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Orientador: João Antônio Pereira / Banca: Luiz de Paula do Nascimento / Banca: Domingos Alves Rade / Resumo: A Análise Modal envolvendo apenas as respostas da estrutura é ainda um desafio que requer o uso de técnicas de identificação especiais. Este trabalho discute a identificação baseada apenas na resposta utilizando um método de identificação no tempo, mais especificamente, o método Identificação Estocástica de Subespaço. É mostrado que uma estrutura vibrando excitada por forças não conhecidas, pode ser modelada como um modelo de espaço de estado estocástico. A partir da aplicação de técnicas numéricas robustas como fatorização QR e Decomposição em Valores Singulares para a matriz bloco de Hankel semi-infinita, contendo os dados de resposta, é obtida a estimativa dos estados do modelo. Uma vez que os estados são conhecidos, o sistema de matrizes é encontrado através da solução de um problema de mínimos quadrados. Encontrado o modelo matemático da estrutura, os parâmetros modais são estimados diretamente através da decomposição em autovalores. O trabalho apresenta ainda uma metodologia que utiliza a função densidade de probabilidade para identificar possíveis componentes harmônicos contidos nos sinais de respostas. Os sinais são filtrados em uma faixa de freqüência contendo um provável modo e é verificado se este corresponde a um modo natural ou operacional. A metodologia é avaliada com dados simulados e experimentais e os resultados obtidos mostraram-se promissores para identificação dos parâmetros modais de sistemas estocásticos lineares e invariantes no tempo, utilizando apenas as respostas. / Abstract: Modal analysis using output-only measurements is still a challenge in the experimental modal analysis community. It requires the use of special modal identification techniques. This work discusses the concepts involved in the output-only modal analysis and the implementation of the Stochastic Subspace Identification time domain method. It is shown that a vibrating structure excited by an unknown force can be modelled as a stochastic state space model. In this approach, the SSI method estimates the state sequences directly from the response data and the modal parameters are estimated by using the eigenvalues decomposition of the state matrix. The steps of the procedure are implemented using the well-known numerical linear algebra algorithms, Singular Value Decomposition and the QR decomposition. It also includes a methodology based on the Probability Density Function to identify harmonic components of the response signals. The signals are filtering in a range of frequency containing a mode, to verify if it is a natural or operational mode. The approach is evaluated with simulated and experimental data and the results have shown to be promising to identify the modal parameters of stochastic linear time-invariant systems, based only on the output data. / Mestre

In most applications, the structure components have to be tested under different loading conditions before being placed in operation. A reliable and low cost measuring technique is desirable. However, most currently employed measuring approaches can only provide the structural response at several discrete locations. The accuracy of the measurements varies with the location and orientation of the sensors. Practically, it is not possible to place sensors at all the critical locations for different excitations. Therefore, an approach that derives the full field response using a limited set of measured data is desirable. In contrast to experimental full field measurement techniques, the expansion approach involves analytically expanding the limited measurements to all the degrees of freedom of the structure. Among all the analytical methods, the modal expansion method is computationally efficient and thus more suitable for real time expansion of measured data. In this method, the full-field response is approximated by the linear combination of mode shapes. In previous studies, the modal expansion method is limited by errors from mode aliasing, inaccuracy of the calculated mode shapes and the noise in measurements. In order to overcome these limitations, the modal expansion method is enhanced by mode selection and error compensation in this study. First, the key parameters used in modal expansion method were analyzed using a cantilever beam model and a method for optimal placement of sensors was developed. A mode selection method and error compensation method based on operation modal analysis and adaptive compressed sensing techniques were then developed to reduce the effects of mode aliasing, mode shape inaccuracy and measurement noise. The developed approach was further tested virtually using a numerical model of rotor 67. The numerical model was created using a two-way coupled fluid structure interaction technique. By developing these methods, the enhanced modal expansion approach can provide full field response for structures under different load conditions. Compared to the traditional modal expansion method, it can expand the data with high noise and under general dynamic loading. / Doctor of Philosophy / Accurate knowledge of the strain and stress at critical locations of a given structure is crucial when assessing its integrity. However, currently employed measuring approaches can only provide the structural response at several discrete locations. Practically, it is not possible to place sensors at all the critical locations for different excitations. Therefore, an approach that derives the full field response using a limited set of measured data is desirable. Compared to experimental full field measurement techniques, the expansion approach is focused on analytically expanding the limited measurements to all the degrees of freedom of the structure. Among all the analytical methods, the modal expansion method is computationally efficient and thus more suitable for real-time expansion of measured data. The current modal expansion method is limited by errors from mode aliasing, inaccuracy of the mode shapes, and the noise in measurements. Therefore, an enhanced method is proposed to overcome these shortcomings of the modal expansion. The following objectives are accomplished in this study: 1) Develop a method for optimal placement of sensors for modal expansion; 2) Eliminate the mode aliasing effects by determining the significance of participated modes using operational modal analysis techniques; 3) Compensate for the noise in measurements and computational model by implementing the compressed sensing approach. After accomplishing these goals, the developed approach is able to provide full field response for structures under different load conditions. Compared to the traditional modal expansion method, it can expand the data under dynamic loading; it also shows promise in reducing the effects of noise and errors. The developed approach is numerically tested using fluid-structure interaction model of rotor 67 fan blade.

