Health indicators (HIs) are central to diagnosing and prognosing the condition of aerospace composite structures, enabling efficient maintenance and operational safety. However, extracting reliable HIs remains challenging due to variability in material properties, stochastic damage evolution, and diverse damage modes. Manufacturing defects (e.g., disbonds) and in-service incidents (e.g., bird strikes) further complicate this process. This study presents a comprehensive data-driven framework that learns HIs via two learning approaches integrated with multi-domain signal processing. Because ground-truth HIs are unavailable, a semi-supervised and an unsupervised approach are proposed: (i) a diversity deep semi-supervised anomaly detection (Diversity-DeepSAD) approach augmented with continuous auxiliary labels used as hypothetical damage proxies, which overcomes the limitation of prior binary labels that only distinguish healthy and failed states while neglecting intermediate degradation, and (ii) a degradation-trend-constrained variational autoencoder (DTC-VAE), in which the monotonicity criterion is embedded via an explicit trend constraint. Guided waves with multiple excitation frequencies are used to monitor single-stiffener composite structures under fatigue loading. Time, frequency, and time-frequency representations are explored, and per-frequency HIs are fused via unsupervised ensemble learning to mitigate frequency dependence and reduce variance. Using fast Fourier transform features, the augmented Diversity-DeepSAD model achieved 81.6% performance, while DTC-VAE delivered the most consistent HIs with 92.3% performance, outperforming existing baselines.