Armen Der Kiureghian

Multivariate distribution models with prescribed marginals and covariances

Abstract Two multivariate distribution models consistent with prescribed marginal distributions and covariances are presented. The models are applicable to arbitrary number of random variables and are particularly suited for engineering applications. Conditions for validity of each model and applicable ranges of correlation coefficients between the variables are determined. Formulae are developed which facilitate evaluation of the model parameters in terms of the prescribed marginals and covariances. Potential uses of the two models in engineering are discussed.

Optimization algorithms for structural reliability

Abstract Several optimization algorithms are evaluated for application in structural reliability, where the minimum distance from the origin to the limit-state surface in the standard normal space is required. The objective is to determine the suitability of the algorithms for application to linear and nonlinear finite element reliability problems. After a brief review, five methods are compared through four numerical examples. Comparison criteria are the generality, robustness, efficiency, and capacity of each method.

Multiple design points in first and second-order reliability

A method is developed to successively find the multiple design points of a component reliability problem, when they exist on the limit-state surface. FORM or SORM approximations at each design point followed by a series system reliability analysis is shown to lead to improved estimates of the failure probability. Three example applications show the generality and robustness of the method.

Comparison of finite element reliability methods

The spectral stochastic finite element method (SSFEM) aims at constructing a probabilistic representation of the response of a mechanical system, whose material properties are random fields. The response quantities, e.g. the nodal displacements, are represented by a polynomial series expansion in terms of standard normal random variables. This expansion is usually post-processed to obtain the second-order statistical moments of the response quantities. However, in the literature, the SSFEM has also been suggested as a method for reliability analysis. No careful examination of this potential has been made yet. In this paper, the SSFEM is considered in conjunction with the first-order reliability method (FORM) and with importance sampling for finite element reliability analysis. This approach is compared with the direct coupling of a FORM reliability code and a finite element code. The two procedures are applied to the reliability analysis of the settlement of a foundation lying on a randomly heterogeneous soil layer. The results are used to make a comprehensive comparison of the two methods in terms of their relative accuracies and efficiencies.

Dynamic response sensitivity of inelastic structures

Abstract A general finite element solution method for the dynamic response sensitivity of inelastic structures is developed. Employing a direct differentiation method, the gradient equation of motion is solved without iteration and by taking advantage of the available solution of the response. Special attention is given to sensitivities with respect to inelastic material parameters and detailed derivations are made for the J 2 plasticity model with a linear hardening rule. The method can be applied to any other inelastic material model that has an analytically defined yield function and flow rule. The formulation is easily incorporated in existing finite element codes. Numerical examples demonstrate the accuracy and efficiency of the method.

PROBABILISTIC SEISMIC DEMAND MODELS AND FRAGILITY ESTIMATES FOR RC BRIDGES

A Bayesian methodology to construct probabilistic seismic demand models for the components of a structural system is developed. Existing deterministic models and obserational data are used. The demand models are combined with previously developed capacity models for reinforced concrete (RC) bridge columns to estimate the seismic fragilities of bridge components and systems. The approach properly accounts for all relevant uncertainties, including model error. Application to two bridge examples typical of modern California practice is presented.

Bayesian Network Enhanced with Structural Reliability Methods: Methodology

We combine Bayesian networks (BNs) and structural reliability methods (SRMs) to create a new computational framework, termed enhanced BN (eBN), for reliability and risk analysis of engineering structures and infrastructure. BNs are efficient in representing and evaluating complex probabilistic dependence structures, as present in infrastructure and structural systems, and they facilitate Bayesian updating of the model when new information becomes available. On the other hand, SRMs enable accurate assessment of probabilities of rare events represented by computationally demanding physically based models. By combining the two methods, the eBN framework provides a unified and powerful tool for efficiently computing probabilities of rare events in complex structural and infrastructure systems in which information evolves in time. Strategies for modeling and efficiently analyzing the eBN are described by way of several conceptual examples. The companion paper applies the eBN methodology to example structural and infrastructure systems.

An evolutionary model for earthquake ground motion

Abstract A simple and versatile evolutionary random process model for describing the earthquake ground motion is proposed. The model is composed of individually modulated component stationary processes, each component representing the energy in the process in a narrow band of frequencies. Methods for identifying the model parameters from a recorded accelerogram and for simulating sample functions are described. The model accounts for both temporal and spectral nonstationarity of the motion and is convenient for random vibration analysis.

Probabilistic models for the initiation of seismic soil liquefaction

Abstract A Bayesian framework for probabilistic assessment of the initiation of seismic soil liquefaction is described. A database, consisting of post-earthquake field observations of soil performance, in conjunction with in situ “index” test results is used for the development of probabilistically-based seismic soil liquefaction initiation correlations. The proposed stochastic model allows full and consistent representation of all relevant uncertainties. including (a) measurement/estimation errors, (b) model imperfection, (c) statistical uncertainty, and (d) inherent variabilities. Different sets of probabilistic liquefaction boundary curves are developed for the seismic soil liquefaction initiation hazard problem, representing various sources of uncertainty that are intrinsic to the problem. The resulting correlations represent a significant improvement over prior efforts, producing predictive relationships with enhanced accuracy and greatly reduced overall model uncertainty.

Reliability analysis of contaminant transport in saturated porous media

An approach to probabilistic modeling of contaminant transport based on the first- and second-order reliability methods (FORM and SORM) is presented. FORM and SORM were initially developed for structural reliability applications to estimate the occurrence of low-probability events. They can be readily used with both analytical and numerical models and do not require restrictive assumptions about the problem geometry or about the properties of the media. Sensitivity information is obtained as an integral part of these analyses and is used to identify the variables or parameters which have a major influence on the estimate of probability. Example reliability analyses of one- and two-dimensional transport are used to illustrate the approach, and the accuracy of the reliability methods is evaluated in comparison with Monte Carlo simulations. The results show that FORM increasingly overestimates the probability of exceedance as the spatial variability of the domain increases. SORM, on the other hand, accounts for the nonlinearity of the limit state surface and gives results consistent with Monte Carlo simulation over a range of coefficient of variation of K from 0.1 to 0.7. In addition, the FORM/SORM analyses are shown to provide a computational advantage over the Monte Carlo simulation for low-probability events, because the computational effort is independent of the probability and the results also include sensitivity information. Finally, an example application of system reliability using FORM and SORM shows that problems with multiple limit state surfaces can be readily analyzed and the computational effort is proportional to the number and complexity of the limit state functions.