique comment obtenir l'information de position à partir de l'injection des signaux (en utilisant le modèle proposé). Nous donnons une relation explicite entre les oscillations des courants statoriques et la position du rotor; cette relation est utilisée en temps réel. Ce modèle de saturation magnétique ainsi que la procédure d'estimation de position ont été testés et validés sur deux types de moteurs : avec des aimants permanents à l'intérieur ou sur la surface du rotor. Les résultats expérimentaux obtenus sur un banc de test montrent que les erreurs d'estimation de la position du rotor n'excèdent pas quelques degrés électriques dans la zone d'opération à basse vitesse.

Nous développons dans cette thèse, des méthodes de bootstrap pour les données financières de hautes fréquences. Les deux premiers essais focalisent sur les méthodes de bootstrap appliquées à l’approche de "pré-moyennement" et robustes à la présence d’erreurs de microstructure. Le "pré-moyennement" permet de réduire l’influence de l’effet de microstructure avant d’appliquer la volatilité réalisée. En se basant sur cette ap- proche d’estimation de la volatilité intégrée en présence d’erreurs de microstructure, nous développons plusieurs méthodes de bootstrap qui préservent la structure de dépendance et l’hétérogénéité dans la moyenne des données originelles. Le troisième essai développe une méthode de bootstrap sous l’hypothèse de Gaussianité locale des données financières de hautes fréquences. Le premier chapitre est intitulé: "Bootstrap inference for pre-averaged realized volatility based on non-overlapping returns". Nous proposons dans ce chapitre, des méthodes de bootstrap robustes à la présence d’erreurs de microstructure. Particulièrement nous nous sommes focalisés sur la volatilité réalisée utilisant des rendements "pré-moyennés" proposés par Podolskij et Vetter (2009), où les rendements "pré-moyennés" sont construits sur des blocs de rendements à hautes fréquences consécutifs qui ne se chevauchent pas. Le "pré-moyennement" permet de réduire l’influence de l’effet de microstructure avant d’appliquer la volatilité réalisée. Le non-chevauchement des blocs fait que les rendements "pré-moyennés" sont asymptotiquement indépendants, mais possiblement hétéroscédastiques. Ce qui motive l’application du wild bootstrap dans ce contexte. Nous montrons la validité théorique du bootstrap pour construire des intervalles de type percentile et percentile-t. Les simulations Monte Carlo montrent que le bootstrap peut améliorer les propriétés en échantillon fini de l’estimateur de la volatilité intégrée par rapport aux résultats asymptotiques, pourvu que le choix de la variable externe soit fait de façon appropriée. Nous illustrons ces méthodes en utilisant des données financières réelles. Le deuxième chapitre est intitulé : "Bootstrapping pre-averaged realized volatility under market microstructure noise". Nous développons dans ce chapitre une méthode de bootstrap par bloc basée sur l’approche "pré-moyennement" de Jacod et al. (2009), où les rendements "pré-moyennés" sont construits sur des blocs de rendements à haute fréquences consécutifs qui se chevauchent. Le chevauchement des blocs induit une forte dépendance dans la structure des rendements "pré-moyennés". En effet les rendements "pré-moyennés" sont m-dépendant avec m qui croît à une vitesse plus faible que la taille d’échantillon n. Ceci motive l’application d’un bootstrap par bloc spécifique. Nous montrons que le bloc bootstrap suggéré par Bühlmann et Künsch (1995) n’est valide que lorsque la volatilité est constante. Ceci est dû à l’hétérogénéité dans la moyenne des rendements "pré-moyennés" au carré lorsque la volatilité est stochastique. Nous proposons donc une nouvelle procédure de bootstrap qui combine le wild bootstrap et le bootstrap par bloc, de telle sorte que la dépendance sérielle des rendements "pré-moyennés" est préservée à l’intérieur des blocs et la condition d’homogénéité nécessaire pour la validité du bootstrap est respectée. Sous des conditions de taille de bloc, nous montrons que cette méthode est convergente. Les simulations Monte Carlo montrent que le bootstrap améliore les propriétés en échantillon fini de l’estimateur de la volatilité intégrée par rapport aux résultats asymptotiques. Nous illustrons cette méthode en utilisant des données financières réelles. Le troisième chapitre est intitulé: "Bootstrapping realized covolatility measures under local Gaussianity assumption". Dans ce chapitre nous montrons, comment et dans quelle mesure on peut approximer les distributions des estimateurs de mesures de co-volatilité sous l’hypothèse de Gaussianité locale des rendements. En particulier nous proposons une nouvelle méthode de bootstrap sous ces hypothèses. Nous nous sommes focalisés sur la volatilité réalisée et sur le beta réalisé. Nous montrons que la nouvelle méthode de bootstrap appliquée au beta réalisé était capable de répliquer les cummulants au deuxième ordre, tandis qu’il procurait une amélioration au troisième degré lorsqu’elle est appliquée à la volatilité réalisée. Ces résultats améliorent donc les résultats existants dans cette littérature, notamment ceux de Gonçalves et Meddahi (2009) et de Dovonon, Gonçalves et Meddahi (2013). Les simulations Monte Carlo montrent que le bootstrap améliore les propriétés en échantillon fini de l’estimateur de la volatilité intégrée par rapport aux résultats asymptotiques et les résultats de bootstrap existants. Nous illustrons cette méthode en utilisant des données financières réelles.
