Systematic and multifactor risk models revisited

Systematic and multifactor risk models are revisited via methods which were already successfully developed in signal processing and in automatic control. The results, which bypass the usual criticisms on those risk modeling, are illustrated by several successful computer experiments.Comment: First Paris Financial Management Conference, Paris : France (2013

Non-asymptotic fractional order differentiators via an algebraic parametric method

Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie's modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations

Parameters estimation of a noisy sinusoidal signal with time-varying amplitude

In this paper, we give estimators of the frequency, amplitude and phase of a noisy sinusoidal signal with time-varying amplitude by using the algebraic parametric techniques introduced by Fliess and Sira-Ramirez. We apply a similar strategy to estimate these parameters by using modulating functions method. The convergence of the noise error part due to a large class of noises is studied to show the robustness and the stability of these methods. We also show that the estimators obtained by modulating functions method are robust to "large" sampling period and to non zero-mean noises

Determinación del Desbalance en Sistemas Rotor-cojinete a velocidad constante: Método de Identificación Algebraica

The development of a mathematical model for an on-line algebraic identifier is presented in this work. This model is used for determining the unbalance and its related angular position on vibrating rotor-dynamic systems of multiple degrees of freedom. The proposed identifier was obtained from the basis of a finite element mathematical model for rotating systems of multiple degrees of freedom. The model was developed under the consideration of four degrees of freedom beam-type element, where rotational inertia, gyroscopic moments, shearing strains and inner and outer damping effects were included. The on time behavior of proposed identifier was assessed for unbalance identification and its related angular position; the constant-speed unbalanced vibration response obtained from numerical simulation was used as input data

Identification of fractional order systems using modulating functions method

The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations

Estimation of the transverse sway motion of a biped robot during the march

Debido al balanceo generado por la dinámica natural y perturbaciones durante la marcha de un robot humanoide, es difícil predecir su postura en determinado instante a lo largo de la misma, complicando así el desarrollo de tareas de manipulación, cooperación, evasión de obstáculos, retroalimentación servo-visual, entre otras. En este documento se describe una metodología para predecir el movimiento de balanceo en el plano transversal del robot, a partir de la trayectoria de un punto fijo en su estructura mecánica. Se considera el estudio de dos modelos matemáticos para aproximar el movimiento de balanceo del humanoide: aproximación mediante una función sinusoidal y aproximación por series de Fourier. En ambos casos, es necesario el conocimiento de los parámetros involucrados del modelo, por lo que se implementan tres técnicas de aproximación paramétrica: mínimos cuadrados e identificación algebraica para el caso de la aproximación sinusoidal, y el cálculo de coeficientes para el caso de las series de Fourier. Para validar la metodología, se lleva a cabo el seguimiento del robot en tiempo real puesto que la trayectoria del punto de interés es afectada por diversos factores como la fricción, inclinación e imperfecciones de la superficie, el estado de conservación del robot, entre otros. A partir de diversos experimentos, se desarrolla una comparación cuantitativa entre las diferentes aproximaciones para verificar aquel que mejor reproduce a la dinámica del balanceo del robot.Peer Reviewe

An adaptive pneumatic suspension based on the estimation of the excitation frequency

A pneumatic suspension that can adapt itself to the incoming vibration is presented in this paper. A switching control strategy between two different configurations is proposed and studied. The objective is to avoid undesirable resonant frequencies. The control procedure is based on the pre-knowledge of the incoming vibration frequency, and when this frequency is unknown, a very efficient prediction technique is used. The results show that the adaptable suspension has improved performance as compared to any of its passive counterparts. The transient response when switching typically takes less than three cycles and does not hinder the suspension performance

A property of the elementary symmetric functions”,

Abstract In this paper, a relation between the elementary symmetric functions on the frequencies of multi-sine wave signal and its multiple integrals is proposed. In particular, such relation is useful to obtain a closed-form expression for the frequencies estimation. The approach used herein is based on the algebraic derivative method in the frequency domain, which allows to yield exact formula in terms of multiple integrals of the signal when placed in the time domain. Moreover, it allows to free oneself from the hypothesis of uniform sampling. Two different ways to approach the estimation are advised, the first is based on least-squares estimation, while the second one is based on the solution of a linear system of dimension equal to the number of sinusoidal components involved. For an easy time realization of such formula, a time-varying filter is proposed. Due to use of multiple integrals of the signal, the resulting parameters estimation is accurate in the face of large measurement noise. To corroborate the theoretical analysis and to investigate the performance of the developed algorithm, computer simulated and laboratory experiments data records are processed