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.

scholarly journals How to compare performance of robust design optimization algorithms, including a novel method

2017 ◽  
Vol 31 (3) ◽  
pp. 286-297 ◽  
Author(s):  
Johan A. Persson ◽  
Johan Ölvander
Keyword(s):  
Robust Optimization ◽  
Design Optimization ◽  
Robust Design ◽  
Performance Metrics ◽  
Computational Cost ◽  
Optimization Method ◽  
Engineering Problem ◽  
Robust Design Optimization ◽  
Optimization Approach ◽  
Novel Method

AbstractThis paper proposes a method to compare the performances of different methods for robust design optimization of computationally demanding models. Its intended usage is to help the engineer to choose the optimization approach when faced with a robust optimization problem. This paper demonstrates the usage of the method to find the most appropriate robust design optimization method to solve an engineering problem. Five robust design optimization methods, including a novel method, are compared in the demonstration of the comparison method. Four of the five compared methods involve surrogate models to reduce the computational cost of performing robust design optimization. The five methods are used to optimize several mathematical functions that should be similar to the engineering problem. The methods are then used to optimize the engineering problem to confirm that the most suitable optimization method was identified. The performance metrics used are the mean value and standard deviation of the robust optimum as well as an index that combines the required number of simulations of the original model with the accuracy of the obtained solution. These measures represent the accuracy, robustness, and efficiency of the compared methods. The results of the comparison show that sequential robust optimization is the method with the best balance between accuracy and number of function evaluations. This is confirmed by the optimizations of the engineering problem. The comparison also shows that the novel method is better than its predecessor is.

scholarly journals Stochastic simulation and robust design optimization of integrated photonic filters

Nanophotonics ◽  
2017 ◽  
Vol 6 (1) ◽  
pp. 299-308 ◽  
Author(s):  
Tsui-Wei Weng ◽  
Daniele Melati ◽  
Andrea Melloni ◽  
Luca Daniel
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Ring Resonator ◽  
Process Variations ◽  
Robust Design Optimization ◽  
Generalized Polynomial ◽  
Optimization Simulation ◽  
The Mean ◽  
Sparsity Structure ◽  
Mean Square Errors

AbstractManufacturing variations are becoming an unavoidable issue in modern fabrication processes; therefore, it is crucial to be able to include stochastic uncertainties in the design phase. In this paper, integrated photonic coupled ring resonator filters are considered as an example of significant interest. The sparsity structure in photonic circuits is exploited to construct a sparse combined generalized polynomial chaos model, which is then used to analyze related statistics and perform robust design optimization. Simulation results show that the optimized circuits are more robust to fabrication process variations and achieve a reduction of 11%–35% in the mean square errors of the 3 dB bandwidth compared to unoptimized nominal designs.

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.

Robust Design Optimization Under Mixed Uncertainties With Stochastic Expansions

2013 ◽  
Vol 135 (8) ◽  
Author(s):  
Yi Zhang ◽  
Serhat Hosder
Keyword(s):  
Monte Carlo ◽  
Robust Optimization ◽  
Objective Function ◽  
Design Optimization ◽  
Robust Design ◽  
Optimization Technique ◽  
Response Surfaces ◽  
Robust Design Optimization ◽  
Stochastic Expansions ◽  
Mixed Uncertainties

The objective of this paper is to introduce a computationally efficient and accurate approach for robust optimization under mixed (aleatory and epistemic) uncertainties using stochastic expansions that are based on nonintrusive polynomial chaos (NIPC) method. This approach utilizes stochastic response surfaces obtained with NIPC methods to approximate the objective function and the constraints in the optimization formulation. The objective function includes a weighted sum of the stochastic measures, which are minimized simultaneously to ensure the robustness of the final design to both inherent and epistemic uncertainties. The optimization approach is demonstrated on two model problems with mixed uncertainties: (1) the robust design optimization of a slider-crank mechanism and (2) robust design optimization of a beam. The stochastic expansions are created with two different NIPC methods, Point-Collocation and Quadrature-Based NIPC. The optimization results are compared to the results of another robust optimization technique that utilizes double-loop Monte Carlo sampling (MCS) for the propagation of mixed uncertainties. The optimum designs obtained with two different optimization approaches agree well in both model problems; however, the number of function evaluations required for the stochastic expansion based approach is much less than the number required by the Monte Carlo based approach, indicating the computational efficiency of the optimization technique introduced.

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.

General Robust Design by Semi-Second-Order Taylor Expansion

2008 ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Taylor Expansion ◽  
Random Variables ◽  
Second Order ◽  
Robust Design Optimization ◽  
Integration Strategy ◽  
Interval Variables ◽  
Standard Deviations ◽  
Robustness Assessment

The purpose of robust design optimization is to minimize variations in design performances and therefore to make the design insensitive to uncertainties. Current robust design methods fall into two types — probabilistic robust design and worst-case (interval) robust design. The former method is used when random variables are involved. In this method, robustness is measure by standard deviations of design performances. The later method is used when uncertainties are represented by intervals. The widths of design performances are then used to measure robustness. In many engineering application, both random variables and interval variables may exist simultaneously. In this paper, a general approach to robust design optimization is proposed. The generality comes from the ability to handle both random and interval variables. To alleviate the computational burden, we employ a previously developed general robustness assessment method — semi-second-order Taylor expansion method, to evaluate the maximum and minimum standard deviations of a design performance. An efficient integration strategy of the general robustness assessment and optimization is proposed. With the integration strategy, the number of function calls can be reduced while good accuracy is maintained. A robust shaft design problem is given for demonstration.