We develop in this thesis bootstrap methods for high frequency financial data. The first two chapters focalise on bootstrap methods for the "pre-averaging" approach, which is robust to the presence of market microstructure effects. The main idea underlying this approach is that we can reduce the impact of the noise by pre-averaging high frequency returns that are possibly contaminated with market microstructure noise before applying a realized volatility-like statistic. Based on this approach, we develop several bootstrap methods, which preserve the dependence structure and the heterogeneity in the mean of the original data. The third chapter shows how and to what extent the local Gaussian- ity assumption can be explored to generate a bootstrap approximation for covolatility measures. The first chapter is entitled "Bootstrap inference for pre-averaged realized volatility based on non-overlapping returns". The main contribution of this chapter is to propose bootstrap methods for realized volatility-like estimators defined on pre-averaged returns. In particular, we focus on the pre-averaged realized volatility estimator proposed by Podolskij and Vetter (2009). This statistic can be written (up to a bias correction term) as the (scaled) sum of squared pre-averaged returns, where the pre-averaging is done over all possible non-overlapping blocks of consecutive observations. Pre-averaging reduces the influence of the noise and allows for realized volatility estimation on the pre-averaged returns. The non-overlapping nature of the pre-averaged returns implies that these are asymptotically independent, but possibly heteroskedastic. This motivates the application of the wild bootstrap in this context. We provide a proof of the first order asymptotic validity of this method for percentile and percentile-t intervals. Our Monte Carlo simulations show that the wild bootstrap can improve the finite sample properties of the existing first order asymptotic theory provided we choose the external random variable appropriately. The second chapter is entitled "Bootstrapping pre-averaged realized volatility under market microstructure noise ". In this chapter we propose a bootstrap method for inference on integrated volatility based on the pre-averaging approach of Jacod et al. (2009), where the pre-averaging is done over all possible overlapping blocks of consecutive observations. The overlapping nature of the pre-averaged returns implies that these are m-dependent with m growing slowly with the sample size n. This motivates the application of a blockwise bootstrap method. We show that the “blocks of blocks” bootstrap method suggested by Politis and Romano (1992) (and further studied by Bühlmann and Künsch (1995)) is valid only when volatility is constant. The failure of the blocks of blocks bootstrap is due to the heterogeneity of the squared pre-averaged returns when volatility is stochastic. To preserve both the dependence and the heterogeneity of squared pre-averaged returns, we propose a novel procedure that combines the wild bootstrap with the blocks of blocks bootstrap. We provide a proof of the first order asymptotic validity of this method for percentile intervals. Our Monte Carlo simulations show that the wild blocks of blocks bootstrap improves the finite sample properties of the existing first order asymptotic theory. The third chapter is entitled "Bootstrapping realized volatility and realized beta under a local Gaussianity assumption". The financial econometric of high frequency data litera- ture often assumed a local constancy of volatility and the Gaussianity properties of high frequency returns in order to carry out inference. In this chapter, we show how and to what extent the local Gaussianity assumption can be explored to generate a bootstrap approximation. We show the first-order asymptotic validity of the new wild bootstrap method, which uses the conditional local normality properties of financial high frequency returns. In addition to that we use Edgeworth expansions and Monte Carlo simulations to compare the accuracy of the bootstrap with other existing approaches. It is shown that at second order, the new wild bootstrap matches the cumulants of realized betas-based t-statistics, whereas it provides a third-order asymptotic refinement for realized volatility. Monte Carlo simulations suggest that our new wild bootstrap methods improve upon the first-order asymptotic theory in finite samples and outperform the existing bootstrap methods for realized covolatility measures. We use empirical work to illustrate its uses in practice.

