Point group identification algorithm in dynamic response analysis of nonlinear stochastic systems

Recently Sarsri et al., In another work, Sarsri et al.,

Estimation and analysis of nonlinear stochastic systems (Ph.D. Thesis abstr.)

The adjoint simulation method is an efficient, computerised method for the performance analysis of linear time varying systems excited by deterministic and/or stochastic inputs. It is based on the impulse response function (or weighting function) of the so-called adjoint system---an associated linear system derived from the original system by clever utilisation of the mathematical principle of duality. We demonstrate the power of adjoint simulation in the context of guided missile homing loop studies and present a Matlab tool for its speedy implementation and execution. As an example, the tool analyses the miss distance performance of a generic guided missile against an evading target in two dimensional space. References Statistical performance analysis of nonlinear stochastic systems by the Monte Carlo method volume 23-1 of Mathematics and Computers in Simulation J. , pages 21--23, 1981. doi:10.1016/0378-4754(81)90004-5 Zarchan, P. Tactical and Strategic Missile Guidance , 5th Edition, AIAA Progress in Astronautics and Aeronautics, 2007. Weiss, M. Adjoint Method for Missile Performance Analysis on State-Space Models, volume 28-2 of Guidance, Control and Dynamics J. , pages 236--248, AIAA ,2005. Laning, J. H. and Battin, R. H. Random Processes in Automatic Control , McGraw-Hill Book Company, New York, NY, 1956. D. Bucco and M. Weiss. Development of a Matlab/Simulink Tool to Facilitate System Analysis and Simulation via the Adjoint and Covariance Methods, AIAA MST Conference , Aug 2007. http://www.aiaa.org/agenda.cfm?lumeetingid=1501&formatview=1&dateget=22-Aug-07 DeRusso, P. M., Roy, R. J., Close, C. M., and Desrochers, A. A. State Variables for Engineers, 2nd Edition , John Wiley and Sons, Inc., New York, NY, 1998. Moretti, G. Best Practices for Adopting Model-Based Design in Electronic System Development, White-paper, Gabe on EDA , 2007. http//www.mathworks.com/products/simulink/technicalliterature.html

A copula-based Gaussian mixture closure method for stochastic response of nonlinear dynamic systems

Method of matrix continued fractions for the analysis of nonlinear stochastic systems

In this paper, stability analysis of deterministic and stochastic nonlinear discrete-time dynamical systems is considered. It is shown that some difficulties, such as independency or identical distribution of random variable sequence, that may arise in using Lyapunov's and LaSalle's approaches for stability analysis of discrete-time stochastic systems may be overcome by means of fixed point theory. Furthermore, suitable definitions of stability are provided. Ultimately, numerical examples are given in order to show the results.

In this study stochastic analysis of non-linear dynamical systems under α-stable,
\nmultiplicative white noise has been conducted. The analysis has dealt with a special class of α-stable
\nstochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the
\nprobability density function or of the characteristic function of the dynamical response may be obtained
\nconsidering the dynamical system forced by a Gaussian white noise with an uncertain factor with α/2-
\nstable distribution. This consideration yields the probability density function or the characteristic function
\nof the response by means of a simple integral involving the probability density function of the system
\nunder Gaussian white noise and the probability density function of the α/2-stable random parameter. Some
\nnumerical applications have been reported assessing the reliability of the proposed formulation. Moreover
\na proper way to perform digital simulation of the sub-Gaussian α-stable random process preventing
\ndynamical systems from numerical overflows has been reported and discussed in detail.

Surrogate modeling immersed probability density evolution method for structural reliability analysis in high dimensions

Large degree of uncertainties may exist simultaneously in system parameters and external excitations of engineering structures. To capture the performance of such nonlinear multi-degree-of-freedom structures is still a great challenge in stochastic dynamics. In the present paper, the probability density evolution method is adopted and extended to reduce the dimension of parametric FPK equation of an uncertain-parameter structure subjected to additively white noise process. Numerical examples validate the proposed algorithm. Problems to be further studied are discussed.

Comparison of PDEM and MCS: Accuracy and efficiency

Analysis of Nonlinear Systems with Stochastic Input and Stochastic Parameters—II

Structural design optimization under dynamic reliability constraints based on the probability density evolution method and highly-efficient sensitivity analysis

In this study, a general technique for the analysis of time-period nonlinear dynamical systems is presented. The method is based on the fact that all quasilinear periodic systems can be replaced by similar systems whose linear parts are time invariant via the well-known Liapunov-Floquet (L-F) transformation. A general procedure for the computation of L-F transformation in terms of Chebyshev polynomials is outlined. Once the transformation has been applied, a periodic orbit in original coordinates has a fixed point representation in the transformed coordinates. The stability and bifurcation analysis of the transformed equations are studied by employing thetime-dependent normal form theory and time-dependent centre manifold reduction. For the two examples considered, the three generic codimension-one bifurcations, viz, Hopf, flip and tangent, are analysed. The methodology is semi-analytic in nature and provides a quantitative measure of stability even under critical conditions. Unlike the perturbation or averaging techniques, this method is applicable even to those systems where the periodic term in the linear part does not contain a small parameter or a generating solution does not exist due to the absence of the time-invariant term in the linear part.

Application of asymptotic methods of oscillation theory to an analysis of stochastic nonlinear lumped oscillatory systems. Part II

This paper proposed a method analyzing crowd-induced stochastic vibration response by the dynamic reliability method. The efficiency of the probability density evolution method (PDEM) is improved by embedding the Kullback-Leibler (K-L) relative sensitivity analysis in response analysis of stochastic dynamic system. Then the complicated point selection technique of high dimension uncertain variables is avoided. The proposed method is illustrated by the response analysis of random crowd-structure interaction system where the load parameter randomness is considered. The acceleration induced by the crossing of crowd is predicted with the proposed method. Results obtained highlight the computation improvement in PDEM probabilistic response analysis in high dimension dynamic system. And the method could be used as an efficient way to predict and evaluate vibration serviceability of structures with human-induced vibration.