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CONTENTS
Volume 25, Number 3, February20 2007
 

Abstract
In this paper a brief overview of methods to assess the reliability of mechanical systems and structures is presented. A selection of computational procedures, stochastic structural dynamics, stochastic fatigue crack growth and reliability based optimization are discussed. It is shown that reliability based methods may form the basis for a rational decision making.

Key Words
structural reliability; uncertainty analysis; computational methods

Address
G. I. Schueller; Institute of Engineering Mechanics, Leopold-Franzens University, Technikerstr. 13, 6020 Innsbruck, Austria, EU

Abstract
Current seismic design guidelines in Japan are diverse in the seismic ground strain estimates, because the concepts on a horizontally propagating wave model are not consistent in various seismic design guidelines including gas, water and other underground structures.
The purpose of this study is (a) to derive the analytical methods to estimate the ground strains for incident seismic waves, (b) to develop a statistical estimation technique of the ground strains, and finally (c) to compare the theoretical estimation with the observed data which was measured at 441 sites in the 1999 Chi-Chi Earthquake in Taiwan.

Key Words
ground strain; spatial variation; buried pipelines; seismic waves

Address
Takeshi Koike, Osamu Maruyama, and Lessandro Estelito Garciano; Musashi Institute of Technology, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo, 158-8557, Japan

Abstract
Model-based predictions of structural behavior are negatively affected by uncertainties of various type and in various stages of the structural analysis. The present paper focusses on dynamic analysis and addresses the effects of uncertainties concerning material and geometric parameters, mainly in the context of modal analysis of large-scale structures. Given the large number of uncertain parameters arising in this case, highly scalable simulation-based methods are adopted, which can deal with possibly thousands of uncertain parameters. In order to solve the reliability problem, i.e., the estimation of very small exceedance probabilities, an advanced simulation method called Line Sampling is used. In combination with an efficient algorithm for the estimation of the most important uncertain parameters, the method provides good estimates of the failure probability and enables one to quantify the error in the estimate. Another aspect here considered is the uncertainty quantification for closely-spaced eigenfrequencies. The solution here adopted represents each eigenfrequency as a weighted superposition of the full set of eigenfrequencies. In a case study performed with the FE model of a satellite it is shown that the effects of uncertain parameters can be very different in magnitude, depending on the considered response quantity. In particular, the uncertainty in the quantities of interest (eigenfrequencies) turns out to be mainly caused by very few of the uncertain parameters, which results in sharp estimates of the failure probabilities at low computational cost.

Key Words
uncertainty modeling; uncertainty quantification; model uncertainties; structural reliability; Monte Carlo simulation

Address
M. F. Pellissetti and G. I. Schueller; Institute of Engineering Mechanics, Leopold-Franzens University, Technikerstr. 13, 6020 Innsbruck, Austria, EU

Abstract
Uncertainties enter a complex analysis from a variety of sources: variability, lack of data, human errors, model simplification and lack of understanding of the underlying physics. However, for many important engineering applications insufficient data are available to justify the choice of a particular probability density function (PDF). Sometimes the only data available are in the form of interval estimates which represent, often conflicting, expert opinion. In this paper we demonstrate that Bayesian estimation techniques can successfully be used in applications where only vague interval measurements are available. The proposed approach is intended to fit within a probabilistic framework, which is established and widely accepted. To circumvent the problem of selecting a specific PDF when only little or vague data are available, a hierarchical model of a continuous family of PDF?s is used. The classical Bayesian estimation methods are expanded to make use of imprecise interval data. Each of the expert opinions (interval data) are interpreted as random interval samples of a parent PDF. Consequently, a partial conflict between experts is automatically accounted for through the likelihood function.

Key Words
modal uncertainty; interval data; Beyesian analysis; expert knowledge; conflicting data

Address
Ben H. Thacker and Luc J. Huyse; Materials Engineering Department, Southwest Research Institute,
6220 Culebra Road, San Antonio, Texas, USA

Abstract
A novel methodology, referred to as Auxiliary Domain Method (ADM), allowing for a very efficient solution of nonlinear reliability problems is presented. The target nonlinear failure domain is first populated by samples generated with the help of a Markov Chain. Based on these samples an auxiliary failure domain (AFD), corresponding to an auxiliary reliability problem, is introduced. The criteria for selecting the AFD are discussed. The emphasis in this paper is on the selection of the auxiliary linear failure domain in the case where the original nonlinear reliability problem involves multiple objectives rather than a single objective. Each reliability objective is assumed to correspond to a particular response quantity not exceeding a corresponding threshold. Once the AFD has been specified the method proceeds with a modified subset simulation procedure where the first step involves the direct simulation of samples in the AFD, rather than standard Monte Carlo simulation as required in standard subset simulation. While the method is applicable to general nonlinear reliability problems herein the focus is on the calculation of the probability of failure of nonlinear dynamical systems subjected to Gaussian random excitations. The method is demonstrated through such a numerical example involving two reliability objectives and a very large number of random variables. It is found that ADM is very efficient and offers drastic improvements over standard subset simulation, especially when one deals with low probability failure events.

Key Words
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Address
Lambros Katafygiotis; Department of Civil Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
Torgeir Moan; Department of Marine Technology, NTNU, Trondheim, NO-7491, Norway
Sai Hung Cheung; Department of Civil Engineering, California Institute of Technology, 1200 East California Boulevard, Pasadena, California, CA 91125, USA


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