AbstractFor more than a century, breeding has delivered huge benefits as a major driver of increased wheat productivity and of stability in the face of inevitable disease threats. Thus, the real cost of this staple grain has been reduced for billions of consumers. Steady breeding progress has been seen across many important traits of wheat, currently for potential yield averaging about 0.6% p.a. This yield progress continues to rely of extensive multilocational yield testing but has, however, become more difficult, even as new breeding techniques have improved efficiency. Breeding will continue to evolve as new approaches, being proposed with increasing frequency, are tested and found useful or not. High throughput phenotyping (HTPP), applying modern crop physiology, and molecular markers and genomic selection (GS) are in this phase right now. Such new techniques, along with pre-breeding for new traits, will likely play a larger role in this future improvement of wheat. New tools will also include genetic engineering (GE), as society’s need for its benefits become more urgent. The steady privatization of breeding seems unlikely to cease in the developed world but will continue to struggle elsewhere. It would seem wise, however, that a significant portion of the world’s pre-breeding research remains in the public sector, while maintaining close and equitable contact with those delivering new varieties.

In this paper, channel estimation algorithms are proposed and compared for uplink WiMAX systems, which are OFDMA based. These algorithms are investigated based on a dynamic resource allocation scheme, and it is shown that each of them is suitable to specific system scenarios. For example, for a system with a bandwidth of 10MHz operating in the low frequency region (2-11GHz), a two-dimensional averaging algorithm outperforms other algorithms, such as a bilinear interpolation algorithm, because the correlations between the pilots and signals are sufficiently high in both the frequency and the time dimensions.

Abstract Digital Signal Processing reviews technical considerations for digital signal processing applied to clinical neurophysiologic studies. Digital instruments are replacing analog systems because of convenient storage, retrieval, and review of studies and improved reliability of interpretation. Digitization involves quantization and sampling. Quantization is characterized by quantum size, number of bits, and input range. Sampling is characterized by sampling interval and sampling frequency. The sampling theorem specifies the minimum sampling frequency necessary to adequately represent igher frequency components of a signal. Sampling at less than this frequency produces aliasing. Signal averaging is used for evoked potential and nerve conduction studies, repetitive transient waveforms, and movement-associated potentials. Digital filtering removes unwanted frequency components from a signal by means of software algorithms. In contrast, analog filtering uses electrical circuit components like resisters, capacitors, and coils to remove unwanted frequency components. Both types of filters can be classified as low-pass, high-pass, bandpass, or notch filters. Interval analysis, autocorrelation analysis, and spectral analysis are ways to quantify the frequency content of a signal. Pattern recognition is used to detect waveforms with characteristic features.

