The main intent of this paper is to represent a systematic algorithm capable of deriving the equations of motion of N-flexible link manipulators with revolute-prismatic joints. The existence of the prismatic joints to...
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The main intent of this paper is to represent a systematic algorithm capable of deriving the equations of motion of N-flexible link manipulators with revolute-prismatic joints. The existence of the prismatic joints together with the revolute ones makes the derivation of governing equations difficult. Also, the variations of the flexible parts of the links, with respect to time cause the associated mode shapes of the links to vary instantaneously. So, to derive the kinematic and dynamic equations of motion for such a complex system, the recursive Gibbs-Appell formulation is applied. For a comprehensive and accurate modeling of the system, the coupling effects due to the simultaneous rotating and reciprocating motions of the flexible arms as well as the dynamic interactions between large movements and small deflections are also included. In this study, the links are modeled based on the Euler-Bernoulli beam theory and the assumed mode method. Also, the effects of gravity as well as the longitudinal, transversal and torsional vibrations have been considered in the formulations. Moreover, a recursive algorithm based on 3 x 3 rotational matrices has been applied in order to derive the system's dynamic equations of motion, symbolically and systematically. Finally, a numerical simulation has been performed by means of a developed computer program in order to demonstrate the ability of this algorithm in deriving and solving the equations of motion related to such systems.
We consider the problem of constructing an on-line (recursive) algorithm for tracking a conditional spatial median, a center of a multivariate distribution. In the one-dimensional case we also track conditional quanti...
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We consider the problem of constructing an on-line (recursive) algorithm for tracking a conditional spatial median, a center of a multivariate distribution. In the one-dimensional case we also track conditional quantiles of arbitrary level. We establish a nonasymptotic upper bound for the L-p-risk of the algorithm, which is then minimized under different assumptions on the magnitude of the variation of the spatial median or quantile. We derive convergence rates for the examples we consider.
The paper discusses recursive computation problems of the criterion functions of several least squares type parameter estimation methods for linear regression models, including the well-known recursive least squares (...
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The paper discusses recursive computation problems of the criterion functions of several least squares type parameter estimation methods for linear regression models, including the well-known recursive least squares (RLS) algorithm, the weighted RLS algorithm, the forgetting factor RLS algorithm and the finite-data-window RLS algorithm without or with a forgetting factor. The recursive computation formulas of the criterion functions are derived by using the recursive parameter estimation equations. The proposed recursive computation formulas can be extended to the estimation algorithms of the pseudo-linear regression models for equation error systems and output error systems. Finally, the simulation example is provided. (C) 2013 Elsevier Inc. All rights reserved.
In multi-state systems (MSS) reliability problems, it is assumed that the components of each subsystem have different performance rates with certain probabilities. This leads into extensive computational efforts invol...
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In multi-state systems (MSS) reliability problems, it is assumed that the components of each subsystem have different performance rates with certain probabilities. This leads into extensive computational efforts involved in using the commonly employed universal generation function (UGF) and the recursive algorithm to obtain reliability of systems consisting of a large number of components. This research deals with evaluating non-repairable three-state systems reliability and proposes a novel method based on a Markov process for which an appropriate state definition is provided. It is shown that solving the derived differential equations significantly reduces the computational time compared to the UGF and the recursive algorithm. (C) 2014 Elsevier Ltd. All rights reserved.
In this paper, a recursive algorithm is developed to estimate the parameters of a partial differential equation as a continuous two-dimensional (2-D) system in the presence of additive colored noise. The system is mod...
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In this paper, a recursive algorithm is developed to estimate the parameters of a partial differential equation as a continuous two-dimensional (2-D) system in the presence of additive colored noise. The system is modelled as hybrid Box-Jenkins model. No comprehensive algorithm for identification of continuous 2-D systems simultaneous with noise process parameter estimation has been proposed so far. Also, there is no recursive method to identify the continuous 2-D systems. The proposed algorithm estimates the noise-free system parameters and colored noise process parameters based on the instrumental variable method simultaneously. Finally, the performance of the proposed method is evaluated by a numerical example.
The paper presents a novel approach to approximation of a linear transfer function model, based on dynamic properties represented by a frequency response, e. g., determined as a result of discrete-time identification....
