Identificação dos parâmetros modais utilizando apenas as respostas da estrutura: identificação no domínio do tempo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo e implementação do método de Ewins-Gleeson para identificação de parâmetros modais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Programa computacional com interface gráfica para identificação estocástica de parâmetros modais de estruturas civis: aplicação em pontes e torres de linha de transmissão

O interesse no comportamento dinâmico de estruturas metálicas vem crescendo nas últimas décadas no Brasil, em decorrência de acidentes com colapso total de algumas estruturas devido às vibrações ambientes em diversas regiões do país. Na região amazônica, por exemplo, onde esse tipo de estrutura deve vencer obstáculos como florestas e rios de grande largura, casos de colapso total de estruturas metálicas também são relatados. O foco principal dessa dissertação é o estudo do comportamento modal de estruturas metálicas submetidas às vibrações ambientes cuja magnitude das forças de excitação é desconhecida. Dois estudos de caso são apresentados: no primeiro deles, o comportamento modal de uma torre de linha de transmissão de energia elétrica é investigado; e no segundo caso, tanto o comportamento modal como os níveis de desconforto de uma ponte são estudados. Os estudos realizados neste último caso visam avaliar os níveis de desconforto da ponte quando submetida às excitações ambientes como rajadas de vento e o tráfego de veículo de acordo a norma brasileira NBR 8800 (1986). Em ambos os estudos de caso foram realizadas análises experimentais e computacionais. Na etapa experimental, ambas as estruturas foram monitoradas com emprego de um conjunto de acelerômetros de baixa freqüência e também de um sistema de aquisição apropriados para ensaios de vibração de estruturas civis. Como é muito difícil medir a magnitude das forças de excitação ambientes, foram utilizados os métodos de identificação estocásticos SSI-DATA e SSI-COV para extração de parâmetros modais de estruturas civis a partir somente dos dados de resposta coletados nos ensaios de vibração. Entre as atividades desenvolvidas nessa etapa, destaca-se a criação de um programa computacional com recursos do Graphical User Interface (GUI) da plataforma Matlab®, destinado à identificação modal de estruturas civis com o emprego dos referidos métodos estocásticos. Esse programa é constituído de três módulos: o primeiro é destinado ao processamento e tratamento dos sinais coletados nos ensaios de vibração; o segundo é utilizado para adicionar as informações do posicionamento dos acelerômetros utilizados nos arquivos dos sinais de resposta; e o terceiro e último módulo é destinado à identificação a partir dos arquivos de dados de resposta processados nos dois primeiros módulos. Na etapa das análises teóricas, foram criados modelos numéricos utilizando o método dos elementos finitos para simular o comportamento dinâmico das estruturas analisadas. Comparando os resultados obtidos em ambas as etapas de análise, verifica-se que resultados experimentais e teóricos apresentaram parâmetros bastante próximos entre si nos primeiros modos de vibração. Os resultados experimentais mostraram que ambos os métodos estocásticos foram muito eficientes na identificação das estruturas ensaiadas.

Flutter analysis including structural uncertainties

The common practice in industry is to perform flutter analyses considering the generalized stiffness and mass matrices obtained from finite element method (FEM) and aerodynamic generalized force matrices obtained from a panel method, as the doublet lattice method. These analyses are often reperformed if significant differences are found in structural frequencies and damping ratios determined from ground vibration tests compared to FEM. This unavoidable rework can result in a lengthy and costly process of analysis during the aircraft development. In this context, this paper presents an approach to perform flutter analysis including uncertainties in natural frequencies and damping ratios. The main goal is to assure the nominal system’s stability considering these modal parameters varying in a limited range. The aeroelastic system is written as an affine parameter model and the robust stability is verified solving a Lyapunov function through linear matrix inequalities and convex optimization

Application of Volterra series in nonlinear mechanical system identification and in structural health monitoring problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Computational Methods for Identification of Vibrating Structures

