No description available.

This study introduces new families of wavelets. The first is directly derived from the response of Second Order Underdamped Linear-Time-Invariant (SOULTI) systems, while the second is a generalization of the first to the complex domain and is similar to the Laplace transform kernel function. The first takes the acronym of SOULTI wavelet, while the second is named the Laplace wavelet. The most important criteria for a function or signal to be a wavelet is the ability to recover the original signal back from its continuous wavelet transform. It is shown that it is possible to recover back the original signal once the SOULTI or the Laplace wavelet transform is applied to decompose the signal. It is found that both wavelet transforms satisfy linear differential equations called the reconstructing differential equations, which are closely related to the differential equations that produce the wavelets. The new wavelets can have well defined Time-Frequency resolutions, and they have useful properties; a direct relation between the scale and the frequency, unique transform formulas that can be easily obtained for most elementary signals such as unit step, sinusoids, polynomials, and decaying harmonic signals, and linear relations between the wavelet transform of signals and the wavelet transform of their derivatives and integrals. The defined wavelets are applied to system analysis applications. The new wavelets showed accurate instantaneous frequency identification and modal decomposition of LTI Multi-Degree of Freedom (MDOF) systems and it showed better results than the Short-time Fourier Transform (STFT) and the other harmonic wavelets used in time-frequency analysis. The modal decomposition is applied for modal parameters identification, and the properties of the Laplace and the SOULTI wavelet transforms allows analytical and accurate identification methods. / Ph. D.

Thesis (MScEng)--University of Stellenbosch, 2000. / ENGLISH ABSTRACT: Air pollution is a major concern III the Cape Metropole. A major contributor to the air pollution problem is road transport. For this reason, a national vehicle emissions study is in progress with the aim of developing a national policy regarding motor vehicle emissions and control. Such a policy could bring about vehicle emission control and regulatory measures, which may have far-reaching social and economic effects. Air pollution models are important tools 10 predicting the effectiveness and the possible secondary effects of such policies. It is therefore essential that these models are fundamentally sound to maintain a high level of prediction accuracy. Complex air pollution models are available, but they require spatial, time-resolved information of emission sources and a vast amount of processing power. It is unlikely that South African cities will have the necessary spatial, time-resolved emission information in the near future. An alternative air pollution model is one that is based on the Gaussian Plume Model. This model, however, relies on gross simplifying assumptions that affect model accuracy. It is proposed that statistical and mathematical analysis techniques will be the most viable approach to modelling air pollution in the Cape Metropole. These techniques make it possible to establish statistical relationships between pollutant emissions, meteorological conditions and pollutant concentrations without gross simplifying assumptions or excessive information requirements. This study investigates two analysis techniques that fall into the aforementioned category, namely, Non-linear Time Series Analysis (specifically, the method of delay co-ordinates) and Singular Spectrum Analysis (SSA). During the past two decades, important progress has been made in the field of Non-linear Time Series Analysis. An entire "toolbox" of methods is available to assist in identifying non-linear determinism and to enable the construction of predictive models. It is argued that the dynamics that