Operational modal analisys using joint statistical analysis of multiple records

In Operational Modal Analysis (OMA) of a structure, the data acquisition process may be repeated many times. In these cases, the analyst has several similar records for the modal analysis of the structure that have been obtained at di�erent time instants (multiple records). The solution obtained varies from one record to another, sometimes considerably. The differences are due to several reasons: statistical errors of estimation, changes in the external forces (unmeasured forces) that modify the output spectra, appearance of spurious modes, etc. Combining the results of the di�erent individual analysis is not straightforward. To solve the problem, we propose to make the joint estimation of the parameters using all the records. This can be done in a very simple way using state space models and computing the estimates by maximum-likelihood. The method provides a single result for the modal parameters that combines optimally all the records.

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.

Teaching and evaluating mechanical vibrations with Matlab®

The study of the response of mechanical systems to external excitations, even in the simplest cases, involves solving second-order ordinary differential equations or systems thereof. Finding the natural frequencies of a system and understanding the effect of variations of the excitation frequencies on the response of the system are essential when designing mechanisms [1] and structures [2]. However, faced with the mathematical complexity of the problem, students tend to focus on the mathematical resolution rather than on the interpretation of the results. To overcome this difficulty, once the general theoretical problem and its solution through the state space [3] have been presented, Matlab®[4] and Simulink®[5] are used to simulate specific situations. Without them, the discussion of the effect of slight variations in input variables on the outcome of the model becomes burdensome due to the excessive calculation time required. Conversely, with the help of those simulation tools, students can easily reach practical conclusions and their evaluation can be based on their interpretation of results and not on their mathematical skills

Modelos para el análisis dinámico y la predicción a corto plazo de los precios de la electricidad en mercados liberalizados

En esta tesis se va a describir y aplicar de forma novedosa la técnica del alisado exponencial multivariante a la predicción a corto plazo, a un día vista, de los precios horarios de la electricidad, un problema que se está estudiando intensivamente en la literatura estadística y económica reciente. Se van a demostrar ciertas propiedades interesantes del alisado exponencial multivariante que permiten reducir el número de parámetros para caracterizar la serie temporal y que al mismo tiempo permiten realizar un análisis dinámico factorial de la serie de precios horarios de la electricidad. En particular, este proceso multivariante de elevada dimensión se estimará descomponiéndolo en un número reducido de procesos univariantes independientes de alisado exponencial caracterizado cada uno por un solo parámetro de suavizado que variará entre cero (proceso de ruido blanco) y uno (paseo aleatorio). Para ello, se utilizará la formulación en el espacio de los estados para la estimación del modelo, ya que ello permite conectar esa secuencia de modelos univariantes más eficientes con el modelo multivariante. De manera novedosa, las relaciones entre los dos modelos se obtienen a partir de un simple tratamiento algebraico sin requerir la aplicación del filtro de Kalman. De este modo, se podrán analizar y poner al descubierto las razones últimas de la dinámica de precios de la electricidad. Por otra parte, la vertiente práctica de esta metodología se pondrá de manifiesto con su aplicación práctica a ciertos mercados eléctricos spot, tales como Omel, Powernext y Nord Pool. En los citados mercados se caracterizará la evolución de los precios horarios y se establecerán sus predicciones comparándolas con las de otras técnicas de predicción. ABSTRACT This thesis describes and applies the multivariate exponential smoothing technique to the day-ahead forecast of the hourly prices of electricity in a whole new way. This problem is being studied intensively in recent statistics and economics literature. It will start by demonstrating some interesting properties of the multivariate exponential smoothing that reduce drastically the number of parameters to characterize the time series and that at the same time allow a dynamic factor analysis of the hourly prices of electricity series. In particular this very complex multivariate process of dimension 24 will be estimated by decomposing a very reduced number of univariate independent of exponentially smoothing processes each characterized by a single smoothing parameter that varies between zero (white noise process) and one (random walk). To this end, the formulation is used in the state space model for the estimation, since this connects the sequence of efficient univariate models to the multivariate model. Through a novel way, relations between the two models are obtained from a simple algebraic treatment without applying the Kalman filter. Thus, we will analyze and expose the ultimate reasons for the dynamics of the electricity price. Moreover, the practical aspect of this methodology will be shown by applying this new technique to certain electricity spot markets such as Omel, Powernext and Nord Pool. In those markets the behavior of prices will be characterized, their predictions will be formulated and the results will be compared with those of other forecasting techniques.

