Random Decrement Based Vibration Analysis of Nonlinear Systems

Research output: ThesisPh.D. thesis

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The current thesis investigates issues regarding the fundamental assumption of linear systems in operational modal analysis (OMA). OMA is the estimation of modal parameters; namely natural frequencies, damping ratios and unscaled mode shapes, from vibration measurements in a setting where the input forces stems from ambient sources and are not measured. Generally, there is an absence of methods for investigating if a given system behaves linearily based on vibration responses. If the assumption of a linear system is confirmed as part of the vibration analysis, the identified modal parameters can be associated with greater confidence and certainty that they are correct. For systems where the assumption of linearity cannot be confirmed, one of two things can be done. i) Apply OMA knowing the system is nonlinear and taking this into account when interpreting the estimated modal parameters. Or ii) address the nonlinear behavior in some way. Current analysis procedures in OMA generally neglect investigating the fundamental assumption of linearity.

The random decrement (RD) technique is a well known analysis method used in OMA and other research fields. The aim of this thesis is to improve and develop methods for analyzing vibration responses in regards to the fundamental assumption of linearity present in OMA using the RD technique. This includes an analysis procedure for accepting or rejecting the assumption of linearity based on the vibration response alone. Further, it is investigated if methods based on the RD technique can be developed with the purpose of analyzing the nonlinear behavior itself when only the vibration response is known. Established methods for estimating amplitude dependent modal parameters are investigated and adjustments are suggested to improve analysis outcomes.

The vibration response from both computer simulated models and experimental setups with various nonlinearities are investigated as part of the development of methods proposed in the current thesis.

A parameter capable of indicating when a response signal stems from a nonlinear system is introduced in the present work. Two parameters for characterizing nonlinear behavior as frequency or damping related are also introduced. Together, these three parameters forms novel analysis procedures for investigating nonlinear behavior when only the response signal is known.

A recipe for estimating amplitude dependent modal parameters using the RD technique is proposed. This includes signal preprocessing, choosing RD parameters, and considerations when performing parametric estimation.

From the introduction of novel analysis methods for investigating nonlinear behavior, work of the present thesis is concluded to advance the field of vibration analysis and pushing the boundaries for what information can be known about a system from the vibration response alone.
Original languageEnglish
Awarding Institution
  • University of Southern Denmark
  • Brandt, Anders, Principal supervisor
Date of defence24. Jun 2021
Publication statusPublished - 31. Mar 2021


  • Random decrement
  • Nonlinear system
  • Vibration analysis
  • Random vibrations


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