Rozprawy doktorskie na temat „Vibration filtering”

International Telemetering Conference Proceedings / October 22-25, 2001 / Riviera Hotel and Convention Center, Las Vegas, Nevada
The accurate measurement of shock and vibration data via flight telemetry is necessary to validate structural models, indicate off-nominal system performance, and/or generate environmental qualification criteria for airborne systems. Digital telemetry systems require anti-aliasing filters designed into them. If not properly selected and located, these filters can distort recorded time histories and modify their spectral content. This paper provides filter design guidance to optimize the quality of recorded flight structural dynamics data. It is based on the anticipated end use of the data. Examples of filtered shock data are included.

Rolling element bearings are one of the most significant elements and frequently-used components in mechanical systems. Bearing fault detection and diagnosis is important for preventing productivity loss and averting catastrophic failures of mechanical systems. In industrial applications, bearing life is often difficult to predict due to different application conditions, load and speed variations, as well as maintenance practices. Therefore, reliable fault detection is necessary to ensure productive and safe operations. Vibration analysis is the most widely used method for detection and diagnosis of bearing malfunctions. A measured vibration signal from a sensor is often contaminated by noise and vibration interference components. Over the years, many methods have been developed to reveal fault signatures, and remove noise and vibration interference components. Though many vibration based methods have been proposed in the literature, the high frequency resonance (HFR) technique is one of a very few methods have received certain industrial acceptance. However, the effectiveness of the HFR methods depends, to a great extent, on some parameters such as bandwidth and centre frequency of the fault excited resonance, and window length. Proper selection these parameters is often a knowledge-demanding and time-consuming process. In particular, the filter designed based on the improperly selected bandwidth and center frequency of the fault excited resonance can filter out the true fault information and mislead the detection/diagnosis decisions. In addition, even if these parameters can be selected properly at beginning of each process, they may become invalid in a time-varying environment after a certain period of time. Hence, they may have to be re-calculated and updated, which is again a time-consuming and error-prone process. This undermines the practical significance of the above methods for online monitoring of bearing conditions. To overcome the shortcomings of existing methods, the following four non-parametric and non-filtering methods are proposed: 1. An amplitude demodulation differentiation (ADD) method, 2. A calculus enhanced energy operator (CEEO) method, 3. A higher order analytic energy operator (HO_AEO) approach, and 4. A higher order energy operator fusion (HOEO_F) technique. The proposed methods have been evaluated using both simulated and experimental data.

Noise and degradation reduction is of significant importance in virtually all systems where these phenomena are present, specifically in the fields of signal and image processing.  The effect of image processing on target detection is of significant interest because noise and degradations can greatly reduce the effectiveness of detection algorithms, due to the presence of high intensity noise which is often mistaken as a target.  In signal processing, noise in vibration data, or any time-series data, can reduce the accuracy of measurement and can prevent the passing of useful information.    
Many filters that have been developed are designed to reduce a single class of noise, such as Wiener and Frost filters.  When these filters are applied to types of noise that they were not designed for, the effect of the noise reduction can be greatly reduced.  The proposed Two-Stage Non-Adaptive Convolution (TSNAC) filter significantly reduces both additive and multiplicative noise in these two unique systems.
The performance of these filters is compared through several Image Quality (IQ) metrics.
It will be shown that the proposed TSNAC filter reduces noise and degradations more effectively in both SAR images and synthetic vibration data than the competing filters.  It will show higher IQ scores, greater computational efficiency in target detection, and significant improvement in signal restoration of simulated vibration data.

Master of Science

During strong earthquakes structural systems exhibit nonlinear behavior due to low-cycle fatigue, cracking, yielding and/or fracture of constituent elements. After a seismic event it is essential to assess the state of damage of structures and determine if they can safely resist aftershocks or future strong motions. The current practice in post-earthquake damage assessment relies mainly on visual inspections and local testing. These approaches are limited to the ability of inspectors to reach all potentially damaged locations, and are typically intended to detect damage near the outer surfaces of the structure leaving the possibility of hidden undetected damage. Some structures in seismic prone-regions are instrumented with an array of sensors that measure their acceleration at different locations. We operate under the premise that acceleration response measurements contain information about the state of damage of structures, and it is of interest to extract this information and use it in post-earthquake damage assessment and decision making strategies. The objective of this dissertation is to show that Bayesian filters can be successfully employed to estimate the nonlinear dynamic response of instrumented structural systems. The estimated response is subsequently used for structural damage diagnosis. Bayesian filters combine dynamic response measurements at limited spatial locations with a nonlinear dynamic model to estimate the response of stochastic dynamical systems at the model degrees-of-freedom. The application of five filters is investigated: the extended, unscented and ensemble Kalman filters, the particle filter and the model-based observer. The main contributions of this dissertation are summarized as follows: i) Development of a filtering-based mechanistic damage assessment framework; ii) Experimental validation of Bayesian filters in small and large-scale structures; iii) Uncertainty quantification and propagation of response and damage estimates computed using Bayesian filters.

Thesis (M.S.) -- Worcester Polytechnic Institute.
Keywords: Threshold Forces; Vibrations; Signal Processing; Force Adaptive Grinding; Diamond Roll Dressing. Includes bibliographical references (p. 29 ).

