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Research Papers: Design Automation

Multi-Objective Robust Optimization Using a Postoptimality Sensitivity Analysis Technique: Application to a Wind Turbine Design

[+] Author and Article Information
Weijun Wang

Ecole Centrale de Nantes,
Institut de Recherche en Communications et
Cybernétique de Nantes,
1 rue de la Noë,
Nantes 44321, France
e-mail: weijun.wang@irccyn.ec-nantes.fr

Stéphane Caro

CNRS,
Institut de Recherche en Communications et
Cybernétique de Nantes,
UMR CNRS 6597, France
e-mail: stephane.caro@irccyn.ec-nantes.fr

Fouad Bennis

Ecole Centrale de Nantes,
Institut de Recherche en Communications et
Cybernétique de Nantes,
1 rue de la Noë,
Nantes 44321, France
e-mail: fouad.bennis@irccyn.ec-nantes.fr

Ricardo Soto

Pontificia Universidad Católica de Valparaíso,
Av. Brasil 2950,
Valparaíso 2362807, Chile
Universidad Autónoma de Chile,
Av. Pedro de Valdivia 641,
Santiago 7500138, Chile
e-mail: ricardo.soto @ucv.cl

Broderick Crawford

Universidad Finis Terrae,
Av. Pedro de Valdivia 1509,
Santiago 7501015, Chile
Facultad de Ingeniería y Tecnología,
Universidad San Sebastián,
Bellavista 7, Recoleta,
Santiago 8420524, Chile
e-mail: broderick.crawford@ucv.cl

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 9, 2013; final manuscript received September 3, 2014; published online November 14, 2014. Assoc. Editor: David Gorsich.

J. Mech. Des 137(1), 011403 (Jan 01, 2015) (11 pages) Paper No: MD-13-1403; doi: 10.1115/1.4028755 History: Received September 09, 2013; Revised September 03, 2014; Online November 14, 2014

Toward a multi-objective optimization robust problem, the variations in design variables (DVs) and design environment parameters (DEPs) include the small variations and the large variations. The former have small effect on the performance functions and/or the constraints, and the latter refer to the ones that have large effect on the performance functions and/or the constraints. The robustness of performance functions is discussed in this paper. A postoptimality sensitivity analysis technique for multi-objective robust optimization problems (MOROPs) is discussed, and two robustness indices (RIs) are introduced. The first one considers the robustness of the performance functions to small variations in the DVs and the DEPs. The second RI characterizes the robustness of the performance functions to large variations in the DEPs. It is based on the ability of a solution to maintain a good Pareto ranking for different DEPs due to large variations. The robustness of the solutions is treated as vectors in the robustness function space (RF-Space), which is defined by the two proposed RIs. As a result, the designer can compare the robustness of all Pareto optimal solutions and make a decision. Finally, two illustrative examples are given to highlight the contributions of this paper. The first example is about a numerical problem, whereas the second problem deals with the multi-objective robust optimization design of a floating wind turbine.

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Figures

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Fig. 1

The performances of solutions vary around their nominal values in the PF-Space, with regard to small variations in DVs and DEPs

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Fig. 2

The distribution of the ith performance function as a function of small variations in DVs and DEPs

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Fig. 3

The performances of solutions vary greatly in the PF-Space due to large variations in DEPs

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Fig. 4

The positions of the Pareto optimal solutions in a new environment

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Fig. 5

Each Pareto optimal solution has a corresponding position in the RF-Space

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Fig. 6

A flow chart illustrating the proposed postoptimality sensitivity analysis technique

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Fig. 7

Values of the performance functions f1 and f2 for p = 3, p = 5 and p = 8, respectively

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Fig. 8

The positions of the alternative solutions for the numerical example in the RF-Space

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Fig. 9

Schematic of a floating HAWT rotor with two simplified morphing blades

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Fig. 10

The obtained Pareto front for the MOOP of HAWT design

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Fig. 11

The positions of the alternative solutions in different design environments

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Fig. 12

The positions of the alternative solutions and initial design in the RF-Space

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Fig. 13

Comparison of all alternative solutions and solutions A,B,C,D,E, and F in the decision space, PF-Space and RF-Space

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Fig. 14

3D models for the six selected solutions A,B,C,D,E, and F

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Fig. 15

The generated samples and the nominal values of these six solutions with regard to small variations in DVs and DEPs

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