Multidisciplinary Analysis and Optimization

Sensitivity Analysis

With sensitivity analysis, the system complexity can be reduced and the cause-and-effect relationship can be explained:

  • Which model parameters contribute the most to output variability and, possible, require additional research to strengthen the knowledge base, thereby reducing output uncertainty.
  • Which parameters are insignificant and can be eliminated from the final model
  • Which parameters interact with each other.

OptiY® can compute not only local sensitivity, but also global sensitivity for any output-function with any input-distribution.

Local Sensitivity

Partial derivatives and correlation coefficients are defined as local sensitivities The local sensitivities can be used only, if the correlation between inputs and outputs is linear.

Global Sensitivity

The local sensitivities have only a small explanatory power of parameter influences, because partial derivatives are calculated only at upper and lower bounds. The inputs scatter however in the entire design space, which is frequently nonlinear. Therefore, a global sensitivity as Sobol index must be considered. The main effect is the quotient of the output variance caused by a single input to the output variance caused by all inputs. The total effect results from the main effect and the interactions between inputs.

Dynamical Systems

The 1D global variance based sensitivity indexes as main-effect or total-effect for the entire time signal can be calculated by 1D probabilistic simulation with OptiY. With results of 1D sensitivities, designer have got a powerful tool to get deeper information of the dynamical systems in the early design stage without prototypes to make the right design decisions related in reliability and quality.