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.

Space-time Measurements of Oceanic Sea States

Stereo video techniques are effective for estimating the space–time wave dynamics over an area of the ocean. Indeed, a stereo camera view allows retrieval of both spatial and temporal data whose statistical content is richer than that of time series data retrieved from point wave probes. We present an application of the Wave Acquisition Stereo System (WASS) for the analysis of offshore video measurements of gravity waves in the Northern Adriatic Sea and near the southern seashore of the Crimean peninsula, in the Black Sea. We use classical epipolar techniques to reconstruct the sea surface from the stereo pairs sequentially in time, viz. a sequence of spatial snapshots. We also present a variational approach that exploits the entire data image set providing a global space–time imaging of the sea surface, viz. simultaneous reconstruction of several spatial snapshots of the surface in order to guarantee continuity of the sea surface both in space and time. Analysis of the WASS measurements show that the sea surface can be accurately estimated in space and time together, yielding associated directional spectra and wave statistics at a point in time that agrees well with probabilistic models. In particular, WASS stereo imaging is able to capture typical features of the wave surface, especially the crest-to-trough asymmetry due to second order nonlinearities, and the observed shape of large waves are fairly described by theoretical models based on the theory of quasi-determinism (Boccotti, 2000). Further, we investigate space–time extremes of the observed stationary sea states, viz. the largest surface wave heights expected over a given area during the sea state duration. The WASS analysis provides the first experimental proof that a space–time extreme is generally larger than that observed in time via point measurements, in agreement with the predictions based on stochastic theories for global maxima of Gaussian fields.