Stochastic Interpolation of Spatial Random Fields by BF/MCF-ISM

In the past, interpolation of random fields was successfully treated by Kriging methods for Gaussian fields, and by conditional simulation techniques for a class of non-Gaussian translation fields. Recently, bootstrap filter/Monte Carlo filter (BF/MCF) is extensively used for interpolation of general non-Gaussian fields. However, while BF/MCF is a versatile tool to interpolate non-Gaussian fields, that is an algorithm of generating a set of sample realizations of both a predicted state vector and a filtered state vector, the computational cost is expensive due to the required sample size. In order to reduce the required sample size, an importance sampling function derived from the updating theory of Gaussian fields is applied to the ordinary BF/MCF. Interpolation of spatial fields is first demonstrated by using numerically simulated data, and the BF/MCF incorporated with importance sampling technique (BF/MCF-ISM) for the state estimation of conditional non-Gaussian fields is performed with respect to its efficiency in variance reduction.     

Spectral Analysis and Parametric Study of Stochastic Pavement Loads

This paper investigates the effects of vehicle parameters, speed, and surface roughness on the power spectral density (PSD) of stochastic pavement loads. Pavement surface roughness is modeled as a zero-mean stationary random field. A quarter-vehicle model is established to simulate the vibrations of heavy and passenger vehicles with typical parameters. Tire damping is also included in the consideration of stochastic pavement loads; this was assumed to be zero in many previous investigations. The PSD roughness proposed by the ISO is adopted in the simulation of the loads. An important indicator of the stochastic loads, the so-called energy cumulative distribution function, is introduced to describe the frequency distribution of load energy. The results show that passenger vehicles produce more high-frequency loads than heavy vehicles, while more of the loads generated by heavy vehicle are primarily distributed in the low-frequency region. It is also found that the effect of tire damping on stochastic pavement loads is not negligible especially if the loads of interest are concentrated in the high-frequency region. The results of the study may be useful in optimum design of vehicle suspensions and prediction of dynamic pavement response.     

Simulation of Binary Random Fields with Applications to Two-Phase Random Media

This paper introduces a methodology for simulation of binary random fields according to their prescribed autocorrelation function. It starts with a brief outline of the essential features of binary random fields and their implications in modeling two-phase random media. The exposition of the proposed methodology is done in two steps. In the first step, an algorithm is introduced to obtain samples of a binary field from generated realizations of a Gaussian field, using the theory of zero crossings of Gaussian fields. This mapping constitutes essentially a nonlinear transformation with memory of the Gaussian sample functions. In the second step, an iterative algorithm is introduced that allows the determination of the probabilistic characteristics of the underlying Gaussian field, so that the resulting binary field obtained through the proposed nonlinear transformation has a prescribed autocorrelation function. Several numerical examples are provided to demonstrate the capabilities of the methodology, especially in modeling two-phase random media. The methodology is shown to have a wide range of applicability and its computational cost is small, especially when a large number of realizations is needed.     

Simulation of Multidimensional Binary Random Fields with Application to Modeling of Two-Phase Random Media

This paper proposes a methodology for simulation of binary random fields with application to the problem of generating sample realizations of two-phase random media. The methodology is based on the concept of nonlinear transformations with memory of Gaussian random fields. The simulation is performed according to the autocorrelation function of the binary field which contains considerable information about the microstructural characteristics of the medium. The determination of the probabilistic characteristics of the underlying Gaussian field is achieved through an iterative procedure that was introduced in a previous paper by the same authors in one dimension and is extended here to multiple dimensions. Limiting cases and alternative mappings are also presented. The capabilities of the methodology are demonstrated in a series of examples.     

Joint First-Passage Probability and Reliability of Systems under Stochastic Excitation

The first-passage probability, describing the probability that a scalar process exceeds a prescribed threshold during an interval of time, is of great engineering interest. This probability is essential for estimating the reliability of a structural component whose response is a stochastic process. When considering the reliability of an engineering system composed of several interdependent components, the probability that two or more response processes exceed their respective safe thresholds during the operation time of the system is an equally essential quantity. This paper proposes simple and accurate formulas for approximating this joint first-passage probability of a vector process. The nth order joint first-passage probability is obtained from a recursive formula involving lower order joint first-passage probabilities and the out-crossing probability of the vector process over a safe domain. Interdependence between the crossings is approximately accounted for by considering the clumping of these events. The accuracy of the proposed formulas is examined by comparing analytical estimates with those obtained from Monte Carlo simulations for stationary Gaussian processes. As an example application, the reliability of a system of interconnected equipment items subjected to a stochastic earthquake excitation is estimated by linear programming bounds employing marginal and joint component fragilities obtained by the proposed formulas.     

