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How to Perform Optimisation Under Uncertainty

This NAFEMS publication, contributed by the ESTEcO engineering software company, focuses on Design Optimisation Under Uncertainty (OUU) methods. Further valuable insights on OUU are provided by the Dynardo engineering software company in a companion NAFEMS publication Irobust Design Optimization in Virtual Product Development" by Johannes Will.

This publication provides:

a) a description of the Smoothing Spline ANOVA (SSYANOVA) screening method,

b) a comparison of Uncertainty Quantification (UQ) methods: sample based and Polynomial chaos Expansion (PcE), 

c) and a description of robust Design Optimisation (rDO) and reliability Based Design Optimisation (rBDO) methods.

The author illustrates the best practices in the application of these methods through three examples of increasing complexity, namely: an H beam subject to a vertical load, robust design of a building structure subject to stochastic seismic disturbances and a boomerang shape design. The complexity of component design originates from a number of interacting factors. The design engineer has to find a practical resolution to the following questions, while satisfying the budget/time/computing resource constraints of a project:

a) What is the best representation for the model input parameter uncertainty given the current state of engineering NnowYhow? (Are parameter distributions known, or only ranges are known? Are uncertain parameters spatially correlated?) 

b) How can the design degrees of freedom be reduced to a manageable level so that the optimisation problem can be resized based on the available computational resources? 

c) What is a good choice of a metaYmodel and how can the uncertainty of point-wise predictions of such models be consistently combined with input uncertainty? 

d) What are the most appropriate measures of component design robustness and/or reliability? 

e) For a given UQ method, up to which precision levels are the robustness measures evaluated? 

f) How can component design optimisation be performed in the presence of uncertainty? What feasible approaches are available and how to select the most appropriate one for a specific problem?

The importance of adopting a systematic approach in the use of modern computational design tools for OUU is highlighted in this guide.


  1. Introduction 

  2. Techniques
  3. H Beam Example
  4. Structural Engineering Example

  5. Boomerang Example

  6. Conclusions

  7. Abbreviations and Acronyms

  8. References

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Mariapia Marchi

First Published 

January 2017
Softback, 34 Pages