A simulation algorithm is proposed to generate sample functions of a stationary, multivariate stochastic process according to its prescribed cross-spectral density matrix. If the components of the vector process correspond to different locations in space, then the process is nonhomogeneous in space. The ensemble cross-correlation matrix of the generated sample functions is identical to the corresponding target. The simulation algorithm generates ergodic sample functions in the sense that the temporal cross-correlation matrix of each and every generated sample function is identical to the corresponding target, when the length of the generated sample function is equal to one period (the generated sample functions are periodic). The proposed algorithm is based on an extension of the spectral representation method and is very efficient computationally since it takes advantage of the fast Fourier transform technique. The generated sample functions are Gaussian in the limit as the number of terms in the frequency discretization of the cross-spectral density matrix approaches infinity. An example involving simulation of turbulent wind velocity fluctuations is presented in order to demonstrate the capabilities and efficiency of the proposed algorithm.

Simulation of Ergodic Multivariate Stochastic Processes

Non-stationary stochastic vector processes: seismic ground motion applications

Probabilistic description of nonlinear waves with a narrow-band spectrum is simplified to a form in which each realization of the surface displacement becomes an amplitude-modulated Stokes wave with a mean frequency and random phase. Under appropriate conditions this simplification provides a convenient yet rigorous means of describing nonlinear effects on sea surface properties in a semiclosed or closed form. In particular, it is shown that surface displacements are non-Gaussian and skewed, as was previously predicted by the Gram-Charlier approximation; that wave heights are Rayleigh distributed, just as in the linear case; and that crests are non-Rayleigh.

Narrow-band nonlinear sea waves

Reliability-based Optimization is a most appropriate and advantageous methodology for structural design. Its main feature is that it allows determining the best design solution (with respect to prescribed criteria) while explicitly considering the unavoidable effects of uncertainty. In general, the application of this methodology is numerically involved, as it implies the simultaneous solution of an optimization problem and also the use of specialized algorithms for quantifying the effects of uncertainties. In view of this fact, several approaches have been developed in the literature for applying this methodology in problems of practical interest. This contribution provides a survey on approaches for performing Reliability-based Optimization, with emphasis on the theoretical foundations and the main assumptions involved. Early approaches as well as the most recently developed methods are covered. In addition, a qualitative comparison is performed in order to provide some general guidelines on the range of applicability on the different approaches discussed in this contribution.

A survey on approaches for reliability-based optimization

Random fields and stochastic finite elements

Simulation of random envelope processes.

Modern control theory has been successfully applied to control the motions of aerospace vehicles. An exploratory study is made herein to investigate the feasibility of applying such a theory to control the vibration of civil engineering structures under random loadings. It is assumed that random excitations to structures, such as wind loads and earthquakes, can be modeled by passing either a stationary Gaussian white noise or a nonstationary Gaussian shot noise through a filter. The performance index to be minimized consists of the covariances of both the structural responses and the control forces. Under these conditions, the optimal control law is a linear feedback control. The optimal control forces are obtained by solving a matrix Riccati equation. Applications of the optimal control to a multi-degree-of-freedom structure, under stationary wind loads and nonstationary earthquakes, are demonstrated. It is shown that significant reduction in covariances of the structural responses can be achieved by the use of an active control system.

Application of Optimal Control Theory to Civil Engineering Structures

On the normality and accuracy of simulated random processes

The definition of stationary random envelope proposed by Cramer and Leadbetter, is extended to the envelope of nonstationary random process possessing evolutionary power spectral densities. The density function, the joint density function, the moment function, and the crossing rate of a level of the nonstationary envelope process are derived. Based on the envelope statistics, approximate solutions to the first excursion probability of nonstationary random processes are obtained. In particular, applications of the first excursion probability to the earthquake engineering problems are demonstrated in detail.

Nonstationary Envelope Process and First Excursion Probability

A well‐posed boundary‐value problem is obtained of the first‐passage probability for a linear single‐degree‐of‐freedom vibratory system with a linear viscous damping and subjected to either stationary or nonstationary white‐noise excitation.

Jann-Nan Yang

Papers

Simulation of random envelope processes.

Application of Optimal Control Theory to Civil Engineering Structures

On the normality and accuracy of simulated random processes

Nonstationary Envelope Process and First Excursion Probability

First‐Passage Time Problem