###### Abstract  
Analyzing eigenfrequencies by acoustic resonance testing enables a fast screening of components regarding structural defects. The eigenfrequencies of each specific part depend on the general geometric and material properties, including tolerable part-to-part variations, as well as on possible structural flaws. Separating good parts from defective ones is not straightforward and each application-specific sorting algorithm is usually found from experimental training data. However, there are limitations and training data collection may be intricate. We worked on this challenge focusing on machine-made model parts varying slightly in geometry. The application objective was the eigenfrequency-based detection of parts featuring a through-hole test defect drilled into some of the parts and enlarged stepwise. The eigenfrequencies were measured concomitantly. Unlike the industry standard, our approach is based on synthetic training data created mainly by simulation techniques, which resulted in a principally satisfactory classification of the good and defective parts. However, the parts with small defects were not identified from the eigenfrequencies alone, due to overlaying geometric variations. In order to counteract such noise and to improve defect detection based on synthetic training data, the specific actual part geometry was used, in the sense of additional a priori information. A multimodal data evaluation model showed a clearly enhanced sorting power. acoustic resonance testing; resonance inspection; nondestructive defect detection; sorting algorithm; geometric variations; part-to-part variations; simulation-based training data; synthetic training data; a priori component information; multimodal data evaluation +
Footnote †: journal: Applied  
testability of an entire component volume in seconds, favorable hardware costs, excellent automation options, and environmental friendliness. Various implementation options are available for the respective ART steps, connected with specific advantages and challenges. However, an ART usually involves an active mechanical excitation of the test object (for example, impact or sweep excitation), followed by recording the vibration response (for example, via a microphone or with a contact sensor). After the signal acquisition and digitalization, various filtering and transformation steps as well as methods for the extraction of acoustic characteristics, such as eigenfrequencies, amplitudes, or damping values, may be carried out with the measurement data. By applying a suitable algorithm to the signal data or the derived acoustic characteristics, the test object is finally classified with regard to the application objective, for example, categorized as good or as defective. ART is an acoustic method in the field of nondestructive testing (NDT). In contrast to ultrasonic testing, which focuses on the local interaction of sound waves with anomalies, ART analyzes the resonant vibration behavior of the entire test object. There are also other approaches that use such vibrations, for example, resonant ultrasound spectroscopy (RUS). RUS can be used for the nondestructive evaluation of the elastic properties from defined samples, based on a swept sine excitation. However, despite this common target of RUS including the evaluation of high frequencies and special algorithms, the term RUS is also used in NDT with regard to structural defects, see [6; 7]. In this sense, RUS and ART, among other common names, are synonyms. For the purpose of a thematic delimitation, we limited the scope in the following to the works that are directly related to ART as a fast NDT-screening method for mostly engineering series parts that are subject to practice-effects. Within the last ten years, some works focusing on the ART detection of cracked automotive parts were performed taking advantage of intelligent classification methods [8; 9]. For the good defective distinction of tubular components, the ART data were evaluated in combination with the component weight and hardness [10].