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

The use of computer experiments and surrogate approximations (metamodels) introduces a source of uncertainty in simulation-based design that we term model interpolation uncertainty. Most existing approaches for treating interpolation uncertainty in computer experiments have been developed for deterministic optimization and are not applicable to design under uncertainty in which randomness is present in noise and/or design variables. Because the random noise and/or design variables are also inputs to the metamodel, the effects of metamodel interpolation uncertainty are not nearly as transparent as in deterministic optimization. In this work, a methodology is developed within a Bayesian framework for quantifying the impact of interpolation uncertainty on the robust design objective, under consideration of uncertain noise variables. By viewing the true response surface as a realization of a random process, as is common in kriging and other Bayesian analyses of computer experiments, we derive a closed-form analytical expression for a Bayesian prediction interval on the robust design objective function. This provides a simple, intuitively appealing tool for distinguishing the best design alternative and conducting more efficient computer experiments. We illustrate the proposed methodology with two robust design examples—a simple container design and an automotive engine piston design with more nonlinear response behavior and mixed continuous-discrete design variables.

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Reliability Based Optimization of Submarine Pressure Hulls With Inelastic Interstiffener Buckling Failure

Volume 3: Safety and Reliability; Materials Technology; Douglas Faulkner Symposium on Reliability and Ultimate Strength of Marine Structures ◽

10.1115/omae2006-92084 ◽

2006 ◽

Author(s):

P. Radha ◽

K. Rajagopalan

Keyword(s):

Unconstrained Minimization ◽

Computer Code ◽

Correction Method ◽

Penalty Function Method ◽

Simulation Design ◽

Design Variables ◽

Minimization Technique ◽

Buckling Failure ◽

Optimal Values ◽

Reliability Based Optimization

Uncertainties that exist in modelling and simulation, design variables and parameters, manufacturing processes etc., may lead to large variations in the performance characteristics of the system. Optimized deterministic designs determined without considering uncertainties can be unreliable and may lead to catastrophic failure of the structure being designed. Reliability based optimization (RBO) is a methodology that addresses these problems. In this paper the reliability based optimization of submarine pressure hulls in which the failure gets governed by inelastic interstiffener buckling has been described. The problem has been formulated to minimize the ratio of weight of shell-stiffener geometry to the weight of liquid displaced, subjected to reliability based inelastic interstiffener buckling constraint. Since the methods of analysis of inelastic buckling failure of submarine pressure hulls are inadequate, in the present study the Johnson-Ostenfeld inelastic correction method has been adopted for formulating the constraint. By considering spacing of the stiffener, thickness of the plating and depth of the stiffener as the design variables, Sequential Unconstrained Minimization Technique (SUMT) has been used to solve the design problem. RBO has been carried out to get the optimal values of these design variables for a target reliability index using Interior Penalty Function Method for which an efficient computer code in C++ has been developed.

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A method for nonlinear optimization with discrete design variables

10.2514/6.1987-789 ◽

1987 ◽

Cited By ~ 2

Author(s):

GREGORY OLSEN ◽

GARRET VANDERPLAATS

Keyword(s):

Nonlinear Optimization ◽

Design Variables ◽

Discrete Design Variables

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Reliability Based Optimization of Steel Monopod Offshore-Towers

Volume 2: Structures, Safety and Reliability ◽

10.1115/omae2008-57174 ◽

2008 ◽

Cited By ~ 2

Author(s):

H. Karadeniz ◽

V. Togan ◽

T. Vrouwenvelder

Keyword(s):

Natural Frequency ◽

Cross Section ◽

Sequential Quadratic Programming ◽

Limit State ◽

State Function ◽

Wave Loading ◽

Extreme Wave ◽

Design Variables ◽

Reliability Based Optimization ◽

Numerical Strategy

In this work, the implementation of reliability-based optimization (RBO) of a circular steel monopod-offshore-tower with constant and variable diameters (represented by segmentations) and thicknesses is presented. The tower is subjected to the extreme wave loading. For this purpose, the deterministic optimization of the tower is performed with constraints including stress, buckling, and the lowest natural frequency firstly. Then, a reliability-based optimization of the tower is performed. The reliability index is calculated from FORM using a limit state function based on the lowest natural frequency. The mass of the tower is considered as being the objective function; the thickness and diameter of the cross-section of the tower are taken as being design variables of the optimization. The numerical strategy employed for performing the optimization uses the IMSL-Libraries routine that is based on the Sequential Quadratic Programming (SQP). In addition, to check the results obtained from aforementioned procedure, the RBO of the tower is also performed using the genetic algorithms (GA) tool of the MATLAB. Finally, a demonstration of an example monopod tower is presented.

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Size and Topology Optimization for Trusses with Discrete Design Variables by Improved Firefly Algorithm

Mathematical Problems in Engineering ◽

10.1155/2017/1457297 ◽

2017 ◽

Vol 2017 ◽

pp. 1-12 ◽

Cited By ~ 3

Author(s):

Yue Wu ◽

Qingpeng Li ◽

Qingjie Hu ◽

Andrew Borgart

Keyword(s):

Topology Optimization ◽

Firefly Algorithm ◽

Optimization Problems ◽

Optimization Method ◽

Structural Topology ◽

Discrete Variables ◽

And Topology ◽

Design Variables ◽

Improved Firefly Algorithm ◽

Discrete Design Variables

Firefly Algorithm (FA, for short) is inspired by the social behavior of fireflies and their phenomenon of bioluminescent communication. Based on the fundamentals of FA, two improved strategies are proposed to conduct size and topology optimization for trusses with discrete design variables. Firstly, development of structural topology optimization method and the basic principle of standard FA are introduced in detail. Then, in order to apply the algorithm to optimization problems with discrete variables, the initial positions of fireflies and the position updating formula are discretized. By embedding the random-weight and enhancing the attractiveness, the performance of this algorithm is improved, and thus an Improved Firefly Algorithm (IFA, for short) is proposed. Furthermore, using size variables which are capable of including topology variables and size and topology optimization for trusses with discrete variables is formulated based on the Ground Structure Approach. The essential techniques of variable elastic modulus technology and geometric construction analysis are applied in the structural analysis process. Subsequently, an optimization method for the size and topological design of trusses based on the IFA is introduced. Finally, two numerical examples are shown to verify the feasibility and efficiency of the proposed method by comparing with different deterministic methods.

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