The low frequency (0-500 Hz) automotive noise and vibration behavior is influenced by the rolling dynamics of the tire. Driven by pressing environmental concerns, the automotive industry has strived to innovate fuel-efficient and quieter powertrain systems over the last decade. This has eventually led to the prevalence of hybrid and electric vehicles. With the noise masking effect of the engine orders being absent, the interior structure-borne noise is dominated by the tire pavement interaction under 500 Hz. This necessitates an accurate estimation of rolling tire dynamics. To this date, there is no direct procedure available for modal analysis of rolling tires with tread patterns under realistic operating conditions. The present start-of-art laser vibrometer based non-contact measurements are limited to tread vibration measurement of smooth tires only in a lab environment. This study focuses on devising an innovative strategy to use a wireless Tire Cavity Accelerometer (TCA) and two optical sensors in a tire on drum setup with cleat excitation to characterize dynamics of tread vibration in an appreciably easier, time and cost-effective approach. In this approach, First, the TCA vibration signal in a single test run is clustered into several groups representing an array of virtual sensor position at different circumferential positions. Then modal identification has been performed using both parametric and non-parametric operational modal identification procedures. Furthermore, relevant conclusions are drawn about the observed modal properties of the tire under rolling including the limitations of the proposed method. The method proposed here, as is, can be applied to a treaded tire and can also be implemented in an on-road test setup. / Master of Science / The low frequency(0-500 Hz) interior noise and vibration of an automobile is primarily influenced by the dynamics of the rolling tire. In recent studies, the laser vibrometer with moving mirrors for measurement of vibration on the tread of a rotating tire has been used. However, these are limited to tires without tread pattern. In this study, an innovative experimental way of performing operational modal analysis using the Tire cavity Accelerometer (TCA) and optical sensors is presented. The proposed method is simpler in terms of instrumentation and cost and time-effective. This method, as is, can also be implemented in case of a treaded tire

Civil infrastructure failure is hard to predict, both in terms of occurrence and impact. This is due to combination of many factors, including highly variable environmental and operational conditions, complex construction and materials, and the sheer size of these structures. Often, the mitigation strategy is visual inspection and regular maintenance, which can be time-consuming and may not address root causes of failure. One potential solution to anticipating infrastructure failure and mitigating its consequences is the use of distributed sensors to monitor the physical state of a structure, an area of research known commonly as structural health monitoring, or SHM. This approach can be applied in a variety of contexts: safety during and after natural disasters, evaluation of building construction quality and life-cycle assessment for performance based design frameworks. In one way or another, SHM methods always require a ``baseline,'' a set of physical features which describes the behavior of a healthy structure. Often, the baseline is defined in terms of modal parameters: natural frequencies, damping ratios, and mode shapes. Although changes in modal parameters are indicative of structural damage, they are also indicative of a slew of non-damage factors, such as signal-to-noise ratio, environmental conditions, and the characteristics of forces exciting the structure. In many cases, the degree of observed modal parameter changes due to non-damage factors can be much greater than that due to damage itself. This is especially true of low-frequency modal parameters. For example, the fundamental frequency of a building is more sensitive to global influences like temperature than local structural changes like a cracked column. It has been proposed that extracting modal parameters at higher frequencies may be the key to improving the damage-sensitivity of SHM methods. However, for now, modal analysis of civil structures has been limited to low frequency ambient excitation and sparse sensor networks, due to practical limitations. Two key components for high-frequency modal analysis have yet to be studied: 1) Sufficient excitation at high frequencies and 2) high-resolution (high sensor density) measurements. The unifying goal of this work is to expand modal analysis in these two areas by applying novel instrumentation and experimental methods to two full-scale buildings, Goodwin Hall and Ernest Cockrell Jr. Hall. This enables realistic, practical insights into the limitations and benefits of the high-frequency SHM approach. Throughout, analyses are supported through the novel integration of uncertainty quantification techniques which so far has been under-utilized in the field. This work is divided into three experimental areas, with approaches centering on the identification of modal parameters. The first area is the application of high spacial resolution sensor networks in combination to ambient vibration testing. The second is the implementation of a robust automation and monitoring strategy for complex dynamic