System identification deals with the problem of building mathematical models of dynamical systems based on observed data from the system" [1]. In the context of civil engineering, the system refers to a large scale structure such as a building, bridge, or an offshore structure, and identification mostly involves the determination of modal parameters (the natural frequencies, damping ratios, and mode shapes). This paper presents some modal identification results obtained using a state-of-the-art time domain system identification method (data-driven stochastic subspace algorithms [2]) applied to the output-only data measured in a steel arch bridge. First, a three dimensional finite element model was developed for the numerical analysis of the structure using ANSYS. Modal analysis was carried out and modal parameters were extracted in the frequency range of interest, 0-10 Hz. The results obtained from the finite element modal analysis were used to determine the location of the sensors. After that, ambient vibration tests were conducted during April 23-24, 2009. The response of the structure was measured using eight accelerometers. Two stations of three sensors were formed (triaxial stations). These sensors were held stationary for reference during the test. The two remaining sensors were placed at the different measurement points along the bridge deck, in which only vertical and transversal measurements were conducted (biaxial stations). Point estimate and interval estimate have been carried out in the state space model using these ambient vibration measurements. In the case of parametric models (like state space), the dynamic behaviour of a system is described using mathematical models. Then, mathematical relationships can be established between modal parameters and estimated point parameters (thus, it is common to use experimental modal analysis as a synonym for system identification). Stable modal parameters are found using a stabilization diagram. Furthermore, this paper proposes a method for assessing the precision of estimates of the parameters of state-space models (confidence interval). This approach employs the nonparametric bootstrap procedure [3] and is applied to subspace parameter estimation algorithm. Using bootstrap results, a plot similar to a stabilization diagram is developed. These graphics differentiate system modes from spurious noise modes for a given order system. Additionally, using the modal assurance criterion, the experimental modes obtained have been compared with those evaluated from a finite element analysis. A quite good agreement between numerical and experimental results is observed.

Joint statistical analysis of multiple measurement setups for the estimation of vibrational modes

Computing the modal parameters of large structures in Operational Modal Analysis often requires to process data from multiple non simultaneously recorded setups of sensors. These setups share some sensors in common, the so-called reference sensors that are fixed for all the measurements, while the other sensors are moved from one setup to the next. One possibility is to process the setups separately what result in different modal parameter estimates for each setup. Then the reference sensors are used to merge or glue the different parts of the mode shapes to obtain global modes, while the natural frequencies and damping ratios are usually averaged. In this paper we present a state space model that can be used to process all setups at once so the global mode shapes are obtained automatically and subsequently only a value for the natural frequency and damping ratio of each mode is computed. We also present how this model can be estimated using maximum likelihood and the Expectation Maximization algorithm. We apply this technique to real data measured at a footbridge.

