Robust Design Optimization

The Robust Design Optimization (RDO) combines CAE-based optimization with robustness evaluation and allows a product optimization with a synchronized assurance of robustness. optiSLang provides iterative as well as simultaneous methods for variance-based and reliability-based RDO including tasks conforming to Design For Six Sigma (DFSS).

Best Practice


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Varying location of the optima and contour lines of constraints as a consequence of uncertainties

  • Definition of the design space of optimization variables as well as the robustness space of all scattering variables
  • Initial sensitivity analysis within the design space as well as initial robustness evaluation within the space of scattering variables in order to identify important parameters, optimization potential, initial violation probabilities and safety margins
  • Variance-based RDO for tasks with low sigma level
  • Reliability-based RDO for tasks with high sigma level
  • Sequential RDO with deterministic optimization and stepwise adjusted safety factors as best practice method in the majority of cases
  • Simultaneous RDO for tasks with sharply varying safety margins
  • Recommendation of final reliability proof for tasks with a sigma level higher than three



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Variance-based RDO samples using ARSM in combination with Advanced LHS

Variance-based RDO

  • Evolutionary algorithm, genetic algorithms, ARSM
  • Evolutionary algorithm combined with robustness evaluation
  • Adaptive response surfaces in combination with robustness evaluation

Reliability-based RDO

  • Evolutionary algorithm, genetic algorithms, ARSM
  • Evolutionary algorithm combined with First Order Reliability Method (FORM)
  • Adaptive response surfaces for optimization and reliability analysis

Postprocessing & Visualization


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  • Histograms
  • Anthill plots to visualize deterministic response values
  • Additional illustration of statistical evaluation of the robustness measures
  • Violation probabilities and sensitivity indices of robustness measures


Practical Application Examples


practical application examples


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