Strategies for Improving the Comparison of Frequency Response Functions with Similarity Metrics

Determining the similarity of an existing structure with a reference structure is an important problem in structural dynamics. For this purpose, many metrics have been developed to quantify the similarity of frequency spectra, such as two transfer functions. However, these approaches yield an aggregate or single numerical score for the similarity over an entire frequency range. This paper, instead, applies these common similarity metrics across a range of frequencies and plots the results to illustrate instances where counterintuitive results can occur. For example, the highest degree of similarity often occurs at a frequency where the two frequency spectra appear to diverge. The result is that counterintuitive cases can be corrected by applying a log frequency shift to the response, enabling better comparisons. Additionally, a similarity metric that compares the phase of the frequency spectra can be applied to make further comparisons. This paper seeks to verify the new methods presented in Manring et al. (J Sound Vib 539:117255, 2022) using a modified experiment and proposes a windowing method as another tool for comparing similar transfer functions. The authors investigate these approaches while applying historical measures of similarity, to provide a more intuitive result for a similarity score. While the shifted frequency spectra can now provide more intuitive comparisons of the degree of similarity, the degree of shifting the frequency segments provides an additional opportunity to quantify the differences in the frequency spectra. The developed approaches were applied to both theoretical and experimental systems.