Structural and Multidisciplinary Optimization

, Volume 58, Issue 5, pp 2135–2162 | Cite as

Analytical moment based approximation for robust design optimization

  • Tanmoy ChatterjeeEmail author
  • Souvik Chakraborty
  • Rajib Chowdhury


The role of robust design optimization (RDO) has been eminent, ascertaining optimal configuration of engineering systems in the presence of uncertainties. However, computational aspect of RDO can often get tediously intensive in dealing with large scale systems. To address this issue, hybrid polynomial correlated function expansion (H-PCFE) based RDO framework has been developed for solving computationally expensive problems. H-PCFE performs as a bi-level approximation tool, handling the global model behavior and local functional variation. Analytical formula for the mean and standard deviation of the responses have been proposed, which reduces significant level of computations as no further simulations are required for evaluating the statistical moments within the optimization routine. Implementation of the proposed approaches have been demonstrated with two benchmark examples and two practical engineering problems. The performance of H-PCFE and its analytical version have been assessed by comparison with direct Monte Carlo simulation (MCS). Comparison with popular state-of-the-art techniques has also been presented. Excellent results in terms of accuracy and computational effort obtained makes the proposed methodology potential for further large scale industrial applications.


Hybrid PCFE Robust design optimization Analytical moments Homotopy algorithm 



Tanmoy Chatterjee and Rajib Chowdhury acknowledge the support of CSIR via Grant No. 22(0712)/16/EMR-II.

Supplementary material


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Tanmoy Chatterjee
    • 1
    Email author
  • Souvik Chakraborty
    • 2
    • 3
  • Rajib Chowdhury
    • 1
  1. 1.Department of Civil EngineeringIndian Institute of Technology RoorkeeRoorkeeIndia
  2. 2.Department of Aerospace and Mechanical EngineeringUniversity of Notre DameNotre DameUSA
  3. 3.Center for Informatics and Computational ScienceUniversity of Notre DameNotre DameUSA

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