Stochastic Response of a Random Mass Structure

This paper proposes a polynomial approximation approach for the estimation of the stochastic response of a random mass structure subjected to an evolutionary random excitation. A bounded, monopeak, and symmetrically distributed probability density function, called λ-PDF, together with the Gegenbauer polynomial approximation, is introduced to deal with stochastic dynamic response problems of the random mass structures. The λ-PDF model is used to describe the random parameters in the engineering random structures. And then the Gegenbauer polynomial approximation method is used to reduce the random structures into its deterministic equivalent one. The numerical example shows the effectiveness of the proposed method to explore dynamic phenomena in random structures.     

Probabilistic Settlement Analysis by Stochastic and Random Finite-Element Methods

The paper discusses finite element models for predicting the elastic settlement of a strip footing on a variable soil. The paper then goes on to compare results obtained in a probabilistic settlement analysis using a stochastic finite element method based on first order second moment approximations, with the random finite element method based on generation of random fields combined with Monte Carlo simulations. The paper highlights the deficiencies of probabilistic methods that are unable to properly account for spatial correlation.     

Influence of Spatial Variability on Slope Reliability Using 2-D Random Fields

The paper investigates the probability of failure of slopes using both traditional and more advanced probabilistic analysis tools. The advanced method, called the random finite-element method, uses elastoplasticity in a finite-element model combined with random field theory in a Monte-Carlo framework. The traditional method, called the first-order reliability method, computes a reliability index which is the shortest distance (in units of directional equivalent standard deviations) from the equivalent mean-value point to the limit state surface and estimates the probability of failure from the reliability index. Numerical results show that simplified probabilistic analyses in which spatial variability of soil properties is not properly accounted for, can lead to unconservative estimates of the probability of failure if the coefficient of variation of the shear strength parameters exceeds a critical value. The influences of slope inclination, factor of safety (based on mean strength values), and cross correlation between strength parameters on this critical value have been investigated by parametric studies in this paper. The results indicate when probabilistic approaches, which do not model spatial variation, may lead to unconservative estimates of slope failure probability and when more advanced probabilistic methods are warranted.     

Lateral Force Induced by Rectangular Surcharge Loads on a Cross-Anisotropic Backfill

This article presents approximate but analytical-based solutions for computing the lateral force (force per unit length) and centroid location induced by horizontal and vertical surcharge surface loads resting on a cross-anisotropic backfill. The surcharge loading types include: point load, finite line load, and uniform rectangular area load. The planes of cross-anisotropy are assumed to be parallel to the ground surface of the backfill. Although the presented solutions have never been proposed in existing literature, they can be derived by integrating the lateral stress solutions recently addressed by the author. It is clear that the type and degree of geomaterial anisotropy, loading distances from the retaining wall, and loading types significantly influence the derived solutions. An example is given for practical applications to illustrate the type and degree of soil anisotropy, as well as the loading types on the lateral force and centroid location in the isotropic/cross-anisotropic backfills caused by the horizontal and vertical uniform rectangular area loads. The results show that both the lateral force and centroid location in a cross-anisotropic backfill are quite different from those in an isotropic one. The derived solutions can be added to other lateral pressures, such as earth or water pressure, which are necessary in the stability and structural analysis of a retaining wall. In addition, they can be utilized to simulate more realistic conditions than the surcharge strip loading in geotechnical engineering for the backfill geomaterials are cross-anisotropic.     

Attentional Modulation of the Visual Motion Aftereffect Has a Central Cognitive Locus: Evidence of Interference by the Postcategorical on the Precategorical.

An attentionally demanding task undertaken during adaptation to motion reduces the duration of the subsequent motion aftereffect (A. Chaudhuri, 1990). Previous studies have suggested that this effect is intramodal in character, reflecting the selective deployment of visual attention. The present study demonstrates that nonvisual tasks, performed concurrently with motion adaptation, can significantly reduce the duration of the ensuing aftereffect. Three experiments converge on the conclusion that postcategorical processes can influence otherwise unrelated concurrent precategorical processes. The experiments also show that neither perceptual input nor motor output components of the attentional task are responsible for the subsequent reduction in motion of aftereffect. The results suggest a reappraisal of findings in this area and of the general distinction between perception and cognition. (PsycINFO Database Record (c) 2010 APA, all rights reserved)