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The paper presents a novel approach to approximation of a linear transfer function model, based on dynamic properties represented by a frequency response, e. g., determined as a result of discrete-time identification. The approximation is derived for minimization of a non-quadratic performance index. This index can be determined as an exponent or absolute norm of an error. Two algorithms for determination of the approximation coefficients are considered, a batch processing one and a recursive scheme, based on the well-known on-line identification algorithm. The proposed approach is not sensitive to local outliers present in the original frequency response. Application of the approach and its features are presented on examples of two simple dynamic systems.
Two dimensional Fredholm integral equation of the second kind (2DF-II) on a bounded domain D is regarded as the problem with characteristic values. A two dimensional function-valued Pade-type approximation(2DFPTA) is ...
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Two dimensional Fredholm integral equation of the second kind (2DF-II) on a bounded domain D is regarded as the problem with characteristic values. A two dimensional function-valued Pade-type approximation(2DFPTA) is defined. Its error formulas and convergence theorems are presented. To obtain higher order 2DFPTA, a determinantal expression and its recursive algorithm are given. In the end three numerical examples are tested, where one on the unit triangle of vertices (0, 0), (0, 1), (1, 0) and the other two on the square. The testing results show that 2DFPTA method is more accurate. (C) 2014 Elsevier Inc. All rights reserved.
This paper presents the estimation considering the Second Probability Moment applied to a simplified Third Order Stochastic Process. Model commonly used to describe smoothing systems as a synchronous motor. Its values...
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This paper presents the estimation considering the Second Probability Moment applied to a simplified Third Order Stochastic Process. Model commonly used to describe smoothing systems as a synchronous motor. Its values used into the model describe and estimate the Black Box system behavior. In the design three parameters based on covariance P-k and Q(k) are calculated The stochastic variable depends on the three gains and three functional estimation errors, respectively, developing the stochastic identification by a reference model that converges in almost all points with 10 iterations in recursive estimation. The results demonstrate a theoretical experiment using the Matlab (R) obtaining the parameters and the third order model to converge in accordance to the reference signal. The accuracy achieved in thousandths was in a Supermartingale sense and. implementation performed as a function of recursive estimation.
Complexity of a recursive algorithm typically is related to the solution to a recurrence equation based on its recursive structure. For a broad class of recursive algorithms we model their complexity in what we call t...
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Complexity of a recursive algorithm typically is related to the solution to a recurrence equation based on its recursive structure. For a broad class of recursive algorithms we model their complexity in what we call the complexity approach space, the space of all functions in X = ]0, aaEuro parts per thousand] (Y) , where Y can be a more dimensional input space. The set X, which is a dcpo for the pointwise order, moreover carries the complexity approach structure. There is an associated selfmap I broken vertical bar on the complexity approach space X such that the problem of solving the recurrence equation is reduced to finding a fixed point for I broken vertical bar. We will prove a general fixed point theorem that relies on the presence of the limit operator of the complexity approach space X and on a given well founded relation on Y. Our fixed point theorem deals with monotone selfmaps I broken vertical bar that need not be contractive. We formulate conditions describing a class of recursive algorithms that can be treated in this way.
Sampling from probability distributions in high dimensional spaces is generally impractical. Diffusion processes with invariant equilibrium distributions can be used as a means to generate approximations. An important...
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Sampling from probability distributions in high dimensional spaces is generally impractical. Diffusion processes with invariant equilibrium distributions can be used as a means to generate approximations. An important task in such an endeavor is to design an equilibrium-preserving drift to accelerate the convergence. Starting from a reversible diffusion, it is desirable to depart for non-reversible dynamics via a perturbed drift so that the convergence rate is maximized with the common equilibrium. In the Gaussian diffusion acceleration, this problem can be cast as perturbing the inverse of a given covariance matrix by skew-symmetric matrices so that all resulting eigenvalues have identical real part. This paper describes two approaches to obtain the optimal rate of Gaussian diffusion. The asymptotical approach works universally for arbitrary Ornstein-Uhlenbeck processes, whereas the direct approach can be implemented as a fast divide-and-conquer algorithm. A comparison with recently proposed LeliSvre-Nier-Pavliotis algorithm is made.
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