Structural optimization of uncertain dynamical systems considering mixed-design variables

Jensen, Héctor A.; Sepulveda, Juan G.

doi:10.1016/j.probengmech.2010.08.005

Cited by 19 publications

(6 citation statements)

References 26 publications

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“…The level of effectiveness of the above sequential optimization scheme depends on the degree of convexity of the functions involved in the optimization problem. For example, if the curvatures are not too large and relatively uniform throughout the design space the proposed algorithm converges within a few iterations [12,27]. For more general cases, methods based on trust regions and line search methodologies may be more appropriate [28][29][30].…”

Section: Solution Schemementioning

confidence: 99%

“…Such probabilities are estimated by an adaptive Markov chain Monte Carlo procedure [9]. A sequential optimization approach based on global conservative, convex, and separable approximations is implemented for solving the optimization problem [10][11][12]. The optimization scheme is combined with the use of common random numbers throughout all iterations in the optimization process.…”

Section: Introductionmentioning

confidence: 99%

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Robust Stochastic Design of Base-Isolated Structural Systems

Jensen

Sepulveda

Becerra

2012

Int J Uncertainty Quantification

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The development of a general framework for robust reliability-based design of base-isolated structural systems under uncertain conditions is presented. The uncertainties about the structural parameters as well as the variability of future excitations are characterized in a probabilistic manner. Isolation elements composed of nonlinear lead rubber bearings are used to model the isolation system. The optimal design problem is formulated as a nonlinear constrained minimization problem involving multiple design requirements, including reliability constraints related to the structural performance. Failure events defined by a large number of random variables are used to characterize the reliability of the system. A sequential optimization approach based on global conservative, convex, and separable approximations is implemented for solving the optimization problem. An example problem that considers a 10-story building under stochastic ground excitation illustrates the beneficial effects of base-isolation systems in reducing the superstructure response.

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Section: Solution Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Stochastic Design of Base-Isolated Structural Systems

Jensen

Sepulveda

Becerra

2012

Int J Uncertainty Quantification

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“…The third class of approaches consists of decoupling the discrete optimization and reliability analysis steps by creating local approximate representations of the reliability, e.g. [29,30,31,32,33,34]. As an additional remark, it should be noted that RBO formulations addressing both discrete and continuous design variables (which are termed as mixed discrete-continuous) also constitute another important class of problems, see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…As an additional remark, it should be noted that RBO formulations addressing both discrete and continuous design variables (which are termed as mixed discrete-continuous) also constitute another important class of problems, see e.g. [31,35,36].…”

Section: Introductionmentioning

confidence: 99%

Fully decoupled reliability-based optimization of linear structures subject to Gaussian dynamic loading considering discrete design variables

Faes

Valdebenito

2021

Mechanical Systems and Signal Processing

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Reliability-based optimization (RBO) offers the possibility of finding an optimal design for a system according to a prescribed criterion while explicitly taking into account the effects of uncertainty. However, due to the necessity of solving simultaneously a reliability problem nested in an optimization procedure, the corresponding computational cost is usually high, impeding the applicability of the methods. This computational cost is even enlarged further when one or several design variables must belong to a discrete set, due to the requirement of resorting to integer programming optimization algorithms. To alleviate this issue, this contribution proposes a fully decoupled approach for a specific class of problems, namely minimization of the failure probability of a linear system subjected to an uncertain dynamic load of the Gaussian type, under the additional constraint that the design variables are integer-valued. Specifically, by using the operator norm framework, as developed by the authors in previous work, this paper shows that by reducing the RBO problem with discrete design variables to the solution of a single deterministic optimization problem followed by a single reliability analysis, a large gain in numerical efficiency can be obtained without compromising the accuracy of the resulting optimal design. The application and capabilities of the proposed approach are illustrated by means of two examples.

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“…The damper design was formulated as an optimization problem with a single objective function and multiple reliability constraints. The problem solution was sought through a sequential optimization approach (Jensen and Sepulveda 2011) that involved a converging series of approximate reliability analyses.…”

Section: Introductionmentioning

confidence: 99%

Efficient Approach for the Reliability-Based Design of Linear Damping Devices for Seismic Protection of Buildings

Tubaldi

Barbato

Dall’Asta

2016

ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng.

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This paper presents an efficient reliability-based methodology for the seismic design of viscous/viscoelastic dissipative devices in independent and/or coupled buildings. The proposed methodology is consistent with modern performance-based earthquake engineering frameworks and explicitly considers the uncertainties affecting the seismic input and the model parameters, as well as the correlation between multiple limit states. The proposed methodology casts the problem of the dampers’ design for a target performance objective in the form of a reliability-based optimization problem with a probabilistic constraint. The general approach proposed in this study is specialized to stochastic seismic excitations and performance levels for which the structural behavior can be assumed as linear elastic. Under these conditions, the optimization problem is solved efficiently by taking advantage of existing analytical techniques for estimating the system reliability. This analytical design solution is an approximation of the optimal design and can be used as a hot-start point for simulation-based techniques, which can be employed to find the optimal design solution. An efficient correction formula is proposed to obtain an improved design solution that is generally sufficiently close for engineering purposes to the optimal design solution obtained from significantly more-computationally-expensive simulation-based techniques. The proposed design methodology is illustrated and validated by considering two steel buildings modeled as linear elastic multiple-degree-of-freedom systems for different linear damper properties and collocation, for both independent and coupled configurations

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Structural optimization of uncertain dynamical systems considering mixed-design variables

Cited by 19 publications

References 26 publications

Robust Stochastic Design of Base-Isolated Structural Systems

Robust Stochastic Design of Base-Isolated Structural Systems

Fully decoupled reliability-based optimization of linear structures subject to Gaussian dynamic loading considering discrete design variables

Efficient Approach for the Reliability-Based Design of Linear Damping Devices for Seismic Protection of Buildings

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