Dynamic identification of structures: experimental assessment of modal parameteres through methods in frequency domain, in time-frequency domain and model updating

Among the experimental methods commonly used to define the behaviour of a full scale system, dynamic tests are the most complete and efficient procedures. A dynamic test is an experimental process, which would define a set of characteristic parameters of the dynamic behaviour of the system, such as natural frequencies of the structure, mode shapes and the corresponding modal damping values associated. An assessment of these modal characteristics can be used both to verify the theoretical assumptions of the project, to monitor the performance of the structural system during its operational use. The thesis is structured in the following chapters: The first introductive chapter recalls some basic notions of dynamics of structure, focusing the discussion on the problem of systems with multiply degrees of freedom (MDOF), which can represent a generic real system under study, when it is excited with harmonic force or in free vibration. The second chapter is entirely centred on to the problem of dynamic identification process of a structure, if it is subjected to an experimental test in forced vibrations. It first describes the construction of FRF through classical FFT of the recorded signal. A different method, also in the frequency domain, is subsequently introduced; it allows accurately to compute the FRF using the geometric characteristics of the ellipse that represents the direct input-output comparison. The two methods are compared and then the attention is focused on some advantages of the proposed methodology. The third chapter focuses on the study of real structures when they are subjected to experimental test, where the force is not known, like in an ambient or impact test. In this analysis we decided to use the CWT, which allows a simultaneous investigation in the time and frequency domain of a generic signal x(t). The CWT is first introduced to process free oscillations, with excellent results both in terms of frequencies, dampings and vibration modes. The application in the case of ambient vibrations defines accurate modal parameters of the system, although on the damping some important observations should be made. The fourth chapter is still on the problem of post processing data acquired after a vibration test, but this time through the application of discrete wavelet transform (DWT). In the first part the results obtained by the DWT are compared with those obtained by the application of CWT. Particular attention is given to the use of DWT as a tool for filtering the recorded signal, in fact in case of ambient vibrations the signals are often affected by the presence of a significant level of noise. The fifth chapter focuses on another important aspect of the identification process: the model updating. In this chapter, starting from the modal parameters obtained from some environmental vibration tests, performed by the University of Porto in 2008 and the University of Sheffild on the Humber Bridge in England, a FE model of the bridge is defined, in order to define what type of model is able to capture more accurately the real dynamic behaviour of the bridge. The sixth chapter outlines the necessary conclusions of the presented research. They concern the application of a method in the frequency domain in order to evaluate the modal parameters of a structure and its advantages, the advantages in applying a procedure based on the use of wavelet transforms in the process of identification in tests with unknown input and finally the problem of 3D modeling of systems with many degrees of freedom and with different types of uncertainty.

The discrete Pascal transform and its applications

We introduce a new discrete polynomial transform constructed from the rows of Pascal’s triangle. The forward and inverse transforms are computed the same way in both the oneand two-dimensional cases, and the transform matrix can be factored into binary matrices for efficient hardware implementation. We conclude by discussing applications of the transform in

Wavelet-denoising of electroencephalogram and the absolute slope method: a new tool to improve electroencephalographic localization and lateralization

OBJECTIVE: In ictal scalp electroencephalogram (EEG) the presence of artefacts and the wide ranging patterns of discharges are hurdles to good diagnostic accuracy. Quantitative EEG aids the lateralization and/or localization process of epileptiform activity. METHODS: Twelve patients achieving Engel Class I/IIa outcome following temporal lobe surgery (1 year) were selected with approximately 1-3 ictal EEGs analyzed/patient. The EEG signals were denoised with discrete wavelet transform (DWT), followed by computing the normalized absolute slopes and spatial interpolation of scalp topography associated to detection of local maxima. For localization, the region with the highest normalized absolute slopes at the time when epileptiform activities were registered (>2.5 times standard deviation) was designated as the region of onset. For lateralization, the cerebral hemisphere registering the first appearance of normalized absolute slopes >2.5 times the standard deviation was designated as the side of onset. As comparison, all the EEG episodes were reviewed by two neurologists blinded to clinical information to determine the localization and lateralization of seizure onset by visual analysis. RESULTS: 16/25 seizures (64%) were correctly localized by the visual method and 21/25 seizures (84%) by the quantitative EEG method. 12/25 seizures (48%) were correctly lateralized by the visual method and 23/25 seizures (92%) by the quantitative EEG method. The McNemar test showed p=0.15 for localization and p=0.0026 for lateralization when comparing the two methods. CONCLUSIONS: The quantitative EEG method yielded significantly more seizure episodes that were correctly lateralized and there was a trend towards more correctly localized seizures. SIGNIFICANCE: Coupling DWT with the absolute slope method helps clinicians achieve a better EEG diagnostic accuracy.

