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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
831

Simulation-Based Portfolio Optimization with Coherent Distortion Risk Measures / Simuleringsbaserad portföljoptimering med koherenta distortionsriskmått

Prastorfer, Andreas January 2020 (has links)
This master's thesis studies portfolio optimization using linear programming algorithms. The contribution of this thesis is an extension of the convex framework for portfolio optimization with Conditional Value-at-Risk, introduced by Rockafeller and Uryasev. The extended framework considers risk measures in this thesis belonging to the intersecting classes of coherent risk measures and distortion risk measures, which are known as coherent distortion risk measures. The considered risk measures belonging to this class are the Conditional Value-at-Risk, the Wang Transform, the Block Maxima and the Dual Block Maxima measures. The extended portfolio optimization framework is applied to a reference portfolio consisting of stocks, options and a bond index. All assets are from the Swedish market. The returns of the assets in the reference portfolio are modelled with elliptical distribution and normal copulas with asymmetric marginal return distributions. The portfolio optimization framework is a simulation-based framework that measures the risk using the simulated scenarios from the assumed portfolio distribution model. To model the return data with asymmetric distributions, the tails of the marginal distributions are fitted with generalized Pareto distributions, and the dependence structure between the assets are captured using a normal copula. The result obtained from the optimizations is compared to different distributional return assumptions of the portfolio and the four risk measures. A Markowitz solution to the problem is computed using the mean average deviation as the risk measure. The solution is the benchmark solution which optimal solutions using the coherent distortion risk measures are compared to. The coherent distortion risk measures have the tractable property of being able to assign user-defined weights to different parts of the loss distribution and hence value increasing loss severities as greater risks. The user-defined loss weighting property and the asymmetric return distribution models are used to find optimal portfolios that account for extreme losses. An important finding of this project is that optimal solutions for asset returns simulated from asymmetric distributions are associated with greater risks, which is a consequence of more accurate modelling of distribution tails. Furthermore, weighting larger losses with increasingly larger weights show that the portfolio risk is greater, and a safer position is taken. / Denna masteruppsats behandlar portföljoptimering med linjära programmeringsalgoritmer. Bidraget av uppsatsen är en utvidgning av det konvexa ramverket för portföljoptimering med Conditional Value-at-Risk, som introducerades av Rockafeller och Uryasev. Det utvidgade ramverket behandlar riskmått som tillhör en sammansättning av den koherenta riskmåttklassen och distortions riksmåttklassen. Denna klass benämns som koherenta distortionsriskmått. De riskmått som tillhör denna klass och behandlas i uppsatsen och är Conditional Value-at-Risk, Wang Transformen, Block Maxima och Dual Block Maxima måtten. Det utvidgade portföljoptimeringsramverket appliceras på en referensportfölj bestående av aktier, optioner och ett obligationsindex från den Svenska aktiemarknaden. Tillgångarnas avkastningar, i referens portföljen, modelleras med både elliptiska fördelningar och normal-copula med asymmetriska marginalfördelningar. Portföljoptimeringsramverket är ett simuleringsbaserat ramverk som mäter risk baserat på scenarion simulerade från fördelningsmodellen som antagits för portföljen. För att modellera tillgångarnas avkastningar med asymmetriska fördelningar modelleras marginalfördelningarnas svansar med generaliserade Paretofördelningar och en normal-copula modellerar det ömsesidiga beroendet mellan tillgångarna. Resultatet av portföljoptimeringarna jämförs sinsemellan för de olika portföljernas avkastningsantaganden och de fyra riskmåtten. Problemet löses även med Markowitz optimering där "mean average deviation" används som riskmått. Denna lösning kommer vara den "benchmarklösning" som kommer jämföras mot de optimala lösningarna vilka beräknas i optimeringen med de koherenta distortionsriskmåtten. Den speciella egenskapen hos de koherenta distortionsriskmåtten som gör det möjligt att ange användarspecificerade vikter vid olika delar av förlustfördelningen och kan därför värdera mer extrema förluster som större risker. Den användardefinerade viktningsegenskapen hos riskmåtten studeras i kombination med den asymmetriska fördelningsmodellen för att utforska portföljer som tar extrema förluster i beaktande. En viktig upptäckt är att optimala lösningar till avkastningar som är modellerade med asymmetriska fördelningar är associerade med ökad risk, vilket är en konsekvens av mer exakt modellering av tillgångarnas fördelningssvansar. En annan upptäckt är, om större vikter läggs på högre förluster så ökar portföljrisken och en säkrare portföljstrategi antas.
832