Metodología de Ejecución y Explotación de los Ensayos en Vuelo de Flameo

El flameo o flutter es un fenómeno vibratorio debido a la interacción de fuerzas inerciales, elásticas y aerodinámicas. Consiste en un intercambio de energía, que se puede observar en el cambio de amortiguamientos, entre dos o más modos estructurales, denominados modos críticos, cuyas frecuencias tienden a acercarse (coalescencia de frecuencias). Los ensayos en vuelo de flameo suponen un gran riesgo debido a la posibilidad de una perdida brusca de estabilidad aeroelástica (flameo explosivo) con la posibilidad de destrucción de la aeronave. Además existen otros fenómenos asociados que pueden aparecer como el LCO (Limit Cycle Oscillation) y la interacción con los mandos de vuelo. Debido a esto, se deben llevar a cabo análisis exhaustivos, que incluyen GVT (vibraciones en tierra), antes de comenzar los ensayos en vuelo, y estos últimos deben ser ejecutados con robustos procedimientos. El objetivo de los ensayos es delimitar la frontera de estabilidad sin llegar a ella, manteniéndose siempre dentro de la envolvente estable de vuelo. Para lograrlo se necesitan métodos de predicción, siendo el “Flutter Margin”, el más utilizado. Para saber cuánta estabilidad aeroelástica tiene el avión y lo lejos que está de la frontera de estabilidad (a través de métodos de predicción) los parámetros modales, en particular la frecuencia y el amortiguamiento, son de vital importancia. El ensayo en vuelo consiste en la excitación de la estructura a diferentes condiciones de vuelo, la medición de la respuesta y su análisis para obtener los dos parámetros mencionados. Un gran esfuerzo se dedica al análisis en tiempo real de las señales como un medio de reducir el riesgo de este tipo de ensayos. Existen numerosos métodos de Análisis Modal, pero pocos capaces de analizar las señales procedentes de los ensayos de flameo, debido a sus especiales características. Un método novedoso, basado en la Descomposición por Valores Singulares (SVD) y la factorización QR, ha sido desarrollado y aplicado al análisis de señales procedentes de vuelos de flameo del F-18. El método es capaz de identificar frecuencia y amortiguamiento de los modos críticos. El algoritmo se basa en la capacidad del SVD para el análisis, modelización y predicción de series de datos con características periódicas y en su capacidad de identificar el rango de una matriz, así como en la aptitud del QR para seleccionar la mejor base vectorial entre un conjunto de vectores para representar el campo vectorial que forman. El análisis de señales de flameo simuladas y reales demuestra, bajo ciertas condiciones, la efectividad, robustez, resistencia al ruido y capacidad de automatización del método propuesto. ABSTRACT Flutter involves the interaction between inertial, elastic and aerodynamic forces. It consists on an exchange of energy, identified by change in damping, between two or more structural modes, named critical modes, whose frequencies tend to get closer to each other (frequency coalescence). Flight flutter testing involves high risk because of the possibility of an abrupt lost in aeroelastic stability (hard flutter) that may lead to aircraft destruction. Moreover associated phenomena may happen during the flight as LCO (Limit Cycle Oscillation) and coupling with flight controls. Because of that, intensive analyses, including GVT (Ground Vibration Test), have to be performed before beginning the flights test and during them consistent procedures have to be followed. The test objective is to identify the stability border, maintaining the aircraft always inside the stable domain. To achieve that flutter speed prediction methods have to be used, the most employed being the “Flutter Margin”. In order to know how much aeroelastic stability remains and how far the aircraft is from the stability border (using the prediction methods), modal parameters, in particular frequency and damping are paramount. So flight test consists in exciting the structure at various flight conditions, measuring the response and identifying in real-time these two parameters. A great deal of effort is being devoted to real-time flight data analysis as an effective way to reduce the risk. Numerous Modal Analysis algorithms are available, but very few are suitable to analyze signals coming from flutter testing due to their special features. A new method, based on Singular Value Decomposition (SVD) and QR factorization, has been developed and applied to the analysis of F-18 flutter flight-test data. The method is capable of identifying the frequency and damping of the critical aircraft modes. The algorithm relies on the capability of SVD for the analysis, modelling and prediction of data series with periodic features and also on its power to identify matrix rank as well as QR competence for selecting the best basis among a set of vectors in order to represent a given vector space of such a set. The analysis of simulated and real flutter flight test data demonstrates, under specific conditions, the effectiveness, robustness, noise-immunity and the capability for automation of the method proposed.