govern a pollution system are inherently non-linear due to the strong correlation with weather patterns and the complexity of the chemical reactions and physical transport of the pollutants. In addition to this, a statistical technique (the method of surrogate data) showed that a pollution data set, the oxides of Nitrogen (NOx), displayed a degree of non-linearity, albeit that there was a high degree of noise contamination. This suggested that a pollution data set will be amenable to non-linear analysis and, hence, Non-linear Time Series Analysis was applied to the data set. SSA, on the other hand, is a linear data analysis technique that decomposes the time series into statistically independent components. The basis functions, in terms of which the data is decomposed, are data-adaptive which makes it well suited to the analysis of non-linear systems exhibiting anharmonic oscillations. The statistically independent components, into which the data has been decomposed, have limited harmonic content. Consequently, these components are more amenable to prediction than the time series itself. The fact that SSA's ability has been proven in the analysis of short, noisy non-linear signals prompted the use of this technique. The aim of the study was to establish which of these two techniques is best suited to the modelling of air pollution data. To this end, a univariate model to predict NOx concentrations was constructed using each of the techniques. The prediction ability of the respective model was assumed indicative of the accuracy of the model. It was therefore used as the basis against which the two techniques were evaluated. The procedure used to construct the model and to quantify the model accuracy, for both the Non-linear Time Series Analysis model and the SSA model, was consistent so as to allow for unbiased comparison. In both cases, no noise reduction schemes were applied to the data prior to the construction of the model. The accuracy of a 48-hour step-ahead prediction scheme and a lOO-hour step-ahead prediction scheme was used to compare the two techniques. The accuracy of the SSA model was markedly superior to the Non-linear Time Series model. The paramount reason for the superior accuracy of the SSA model is its adept ability to analyse and cope with noisy data sets such as the NOx data set. This observation provides evidence to suggest that Singular Spectrum Analysis is better suited to the modelling of air pollution data. It should therefore be the analysis technique of choice when more advanced, multivariate modelling of air pollution data is carried out. It is recommended that noise reduction schemes, which decontaminate the data without destroying important higher order dynamics, should be researched. The application of an effective noise reduction scheme could lead to an improvement in model accuracy. In addition to this, the univariate SSA model should be extended to a more complex multivariate model that explicitly encompasses variables such as traffic flow and weather patterns. This will explicitly expose the inter-relationships between the variables and will enable sensitivity studies and the evaluation of a multitude of scenarios. / AFRIKAANSE OPSOMMING: Die hoë vlak van lugbesoedeling in die Kaapse Metropool is kommerwekkend. Voertuie is een van die hoofoorsake, en as gevolg hiervan word 'n landswye ondersoek na voertuigemissie tans onderneem sodat 'n nasionale beleid opgestel kan word ten opsigte van voertuigemissie beheer. Beheermaatreëls van so 'n aard kan verreikende sosiale en ekonomiese uitwerkings tot gevolg hê. Lugbesoedelingsmodelle is van uiterste belang in die voorspelling van die effektiwiteit van moontlike wetgewing. Daarom is dit noodsaaklik dat hierdie modelle akkuraat is om 'n hoë vlak van voorspellingsakkuraatheid te handhaaf. Komplekse modelle is beskikbaar, maar hulle verg tyd-ruimtelike opgeloste inligting van emmissiebronne en baie berekeningsvermoë. Dit is onwaarskynlik dat Suid-Afrika in die nabye toekoms hierdie tydruimtelike inligting van emissiebronne gaan hê. 