This thesis concerns models based on Statistical Energy Analysis (SEA) to predict bending wave vibration in heavyweight buildings from structure-borne sound sources such as machinery. These sources tend to inject most power in the low- and mid-frequency ranges where the walls and floors have low mode counts and low modal overlap for which calculated Coupling Loss Factors (CLFs) from semi-infinite plate theory can be in error. For machinery it is necessary to predict vibration on walls/floors that are remote from the source room. In this situation, propagation across successive structural junctions causes spatial filtering of the wave field and the assumption of a diffuse field in each plate subsystem breaks down. The predictive approach described in the European Standard EN12354 uses SEA path analysis which assumes that transmission is dominated by first-order paths. However the feasibility of extending the concept of path analysis to walls and floors of rooms that are distant from the source room(i.e. not adjacent) is unknown. These issues are addressed in the thesis. The feasibility of SEA path analysis was assessed by quantifying the total contribution to receiver subsystem energy from paths containing specified numbers of CLFs. For receiving subsystems which are attached directly to the source subsystem, the EN12354 approach was found to underestimate the energy levels. For rooms remote from the source room, path analysis was found to significantly underestimate the vibration of the walls/floors which form the receiver room. Alternative approaches to improve predictions in large heavyweight buildings were assessed through comparison with Monte-Carlo Finite Element Method (MCFEM) models which were validated on a small heavyweight building. Matrix SEA was used with CLFs calculated for L-, T- and X-junctions using analytical models for rectangular plates to try and incorporate modal features. For isolated junctions, there was good agreement with MCFEM but in large buildings. However, it was unable to predict the peaks and troughs in the vibration response to one-third octave band accuracy although it can estimate the envelope response for plates that are directly connected to the source plate. In general, matrix SEA using finite plate theory CLFs does not improve the prediction in one-third octave bands when the statistical mode count is less than unity. Ray tracing was therefore investigated which showed that the angular distribution of power incident on the plate edges differed significantly from a diffuse field. Computationally efficient ray tracing was then developed for inclusion in Advanced SEA (ASEA) models to account for indirect coupling between plate subsystems. ASEA gave significant improvements over matrix SEA when there were large numbers of structural junctions between the source and receiving plates.

The presence of vibration is an important problem in many engineering applications. Various passive techniques have traditionally been used in order to reduce waves and vibrations, and their harmful effects. Passive techniques are, however, difficult to apply in the low frequency region. In addition, the use of passive techniques often involve adding mass to the system, which is undesirable in many applications.

As an alternative, active techniques can be used to manipulate system dynamics and to control the propagation of waves and vibrations. This thesis deals with modeling, estimation and active control of systems that have resonant dynamics. The systems are exposed to stochastic disturbances. Some of them excite the system and generate vibrational responses and other corrupt measured signals.

Feedback control of a beam with attached piezoelectrical elements is studied. A detailed modeling approach is described and system identification techniques are employed for model order reduction. Disturbance attenuation of a non-measured variable shows to be difficult. This issue is further analyzed and the problems are shown to depend on fundamental design limitations.

Feedforward control of traveling waves is also considered. A device with properties analogous to those of an electrical diode is introduced. An `ideal´ feedforward controller based on the mechanical properties of the system is derived. It has, however, poor noise rejection properties and it therefore needs to be modified. A number of feedforward controllers that treat the measurement noise in a statistically sound way are derived.

Separation of overlapping traveling waves is another topic under investigation. This operation also is sensitive to measurement noise. The problem is thoroughly analyzed and Kalman filtering techniques are employed to derive wave estimators with high statistical performance.

Finally, a nonlinear regression problem with close connections to unbalance estimation of rotating machinery is treated. Different estimation techniques are derived and analyzed with respect to their statistical accuracy. The estimators are evaluated using the example of separator balancing.

Cette thèse porte sur la conception et la caractérisation de micro-dispositifs à ondes acoustiques multicouches. La cinquième génération de communication (5G) nécessite des résonateurs acoustiques plus performants (fréquences > 3GHz, bande passante plus large). Dans ce contexte, nous avons conçu et optimisé par simulation FEM la géométrie de résonateurs à ondes de Lamb à base d’AlScN. Le dispositif final, constitué d’une couche composée de 30% de Sc et déposée sur un miroir de Bragg W/SiO2, montre d’excellentes performances (coefficient de couplage de 5% et facteur de qualité de 768) et un bon accord avec la simulation. Pour caractériser la surface de BAW et SAW sur la gamme de fréquence 5G, nous avons également conçu et développé un interféromètre hétérodyne. Ce dernier a été utilisé avec succès pour caractériser des vibrations de surface d'une amplitude comprise entre 1 et 10 pm à 5,95 GHz. Par ailleurs, grâce à leur robustesse et leur capacité à être interrogé sans-fil, les capteurs SAW sont utilisés dans des environnements difficiles et suscitent un grand intérêt pour les applications médicales et de contrôle de santé intégré. Récemment, l’introduction d’empilements multi-matériaux offre de nouvelles opportunités de développements. Nous avons ainsi étudié un capteur de pression composé de deux couches complémentaires, ainsi qu'un capteur dit package-less utilisant des couches d’impédances acoustiques différentes. Pour concevoir ces nouveaux capteurs, nous avons développé un outil de simulation reposant sur l'extraction de paramètres de couplage de modes et tenant compte des effets de la température, des contraintes et des déformations pour estimer leur sensibilité
This thesis deals with the design and characterization of multilayer acoustic wave micro-devices. The fifth generation of communication (5G) requires more efficient acoustic resonators (frequencies > 3GHz, wider bandwidth). In this context, we have designed and optimized using FEM simulation, the geometry of Lamb wave resonator based on AlScN. The final device, consisting of a layer composed of 30% Sc and deposited on a Bragg W/SiO2 mirror, shows excellent performance (coupling coefficient of 5% and quality factor of 768) as well as a good agreement with the simulation. To characterize the surface of BAW and SAW over the 5G frequency range, we also designed and developed a heterodyne interferometer. The latter has been used successfully to characterize surface vibrations with amplitudes between 1 and 10 pm at 5.95 GHz. Furthermore, thanks to their robustness and ability to be wirelessly interrogated,SAW sensors are used in harsh environments and are of great interest for medical applications and structural health monitoring. Recently, the introduction of multi-material stacks offers new development opportunities. We thus studied a pressure sensor composed of two complementary layers, as well as a so-called package- less sensor using different acoustic impedance layers. To design these new sensors, we have developed a simulation tool based on the extraction of mode coupling parameters and taking into account the effects of temperature, stresses and strains to estimate their sensitivity