This study proposes a method for estimating the topographical distribution of Visual Evoked Potentials (VEPs) from separated power spectrum components by a combination of models. VEPs with various temporal frequencies were recorded from nine healthy adults. The original power spectrum consisted of the VEP; background activities, artifacts, and other components were then obtained. To extract the VEP components from the original power spectrum, models corresponding to background activities, especially for posterior alpha rhythm, the low-frequency component and the high-frequency component, caused due to the EMG artifact, were constructed, and the relevant parameters were estimated. Finally, VEP components were calculated by subtracting them from the original power spectrum. The topographical distribution of the first harmonic (1F) and second harmonic (2F) components of the VEP were obtained by the proposed method. The estimation of the other components, aside from the VEPs, was also investigated. The merits and usefulness of the proposed method were analyzed with a comparison to the conventional stimulus-locked averaging method. The proposed method has several advantageous points compared to the conventional averaging method. Specifically, the posterior alpha rhythm and the EMG artifact were accounted for directly in the estimation of the VEP components. Therefore, an accurate estimation of the VEP components can be performed even the measurement of the components are prone to the error.

Much of what we know about the structure of the boundary layer is empirical, the result of painstaking analysis of observational data. As our understanding of the boundary layer evolved, so did our ability to define more clearly the requirements for sensing atmospheric variables and for processing that information. Decisions regarding choice of sampling rates, averaging time, detrending, ways to minimize aliasing, and so on, became easier to make. We find we can even standardize most procedures for real-time processing. The smaller, faster computers, now within the reach of most boundary layer scientists, offer virtually unlimited possibilities for processing and displaying results even as an experiment is progressing. The information we seek, for the most part, falls into two groups: (1) time-averaged statistics such as the mean, variance, covariance, skewness, and kurtosis and (2) spectra and cospectra of velocity components and scalars such as temperature and humidity. We discuss them separately because of different sampling and processing requirements for the two. A proper understanding of these requirements is essential for the successful planning of any experiment. In this chapter we discuss these considerations in some detail with examples of methods used in earlier applications. We will assume that sensors collecting the data have adequate frequency response, precision, and long-term stability and that the sampling is performed digitally at equally spaced intervals. We also assume that the observation heights are chosen with due regard to sensor response and terrain roughness. For calculations of means and higher order moments we need time series that are long enough to include all the relevant low-frequency contributions to the process, sampled at rates fast enough to capture all the high-frequency contributions the sensors are able to measure. Improper choices of averaging times and sampling rates can indeed compromise our statistics. We need to understand how those two factors affect our measurements in order to make sensible decisions on how long and how fast to sample.

Polluted by the noise of the observation, precision of satellite timing based on pseudoranges can merely reach tens of nanoseconds. Considering the sharply increasing demand of high-precision timing in the many fields, a traceable precise timing system has been proposed, which means having a connection with UTC (Coordinated Universal Time). We introduce the principle of the PPP (Precise Point Positioning) timing system and conduct the experiment with the form of zero baseline, long baseline, and very long baseline, simultaneously, CV (Common View) and AV (All in View) timing solution are used for comparison. Finally, the system performance has been evaluated from the aspects of precision and stability. The results show, when the Rubidium module is the frequency source of the user terminal, the 1 PPS timing accuracy of 904 km achieved by this method is 0.32 ns, and the frequency stability can achieve about 9.51e-13, 5.58e-13 and 1.37e-13 at the averaging time of 100 s, 1000 s and 10000 s. The timing bias is approximate 2 ns. Besides, the variation of the temperature will affect the timing results. Compared to the pseudorange timing solution, improvement on the PPP short term stability is more obvious than that of long term stability.