'n Alternatiewe lugbesoedelingsmodel is dié wat gebaseer is op die "Guassian Plume". Hierdie model berus egter op oorvereenvoudigde veronderstellings wat die akkuraatheid van die model beïnvloed. Daar word voorgestel dat statistiese en wiskundige analises die mees lewensvatbare benadering tot die modellering van lugbesoedeling in die Kaapse Metropool sal wees. Hierdie tegnieke maak dit moontlik om 'n statistiese verwantskap tussen besoedelingsbronne, meteorologiese toestande en besoedeling konsentrasies te bepaal sonder oorvereenvoudigde veronderstellings of oormatige informasie vereistes. Hierdie studie ondersoek twee analise tegnieke wat in die bogenoemde kategorie val, naamlik, Nie-lineêre Tydreeks Analise en Enkelvoudige Spektrale Analise (ESA). Daar is in die afgelope twee dekades belangrike vooruitgang gemaak in die studieveld van Nie-lineêre Tydreeks Analise. 'n Volledige stel metodes is beskikbaar om nie-lineêriteit te identifiseer en voorspellingsmodelle op te stel. Dit word geredeneer dat die dinamika wat 'n besoedelingsisteem beheer nie-lineêr is as gevolg van die sterk verwantskap wat dit toon met weerpatrone asook die kompleksiteit van die chemiese reaksies en die fisiese verplasing van die besoedelingstowwe. Bykomend verskaf 'n statistiese tegniek (die metode van surrogaatdata) bewyse dat 'n lugbesoedelingsdatastel, die okside van Stikstof (NOx), melineêre gedrag toon, alhoewel daar 'n hoë geraasvlak is. Om hierdie rede is die besluit geneem om Nie-lineêre Tydreeks Analise aan te wend tot die datastel. ESA daarenteen, is 'n lineêre data analise tegniek. Dit vereenvoudig die tydreeks tot statistiese onafhanklike komponente. Die basisfunksies, in terme waarvan die data vereenvoudig is, is data-aanpasbaar en dit maak hierdie tegniek gepas vir die analise van nielineêre sisteme. Die statisties onafhanklike komponente het beperkte harmoniese inhoud, met die gevolg dat die komponente aansienlik makliker is om te voorspel as die tydreeks self. ESA se effektiwitiet is ook al bewys in die analise van kort, hoë-graas nie-lineêre seine. Om hierdie redes, is ESA toegepas op die lugbesoedelings data. Die doel van die ondersoek was om vas te stel watter een van die twee tegnieke meer gepas is om lugbesoedelings data te analiseer. Met hierdie doelwit in sig, is 'n enkelvariaat model opgestel om NOx konsentrasies te voorspel met die gebruik van elk van die tegnieke. Die voorspellingsvermoë van die betreklike model is veronderstelom as 'n maatstaf van die model se akkuraatheid te kan dien en dus is dit gebruik om die twee modelle te vergelyk. 'n Konsekwente prosedure is gevolg om beide die modelle te skep om sodoende invloedlose vergelyking te verseker. In albei gevalle was daar geen geraasverminderings-tegnieke toegepas op die data nie. Die akuraatheid van 'n 48-uur voorspellingsmodel en 'n 100-uur voorspellingsmodel was gebruik vir die vergelyking van die twee tegnieke. Daar is bepaal dat die akkuraatheid van die ESA model veel beter as die Nie-lineêre Tydsreeks Analise is. Die hoofrede vir die ESA se hoër akkuraatheid is die model se vermoë om data met hoë geraasvlakke te analiseer. Hierdie ondersoek verskaf oortuigende bewyse dat Enkelvoudige Spektrale Analiese beter gepas is om lugbesoedelingsdata te analiseer en gevolglik moet hierdie tegniek gebruik word as meer gevorderde, multivariaat analises uitgevoer word. Daar word aanbeveel dat geraasverminderings-tegnieke, wat die data kan suiwer sonder om belangrike hoë-orde dinamika uit te wis, ondersoek moet word. Hierdie toepassing van effektiewe geraasverminderings-tegniek sal tot 'n verbetering in model-akkuraatheid lei. Aanvullend hiertoe, moet die enkele ESA model uitgebrei word tot 'n meer komplekse multivariaat model wat veranderlikes soos verkeersvloei en weerpatrone insluit. Dit sal die verhoudings tussen veranderlikes ten toon stel en sal sensitiwiteit-analises en die evaluering van menigte scenarios moontlik maak.

