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The usefulness of machine learning algorithms is highly dependent on the formulation of relevant features that sufficiently represent the model. Acoustic resonance spectra consist of a series of peaks, representing resonant modes of the system and contain detailed information about the system structure, material, boundary forces, etc. We present a technique for extracting useful features from dense acoustic resonance spectra of multi-component systems. For simple geometries, the resonance spectrum is relatively sparse and it is feasible to track individual peaks to quantify properties of the system. However, for multi-component systems, the acoustic resonance spectra consist of overlapping peaks, corresponding to resonances in different components. As a result, a high density of peaks exists, and some peak positions are sensitive to changes in the contact between components. Thus, tracking specific resonance modes becomes challenging. Instead, we combine principles from wavelet transformation, nonlinear normalization, and genetic algorithm optimization to extract useful features from complicated acoustic resonance spectra. We demonstrate this technique on simulated acoustic resonance spectra for multi-layer structures. Here, we are measuring the thickness of a specific layer, which is hampered by changes in the acoustic resonance spectrum due to variation in the other layer thicknesses as well as delamination defects.