Câmeras embarcadas em sistemas robóticos móveis com sensoriamento visual geralmente são afetadas pelo movimento de seu suporte quando é necessária a aquisição de imagens com alta confiabilidade. Algumas câmeras disponíveis no mercado já estão equipadas com sistemas de estabilização de imagens, implementados nas lentes da câmera ou no sensor de imagem. Esses sistemas são relativamente caros para serem instalados em sistemas robóticos móveis aéreos ou terrestres de pequeno porte. Outro conceito que tem sido utilizado para alcançar a estabilização consiste em adotar sensores inerciais, algoritmos de visão computacional e aplicação de filtros digitais para estimativa e suavização de movimento. Esta dissertação tem por finalidade apresentar um sistema de estabilização digital de vídeo em conjunto com um acelerômetro para detectar movimentos da câmera. Considera-se que a câmera está instalada sobre plataforma instável ou em veículo em movimento, assim, utiliza-se filtragem robusta para minimizar o efeito da vibração sobre a câmera. Vários experimentos são realizados adicionando vibração em vídeo por meio de simulações em computador. Considera-se também experimentos em ambiente real com a câmera montada em um suporte dentro de um veículo em movimento. A principal contribuição deste trabalho é a realização de um estudo comparativo para analisar a vantagem de se usar uma abordagem robusta entre os métodos de filtragem comumente utilizados em sistemas de estabilização de vídeo.
Embedded cameras in robotic systems usually are susceptible to movements of your basis. The measurements can be affected mainly when they should obtain high performance in actual applications. Although some cameras available on the market are already equipped with an optical image stabilization system, implemented either in the camera lenses or in the image sensor. They are usually expensive to be installed into small aerial or land robotic systems. This dissertation presents a video stabilization system coupled with an accelerometer for motion detection at an unstable platform. It is embedded in a vehicle. Robust filtering is used to minimize vibration effects on the camera. Several experiments were performed, adding either vibrations via computer simulations and taking images from the camera with the vehicle moving. The main contribution of this work is the accomplishment of a comparative study to analyse the advantages of applying a robust approach among others filtering methods that frequently are used to video stabilizing systems.

Dans sa recherche constante pour améliorer le confort des usagers, l'industrie automobile cherche à réduire les nuisances sonores dans les habitacles automobiles. Une des principales sources responsables de la gêne ressentie est l'écoulement turbulent qui se développe autour de la voiture. Celui-ci est caractérisé par des variations de pressions pariétales particulièrement importantes et localisées en particulier sur les vitrages avants du véhicule. L'objectif de cette étude est de mesurer et de caractériser la sollicitation aéroacoustique subie par le vitrage à l'aide d'une méthode vibratoire inverse nommée RIC (Résolution Inverse Corrigée). Le principe est de mesurer le déplacement de la vitre et de le réinjecter dans l'équation inverse du mouvement de la structure pour calculer la pression pariétale. Cette technique repose sur la discrétisation d'un schéma aux différences finies judicieusement choisi suivant le filtrage visé. Il est alors possible de contrôler et choisir le filtrage apporté par le schéma en modifiant les coefficients qui le constituent. La démarche présentée repose sur la synthèse de filtres numériques et différentes approches sont proposées. Les différents schémas aux différences finies calculés à partir de ces méthodes sont appliqués, par simulations numériques et expérimentalement, sur le cas simple d'une plaque et sur les différents vitrages d'un véhicule placé en soufflerie
In a constant search for user comfort, the automotive industry tries to reduce the annoying noises inside the passenger compartment of cars. These noises are mainly caused by the turbulence developed on the car window glass.Turbulent flow is characterized by particularly high wall pressure variations on the windows of the vehicle. The aim of this study is to measure the aeroacoustic load on the car window glass using the vibratory reverse method called Force Analysis Technique (FAT). The principle of this method is based on measuring the plate displacement field which is injected into the motion equation of the plate in order to calculate the force distribution exciting the structure. In order to do so, spatial derivatives are calculated by approximation using a judiciously selected finite difference model. It becomes possible to control and choose the filtering realized by the finite difference scheme by changing its coefficients. This technique is based on digital filter synthesis and different approaches are proposed. New finite different schemes are then applied on a plate and on car window glasses by computer simulations and experiments. Experiments are realized in an anechoïc wind tunel on a real car

