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Special section: Methods for Uncertainty Computing Either Uncertainty Propagation or Optimization Under Uncertainty

Sequential Quadratic Programming for Robust Optimization With Interval Uncertainty

[+] Author and Article Information
Jianhua Zhou, Shuo Cheng

 University of Michigan-Shanghai, Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China

Mian Li1

 University of Michigan-Shanghai, Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, Chinamianli@sjtu.edu.cn

1

Corresponding author.

J. Mech. Des 134(10), 100913 (Sep 28, 2012) (13 pages) doi:10.1115/1.4007392 History: Received January 13, 2012; Revised June 03, 2012; Published September 21, 2012; Online September 28, 2012

Uncertainty plays a critical role in engineering design as even a small amount of uncertainty could make an optimal design solution infeasible. The goal of robust optimization is to find a solution that is both optimal and insensitive to uncertainty that may exist in parameters and design variables. In this paper, a novel approach, sequential quadratic programming for robust optimization (SQP-RO), is proposed to solve single-objective continuous nonlinear optimization problems with interval uncertainty in parameters and design variables. This new SQP-RO is developed based on a classic SQP procedure with additional calculations for constraints on objective robustness, feasibility robustness, or both. The obtained solution is locally optimal and robust. Eight numerical and engineering examples with different levels of complexity are utilized to demonstrate the applicability and efficiency of the proposed SQP-RO with the comparison to its deterministic SQP counterpart and RO approaches using genetic algorithms. The objective and/or feasibility robustness are verified via Monte Carlo simulations.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Flow chart of SQP-RO

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Figure 2

Solutions comparison and objective robustness

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Figure 3

Robustness comparison of two-bar truss

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Figure 4

Robustness comparison of speed reducer

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Figure 5

A Compression spring (courtesy of Ref. [29])

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Figure 6

Robustness comparison of compression spring

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