(   vill   )(   will  ) : tankar i närheten av två halvcirklar thoughts near a broken circle / (   vill   )(   will  ) : tankar i närheten av två halvcirklar thoughts near a broken circle

Boman, Ida January 2022 (has links)
Marken är något fundamentalt. Jag dras till att skapa hålrum och att gjuta av dem. Låta händerna leda. Det är något som attraherar mig med att inte riktigt kunna föreställa mig formen av hålrummet i tanken, att det är ett glapp i överföringen mellan händernas rörelser och tankens. Att värdera det definierade högre än det odefinierade, vill jag lägga i en parantes.  Vi använder språk som materia, vi bygger betydelser, rum som skapar sammanhang, stödkonstruktioner, konstruktion som är dikt, som är en rörelse som är jord som är ett arbete som är sten som är en förflyttning som är trä som är en handling som är metall som är nära intill, att skulptera en tanke. Det är idén om att kroppen har en korrekt form som gör kroppen korrupt. Den brutna cirkeln är på ett sätt en helhet av två korrupta kroppar. Kategorier och definitioner är något verkligt, oavsett hur de är skapade eller kommit till. Vi uppmärksammar genast om något är konstigt. Två enheter som vi uppfattar som separata, är separata. Om de inte varit separata skulle vi uppfattat de som ett och inte som två. Det här ser vi omedelbart. Om vi inte är i ett främmande sammanhang med främmande definitioner, men då kommer säkerligen någon ganska snart att uppmärksamma oss på hur saker hänger ihop. Människor är hjälpsamma på sådant sätt. / My work may be described as bordering between sculpture and installation, intuitive and conceptual, it could in a way be seen as a broken circle, as one, but i will work hard to make the two entities, the two seemingly half circle shaped entities, to be separate, to be two.  I will assert they are one work but also not, I will assert their indepencence, they are two. The bridge, the connection, will (or will not) happen in the thought, not by sight. There will be no side-by-side, object dialog in near space, rather association through memory and through distance. Like an object or some kind of occurence is planted early on in a movie and then reoccurs later on with the purpuse to further the understanding of course of events.  We tend to read two half circles near each other as a whole circle. Robert Morris made two half circles with only a thin lit gap underlining their distinct form, but at the same time dissolving them as a broken circle. It is the idea of of a correct body that makes a body corrupt. The broken circle is in a way the whole of two corrupt bodies.
833

Juice/JDC ion measurement perturbations caused by spacecraft charging in the solar wind and Earth’s magnetosheath

van Winden, Derek January 2024 (has links)
In July 2031, a new chapter in the exploration of the Jovian system will begin with the arrival of the Jupiter Icy Moons Explorer (Juice) at Jupiter. Launched on April 14 2024 as part of ESA’s Cosmic Vision programme, the mission aims to study Jupiter and its icy Galilean moons Callisto, Europa, and Ganymede. Juice carries a whole suite of instruments for in-situ and remote ground observations, one of which is the Jovian plasma Dynamics and Composition analyser (JDC). As a part of the Particle Environment Package (PEP), the particle detector will measure the energy, mass, charge and arrival direction of ions and electrons in the Jovian magnetosphere. Spacecraft charging caused by interactions between the spacecraft and its surrounding plasma environment poses a significant problem for JDC because the electrostatic potential of the spacecraft accelerates/decelerates charged particles, resulting in distorted measurements, particularly for the lowest energy particles.  In this report, we show the results of spacecraft charging and instrument simulations performed in the Spacecraft Plasma Interaction System (SPIS) for the solar wind and Earth’s magnetosheath—two environments that Juice will encounter at the start of the cruise phase. We found that the conductive surfaces that cover the majority of the spacecraft become positively charged as a result of a large photoelectron current in both the solar wind and magnetosheath environments. We show that these surfaces are expected to reach potentials of 9 V in the solar wind and 4 V in the magnetosheath. The four radiators on Juice that are covered with dielectric paint and shaded by the sun shield become negatively charged in both simulated environments. The radiator potentials can be as low as -40 V in the solar wind and -100 V in the magnetosheath. We also conclude that due to blocking by the spacecraft main body, the ion population cannot be sampled in the solar wind unless a spacecraft roll is performed. Furthermore, due to the high ion f low energy, spacecraft charging will not influence JDC measurements in this environment.  In the magnetosheath, the ion population can be sampled by JDC, and we identified three distortion mechanisms: (1) repulsion by the main body, (2) attraction by two of the radiators, and (3) repulsion by the MAG boom. Of all the distortion modes, the one originating from a negatively charged (-67.8 V) radiator close to JDC is the strongest, affecting ions with energies above 80 eV. The least powerful but most prevalent mode is the repulsion of ions by the main body. Our results can be compared with future in-situ measurements to identify distortion mechanisms well ahead of the science phase in which the scientifically important measurements will be carried out.
834