3D Wavelet-based Fusion Techniques for Biomedical Imaging

Hoy en día las técnicas de adquisición de imágenes tridimensionales son comunes en diversas áreas, pero cabe destacar la relevancia que han adquirido en el ámbito de la imagen biomédica, dentro del cual encontramos una amplia gama de técnicas como la microscopía confocal, microscopía de dos fotones, microscopía de fluorescencia mediante lámina de luz, resonancia magnética nuclear, tomografía por emisión de positrones, tomografía de coherencia óptica, ecografía 3D y un largo etcétera. Un denominador común de todas esas aplicaciones es la constante necesidad por aumentar la resolución y la calidad de las imágenes adquiridas. En algunas de dichas técnicas de imagen tridimensional se da una interesante situación: aunque que cada volumen adquirido no contiene información suficiente para representar el objeto bajo estudio dentro de los parámetros de calidad requeridos por algunas aplicaciones finales, el esquema de adquisición permite la obtención de varios volúmenes que representan diferentes vistas de dicho objeto, de tal forma que cada una de las vistas proporciona información complementaria acerca del mismo. En este tipo de situación es posible, mediante la combinación de varias de esas vistas, obtener una mejor comprensión del objeto que a partir de cada una de ellas por separado. En el contexto de esta Tesis Doctoral se ha propuesto, desarrollado y validado una nueva metodología de proceso de imágenes basada en la transformada wavelet disc¬reta para la combinación, o fusión, de varias vistas con información complementaria de un mismo objeto. El método de fusión propuesto aprovecha la capacidad de descom¬posición en escalas y orientaciones de la transformada wavelet discreta para integrar en un solo volumen toda la información distribuida entre el conjunto de vistas adquiridas. El trabajo se centra en dos modalidades diferentes de imagen biomédica que per¬miten obtener tales adquisiciones multi-vista. La primera es una variante de la micro¬scopía de fluorescencia, la microscopía de fluorescencia mediante lámina de luz, que se utiliza para el estudio del desarrollo temprano de embriones vivos en diferentes modelos animales, como el pez cebra o el erizo de mar. La segunda modalidad es la resonancia magnética nuclear con realce tardío, que constituye una valiosa herramienta para evaluar la viabilidad del tejido miocárdico en pacientes con diversas miocardiopatías. Como parte de este trabajo, el método propuesto ha sido aplicado y validado en am¬bas modalidades de imagen. En el caso de la aplicación a microscopía de fluorescencia, los resultados de la fusión muestran un mejor contraste y nivel de detalle en comparación con cualquiera de las vistas individuales y el método no requiere de conocimiento previo acerca la función de dispersión puntual del sistema de imagen. Además, los resultados se han comparado con otros métodos existentes. Con respecto a la aplicación a imagen de resonancia magnética con realce tardío, los volúmenes fusionados resultantes pre-sentan una mejora cuantitativa en la nitidez de las estructuras relevantes y permiten una interpretación más sencilla y completa de la compleja estructura tridimensional del tejido miocárdico en pacientes con cardiopatía isquémica. Para ambas aplicaciones los resultados de esta tesis se encuentran actualmente en uso en los centros clínicos y de investigación con los que el autor ha colaborado durante este trabajo. Además se ha puesto a libre disposición de la comunidad científica la implementación del método de fusión propuesto. Por último, se ha tramitado también una solicitud de patente internacional que cubre el método de visualización desarrollado para la aplicación de Resonancia Magnética Nuclear. Abstract Nowadays three dimensional imaging techniques are common in several fields, but es-pecially in biomedical imaging, where we can find a wide range of techniques including: Laser Scanning Confocal Microscopy, Laser Scanning Two Photon Microscopy, Light Sheet Fluorescence Microscopy, Magnetic Resonance Imaging, Positron Emission To-mography, Optical Coherence Tomography, 3D Ultrasound Imaging, etc. A common denominator of all those applications being the constant need for further increasing resolution and quality of the acquired images. Interestingly, in some of the mentioned three-dimensional imaging techniques a remarkable situation arises: while a single volume does not contain enough information to represent the object being imaged within the quality parameters required by the final application, the acquisition scheme allows recording several volumes which represent different views of a given object, with each of the views providing complementary information. In this kind of situation one can get a better understanding of the object by combining several views instead of looking at each of them separately. Within such context, in this PhD Thesis we propose, develop and test new image processing methodologies based on the discrete wavelet transform for the combination, or fusion, of several views containing complementary information of a given object. The proposed fusion method exploits the scale and orientation decomposition capabil¬ities of the discrete wavelet transform to integrate in a single volume all the available information distributed among the set of acquired views. The work focuses in two different biomedical imaging modalities which provide such multi-view datasets. The first one is a particular fluorescence microscopy technique, Light-Sheet Fluorescence Microscopy, used for imaging and gaining understanding of the early development of live embryos from different animal models (like zebrafish or sea urchin). The second is Delayed Enhancement Magnetic Resonance Imaging, which is a valuable tool for assessing the viability of myocardial tissue on patients suffering from different cardiomyopathies. As part of this work, the proposed method was implemented and then validated on both imaging modalities. For the fluorescence microscopy application, the fusion results show improved contrast and detail discrimination when compared to any of the individual views and the method does not rely on prior knowledge of the system’s point spread function (PSF). Moreover, the results have shown improved performance with respect to previous PSF independent methods. With respect to its application to Delayed Enhancement Magnetic Resonance Imaging, the resulting fused volumes show a quantitative sharpness improvement and enable an easier and more complete interpretation of complex three-dimensional scar and heterogeneous tissue information in ischemic cardiomyopathy patients. In both applications, the results of this thesis are currently in use in the clinical and research centers with which the author collaborated during his work. An imple¬mentation of the fusion method has also been made freely available to the scientific community. Finally, an international patent application has been filed covering the visualization method developed for the Magnetic Resonance Imaging application.

