A convex hull approach for the reliability-based design optimization of nonlinear transient dynamic problems

Missoum, Samy; Ramu, Palaniappan; Haftka, Raphael T.

doi:10.1016/j.cma.2006.12.008

Cited by 59 publications

(37 citation statements)

References 10 publications

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“…These methodologies can be classified into two groups: robust optimization (RO) [5,6] and reliability-based optimization (RBO) [7,8]. Based on purely deterministic analysis RO methods attempt to maximize the deterministic performance and simultaneously to minimize the sensitivity of the performance with respect to random parameters.…”

Section: Introductionmentioning

confidence: 99%

Reliability-based optimization of trusses with random parameters under dynamic loads

Wriggers

Gao

et al. 2011

Comput Mech

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In this work, a reliability-based optimization technique is addressed to obtain the minimum mean value of random mass of the structures with random parameters under stationary stochastic process excitation. The challenge of the problem lies in randomness involved from both structural parameters and dynamic load, which renders the structural reliability becoming the random dynamic reliability of the first passage problem. In order to obtain minimum mean value of random gross mass, element and system dynamic reliability constraints are constructed, respectively, and the structural sizing and shape optimization models based on the dynamic reliability are then presented. Moreover, among two optimal strategies proposed for optimization models, the second one can effectively reduce the workload by avoiding the computation of the variance of the dynamic response during the iterative process. Finally, the implementation of three examples is discussed to display the feasibility and validity of optimization technique given.

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Section: Introductionmentioning

confidence: 99%

Reliability-based optimization of trusses with random parameters under dynamic loads

Wriggers

Gao

et al. 2011

Comput Mech

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“…The classification approach and the construction of explicit boundaries using SVM have several advantages, such as the handling of discontinuous and binary responses (Missoum et al 2007;Basudhar and Missoum 2009). Another major advantage of the classification approach is the reduction of several constraints (or failure modes) to a single SVM expression.…”

Section: Introductionmentioning

confidence: 99%

Constrained efficient global optimization with support vector machines

Basudhar

Dribusch

Lacaze

et al. 2012

Struct Multidisc Optim

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127

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This paper presents a methodology for constrained efficient global optimization (EGO) using support vector machines (SVMs). While the objective function is approximated using Kriging, as in the original EGO formulation, the boundary of the feasible domain is approximated explicitly as a function of the design variables using an SVM. Because SVM is a classification approach and does not involve response approximations, this approach alleviates issues due to discontinuous or binary responses. More importantly, several constraints, even correlated, can be represented using one unique SVM, thus considerably simplifying constrained problems. In order to account for constraints, this paper introduces an SVM-based "probability of feasibility" using a new Probabilistic SVM model. The proposed optimization scheme is constituted of two levels. In a first stage, a global search for the optimal solution is performed based on the "expected improvement" of the objective function and the probability of feasibility. In a second stage, the SVM boundary is locally refined using an adaptive sampling scheme. An unconstrained and a constrained formulation of the optimization problem are presented and compared. Several analytical examples are used to test the formulations. In particular, a problem with 99 constraints and an aeroelasticity problem with binary A. Basudhar · C. Dribusch · S. Lacaze · S. Missoum (B) Aerospace and Mechanical Engineering Department, output are presented. Overall, the results indicate that the constrained formulation is more robust and efficient.

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“…The optimization can then be solved using a gradient-based method such as sequential quadratic programming (SQP) or global methods if local optima are present [15,16] without requiring any further aeroelasticity analysis.…”

Section: Rbdo Solution Schemementioning

confidence: 99%

“…The latter feature is essential for problems with discontinuous behaviors or binary behaviors (accept or reject). This was demonstrated by the first author for crashworthiness and buckling problems [15,16] as well as biomedical device design [17]. The explicit boundaries are created using a support vector machine (SVM) that can create multidimensional, nonlinear, and disjoint boundaries.…”

Section: Introductionmentioning

confidence: 99%

Reliability-Based Design Optimization of Nonlinear Aeroelasticity Problems

Missoum

Dribusch

Beran

2010

Journal of Aircraft

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This paper introduces a methodology for the reliability-based design optimization of systems with nonlinear aeroelastic constraints. The approach is based on the construction of explicit flutter and subcritical limit cycle oscillation boundaries in terms of deterministic and random design variables. The boundaries are constructed using a support vector machine that provides a way to efficiently evaluate probabilities of failure and solve the reliabilitybased design optimization problem. Another major advantage of the approach is that it efficiently manages the discontinuities that might appear during subcritical limit cycle oscillations. The proposed approach is applied to the construction of flutter and subcritical limit cycle oscillation boundaries for a two-degree-of-freedom airfoil with nonlinear stiffnesses. The solution of a reliability-based design optimization problem with a constraint on the probability of subcritical limit cycle oscillation is also provided.

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A convex hull approach for the reliability-based design optimization of nonlinear transient dynamic problems

Cited by 59 publications

References 10 publications

Reliability-based optimization of trusses with random parameters under dynamic loads

Reliability-based optimization of trusses with random parameters under dynamic loads

Constrained efficient global optimization with support vector machines

Reliability-Based Design Optimization of Nonlinear Aeroelasticity Problems

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