A simulation algorithm is developed for generating realizations of non-Gaussian stationary translation processes \iX(\it) with a specified marginal distribution and covariance function. Translation processes are memoryless nonlinear transformations \IX(t)=g[Y(t)]\N of stationary Gaussian processes \iY(\it). The proposed simulation algorithm has three steps. First, the memoryless nonlinear transformation \ig and the covariance function of \iY(\it) need to be determined from the condition that the marginal distribution and the covariance functions of \iX(\it) need to be determined from the condition that the marginal distribution and the covariance functions of \iX(\it) coincide with specified target functions. It is shown that there is a transformation \ig giving the target marginal distribution for \iX(\it). However, it is not always possible to find a covariance function of \iY(\it) yielding the target covariance function for \iX(\it). Second, realizations of \iY(\it) have to be generated. Any algorithm for generating samples of Gaussian processes can be used to produce samples of \iY(\it). Third, samples of \iX(\it) can be obtained from samples of \iY(\it) and the mapping of \iX(\it)=\ig[\iY(\it)]. The proposed simulation algorithm is demonstrated by several examples, including the case of non-Gaussian translation random field.

Simulation of stationary non-Gaussian translation processes

Simulation of second-order processes using Karhunen–Loeve expansion

Computational stochastic mechanics – recent advances

The problem of identification of the modal parameters of a structural model using measured ambient response time histories is addressed. A Bayesian spectral density approach (BSDA) for modal updating is presented which uses the statistical properties of a spectral density estimator to obtain not only the optimal values of the updated modal parameters but also their associated uncertainties by calculating the posterior joint probability distribution of these parameters. Calculation of the uncertainties of the identified modal parameters is very important if one plans to proceed with the updating of a theoretical finite element model based on modal estimates. It is found that the updated PDF of the modal parameters can be well approximated by a Gaussian distribution centred at the optimal parameters at which the posterior PDF is maximized. Examples using simulated data are presented to illustrate the proposed method. Copyright © 2001 John Wiley & Sons, Ltd.

Bayesian spectral density approach for modal updating using ambient data

The problem of identification of the modal parameters of a structural model using measured ambient response time histories is addressed. A Bayesian Fast Fourier Transform approach (BFFTA) for modal updating is presented which uses the statistical properties of the Fast Fourier transform (FFT) to obtain not only the optimal values of the updated modal parameters but also their associated uncertainties, calculated from their joint probability distribution. Calculation of the uncertainties of the identified modal parameters is very important when one plans to proceed with the updating of a theoretical finite element model based on modal estimates. The proposed approach requires only one set of response data in contrast to many of the existing frequency-based approaches which require averaging. It is found that the updated PDF can be well approximated by a Gaussian distribution centred at the optimal parameters at which the posterior PDF is maximized. Examples using simulated data are presented to illustrate ...

Bayesian Fast Fourier Transform Approach for Modal Updating Using Ambient Data

Non-Gaussian data and probalilistic methods classes of non-Gaussian processes simulation of non-Gaussian processes response of linear systems to non-Gaussian inputs.

Mircea Grigoriu

Papers

Applied non-Gaussian processes : examples, theory, simulation, linear random vibration, and MATLAB solutions