Accelerating FPGA-based evolution of wavelet transform filters by optimized task scheduling

Adaptive embedded systems are required in various applications. This work addresses these needs in the area of adaptive image compression in FPGA devices. A simplified version of an evolution strategy is utilized to optimize wavelet filters of a Discrete Wavelet Transform algorithm. We propose an adaptive image compression system in FPGA where optimized memory architecture, parallel processing and optimized task scheduling allow reducing the time of evolution. The proposed solution has been extensively evaluated in terms of the quality of compression as well as the processing time. The proposed architecture reduces the time of evolution by 44% compared to our previous reports while maintaining the quality of compression unchanged with respect to existing implementations. The system is able to find an optimized set of wavelet filters in less than 2 min whenever the input type of data changes.

Inversion Formulas for the q-Riemann-Liouville and q-Weyl Transforms Using Wavelets

Mathematics Subject Classification: 42A38, 42C40, 33D15, 33D60

High performance shift invariant motion estimation and compensation in wavelet domain video compression

The contributions of this dissertation are in the development of two new interrelated approaches to video data compression: (1) A level-refined motion estimation and subband compensation method for the effective motion estimation and motion compensation. (2) A shift-invariant sub-decimation decomposition method in order to overcome the deficiency of the decimation process in estimating motion due to its shift-invariant property of wavelet transform. ^ The enormous data generated by digital videos call for an intense need of efficient video compression techniques to conserve storage space and minimize bandwidth utilization. The main idea of video compression is to reduce the interpixel redundancies inside and between the video frames by applying motion estimation and motion compensation (MEMO) in combination with spatial transform coding. To locate the global minimum of the matching criterion function reasonably, hierarchical motion estimation by coarse to fine resolution refinements using discrete wavelet transform is applied due to its intrinsic multiresolution and scalability natures. ^ Due to the fact that most of the energies are concentrated in the low resolution subbands while decreased in the high resolution subbands, a new approach called level-refined motion estimation and subband compensation (LRSC) method is proposed. It realizes the possible intrablocks in the subbands for lower entropy coding while keeping the low computational loads of motion estimation as the level-refined method, thus to achieve both temporal compression quality and computational simplicity. ^ Since circular convolution is applied in wavelet transform to obtain the decomposed subframes without coefficient expansion, symmetric-extended wavelet transform is designed on the finite length frame signals for more accurate motion estimation without discontinuous boundary distortions. ^ Although wavelet transformed coefficients still contain spatial domain information, motion estimation in wavelet domain is not as straightforward as in spatial domain due to the shift variance property of the decimation process of the wavelet transform. A new approach called sub-decimation decomposition method is proposed, which maintains the motion consistency between the original frame and the decomposed subframes, improving as a consequence the wavelet domain video compressions by shift invariant motion estimation and compensation. ^

