Applying Robust Design Optimization to Large Systems

2014 ◽  
Author(s):  
Matthew G. McIntire ◽  
Veronika Vasylkivska ◽  
Christopher Hoyle ◽  
Nathan Gibson
Keyword(s):  
Robust Optimization ◽  
Dimension Reduction ◽  
Robust Design ◽  
Large Scale ◽  
Robust Design Optimization ◽  
Probabilistic Constraints ◽  
Operational Control ◽  
Revenue Optimization ◽  
Large Scale Systems ◽  
Uncertainty Space

While Robust Optimization has been utilized for a variety of design problems, application of Robust Design to the control of large-scale systems presents unique challenges to assure rapid convergence of the solution. Specifically, the need to account for uncertainty in the optimization loop can lead to a prohibitively expensive optimization using existing methods when using robust optimization for control. In this work, a robust optimization framework suitable for operational control of large scale systems is presented. To enable this framework, robust optimization uses a utility function for the objective, dimension reduction in the uncertainty space, and a new algorithm for evaluating probabilistic constraints. The proposed solution accepts the basis in utility theory, where the goal is to maximize expected utility. This allows analytic gradient and Hessian calculations to be derived to reduce the number of iterations required. Dimension reduction reduces uncertain functions to low dimensional parametric uncertainty while the new algorithm for evaluating probabilistic constraints is specifically formulated to reuse information previously generated to estimate the robust objective. These processes reduce the computational expense to enable robust optimization to be used for operational control of a large-scale system. The framework is applied to a multiple-dam hydropower revenue optimization problem, then the solution is compared with the solution given by a non-probabilistic safety factor approach. The solution given by the framework is shown to dominate the other solution by improving upon the expected objective as well as the joint failure probability.

Robust Optimization of Large-Scale Systems

1995 ◽  
Vol 43 (2) ◽  
pp. 264-281 ◽  
Author(s):  
John M. Mulvey ◽  
Robert J. Vanderbei ◽  
Stavros A. Zenios
Keyword(s):  
Robust Optimization ◽  
Large Scale ◽  
Large Scale Systems

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.

Multi-Objective Robust Design Optimization and Knowledge Mining of a Centrifugal Fan That Takes Dimensional Uncertainty Into Account

2008 ◽  
Author(s):  
Kazuyuki Sugimura ◽  
Shinkyu Jeong ◽  
Shigeru Obayashi ◽  
Takeshi Kimura
Keyword(s):  
Data Mining ◽  
Robust Optimization ◽  
Robust Design ◽  
Rough Set Theory ◽  
Optimization Techniques ◽  
Robust Design Optimization ◽  
Centrifugal Fan ◽  
Data Mining Techniques ◽  
Multi Objective ◽  
Design Variables

A new design approach named MORDE (multi-objective robust design exploration), in which multi-objective robust optimization techniques and data mining techniques are combined, is proposed in this paper. We first developed a widely applicable design framework for multi-objective robust optimization. In this framework, probabilistic representation of design variables are introduced and Kriging models are used to approximate relations between design variables with uncertainty and multiple design objectives. A multi-objective genetic algorithm optimizes the mean and standard deviation of the responses. We then applied the framework to the real-world design problem of a centrifugal fan used in a washer-dryer. Taking dimensional uncertainty into account, we optimized the means and standard deviations of the resulting distributions of fan efficiency and turbulent noise level. Steady Reynolds-averaged Navier Stokes simulations were used to build Kriging models that approximate these objective functions. With the obtained non-dominated solutions, we demonstrated how to analyze features of solutions and select design candidates. We also attempted to acquire design knowledge by applying several data mining techniques. Self-organizing map was used to visualize and reuse the high dimensional design data. Decision tree analysis and rough set theory were used to extract design rules to improve the product’s performance. We also discussed differences in types of rules, which were extracted by both methods.

scholarly journals Structural optimization considering the probabilistic system response

2004 ◽  
Vol 31 (3-4) ◽  
pp. 361-394 ◽  
Author(s):  
M. Papadrakakis ◽  
N.D. Lagaros ◽  
V. Plevris
Keyword(s):  
Structural Optimization ◽  
Design Optimization ◽  
Robust Design ◽  
Large Scale ◽  
Optimization Problem ◽  
Structural Parameters ◽  
Dominant Role ◽  
Robust Design Optimization ◽  
Design Parameters ◽  
System Response

In engineering problems, the randomness and uncertainties are inherent and the scatter of structural parameters from their nominal ideal values is unavoidable. In Reliability Based Design Optimization (RBDO) and Robust Design Optimization (RDO) the uncertainties play a dominant role in the formulation of the structural optimization problem. In an RBDO problem additional non deterministic constraint functions are considered while an RDO formulation leads to designs with a state of robustness, so that their performance is the least sensitive to the variability of the uncertain variables. In the first part of this study a metamodel assisted RBDO methodology is examined for large scale structural systems. In the second part an RDO structural problem is considered. The task of robust design optimization of structures is formulated as a multi-criteria optimization problem, in which the design variables of the optimization problem, together with other design parameters such as the modulus of elasticity and the yield stress are considered as random variables with a mean value equal to their nominal value. .

Robust Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition

2016 ◽  
Author(s):  
Xuchun Ren ◽  
Sharif Rahman
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Large Scale ◽  
Design Sensitivity ◽  
Robust Design Optimization ◽  
Score Functions ◽  
Design Sensitivities ◽  
Sparse Polynomial ◽  
Dimensional Decomposition ◽  
Polynomial Dimensional Decomposition

This work proposes a new methodology for robust design optimization (RDO) of complex engineering systems. The method, capable of solving large-scale RDO problems, involves (1) an adaptive-sparse polynomial dimensional decomposition (AS-PDD) for stochastic moment analysis of a high-dimensional stochastic response, (2) a novel integration of score functions and AS-PDD for design sensitivity analysis, and (3) a multi-point design process, facilitating standard gradient-based optimization algorithms. Closed-form formulae are developed for first two moments and their design sensitivities. The method allow that both the stochastic moments and their design sensitivities can be concurrently determined from a single stochastic simulation or analysis. Precisely for this reason, the multi-point framework of the proposed method affords the ability of solving industrial-scale problems with large design spaces. The robust shape optimization of a three-hole bracket was accomplished, demonstrating the efficiency of the new method to solve industry-scale RDO problems.

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.

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