Quantification of Uncertainty in Structural Dynamic models

In engineering fields, estimated quantities are used in different engineering applications all the time. The estimated quantities are ideally provided along with uncertainty estimates, enabling engineers to assess the quality of the estimates. In the field of vibrations, natural frequencies, damping ratios, participation vectors, and mode shapes constitute the modal parameters, and these are important in different applications, such as the design and troubleshooting of mechanical components and structures, structural health monitoring, virtual sensing, and reliability.

Experimentally, estimates of the modal parameters can be obtained using Experimental Modal Analysis (EMA) or Operational Modal Analysis (OMA). For EMA, the modal parameters are estimated from response and excitation force measurements, while for OMA, the modal parameters are estimated solely from response measurements.

Modal parameters have historically been estimates without uncertainty estimates, but in recent years, more effort has been put into estimating the uncertainty of these estimates (especially for OMA). In the present work, uncertainty estimates for the modal parameters are derived for EMA using the frequency-domain modal parameter estimation algorithm called polyreference Least-Squares Complex Frequency-domain (pLSCF), which uses Frequency Response Functions as input.

This thesis consists of two parts: a summarizing part and journal- and conference-publications. The theoretical work is presented at the beginning of the summarizing part, where the uncertainty of the measured signals is quantified and propagated to the modal parameters through the conventional FRF estimators and the pLSCF algorithm. The uncertainty quantification and propagation are validated using simulated data from a simple mechanical system.

The experimental work is presented at the end of the summarizing part. It consists of repeated experiments on a simple structure, where the noise assumptions from the theoretical part are validated. Furthermore, the uncertainty of the FRFs and modal parameters are estimated using the uncertainty expressions developed, and the estimated uncertainties are compared to the sample uncertainties.
The outcome of the work is uncertainty expressions for the FRF estimators
and modal parameters validated through simulated data and experimental
data.