Estimação de potência em tempo real utilizando a transformada wavelet

The goal of the power monitoring in electrical power systems is to promote the reliablility as well as the quality of electrical power.Therefore, this dissertation proposes a new theory of power based on wavelet transform for real-time estimation of RMS voltages and currents, and some power amounts, such as active power, reactive power, apparent power, and power factor. The appropriate estimation the of RMS and power values is important for many applications, such as: design and analysis of power systems, compensation devices for improving power quality, and instruments for energy measuring. Simulation and experimental results obtained through the proposed MaximalOverlap Discrete Wavelet Transform-based method were compared with the IEEE Standard 1459-2010 and the commercial oscilloscope, respectively, presenting equivalent results. The proposed method presented good performance for compact mother wavelet, which is in accordance with real-time applications.

Monitoramento e identificação numérico e experimental de danos em vigas e pontes de aço e concreto utilizando transformadas de wavelet

Tese (doutorado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Civil e Ambiental, 2015.

Kernel machines for epilepsy diagnosis via EEG signal classification: A comparative study

Objective: We carry out a systematic assessment on a suite of kernel-based learning machines while coping with the task of epilepsy diagnosis through automatic electroencephalogram (EEG) signal classification. Methods and materials: The kernel machines investigated include the standard support vector machine (SVM), the least squares SVM, the Lagrangian SVM, the smooth SVM, the proximal SVM, and the relevance vector machine. An extensive series of experiments was conducted on publicly available data, whose clinical EEG recordings were obtained from five normal subjects and five epileptic patients. The performance levels delivered by the different kernel machines are contrasted in terms of the criteria of predictive accuracy, sensitivity to the kernel function/parameter value, and sensitivity to the type of features extracted from the signal. For this purpose, 26 values for the kernel parameter (radius) of two well-known kernel functions (namely. Gaussian and exponential radial basis functions) were considered as well as 21 types of features extracted from the EEG signal, including statistical values derived from the discrete wavelet transform, Lyapunov exponents, and combinations thereof. Results: We first quantitatively assess the impact of the choice of the wavelet basis on the quality of the features extracted. Four wavelet basis functions were considered in this study. Then, we provide the average accuracy (i.e., cross-validation error) values delivered by 252 kernel machine configurations; in particular, 40%/35% of the best-calibrated models of the standard and least squares SVMs reached 100% accuracy rate for the two kernel functions considered. Moreover, we show the sensitivity profiles exhibited by a large sample of the configurations whereby one can visually inspect their levels of sensitiveness to the type of feature and to the kernel function/parameter value. Conclusions: Overall, the results evidence that all kernel machines are competitive in terms of accuracy, with the standard and least squares SVMs prevailing more consistently. Moreover, the choice of the kernel function and parameter value as well as the choice of the feature extractor are critical decisions to be taken, albeit the choice of the wavelet family seems not to be so relevant. Also, the statistical values calculated over the Lyapunov exponents were good sources of signal representation, but not as informative as their wavelet counterparts. Finally, a typical sensitivity profile has emerged among all types of machines, involving some regions of stability separated by zones of sharp variation, with some kernel parameter values clearly associated with better accuracy rates (zones of optimality). (C) 2011 Elsevier B.V. All rights reserved.

Generation of self-similar Gaussian time series by means of the DWT and DWPT variance maps

Due to the several kinds of services that use the Internet and data networks infra-structures, the present networks are characterized by the diversity of types of traffic that have statistical properties as complex temporal correlation and non-gaussian distribution. The networks complex temporal correlation may be characterized by the Short Range Dependence (SRD) and the Long Range Dependence - (LRD). Models as the fGN (Fractional Gaussian Noise) may capture the LRD but not the SRD. This work presents two methods for traffic generation that synthesize approximate realizations of the self-similar fGN with SRD random process. The first one employs the IDWT (Inverse Discrete Wavelet Transform) and the second the IDWPT (Inverse Discrete Wavelet Packet Transform). It has been developed the variance map concept that allows to associate the LRD and SRD behaviors directly to the wavelet transform coefficients. The developed methods are extremely flexible and allow the generation of Gaussian time series with complex statistical behaviors.