L'objectif de cette recherche est de construire un modèle réduit de petite dimension pour prévoir les réponses dynamiques dans une bande BF sur les parties rigides d'un véhicule automobile complet. Un tel modèle réduit "léger" est une aide à la phase de conception en "Avant Projet" de ces véhicules qui ont la particularité de présenter de nombreux modes élastiques locaux en BF dues à la présence de nombreuses parties flexibles et d'équipements. Pour la construction du modèle réduit, nous avons introduit une base non usuelle de l'espace admissible des déplacements globaux. La construction de cette base requiert la décomposition en sous-domaines du domaine de la structure qui peut présenter une très grande complexité géométrique et dont les modèles EF font intervenir de très nombreux types d'éléments finis. Cette décomposition en sous-domaines a été réalisée par la Fast Marching Method que nous avons due étendre pour pouvoir traiter la complexité des modèles EF des véhicules automobiles. Puis les équations matricielles du modèle EF sont projetées sur cette base. Afin de prendre en compte les incertitudes sur les paramètres du modèle, les incertitudes de modèle induites par les erreurs de modélisation et enfin les incertitudes liées à la non prise en compte des contributions locales dans le modèle réduit des déplacements globaux, un unique modèle probabiliste non paramétrique de ces trois sources d'incertitude a été implémenté sur le modèle réduit construit avec les vecteurs propres globaux. Les paramètres de dispersion de ce modèle probabiliste ont été identifiés en utilisant le principe du maximum de vraisemblance et des réponses obtenues à l'aide d'un modèle stochastique de référence qui inclut des informations expérimentales résultant de travaux précédents. Le modèle réduit stochastique, pour la prévision des déplacements globaux sur les parties rigides dans la bande BF qui a été développé, a été validé sur un modèle de structure automobile "nue" puis a été appliqué avec succès sur un modèle complet de véhicule automobile
The objective of this research is to construct a reduced-order model to predict the dynamical response, in the LF band, of the stiff parts of a complete automotive vehicle in order to facilitate the draft design. The vehicles under consideration have many elastic modes in LF due to the presence of many flexible parts and equipments. To build such a model, we introduced a non-usual basis of the admissible space of global displacements. The construction of this basis requires the decomposition of the domain of the structure. This subdomain decomposition is performed by using the Fast Marching Method that we have extended to take into account the high complexity of the mesh of an automotive vehicle. Then the matrix equations of the FE model are projected on this basis. To take into account the system parameters uncertainties, the model uncertainties induced by the modeling errors and finally, the uncertainties related to the neglecting of local contributions in the reduced-order model, a nonparametric probabilistic model of the three sources of uncertainties has been implemented on the reduced-order model constructed with the global displacements eigenvectors. The dispersion parameters of the probabilistic model are identified using the maximum likelihood method and the responses obtained from a stochastic reference model which includes experimental data resulting from previous works. This stochastic model which has been designed for the prediction of the global displacements of the rigid parts in the LF band is validated on a simple structure of an automotive model and has been successfully applied on a complete model of automotive vehicle

University of Technology, Sydney. Faculty of Engineering and Information Technology.
Vibration is usually undesirable and yet it occurs in most machines, vehicles, structures, buildings and dynamic systems. The resulting unpleasant motions and the dynamic stresses may lead to fatigue and failure of the structure or machines. In the field of civil engineering, control and identification of the state of health of the structure during the dynamic loads, such as earthquakes and attempt to suppress the vibrations and detect any damage or potential hazard are of vital importance and have posed a great challenge to the research community. This thesis presents new techniques for optimisation, real-time health monitoring and semi-active vibration control of structures subjected to seismic loads. First, a new encoding scheme is presented for a fuzzy-based nonlinear system identification methodology, using subtractive Fuzzy C-Mean clustering and non-dominated sorting genetic algorithm. The method is able to automatically select the best inputs as well as the structure of the fuzzy model in such a way that both accuracy and compactness of model are guaranteed. The proposed method is then employed to identify the forward and inverse models of a MR damper. Numerical and Experimental results show that the developed evolving TSK fuzzy model can identify and grasp the nonlinear dynamics of both forward and inverse systems very well, while a small number of inputs and fuzzy rules are required for this purpose. The optimal design and placement of control devices, is an important problem that affects the control of civil engineering structures. This study also presents a multi-objective optimisation method for simultaneous finding of optimal number and location of actuators and MR dampers, in active and semi-active controlled structures. The method is applied to a nonlinear 20-storey benchmark building. The obtained optimal layout of active actuators is compared to the original benchmark problem definition in which 25 actuators are located in non-optimal places. Results show the effect of proposed strategy where similar level of structural performance, in terms of proposed objective indices, is achieved by use of only 7 actuators in optimal locations. Also, the optimal configuration of different number of MR dampers in the same nonlinear benchmark building is also studied. Results are then compared with optimal locations of actuators in the equivalent active system and the differences are shown. Two new semi-active control algorithms named TSKInv and MaxMin, are also introduced in this research study to convert the force generated by nominal controller to the required voltage of MR dampers. TSKInv algorithm is developed by modelling the inverse dynamics of MR damper using TSK fuzzy inference systems and MaxMin controller is designed based on the maximum (maximum voltage) and minimum (minimum voltage) load of MR damper at each time-step. Applications of these two newly developed methods are compared to some other semi-active control strategies through the 20-storey nonlinear benchmark building. Results show the superiority of these two models over the other algorithms in tracking the desired force using less amount of control force and power. Also, an investigation on different Kalman Filtering algorithms used in system identification is carried out in this dissertation work, on which EKF, IEKF, UKF and IUKF have been applied to some numerical examples to estimate the parameters of targeted structures in real-time using acceleration responses only. Results demonstrate that IUKF and UKF are the most reliable and robust estimators even if the structure is highly nonlinear and measured data are contaminated with noise. Then, a novel recursive least square based method with adaptive multiple forgetting factor is proposed and applied to different structural identification problems with unknown excitations. It is found from the results that, the proposed algorithm can effectively identify the time-varying parameters as well as the unknown inputs to the structure with high computational efficiency. Using the developed techniques, this project aims to prepare a platform for real-time structural integrity assessment of civil infrastructures, during or after earthquakes.

