Estimation of Statistical Distributions for Modal Parameters Identified From Averaged Frequency Response Function Data

Abstract

An algorithm is presented to estimate the statistical distributions of identified modal parameters based on the random errors associated with averaged frequency response function (FRF) estimates. In this study, the modal parameters are assumed to be random variables and the objective is to estimate their dis tribution statistics (e.g., mean and variance). The algorithm first uses a classical approach to estimate the error on the averaged FRF using the coherence function averaged over an ensemble of measured samples. A Monte Carlo simulation approach is then used to propagate the estimated spectral function errors through the modal parameter identification process. A bootstrap estimate of the modal parameter distribution over the full ensemble of individual measurement samples is used to verify the accuracy of the Monte Carlo algo rithm. The statistics of the resulting modal parameter distribution are suitable for use as weights or filtering criteria in model correlation and damage identification schemes. Convergence criteria for determining how many Monte Carlo simulations are required are also presented and discussed. The technique is demonstrated via application to a simulated FRF with known parameter distributions and to experimental data from tests of an in situ bridge.