A Random Nonstationary Pulse Train Model

A simple and mathematically tractable model of a nonstationary process is developed.The process is the sum of waves where the parameters of the waves are random.Explicit expres-sions for the mean and autocorrelation function at each position as a function of time are obtained.In the case of infinite time,the model evolves into a stationary process.The time-frequency distri-bution at each position is also obtained.An explicit example is given where the initial waves are Gaussian.The case where there is dispersion in the propagation is also discussed.

A COMPUTATIONAL METHOD FOR FIRST-EXCURSION RELIABILITY

An efficient computational method is suggested for the first-excursion reliability assessment of nonstationary process. In the proposed method, the nonlinear performance function is Linearized at the Hasofer-Lind point obtained by an iterative algorithm. The problem of the nonstationary processes is solved by the discrete-time method, in which the precision can be controlled by choosing the steps of discretization. The derived formulae can be conveniently degraded to calculate both the first-excursion reliability with linear performance function of stationary processes and the time-independent reliability. The suggested method is useful for the analysis of components and systems with nonstationary responses in structural design where some uncertainties are represented by a vector of nonstationary processes. Examples are given to demonstrate the fast convergency and effectiveness of the presented method.

A direct probabilistic approach to solve state equations for nonlinear systems under random excitation

In this paper, a direct probabilistic approach（DPA） is presented to formulate and solve moment equations for nonlinear systems excited by environmental loads that can be either a stationary or nonstationary random process.The proposed method has the advantage of obtaining the response＇s moments directly from the initial conditions and statistical characteristics of the corresponding external excitations. First, the response＇s moment equations are directly derived based on a DPA, which is completely independent of the It？/filtering approach since no specific assumptions regarding the correlation structure of excitation are made.By solving them under Gaussian closure, the response＇s moments can be obtained. Subsequently, a multiscale algorithm for the numerical solution of moment equations is exploited to improve computational efficiency and avoid much wall-clock time. Finally, a comparison of the results with Monte Carlo（MC） simulation gives good agreement.Furthermore, the advantage of the multiscale algorithm in terms of efficiency is also demonstrated by an engineering example.

Controlling cooperativity of a metastable open system coupled weakly to a noisy environment

The notion of cooperativity comprises a specific characteristic of a multipartite system concerning its ability to demonstrate a sigmoidal-type response of varying sensitivities to input stimuli in transitions between states under controlled conditions.From a statistical physics viewpoint,in this work we attempt to describe the cooperativity by the stability of a metastable open system with respect to irreversibility.To treat the evolution of a system weakly coupled to the environment in a kinetic framework,we consider two fluctuating energy levels of different dimensionalities,initial population of one level,reversible transitions of population between the levels,and irreversible depopulation of another level.An average is made over level fluctuations and environment vibrations so that an inter-level transition rate can be obtained accounting for the influences of external control on level position and dimensionality.It is found that the cooperativity of the two-level system is bounded approximately between 0.736 and unity,with the lower bound indicating worsening system stability.

INFLUENCES OF NONSTATIONARY PROCESS ON INTERNAL PARAMETERS AND WIND PROFILES IN THE PLANETARY BOUNDARY LAYER

In this paper,under the assumption of neutral and barotropic atmosphere,by means of the analytic solution of motion equation of PBL,the influences of nonstationary process on the internal parameters u_*/A(A is the wind speed at the top of PBL)and ■(the angle between winds near the surface and at the top of PBL)of PBL are investigated in which the wind direction at the top of PBL is a periodic function of time but the wind speed at the top of PBL does not change.The u_*/A increases and ■ decreases when the wind direction at the top of PBL rotates anticlockwise and vice versa.Hence the parameterization of PBL in the large-scale models derived under the stationary condition should be corrected by accounting for the nonstationary process.The similar results are obtained in the numerical solution of the motion equation of PBL.The influences of this nonstationary process on the profiles of the wind in PBL are also analyzed.