structures. The third is the testing of a novel method for performing experimental modal analysis on buildings emph{in situ}. The combination of results from these experiments emphasizes key challenges in establishing reliable high-frequency, high-resolution modal parameter ``baselines'' for structural health monitoring (SHM) of civil infrastructure. The first study presented in this work involved the identification of modal parameters from a five-story building, Goodwin Hall, using operational modal analysis (OMA) on ambient vibration data. The analysis began with a high spacial density network of 98 accelerometers, later expanding this number to 117. A second extensional study then used this data as reference to implement a novel automation method, enabling the identification of long-term patterns in the building's response behavior. Three dominant sources of ambient excitation were identified for Goodwin Hall: wind, human-induced loading, and consistent low-level vibrations from machinery, etc. It was observed that the amplitude of excitation, regardless of source, had significant effects on the estimated natural frequencies and damping ratios. Namely, increased excitation translated to lower natural frequencies and higher damping. In addition, the sources had different characteristics in terms of excitation direction and bandwidth, which contributed to significantly different results depending on the ambient excitation employed. This has significant implications for ambient-based methods that assume that all ambient vibrations are broadband random noise. The third and final study demonstrated the viability of emph{in situ} seismic testing for controlled excitation of full-scale civil structures, also known as experimental modal analysis (EMA). The study was performed by exciting Ernest Cockrell Jr. Hall in Austin, Texas with both vertical and lateral ground waves from seismic shaker truck, T-Rex. The EMA results were compared to a standard operational modal analysis (OMA) procedure which relies on passive ambient vibrations. The study focused on a frequency bandwidth from 0 to 11 Hz, which was deemed high frequency for such a massive structure. In cases were coherence was good, the confidence comparable or better than OMA, with the added advantage that the EMA tests took only a fraction of the time. The ability to control excitation direction in EMA enabled the identification of new structural information that was not observed OMA. It is proposed that the combination of high spacial resolution instrumentation and emph{in situ} excitation have the potential to achieve reliable high-frequency characterization, which are not only more sensitive to local damage but also, in some cases, less sensitive to variations in the excitation conditions. / Ph. D. / Civil structures, like buildings and bridges, become weaker as they age, increasing their risk of collapse due to sever weather, earthquakes, and heavy traffic. Engineers regularly inspect civil structures to ensure they are in good shape, but it is difficult do a full assessment by eye since many defects can be hidden. Structural Health Monitoring, or SHM for short, is an approach that uses permanent vibration sensors to continuously inspect civil structures. Any activity, like blowing wind or moving traffic on bridge, produces small vibrations which can be analyzed to assess the “health” of the structure. This approach can detect some invisible defects, but there is still debate about whether it can detect them when they are small and early on in the life of a structure. If SHM can’t issue early warnings, then there is little incentive to spend large amounts of money on a sensor system. To capture small defects, a sensor system needs a large number of sensors, hence the term high-resolution in the title. In addition, the structure being tested needs to vibrate rapidly (that is at high-frequencies) in order for the high-resolution information to be useful. So far, there have been no tests of this kind on civil structures, especially buildings. Instead, most sensor systems have contained a relatively low number of sensors tested with low-frequency vibrations. This works fills in this gap by testing two different buildings with SHM sensor systems. The first experiment uses a very high number of sensors to analyze the vibrations of Goodwin Hall on the Virginia Tech campus. The vibrations in this building are produced by wind and people walking inside. The second experiment uses a standard number of sensors, but explores a new method of vibrating buildings. This method uses a truck with a large hydraulic piston to shake the ground near the E. Cockrell Jr. building (University of Austin-Texas), essentially creating a tiny earthquake. The experiments show that both testing techniques provide more useful information than standard ones alone. For the first experiment, using more sensors meant the analysis could better distinguish the structural characteristics of the building. For the second, the artificial “earthquake” enabled the measurement of high-frequency vibrations, something which was not possible by relying on wind or people to vibrate the building. Although these new approaches are not used to inspect for damage, they have laid the foundation for improving the early-warning capabilities of SHM systems. This could mean that buildings and other structures can be repaired sooner, remain in operation longer, and cost the owners less money in the end!

