An interpolating stochastic process for simulation of conditional random fields

This paper presents a method of generating an interpolating stochastic process for simulation of conditional random fields involving deterministic time functions, which is to be used as a major tool for stochastic interpolation of earthquake ground motions. Closed form solutions are derived for conditional probability density functions for Fourier coefficients, or harmonic amplitudes and phase angles of interpolating motions conditioned by a given number of deterministic time functions through cross-spectral density functions. Numerical examples for the analytical results as well as those for simulated interpolating motions are presented.     

Modeling of two-dimensional random fields

This paper presents a method of conditional stochastic modeling of two-dimensional fields which can be used to predict values at certain field points at a given time, based on field values at other locations at the same time and on data about second order field moments at given points. For computer simulations, the Gaussian truncated distributions are used. The aim of this work is also to present a derivation of a formula for the probability density of an n-dimensional random variable with the Gaussian conditional truncated distribution. As a numerical example, a soil contamination field described by correlation functions corresponding to the white noise field, the Shinozuka field and the Markov field is analyzed. The acceptance-rejection method is applied to generate covariance matrices and vectors of field values. Then, conditional expected field values for adequate correlation functions are calculated.     

First-passage failure of quasi linear systems subject to multi-time-delayed feedback control and wide-band random excitation

A procedure for studying the first-passage failure of quasi-linear systems subject to multi-time-delayed feedback control and wide-band random excitation is proposed. The stochastic averaging method for quasi-integrable Hamiltonian systems is first introduced. The backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are then established. The conditional reliability function, the conditional probability density and moments of first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. An example is given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the proposed procedure. The effects of time delay in feedback control forces on the conditional reliability function, conditional probability density and moments of first-passage time are analyzed.     

A harmonic-wavelet-based representation for non-stationary stochastic excitations

Representation of nonstationary stochastic excitations is crucial for stochastic response analyses of (time-varying) linear and nonlinear structural systems. This paper proposes a new representation method of non-stationary stochastic excitations based on the generalized harmonic wavelet (GHW) that takes the phase angles and frequencies as basic random variables. The orthogonal properties of the discrete-form spectral process increments describing non-stationary stochastic processes are formulated. Then the GHW-based representation is derived by using the orthogonal properties. This method can be used to accurately reproduce non-stationary stochastic excitations with the target asymptotic Gaussianity and evolutionary power spectrum density. The effectiveness and accuracy of the proposed method have been validated via numerical examples. This study provides a novel way for the representation of non-stationary processes and deserves to be applied in the stochastic response analyses of structures.     

多阻尼比设计反应谱的非平稳地震动场拟合

采用频域调整方法生成与设计反应谱相吻合的地震动,并利用解析迭代方法计算地震动的反应谱,提出了迭代计算的收敛准则。在相关地震动场模拟方法中,将相位差谱的统计模型引入空间相关非平稳地震动场的模拟方法之中,利用快速傅里叶变换技术生成地震动场。将设计反应谱的地震动拟合与非平稳地震动场的合成结合在一起,解决了多阻尼比设计反应谱的非平稳地震动场拟合问题。     

高斯白噪声激励下拟可积哈密顿系统的可靠性

研究非共振的拟可积哈密顿系统在受高斯白噪声外激励下的可靠性。利用由随机平均法导出的关于系统的独立运动积分或作用变量的随机平均方程，通过拟可积哈密顿系统的特性以及对漂移与扩散系数作出的一些假定，给出了系统的可靠性函数以及首次穿越损坏的条件转移慨率密度函数所满足的后向柯尔莫哥洛夫方程和福克-普朗克方程，并进一步详细地讨论了其边界与可解性条件。通过一个实例的分析以及有限差分方法得出的数值结果表明，关于系统的可靠性函数以及首次穿越损坏的条件转移概率密度函数方面的结果是比较合理的，这也表明此分析方法是正确的。     

A translation model for non-stationary, non-Gaussian random processes

A model for simulation of non-stationary, non-Gaussian processes based on non-linear translation of Gaussian random vectors is presented. This method is a generalization of traditional translation processes that includes the capability of simulating samples with spatially or temporally varying marginal probability density functions. A formal development of the properties of the resulting process includes joint probability density function, correlation distortion and lower and upper bounds that depend on the target marginal distributions. Examples indicate the possibility of exactly matching a wide range of marginal pdfs and second order moments through a simple interpolating algorithm. Furthermore, the application of the method in simulating statistically inhomogeneous random media is investigated, using the specific case of binary translation with stationary and non-stationary target correlations.     

Solutions of the FPK equation for time-delayed dynamical systems with the continuous time approximation method

This paper presents a method of finite-dimensional Markov process (FDMP) approximation for stochastic dynamical systems with time delay and numerical solutions of probability density functions of the systems. Solutions of probability density functions of time-delayed systems are rare in the literature. The FDMP method preserves the standard state space format of the system, and allows us to apply all the existing methods and theories for analysis and control of stochastic dynamical systems and to compute the probability density functions efficiently. The solutions of the FPK equation for a linear time-delayed stochastic system are presented. The effects of different spectral differentiation schemes for the FDMP method on the probability density functions are compared.     

Non-Gaussian random processes in ocean engineering

This paper presents a state-of-the-art review on stochastic analysis and probabilistic prediction of non-Gaussian random processes in ocean engineering. The derivation of probability density functions which constitute the basis for stochastic analysis of non-Gaussian processes is discussed in detail, and then the probability distributions of peaks and troughs of non-Gaussian random process is discussed to provide information necessary for engineering design. As an example of application of these probability distribution functions, the procedure for predicting responses of an offshore structure which has substantial non-linear characteristics in random seas is presented.     

Stochastic control of hysteretic structural systems

A method of stochastic optimal control of hysteretic structural systems under earthquake excitations is presented. Stochastic estimation and control problems are formulated in the form of Itô stochastic differential equations on the basis of the theory of continuous Markov processes. The conditional moment equations given observation data are derived for nonlinear filtering, and are closed by introducing appropriate analytical form of the conditional probability density functions of the state variables. Under the assumption that the admissible controls are expressed as functions of the conditional moment functions the Bellman equation is derived. If the spatial variables of the Bellman equation are defined by a part of the full set of conditional moment functions appearing in the closed moment equations, the resulting Bellman equation is coupled with conditional moment equations both for filtering and for prediction. The Gaussian and non-Gaussian stochastic linearization techniques combined with simple solution techniques to the Bellman equation are examined to solve the Bellman equation or extended Riccati equations without prediction procedures.