<p>Monitoring the operational state of manufacturing equipment is essential for improving productivity and ensuring process reliability in modern manufacturing. Sound has gained increasing attention as a non-contact and cost-effective solution for real-time monitoring. However, implementing sound-based monitoring using data-driven methods faces two critical challenges. First, machine sound is unstructured and highly context-dependent, making it difficult to isolate signals from individual components. Second, the limited diversity of curated datasets hinders the training of models that generalize across operational states. In machine tool operational state monitoring, to address these challenges, a two-fold approach is proposed: a structured warm-up cycle that enables isolation of sound signatures from key machine tool components, and a data augmentation pipeline that superposes interpolated component-wise signals to synthesize realistic multi-component sounds. Individual component signals are modeled as outputs of linear time-invariant (LTI) systems, and their frequency-domain representations are characterized using statistical features. This approximation enables physically meaningful modeling of component-wise sound behavior and supports scalable data synthesis. In data-scarce manufacturing settings, regression-based interpolation of spectral features enables the synthesis of component sounds under unseen conditions, such as varying spindle or axis speeds. This strategy expands the diversity of training data without requiring additional labeling. The proposed approach is applied to train a lightweight 1D convolutional neural network for multi-label classification of machine operations. Compared to conventional augmentation methods, it achieves a 26.2% improvement in macro F1 score, demonstrating the effectiveness of structured sound augmentation in enhancing model performance and generalizability.</p>