ON THE RATE-COST TRADEOFF OF GAUSSIAN LINEAR CONTROL SYSTEMS WITH RANDOM COMMUNICATION DELAY

Jia Zhang (13176651) 01 August 2022 (has links)
<p>    </p> <p>This thesis studies networked Gaussian linear control systems with random delays. Networked control systems is a popular topic these years because of their versatile applications in daily life, such as smart grid and unmanned vehicles. With the development of these systems, researchers have explored this area in two directions. The first one is to derive the inherent rate-cost relationship in the systems, that is the minimal transmission rate needed to achieve an arbitrarily given stability requirement. The other one is to design achievability schemes, which aim at using as less as transmission rate to achieve an arbitrarily given stability requirement. In this thesis, we explore both directions. We assume the sensor-to-controller channels experience independently and identically distributed random delays of bounded support. Our work separates into two parts. In the first part, we consider networked systems with only one sensor. We focus on deriving a lower bound, R_{LB}(D), of the rate-cost tradeoff with the cost function to be E{| <strong>x^</strong>T<strong>x </strong>|} ≤ D, where <strong>x </strong>refers to the state to be controlled. We also propose an achievability scheme as an upper bound, R_{UB}(D), of the optimal rate-cost tradeoff. The scheme uses lattice quantization, entropy encoder, and certainty-equivalence controller. It achieves a good performance that roughly requires 2 bits per time slot more than R_{LB}(D) to achieve the same stability level. We also generalize the cost function to be of both the state and the control actions. For the joint state-and-control cost, we propose the minimal cost a system can achieve. The second part focuses on to the covariance-based fusion scheme design for systems with multiple > 1 sensors. We notice that in the multi-sensor scenario, the outdated arrivals at the controller, which many existing fusion schemes often discard, carry additional information. Therefore, we design an implementable fusion scheme (CQE) which is the MMSE estimator using both the freshest and outdated information at the controller. Our experiment demonstrates that CQE out-performances the MMSE estimator using the freshest information (LQE) exclusively by achieving a 15% smaller average L2 norm using the same transmission rate. As a benchmark, we also derive the minimal achievable L2 norm, Dmin, for the multi-sensor systems. The simulation shows that CQE approaches Dmin significantly better than LQE. </p>
835

High Performance RF and Basdband Analog-to-Digital Interface for Multi-standard/Wideband Applications