Στην παρούσα διατριβή διερευνήθηκε για πρώτη φορά η δυνατότητα επέκτασης του ορίου εφαρμογής της γεωδαιτικής μεθόδου μέτρησης μετακινήσεων σε πλέον άκαμπτες (υψίσυχνες) κατασκευές με τη χρήση οργάνων GPS δειγματοληψίας 100Hz. Τα όργανα αυτά αποτελούν πρόκληση για διάφορους τομείς καθώς έχουν δυνατότητα δειγματοληψίας σχεδόν ίδιας τάξης μεγέθους με όργανα που χρησιμοποιούνται παραδοσιακά για την καταγραφή δυναμικών κινήσεων όπως επιταχυνσιογράφοι, σεισμόμετρα κτλ. Στην παρούσα διατριβή μελετήθηκαν τα χαρακτηριστικά του θορύβου των οργάνων GPS-100Hz μέσα από συστηματικά πειράματα “supervised learning”, όπου στατικοί δέκτες ή δέκτες κινούμενοι σε γνωστές οριζόντιες και κατακόρυφες τροχιές, επέτρεπαν να καταγραφεί και να αναλυθεί ο στατικός και δυναμικός θόρυβος διαφόρων τύπων. Η περαιτέρω μελέτη του θορύβου έδειξε ότι οι συσχετίσεις και το εύρος του επηρεάζονται σημαντικά από το εύρος συχνοτήτων του βρόχου PLL (Phase-Locked Loop bandwidth) του δέκτη GPS. Η χρήση βρόχου PLL με εύρος συχνοτήτων (bandwidth) 100Hz εξασφαλίζει ασυσχέτιστες μετρήσεις αλλά αυξάνει σημαντικά το εύρος του θορύβου (τυπική απόκλιση περίπου 3mm στους οριζόντιους άξονες και περίπου 6-7mm στον κατακόρυφο). Το φάσμα συχνοτήτων του θορύβου των χρονοσειρών συντεταγμένων GPS-100Hz χαρακτηρίζεται από μη τυχαίο (χρωματισμένο) θόρυβο στις χαμηλές συχνότητες (μέχρι περίπου 0.5Hz) και πρακτικά τυχαίο θόρυβο για τις υψηλές συχνότητες. Επιπλέον λόγω της δυνατότητας υψηλού ρυθμού δειγματοληψίας των οργάνων GPS-100Hz, έγινε δυνατό να διερευνηθεί για πρώτη φορά το φαινόμενο της δυναμικής πολυανάκλασης του δορυφορικού σήματος από κινούμενες ανακλαστικές επιφάνειες (dynamic multipath) και η επίδρασή του στις χρονοσειρές στιγμιαίων συντεταγμένων GPS. Με βάση τα συμπεράσματα της ανάλυσης των πειραματικών δεδομένων αναπτύχθηκε μεθοδολογία απομείωσης του θορύβου των χρονοσειρών στιγμιαίων μετατοπίσεων κατασκευών ενδιαφέροντος Πολιτικού Μηχανικού με βάση ψηφιακά φίλτρα ζώνης. Η μεθοδολογία αυτή επιτρέπει να εκτιμηθούν οριζόντιες και κατακόρυφες μετακινήσεις της τάξης των λίγων χιλιοστών. Η παραπάνω μεθοδολογία εφαρμόστηκε στις καταγραφές των ταλαντώσεων μίας ξύλινης πεζογέφυρας στην περιοχή της Πάτρας. Από αφιλτράριστες μετρήσεις GPS-100Hz εκτιμήθηκε εύρος εγκάρσιας ταλάντωσης της τάξης των 60-70mm και συχνότητα ταλάντωσης 0.92Hz. Στον κατακόρυφο άξονα εκτιμήθηκε συχνότητα ταλάντωσης 6.5Hz ενώ μετά την απομάκρυνση του θορύβου των μετρήσεων εκτιμήθηκε εύρος κατακόρυφης ταλάντωσης της τάξης των 3mm. Η πειραματική και αναλυτική διερεύνηση δείχνουν ότι η υψηλή δειγματοληψία που παρέχουν τα νέα όργανα GPS-100Hz προσφέρει δυνατότητα καλύτερης εκτίμησης των χαρακτηριστικών ταλάντωσης (συχνότητα/εύρος) σχετικά εύκαμπτων κατασκευών αλλά και επέκτασης των ορίων εφαρμογής του GPS σε μέτρηση δυναμικών μετακινήσεων δύσκαμπτων κατασκευών (ιδιοσυχνότητα μεγαλύτερη των 5Hz) με εύρος μέχρι λίγα χιλιοστά.
The possibility of the newly introduced GNSS receivers, with sampling rate up to 100Hz, for broadening the limits of application of GPS technology toward measuring the displacements of stiff (high-frequency) Civil Engineering Structures was studied in the present thesis. The new generation GPS receivers present a great challenge for various applications since they offer a sampling rate similar to the sampling rate of traditional instruments used in vibration measurement/monitoring like accelerometers and seismometers. The noise characteristics of the 100Hz GPS measurements were studied on the basis of systematic “supervised learning” experiments where instantaneous coordinate time-series from stationary receivers or receivers performing motions with known characteristics permitted to study static and dynamic noise of several types including noise due to dynamic multipath. The last phenomenon has been identified during the measurements of the response of bridges due to excitation by passing vehicles. The study of noise characteristics indicated that the correlations and noise amplitude is highly dependent on the PLL (Phase-Locked Loop) bandwidth used by the GPS receiver. The use of a 100Hz PLL bandwidth ensures uncorrelated instantaneous coordinates but at the cost of high amplitude noise (standard deviation approximately 3mm and 6-7mm along the horizontal and vertical axes respectively). The noise spectrum is characterized by a power-law with colored noise affecting low frequencies up to approximately 0.5Hz and white noise affecting higher frequencies. A methodology for the reduction of noise of the instantaneous coordinate time-series using band-pass filtering has been designed on the basis of the results of the experimental data. Application of the methodology permits the identification of millimeter level dynamic displacements similar to the ones developed during structural vibrations. The methodology was applied on the measurements of the oscillations of a timber bridge in Patras, Greece. Oscillation amplitudes around 60-70mm and a fundamental natural frequency of 0.92Hz were identified along the lateral axis of the bridge on the basis of unfiltered GPS coordinates. The first natural frequency along the vertical axis was estimated at 6.5Hz. After the de-noising of the GPS coordinates vertical oscillation amplitudes of around 3mm were successfully identified. The main result from the experimental and analytical investigation carried out in the present thesis is that the newly introduced GPS receivers with sampling rate up to 100Hz provide the opportunity of more detailed measurement of the oscillations and extraction of the dynamic characteristics of relatively flexible structures as well as the broadening of the limits of applications of GPS toward the measurement of dynamic displacements of stiff (natural frequencies >5Hz) structures.

