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.

A Robust Design Optimization Framework for Systematic Model-Based Calibration of Engine Control Systems

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
Hoseinali Borhan ◽  
Edmund Hodzen
Keyword(s):  
Control System ◽  
Design Optimization ◽  
Robust Design ◽  
Closed Loop ◽  
Optimization Technique ◽  
Loop System ◽  
Robust Design Optimization ◽  
Engine Control ◽  
Closed Loop System ◽  
Model Based

In this paper, a systematic model-based calibration framework basing on robust design optimization technique is developed for engine control system. In this framework, the control system is calibrated in an optimization fashion where both performance and robustness of the closed-loop system to uncertainties are optimized. The proposed calibration process has three steps: in the first step, the optimal performance of the system at the nominal conditions, where the effects of uncertainties are ignored, is computed by formulation of the controller calibration as an optimization problem. The capabilities of the controller are fully explored at nominal conditions. In the second step, the robustness and sensitivity of a selected control design to the system uncertainties are analyzed using Monte Carlo simulation. In the third step, robust design optimization is applied to optimize both performance and robustness of the closed-loop system to the uncertainties. The robustness capabilities of the controller are fully explored and the one that satisfies both performance and robustness requirements is selected. This process is implemented for the calibration of an advanced diesel air path control system with a variable geometry turbocharger (VGT) and dual loop exhaust gas recirculation (EGR) architecture.

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 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.

Study of Uncertainties and Objective Function Modeling Effects on Probabilistic Optimization Results

2019 ◽  
Vol 5 (4) ◽  
Author(s):  
Oussama Braydi ◽  
Pascal Lafon ◽  
Rafic Younes
Keyword(s):  
Standard Deviation ◽  
Objective Function ◽  
Design Optimization ◽  
Robust Design ◽  
Optimization Design ◽  
Robust Design Optimization ◽  
Deterministic Case ◽  
Objective Functions ◽  
Design Problems ◽  
Probabilistic Optimization

Abstract In this work, we study the effect of uncertainties modeling and the choice of objective function on the results of optimization design problems in deterministic and probabilistic contexts. Uncertainties modeling are studied in two cases identified in the literature. The results show how the choice of two different objective functions, which lead to the same results in deterministic case, may lead to opposite results in probabilistic case. Also, the results show how the uncertainties modeling type can affect the antagonism between mean and standard deviation in the reliability-based robust design optimization (RBRDO) problems. Three mechanical applications chosen from the literature are used to illustrate these cases.

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