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Reliability Based Design Optimization Using Automatic Differentiation

[+] Author Affiliations
K. Pugazhendhi, A. K. Dhingra

University of Wisconsin, Milwaukee, WI

Paper No. IMECE2011-65912, pp. 511-519; 9 pages
doi:10.1115/IMECE2011-65912
From:
  • ASME 2011 International Mechanical Engineering Congress and Exposition
  • Volume 9: Transportation Systems; Safety Engineering, Risk Analysis and Reliability Methods; Applied Stochastic Optimization, Uncertainty and Probability
  • Denver, Colorado, USA, November 11–17, 2011
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5495-2
  • Copyright © 2011 by ASME

abstract

Typically, a reliability based design optimization (RBDO) problem is solved as a nested optimization problem because an evaluation of the probabilistic constraint(s) involves solving a minimization problem. Over the years, a number of algorithms have been developed to solve the RBDO problem efficiently. All of these approaches involve an evaluation of derivatives of the responses. In this paper, a decoupled approach using automatic differentiation (AD) is presented to solve the RBDO problem. The proposed approach employs AD to evaluate the reliability, as well as to evaluate the sensitivity of the most probable point (MPP) with respect to the design variables. Since these evaluations involve a computation of the Jacobian and the Hessian, a use of AD improves the accuracy while simultaneously reducing the required number of response evaluations. The applicability of the proposed approach is shown through examples of increasing complexity ranging from problems where closed form solutions are available for evaluation of response to situations where finite element analysis is needed to compute the system response.

Copyright © 2011 by ASME

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