Search results for "White Noise"
showing 10 items of 132 documents
Efficient solution of the first passage problem by Path Integration for normal and Poissonian white noise
2015
Abstract In this paper the first passage problem is examined for linear and nonlinear systems driven by Poissonian and normal white noise input. The problem is handled step-by-step accounting for the Markov properties of the response process and then by Chapman–Kolmogorov equation. The final formulation consists just of a sequence of matrix–vector multiplications giving the reliability density function at any time instant. Comparison with Monte Carlo simulation reveals the excellent accuracy of the proposed method.
Non-linear Systems Under Poisson White Noise Handled by Path Integral Solution
2008
An extension of the path integral to non-linear systems driven by a Poissonian white noise process is presented. It is shown that at the limit when the time increment becomes infinitesimal the Kolmogorov— Feller equation is fully restored. Applications to linear and non-linear systems with different distribution of the Dirac's deltas occurrences are performed and results are compared with analytical solutions (when available) and Monte Carlo simulation.
Higher order statistics of the response of MDOF linear systems excited by linearly parametric white noises and external excitations
1997
The aim of this paper is the evaluation of higher order statistics of the response of linear systems subjected to external excitations and to linearly parametric white noise. The external excitations considered are deterministic or filtered white noise processes. The procedure implies the knowledge of the transition matrix connected to the linear system; this, however, has already been evaluated for obtaining the statistics at single times. The method, which avoids making further integrations for the evaluation of the higher order statistics, is very advantageous from a computational point of view.
Higher order statistics of the response of MDOF linear systems under polynomials of filtered normal white noises
1997
This paper exploits the work presented in the companion paper in order to evaluate the higher order statistics of the response of linear systems excited by polynomials of filtered normal processes. In fact, by means of a variable transformation, the original system is replaced by a linear one excited by external and linearly parametric white noise excitations. The transition matrix of the new enlarged system is obtained simply once the transition matrices of the original system and of the filter are evaluated. The method is then applied in order to evaluate the higher order statistics of the approximate response of nonlinear systems to which the pseudo-force method is applied.
Path integral solution handled by Fast Gauss Transform
2009
Abstract The path integral solution method is an effective tool for evaluating the response of non-linear systems under Normal White Noise, in terms of probability density function (PDF). In this paper it has been observed that, using short-time Gaussian approximation, the PDF at a given time instant is the Gauss Transform of the PDF at an earlier close time instant. Taking full advantage of the so-called Fast Gauss Transform a new integration method is proposed. In order to overcome some unsatisfactory trends of the classical Fast Gauss Transform, a new version termed as Symmetric Fast Gauss Transform is also proposed. Moreover, extensions to the two Fast Gauss Transform to MDOF systems ar…
Path Integral Method for Nonlinear Systems Under Levy White Noise
2017
In this paper, the probabilistic response of nonlinear systems driven by alpha-stable Lévy white noises is considered. The path integral solution is adopted for determining the evolution of the probability density function of nonlinear oscillators. Specifically, based on the properties of alpha-stable random variables and processes, the path integral solution is extended to deal with Lévy white noises input with any value of the stability index alpha. It is shown that at the limit when the time increments tend to zero, the Einstein–Smoluchowsky equation, governing the evolution of the response probability density function, is fully restored. Application to linear and nonlinear systems under…
Approximate solution of the Fokker-Planck-Kolmogorov equation
2002
The aim of this paper is to present a thorough investigation of approximate techniques for estimating the stationary and non-stationary probability density function (PDF) of the response of nonlinear systems subjected to (additive and/or multiplicative) Gaussian white noise excitations. Attention is focused on the general scheme of weighted residuals for the approximate solution of the Fokker-Planck-Kolmogorov (FPK) equation. It is shown that the main drawbacks of closure schemes, such as negative values of the PDF in some regions, may be overcome by rewriting the FPK equation in terms of log-probability density function (log-PDF). The criteria for selecting the set of weighting functions i…
Stochastic response of a fractional vibroimpact system
2017
Abstract The paper proposes a method to investigate the stochastic dynamics of a vibroimpact single-degree-of-freedom fractional system under a Gaussian white noise input. It is assumed that the system has a hard type impact against a one-sided motionless barrier, which is located at the system’s equilibrium position; furthermore, the system under study is endowed with an element modeled with fractional derivative. The proposed method is based on stochastic averaging technique and overcome the particular difficulty due to the presence of fractional derivative of an absolute value function; particularly an analytical expression for the system’s mean squared response amplitude is presented an…
Probabilistic characterization of nonlinear systems under Poisson white noise via complex fractional moments
2014
In this paper, the probabilistic characterization of a nonlinear system enforced by Poissonian white noise in terms of complex fractional moments (CFMs) is presented. The main advantage in using such quantities, instead of the integer moments, relies on the fact that, through the CFMs the probability density function (PDF) is restituted in the whole domain. In fact, the inverse Mellin transform returns the PDF by performing integration along the imaginary axis of the Mellin transform, while the real part remains fixed. This ensures that the PDF is restituted in the whole range with exception of the value in zero, in which singularities appear. It is shown that using Mellin transform theorem…
Cross-correlation and cross-power spectral density representation by complex spectral moments
2017
Abstract A new approach to provide a complete characterization of normal multivariate stochastic vector processes is presented in this paper. Such proposed method is based on the evaluation of the complex spectral moments of the processes. These quantities are strictly related to the Mellin transform and they are the generalization of the integer-order spectral moments introduced by Vanmarcke. The knowledge of the complex spectral moments permits to obtain the power spectral densities and their cross counterpart by a complex series expansions. Moreover, with just the aid of some mathematical properties the complex fractional moments permit to obtain also the correlation and cross-correlatio…