碩士
國立臺灣大學
機械工程學研究所
99
In recent years, Virtual Reality technology has become an important tool for product design. VR technology can be used to create immersive and intuitive design environments in which designers can create virtual prototypes and perform tasks in new ways. However, to simulate realistic interactions between humans and virtual objects, high quality haptic feedback is needed. Many prior studies describe force feedback systems. On the other hand, tactile feedback, especially surface texture feedback, has not been considered thoroughly. Prior systems only use simple vibrations with different amplitudes or frequencies to represent different surface types. This study presents a vibration synthesis method that can be used to create surface texture sensations for general textured surfaces. The method is based upon linear filtering and Neural Network theories. A prototype system was built and tested. The system uses a micro speaker to create complex vibrations. The speaker is small enough to be embedded or integrated into a haptic glove. Results show that the method can be used to simulate a wide variety of surface textures. In user tests, the system had a significant positive effect on surface texture perception.

The study of randomly excited nonlinear dynamical systems forms the focus of this thesis. We discuss two classes of problems: first, the characterization of nonlinear random response of the system before it comes into existence and, the second, assimilation of measured responses into the mathematical model of the system after the system comes into existence. The first class of problems constitutes forward problems while the latter belongs to the class of inverse problems. An outstanding feature of these problems is that they are almost always not amenable for exact solutions. We tackle in the present study these two classes of problems using Monte Carlo simulation tools in conjunction with Markov process theory, Bayesian model updating strategies, and particle filtering based dynamic state estimation methods. It is well recognized in literature that any successful application of Monte Carlo simulation methods to practical problems requires the simulation methods to be reinforced with effective means of controlling sampling variance. This can be achieved by incorporating any problem specific qualitative and (or) quantitative information that one might have about system behavior in formulating estimators for response quantities of interest. In the present thesis we outline two such approaches for variance reduction. The first of these approaches employs a substructuring scheme, which partitions the system states into two sets such that the probability distribution of the states in one of the sets conditioned on the other set become amenable for exact analytical solution. In the second approach, results from data based asymptotic extreme value analysis are employed to tackle problems of time variant reliability analysis and updating of this reliability. We exemplify in this thesis the proposed approaches for response estimation and model updating by considering wide ranging problems of interest in structural engineering, namely, nonlinear response and reliability analyses under stationary and (or) nonstationary random excitations, response sensitivity model updating, force identification, residual displacement analysis in instrumented inelastic structures under transient excitations, problems of dynamic state estimation in systems with local nonlinearities, and time variant reliability analysis and reliability model updating. We have organized the thesis into eight chapters and three appendices. A resume of contents of these chapters and appendices follows. In the first chapter we aim to provide an overview of mathematical tools which form the basis for investigations reported in the thesis. The starting point of the study is taken to be a set of coupled stochastic differential equations, which are obtained after discretizing spatial variables, typically, based on application of finite element methods. Accordingly, we provide a summary of the following topics: (a) Markov vector approach for characterizing time evolution of transition probability density functions, which includes the forward and backward Kolmogorov equations, (b) the equations governing the time evolution of response moments and first passage times, (c) numerical discretization of governing stochastic differential equation using Ito-Taylor’s expansion, (d) the partial differential equation governing the time evolution of transition probability density functions conditioned on measurements for the study of existing instrumented structures, (e) the time evolution of response moments conditioned on measurements based on governing equations in (d), and (f) functional recursions for evolution of multidimensional posterior probability density function and posterior filtering density function, when the time variable is also discretized. The objective of the description here is to provide an outline of the theoretical formulations within which the problems of response estimation and model updating are formulated in the subsequent chapters of the present thesis. We briefly state the class of problems, which are amenable for exact solutions. We also list in this chapter major text books, research monographs, and review papers relevant to the topics of nonlinear random vibration analysis and dynamic state estimation. In Chapter 2 we provide a review of literature on solutions of problems of response analysis and model updating in nonlinear dynamical systems. The main focus of the review is on Monte Carlo simulation based methods for tackling these problems. The review accordingly covers numerical methods for approximate solutions of Kolmogorov equations and associated moment equations, variance reduction in simulation based analysis of Markovian systems, dynamic state estimation methods based on Kalman filter and its variants, particle filtering, and variance