Articles written in Sadhana
Volume 29 Issue 6 December 2004 pp 589-604
A couple of non-convex search strategies, based on the genetic algorithm, are suggested and numerically explored in the context of large-deflection analysis of planar, elastic beams. The first of these strategies is based on the stationarity of the energy functional in the equilibrium state and may therefore be considered weak. The second approach, on the other hand, attempts to directly solve the governing differential equation within an optimisation framework and such a solution may be thought of as strong. Several numerical illustrations and verifications with ‘exact’ solutions, if available, are provided
Volume 31 Issue 4 August 2006 pp 291-292
Volume 31 Issue 4 August 2006 pp 399-427
The problem of identification of parameters of nonlinear structures using dynamic state estimation techniques is considered. The process equations are derived based on principles of mechanics and are augmented by mathematical models that relate a set of noisy observations to state variables of the system. The set of structural parameters to be identified is declared as an additional set of state variables. Both the process equation and the measurement equations are taken to be nonlinear in the state variables and contaminated by additive and (or) multiplicative Gaussian white noise processes. The problem of determining the posterior probability density function of the state variables conditioned on all available information is considered. The utility of three recursive Monte Carlo simulation-based filters, namely, a probability density function-based Monte Carlo filter, a Bayesian bootstrap filter and a filter based on sequential importance sampling, to solve this problem is explored. The state equations are discretized using certain variations of stochastic Taylor expansions enabling the incorporation of a class of non-smooth functions within the process equations. Illustrative examples on identification of the nonlinear stiffness parameter of a Duffing oscillator and the friction parameter in a Coulomb oscillator are presented.