Non uniform embedding based on relevance analysis with reduced computational complexity: application to the detection of pathologies from biosignal recordings

Nonlinear analysis tools for studying and characterizing the dynamics of physiological signals have gained popularity, mainly because tracking sudden alterations of the inherent complexity of biological processes might be an indicator of altered physiological states. Typically, in order to perform an analysis with such tools, the physiological variables that describe the biological process under study are used to reconstruct the underlying dynamics of the biological processes. For that goal, a procedure called time-delay or uniform embedding is usually employed. Nonetheless, there is evidence of its inability for dealing with non-stationary signals, as those recorded from many physiological processes. To handle with such a drawback, this paper evaluates the utility of non-conventional time series reconstruction procedures based on non uniform embedding, applying them to automatic pattern recognition tasks. The paper compares a state of the art non uniform approach with a novel scheme which fuses embedding and feature selection at once, searching for better reconstructions of the dynamics of the system. Moreover, results are also compared with two classic uniform embedding techniques. Thus, the goal is comparing uniform and non uniform reconstruction techniques, including the one proposed in this work, for pattern recognition in biomedical signal processing tasks. Once the state space is reconstructed, the scheme followed characterizes with three classic nonlinear dynamic features (Largest Lyapunov Exponent, Correlation Dimension and Recurrence Period Density Entropy), while classification is carried out by means of a simple k-nn classifier. In order to test its generalization capabilities, the approach was tested with three different physiological databases (Speech Pathologies, Epilepsy and Heart Murmurs). In terms of the accuracy obtained to automatically detect the presence of pathologies, and for the three types of biosignals analyzed, the non uniform techniques used in this work lightly outperformed the results obtained using the uniform methods, suggesting their usefulness to characterize non-stationary biomedical signals in pattern recognition applications. On the other hand, in view of the results obtained and its low computational load, the proposed technique suggests its applicability for the applications under study.

Monte Carlo limit cycle characterization

The fixed point implementation of IIR digital filters usually leads to the appearance of zero-input limit cycles, which degrade the performance of the system. In this paper, we develop an efficient Monte Carlo algorithm to detect and characterize limit cycles in fixed-point IIR digital filters. The proposed approach considers filters formulated in the state space and is valid for any fixed point representation and quantization function. Numerical simulations on several high-order filters, where an exhaustive search is unfeasible, show the effectiveness of the proposed approach.

Comment: Is memristor a dynamic element?

The authors present a charge/flux formulation of the equations of memristive circuits, which seemingly show that the memristor should not be considered as a dynamic circuit element. Here, is shown that this approach implicitly reduces the dynamic analysis to a certain subset of the state space in such a way that the dynamic contribution of memristors is hidden. This reduction might entail a substantial loss of information, regarding e.g. the local stability properties of the circuit. Two examples illustrate this. It is concluded that the memristor, even with its unconventional features, must be considered as a dynamic element.

Asymptotic optimality of RESTART estimators in highly dependable systems

Abstract We consider a wide class of models that includes the highly reliable Markovian systems (HRMS) often used to represent the evolution of multi-component systems in reliability settings. Repair times and component lifetimes are random variables that follow a general distribution, and the repair service adopts a priority repair rule based on system failure risk. Since crude simulation has proved to be inefficient for highly-dependable systems, the RESTART method is used for the estimation of steady-state unavailability and other reliability measures. In this method, a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of a rare event (e.g., a system failure) is higher. The main difficulty involved in applying this method is finding a suitable function, called the importance function, to define the regions. In this paper we introduce an importance function which, for unbalanced systems, represents a great improvement over the importance function used in previous papers. We also demonstrate the asymptotic optimality of RESTART estimators in these models. Several examples are presented to show the effectiveness of the new approach, and probabilities up to the order of 10-42 are accurately estimated with little computational effort.

