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Robust design with variability response functions;an alternative approach

STRUCTURAL SAFETY 2016年 59卷 1-8页

作者： Kokkinos, Odysseas Papadopoulos, Vissarion Natl Tech Univ Athens Inst Struct Anal & Seism Res 9 Iroon PolytechZografou Campus Athens 15780 Greece

In this work a different Robust Design Optimization (RDO) approach is proposed implementing the concept of variability response Function (VRF), which is a function that when combined with the power spectral density of the stochastic field that models the system's uncertainty, formulates an integral expression for the variance of the system's response. The basic idea is to exploit a very well-known property of the VRF, which is its independence of the stochastic system parameters, in order to obtain global optima that depend only on the deterministic parameters of the problem. This way, optimal structural designs are achieved which are globally insensitive to uncertainties, that is to say they are free of the spectral-distribution characteristics of the stochastic fields modeling the uncertainties. This is achieved by setting in addition to the total material cost, the maximum VRF value as an objective function. The advantages of using the proposed methodology over traditional Robust Design Optimization are illustrated through an application to a frame-type structure where it is demonstrated that the designs achieved through classical RDO for a given stochastic field description are not optimal for a variation on the spectral properties of the random field modeling the system uncertainty, while optimal designs obtained with the VRF-based RDO remain optimum for the worst case scenario stochastic fields. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： variability response functions Stochastic finite element analysis Robust Design Optimization Stochastic dynamic systems Multi objective Genetic Algorithm

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Generalized variability response functions for two-dimensional elasticity problems

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2014年第0期272卷 121-137页

作者： Teferra, Kirubel Arwade, Sanjay R. Deodatis, George Weidlinger Associates New York NY 10005 USA Univ Massachusetts Dept Civil & Environm Engg Amherst MA 01002 USA Columbia Univ Dept Civil Engg & Engg Mech New York NY 10027 USA

The ability to determine probabilistic characteristics of response quantities in structural mechanics (e.g. displacements, stresses) as well as effective material properties is restricted due to lack of information on the probabilistic characteristics of the uncertain system parameters. The concept of the variability response function (VRF) has been proposed as a means to systematically capture the effect of the stochastic spectral characteristics of uncertain system parameters modeled by homogeneous random fields on the uncertain structural response. The key property of the VRF in its classical sense is its independence from the marginal probability distribution function (PDF) and the spectral density function (SDF) of the uncertain system parameters (it depends only on the deterministic structural configuration and boundary conditions). Proofs have been provided for the existence of VRFs for linear and some nonlinear statically determinate beams. For statically indeterminate structures, the Monte Carlo based generalized variability response function (GVRF) methodology has been proposed recently as a generalization of the VRF concept to indeterminate linear and some nonlinear beams. The methodology computes GVRFs, which are analogous to VRFs for statically determinate structures, and evaluates their dependence (or lack thereof) on the PDF and SDF of the random field, thereby providing an estimate of the accuracy of the GVRF. In this paper, the GVRF methodology is extended to problems involving two-dimensional, linear continua whose stochasticity is characterized by statistically homogeneous random fields. After detailing the GVRF methodology for two-dimensional random fields, two numerical examples are provided: GVRFs are computed for the displacement response and for the effective compliance of linear plane stress systems. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Uncertainty quantification Effective properties Random fields variability response functions

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variability response functions for beams with nonlinear constitutive laws

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PROBABILISTIC ENGINEERING MECHANICS 2012年 29卷 139-148页

作者： Teferra, Kirubel Deodatis, George Columbia Univ Dept Civil Engg & Engg Mech New York NY 10027 USA

The ability to determine probabilistic information of response quantities in structural mechanics (e.g. displacements, stresses) is restricted due to lack of information on the probabilistic characteristics of uncertain system parameters. The concept of the variability response Function (VRF) has been proposed as a means to systematically capture the effect of the stochastic spectral characteristics of uncertain system parameters modeled by homogeneous stochastic fields on the uncertain structural response. The key property of the VRF in its classical sense is its independence from the marginal probability distribution function (PDF) and the spectral density function (SDF) of the uncertain system parameters (it depends only on the deterministic structural configuration and boundary conditions). In this paper, the existence, the uniqueness, and the SDF- and PDF-independence of a variability response function is formally proven for the first time for statically determinate beam structures following a specific class of nonlinear constitutive laws (power laws). For statically indeterminate nonlinear structures, the generalized variability response function (GVRF) methodology is shown to produce GVRFs for statically indeterminate nonlinear beams with a square-root constitutive law that are almost SDF-independent and only mildly dependent on the marginal PDF. This PDF-dependence is not significant and all GVRFs computed in this study have very similar shapes. This is important as it implies that conclusions related to the effect of correlation length scales on the response uncertainty can be inferred in general. However, the GVRF methodology for nonlinear statically indeterminate structures is only suitable when a closed-form expression is known to exist for the VRF of statically determinate structures having the same constitutive law. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Uncertainty quantification Nonlinear constitutive laws Random fields variability response functions

