scholarly journals Reliability-Based Robust Design Optimization of Structures Considering Uncertainty in Design Variables

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Shujuan Wang ◽  
Qiuyang Li ◽  
Gordon J. Savage
Keyword(s):  
Sensitivity Analysis ◽  
Design Optimization ◽  
Robust Design ◽  
Structural Reliability ◽  
Computational Cost ◽  
Optimization Process ◽  
Robust Design Optimization ◽  
Global Approximation ◽  
Design Variables ◽  
Uncertainty In Design

This paper investigates the structural design optimization to cover both the reliability and robustness under uncertainty in design variables. The main objective is to improve the efficiency of the optimization process. To address this problem, a hybrid reliability-based robust design optimization (RRDO) method is proposed. Prior to the design optimization, the Sobol sensitivity analysis is used for selecting key design variables and providing response variance as well, resulting in significantly reduced computational complexity. The single-loop algorithm is employed to guarantee the structural reliability, allowing fast optimization process. In the case of robust design, the weighting factor balances the response performance and variance with respect to the uncertainty in design variables. The main contribution of this paper is that the proposed method applies the RRDO strategy with the usage of global approximation and the Sobol sensitivity analysis, leading to the reduced computational cost. A structural example is given to illustrate the performance of the proposed method.

Mini-Max Type Formulation of Strict Robust Design Optimization Under Correlative Variation

2002 ◽  
Author(s):  
Noriyasu Hirokawa ◽  
Kikuo Fujita
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Design Space ◽  
Computational Cost ◽  
Robust Design Optimization ◽  
Maximization Problem ◽  
Quadratic Polynomials ◽  
Feasibility Assessment ◽  
Design Variation ◽  
Definition Of

This paper proposes a mini-max type formulation for strict robust design optimization under correlative variation based on design variation hyper sphere and quadratic polynomial approximation. While various types of formulations and techniques have been developed for computational robust design, they confront the compromise among modeling of parameter variation, feasibility assessment, definition of optimality such as sensitivity, and computational cost. The formulation of this paper aims that all points within the distribution region are thoroughly optimized. For this purpose, the design space with correlative variation is diagonalized and isoparameterized into a hyper sphere, and the functions of nominal constraints and the nominal objective are modeled as quadratic polynomials. These transformation and approximation enable the analytical discrimination of inner or boundary type on the worst design and its quantified values with less computation cost under a certain condition, and bring the procedural definition of the strictly robust optimality of a design as a maximization problem. The minimization of this formulation, that is, mini-max type optimization, can find the robust design under the above meaning. Its validity is ascertained through numerical examples.

scholarly journals Robust Design Optimization for Low-Cost Concrete Box-Girder Bridge

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 398 ◽  
Author(s):  
Vicent Penadés-Plà ◽  
Tatiana García-Segura ◽  
Víctor Yepes
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Computational Cost ◽  
Robust Design Optimization ◽  
Structural Behavior ◽  
Uncertain Parameters ◽  
Box Girder ◽  
Structural Problems ◽  
Concrete Box Girder ◽  
High Computational Cost

The design of a structure is generally carried out according to a deterministic approach. However, all structural problems have associated initial uncertain parameters that can differ from the design value. This becomes important when the goal is to reach optimized structures, as a small variation of these initial uncertain parameters can have a big influence on the structural behavior. The objective of robust design optimization is to obtain an optimum design with the lowest possible variation of the objective functions. For this purpose, a probabilistic optimization is necessary to obtain the statistical parameters that represent the mean value and variation of the objective function considered. However, one of the disadvantages of the optimal robust design is its high computational cost. In this paper, robust design optimization is applied to design a continuous prestressed concrete box-girder pedestrian bridge that is optimum in terms of its cost and robust in terms of structural stability. Furthermore, Latin hypercube sampling and the kriging metamodel are used to deal with the high computational cost. Results show that the main variables that control the structural behavior are the depth of the cross-section and compressive strength of the concrete and that a compromise solution between the optimal cost and the robustness of the design can be reached.

Multidisciplinary Robust Design Optimization of an Internal Combustion Engine

2003 ◽  
Vol 125 (1) ◽  
pp. 124-130 ◽  
Author(s):  
Charles D. McAllister ◽  
Timothy W. Simpson
Keyword(s):  
Internal Combustion Engine ◽  
Design Optimization ◽  
Robust Design ◽  
Combustion Engine ◽  
Internal Combustion ◽  
Collaborative Optimization ◽  
Robust Design Optimization ◽  
Optimization Framework ◽  
Design Variables ◽  
Multiobjective Approach

In this paper, we introduce a multidisciplinary robust design optimization formulation to evaluate uncertainty encountered in the design process. The formulation is a combination of the bi-level Collaborative Optimization framework and the multiobjective approach of the compromise Decision Support Problem. To demonstrate the proposed framework, the design of a combustion chamber of an internal combustion engine containing two subsystem analyses is presented. The results indicate that the proposed Collaborative Optimization framework for multidisciplinary robust design optimization effectively attains solutions that are robust to variations in design variables and environmental conditions.