Timber is a building material that is becoming more common and of interest for use in high-rise buildings. One of the reasons is that timber requires less energy input for the manufacturing process of the material compared to non-wood based materials. When designing high- rise timber buildings it is of great significance to understand the dynamic behavior of the structure. One method to obtain the dynamic properties is to use Operational Modal Analysis, which is based on the structural response from operational use. Finite element (FE) analysis is a tool which can be used for dynamic analysis for large structures. In this study an Operation Modal Analysis (OMA) was conducted on a four-story timber building in Växjö. A finite element model was created of the same building using commercial FE packages. Based on the mode shapes and natural frequencies obtained from the OMA, the FE model was fine-tuned. The purpose of this thesis is to gain knowledge of which parameters that might have a significant role in finite element modelling for a structural dynamic analysis. The aim is to develop a finite element model that accurately simulates the dynamic behavior of the tested building. It was shown from the result that is possible with an enough detailed FE model to capture the dynamic behaviour of a structure. The parameters that had the largest effect on the result can be pointed to the mass and the stiffness of the structure. / Trä är ett byggnadsmaterial som börjar bli allt mer vanligt och är av intresse att använda som stommaterial för höga byggnader. En anledning till detta är att det krävs mindre energi i tillverkningsfasen för trä jämfört med stål och betong. Vid dimensionering av höga träbyggnader är det essentiellt att förstå byggnadens dynamiska egenskaper. För att ta fram en byggnads dynamiska egenskaper kan en metod som benämns Operational Modal Analysis (OMA) tillämpas vilken baseras på byggnadens rörelser vid daglig användning. Finita element (FE) metoden är ett verktyg som kan användas vid dynamisk analys för större byggnader. I detta arbete genomfördes en OMA för ett fyravåningshus med trästomme beläget i Växjö. Genom användning av kommersiella FE-mjukvaror togs en finita element modell av samma byggnad fram. Baserat på de egenfrekvenser och egenmoder erhållna från OMA, uppdaterades FE-modellen därefter. Syftet med detta arbete är att erhålla kunskap kring vilka parametrar som har betydelse vid FE-modellering med hänsyn till dynamisk analys. Syftet är även att validera den prototyp av datainsamlingsenhet som använts vid fältmätningen. Målet med arbetet är att ta fram en FE-modell som på ett korrekt sätt beskriver den testade byggnadens dynamiska beteende. Resultatet av arbetet påvisar att med en tillräckligt detaljerad FE-modell är det möjligt att erhålla en byggnads dynamiska egenskaper. De parametrar som har störst inverkan på resultatet är byggnadens styvhet och inkluderad massa.