Auditory Brainstem Responses (ABR) are short-latency electric potentials from the auditory nervous system that can be evoked by presenting transient acoustic stimuli to the ear. Sources of the ABR are the auditory nerve and brainstem auditory nuclei. Clinical application of ABRs includes identification of the site of lesion in retrocochlear hearing loss, establishing functional integrity of the auditory nerve, and objective audiometry. Recording of ABR requires a measurement setup with a high-quality amplifier with adequate filtering and low skin-electrode impedance to reduce non-physiological interference. Furthermore, signal averaging and artifact rejection are essential tools for obtaining a good signal-to-noise ratio. Comparing latencies for different peaks at different stimulus intensities allows the determination of hearing threshold, location of the site of lesion, and establishment of neural integrity. Audiological assessment of infants who are referred after failing hearing screening relies on accurate estimation of hearing thresholds. Frequency-specific ABR using tone-burst stimuli is a clinically feasible method for this. Appropriate correction factors should be applied to estimate the hearing threshold from the ABR threshold. Whenever possible, obtained thresholds should be confirmed with behavioral testing. The Binaural Interaction Component of the ABR provides important information regarding binaural processing in the brainstem.

The utility of single-pulse electrical stimulation (SPES) for epilepsy surgery has been highlighted in the last decade. When applied at a frequency of about 1 Hz, it can probe cortico-cortical connections by averaging electrocorticographic signal time-locked to stimuli to record cortico-cortical evoked potentials (CCEPs) emanating from adjacent and remote cortices. Although limited to patients undergoing invasive presurgical evaluations, CCEPs provide a novel way to explore inter-regional connectivity in vivo in the living human brain to probe functional brain networks such as language and cognitive motor networks. In addition to its impact on basic systems neuroscience, this method, in combination with 50 Hz electrical cortical stimulation, can contribute clinically to the mapping of functional brain systems by tracking cortico-cortical connections among functional cortical regions in individual patients. This approach may help identify normal cortico-cortical networks in pathological brain, or plasticity of brain systems in conjunction with pathology. Because of its high practical value, it has been applied to intraoperative monitoring of functional brain networks in patients with brain tumours. With regard to epilepsy, SPES has been used to probe cortical excitability of the focus (epileptogenicity) and seizure networks. Both early (i.e. CCEP) and delayed responses are regarded as surrogate markers of epileptogenicity. With regard to its potential impact on human brain connectivity maps, worldwide collaboration is warranted to establish standardized CCEP connectivity maps as a solid reference for non-invasive connectome research.

Unusually high incidences of dwarfism and an endemic osteoarthritis, called Mseleni Joint Disease (MJD), occur on the flat, sandy coastal plain of Maputaland. This rare disease begins with stiffness and pain in the joints and progresses to varying degrees of disability, with some of the afflicted requiring aid in walking and others completely immobile. Almost 3% of local adults are dwarfs, while 38% of women and 11% of men have MJD (Fellingham 1973, Lockitch 1974). Medical studies since the 1970s have examined hematological, radiological, mycotoxicological, and genetic factors, and made comparisons with other diseases (Ballo 1996, Burger 1973, Lockitch 1973, Marasas 1986), yet have been fruitless in determining the etiology of MJD or the dwarfism. Dwarfism has been linked to Zn deficiencies in other areas and several bone-related disorders have been associated with P, Ca, and Mg deficiencies (Hidiroglou 1980). Calcium, Mg, Mn, and F deficiencies have all been speculated as possible causative factors of MJD (Fincham 1981, 1986), and the possibility of soil-derived nutrient deficiencies within this landscape is addressed. Maputaland is located on the northeast corner of South Africa, occupying an area about 50 by 100 km. It has a warm, subtropical climate, with summer rainfall occurring as cyclonic events, and varying from 1000 mm at the coast to 600 mm near Mseleni. Summer temperatures are high, averaging 29° C, and winters mild at 17° C. The region has high floral and faunal diversity and endemism (van Wyk 1996), and contains 15 major vegetation zones. Geologically, Maputaland is covered with recent Quaternary sands, with several north-south paleodune cordons parallel to the coast. There is little relief and, besides the coastal dunes reaching almost 200 m above mean sea level, the average elevation is 100 m. No rivers cross the plain, but groundwater is frequently exposed at the surface, as evidenced by Lake Sibayi and the numerous pans in the region. Soils are mostly the Waterton family of the Fernwood form (thermic, coated Typic Quartzipsamments) (SCWG 1991, USDA 1999). These sands are inherently infertile, vary in pH from neutral to acidic, have a low cation exchange capacity, low organic matter content, and are dominated in the clay fraction by kaolinite.

