# Curve Fitting OMA Measurements

Experimental modal parameters are normally estimated by curve fitting a set of Frequency Response Functions (FRFs).  To calculate an FRF, all excitation forces must be simultaneously acquired with each structural response caused by the excitation forces.

## Output-only Measurements

Structural responses can always be acquired, even when the excitation forces are not acquired.

• Fourier spectra, Cross spectra & ODS FRFs can be calculated from Output only, response only, or operating data

## Operating Modal Analysis

Operating Modal Analysis (OMA) is the process of extracting modal parameters (called operating mode shapes) from a set of output-only measurements.

## Flat Force Spectrum

FRF-based curve fitting is applied mainly around the resonance peaks in a Fourier spectrum, Cross spectrum, or ODS FRF. If the following assumption is met, then peaks in these output-only measurements are assumed to be caused by the excitation of resonances, or modes of vibration.

ASSUMPTION:  If the frequency spectrum of the un-measured excitation forces is assumed to be "relatively flat", then operating mode shapes can be extracted from output-only measurements using FRF-based curve fitting methods

## Curve Fitting Fourier Spectra

A Fourier spectrum is the FFT of single channel time waveform.

•  If all response time waveforms are simultaneously acquired, operating mode shapes can be extracted from a set of Fourier spectra using FRF-based curve fitting methods

## Curve Fitting Cross Spectra

A Cross spectrum is a cross channel measurement that is calculated between two channels of response data.  The correct relative magnitude & phase between all Roving responses is preserved if all Cross spectra are calculated between a Roving response and the same (fixed) Reference response.

• Multiple Measurement Sets of Cross spectra can be calculated from one or more simultaneously acquired Roving responses and the same (fixed) Reference response.

• After a DeConvolution window has been applied to a set of Cross spectra, Operating mode shapes can be extracted from them using FRF-based curve fitting methods

## Curve Fitting ODS FRFs

An ODS FRF is a "hybrid" cross channel measurement that is calculated between two channels of response data.  The magnitude of the ODS FRF is the Auto spectrum of a Roving response and the phase is the phase of the Cross spectrum between the Roving and a (fixed) Reference response.  The correct relative magnitude & phase between all Roving responses is preserved if all ODS FRFs are calculated between a Roving response and the same (fixed) Reference response.

• Multiple Measurement Sets of ODS FRFs can be calculated from one or more simultaneously acquired Roving responses and the same (fixed) Reference response.

• After a DeConvolution window has been applied to a set of ODS FRFs, Operating mode shapes can be extracted from then using FRF-based curve fitting methods