Zhang, Heng 2010 December 1900 (has links)
The prevalence of wireless standards and the introduction of dynamic standards/applications, such as software-defined radio, necessitate the next generation wireless devices that integrate multiple standards in a single chip-set to support a variety of services. To reduce the cost and area of such multi-standard handheld devices, reconfigurability is desirable, and the hardware should be shared/reused as much as possible. This research proposes several novel circuit topologies that can meet various specifications with minimum cost, which are suited for multi-standard applications. This doctoral study has two separate contributions: 1. The low noise amplifier (LNA) for the RF front-end; and 2. The analog-to-digital converter (ADC). The first part of this dissertation focuses on LNA noise reduction and linearization techniques where two novel LNAs are designed, taped out, and measured. The first LNA, implemented in TSMC (Taiwan Semiconductor Manufacturing Company) 0.35Cm CMOS (Complementary metal-oxide-semiconductor) process, strategically combined an inductor connected at the gate of the cascode transistor and the capacitive cross-coupling to reduce the noise and nonlinearity contributions of the cascode transistors. The proposed technique reduces LNA NF by 0.35 dB at 2.2 GHz and increases its IIP3 and voltage gain by 2.35 dBm and 2dB respectively, without a compromise on power consumption. The second LNA, implemented in UMC (United Microelectronics Corporation) 0.13Cm CMOS process, features a practical linearization technique for high-frequency wideband applications using an active nonlinear resistor, which obtains a robust linearity improvement over process and temperature variations. The proposed linearization method is experimentally demonstrated to improve the IIP3 by 3.5 to 9 dB over a 2.5–10 GHz frequency range. A comparison of measurement results with the prior published state-of-art Ultra-Wideband (UWB) LNAs shows that the proposed linearized UWB LNA achieves excellent linearity with much less power than previously published works. The second part of this dissertation developed a reconfigurable ADC for multistandard receiver and video processors. Typical ADCs are power optimized for only one operating speed, while a reconfigurable ADC can scale its power at different speeds, enabling minimal power consumption over a broad range of sampling rates. A novel ADC architecture is proposed for programming the sampling rate with constant biasing current and single clock. The ADC was designed and fabricated using UMC 90nm CMOS process and featured good power scalability and simplified system design. The programmable speed range covers all the video formats and most of the wireless communication standards, while achieving comparable Figure-of-Merit with customized ADCs at each performance node. Since bias current is kept constant, the reconfigurable ADC is more robust and reliable than the previous published works.
836

A Risk Based Approach to Module Tolerance Specification

Shahtaheri, Yasaman 22 April 2014 (has links)
This research investigates tolerance strategies for modular systems on a project specific basis. The objective of the proposed research is to form a guideline for optimizing the construction costs/risks with the aim of developing an optimal design of resilient modular systems. The procedures for achieving the research objective included: (a) development of 3D structural analysis models of the modules, (b) strength/stability investigation of the structure, (c) developing the fabrication cost function, (e) checking elastic and inelastic distortion, and (f) constructing the site-fit risk functions. The total site-fit risk function minimizes the cost/risk associated with fabrication, transportation; alignment, rework, and safety, while maximizing stiffness in terms of story drift values for site re-alignment and fitting alternatives. The fabrication cost function was developed by collecting 61 data points for the investigated module chassis using the SAP2000 software while reducing the initial section sizes, in addition to the fabrication costs at each step (61 steps). With the reduction of the structural reinforcement, story drift values increase, therefore there will be a larger distortion in the module. This generic module design procedure models a trade-off between the amount of reinforcement and expected need for significant field alterations. Structural design software packages such as SAP2000, AutoCAD, and Autodesk were used in order to model and test the module chassis. This research hypothesizes that the influential factors in the site-fit risk functions are respectively: fabrication, transportation, alignment, safety, and rework costs/risks. In addition, the site-fit risk function provides a theoretical range of possible solutions for the construction industry. The maximum allowable modular out-of-tolerance value, which requires the minimum amount of cost with respect to the defined function, can be configured using this methodology. This research concludes that over-reinforced or lightly-reinforced designs are not the best solution for mitigating risks, and reducing costs. For this reason the site-fit risk function will provide a range of pareto-optimal building solutions with respect to the fabrication, transportation, safety, alignment, and rework costs/risks.
837

