Nonlinear Dynamics

, Volume 98, Issue 1, pp 375–394 | Cite as

Global sensitivity analysis for the design of nonlinear identification experiments

  • Alana LundEmail author
  • Shirley J. Dyke
  • Wei Song
  • Ilias Bilionis
Original Paper


Bayesian inference techniques have been used extensively in recent years for parameter estimation in nonlinear systems. Despite the many advances made in the field, highly nonlinear systems can still be challenging to identify. Of key interest is the challenge in establishing the identifiability of the model with respect to various excitation signals and, in particular, doing so prior to the collection of experimental data. Global sensitivity analysis techniques provide a perspective on this problem that is well-suited to informing the design of identification experiments for use with Bayesian inference techniques. These methods quantify the relative importance of the parameters to the model response by decomposing the variance of the response into contributions from the respective parameters. The sensitivities obtained provide a valuable indication of the information available for parameter estimation in the response of a system to a particular excitation. In this study, nonlinear model parameters are identified based on experimental responses from a nonlinear energy sink device with the unscented Kalman filter. The experimental identification results are compared with those of a Sobol’ sensitivity analysis on the system model to demonstrate how global sensitivity analysis can be used as a method to preselect experimental excitations for use with Bayesian inference techniques.


Sobol’ sensitivity analysis Design of experiments System identification Nonlinear energy sink Unscented Kalman filter Identifiability 



This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1333468. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors would also like to acknowledge the work of Christian Silva, who designed and built the NES device used in this study.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Purdue UniversityWest LafayetteUSA
  2. 2.Purdue UniversityWest LafayetteUSA
  3. 3.University of AlabamaTuscaloosaUSA

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