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Stochastic variability of effective properties via the generalized variability response function

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COMPUTERS & STRUCTURES 2012年第Nov.期110卷 107-115页

作者： Teferra, Kirubel Arwade, Sanjay R. Deodatis, George Weidlinger Associates Inc New York NY 10005 USA Univ Massachusetts Dept Civil & Environm Engg Amherst MA 01002 USA Columbia Univ Dept Civil Engg & Engg Mech New York NY 10027 USA

Homogenization of randomly heterogeneous material properties into effective properties is an essential procedure in facilitating the analysis of a wide range of mechanics problems. Although formulas exist to calculate deterministic effective properties for structures larger than the representative volume element (RVE), no general method other than Monte Carlo simulation exists to evaluate the variability of these effective properties for structures smaller than the RVE. In a recent paper [1], a method was proposed for evaluating the stochastic variability of effective properties by incorporating the variability response function (VRF) concept. Subsequently, the existence of the VRF for effective properties for linear, statically determinate structures was formally proven. The concept of the VRF has been proposed as a means to systematically capture the effect of the spectral characteristics of uncertain system parameters modeled by homogeneous stochastic fields on the uncertain structural response. Although the existence of VRFs can be formally proven only for statically determinate structures, a Monte Carlo-based methodology has been proposed recently as a generalization of the VRF concept [19]. In this paper, this methodology is extended to establish estimates of the VRF for effective properties of statically indeterminate beams. (c) 2012 Elsevier Ltd. All rights reserved.

关键词： Uncertainty quantification Effective properties Random fields variability response functions

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A hierarchy of upper bounds on the response of stochastic systems with large variation of their properties: random field case

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PROBABILISTIC ENGINEERING MECHANICS 2003年第4期18卷 365-375页

作者： Deodatis, G Graham-Brady, L Micaletti, R Columbia Univ Dept Civil Engn & Engn Mech New York NY 10027 USA Johns Hopkins Univ Dept Civil Engn Baltimore MD 21218 USA

This paper is the second of a two-part series that constitutes an effort to establish spectral- and probability-distribution-free upper bounds on various probabilistic indicators of the response of stochastic systems. The concept of the generalized variability response function is introduced and used with the aid of associated fields to extend the upper bounds established in the first paper for the special case of material property variations modeled by random variables to more general problems involving random fields. Specifically, a hierarchy of spectral- and probability-distribution-free upper bounds on the mean, variance, and exceedance values of the response of stochastic systems is established when only the coefficient of variation and lower limit of the stochastic material properties are known. Furthermore, a hierarchy of probability-distribution-free upper bounds on these quantities is established when the spectral density function describing the stochastic material properties is known in addition to the coefficient of variation and the lower limit. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： stochastic finite element methods variability response functions stochastic simulation

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response and eigenvalue analysis of stochastic finite element systems with multiple correlated material and geometric properties

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PROBABILISTIC ENGINEERING MECHANICS 2001年第1期16卷 11-29页

作者： Graham, LL Deodatis, G Univ Virginia Dept Civil Engn Charlottesville VA 22903 USA Princeton Univ Dept Civil Engn & Operat Res Princeton NJ 08544 USA

The variability of the random response displacements and eigenvalues of structures with multiple uncertain material and geometric properties are studied in this paper using variability response functions. The material and geometric properties are assumed to be described by cross-correlated stochastic fields. Specifically, two types of problems are considered: the response displacement variability of plane stress/plane strain structures with stochastic elastic modulus, Poisson's ratio, and thickness, and the eigenvalue variability of beam and plate structures with stochastic elastic modulus and mass density. The variance of the displacement/eigenvalue is expressed as the sum of integrals that involve the auto-spectral density functions characterizing the structural properties, the cross-spectral density functions between the structural properties, and the deterministic variability response functions. This formulation yields separate terms for the contributions to the response displacement/eigenvalue variability from the auto-correlation of each of the material/geometric properties, and from the crosscorrelation between these properties. The variability response functions are used to compute engineering-wise very important spectral-distribution-free realizable upper bounds of the displacement/eigenvalue variability. Using this formulation, it is also possible to compute the displacement/eigenvalue variability for prescribed auto- and cross-spectral density functions. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： eigenvalue stochastic finite element methods variability response functions

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