Practical Robust Design Optimization Using Evolutionary Algorithms

2011 ◽  
Vol 133 (10) ◽  
Author(s):  
Amit Saha ◽  
Tapabrata Ray
Keyword(s):  
Evolutionary Algorithms ◽  
Robust Optimization ◽  
Design Optimization ◽  
Robust Design ◽  
Optimal Solution ◽  
Optimization Procedure ◽  
Computational Design ◽  
Robust Design Optimization ◽  
Function Evaluation ◽  
Engineering Design Problems

Robust design optimization (RDO) seeks to find optimal designs which are less sensitive to the uncontrollable variations that are often inherent to the design process. Studies using Evolutionary Algorithms (EAs) for RDO are not too many. In this work, we propose enhancements to an EA based robust optimization procedure with explicit function evaluation saving strategies. The proposed algorithm, IDEAR, takes into account a specified expected uncertainty in the design variables and then imposes the desired robustness criteria during the optimization process to converge to robust optimal solution(s). We pick up a number of Bi-objective engineering design problems from the standard literature and study them in the proposed robust optimization framework to demonstrate the enhanced performance. A cross-validation study is performed to analyze whether the solutions obtained are truly robust and also make some observations on how robust optimal solutions differ from the performance maximizing solutions in the design space. We perform a rigorous analysis of the key features of IDEAR to illustrate its functioning. The proposed function evaluation saving strategies are generic and their applications are worth exploring in other areas of computational design optimization.

Robust Design Optimization of Gear Parameters for a Wind Turbine Using Interval Analysis

2010 ◽  
Vol 224 (10) ◽  
pp. 2235-2245 ◽  
Author(s):  
R Dong ◽  
W Sun ◽  
H Xu
Keyword(s):  
Wind Turbine ◽  
Design Optimization ◽  
Robust Design ◽  
Optimization Method ◽  
Mean Value ◽  
Robust Design Optimization ◽  
Upper And Lower Bounds ◽  
Interval Numbers ◽  
Minimum Sensitivity ◽  
The Mean

A robust design optimization method is suggested to optimize the system parameters of a gear transmission for a wind turbine with minimum sensitivity of fatigue strength to variations in uncertain application factor, dynamic load coefficient, material property parameters, and other coefficients representing unknown working condition. Interval numbers are employed to model the uncertainties by which only the upper and lower bounds are needed. Based on interval mathematics, the original real-valued objective and constraint functions are replaced by the interval-valued functions, which directly represent the variation bounds of the new functions under uncertainty. The single-objective function is converted into two-objective functions for minimizing the mean value and the variation, and the constraint functions are reformulated with the acceptable robustness level, resulting in a bi-level mathematical model. The optimization results of gear parameter demonstrate the validity and feasibility of the presented method.

A novel metamodel management strategy for robust trajectory design of an expendable launch vehicle

2019 ◽  
Vol 234 (2) ◽  
pp. 236-253 ◽  
Author(s):  
J Roshanian ◽  
AA Bataleblu ◽  
M Ebrahimi
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Management Strategy ◽  
Optimization Problems ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Launch Vehicle ◽  
Robust Design Optimization ◽  
Trajectory Design ◽  
Local Optima

Uncertainty-based design optimization has been widely acknowledged as an advanced methodology to address competing objectives of aerospace vehicle design, such as reliability and robustness. Despite the usefulness of uncertainty-based design optimization, the computational burden associated with uncertainty propagation and analysis process still remains a major challenge of this field of study. The metamodeling is known as the most promising methodology for significantly reducing the computational cost of the uncertainty propagation process. On the other hand, the nonlinearity of the uncertainty-based design optimization problem's design space with multiple local optima reduces the accuracy and efficiency of the metamodels prediction. In this article, a novel metamodel management strategy, which controls the evolution during the optimization process, is proposed to alleviate these difficulties. For this purpose, a combination of improved Latin hypercube sampling and artificial neural networks are involved. The proposed strategy assesses the created metamodel accuracy and decides when a metamodel needs to be replaced with the real model. The metamodeling and metamodel management strategy are conspired to propose an augmented strategy for robust design optimization problems. The proposed strategy is applied to the multiobjective robust design optimization of an expendable launch vehicle. Finally, based on non-dominated sorting genetic algorithm-II, a compromise between optimality and robustness is illustrated through the Pareto frontier. Results illustrate that the proposed strategy could improve the computational efficiency, accuracy, and globality of optimizer convergence in uncertainty-based design optimization problems.

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