A comparison study of modal parameter confidence intervals computed using the Monte Carlo and Bootstrap techniques

This paper presents a comparison of two techniques used to estimate the statistical confidence intervals on modal parameters identified from measured vibration data. The first technique is Monte Carlo simulation, which involves the repeated simulation of random data sets based on the statistics of the measured data and an assumed distribution of the variability in the measured data. A standard modal identification procedure is repeatedly applied to the randomly perturbed data sets to form a statistical distribution on the identified modal parameters. The second technique is the Bootstrap approach, where individual Frequency Response Function (FRF) measurements are randomly selected with replacement to form an ensemble average. This procedure, in effect, randomly weights the various FRF measurements. These weighted averages of the FRFs are then put through the modal identification procedure. The modal parameters identified from each randomly weighted data set are then used to define a statistical distribution for these parameters. The basic difference in the two techniques is that the Monte Carlo technique requires the assumption on the form of the distribution of the variability in the measured data, while the bootstrap technique does not. Also, the Monte Carlo technique can only estimate random errors, while the bootstrap statistics represent both random and bias (systematic) variability such as that arising from changing environmental conditions. However, the bootstrap technique requires that every frequency response function be saved for each average during the data acquisition process. Neither method can account for bias introduced during the estimation of the FRFs. This study has been motivated by a program to develop vibration-based damage identification procedures.