Automated reduction of statistical errors in the estimated correlation function matrix for operational modal analysis

Marius Tarpø*, Tobias Friis, Peter Olsen, Martin Juul, Christos Georgakis, Rune Brincker

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


In operational modal analysis, the correlation function matrix is treated as multiple free decays from which system parameters are extracted. The finite time length of the measured system response, however, introduces statistical errors into the estimated correlation function matrix. These errors cause both random and bias errors that transfer to an identification process of the modal parameters. The bias error is located on the envelope of the modal correlation functions, thus violating the assumption that the correlation function matrix contains multiple free decays. Therefore, the bias error transmits to the damping estimates in operational modal analysis. In this paper, we show an automated algorithm that reduces the bias error caused by the statistical errors. This algorithm identifies erratic behaviour in the tail region of the modal correlation function and reduces this noise tail. The algorithm is tested on a simulation case and experimental data of the Heritage Court Building, Canada. Based on these studies, the algorithm reduces bias error and uncertainty on the damping estimates and increases stability in the identification process.
Original languageEnglish
JournalMechanical Systems and Signal Processing
Pages (from-to)790-805
Publication statusPublished - 2019


  • Operational modal analysis
  • Correlation function matrix
  • Uncertainty
  • Bias reduction
  • Estimation error

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