reduction based on Rao-Blackwellization. In this review we chiefly cover papers that have contributed to the growth of the methodology. We also cover briefly, the efforts made in applying the ideas to structural engineering problems. Based on this review, we identify the problems of variance reduction using substructuring schemes and data based extreme value analysis and, their incorporation into response estimation and model updating strategies, as problems requiring further research attention. We also identify a range of problems where these tools could be applied. We consider the development of a sequential Monte Carlo scheme, which incorporates a substructuring strategy, for the analysis of nonlinear dynamical systems under random excitations in Chapter 3. The proposed substructuring ensures that a part of the system states conditioned on the remaining states becomes Gaussian distributed and is amenable for an exact analytical solution. The use of Monte Carlo simulations is subsequently limited for the analysis of the remaining system states. This clearly results in reduction in sampling variance since a part of the problem is tackled analytically in an exact manner. The successful performance of the proposed approach is illustrated by considering response analysis of a single degree of freedom nonlinear oscillator under random excitations. Arguments based on variance decomposition result and Rao-Blackwell theorems are presented to demonstrate that the proposed variance reduction indeed is effective. In Chapter 4, we modify the sequential Monte Carlo simulation strategy outlined in the preceding chapter to incorporate questions of dynamic state estimation when data on measured responses become available. Here too, the system states are partitioned into two groups such that the states in one group become Gaussian distributed when conditioned on the states in the other group. The conditioned Gaussian states are subsequently analyzed exactly using the Kalman filter and, this is interfaced with the analysis of the remaining states using sequential importance sampling based filtering strategy. The development of this combined Kalman and sequential importance sampling filtering method constitutes one of the novel elements of this study. The proposed strategy is validated by considering the problem of dynamic state estimation in linear single and multi-degree of freedom systems for which exact analytical solutions exist. In Chapter 5, we consider the application of the tools developed in Chapter 4 for a class of wide ranging problems in nonlinear random vibrations of existing systems. The nonlinear systems considered include single and multi-degree of freedom systems, systems with memoryless and hereditary nonlinearities, and stationary and nonstationary random excitations. The specific applications considered include nonlinear dynamic state estimation in systems with local nonlinearities, estimation of residual displacement in instrumented inelastic dynamical system under transient random excitations, response sensitivity model updating, and identification of transient seismic base motions based on measured responses in inelastic systems. Comparisons of solutions from the proposed substructuring scheme with corresponding results from direct application of particle filtering are made and a satisfactory mutual agreement is demonstrated. We consider next questions on time variant reliability analysis and corresponding model updating in Chapters 6 and 7, respectively. The research effort in these studies is focused on exploring the application of data based asymptotic extreme value analysis for problems on hand. Accordingly, we investigate reliability of nonlinear vibrating systems under stochastic excitations in Chapter 6 using a two-stage Monte Carlo simulation strategy. For systems with white noise excitation, the governing equations of motion are interpreted as a set of Ito stochastic differential equations. It is assumed that the probability distribution of the maximum over a specified time duration in the steady state response belongs to the basin of attraction of one of the classical asymptotic extreme value distributions. The first stage of the solution strategy consists of selection of the form of the extreme value distribution based on hypothesis testing, and, the next stage involves the estimation of parameters of the relevant extreme value distribution. Both these stages are implemented using data from limited Monte Carlo simulations of the system response. The proposed procedure is illustrated with examples of linear/nonlinear systems with single/multiple degrees of freedom driven by random excitations. The predictions from the proposed method are compared with the results from large scale Monte Carlo simulations, and also with the classical analytical results, when available, from the theory of out-crossing statistics. Applications of the proposed method for vibration data obtained from laboratory conditions are also discussed. In Chapter 7 we consider the problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations. Here we assume that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes’ theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplified by considering the reliability analysis of a few low dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on limited amount of pertinent Monte Carlo simulations. A summary of the contributions made and a few suggestions for future work are presented in Chapter 8. The thesis also contains three appendices. Appendix A provides details of the order 1.5 strong Taylor scheme that is extensively employed at several places in the thesis. The formulary pertaining to the bootstrap and sequential importance sampling particle filters is provided in Appendix B. Some of the results on characterizing conditional probability density functions that have been used in the development of the combined Kalman and sequential importance sampling filter in Chapter 4 are elaborated in Appendix C.