Análisis dinámico experimental de edificios esbeltos

Es conocido que la variación del comportamiento dinámico de las estructuras puede ser empleado dentro de un sistema de monitorización de su integridad estructural. Así, este estudio tiene como objetivo comprender el comportamiento dinámico de edificios esbeltos, frente a diferentes agentes ambientales como la temperatura y/o dirección y velocidad del viento. En el marco de esta investigación, se estudian dos edificios: la Torre de la ETSI (Escuela Técnica Superior de Ingenieros) de Caminos, Canales y Puertos de la UPM (Universidad Politécnica de Madrid) y un edificio de viviendas situado en la calle de Arturo Soria de Madrid. Los datos medioambientales antes mencionados, se registraron con sendas estacionales meteorológicas situadas en las azoteas de ambos edificios. Se realiza el análisis modal operacional de ambas estructuras. Este análisis se realiza a partir de las mediciones de las aceleraciones ante excitaciones ambientales, es un análisis basado sólo en la respuesta de la estructura. Por tanto, no es necesario interrumpir el funcionamiento en servicio de la instalación, obteniendo su comportamientos en este estado. A partir de este análisis, se obtienen las frecuencias naturales, los amortiguamientos modales y las formas modales. Así, en este trabajo se ha estudiado la relación existente entre la variación en la estimación de las frecuencias naturales y la variación de los agentes ambientales (fundamentalmente la temperatura). Los ensayos dinámicos en los dos edificios mencionados anteriormente, se han realizado utilizando acelerómetros de alta sensibilidad sincronizados inalámbricamente, lo cual ha simplificado el trabajo experimental si lo comparamos con los sistemas tradicionales. Como resultado del trabajo realizado se pueden destacar los siguientes puntos: (i) se ha visto que con el equipamiento disponible se pueden realizar análisis dinámicos de edificios, (ii) se ha mejorado el conocimiento dinámico de estas estructuras, y (iii) se ha visto la importancia que pueden tener los agentes ambientales dependiendo por un lado del tipo estructura del edificio. A partir del trabajo, se podrían actualizar modelos matemáticos que sirvan para la predicción de daños en las estructuras, y por otro, se podrán eliminar los efectos de los agentes ambientales, lo cual es un punto vital si se quiere emplear los parámetros modales para el cálculo de indices de daño. La aplicación de este tipo de investigación ayudará a tener una información mayor sobre el comportamiento de las estructuras y así, en el futuro, poder realizar distintos tipos de procesos, como la formulación de modelos matemáticos que reflejen con mayor fidelidad el comportamiento real. De esta forma, la monitorización de los agentes medioambientales permitirán valorar la influencia de estas variaciones sobre la estructura pudiéndose eliminar estos efectos. Con ello, se mejora la incertidumbre en la variación de frecuencias que puede ser utilizada como un sistema de activación de alarmas frente a la detección de daños estructurales. It is known that the variation of the dynamic behavior of structures can be used within a system to monitor structural integrity. So, this study aims to understand the dynamic behavior of slender buildings, against different environmental agents such as temperature and / or wind direction and velocity. As part of this investigation, two buildings are studied: the ETSI's (Escuela Técnica Superior de Ingenieros) main tower of Escuela de Caminos, Canales y Puertos of UPM (Universidad Politécnica de Madrid) and a residential building located in the streets Arturo Soria Madrid. The environmental data were recorded with weather stations located on the roof of both buildings. In both structures a modal operational analysis has been carried out. This analysis is performed from the measurements of the acceleration to the environmental excitation, this analysis is based only on the response of the structure. Therefore, it is not necessary to interrupt the operation of the structure, getting its behavior in this state. From this analysis, the natural frequencies, modal damping and mode shapes are obtained. So, in this work we have studied the existing relationship between the variation in the estimate of the natural frequencies and the variation of environmental agents (mainly temperature). The dynamic tests in the two buildings mentioned above, have been made using high-sensitivity accelerometers wirelessly synchronized, which has simplified the experimental work when compared to traditional systems. As a result of work performed can highlight the following points: (i) it has been found that with the available equipment can perform dynamic analysis of buildings, (ii) has improved dynamic knowledge of these structures, and, (iii) can be seen the potential importance of environmental agents depending on the type of building structure. From the work, mathematical models can be updated that serve to prediction of damage to structures, and on the other side, may eliminate the effects of environmental agents, which is a vital point if you want to use the modal parameters for calculating damage ratings. The application of this type of research will help to have more information about the behavior of structures and so, in the future, conduct various processes, as the formulation of mathematical models that reflect more accurately an actual behavior. In this way the monitoring of environmental agents will allow evaluate the influence of these variations on the structure being possible eliminate these effects. Thereby, improvement the uncertainty in the frequencies variation that can be used as an alarm activation system from detection of structural damage.

Using the EM algorithm to estimate the state space model for OMAX

This paper presents a time-domain stochastic system identification method based on Maximum Likelihood Estimation and the Expectation Maximization algorithm that is applied to the estimation of modal parameters from system input and output data. The effectiveness of this structural identification method is evaluated through numerical simulation. Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the simulated structure are estimated applying the proposed identification method to a set of 100 simulated cases. The numerical results show that the proposed method estimates the modal parameters with precision in the presence of 20% measurement noise even. Finally, advantages and disadvantages of the method have been discussed.

Beam Spectral Element with FRP Debonding

The behaviour of the interface between the FRP and the concrete is the key factor controlling debonding failures in FRP-strengthened RC structures. This defect can cause reductions in static strength, structural integrity and the change in the dynamic behavior of the structure. The adverse effect on the dynamic behavior of the defects can be utilized as an effective means for identifying and assessing both the location and size of debonding at its earliest stages. The presence of debonding changes the structural dynamic characteristics and might be traced in modal parameters, dynamic strain and wave patterns etc. Detection of minor local defects, as those origin of a future debonding, requires working at high frequencies so that the wavelength of the excited is small and sensitive enough to detect local damage. The development of a spectral element method gives a large potential in high-frequency structural modeling. In contrast to the conventional finite element, since inertial properties are modeled exactly few elements are necessary to capture very accurate solutions at the highest frequencies in large regions. A wide variety of spectral elements have been developed for structural members over finite and semi-infinite regions. The objective of this paper is to develop a Spectral Finite Element Model to efficiently capture the behavior of intermediate debonding of a FRP strengthened RC beam during wave-based diagnostics.

