Frequency Band Averaging of Spectral Densities for Updating Finite Element Models

Abstract

The successful operation of proposed precision spacecraft will require finite element models that are accurate to much higher frequencies than the standard application. The hallmark of this mid-frequency range, between low-frequency modal analysis and high-frequency statistical energy analysis, is high modal density. The modal density is so high, and the sensitivity of the modes with respect to modeling errors and uncertainty is so great that test/analysis correlation and model updating based on traditional modal techniques no longer work. This paper presents an output error approach for finite element model updating that uses a new test/analysis correlation metric that maintains a direct connection to physical response. The optimization is gradient based. The metric is based on frequency band averaging of the output power spectral densities with the central frequency of the band running over the complete frequency range of interest. The results of this computation can be interpreted in several different ways, but the immediate physical connection is that it produces the mean-square response, or energy, of the system to random input limited to the averaging frequency band. The use of spectral densities has several advantages over using frequency response directly, such as the ability to easily include data from all inputs at once, and the fact that the metric is real. It is shown that the averaging process reduces the sensitivity of the optimization due to resonances that plague many output error model updating approaches.