Transformaciones urbanas del siglo XVIII en el antiguo Reino de Chile

La tesis analiza la trayectoria de las ciudades chilenas tomando como referencias la extensión, vastedad, proporciones y diversidad del paisaje en una región remota, ubicada en el confín del continente, aislada por el desierto de Atacama y la cordillera de Los Andes y que comprendía algunos de los territorios más desconocidos del Nuevo Mundo. El contexto temporal es el siglo XVIII, el período más activo de la colonización, cuando las primeras fundaciones tenían niveles de desarrollo que se expresaban en rasgos particulares, se construyen numerosas ciudades y se perfilan los contrastes entre el modelo teórico de ciudad y las ciudades reales. OBJETIVOS Analizar la forma, funciones y significado de las ciudades como respuestas a la extensión, vastedad, proporciones y diversidad del paisaje. Explorar los avances en el conocimiento del territorio y las nuevas interpretaciones del paisaje como bases para definir las estrategias de colonización y nuevas fundaciones Estudiar las influencias específicas del entorno sobre las estructuras urbanas Estos objetivos buscan aportar al conocimiento de la urbanización colonial en Chile rescatando las características distintivas del proceso según los diferentes ámbitos territoriales. METODOLOGÍA Se seleccionaron 22 ciudades como ejemplos de las transformaciones urbanas en Chile, según los paisajes y contextos culturales. Las ciudades se observaron como partes de un sistema de colonización en un territorio extenso y como individualidades fundadas en sitios específicos, cuyas cualidades se expresan en el paisaje del entorno de cada núcleo urbano. CONCLUSIONES La tesis confirma que la colonización de Chile fue una empresa militar y de dominio espacial del territorio. Las ciudades sostenían la conquista y el arraigo mediante estructuras urbanas regulares porque, la cuadricula -además de facilitar el trazado y el repartimiento de los lotes era símbolo de estabilidad en una región hostil y sujeta a la acción inesperada y destructora de la naturaleza, una forma orientadora en la vastedad y una expresión de orden y medida que contrastaba con la diversidad y extensión del paisaje. A pesar de la primacía de la cuadrícula, las ciudades no eran simples imitaciones de anteriores fundaciones; con el avance colonizador se afirmaba el anclaje de cada ciudad al paisaje del sitio de fundación, se perfeccionaban la forma y funciones urbanas mediante la adaptación al entorno y se fortalecía el arraigo de los a los nuevos paisajes que se iban construyendo. Las transformaciones urbanas dependían de los desafíos territoriales, las expectativas de los gobernantes y capacidades técnicas. Los cambios principales se manifiestan en el siglo XVIII, cuando las distintas zonas de Chile se colonizaron con estrategias afines a sus características geográficas y culturales y a las diferencias entre valles mineros, valles agrícolas, el litoral y las islas. El análisis revela que el desarrollo urbano de las ciudades fue condicionado por el relieve, la relación con otros núcleos urbanos y caminos, los recursos del lugar, la integración con estructuras colonizadoras -hacienda, fuerte o misión- predominantes en cada territorio y las interpretaciones del paisaje que se proponían desde la filosofía y las ciencias ilustradas. ABSTRACT INTRODUCTION The thesis analyzes the trajectory of the Chilean cities taking as reference the extension, vastness, proportions and diversity of landscape in a remote region, located on the edge of the continent, isolated by the Atacama Desert and the Andes mountains and comprising some of the most unknown territories of the New World. The temporal context is the eighteenth century, the most active of colonization, when the first foundations had levels of development that were expressed in particular forms; in this period many cities are built and the contrasts between the theoretical model of the city and the royal cities are emerging . OBJECTIVES •Analyze the form, function and significance of cities as responses to the extension, vastness, proportions and diversity of landscape. •Explore the advances in knowledge of the territory and the new interpretations of the landscape as a basis for defining the strategies of colonization and new foundations •Examine specific environmental influences on urban structures These objectives seek to contribute to the knowledge of colonial urbanization in Chile rescuing the distinctive characteristics of the process according to the different territorial areas. METHODOLOGY 22 cities as examples of urban transformation in Chile were selected according as the landscapes and cultural contexts. The cities were seen as part of a settlement system in a large territory and as individuals elements based on specific sites, whose qualities are expressed in the landscape around of each urban center. CONCLUSIONS The thesis confirms that the colonization of Chile was a military and space control of the territory. The cities holding the conquest and establishment through regular urban structures because, besides grid to facilitate the tracing and the division of the urban space was a symbol of stability in a hostile region and subject to unexpected and destructive action of nature, a guiding how the vastness and an expression of order and as contrasted with the diversity and extent of the landscape. Despite the primacy of the grid, the cities were not mere imitations of earlier foundations; as colonization progresses, the landscape of the place stated in each city, form and urban functions are improved by adapting the environment and establishment the landscapes that were recently built. Urban transformations depend on the territorial challenges, expectations of governments and technical capabilities. The main changes are manifested in the eighteenth century, when different areas of Chile are colonized with strategies related to its geographical and cultural characteristics and differences between mining valleys, agricultural valleys, the coast and islands. The analysis reveals that the urban development of cities was conditioned by relief, relative to other urban centers and roads, resources, integration with other colonial structures –farmers, missions or forts- dominant in each territory and the interpretations of landscape that is proposed from philosophy and illustrated science.

