A. Colombo¹, U. Galvanetto²

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.3, pp. 235-254, 2009, DOI:10.3970/cmes.2009.053.235

Abstract The paper addresses the problem of computing the stable manifolds of equilibria and limit cycles of saddle type in piecewise smooth dynamical systems. All singular points that are generically present along one-dimensional or two-dimensional manifolds are classified and such a classification is then used to define a method for the numerical computation of the stable manifolds. Finally the proposed method is applied to the case of a stick-slip oscillator. More >

Hung-Chang Lee¹, Chein-Shan Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.1, pp. 1-26, 2009, DOI:10.3970/cmes.2009.041.001

Abstract The group-preserving schemes developed by Liu (2001) for integrating ordinary differential equations system were adopted the Cayley transform and Padé approximants to formulate the Lie group from its Lie algebra. However, the accuracy of those schemes is not better than second-order. In order to increase the accuracy by employing the group-preserving schemes on ordinary differential equations, according to an efficient technique developed by Runge and Kutta to raise the order of accuracy from the Euler method, we combine the Runge-Kutta method on the group-preserving schemes to obtain the higher-order numerical methods of group-preserving type. They provide single-step explicit time integrators… More >

B Radhika¹, S S P,a¹, C S Manohar^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 79-110, 2008, DOI:10.3970/cmes.2008.027.079

Abstract Reliability of nonlinear vibrating systems under stochastic excitations is investigated using a two-stage Monte Carlo simulation strategy. For systems with white noise excitation, the governing equations of motion are interpreted as a set of Ito stochastic differential equations. It is assumed that the probability distribution of the maximum in the steady state response belongs to the basin of attraction of one of the classical asymptotic extreme value distributions. The first stage of the solution strategy consists of selection of the form of the extreme value distribution based on hypothesis tests, and the next stage involves the estimation of parameters of… More >

Nagalinga Rajan, Soumyendu Raha¹

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.2, pp. 91-116, 2008, DOI:10.3970/cmes.2008.023.091

Abstract The article describes a numerical method for time domain integration of noisy dynamical systems originating from engineering applications. The models are second order stochastic differential equations (SDE). The stochastic process forcing the dynamics is treated mainly as multiplicative noise involving a Wiener Process in the Itô sense. The developed numerical integration method is a drift implicit strong order 2.0 method. The method has user-selectable numerical dissipation properties that can be useful in dealing with both multiplicative noise and stiffness in a computationally efficient way. A generalized analysis of the method including the multiplicative noise is presented. Strong order convergence, user-selectable… More >

John L. Junkins¹, Kamesh Subbarao², Ajay Verma³

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 99-118, 2000, DOI:10.3970/cmes.2000.001.551

Abstract Model reference adaptive control formulations are presented that rigorously impose the dynamical structure of the state space descriptions of several distinct large classes of dynamical systems. Of particular interest, the formulations enable the imposition of exact kinematic differential equation constraints upon the adaptation process that compensates for model errors and disturbances at the acceleration level. Other adaptive control formulations are tailored for redundantly actuated and constrained dynamical systems. The utility of the resulting structured adaptive control formulations is studied by considering examples from nonlinear oscillations, aircraft control, spacecraft control, and cooperative robotic system control. The theoretical and computational results provide… More >

R Sivaprasad^1,2, S Venkatesha¹, C S Manohar^1,3

CMC-Computers, Materials & Continua, Vol.9, No.3, pp. 179-208, 2009, DOI:10.3970/cmc.2009.009.179

Abstract The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on one, two and a 33… More >

Nadipuram R. Prasad¹, Salvador Almanza-Garcia¹, Thomas T. Lu²

CMC-Computers, Materials & Continua, Vol.14, No.1, pp. 1-22, 2009, DOI:10.3970/cmc.2009.014.001

Abstract The paper presents a revolutionary framework for the modeling, detection, characterization, identification, and machine-learning of anomalous behavior in observed phenomena arising from a large class of unknown and uncertain dynamical systems. An evolved behavior would in general be very difficult to correct unless the specific anomalous event that caused such behavior can be detected early, and any consequence attributed to the specific anomaly following its detection. Substantial investigative time and effort is required to back-track the cause for abnormal behavior and to recreate the event sequence leading to such abnormal behavior. The need to automatically detect anomalous behavior is therefore… More >