The objective of this thesis was to compare various approaches for classification of the `good' and `bad' parts via non-destructive resonance testing methods by collecting and analyzing experimental data in the frequency and time domains. A Laser Scanning Vibrometer was employed to measure vibrations samples in order to determine the spectral characteristics such as natural frequencies and amplitudes. Statistical pattern recognition tools such as Hilbert Huang, Fisher's Discriminant, and Neural Network were used to identify and classify the unknown samples whether they are defective or not. In this work, a Finite Element Analysis software packages (ANSYS 13.0 and NASTRAN NX8.0) was used to obtain estimates of resonance frequencies in `good' and `bad' samples. Furthermore, a system identification approach was used to generate Auto-Regressive-Moving Average with exogenous component, Box-Jenkins, and Output Error models from experimental data that can be used for classification