Advertisement

Local Sensitivity Analysis Based on Derivative Approximations

  • Ryan G. McClarren
Chapter

Abstract

This is the first of three successive chapters on the topic of sensitivity analysis, i.e., determining which variables a scalar quantity of interest depends on most strongly. Chapter explores using derivatives as local indicators of sensitivity based on finite difference approximations of first and second-order Taylor expansions. The error in the estimates due to finite differences is discussed, and the complex step approximation is offered as an approach for highly accurate derivative estimates for sensitivities of analytic functions. Second-order sensitivities are presented including both interactions between first-order sensitivities and second-derivative sensitivities.

Supplementary material

430401_1_En_4_MOESM1_ESM.zip (9 kb)
Chapter 4 (zip 9 KB).

References

  1. Griewank A, Walther A (2008) Evaluating derivatives: principles and techniques of algorithmic differentiation, vol 105. SIAM, PhiladelphiaCrossRefGoogle Scholar
  2. Lyness JN, Moler CB (1967) Numerical differentiation of analytic functions. SIAM J Numer Anal 4(2):202–210MathSciNetCrossRefGoogle Scholar
  3. Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis: the primer. Wiley, ChichesterzbMATHGoogle Scholar
  4. Saltelli A, Annoni P, Azzini I, Campolongo F, Ratto M, Tarantola S (2010) Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Comput Phys Commun 181(2):259–270ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Ryan G. McClarren
    • 1
  1. 1.Department of Aerospace and Mechanical EngineeringUniversity of Notre DameNotre DameUSA

Personalised recommendations