Monitoring the structural integrity of aeronautical structures is critical for safety, reducing maintenance costs, and enabling predictive maintenance. However, raw structural health monitoring (SHM) data are often noisy, high-dimensional, and difficult to interpret. To enable condition-based maintenance, it is essential to extract health indicators (HIs)—quantitative representations of structural degradation that evolve consistently over time. Accurately extracting HIs for composite structures is particularly challenging due to complex material behavior and multiple damage sources. While deep learning models offer potential, their application is limited by the lack of run-to-failure data and ground-truth HI labels. To address these challenges, this study proposes a novel approach that divides HI modeling into two tasks: time-independent (spatial) and time-dependent (temporal). This separation allows more effective data utilization, especially in the time-independent case. A semi-supervised spatial model is first developed and fine-tuned using a Bayesian algorithm with a coupled physics-based loss function that integrates both prognostic criteria and simulated labels—explicitly through the former and implicitly through the latter—embedding degradation physics into training. The study also introduces a new adaptive standardization technique for fatigue-based SHM and systematically evaluates principal component analysis (PCA)-based methods for dimensionality reduction prior to spatial and temporal modeling, simplifying subsequent network architectures. In the final stage, following time-based resampling, a semi-supervised temporal model captures HI evolution, with ensemble learning enhancing robustness. Validation on single-stiffener composite panels under fatigue loading, monitored via acoustic emission sensors, confirms the framework's generalizability and performance—achieving up to 90% (±2%) accuracy in prognostic metrics.

Health indicators are indices that act as intermediary links between raw SHM data and prognostic models. An efficient HI should satisfy prognostic requirements such as monotonicity, trendability, and prognosability in such a way that it can be effectively used as an input in a prognostic model for remaining useful life estimation. However, discovering or designing a suitable HI for composite structures is a challenging task due to the inherent complexity of the evolution of damage events in such materials. Previous research has shown that data-driven models are efficient for accomplishing this goal. Large labeled datasets, however, are normally required, and the SHM data can only be labeled, respecting prognostic requirements, after a series of nominally identical structures are tested to failure. In this paper, a semi-supervised learning approach based on implicitly imposing prognostic criteria is adopted to design a novel HI suitable. To this end, single-stiffener composite panels were subjected to compression-compression fatigue loading and monitored using acoustic emission (AE). The AE data after signal processing and feature extraction were fused using a multi-layer LSTM neural network with criteria-based hypothetical targets to generate an intelligent HI. The results confirm the performance of the proposed scenario according to the prognostic criteria.

A health indicator (HI) serves as an intermediary link between structural health monitoring (SHM) data and prognostic models, and an efficient HI should meet prognostic criteria, i.e., monotonicity, trendability, and prognosability. However, designing a proper HI for composite structures is a challenging task due to the complex damage accumulation process during operational conditions. Additionally, designing a HI that is independent of historical SHM data (i.e., from the healthy state until the current state) is even more challenging as HI and remaining useful life prediction are time-dependent phenomena. A reliable SHM technique is required to extract informative time-independent data, and a powerful model is necessary to construct a proper HI from that data. The lamb wave (LW) technique is a useful SHM method that can extract such time-independent data. However, translating the LW data at each time step to the appropriate HI value is a challenge. AI—deep learning in this case—offers significant mathematical potential to meet this difficulty. A semi-supervised learning approach is developed to train the model using the simulated ideal HIs as the targets. The model uses the current LW data, without prior or subsequent data, to output the current HI value. Prognostic criteria are then calculated using the entire HI trajectory until the end-of-life. To validate the proposed approach, aging experiments from NASA’s prognostics data repository are used, which include composite specimens subjected to a tension-tension fatigue loading and monitored using the LW technique. The LW data is first processed using the Hilbert transform, and then, upper and lower signal envelopes in two states – baseline and current time – are used to feed the deep learning model. The results confirm the effectiveness of the proposed approach according to the prognostic criteria. The effect of different triggering frequencies of the LW system on the results is also discussed in terms of the prognostic criteria.

A health indicator (HI) is a valuable index demonstrating the health level of an engineering system or structure, which is a direct intermediate connection between raw signals collected by structural health monitoring (SHM) methods and prognostic models for remaining useful life estimation. An appropriate HI should conform to prognostic criteria, i.e., monotonicity, trendability, and prognosability, that are commonly utilized to measure the HI's quality. However, constructing such a HI is challenging, particularly for composite structures due to their vulnerability to complex damage scenarios. Data-driven models and deep learning are powerful mathematical tools that can be employed to achieve this purpose. Yet the availability of a large dataset with labels plays a crucial role in these fields, and the data collected by SHM methods can only be labeled after the structure fails. In this respect, semi-supervised learning can incorporate unlabeled data monitored from structures that have not yet failed. In the present work, a semi-supervised deep neural network is proposed to construct HI by SHM data fusion. For the first time, the prognostic criteria are used as targets of the network rather than employing them only as a measurement tool of HI's quality. In this regard, the acoustic emission method was used to monitor composite panels during fatigue loading, and extracted features were used to construct an intelligent HI. Finally, the proposed roadmap is evaluated by the holdout method, which shows a 77.3% improvement in the HI's quality, and the leave-one-out cross-validation method, which indicates the generalized model has at least an 81.77% score on the prognostic criteria. This study demonstrates that even when the true HI labels are unknown but the qualified HI pattern (according to the prognostic criteria) can be recognized, a model can still be built that provides HIs aligning with the desired degradation behavior.

Composite structures are highly valued for their strength-to-weight ratio, durability, and versatility, making them ideal for a variety of applications, including aerospace, automotive, and infrastructure. However, potential damage scenarios like impact, fatigue, and corrosion can lead to premature failure and pose a threat to safety. This highlights the importance of monitoring composite structures through structural health monitoring (SHM) and prognostics and health management (PHM) to ensure their safe and reliable operation. SHM provides information on the current state of the structure, while PHM predicts its future behavior and determines necessary maintenance. Health indicators (HIs) play a crucial role in both SHM and PHM, providing information on structural health and behavior, but accurate determination of these indicators can be challenging due to the complexity of material behavior and multiple sources of damage in composite structures. In the present work, a model containing a developed adaptive standardization, a dimension reduction sub-model, a time-independent sub-model, and a time-dependent sub-model is introduced to address this challenge. First, the raw data collected by the acoustic emission technique monitoring composite structures under fatigue loading is processed to provide plenty of statistical features. The extracted features are adaptively standardized according to the available data until the current time. Then, the principal component analysis algorithm is employed to reconstruct a few yet highly informative features out of those statistical features. An artificial neural network is used to regress the principal components to the HI that meets the prognostic criteria. Finally, the last sub-model takes into account the time dependency of HI values during fatigue loading. In comparison to other models, the results show superior performance.