Robust Design Optimization of an Industrial 1.5 Stage Axial Compressor Under Operational and Geometrical Uncertainties

2021 ◽  
Author(s):  
Alexandre Gouttière ◽  
Dirk Wunsch ◽  
Rémy Nigro ◽  
Virginie Barbieux ◽  
Charles Hirsch
Keyword(s):  
Robust Optimization ◽  
Design Optimization ◽  
Robust Design ◽  
Computational Cost ◽  
Axial Compressor ◽  
Secondary Flows ◽  
Robust Design Optimization ◽  
Original Design ◽  
The Mean ◽  
Standard Deviations

Abstract A robust design optimization of a 1.5 stage axial compressor with secondary flows from Safran Aero Boosters is investigated. A total of 9 simultaneous operational and geometrical uncertainties are propagated for the nominal design point as well as for two off-design points, close to stall and choke conditions respectively. These uncertainties, including mass flow rates of the secondary flows, tip gap size of the rotor and highly correlated profiles on the inlet condition, are propagated by the Non-Intrusive Probabilistic Collocation method. In order to understand the effects of the uncertainties on the performances and to minimize the computational cost of the robust optimization, a preliminary uncertainty quantification (UQ) study of the original design is performed to identify and rule out less influential uncertainties. Contrary to what was expected, the imposed geometrical uncertainties on the tip gap are identified to have the relatively smallest influence on the performances by means of scaled sensitivity derivatives. The global objective of the robust design optimization is to minimize the standard deviations of the main compressor performances at all three operating points and to preserve the mean values of these performances. Because the objective functions are standard deviations, this study is only possible in a robust optimization setting, by propagating the simultaneous operational and geometrical uncertainties. A total of 9 stochastic objectives and 15 stochastic constraints are taken into account. The best optimal design preserves the mean performances of the compressor, while the standard deviations are minimized compared with the original design, ensuring a more robust operation. This effect is very pronounced in the off-design points.

Multidisciplinary Robust Design Optimization of an Internal Combustion Engine

2001 ◽  
Author(s):  
Charles D. McAllister ◽  
Timothy W. Simpson
Keyword(s):  
Internal Combustion Engine ◽  
Design Optimization ◽  
Robust Design ◽  
Combustion Engine ◽  
Internal Combustion ◽  
Collaborative Optimization ◽  
Robust Design Optimization ◽  
Optimization Framework ◽  
Design Variables ◽  
Multiobjective Approach

Abstract In this paper, we introduce a multidisciplinary robust design optimization formulation to evaluate uncertainty encountered in the design process. The formulation is a combination of the bi-level Collaborative Optimization framework and the multiobjective approach of the compromise Decision Support Problem. To demonstrate the proposed approach, the design of a combustion chamber of an internal combustion engine containing two subsystem analyses is presented. The results indicate that the proposed Collaborative Optimization framework for multidisciplinary robust design optimization effectively attains solutions that are robust to variations in design variables and environmental conditions.

Alternative Methods for Reliability-Based Robust Design Optimization Including Dimension Reduction Method

2006 ◽  
Author(s):  
Ikjin Lee ◽  
Kyung K. Choi ◽  
Liu Du
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Reduction Method ◽  
Statistical Moments ◽  
Robust Design Optimization ◽  
Quality Loss ◽  
Dimension Reduction Method ◽  
Quality Loss Function ◽  
Performance Function ◽  
Design Variables

The objective of reliability-based robust design optimization (RBRDO) is to minimize the product quality loss function subject to probabilistic constraints. Since the quality loss function is usually expressed in terms of the first two statistical moments, mean and variance, many methods have been proposed to accurately and efficiently estimate the moments. Among the methods, the univariate dimension reduction method (DRM), performance moment integration (PMI), and percentile difference method (PDM) are recently proposed methods. In this paper, estimation of statistical moments and their sensitivities are carried out using DRM and compared with results obtained using PMI and PDM. In addition, PMI and DRM are also compared in terms of how accurately and efficiently they estimate the statistical moments and their sensitivities of a performance function. In this comparison, PDM is excluded since PDM could not even accurately estimate the statistical moments of the performance function. Also, robust design optimization using DRM is developed and then compared with the results of RBRDO using PMI and PDM. Several numerical examples are used for the two comparisons. The comparisons show that DRM is efficient when the number of design variables is small and PMI is efficient when the number of design variables is relatively large. For the inverse reliability analysis of reliability-based design, the enriched performance measure approach (PMA+) is used.

scholarly journals Robust Design Optimization with Penalty Function for Electric Oil Pumps with BLDC Motors

Energies ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 153 ◽  
Author(s):  
Keun-Young Yoon ◽  
Soo-Whang Baek
Keyword(s):  
Optimal Design ◽  
Design Optimization ◽  
Robust Design ◽  
Penalty Function ◽  
Block Diagram ◽  
Robust Design Optimization ◽  
Bldc Motor ◽  
Control Block ◽  
Element Analysis ◽  
Design Variables

In this paper, we propose and evaluate a robust design optimization (RDO) algorithm for the shape of a brushless DC (BLDC) motor used in an electric oil pump (EOP). The components of the EOP system and the control block diagram for driving the BLDC motor are described. Although the conventional deterministic design optimization (DDO) method derives an appropriate combination of design goals and target performance, DDO does not allow free searching of the entire design space because it is confined to preset experimental combinations of parameter levels. To solve this problem, we propose an efficient RDO method that improves the torque characteristics of BLDC motors by considering design variable uncertainties. The dimensions of the stator and the rotor were selected as the design variables for the optimal design and a penalty function was applied to address the disadvantages of the conventional Taguchi method. The optimal design results obtained through the proposed RDO algorithm were confirmed by finite element analysis, and the improvement in torque and output performance was confirmed through experimental dynamometer tests of a BLDC motor fabricated according to the optimization results.

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