Les travaux de recherche présentés dans cette thèse concernent des contributions à l’étude de stabilité des systèmes linéaires à retards avec contrôleurs d’ordre réduit. Cette mémoire est partagée en trois parties.La première partie est axée sur l’étude des systèmes linéaires à retard mono-entré /mono-sortie, bouclées avec un contrôleur de type PID. Inspiré par l’approche géométrique développée par Gu et al. Nous avons proposé une méthode analytique pour trouver la région (ou les régions) de tous les contrôleurs de type PID stabilisant pour le système à retard. Basée sur cette même approche, on a développé un algorithme pour calculer le dégrée de fragilité d’un contrôleur donné de type PID (PI, PD et PID).La deuxième partie de la thèse est axée sur l’étude de stabilité sous une approche NCS (pour son acronyme en anglais : Networked Control System). Plus précisément, nous avons d’abord étudié le problème de la stabilisation en tenant compte des retards induit par le réseau et les effets induits par la période d’échantillonnages. Pour mener une telle analyse nous avons adopté une approche basée sur la théorie des perturbations. Finalement, dans la troisième partie de la thèse nous abordons certains problèmes concernant le comportement des zéros d’une certaine classe de systèmes échantillonnés mono-entré /mono-sortie. Plus précisément, étant donné un système à temps continu, on obtient les intervalles d’échantillonnage garantissant l’invariance du nombre de zéros instables dans chaque intervalle. Pour développer cette analyse, nous adoptons une approche basée sur la perturbation aux valeurs propres. / The research work presented in this thesis concern to the stability analysis of linear time-delay systems with low-order controllers. This thesis is divided into three parts.The first part of the thesis focus on the study of linear SISO (single-input/single-output) systems with input/output delays, where the feedback loop is closed with a controller of PID-type. Inspired by the geometrical approach developed by Gu et al. we propose an analytical method to find the stability regions of all stabilizing controllers of PID-type for the time-delay system. Based on this same approach, we propose an algorithm to calculate the degree of fragility of a given controller of PID- type (PI, PD and PID).The second part of the thesis focuses on the stability analysis of linear systems under an NCS (Networked System Control) based approach. More precisely, we first focus in the stabilization problem by taking into account the induced network delays and the effects induced by the sampling period. To carry out such an analysis we have adopted an eigenvalue perturbation-based approach.Finally, in the third part of the thesis we tackle certain problems concerning to the behavior of the zeros of a certain class of sampled-data SISO systems. More precisely, given a continuous-time system, we obtain the sampling intervals guaranteeing the invariance of the number of unstable zeros in each interval. To perform such an analysis, we adopt an eigenvalue perturbation-based approach.

Les travaux présentés dans ce mémoire traitent de l'identification des systèmes dynamiques représentés sous la forme de modèles linéaires continus à paramètres variant lentement au cours du temps. La complexité du problème d'identification provient d'une part du caractère inconnu de la loi de variation des paramètres et d'autre part de la présence de bruits de nature inconnue sur les signaux mesurés. Les solutions proposées s'appuient sur une combinaison judicieuse du filtre de Kalman en supposant que les variations des paramètres peuvent être représentées sous la forme d'une marche aléatoire et de la méthode de la variable instrumentale qui présente l'avantage d'être robuste vis à vis de la nature des bruits de mesure. Les algorithmes de type récursif sont développés dans un contexte d'identification en boucle ouverte et en boucle fermée. Les différentes variantes se distinguent par la manière dont est construit la variable instrumentale. Inspirée de la solution développée pour les systèmes linéaires à temps invariant, une construction adaptative de la variable instrumentale est suggérée pour pouvoir suivre au mieux l'évolution des paramètres. Les performances des méthodes développées sont évaluées à l'aide de simulations de Monte Carlo et montrent la suprématie des solutions proposées s'appuyant sur la variable instrumentale par rapport celles plus classiques des moindres carrés récursifs. Les aspects pratiques et d'implantation numérique sont d'une importance capitale pour obtenir de bonnes performances lorsque ces estimateurs sont embarqués. Ces aspects sont étudiés en détails et plusieurs solutions sont proposées non seulement pour robustifier les estimateurs vis à vis du choix des hyper-paramètres mais également vis à vis de leur implantation numérique. Les algorithmes développés sont venus enrichir les fonctions de la boîte à outils CONTSID pour Matlab. Enfin, les estimateurs développés sont exploités pour faire le suivi de paramètres de deux systèmes physiques : un benchmark disponible dans la littérature constitué d'un filtre électronique passe-bande et une vanne papillon équipant les moteurs de voiture. Les deux applications montrent le potentiel des approches proposées pour faire le suivi de paramètres physiques variant lentement dans le temps / The work presented in this thesis deals with the identification of dynamic systems represented through continuous-time linear models with slowly time-varying parameters. The complexity of the identification problem comes on the one hand from the unknown character of the parameter variations and on the other hand from the presence of noises of