All doctors working in the ED will regularly meet patients with acute mental health problems. Five percent of total ED attendees are attrib­utable to mental disorder. With nationwide ED attendances averaging 400 000 per week during November to April 2013, the trend shows a growing pressure on emergency services. However, these figures repre­sent just the tip of the true burden of acute mental illness in our com­munities. Stigma, the healthcare funnel, and marginalization often mean that it is the sickest who finally present to the ED. It is also important to recognize the co-morbidity of mental illness and addictions in those seeking help for what initially appear to be physical complaints, as so often the mind and body are closely intertwined. Most common psychiatric presentations to the ED include DSH, alco­hol and substance misuse, delirium, acute psychosis, factitious disorders, medically unexplained symptoms (MUS), and acute stress reactions (such as to trauma). DSH is common but under-recognized. A quarter of people who die by suicide attended the ED in the preceding year. All patients in the ED presenting with self-harm should have a detailed psychosocial assessment. Alcohol is responsible for 0% of all ED attendances. It is also an independent variable, raising the risk of DSH. Substance users are also frequent attendees, with high levels of medical morbidity and mortality. Patients with a dual diagnosis of substance use plus mental illness fre­quently present with multiple psychosocial problems. Acute psychosis may be caused by a functional disorder, such as schizophrenia, but organic conditions must also be considered. Where a patient is extremely disturbed in the ED, restraint and sedation may be necessary to enable safe and adequate assessment. Security presence may also be required to minimize the risk of violence, where this has been identified. Implications for working in the ED are that all doctors should famil­iarize themselves with the management of common acute psychiatric presentations. Know how to access local Trust rapid tranquillization guidelines. Read NICE guidelines for management of self-harm. Seize opportunities to screen for mental illness and social problems.

This paper investigates the effect of vertical vibration on the stability of a dilute suspension of negatively geotactic microorganisms in a fluid layer of finite depth. The case of high-frequency vibration is considered. Solutions of governing equations are decomposed into two components: one which varies slowly with time and a second which varies rapidly with time. An averaging method is utilized to derive the equations describing the mean flow. Linear stability analysis is used to investigate stability of the obtained averaged equations.

Abstract The frequency domain of many problems in structural dynamics encompasses a wide range, covering nearly static behavior up to vibration flow characteristics similar to heat transfer. This work presents an uniform approach for low and high frequency vibration analysis, which is based on Finite Element modeling of the structure. Vibrations in the low frequency range are determined by an efficient superposition technique of complex modes, which accounts accurately for any linear damping effect. The modal method is extended to the high frequency domain by applying different levels of averaging to the response and eigenfrequencies and by the introduction of random properties of modeshapes. The high frequency domain is defined by the size of the Finite Elements, i.e. short wave lengths of high frequency modeshapes cannot be represented by the FE-model. The response computation of isolated structures is extended to substructures of complex systems by prescribing stochastic multi-support base excitation at the substructure boundaries. It may be noted, that the presented approach of stochastic high frequency dynamics contains, as special cases, the expressions of the structural response of Statistical Energy Analysis, Bolotin’s integral method and the results of Asymptotic Modal Analysis.