The study of randomly excited nonlinear dynamical systems forms the focus of this thesis. We discuss two classes of problems: first, the characterization of nonlinear random response of the system before it comes into existence and, the second, assimilation of measured responses into the mathematical model of the system after the system comes into existence. The first class of problems constitutes forward problems while the latter belongs to the class of inverse problems. An outstanding feature of these problems is that they are almost always not amenable for exact solutions. We tackle in the present study these two classes of problems using Monte Carlo simulation tools in conjunction with Markov process theory, Bayesian model updating strategies, and particle filtering based dynamic state estimation methods. It is well recognized in literature that any successful application of Monte Carlo simulation methods to practical problems requires the simulation methods to be reinforced with effective means of controlling sampling variance. This can be achieved by incorporating any problem specific qualitative and (or) quantitative information that one might have about system behavior in formulating estimators for response quantities of interest. In the present thesis we outline two such approaches for variance reduction. The first of these approaches employs a substructuring scheme, which partitions the system states into two sets such that the probability distribution of the states in one of the sets conditioned on the other set become amenable for exact analytical solution. In the second approach, results from data based asymptotic extreme value analysis are employed to tackle problems of time variant reliability analysis and updating of this reliability. We exemplify in this thesis the proposed approaches for response estimation and model updating by considering wide ranging problems of interest in structural engineering, namely, nonlinear response and reliability analyses under stationary and (or) nonstationary random excitations, response sensitivity model updating, force identification, residual displacement analysis in instrumented inelastic structures under transient excitations, problems of dynamic state estimation in systems with local nonlinearities, and time variant reliability analysis and reliability model updating. We have organized the thesis into eight chapters and three appendices. A resume of contents of these chapters and appendices follows. In the first chapter we aim to provide an overview of mathematical tools which form the basis for investigations reported in the thesis. The starting point of the study is taken to be a set of coupled stochastic differential equations, which are obtained after discretizing spatial variables, typically, based on application of finite element methods. Accordingly, we provide a summary of the following topics: (a) Markov vector approach for characterizing time evolution of transition probability density functions, which includes the forward and backward Kolmogorov equations, (b) the equations governing the time evolution of response moments and first passage times, (c) numerical discretization of governing stochastic differential equation using Ito-Taylor’s expansion, (d) the partial differential equation governing the time evolution of transition probability density functions conditioned on measurements for the study of existing instrumented structures, (e) the time evolution of response moments conditioned on measurements based on governing equations in (d), and (f) functional recursions for evolution of multidimensional posterior probability density function and posterior filtering density function, when the time variable is also discretized. The objective of the description here is to provide an outline of the theoretical formulations within which the problems of response estimation and model updating are formulated in the subsequent chapters of the present thesis. We briefly state the class of problems, which are amenable for exact solutions. We also list in this chapter major text books, research monographs, and review papers relevant to the topics of nonlinear random vibration analysis and dynamic state estimation. In Chapter 2 we provide a review of literature on solutions of problems of response analysis and model updating in nonlinear dynamical systems. The main focus of the review is on Monte Carlo simulation based methods for tackling these problems. The review accordingly covers numerical methods for approximate solutions of Kolmogorov equations and associated moment equations, variance reduction in simulation based analysis of Markovian systems, dynamic state estimation methods based on Kalman filter and its variants, particle filtering, and variance reduction based on Rao-Blackwellization. In this review we chiefly cover papers that have contributed to the growth of the methodology. We also cover briefly, the efforts made in applying the ideas to structural engineering problems. Based on this review, we identify the problems of variance reduction using substructuring schemes and data based extreme value analysis and, their incorporation into response estimation and model updating strategies, as problems requiring further research attention. We also identify a range of problems where these tools could be applied. We consider the development of a sequential Monte Carlo scheme, which incorporates a substructuring strategy, for the analysis of nonlinear dynamical systems under random excitations in Chapter 3. The proposed substructuring ensures that a part of the system states conditioned on the remaining states becomes Gaussian distributed and is amenable for an exact analytical solution. The use of Monte Carlo simulations is subsequently limited for the analysis of the remaining system states. This clearly results in reduction in sampling variance since a part of the problem is tackled analytically in an exact manner. The successful performance of the proposed approach is illustrated by considering response analysis of a single degree of freedom nonlinear oscillator under random excitations. Arguments based on variance decomposition result and Rao-Blackwell theorems are presented to demonstrate that the proposed variance reduction indeed is effective. In Chapter 4, we modify the sequential Monte Carlo simulation strategy outlined in the preceding chapter to incorporate questions of dynamic state estimation when data on measured responses become available. Here too, the system states are partitioned into two groups such that the states in one group become Gaussian distributed when conditioned on the states in the other group. The conditioned Gaussian states are subsequently analyzed exactly using the Kalman filter and, this is interfaced with the analysis of the remaining states using sequential importance sampling based filtering strategy. The development of this combined Kalman and sequential importance sampling filtering method constitutes one of the novel elements of this study. The proposed strategy is validated by considering the problem of dynamic state estimation in linear single and multi-degree of freedom systems for which exact analytical solutions exist. In Chapter 5, we consider the application of the tools developed in Chapter 4 for a class of wide ranging problems in nonlinear random vibrations of existing systems. The nonlinear systems considered include single and multi-degree of freedom systems, systems with memoryless and hereditary nonlinearities, and stationary and nonstationary random excitations. The specific applications considered include nonlinear dynamic state estimation in systems with local nonlinearities, estimation of residual displacement in instrumented inelastic dynamical system under transient random excitations, response sensitivity model updating, and identification of transient seismic base motions based on measured responses in inelastic systems. Comparisons of solutions from the proposed substructuring scheme with corresponding results from direct application of particle filtering are made and a satisfactory mutual agreement is demonstrated. We consider next questions on time variant reliability analysis and corresponding model updating in Chapters 6 and 7, respectively. The research effort in these studies is focused on exploring the application of data based asymptotic extreme value analysis for problems on hand. Accordingly, we investigate reliability of nonlinear vibrating systems under stochastic excitations in Chapter 6 using a two-stage Monte Carlo simulation strategy. For systems with white noise excitation, the governing equations of motion are interpreted as a set of Ito stochastic differential equations. It is assumed that the probability distribution of the maximum over a specified time duration in the steady state response belongs to the basin of attraction of one of the classical asymptotic extreme value distributions. The first stage of the solution strategy consists of selection of the form of the extreme value distribution based on hypothesis testing, and, the next stage involves the estimation of parameters of the relevant extreme value distribution. Both these stages are implemented using data from limited Monte Carlo simulations of the system response. The proposed procedure is illustrated with examples of linear/nonlinear systems with single/multiple degrees of freedom driven by random excitations. The predictions from the proposed method are compared with the results from large scale Monte Carlo simulations, and also with the classical analytical results, when available, from the theory of out-crossing statistics. Applications of the proposed method for vibration data obtained from laboratory conditions are also discussed. In Chapter 7 we consider the problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations. Here we assume that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes’ theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplified by considering the reliability analysis of a few low dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on limited amount of pertinent Monte Carlo simulations. A summary of the contributions made and a few suggestions for future work are presented in Chapter 8. The thesis also contains three appendices. Appendix A provides details of the order 1.5 strong Taylor scheme that is extensively employed at several places in the thesis. The formulary pertaining to the bootstrap and sequential importance sampling particle filters is provided in Appendix B. Some of the results on characterizing conditional probability density functions that have been used in the development of the combined Kalman and sequential importance sampling filter in Chapter 4 are elaborated in Appendix C.