unknown nature on the measured signals. The proposed solutions rely on a judicious combination of the Kalman filter assuming that the variations of the parameters can be represented in the form of a random walk, and the method of the instrumental variable which has the advantage of being robust with respect to the nature of the measurement noises. The recursive algorithms are developed in an open-loop and closed-loop identification setting. The different variants are distinguished by the way in which the instrumental variable is built. Inspired by the solution developed for time-invariant linear systems, an adaptive construction of the instrumental variable is suggested in order to be able to follow the evolution of the parameters as well as possible. The performance of the developed methods are evaluated using Monte Carlo simulations and show the supremacy of the proposed solutions based on the instrumental variable compared with the more classical least squares based approaches. The practical aspects and implementation issues are of paramount importance to obtain a good performance when these estimators are used. These aspects are studied in detail and several solutions are proposed not only to robustify the estimators with respect to the choice of hyperparameters but also with respect to their numerical implementation. The algorithms developed have enhanced the functions of the CONTSID toolbox for Matlab. Finally, the developed estimators are considered in order to track parameters of two physical systems: a benchmark available in the literature consisting of a bandpass electronic filter and a throttle valve equipping the car engines. Both applications show the potential of the proposed approaches to track physical parameters that vary slowly over time

"This dissertation proposes a vibration-based approach to detect and monitor structural damage by tracking the instantaneous modal parameters. A change in the instantaneous modal parameters indicates change in the structural health condition. In contrast to many existing structural health monitoring schemes, the proposed approach is less model dependent and works well for both sudden and evolving damage, general loading conditions and complex structures. The instantaneous modal parameters, including modal frequency, mode shape vector and modal damping ratio, are introduced as a bridge between the system properties and time varying vibration modes. The theoretical background of the time-varying vibration modes is developed. It has been shown that for slowly time-varying systems such modes exist and the instantaneous modal parameters have a clear physical interpretation and can be identified from free and forced vibration responses. A set of known techniques are used in an innovative way to identify the instantaneous modal parameters. Applicability of the identification techniques depends on the nature and availability of measurement data. Wavelet ridge method is used to identify the instantaneous modal frequencies and normalized instantaneous mode shape vectors from free vibration data. Wavelet packet sifting technique in conjunction with Hilbert transform and confidence index is proposed to identify the normalized instantaneous mode shape vector from both free and forced vibration data. Time-varying Kalman filter is integrated with the wavelet packet sifting technique to identify the instantaneous modal frequencies and the instantaneous modal damping ratios from free and forced vibration data. The proposed approach has been validated using both simulation and experimental data. The simulation data is obtained from a multi-degree-of-freedom system with time varying stiffness under different loading conditions. Experimental data include both impact testing data from the ASCE benchmark study and shaking-table test data of a full-size two-story wooden building structure, conducted at DPRI, Kyoto University, Japan. It has been shown that the proposed approach can successfully detect and monitor damage and, therefore, has great potential for real applications."

Os sinais de eletromiografia de agulha podem ser modelados por um sistema linear invariante no tempo (SLIT). A pergunta é: Quantos coeficientes são necessários para tal? O presente mestrado estuda, para sinais de eletromiografia de agulha gravados sob as mesmas condições experimentais, como varia o número ótimo de coeficientes autorregressivos com o comprimento das épocas e com a força de contração muscular concomitantemente. O estudo foi realizado tendo como base sinais de 10%, 25%, 50% e 80% da máxima contração voluntária (MCV) e tendo épocas de 500ms, 250ms, 100ms, 50ms e 25ms de seis indivíduos normais. Desta forma, uma função densidade de probabilidade é sugerida para a ordem do modelo autorregressivo que melhor descreva o sinal de eletromiografia obtido a uma força de contração específica e que tenha uma duração de época definida. / Needle electromyography signals (EMG) can be modeled by a linear time invariant system (LTI). The posed question is How many coefficients are needed for an adequate modeling? This Masters dissertation studies how the optimal number of autoregressive coefficients changes concomitantly with the epoch length and the muscle contraction force for needle electromyography signals recorded under the same experimental conditions. The study was conducted on signals from six normal individuals at 10%, 25%, 50% and 80% of the maximum voluntary contraction and epoch lengths of 500ms, 250ms, 100ms, 50ms and 25ms. Thus, a probability density function is suggested for the autoregressive model order that best describes the electromyographic signal obtained at a specific \"contraction force\" and has a defined \"epoch length\".

