Bootstrap Statistics Distribution of Modal Parameters Estimation for the Advanced Combat Helmet

摘要

The classical approach in experimental modal analysis is to consider the modal parameters as deterministic quantities corrupted by additive errors. These errors, in form of measured noise and signal variability, account for the deviation of the measured structural response from the true structural response, and also account for the variability of the estimated modal parameters. A more recent approach is to consider the modal parameters as random variables, so that the distribution of the random source can be estimated. In this work, the bootstrap technique was used to generate the statistical distribution of the estimated modal parameters for a medium size Advanced Combat Helmet (ACH). The estimation of the modal parameters was done using the H_1 technique, which assumed that output only noise was present in the measurements. Bootstrapping was used for the estimation of Frequency Response Function (FRF) from power spectra and cross-power spectra densities measurements. Modal parameters were extracted from the computed FRFs, and the coherence function was used as a measure of reliability of the estimated frequencies. The results obtained from the bootstrap experiments were used to define the statistics for the modal parameter, defining quantities such as mean, variance, and kurtosis for the estimated distributions. Moreover, the analysis of the convergence of the kurtosis allowed an estimation of the gaussianity for the underlying distributions. Simulated results for a single degree-of-freedom system were used to highlight the capability of the proposed approach, while analysis on experimental data was conducted on a medium size ACH.