MEMS-Laser-Display-System / MEMS Laser Display System

Specht, Hendrik 19 October 2011 (has links) (PDF)
In der vorliegenden Arbeit werden die im Zusammenhang mit der Strahlablenkung stehenden Systemaspekte der auf MEMS-Scanner basierenden Laser-Display-Technologie theoretisch analysiert und aus den Ergebnissen die praktische Implementierung eines Laser-Display-Systems als Testplattform vorgenommen. Dabei werden mit einem Ansatz auf Basis zweier 1D-Scanner und einem weiteren Ansatz mit einem 2D-Scanner zwei Varianten realisiert. Darüber hinaus erfolgt die Entwicklung eines bildbasierten Multiparametertestverfahrens, welches sowohl für den Test komplettierter Strahlablenkeinheiten bzw. Projektionsmodule als auch zum umfassenden und zeiteffizienten Test von MEMS-Scannern auf Wafer-Level geeignet ist. Mit diesem Verfahren erfolgt eine Charakterisierung der zwei realisierten Varianten des Laser-Displays. Ausgehend von den Eigenschaften des menschlichen visuellen Systems und den daraus resultierenden Anforderungen an das Bild sowie einer systemtheoretischen Betrachtung des mechanischen Verhaltens von MEMS-Scannern bildet die Ansteuersignalerzeugung für den resonanten Betrieb der schnellen und den quasistatischen Betrieb der langsamen Achse einen Schwerpunkt. Neben dem reinen digitalen Regler- bzw. Filterentwurf sowie mehreren Linearisierungsmaßnahmen beinhaltet dieser auch die Herleitung einer FPGA-basierten Videosignalverarbeitung zur Konvertierung von Scannpattern, Zeitregime und Auflösung mit einer entsprechenden Synchronisierung von Strahlablenkung und Lasermodulation. Auf Grundlage der daraus resultierenden Erkenntnisse über den Zusammenhang zwischen Scanner-/Systemparametern und Bildparametern werden Testbild-Bildverarbeitungsalgorithmus-Kombinationen entwickelt und diese, angeordnet in einer Sequenz, mit einem Kalibrierverfahren zu einem Testverfahren für MEMS-Scanner vervollständigt. Die Ergebnisse dieser Arbeit entstanden im Rahmen von industriell beauftragten F&E-Projekten und fließen in die andauernde Fortführung des Themas beim Auftraggeber ein.
838

Μέθοδοι και διατάξεις απευθείας ηλεκτροακουστικής μετατροπής για ψηφιακό ήχο / Methods and implementations for direct electroacoustic transduction of digital audio

Κοντομίχος, Φώτιος 06 October 2011 (has links)
Η παρούσα διδακτορική διατριβή εστιάστηκε στη μελέτη συστημάτων ακουστικής εκπομπής για απευθείας αναπαραγωγή ψηφιακού ήχου. Η ερευνητική διαδικασία βασίστηκε στον προσδιορισμό και βελτίωση των δυνατοτήτων δύο διαφορετικών υλοποιήσεων ακουστικής μετατροπής: i. Ένα υβριδικό πρωτότυπο θερμοακουστικό στοιχείο και ii. Μια συστοιχία 32 ηλεκτροδυναμικών μεγαφώνων σχεδιασμένη, ώστε να αναπαράγει ψηφιακά ηχητικά σήματα. Η θερμοακουστική μετατροπή προσφέρει μια εναλλακτική τεχνική για υλοποιήσεις ακουστικών στοιχείων. Είναι βασισμένη στο μετασχηματισμό των διακυμάνσεων της θερμικής ενέργειας σε ακουστικό κύμα που προκαλούνται από τη ροή του ηλεκτρικού σήματος ήχου σε μια συσκευή στερεάς κατάστασης που λειτουργεί χωρίς τη χρήση οποιουδήποτε κινούμενου τμήματος ή μηχανισμού. Η υλοποίηση αυτής της τεχνικής ηχητικής αναπαραγωγής, μελετάται με τη χρήση ενός πρωτότυπου μετατροπέα ο οποίος αναπτύχθηκε πάνω σε πλακέτα κρυσταλλικού πυριτίου (silicon wafer). H απόδοση της συσκευής αυτής βελτιώνεται ιδίως όσον αφορά στις μη γραμμικές παραμορφώσεις που προσθέτει ο φυσικός μηχανισμός κατά την αναπαραγωγή των ακουστών συχνοτήτων. Για τις ανάγκες της ερευνητικής μελέτης κατασκευάσθηκε εξειδικευμένο στάδιο οδήγησης, ενώ επίσης αναπτύχθηκαν εργαλεία που προσομοιώνουν την απόδοση αυτών των συσκευών. Οι ψηφιακές συστοιχίες μεγαφώνων (DLAs) σήμερα βασίζονται σε μικρούς μετατροπείς κινούμενου πηνίου για την ανακατασκευή ακουστικών σημάτων από ροές ψηφιακού ήχου. Τα σημαντικά ζητήματα απόδοσης για τα συστήματα αυτά αναλύονται από την παρούσα διατριβή, με στόχο να ερμηνευθεί η απόκριση συχνότητας και οι ρυθμοί των διακριτών (on/off) μεταβάσεων των μεγαφώνων, εξαιτίας των ψηφιακών σημάτων. Λεπτομερείς προσομοιώσεις που επιτρέπουν την πραγματοποίηση συγκρίσεων για μια πανομοιότυπη συστοιχία 32 μετατροπέων η οποία τροφοδοτείται από αναλογικά σήματα, σε παρόμοια τοποθέτηση και ενεργοποίηση των στοιχείων. Οι μελέτες αυτές παράγουν πρωτότυπα αποτελέσματα για τις απαιτήσεις σε ηλεκτρική ενέργεια και την ευαισθησία της συστοιχίας, καταλήγοντας στο συμπέρασμα ότι αυτά τα δύο συστήματα επιτυγχάνουν συγκρίσιμες επιδόσεις. / The present Phd Thesis is focused on the study of acoustic transduction systems for direct digital audio signal emission. The research process was based on the evaluation and optimization of the behavior of two different implementations: i. A novel hybrid thermoacoustic device and ii. A loudspeaker array consisting of 32 moving coil speakers designed for digital audio reproduction. Thermoacoustic transduction offers an alternative technique for transducer implementations, based on the transformation of thermal energy fluctuations into sound after the direct application of the electrical audio signal on a solid state device which operates without the use of any moving/mechanical components. Here, an implementation of this sound generation technique is studied based on a prototype developed on silicon wafer and its performance is optimised, especially with respect to non-linear distortions within the audio band. For the purposes of the research study a specialised driving circuit was constructed and also the appropriate tools were developed to simulate the performance of these devices. Digital loudspeaker arrays currently are based on small moving-coil speakers to reconstruct acoustic signals out of binary audio streams. An overview of significant performance issues for such systems is given here to explain frequency response and speaker discrete transition rates due to the digital data. Detailed simulations provided comparisons for a 32-speaker DLA with similar arrangements of speakers driven by analogue signals. These tests produce novel results for electrical power requirements and array sensitivity, concluding that these two systems achieve comparable performance.
839