Os sinais de eletromiografia de agulha podem ser modelados por um sistema linear invariante no tempo (SLIT). A pergunta é: Quantos coeficientes são necessários para tal? O presente mestrado estuda, para sinais de eletromiografia de agulha gravados sob as mesmas condições experimentais, como varia o número ótimo de coeficientes autorregressivos com o comprimento das épocas e com a força de contração muscular concomitantemente. O estudo foi realizado tendo como base sinais de 10%, 25%, 50% e 80% da máxima contração voluntária (MCV) e tendo épocas de 500ms, 250ms, 100ms, 50ms e 25ms de seis indivíduos normais. Desta forma, uma função densidade de probabilidade é sugerida para a ordem do modelo autorregressivo que melhor descreva o sinal de eletromiografia obtido a uma força de contração específica e que tenha uma duração de época definida. / Needle electromyography signals (EMG) can be modeled by a linear time invariant system (LTI). The posed question is How many coefficients are needed for an adequate modeling? This Masters dissertation studies how the optimal number of autoregressive coefficients changes concomitantly with the epoch length and the muscle contraction force for needle electromyography signals recorded under the same experimental conditions. The study was conducted on signals from six normal individuals at 10%, 25%, 50% and 80% of the maximum voluntary contraction and epoch lengths of 500ms, 250ms, 100ms, 50ms and 25ms. Thus, a probability density function is suggested for the autoregressive model order that best describes the electromyographic signal obtained at a specific \"contraction force\" and has a defined \"epoch length\".

The signal structure is a partial structure representation for dynamic systems. It characterizes the causal relationship between manifest variables and is depicted in a weighted graph, where the weights are dynamic operators. Earlier work has defined signal structure for linear time-invariant systems through dynamical structure function. This thesis focuses on the search for the signal structure of nonlinear systems and proves that the signal structure reduces to the linear definition when the systems are linear. Specifically, this work: (1) Defines the complete computational structure for nonlinear systems. (2) Provides a process to find the complete computational structure given a state space model. (3) Defines the signal structure for dynamic systems in general. (4) Provides a process to find the signal structure for a class of dynamic systems from their complete computational structure.

時間序列分析發展至今,常常發現動態資料的走勢,隨著時間過程而演變.所以傳統的模式配適常無法得到很好的解釋,因此許多學者提出不同的模型建構方法.但是對於初始模式族的選擇,卻充滿相當的主觀與經驗認定成份.本文針對時變型時間序列分析,考慮利用知識庫,由模式庫來判斷初始模式.再藉由遺傳演算法的觀念,建立模式參數的遺傳關係.我們把這種遺傳演算法,稱之為時變遺傳演算法.針對台灣省國中數學教師人數,分別以時變遺傳演算法,狀態空間,與單變量ARIMA來建構模式,並作比較.比較結果發現,時變遺傳演算法較能掌握資料反轉的趨勢,且預測值增加較為平緩.因此時變遺傳演算法在模式建構上將是個不錯的選擇. / In time series analysis, we find often the trend of dynamic data changingwith time. Using the traditional model fitting can't get a good explanationfor dynamic data. Therefore, many savants developed a lot of methods formodel construction. However, these methods are usually influenced by personal viewpoint and experience in model base selection. In this thesis, we discussedtime-variant time series analysis. First, we builded a model base to judge inial models by knowledge base. Then, we set up the genetic relations of themodels' parameter. This method is called Time Variant Genetic Algorithm. We use the data if the number of junior high school mathematic teachers in Taiwan to ccompare the predictive performance of Time Variant Genetic Algorithmwith State Space and ARIMA. The forecasting performance shows the Time VariantGenetic Algorithm takes a better prediction result.