Multiobjective structural damage identification in uncertain environments

Evolutionary algorithms are suitable to solve damage identification problems in a multiobjective context. However, the performance of these methods can deteriorate quickly with increasing noise intensities originating numerous uncertainties. In this paper, a statistic structural damage detection method formulated in a multiobjective context is proposed. The statistic analysis is implemented to take into account the uncertainties existing in the structural model and measured structural modal parameters. The presented method is verified by a number of simulated damage scenarios. The effects of noise and damage levels on damage detection are investigated.

A procedure to track vibration modes under changing external factors: application to a pedestrian bridge

A low-cost vibration monitoring system has been developed and installed on an urban steel- plated stress-ribbon footbridge. The system continuously measures: the acceleration (using 18 triaxial MEMS accelerometers distributed along the structure), the ambient temperature and the wind velocity and direction. Automated output-only modal parameter estimation based on the Stochastic Subspace Identification (SSI) is carried out in order to extract the modal parameters, i.e., the natural frequencies, damping ratios and modal shapes. Thus, this paper analyzes the time evolution of the modal parameters over a whole-year data monitoring. Firstly, for similar environmental/operational factors, the uncertainties associated to the time window size used are studied and quantified. Secondly, a methodology to track the vibration modes has been established since several of them with closely-spaced natural frequencies are identified. Thirdly, the modal parameters have been correlated against external factors. It has been shown that this stress-ribbon structure is highly sensitive to temperature variation (frequency changes of more than 20%) with strongly seasonal and daily trends

Optimal model through identified frequencies of a masonry building structure with wooden floors

The paper presents the analysis of an important historical building: the Saint James Theater in the city of Corfù (Greece) actually used as the Municipality House. The building, located in the center of the city, is made of carves stones and is characterized by a stocky shape and by the presence of wooden floors. The study deals with the structural identification of such structure through the analysis of its ambient vibrations recorded by means of accelerometers with high accuracy. A full dynamic testing was developed using ambient vibrations to identify the main modal parameters and to make a non-destructive characterization of this building. The results of these dynamic tests are compared with the modal analysis of a complex finite element (FE) simulation of the structure. This analysis may present several problems and uncertainties for this stocky building. Due to the presence of wooden floors, the local modes can be highly excited and, as a consequence, the evaluation of the structural modal parameters presents some difficulties.

(Table 1) Detrital modes for sand grains in sediment core CRP-3

Detrital modes determined on 68 sandstone samples from CRP-3 drillcore indicate a continuation of the dynamic history of uplift-related erosion and unroofing previously documented in CRP-1 and CRP-2/2A. The source area is identified very strongly with the Transantarctic Mountains (TAM) Dry Valleys block in southern Victoria Land. Initial unroofing of the TAM comprised removal of much of a former capping sequence of Jurassic Kirkpatrick basalts, which preceded the formation of the Victoria Land Basin. Erosion of Beacon Supergroup outcrops took place during progressive uplift of the TAM in the Oligocene. Earliest CRP-3 Oligocene samples above 788 metres below the sea floor (mbsf) were sourced overwhelmingly in Beacon Supergroup strata, including a recognisable contribution from Triassic volcanogenic Lashly Formation sandstones (uppermost Victoria Group). Moving up-section, by 500 mbsf, the CRP-3 samples are depauperate quartz arenites dominantly derived from the quartzose Devonian Taylor Group. Between c. 500 and 450 mbsf, the modal parameters show a distinctive change indicating that small outcrops of basement granitoids and metamorphic rocks were also being eroded along with the remaining Beacon (mainly Taylor Group) sequence. Apart from enigmatic fluctuations in modal indices above 450 mbsf, similar to those displayed by samples in CRP-2/2A, the CRP-3 modes are essentially constant (within a broad data scatter) to the top of CRP-3. The proportion of exposed basement outcrop remained at < 20 %, indicating negligible uplift (i.e. relative stability) throughout that period.