Multikanálová dekonvoluce obrazů / Multichannel Image Deconvolution

Bradáč, Pavel January 2009 (has links)
This Master Thesis deals with image restoration using deconvolution. The terms introducing into deconvolution theory like two-dimensional signal, distortion model, noise and convolution are explained in the first part of thesis. The second part deals with deconvolution methods via utilization of the Bayes approach which is based on the probability principle. The third part is focused on the Alternating Minimization Algorithm for Multichannel Blind Deconvolution. At the end this algorithm is written in Matlab with utilization of the NAG C Library. Then comparison of different optimization methods follows (simplex, steepest descent, quasi-Newton), regularization forms (Tichonov, Total Variation) and other parameters used by this deconvolution algorithm.
840

Validation and application of advanced soil constitutive models in numerical modelling of soil and soil-structure interaction under seismic loading

Kowalczyk, Piotr Jozef 23 September 2020 (has links)
This thesis presents validation and application of advanced soil constitutive models in cases of seismic loading conditions. Firstly, results of three advanced soil constitutive models are compared with examples of shear stack experimental data for free field response in dry sand for shear and compression wave propagation. Higher harmonic generation in acceleration records, observed in experimental works, is shown to be possibly the result of soil nonlinearity and fast elastic unloading waves. This finding is shown to have high importance on structural response, real earthquake records and reliability of conventionally employed numerical tools. Finally, short study of free field response in saturated soil reveals similar findings on higher harmonic generation. Secondly, two advanced soil constitutive models are used, and their performance is assessed based on examples of experimental data on piles in dry sand in order to validate the ability of the constitutive models to simulate seismic soil-structure interaction. The validation includes various experimental configurations and input motions. The discussion on the results focuses on constitutive and numerical modelling aspects. Some improvements in the formulations of the models are suggested based on the detailed investigation. Finally, the application of one of the advanced soil constitutive models is shown in regard to temporary natural frequency wandering observed in structures subjected to earthquakes. Results show that pore pressure generated during seismic events causes changes in soil stiffness, thus affecting the natural frequency of the structure during and just after the seismic event. Parametric studies present how soil permeability, soil density, input motion or a type of structure may affect the structural natural frequency and time for its return to the initial value. In addition, a time history with an aftershock is analysed to investigate the difference in structural response during the earthquake and the aftershock.

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