Time variant reliability model updating in instrumented dynamical systems based on Girsanov's transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov's transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

Time variant reliability model updating in instrumented dynamical systems based on Girsanov’s transformation

The problem of updating the reliability of instrumented structures based on measured response under random dynamic loading is considered. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov’s transformation for variance reduction is developed. For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. The controls to implement the Girsanov transformation are developed by solving a constrained non-linear optimization problem. Numerical illustrations include studies on a multi degree of freedom linear system and non-linear systems with geometric and (or) hereditary non-linearities and non-stationary random excitations.

Modeling Time-Varying Aggregate Interference in Cognitive Radio Systems, and Application to Primary Exclusive Zone Design

Accurately characterizing the time-varying interference caused to the primary users is essential in ensuring a successful deployment of cognitive radios (CR). We show that the aggregate interference at the primary receiver (PU-Rx) from multiple, randomly located cognitive users (CUs) is well modeled as a shifted lognormal random process, which is more accurate than the lognormal and the Gaussian process models considered in the literature, even for a relatively dense deployment of CUs. It also compares favorably with the asymptotically exact stable and symmetric truncated stable distribution models, except at high CU densities. Our model accounts for the effect of imperfect spectrum sensing, which depends on path-loss, shadowing, and small-scale fading of the link from the primary transmitter to the CU; the interweave and underlay modes or CR operation, which determine the transmit powers of the CUs; and time-correlated shadowing and fading of the links from the CUs to the PU-Rx. It leads to expressions for the probability distribution function, level crossing rate, and average exceedance duration. The impact of cooperative spectrum sensing is also characterized. We validate the model by applying it to redesign the primary exclusive zone to account for the time-varying nature of interference.

Estimation of time variant reliability of randomly parametered non-linear vibrating systems

The problem of time variant reliability analysis of randomly parametered and randomly driven nonlinear vibrating systems is considered. The study combines two Monte Carlo variance reduction strategies into a single framework to tackle the problem. The first of these strategies is based on the application of the Girsanov transformation to account for the randomness in dynamic excitations, and the second approach is fashioned after the subset simulation method to deal with randomness in system parameters. Illustrative examples include study of single/multi degree of freedom linear/non-linear inelastic randomly parametered building frame models driven by stationary/non-stationary, white/filtered white noise support acceleration. The estimated reliability measures are demonstrated to compare well with results from direct Monte Carlo simulations. (C) 2014 Elsevier Ltd. All rights reserved.

The time finite element as a robust general scheme for solving nonlinear dynamic equations including chaotic systems

Schemes that can be proven to be unconditionally stable in the linear context can yield unstable solutions when used to solve nonlinear dynamical problems. Hence, the formulation of numerical strategies for nonlinear dynamical problems can be particularly challenging. In this work, we show that time finite element methods because of their inherent energy momentum conserving property (in the case of linear and nonlinear elastodynamics), provide a robust time-stepping method for nonlinear dynamic equations (including chaotic systems). We also show that most of the existing schemes that are known to be robust for parabolic or hyperbolic problems can be derived within the time finite element framework; thus, the time finite element provides a unification of time-stepping schemes used in diverse disciplines. We demonstrate the robust performance of the time finite element method on several challenging examples from the literature where the solution behavior is known to be chaotic. (C) 2015 Elsevier Inc. All rights reserved.

The time finite element as a robust general scheme for solving nonlinear dynamic equations including chaotic systems

Schemes that can be proven to be unconditionally stable in the linear context can yield unstable solutions when used to solve nonlinear dynamical problems. Hence, the formulation of numerical strategies for nonlinear dynamical problems can be particularly challenging. In this work, we show that time finite element methods because of their inherent energy momentum conserving property (in the case of linear and nonlinear elastodynamics), provide a robust time-stepping method for nonlinear dynamic equations (including chaotic systems). We also show that most of the existing schemes that are known to be robust for parabolic or hyperbolic problems can be derived within the time finite element framework; thus, the time finite element provides a unification of time-stepping schemes used in diverse disciplines. We demonstrate the robust performance of the time finite element method on several challenging examples from the literature where the solution behavior is known to be chaotic. (C) 2015 Elsevier Inc. All rights reserved.