In the paper it is shown that statistical averaging of transport equations (URANS = Unsteady Reynolds Averaged Navier Stokes) imposes no inherent restriction concerning the ability to predict periodic or other deterministic transient flow processes. This even holds for periodic oscillations at relatively high frequencies lying in the spectral range of the inertial sub-range of flow turbulence. As an application, the unsteady behaviour of an isothermal swirling air flow through and behind an airblast-atomizer of a design typical for modern aeroengine combustors is treated. This flow exhibits self-excited oscillations at a frequency of 2.8 kHz. Computations of this flow behaviour based on the numerical solution of the unsteady statistically averaged Navier-Stokes equations are presented. The turbulence model employed in the computations is a k,ε-model modification for swirling flows. The transport equations are discretized by a Finite-Volume method on a curvilinear grid. Calculated mean velocity profiles as well as the predicted dynamic flow behaviour at the nozzle exit agree very well with appropriate LDV- and microphone-measurements.

Data from an array of high frequency response pressure transducers embedded in the casing wall over the tip of a transonic fan are reported. Phase-lock averaging of data from this array was successful in resolving an axial-tangential map of the static pressure rise in the rotor tip, as has been reported by other workers. Phase-lock ensemble RMS processing of the data is shown to be a useful technique that provides insight into the flow physics around the blade tip. Comparison with CFD results allows for more definite identification of features observed in the data. A complex flow field involving the casing wall boundary layer, the blade shock system and the over-tip leakage flow is observed. Differences between CFD data and measurements are explored by way of computational sensitivity studies. Results are reported for a range of throttle settings and speeds.

A new, specially-developed high-frequency-response pressure probe was used to measure the unsteady flow in the interaction region between the pump and the turbine in a hydrodynamic torque converter. In order to reduce the probe diameter, a single-hole, single-sensor cylindrical probe (⌀=1.33mm) was developed, to replace the standard multi-hole probe. The smaller the probe the higher the accuracy in unsteady flow. Therefore this is an improvement over three-hole probe. Three-hole probe measurements were simulated by recording data in three different angular positions. The time variable velocity vectors were determined using the probe’s calibration coefficients and the knowledge of the rotor positions (measured by angle-encoders) for every measurement value. During the data processing, a double ensemble averaging was carried out, taking into account the positions of the pump and the turbine.

Non-smooth piecewise functional isolators are smart passive vibration isolators that can provide effective isolation for high frequency/low amplitude excitation by introducing a soft primary suspension, and by preventing a high relative displacement in low frequency/high amplitude excitation by introducing a relatively damped secondary suspension. In this investigation a linear secondary suspension is attached to a nonlinear primary suspension. The primary is assumed to be nonlinear to model the inherent nonlinearities involved in real suspensions. However, the secondary suspension comes into action only during a short period of time, and in mall domain around resonance. Therefore, a linear assumption for the secondary suspension is reasonable. The dynamic behavior of the system subject to a harmonic base excitation has been analyzed utilizing the analytic results derived by applying the averaging method. The analytic results match very well in the transition between the two suspensions. A sensitivity analysis has shown the effect of varying dynamic parameters in the steady state behavior of the system.

The acoustic characterization of fluid machines, e.g., internal combustion engines, compressors, or fans is of great importance when designing the connected duct systems and its silencers. For machines connected to large ducts where also the non-plane wave range is important, for instance large diesels and gas turbines, a suitable way to characterize the source is to determine the sound power under reflection free conditions. For the low frequency plane wave range in-duct sound power can be measured with the widely used two microphone method. The goal of this study is to investigate how, starting from the two-microphone approach, a suitable wall mounted microphone configuration can be defined and used to estimate the propagating in-duct sound power also beyond the plane wave range. For this purpose an acoustic source test-rig was built and numerical simulations were also conducted. The in-duct sound power from monopole, dipole, and quadrupole source types was determined using twelve wall mounted microphones and cross-spectra averaging methods. The in-duct results were compared against sound power measured using the reverberation room method (ISO 3741). Based on the simulations and the experimental results the best microphone positions and weighting factors were determined.