Chatter, unstable vibration during machining, damages the tool and workpiece. A proper selection of spindle speed and depth of cut are required to prevent chatter during machining. Such proper cutting conditions are usually determined using vibration models of the machining process. Nonetheless, uncertainties in modeling or changes in dynamics during the machining operations can lead to unstable machining vibrations, and chatter may arise even when stable cutting conditions are used in the process planning stage. As a result, online chatter monitoring systems are key to ensuring chatter-free machining operations. Although various chatter monitoring systems are described in the literature, most of the existing methods are suitable for detecting chatter after vibrations become unstable. In order to prevent poor surface finish resulting from chatter marks during the finishing stages of machining, a new monitoring system that is capable of predicting the occurrence of chatter while vibrations are still stable is required. In this thesis, a new approach for predicting the loss of stability during stable turning operations is developed. The new method is based on the identification of the dynamics of self-excited vibrations during turning operations using Operational Modal Analysis (OMA). The numerical simulations and experimental results presented in this thesis confirm the possibility of using Operational Modal Analysis as an online chatter prediction method during stable machining operations. / Graduate

Made available in DSpace on 2014-06-11T19:27:14Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-05-16Bitstream added on 2014-06-13T18:31:07Z : No. of bitstreams: 1 nunesjr_oa_me_ilha.pdf: 970524 bytes, checksum: 9726745cf5f299c04ce31a23c4988b5c (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / A Análise Modal envolvendo apenas as respostas da estrutura é ainda um desafio que requer o uso de técnicas de identificação especiais. Este trabalho discute a identificação baseada apenas na resposta utilizando um método de identificação no tempo, mais especificamente, o método Identificação Estocástica de Subespaço. É mostrado que uma estrutura vibrando excitada por forças não conhecidas, pode ser modelada como um modelo de espaço de estado estocástico. A partir da aplicação de técnicas numéricas robustas como fatorização QR e Decomposição em Valores Singulares para a matriz bloco de Hankel semi-infinita, contendo os dados de resposta, é obtida a estimativa dos estados do modelo. Uma vez que os estados são conhecidos, o sistema de matrizes é encontrado através da solução de um problema de mínimos quadrados. Encontrado o modelo matemático da estrutura, os parâmetros modais são estimados diretamente através da decomposição em autovalores. O trabalho apresenta ainda uma metodologia que utiliza a função densidade de probabilidade para identificar possíveis componentes harmônicos contidos nos sinais de respostas. Os sinais são filtrados em uma faixa de freqüência contendo um provável modo e é verificado se este corresponde a um modo natural ou operacional. A metodologia é avaliada com dados simulados e experimentais e os resultados obtidos mostraram-se promissores para identificação dos parâmetros modais de sistemas estocásticos lineares e invariantes no tempo, utilizando apenas as respostas. / Modal analysis using output-only measurements is still a challenge in the experimental modal analysis community. It requires the use of special modal identification techniques. This work discusses the concepts involved in the output-only modal analysis and the implementation of the Stochastic Subspace Identification time domain method. It is shown that a vibrating structure excited by an unknown force can be modelled as a stochastic state space model. In this approach, the SSI method estimates the state sequences directly from the response data and the modal parameters are estimated by using the eigenvalues decomposition of the state matrix. The steps of the procedure are implemented using the well-known numerical linear algebra algorithms, Singular Value Decomposition and the QR decomposition. It also includes a methodology based on the Probability Density Function to identify harmonic components of the response signals. The signals are filtering in a range of frequency containing a mode, to verify if it is a natural or operational mode. The approach is evaluated with simulated and experimental data and the results have shown to be promising to identify the modal parameters of stochastic linear time-invariant systems, based only on the output data.

All structures have modal properties such as natural frequencies and damping. In engineeringit is often of interest to estimate these modal properties for certain structures, to be used whenmodelling for example fatigue. This is done by computing them from finite element models, by using experimental measurements or both. In the case of doing both, a finite elementmodel is usually established first and adjusted to fit measurements from experiments. Atlas Copco Rock Drills AB is the company where this thesis has been performed and the subject is experimental procedures related to estimating modal properties of the so calledpower pack, which essentially is a modularised engine and hydraulic power source of an Atlas Copco drill rig. Their current method for estimating these properties is a classical procedure which makes use of an impact hammer that an operator strikes the power pack with to induce excitation. Due to concealment of behind other parts the power pack when mounted inside the drill rig, the number of places where the operator is able to strike the power pack in is limited. Another problem with the current procedure is that it can be difficult to strike the power pack with a strong enough impulse to generate reliable results. In this thesis a new experimental procedure for Atlas Copco to use is suggested. It is based on operational modal analysis (OMA), which uses the machinery's excitation from its operational conditions to compute modal estimates. A comparison between different experimental procedures have been done and the suggested procedure is the following: excitation by engine sweep; modal identifcation by the PolyMAX method and mode shape scaling by the harmonic scaling method. An experiment was performed to compare two OMA procedures.The suggested procedure is the one that generated the better results of the two.