Global and local detection of liver steatosis from ultrasound

Liver steatosis is a common disease usually associated with social and genetic factors. Early detection and quantification is important since it can evolve to cirrhosis. Steatosis is usually a diffuse liver disease, since it is globally affected. However, steatosis can also be focal affecting only some foci difficult to discriminate. In both cases, steatosis is detected by laboratorial analysis and visual inspection of ultrasound images of the hepatic parenchyma. Liver biopsy is the most accurate diagnostic method but its invasive nature suggest the use of other non-invasive methods, while visual inspection of the ultrasound images is subjective and prone to error. In this paper a new Computer Aided Diagnosis (CAD) system for steatosis classification and analysis is presented, where the Bayes Factor, obatined from objective intensity and textural features extracted from US images of the liver, is computed in a local or global basis. The main goal is to provide the physician with an application to make it faster and accurate the diagnosis and quantification of steatosis, namely in a screening approach. The results showed an overall accuracy of 93.54% with a sensibility of 95.83% and 85.71% for normal and steatosis class, respectively. The proposed CAD system seemed suitable as a graphical display for steatosis classification and comparison with some of the most recent works in the literature is also presented.

Analysis of multi-scale systemic risk in Brazil's financial market

This work analyzes whether the relationship between risk and returns predicted by the Capital Asset Pricing Model (CAPM) is valid in the Brazilian stock market. The analysis is based on discrete wavelet decomposition on different time scales. This technique allows to analyze the relationship between different time horizons, since the short-term ones (2 to 4 days) up to the long-term ones (64 to 128 days). The results indicate that there is a negative or null relationship between systemic risk and returns for Brazil from 2004 to 2007. As the average excess return of a market portfolio in relation to a risk-free asset during that period was positive, it would be expected this relationship to be positive. That is, higher systematic risk should result in higher excess returns, which did not occur. Therefore, during that period, appropriate compensation for systemic risk was not observed in the Brazilian market. The scales that proved to be most significant to the risk-return relation were the first three, which corresponded to short-term time horizons. When treating differently, year-by-year, and consequently separating positive and negative premiums, some relevance is found, during some years, in the risk/return relation predicted by the CAPM. However, this pattern did not persist throughout the years. Therefore, there is not any evidence strong enough confirming that the asset pricing follows the model.

Unidirectional quantum walks: Evolution and exit times

In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the currently widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in place or move in a fixed direction, e.g., rightward or upward. While both formulations are essentially equivalent, the present approach leads us to consider discrete Fourier transforms, which eventually results in obtaining explicit expressions for the wave functions in terms of finite sums and allows the use of efficient algorithms based on the fast Fourier transform. The wave functions here obtained govern the probability of finding the particle at any given location but determine as well the exit-time probability of the walker from a fixed interval, which is also analyzed.

A Technique for Digital Color Image Watermarking Using ICA

With the increase of use of digital media the need for the methods of multimedia protection becomes extremely important. The number of the solutions to the problem from encryption to watermarking is large and is growing every year. In this work digital image watermarking is considered, specifically a novel method of digital watermarking of color and spectral images. An overview of existing methods watermarking of color and grayscale images is given in the paper. Methods using independent component analysis (ICA) for detection and the ones using discrete wavelet transform (DWT) and discrete cosine transform (DCT) are considered in more detail. A novel method of watermarking proposed in this paper allows embedding of a color or spectral watermark image into color or spectral image consequently and successful extraction of the watermark out of the resultant watermarked image. A number of experiments have been performed on the quality of extraction depending on the parameters of the embedding procedure. Another set of experiments included the test of the robustness of the algorithm proposed. Three techniques have been chosen for that purpose: median filter, low-pass filter (LPF) and discrete cosine transform (DCT), which are a part of a widely known StirMark - Image Watermarking Robustness Test. The study shows that the proposed watermarking technique is fragile, i.e. watermark is altered by simple image processing operations. Moreover, we have found that the contents of the image to be watermarked do not affect the quality of the extraction. Mixing coefficients, that determine the amount of the key and watermark image in the result, should not exceed 1% of the original. The algorithm proposed has proven to be successful in the task of watermark embedding and extraction.