Control of a Nonlinear Teleoperation System by State Convergence

In this work, we proposes a control strategy that allows the remote manipulator follow the local manipulator through the state convergence even if it has a delay in the communication channel. The bilateral control of the teleoperator system considers the case were the human operator applies a constant force on the local manipulator and when the interaction of the remote manipulator with the environment is considered passive. The stability analysis was performed using Lyapunov- Krasovskii functional, it showed for the case with constant delay, that using a proposed control algorithm by state convergence resulted in asymptotically stable, local and remote the nonlinear teleoperation system.

Advances in Control of Teleoperation System by State Convergence

In this work, we proposes a control strategy by state convergence applied to bilateral control of a nonlinear teleoperator system with constant delay. The bilateral control of the teleoperator system considers the case when the human operator applies a constant force on the local manipulator and when the interaction of the remote manipulator with the environment is considered passive. The stability analysis is performed using Lyapunov-Krasovskii functional, it showed that using an control algorithm by state convergence for the case with constant delay, the nonlinear local and remote teleoperation system is asymptotically stable, also speeds converge to zero and position tracking is achieved. This work also presents the implementation of an experimental platform. The mechanical structure of the arm that is located in the remote side has been built and the electric servomechanism has been mounted to control their movement.

Propellantless deorbiting of space debris by bare electrodynamic tethers : final report

A Space tether is a thin, multi-kilometers long conductive wire, joining a satellite and some opposite end mass, and keeping vertical in orbit by the gravity-gradient. The ambient plasma, being highly conductive, is equipotential in its own co-moving frame. In the tether frame, in relative motion however, there is in the plasma a motional electric field of order of 100 V/km, product of (near) orbital velocity and geomagnetic field. The electromotive force established over the tether length allows plasma contactor devices to collect electrons at one polarized-positive (anodic) end and eject electrons at the opposite end, setting up a current along a standard, fully insulated tether. The Lorentz force exerted on the current by the geomagnetic field itself is always drag; this relies on just thermodynamics, like air drag. The bare tether concept, introduced in 1992 at the Universidad Politécnica de Madrid (UPM), takes away the insulation and has electrons collected over the tether segment coming out polarized positive; the concept rests on 2D (Langmuir probe) current-collection in plasmas being greatly more efficient than 3D collection. A Plasma Contactor ejects electrons at the cathodic end. A bare tether with a thin-tape cross section has much greater perimeter and de-orbits much faster than a (corresponding) round bare tether of equal length and mass. Further, tethers being long and thin, they are prone to cuts by abundant small space debris, but BETs has shown that the tape has a probability of being cut per unit time smaller by more than one order of magnitude than the corresponding round tether (debris comparable to its width are much less abundant than debris comparable to the radius of the corresponding round tether). Also, the tape collects much more current, and de-orbits much faster, than a corresponding multi-line “tape” made of thin round wires cross-connected to survive debris cuts. Tethers use a dissipative mechanism quite different from air drag and can de-orbit in just a few months; also, tape tethers are much lighter than round tethers of equal length and perimeter, which can capture equal current. The 3 disparate tape dimensions allow easily scalable design. Switching the cathodic Contactor off-on allows maneuvering to avoid catastrophic collisions with big tracked debris. Lorentz braking is as reliable as air drag. Tethers are still reasonably effective at high inclinations, where the motional field is small, because the geomagnetic field is not just a dipole along the Earth polar axis. BETs is the EC FP7/Space Project 262972, financed in about 1.8 million euros, from 1 November 2010 to 31 January 2014, and carrying out RTD work on de-orbiting space debris. Coordinated by UPM, it has partners Università di Padova, ONERA-Toulouse, Colorado State University, SME Emxys, DLR–Bremen, and Fundación Tecnalia. BETs work involves 1) Designing, building, and ground-testing basic hardware subsystems Cathodic Plasma Contactor, Tether Deployment Mechanism, Power Control Module, and Tape with crosswise and lengthwise structure. 2) Testing current collection and verifying tether dynamical stability. 3) Preliminary design of tape dimensions for a generic mission, conducive to low system-to-satellite mass ratio and probability of cut by small debris, and ohmic-effects regime of tether current for fast de-orbiting. Reaching TRL 4-5, BETs appears ready for in-orbit demostration.