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The goal of this work is to detect flaw formation in wire arc additive manufacturing (WAAM). This process uses an electric arc as the energy source in order to melt metallic wire and deposit the new material, similar to metal inert gas (MIG) welding. Industry has been slow to adopt WAAM due to the lack of process consistency and reliability. The WAAM process is susceptible to a multitude of stochastic disturbances that cause instability in the electric arc. These arc instabilities eventually lead to flaw formation such as porosity, spatter, and excessive deviations in the desired geometry. Therefore, the objective of this work is to detect flaw formation using in-situ acoustic (sound) data from a microphone installed near the electric arc. This data was processed using a novel wavelet integrated graph theory approach. This approach detected the onset of multiple types of flaw formations with a false alarm rate of less than 2%. Using this method, this work demonstrates the potential for in-situ monitoring and flaw detection of the WAAM process in a computationally tractable manner.